Finite Group Databasebeta

← #17242199

Subgroups — #17242199

Order 4352.

2210 conjugacy classes of subgroups.

The subgroup lattice has 1686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537070C211yesmaximal, characteristic, complemented
2#14537067C211yesmaximal, characteristic, complemented
3#14536642C211yesmaximal, characteristic, complemented
4#14536444C211yesmaximal, characteristic, complemented
5#14536423C211yesmaximal, characteristic, complemented
6#14536409C211yesmaximal, characteristic, complemented
7#14536409C211yesmaximal, characteristic, complemented
8#14536102C211yesmaximal, characteristic, complemented
9#14536067C211yesmaximal, characteristic, complemented
10#14536004C211yesmaximal, characteristic, complemented
11#14535893C211yesmaximal, characteristic, complemented
12#14535785C211yesmaximal, characteristic, complemented
13#14535578C211yesmaximal, characteristic, complemented
14#14535426C211yesmaximal, characteristic, complemented
15#14535414C211yesmaximal, characteristic, complemented
16#14535327C211yesmaximal, characteristic, complemented
17#14535227C211yesmaximal, characteristic, complemented
18#14535083C211yesmaximal, characteristic, complemented
19#14534501C211yesmaximal, characteristic, complemented
20#14534501C211yesmaximal, characteristic, complemented
21#14533106C211yesmaximal, characteristic, complemented
22#14533035C211yesmaximal, characteristic, complemented
23#14532910C211yesmaximal, characteristic, complemented
24#14532335C211yesmaximal, characteristic, complemented
25#14532318C211yesmaximal, characteristic, complemented
26#14532265C211yesmaximal, characteristic, complemented
27#14532248C211yesmaximal, characteristic, complemented
28#14531444C211yesmaximal, characteristic, complemented
29#14531441C211yesmaximal, characteristic, complemented
30C2×#11762687C211yesmaximal, characteristic, complemented
31C17×#2493C211yesmaximal, characteristic, complemented
32C23×D68C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×#10587584C2211yescharacteristic, complemented
35C2×#10587561C2211yescharacteristic, complemented
36C2×#10587580C2211yescharacteristic, complemented
37C2×#10587615C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587582C2211yescharacteristic, complemented
40C2×#10587582C2211yescharacteristic, complemented
41C2×#10587564C2211yescharacteristic
42C2×#10587581C2211yescharacteristic, complemented
43C2×#10587581C2211yescharacteristic, complemented
44C2×#10587581C2211yescharacteristic, complemented
45C2×#10587616C2211yescharacteristic
46C2×#10587568C2211yescharacteristic
47C2×#10587568C2211yescharacteristic
48C2×#10587568C2211yescharacteristic
49C2×#10587568C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×#10587567C2211yescharacteristic
52C22×#63227C2211yescharacteristic
53C22×#63227C2211yescharacteristic
54C22×#63227C2211yescharacteristic
55#11762751C2211yescharacteristic, complemented
56#11762750C2211yescharacteristic, complemented
57#11762750C2211yescharacteristic, complemented
58#11762744C2211yescharacteristic, complemented
59#11762743C2211yescharacteristic, complemented
60#11762743C2211yescharacteristic, complemented
61#11762738C2211yescharacteristic, complemented
62#11762738C2211yescharacteristic, complemented
63#11762738C2211yescharacteristic, complemented
64#11762738C2211yescharacteristic, complemented
65#11762738C2211yescharacteristic, complemented
66#11762736C2211yescharacteristic, complemented
67#11762736C2211yescharacteristic, complemented
68#11762736C2211yescharacteristic, complemented
69#11762735C2211yescharacteristic, complemented
70#11762733C2211yescharacteristic, complemented
71#11762731C2211yescharacteristic, complemented
72#11762731C2211yescharacteristic, complemented
73#11762727C2211yescharacteristic
74#11762727C2211yescharacteristic
75#11762727C2211yescharacteristic
76#11762727C2211yescharacteristic
77#11762727C2211yescharacteristic
78#11762727C2211yescharacteristic
79#11762727C2211yescharacteristic
80#11762727C2211yescharacteristic
81#11762727C2211yescharacteristic, complemented
82#11762727C2211yescharacteristic, complemented
83#11762727C2211yescharacteristic, complemented
84#11762727C2211yescharacteristic, complemented
85#11762727C2211yescharacteristic, complemented
86#11762726C2211yescharacteristic, complemented
87#11762726C2211yescharacteristic, complemented
88#11762722C2211yescharacteristic, complemented
89#11762722C2211yescharacteristic, complemented
90#11762719C2211yescharacteristic
91#11762719C2211yescharacteristic
92#11762719C2211yescharacteristic
93#11762719C2211yescharacteristic
94#11762719C2211yescharacteristic
95#11762719C2211yescharacteristic
96#11762719C2211yescharacteristic
97#11762719C2211yescharacteristic
98#11762719C2211yescharacteristic, complemented
99#11762713C2211yescharacteristic, complemented
100#11762711C2211yescharacteristic, complemented
101#11762711C2211yescharacteristic, complemented
102#11762711C2211yescharacteristic, complemented
103#11762710C2211yescharacteristic, complemented
104#11762710C2211yescharacteristic, complemented
105#11762710C2211yescharacteristic, complemented
106#11762706C2211yescharacteristic, complemented
107#11762701C2211yescharacteristic, complemented
108#11762701C2211yescharacteristic, complemented
109#11762701C2211yescharacteristic, complemented
110#11762701C2211yescharacteristic, complemented
111#11762701C2211yescharacteristic, complemented
112#11762700C2211yescharacteristic, complemented
113#11762700C2211yescharacteristic, complemented
114#11762700C2211yescharacteristic, complemented
115#11762700C2211yescharacteristic, complemented
116#11762699C2211yescharacteristic, complemented
117#11762699C2211yescharacteristic, complemented
118#11762699C2211yescharacteristic, complemented
119#11762699C2211yescharacteristic, complemented
120#11762698C2211yescharacteristic, complemented
121#11762698C2211yescharacteristic, complemented
122#11762698C2211yescharacteristic, complemented
123#11762698C2211yescharacteristic, complemented
124#11762698C2211yescharacteristic, complemented
125#11762698C2211yescharacteristic, complemented
126#11762692C2211yescharacteristic, complemented
127#11762691C2211yescharacteristic, complemented
128#11762688C2211yescharacteristic
129#11762687C2211yescharacteristic
130#11762687C2211yescharacteristic
131#11762687C2211yescharacteristic
132#11762687C2211yescharacteristic
133#11762687C2211yescharacteristic
134#11762687C2211yescharacteristic
135#11762687C2211yescharacteristic
136#11762687C2211yescharacteristic
137#11762687C2211yescharacteristic, complemented
138#11762687C2211yescharacteristic, complemented
139#11762687C2211yescharacteristic, complemented
140#11762687C2211yescharacteristic, complemented
141#11762687C2211yescharacteristic, complemented
142#11762687C2211yescharacteristic, complemented
143#11762687C2211yescharacteristic, complemented
144#11762687C2211yescharacteristic, complemented
145#11762687C2211yescharacteristic, complemented
146#11762687C2211yescharacteristic, complemented
147#11762687C2211yescharacteristic, complemented
148#11762686C2211yescharacteristic
149#11762686C2211yescharacteristic
150#11762686C2211yescharacteristic
151#11762684C2211yescharacteristic
152#11762683C2211yescharacteristic, complemented
153#11762683C2211yescharacteristic, complemented
154#11762683C2211yescharacteristic, complemented
155#11762682C2211yescharacteristic
156#11762680C2211yescharacteristic, complemented
157#11762680C2211yescharacteristic, complemented
158#11762673C2211yescharacteristic, complemented
159#11762671C2211yescharacteristic, complemented
160#11762668C2211yescharacteristic, complemented
161#11762668C2211yescharacteristic, complemented
162#11762668C2211yescharacteristic, complemented
163#11762667C2211yescharacteristic
164#11762666C2211yescharacteristic, complemented
165#11762666C2211yescharacteristic, complemented
166#11762664C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169#11762664C2211yescharacteristic
170C22⋊C4×Dic17C2211yescharacteristic
171C2×#10587502C2211yescharacteristic
172C17×#401C2211yescharacteristic, complemented
173C17×#400C2211yescharacteristic, complemented
174C17×#400C2211yescharacteristic, complemented
175C17×#400C2211yescharacteristic, complemented
176C17×#387C2211yescharacteristic, complemented
177C17×#387C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#385C2211yescharacteristic
180C17×#385C2211yescharacteristic
181C17×#383C2211yescharacteristic, complemented
182C17×#381C2211yescharacteristic
183C17×#381C2211yescharacteristic
184C17×#380C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C2×C17×#95C2211yescharacteristic
187C24×D17C2311yescharacteristic
188C24×D17C2311yescharacteristic
189C23×C4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C23×Dic17C2311yescharacteristic
195C23×Dic17C2311yescharacteristic
196C22×D68—24no—
197C22×D68—42no—
198C22×D68—42no—
199C22×D68C2311yescharacteristic
200C22×D68C2311yescharacteristic
201C22×D68C2311yescharacteristic
202C22×D68C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×D68C2311yescharacteristic
205C22×D68C2311yescharacteristic
206C22×D68C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×D68C2311yescharacteristic
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×D68C2311yescharacteristic
212C22×C4×D17—42no—
213C22×C4×D17—42no—
214C22×C4×D17—42no—
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C42×C17C2311yescharacteristic
233C2×C42×C17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236#10587616—42no—
237#10587615—42no—
238#10587615—42no—
239C4×C22⋊D17—42no—
240C2×#63227—42no—
241C2×#63227—42no—
242C2×#63227—42no—
243C2×#63227C2311yescharacteristic
244C2×#63227C2311yescharacteristic
245C2×#63227C2311yescharacteristic
246C2×#63227C2311yescharacteristic
247C2×#63227C2311yescharacteristic
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315#10587584—42no—
316#10587582—42no—
317#10587582—42no—
318#10587581—42no—
319#10587581—42no—
320#10587581—42no—
321#10587580—42no—
322#10587568—24no—
323#10587568—24no—
324#10587568—42no—
325#10587568—42no—
326#10587567—42no—
327#10587564—42no—
328#10587561—42no—
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369C24×C17C2411yescharacteristic
370C23×D17—22no—
371C23×D17—22no—
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—22no—
375C23×D17—41no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17—41no—
379C23×D17—41no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17#4114yes—
384C23×D17C2411yescharacteristic
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C23×D17C2411yescharacteristic
389C23×D17C2411yescharacteristic
390C22×C4×C17—22no—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—22no—
394C22×C4×C17—22no—
395C22×C4×C17—22no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C2×C22⋊D17—22no—
414C2×C22⋊D17—22no—
415C2×C22⋊D17—22no—
416C2×C22⋊D17—22no—
417C2×C22⋊D17—22no—
418C2×C22⋊D17—22no—
419C22×Dic17—22no—
420C22×Dic17—22no—
421C22×Dic17—22no—
422C22×Dic17—41no—
423C22×Dic17—41no—
424C22×Dic17—41no—
425C22×Dic17C2411yescharacteristic
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2411yescharacteristic
428C22×Dic17C2411yescharacteristic
429C22×Dic17C2411yescharacteristic
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C2×D68—22no—
436C2×D68—22no—
437C2×D68—22no—
438C2×D68—22no—
439C2×D68—22no—
440C2×D68—22no—
441C2×D68—22no—
442C2×D68—22no—
443C2×D68—22no—
444C2×D68—41no—
445C2×D68—41no—
446C2×D68—41no—
447C2×D68—41no—
448C2×D68—41no—
449C2×D68—41no—
450C2×D68—41no—
451C2×D68—41no—
452C2×D68—416no—
453C2×D68—41no—
454C2×D68—41no—
455C2×D68—41no—
456C2×D68—41no—
457C2×D68—41no—
458C2×D68—41no—
459C2×D68—41no—
460C2×D68—41no—
461C2×D68—41no—
462C2×D68—41no—
463C2×D68—41no—
464C2×D68—41no—
465C2×D68—41no—
466C2×D68—41no—
467C2×D68—41no—
468C2×D68—41no—
469C2×D68—41no—
470C2×D68—41no—
471C2×D68—41no—
472C2×D68—41no—
473C2×D68—41no—
474C2×D68—41no—
475C2×C4×D17—22no—
476C2×C4×D17—22no—
477C2×C4×D17—22no—
478C2×C4×D17—22no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—41no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
487C2×C4×D17—416no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×Dic34—22no—
495C2×Dic34—41no—
496C2×Dic34—41no—
497C4⋊C4×C17—22no—
498C4⋊C4×C17—22no—
499C4⋊C4×C17—41no—
500C4⋊C4×C17—41no—
501C4⋊C4×C17—41no—
502C4⋊C4×C17—41no—
503C22⋊C4×C17—22no—
504C22⋊C4×C17—22no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17—22no—
507C42×C17—41no—
508C42×C17—41no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511#63227—22no—
512#63227—22no—
513#63227—22no—
514#63227—22no—
515#63227—22no—
516#63227—22no—
517#63227—22no—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—41no—
522#63227—41no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227—41no—
554#63227—41no—
555#63227—41no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560#63227—41no—
561#63227—41no—
562#63227—41no—
563C4⋊Dic17—41no—
564C4⋊Dic17—41no—
565C4⋊Dic17—41no—
566C4⋊Dic17—41no—
567#63225—22no—
568#63225—22no—
569#63225—41no—
570#63225—41no—
571#63225—41no—
572#63225—41no—
573#63225—41no—
574#63225—41no—
575#63225—41no—
576#63225—41no—
577#63225—41no—
578#63225—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583#36758—171nomaximal, Sylow
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17C2×#4112yes—
589C23×C17H(5,𝔽2)12yes—
590C23×C17H(5,𝔽2)12yes—
591C23×C17C2511yescharacteristic
592C22×D17—28no—
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—44no—
634C22×D17—44no—
635C22×D17—44no—
636C22×D17—44no—
637C22×D17—44no—
638C22×D17—44no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—82no—
643C22×D17—82no—
644C22×D17—82no—
645C22×D17—82no—
646C22×D17C2×#4112yes—
647C22×D17C2×#4112yes—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—44no—
690C2×C4×C17—44no—
691C2×C4×C17—82no—
692C2×C4×C17H(5,𝔽2)12yes—
693C22⋊D17—44no—
694C22⋊D17—44no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—44no—
725C2×Dic17—82no—
726C2×Dic17H(5,𝔽2)12yes—
727D68—44no—
728D68—44no—
729D68—44no—
730D68—44no—
731D68—82no—
732D68—82no—
733D68—82no—
734D68—82no—
735D68—82no—
736D68—82no—
737D68—82no—
738D68—82no—
739D68—82no—
740C4×D17—44no—
741C4×D17—44no—
742C4×D17—44no—
743C4×D17—44no—
744C4×D17—82no—
745C4×D17—82no—
746Dic34—82no—
747#2848—171no—
748#2847—171no—
749#2797—171no—
750#2781—171no—
751#2779—171no—
752#2778—171no—
753#2778—171no—
754#2756—171no—
755#2753—171no—
756#2749—171no—
757#2741—171no—
758#2730—171no—
759#2714—171no—
760#2703—171no—
761#2702—171no—
762#2696—171no—
763#2688—171no—
764#2676—171no—
765#2613—171no—
766#2613—171no—
767#2493D1711yescharacteristic, complemented
768#2488—171no—
769#2480—171no—
770#2472—171no—
771#2425—171no—
772#2424—171no—
773#2419—171no—
774#2418—171no—
775#2321—171no—
776#2321—171no—
777C2×#386—171no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17#53814yes—
785C22×C17C22×#4111yescharacteristic
786C22×C17C2×H(5,𝔽2)11yescharacteristic
787C22×C17C2×H(5,𝔽2)11yescharacteristic
788C22×C17C2×H(5,𝔽2)11yescharacteristic
789C22×C17C2×H(5,𝔽2)11yescharacteristic
790C22×C17#58511yescharacteristic
791C22×C17#58511yescharacteristic
792C2×D17—22no—
793C2×D17—22no—
794C2×D17—22no—
795C2×D17—22no—
796C2×D17—22no—
797C2×D17—22no—
798C2×D17—416no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—41no—
811C2×D17—41no—
812C2×D17—41no—
813C2×D17—41no—
814C2×D17—41no—
815C2×D17—41no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C2×D17—41no—
832C2×D17—41no—
833C2×D17—41no—
834C2×D17—41no—
835C2×D17—88no—
836C4×C17—22no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843C4×C17—41no—
844C4×C17—41no—
845C4×C17—41no—
846C4×C17—41no—
847C4×C17—41no—
848C4×C17—41no—
849C4×C17—41no—
850Dic17—22no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856Dic17—41no—
857Dic17—41no—
858Dic17—41no—
859Dic17—41no—
860C23×D4—171no—
861C24×C4—171no—
862C2×#126—171no—
863C2×#124—171no—
864C2×#123—171no—
865C2×#123—171no—
866C2×#123—171no—
867C2×C22⋊Q8—171no—
868C2×C22⋊Q8—171no—
869C2×C22⋊Q8—171no—
870C2×#121—171no—
871C2×#121—171no—
872C2×#121—171no—
873C2×#121—171no—
874C2×#120—171no—
875C2×#120—171no—
876C2×#120—171no—
877C2×#120—171no—
878C2×C4×D4—171no—
879C2×C4×D4—171no—
880C22×C22⋊C4—171no—
881C22×C22⋊C4—171no—
882C22×C22⋊C4—171no—
883#401C2×D1711yescharacteristic, complemented
884#400—171no—
885#400—171no—
886#400—171no—
887#400C2×D1711yescharacteristic, complemented
888#400C2×D1711yescharacteristic, complemented
889#400C2×D1711yescharacteristic, complemented
890#399—171no—
891#398—171no—
892#398—171no—
893#397—171no—
894#397—171no—
895#397—171no—
896#397—171no—
897#397—171no—
898#397—171no—
899#397—171no—
900#397—171no—
901#397—171no—
902#396—171no—
903#396—171no—
904#396—171no—
905#394—171no—
906#394—171no—
907#394—171no—
908#394—171no—
909#394—171no—
910#394—171no—
911#394—171no—
912#394—171no—
913#394—171no—
914#394—171no—
915#394—171no—
916#394—171no—
917#394—171no—
918#394—171no—
919#394—171no—
920#393—171no—
921#393—171no—
922#392—171no—
923#392—171no—
924#392—171no—
925#392—171no—
926#392—171no—
927#392—171no—
928#392—171no—
929#392—171no—
930#392—171no—
931#391—171no—
932#390—171no—
933#390—171no—
934#390—171no—
935#390—171no—
936#390—171no—
937#390—171no—
938#389—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388—171no—
944#388—171no—
945#388—171no—
946#388—171no—
947#388—171no—
948#388—171no—
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#387—171no—
959#387—171no—
960#387C2×D1711yescharacteristic, complemented
961#387C2×D1711yescharacteristic, complemented
962#387C2×D1711yescharacteristic, complemented
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385C2×D1711yescharacteristic
994#385C2×D1711yescharacteristic
995#383C2×D1711yescharacteristic, complemented
996#382—171no—
997#381—171no—
998#381C2×D1711yescharacteristic
999#381C2×D1711yescharacteristic
1000#380—171no—
1001#380—171no—
1002#380—171no—
1003#380—171no—
1004#380—171no—
1005#380—171no—
1006#380C2×D1711yescharacteristic
1007#379—171no—
1008#379—171no—
1009#379—171no—
1010#379—171no—
1011C4×C22⋊C4—171no—
1012C4×C22⋊C4C2×D1711yescharacteristic
1013C2×#95—171no—
1014C2×#95C2×D1711yescharacteristic
1015C2×C17—24no—
1016C2×C17C2×#53811yescharacteristic
1017C2×C17#350511yescharacteristic
1018C2×C17#350511yescharacteristic
1019C2×C17#353211yescharacteristic
1020C2×C17#353311yescharacteristic
1021C2×C17#354211yescharacteristic
1022C2×C17#354211yescharacteristic
1023D17—42no—
1024D17—42no—
1025D17—81no—
1026D17—81no—
1027D17—81no—
1028D17—81no—
1029C25—171no—
1030C25—171no—
1031C22×Q8—171no—
1032C22×D4—171no—
1033C22×D4—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4—171no—
1040C22×D4—171no—
1041C22×D4—171no—
1042C22×D4—171no—
1043C22×D4—171no—
1044C22×D4—171no—
1045C22×D4—171no—
1046C22×D4—171no—
1047C22×D4—344no—
1048C22×D4—682no—
1049C22×D4—682no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—171no—
1056C23×C4—171no—
1057C23×C4—171no—
1058C23×C4—682no—
1059C23×C4—682no—
1060C23×C4—682no—
1061C23×C4C22×D1711yescharacteristic
1062C23×C4C22×D1711yescharacteristic
1063C23×C4C22×D1711yescharacteristic
1064#126—682no—
1065#124—682no—
1066#123—682no—
1067#123—682no—
1068#123—682no—
1069C22⋊Q8—682no—
1070C22⋊Q8—682no—
1071C22⋊Q8—682no—
1072#121—682no—
1073#121—682no—
1074#121—682no—
1075#121—682no—
1076#120—344no—
1077#120—344no—
1078#120—682no—
1079#120—682no—
1080C4×D4—682no—
1081C4×D4—682no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—171no—
1094C2×C4⋊C4—171no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4C22×D1711yescharacteristic
1099C2×C4⋊C4C22×D1711yescharacteristic
1100C2×C4⋊C4C22×D1711yescharacteristic
1101C2×C4⋊C4C22×D1711yescharacteristic
1102C2×C4⋊C4C22×D1711yescharacteristic
1103C2×C4⋊C4C22×D1711yescharacteristic
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—682no—
1159C2×C22⋊C4—682no—
1160C2×C22⋊C4—682no—
1161C2×C22⋊C4C22×D1711yescharacteristic
1162C2×C22⋊C4C22×D1711yescharacteristic
1163C2×C22⋊C4C22×D1711yescharacteristic
1164C2×C22⋊C4C22×D1711yescharacteristic
1165C2×C42—171no—
1166C2×C42—171no—
1167C2×C42—171no—
1168C2×C42—171no—
1169C2×C42C22×D1711yescharacteristic
1170C2×C42C22×D1711yescharacteristic
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95C22×D1711yescharacteristic
1192#95C22×D1711yescharacteristic
1193#95C22×D1711yescharacteristic
1194#95C22×D1711yescharacteristic
1195#95C22×D1711yescharacteristic
1196#95C22×D1711yescharacteristic
1197#95C22×D1711yescharacteristic
1198#95C22×D1711yescharacteristic
1199#95C22×D1711yescharacteristic
1200#95C22×D1711yescharacteristic
1201#95C22×D1711yescharacteristic
1202#95C22×D1711yescharacteristic
1203#95C22×D1711yescharacteristic
1204#95C22×D1711yescharacteristic
1205#95C22×D1711yescharacteristic
1206#95C22×D1711yescharacteristic
1207#95C22×D1711yescharacteristic
1208#95C22×D1711yescharacteristic
1209#95C22×D1711yescharacteristic
1210#95C22×D1711yescharacteristic
1211C17#3675811yescharacteristic, complemented, Sylow
1212C24—171no—
1213C24—171no—
1214C24—174no—
1215C24—171no—
1216C24—171no—
1217C24—171no—
1218C24—171no—
1219C24—342no—
1220C24—342no—
1221C24—342no—
1222C24—342no—
1223C24—342no—
1224C24—681no—
1225C24—681no—
1226C24—681no—
1227C24—681no—
1228C24—681no—
1229C24—681no—
1230C24—681no—
1231C24—681no—
1232C24C23×D1711yescharacteristic
1233C2×Q8—342no—
1234C2×Q8—681no—
1235C2×Q8—681no—
1236C2×D4—342no—
1237C2×D4—342no—
1238C2×D4—342no—
1239C2×D4—342no—
1240C2×D4—342no—
1241C2×D4—342no—
1242C2×D4—342no—
1243C2×D4—342no—
1244C2×D4—342no—
1245C2×D4—342no—
1246C2×D4—342no—
1247C2×D4—342no—
1248C2×D4—342no—
1249C2×D4—342no—
1250C2×D4—342no—
1251C2×D4—681no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4—681no—
1258C2×D4—681no—
1259C2×D4—681no—
1260C2×D4—681no—
1261C2×D4—681no—
1262C2×D4—681no—
1263C2×D4—681no—
1264C2×D4—681no—
1265C2×D4—681no—
1266C2×D4—681no—
1267C2×D4—681no—
1268C2×D4—681no—
1269C2×D4—681no—
1270C2×D4—681no—
1271C2×D4—681no—
1272C2×D4—681no—
1273C2×D4—681no—
1274C2×D4—681no—
1275C2×D4—681no—
1276C2×D4—681no—
1277C2×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4—6816no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—171no—
1299C22×C4—171no—
1300C22×C4—171no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—342no—
1304C22×C4—342no—
1305C22×C4—342no—
1306C22×C4—342no—
1307C22×C4—342no—
1308C22×C4—681no—
1309C22×C4—681no—
1310C22×C4—681no—
1311C22×C4—681no—
1312C22×C4—681no—
1313C22×C4—681no—
1314C22×C4—681no—
1315C22×C4—681no—
1316C22×C4—681no—
1317C22×C4—681no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—6816no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4C23×D1711yescharacteristic
1327C22×C4C23×D1711yescharacteristic
1328C22×C4C23×D1711yescharacteristic
1329C22×C4C23×D1711yescharacteristic
1330C22×C4C23×D1711yescharacteristic
1331C22×C4C23×D1711yescharacteristic
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C22×C4C23×D1711yescharacteristic
1338C22×C4C23×D1711yescharacteristic
1339C22×C4C23×D1711yescharacteristic
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—342no—
1347C4⋊C4—342no—
1348C4⋊C4—681no—
1349C4⋊C4—681no—
1350C4⋊C4—681no—
1351C4⋊C4—681no—
1352C4⋊C4—681no—
1353C4⋊C4—681no—
1354C4⋊C4—681no—
1355C4⋊C4—681no—
1356C4⋊C4—681no—
1357C4⋊C4—681no—
1358C4⋊C4—681no—
1359C4⋊C4—681no—
1360C4⋊C4—681no—
1361C4⋊C4—681no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—342no—
1367C22⋊C4—342no—
1368C22⋊C4—342no—
1369C22⋊C4—342no—
1370C22⋊C4—342no—
1371C22⋊C4—342no—
1372C22⋊C4—342no—
1373C22⋊C4—342no—
1374C22⋊C4—342no—
1375C22⋊C4—342no—
1376C22⋊C4—342no—
1377C22⋊C4—342no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C22⋊C4—681no—
1384C22⋊C4—681no—
1385C22⋊C4—681no—
1386C22⋊C4—681no—
1387C22⋊C4—681no—
1388C22⋊C4—681no—
1389C22⋊C4—681no—
1390C22⋊C4—681no—
1391C22⋊C4—681no—
1392C22⋊C4—681no—
1393C22⋊C4—681no—
1394C22⋊C4—681no—
1395C22⋊C4—681no—
1396C22⋊C4—681no—
1397C22⋊C4—681no—
1398C22⋊C4—681no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4—681no—
1402C22⋊C4—681no—
1403C22⋊C4—681no—
1404C22⋊C4—681no—
1405C22⋊C4—681no—
1406C22⋊C4—681no—
1407C22⋊C4—681no—
1408C22⋊C4—681no—
1409C22⋊C4—681no—
1410C22⋊C4—681no—
1411C22⋊C4—681no—
1412C22⋊C4—681no—
1413C22⋊C4—681no—
1414C22⋊C4—681no—
1415C22⋊C4—681no—
1416C22⋊C4—681no—
1417C22⋊C4—681no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C42—41no—
1421C42—41no—
1422C42—681no—
1423C42—681no—
1424C42—681no—
1425C42—681no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—172no—
1431C23—172no—
1432C23—341no—
1433C23—341no—
1434C23—341no—
1435C23—341no—
1436C23—341no—
1437C23—341no—
1438C23—341no—
1439C23—341no—
1440C23—341no—
1441C23—341no—
1442C23—341no—
1443C23—341no—
1444C23—348no—
1445C23—341no—
1446C23—341no—
1447C23—341no—
1448C23—341no—
1449C23—341no—
1450C23—341no—
1451C23—341no—
1452C23—341no—
1453C23—341no—
1454C23—341no—
1455C23—341no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23—341no—
1461C23—341no—
1462C23—341no—
1463C23—341no—
1464C23—341no—
1465C23—341no—
1466C23—341no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—341no—
1473C23—684no—
1474C23—684no—
1475C23—684no—
1476C23—684no—
1477C23—684no—
1478C23—684no—
1479C23—684no—
1480C23—684no—
1481C23—684no—
1482C23—1362no—
1483C23—1362no—
1484C23—1362no—
1485C23—1362no—
1486C23#41×D1712yes—
1487C23#1058769612yes—
1488C23#1058769612yes—
1489C23C24×D1711yescharacteristic
1490Q8—1362no—
1491D4—684no—
1492D4—684no—
1493D4—684no—
1494D4—684no—
1495D4—684no—
1496D4—684no—
1497D4—1362no—
1498D4—1362no—
1499D4—1362no—
1500D4—1362no—
1501D4—1362no—
1502D4—1362no—
1503D4—1362no—
1504D4—1362no—
1505D4—1362no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—44no—
1548C2×C4—44no—
1549C2×C4—82no—
1550C2×C4—172no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—684no—
1581C2×C4—684no—
1582C2×C4—684no—
1583C2×C4—684no—
1584C2×C4—684no—
1585C2×C4—1362no—
1586C2×C4—1362no—
1587C2×C4—1362no—
1588C2×C4#1058769612yes—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—22no—
1595C22—342no—
1596C22—342no—
1597C22—342no—
1598C22—342no—
1599C22—342no—
1600C22—342no—
1601C22—6816no—
1602C22—681no—
1603C22—681no—
1604C22—681no—
1605C22—681no—
1606C22—681no—
1607C22—681no—
1608C22—681no—
1609C22—681no—
1610C22—681no—
1611C22—681no—
1612C22—681no—
1613C22—681no—
1614C22—681no—
1615C22—681no—
1616C22—681no—
1617C22—681no—
1618C22—681no—
1619C22—681no—
1620C22—681no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—681no—
1625C22—681no—
1626C22—681no—
1627C22—681no—
1628C22—681no—
1629C22—681no—
1630C22—681no—
1631C22—681no—
1632C22—681no—
1633C22—681no—
1634C22—681no—
1635C22—681no—
1636C22—681no—
1637C22—681no—
1638C22—1368no—
1639C22#1176339814yes—
1640C22C2×#41×D1711yescharacteristic
1641C22H(5,𝔽2)×D1711yescharacteristic
1642C22C2×#1058769611yescharacteristic
1643C22C2×#1058769611yescharacteristic
1644C22C2×#1058769611yescharacteristic
1645C22#1176364511yescharacteristic
1646C22#1176364611yescharacteristic
1647C4—22no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—41no—
1658C4—41no—
1659C4—41no—
1660C4—41no—
1661C4—342no—
1662C4—681no—
1663C4—681no—
1664C4—681no—
1665C4—681no—
1666C4—681no—
1667C4—681no—
1668C4—681no—
1669C4—681no—
1670C4—681no—
1671C2—24no—
1672C2—682no—
1673C2—682no—
1674C2—1361no—
1675C2—1361no—
1676C2—1361no—
1677C2—1361no—
1678C2C2×#1176339811yescharacteristic
1679C2#1454261611yescharacteristic
1680C2#1454261911yescharacteristic
1681C2#1454294011yescharacteristic
1682C2#1454295011yescharacteristic
1683C2#1454309311yescharacteristic
1684C2#1454309411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2493C2
hypercenter#2493D17
hypocenterC17#36758
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2493

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14537070C2semidirect
2. #14537067C2semidirect
3. #14536642C2semidirect
4. #14536444C2semidirect
5. #14536423C2semidirect
6. #14536409C2semidirect
7. #14536409C2semidirect
8. #14536102C2semidirect
9. #14536067C2semidirect
10. #14536004C2semidirect
11. #14535893C2semidirect
12. #14535785C2semidirect
13. #14535578C2semidirect
14. #14535426C2semidirect
15. #14535414C2semidirect
16. #14535327C2semidirect
17. #14535227C2semidirect
18. #14535083C2semidirect
19. #14534501C2semidirect
20. #14534501C2semidirect
21. #14533106C2semidirect
22. #14533035C2semidirect
23. #14532910C2semidirect
24. #14532335C2semidirect
25. #14532318C2semidirect
26. #14532265C2semidirect
27. #14532248C2semidirect
28. #14531444C2semidirect
29. #14531441C2semidirect
30. C2×#11762687C2semidirect
31. C17×#2493C2semidirect
34. C2×#10587584C22semidirect
35. C2×#10587561C22semidirect
36. C2×#10587580C22semidirect
39. C2×#10587582C22semidirect
40. C2×#10587582C22semidirect
42. C2×#10587581C22semidirect
43. C2×#10587581C22semidirect
44. C2×#10587581C22semidirect
55. #11762751C22semidirect
56. #11762750C22semidirect
57. #11762750C22semidirect
58. #11762744C22semidirect
59. #11762743C22semidirect
60. #11762743C22semidirect
61. #11762738C22semidirect
62. #11762738C22semidirect
63. #11762738C22semidirect
64. #11762738C22semidirect
65. #11762738C22semidirect
66. #11762736C22semidirect
67. #11762736C22semidirect
68. #11762736C22semidirect
69. #11762735C22semidirect
70. #11762733C22semidirect
71. #11762731C22semidirect
72. #11762731C22semidirect
81. #11762727C22semidirect
82. #11762727C22semidirect
83. #11762727C22semidirect
84. #11762727C22semidirect
85. #11762727C22semidirect
86. #11762726C22semidirect
87. #11762726C22semidirect
88. #11762722C22semidirect
89. #11762722C22semidirect
98. #11762719C22semidirect
99. #11762713C22semidirect
100. #11762711C22semidirect
101. #11762711C22semidirect
102. #11762711C22semidirect
103. #11762710C22semidirect
104. #11762710C22semidirect
105. #11762710C22semidirect
106. #11762706C22semidirect
107. #11762701C22semidirect
108. #11762701C22semidirect
109. #11762701C22semidirect
110. #11762701C22semidirect
111. #11762701C22semidirect
112. #11762700C22semidirect
113. #11762700C22semidirect
114. #11762700C22semidirect
115. #11762700C22semidirect
116. #11762699C22semidirect
117. #11762699C22semidirect
118. #11762699C22semidirect
119. #11762699C22semidirect
120. #11762698C22semidirect
121. #11762698C22semidirect
122. #11762698C22semidirect
123. #11762698C22semidirect
124. #11762698C22semidirect
125. #11762698C22semidirect
126. #11762692C22semidirect
127. #11762691C22semidirect
137. #11762687C22semidirect
138. #11762687C22semidirect
139. #11762687C22semidirect
140. #11762687C22semidirect
141. #11762687C22semidirect
142. #11762687C22semidirect
143. #11762687C22semidirect
144. #11762687C22semidirect
145. #11762687C22semidirect
146. #11762687C22semidirect
147. #11762687C22semidirect
152. #11762683C22semidirect
153. #11762683C22semidirect
154. #11762683C22semidirect
156. #11762680C22semidirect
157. #11762680C22semidirect
158. #11762673C22semidirect
159. #11762671C22semidirect
160. #11762668C22semidirect
161. #11762668C22semidirect
162. #11762668C22semidirect
164. #11762666C22semidirect
165. #11762666C22semidirect
172. C17×#401C22semidirect
173. C17×#400C22semidirect
174. C17×#400C22semidirect
175. C17×#400C22semidirect
176. C17×#387C22semidirect
177. C17×#387C22semidirect
178. C17×#387C22semidirect
181. C17×#383C22semidirect
767. #2493D17semidirect
883. #401C2×D17semidirect
887. #400C2×D17semidirect
888. #400C2×D17semidirect
889. #400C2×D17semidirect
960. #387C2×D17semidirect
961. #387C2×D17semidirect
962. #387C2×D17semidirect
995. #383C2×D17semidirect
1211. C17#36758semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145370702
#145370672
#145366422
#145364442
#145364232
#145364092
#145361022
#145360672
#145360042
#145358932
#145357852
#145355782
#145354262
#145354142
#145353272
#145352272
#145350832
#145345012
#145331062
#145330352
#145329102
#145323352
#145323182
#145322652
#145322482
#145314442
#145314412
C2×#117626872
C17×#24932
#3675817