Finite Group Databasebeta

← #17241537

Subgroups — #17241537

Order 4352.

2130 conjugacy classes of subgroups.

The subgroup lattice has 1678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537067C211yesmaximal, characteristic, complemented
2#14537065C211yesmaximal, characteristic, complemented
3#14535928C211yesmaximal, characteristic, complemented
4#14535919C211yesmaximal, characteristic, complemented
5#14535916C211yesmaximal, characteristic, complemented
6#14535890C211yesmaximal, characteristic, complemented
7#14535883C211yesmaximal, characteristic, complemented
8#14535879C211yesmaximal, characteristic, complemented
9#14535878C211yesmaximal, characteristic, complemented
10#14535373C211yesmaximal, characteristic, complemented
11#14535371C211yesmaximal, characteristic, complemented
12#14535371C211yesmaximal, characteristic, complemented
13#14535368C211yesmaximal, characteristic, complemented
14#14535227C211yesmaximal, characteristic, complemented
15#14535223C211yesmaximal, characteristic, complemented
16#14535222C211yesmaximal, characteristic, complemented
17#14535218C211yesmaximal, characteristic, complemented
18#14534887C211yesmaximal, characteristic, complemented
19#14534755C211yesmaximal, characteristic, complemented
20#14532541C211yesmaximal, characteristic, complemented
21#14532535C211yesmaximal, characteristic, complemented
22#14532535C211yesmaximal, characteristic, complemented
23#14532533C211yesmaximal, characteristic, complemented
24#14532325C211yesmaximal, characteristic, complemented
25#14532319C211yesmaximal, characteristic, complemented
26#14532315C211yesmaximal, characteristic, complemented
27#14532313C211yesmaximal, characteristic, complemented
28#14531483C211yesmaximal, characteristic, complemented
29#14531481C211yesmaximal, characteristic, complemented
30D17×#381C211yesmaximal, characteristic, complemented
31C17×#2743C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33C2×#10587581C2211yescharacteristic
34C2×#10587581C2211yescharacteristic
35C2×#10587581C2211yescharacteristic
36C2×#10587581C2211yescharacteristic
37C2×#10587581C2211yescharacteristic
38C2×#10587616C2211yescharacteristic
39C2×#10587616C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587570C2211yescharacteristic
44C2×#10587570C2211yescharacteristic
45C2×#10587625C2211yescharacteristic
46C2×#10587624C2211yescharacteristic
47C2×#10587568C2211yescharacteristic
48C2×#10587568C2211yescharacteristic
49C2×#10587568C2211yescharacteristic
50C2×#10587623C2211yescharacteristic
51C2×C4×D68C2211yescharacteristic
52C2×#10587579C2211yescharacteristic
53C2×#10587579C2211yescharacteristic
54C2×C4×C22⋊D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57#11762750C2211yescharacteristic, complemented
58#11762750C2211yescharacteristic, complemented
59#11762749C2211yescharacteristic, complemented
60#11762749C2211yescharacteristic, complemented
61#11762748C2211yescharacteristic, complemented
62#11762744C2211yescharacteristic, complemented
63#11762744C2211yescharacteristic, complemented
64#11762744C2211yescharacteristic, complemented
65#11762743C2211yescharacteristic, complemented
66#11762743C2211yescharacteristic, complemented
67#11762742C2211yescharacteristic, complemented
68#11762741C2211yescharacteristic, complemented
69#11762738C2211yescharacteristic, complemented
70#11762737C2211yescharacteristic, complemented
71#11762736C2211yescharacteristic, complemented
72#11762736C2211yescharacteristic, complemented
73#11762735C2211yescharacteristic, complemented
74#11762735C2211yescharacteristic, complemented
75#11762735C2211yescharacteristic, complemented
76#11762734C2211yescharacteristic, complemented
77#11762732C2211yescharacteristic
78#11762731C2211yescharacteristic
79#11762731C2211yescharacteristic
80#11762727C2211yescharacteristic
81#11762727C2211yescharacteristic
82#11762727C2211yescharacteristic, complemented
83#11762727C2211yescharacteristic, complemented
84#11762726C2211yescharacteristic
85#11762725C2211yescharacteristic
86#11762725C2211yescharacteristic
87#11762725C2211yescharacteristic, complemented
88#11762724C2211yescharacteristic
89#11762724C2211yescharacteristic
90#11762724C2211yescharacteristic, complemented
91#11762719C2211yescharacteristic
92#11762719C2211yescharacteristic, complemented
93#11762718C2211yescharacteristic
94#11762718C2211yescharacteristic
95#11762718C2211yescharacteristic, complemented
96#11762718C2211yescharacteristic, complemented
97#11762718C2211yescharacteristic, complemented
98#11762717C2211yescharacteristic
99#11762711C2211yescharacteristic
100#11762709C2211yescharacteristic
101#11762709C2211yescharacteristic
102#11762709C2211yescharacteristic
103#11762703C2211yescharacteristic
104#11762702C2211yescharacteristic, complemented
105#11762701C2211yescharacteristic, complemented
106#11762701C2211yescharacteristic, complemented
107#11762701C2211yescharacteristic, complemented
108#11762700C2211yescharacteristic, complemented
109#11762699C2211yescharacteristic
110#11762698C2211yescharacteristic
111#11762698C2211yescharacteristic, complemented
112#11762698C2211yescharacteristic, complemented
113#11762695C2211yescharacteristic, complemented
114#11762693C2211yescharacteristic, complemented
115#11762692C2211yescharacteristic, complemented
116#11762691C2211yescharacteristic, complemented
117#11762690C2211yescharacteristic, complemented
118#11762690C2211yescharacteristic, complemented
119#11762690C2211yescharacteristic, complemented
120#11762688C2211yescharacteristic
121#11762688C2211yescharacteristic, complemented
122#11762688C2211yescharacteristic, complemented
123#11762687C2211yescharacteristic
124#11762687C2211yescharacteristic
125#11762687C2211yescharacteristic
126#11762687C2211yescharacteristic
127#11762687C2211yescharacteristic
128#11762687C2211yescharacteristic
129#11762687C2211yescharacteristic
130#11762687C2211yescharacteristic
131#11762687C2211yescharacteristic
132#11762687C2211yescharacteristic
133#11762687C2211yescharacteristic
134#11762687C2211yescharacteristic, complemented
135#11762687C2211yescharacteristic, complemented
136#11762687C2211yescharacteristic, complemented
137#11762687C2211yescharacteristic, complemented
138#11762686C2211yescharacteristic
139#11762686C2211yescharacteristic
140#11762685C2211yescharacteristic
141#11762685C2211yescharacteristic
142#11762685C2211yescharacteristic
143#11762685C2211yescharacteristic
144#11762685C2211yescharacteristic, complemented
145#11762685C2211yescharacteristic, complemented
146#11762683C2211yescharacteristic
147#11762683C2211yescharacteristic
148#11762683C2211yescharacteristic
149#11762683C2211yescharacteristic, complemented
150#11762680C2211yescharacteristic
151#11762680C2211yescharacteristic, complemented
152#11762680C2211yescharacteristic, complemented
153#11762672C2211yescharacteristic
154#11762671C2211yescharacteristic
155#11762671C2211yescharacteristic
156#11762671C2211yescharacteristic
157#11762671C2211yescharacteristic
158#11762671C2211yescharacteristic, complemented
159#11762671C2211yescharacteristic, complemented
160#11762671C2211yescharacteristic, complemented
161#11762670C2211yescharacteristic
162#11762670C2211yescharacteristic
163#11762668C2211yescharacteristic
164#11762668C2211yescharacteristic
165#11762667C2211yescharacteristic
166#11762666C2211yescharacteristic
167#11762666C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172C17×#400C2211yescharacteristic, complemented
173C17×#400C2211yescharacteristic, complemented
174C17×#400C2211yescharacteristic, complemented
175C17×#399C2211yescharacteristic, complemented
176C17×#396C2211yescharacteristic
177C17×#394C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#385C2211yescharacteristic, complemented
184C17×#381C2211yescharacteristic
185C17×#381C2211yescharacteristic, complemented
186C17×#380C2211yescharacteristic
187C24×D17C2311yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C23×C4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C22×C22⋊D17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C22×D68C2311yescharacteristic
201C22×D68C2311yescharacteristic
202C22×D68C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×D68C2311yescharacteristic
205C22×D68C2311yescharacteristic
206C22×D68C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×D68C2311yescharacteristic
209C22×C4×D17—24no—
210C22×C4×D17—42no—
211C22×C4×D17—42no—
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247#10587625—42no—
248#10587624—42no—
249#10587623—42no—
250#10587616—42no—
251#10587616—42no—
252C4×C22⋊D17—42no—
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×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307#10587581—24no—
308#10587581—42no—
309#10587581—42no—
310#10587581—42no—
311#10587581—42no—
312#10587579—42no—
313#10587579—42no—
314#10587570—24no—
315#10587570—42no—
316#10587570—42no—
317#10587570—42no—
318#10587570—42no—
319#10587568—42no—
320#10587568—42no—
321#10587568—42no—
322C22⋊C4×D17—42no—
323C22⋊C4×D17—42no—
324C4×D68—42no—
325C17×#95C2311yescharacteristic
326C17×#95C2311yescharacteristic
327C17×#95C2311yescharacteristic
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
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
370C24×C17C2411yescharacteristic
371C23×D17—22no—
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—22no—
375C23×D17—22no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17C2411yescharacteristic
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C23×D17C2411yescharacteristic
383C2×D4×C17—22no—
384C2×D4×C17—41no—
385C2×D4×C17—41no—
386C22×C4×C17—22no—
387C22×C4×C17—22no—
388C22×C4×C17—41no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17C2411yescharacteristic
393C22×C4×C17C2411yescharacteristic
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C2×C22⋊D17—22no—
406C2×C22⋊D17—22no—
407C2×C22⋊D17—22no—
408C2×C22⋊D17—22no—
409C2×C22⋊D17—22no—
410C2×C22⋊D17—22no—
411C2×C22⋊D17—22no—
412C2×C22⋊D17—22no—
413C2×C22⋊D17—41no—
414C2×C22⋊D17—41no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17—41no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17—41no—
422C2×C22⋊D17—41no—
423C2×C22⋊D17—41no—
424C2×C22⋊D17—41no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—41no—
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C2×D68—22no—
444C2×D68—22no—
445C2×D68—22no—
446C2×D68—22no—
447C2×D68—22no—
448C2×D68—22no—
449C2×D68—22no—
450C2×D68—22no—
451C2×D68—22no—
452C2×D68—22no—
453C2×D68—22no—
454C2×D68—22no—
455C2×D68—22no—
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×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—22no—
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—416no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
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×C4×D17—41no—
495C2×C4×D17—41no—
496C2×C4×D17—41no—
497C2×C4×D17—41no—
498C2×C4×D17—41no—
499C2×C4×D17—41no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17#4114yes—
504C4⋊C4×C17—22no—
505C4⋊C4×C17—41no—
506C4⋊C4×C17—41no—
507C4⋊C4×C17—41no—
508C4⋊C4×C17—41no—
509C4⋊C4×C17—41no—
510C4⋊C4×C17—41no—
511C22⋊C4×C17—22no—
512C22⋊C4×C17—22no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17—41no—
515C22⋊C4×C17—41no—
516C22⋊C4×C17—41no—
517C22⋊C4×C17—41no—
518C22⋊C4×C17—41no—
519C22⋊C4×C17—41no—
520C22⋊C4×C17—41no—
521C42×C17—41no—
522C22⋊Dic17—22no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17—41no—
527C22⋊Dic17—41no—
528#63227—22no—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—22no—
535#63227—22no—
536#63227—22no—
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—
563#63227—41no—
564C4⋊Dic17—41no—
565C4⋊Dic17—41no—
566C4⋊Dic17—41no—
567C4⋊Dic17—41no—
568C4⋊Dic17—41no—
569#63225—22no—
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—
582#36731—171nomaximal, Sylow
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17H(5,𝔽2)12yes—
597C23×C17C2511yescharacteristic
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—28no—
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—44no—
631C22×D17—44no—
632C22×D17—44no—
633C22×D17—44no—
634C22×D17—44no—
635C22×D17—44no—
636C22×D17C2×#4112yes—
637C22×D17H(5,𝔽2)12yes—
638C22×D17H(5,𝔽2)12yes—
639C22×D17H(5,𝔽2)12yes—
640D4×C17—82no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
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—44no—
680C2×C4×C17—82no—
681C2×C4×C17C2×#4112yes—
682C22⋊D17—44no—
683C22⋊D17—82no—
684C22⋊D17—82no—
685C22⋊D17—82no—
686C22⋊D17—82no—
687C22⋊D17—82no—
688C22⋊D17—82no—
689C22⋊D17—82no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
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—44no—
723C2×Dic17C2×#4112yes—
724D68—44no—
725D68—44no—
726D68—44no—
727D68—82no—
728D68—82no—
729D68—82no—
730D68—82no—
731D68—82no—
732D68—82no—
733C4×D17—44no—
734C4×D17—44no—
735C4×D17—44no—
736C4×D17—44no—
737C4×D17—82no—
738C4×D17—82no—
739C4×D17—82no—
740C4×D17—82no—
741C4×D17—82no—
742C4×D17—82no—
743C4×D17—82no—
744#2847—171no—
745#2847—171no—
746#2743—171no—
747#2743—171no—
748#2743—171no—
749#2743D1711yescharacteristic, complemented
750#2740—171no—
751#2740—171no—
752#2740—171no—
753#2740—171no—
754#2699—171no—
755#2699—171no—
756#2699—171no—
757#2699—171no—
758#2688—171no—
759#2688—171no—
760#2688—171no—
761#2688—171no—
762#2656—171no—
763#2646—171no—
764#2444—171no—
765#2444—171no—
766#2444—171no—
767#2444—171no—
768#2424—171no—
769#2424—171no—
770#2424—171no—
771#2424—171no—
772#2325—171no—
773#2325—171no—
774C2×#381—171no—
775C22×C17—22no—
776C22×C17—22no—
777C22×C17—22no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17—41no—
783C22×C17—41no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17C22×#4111yescharacteristic
790C22×C17C2×H(5,𝔽2)11yescharacteristic
791C22×C17C2×H(5,𝔽2)11yescharacteristic
792C22×C17C2×H(5,𝔽2)11yescharacteristic
793C22×C17C2×H(5,𝔽2)11yescharacteristic
794C22×C17#58511yescharacteristic
795C22×C17#58511yescharacteristic
796C2×D17—22no—
797C2×D17—22no—
798C2×D17—22no—
799C2×D17—22no—
800C2×D17—22no—
801C2×D17—22no—
802C2×D17—22no—
803C2×D17—22no—
804C2×D17—22no—
805C2×D17—416no—
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#54014yes—
832C4×C17—22no—
833C4×C17—41no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843C4×C17—41no—
844C4×C17—41no—
845Dic17—22no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856C24×C4—171no—
857C2×#121—171no—
858C2×#121—171no—
859C2×#121—171no—
860C2×#121—171no—
861C2×#121—171no—
862C2×#121—171no—
863C2×#121—171no—
864C2×#121—171no—
865C2×#121—171no—
866C2×#121—171no—
867C2×#121—171no—
868C2×#121—171no—
869C2×#121—171no—
870C2×#121—171no—
871C2×#120—171no—
872C2×#120—171no—
873C2×#120—171no—
874C2×#120—171no—
875C2×C4×D4—171no—
876C2×C4×D4—171no—
877C2×C4×D4—171no—
878C2×C4×D4—171no—
879C22×C22⋊C4—171no—
880C22×C22⋊C4—171no—
881#400—171no—
882#400—171no—
883#400—171no—
884#400—171no—
885#400—171no—
886#400C2×D1711yescharacteristic, complemented
887#400C2×D1711yescharacteristic, complemented
888#400C2×D1711yescharacteristic, complemented
889#399—171no—
890#399—171no—
891#399—171no—
892#399C2×D1711yescharacteristic, complemented
893#398—171no—
894#398—171no—
895#398—171no—
896#398—171no—
897#397—171no—
898#397—171no—
899#397—171no—
900#397—171no—
901#397—171no—
902#397—171no—
903#397—171no—
904#397—171no—
905#396—171no—
906#396—171no—
907#396—171no—
908#396C2×D1711yescharacteristic
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#394C2×D1711yescharacteristic
921#392—171no—
922#392—171no—
923#392—171no—
924#392—171no—
925#392—171no—
926#392—171no—
927#392—171no—
928#392—171no—
929#390—171no—
930#390—171no—
931#390—171no—
932#390—171no—
933#388—171no—
934#388—171no—
935#388—171no—
936#388—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388C2×D1711yescharacteristic
944#388C2×D1711yescharacteristic, complemented
945#387—171no—
946#387—171no—
947#387—171no—
948#387—171no—
949#387—171no—
950#387—171no—
951#387—171no—
952#387C2×D1711yescharacteristic, complemented
953#386—171no—
954#386—171no—
955#386—171no—
956#386—171no—
957#386—171no—
958#386—171no—
959#386—171no—
960#386—171no—
961#386—171no—
962#386—171no—
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#386C2×D1711yescharacteristic
980#386C2×D1711yescharacteristic
981#385—171no—
982#385—171no—
983#385—171no—
984#385—171no—
985#385—171no—
986#385—171no—
987#385—171no—
988#385C2×D1711yescharacteristic, complemented
989#381—171no—
990#381—171no—
991#381—171no—
992#381—171no—
993#381—171no—
994#381—171no—
995#381—171no—
996#381—171no—
997#381—171no—
998#381—171no—
999#381C2×D1711yescharacteristic
1000#381C2×D1711yescharacteristic, complemented
1001#380—171no—
1002#380—171no—
1003#380—171no—
1004#380—171no—
1005#380—171no—
1006#380C2×D1711yescharacteristic
1007C2×#95—171no—
1008C2×#95—171no—
1009C2×#95—171no—
1010C2×#95—171no—
1011C2×C17—42no—
1012C2×C17—81no—
1013C2×C17C2×#54011yescharacteristic
1014C2×C17#349011yescharacteristic
1015C2×C17#349311yescharacteristic
1016C2×C17#353411yescharacteristic
1017C2×C17#353411yescharacteristic
1018C2×C17#353411yescharacteristic
1019C2×C17#353411yescharacteristic
1020D17—24no—
1021D17—42no—
1022D17—81no—
1023D17—81no—
1024D17—81no—
1025C25—171no—
1026C22×D4—171no—
1027C22×D4—171no—
1028C22×D4—171no—
1029C22×D4—171no—
1030C22×D4—171no—
1031C22×D4—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×D4C22×D1711yescharacteristic
1044C23×C4—171no—
1045C23×C4—171no—
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—171no—
1056C23×C4—344no—
1057C23×C4—682no—
1058C23×C4—682no—
1059C23×C4C22×D1711yescharacteristic
1060C23×C4C22×D1711yescharacteristic
1061#121—344no—
1062#121—344no—
1063#121—682no—
1064#121—682no—
1065#121—682no—
1066#121—682no—
1067#121—682no—
1068#121—682no—
1069#121—682no—
1070#121—682no—
1071#121—682no—
1072#121—682no—
1073#121—682no—
1074#121—682no—
1075#120—682no—
1076#120—682no—
1077#120—682no—
1078#120—682no—
1079C4×D4—682no—
1080C4×D4—682no—
1081C4×D4—682no—
1082C4×D4—682no—
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×C4⋊C4C22×D1711yescharacteristic
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—682no—
1148C2×C22⋊C4—682no—
1149C2×C22⋊C4C22×D1711yescharacteristic
1150C2×C22⋊C4C22×D1711yescharacteristic
1151C2×C22⋊C4C22×D1711yescharacteristic
1152C2×C22⋊C4C22×D1711yescharacteristic
1153C2×C22⋊C4C22×D1711yescharacteristic
1154C2×C22⋊C4C22×D1711yescharacteristic
1155C2×C22⋊C4C22×D1711yescharacteristic
1156C2×C22⋊C4C22×D1711yescharacteristic
1157C2×C22⋊C4C22×D1711yescharacteristic
1158C2×C22⋊C4C22×D1711yescharacteristic
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—171no—
1162C2×C42C22×D1711yescharacteristic
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
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#95—171no—
1192#95—171no—
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
1207C17#3673111yescharacteristic, complemented, Sylow
1208C24—171no—
1209C24—171no—
1210C24—171no—
1211C24—171no—
1212C24—171no—
1213C24—342no—
1214C24—342no—
1215C24—342no—
1216C24—342no—
1217C24—342no—
1218C24—681no—
1219C24—681no—
1220C24C23×D1711yescharacteristic
1221C24C23×D1711yescharacteristic
1222C2×D4—22no—
1223C2×D4—41no—
1224C2×D4—41no—
1225C2×D4—342no—
1226C2×D4—342no—
1227C2×D4—342no—
1228C2×D4—342no—
1229C2×D4—342no—
1230C2×D4—342no—
1231C2×D4—342no—
1232C2×D4—342no—
1233C2×D4—342no—
1234C2×D4—342no—
1235C2×D4—342no—
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—681no—
1247C2×D4—681no—
1248C2×D4—681no—
1249C2×D4—681no—
1250C2×D4—681no—
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—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—41no—
1281C22×C4—41no—
1282C22×C4—171no—
1283C22×C4—174no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—171no—
1287C22×C4—171no—
1288C22×C4—171no—
1289C22×C4—171no—
1290C22×C4—171no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—342no—
1295C22×C4—342no—
1296C22×C4—342no—
1297C22×C4—342no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—342no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—342no—
1304C22×C4—342no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
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—681no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—681no—
1328C22×C4—6816no—
1329C22×C4—681no—
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
1340C22×C4C23×D1711yescharacteristic
1341C22×C4C23×D1711yescharacteristic
1342C22×C4C23×D1711yescharacteristic
1343C4⋊C4—22no—
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—41no—
1347C4⋊C4—41no—
1348C4⋊C4—41no—
1349C4⋊C4—41no—
1350C4⋊C4—342no—
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—
1362C4⋊C4—681no—
1363C4⋊C4—681no—
1364C4⋊C4—681no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—41no—
1368C22⋊C4—41no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—41no—
1375C22⋊C4—342no—
1376C22⋊C4—342no—
1377C22⋊C4—342no—
1378C22⋊C4—342no—
1379C22⋊C4—342no—
1380C22⋊C4—342no—
1381C22⋊C4—342no—
1382C22⋊C4—342no—
1383C22⋊C4—342no—
1384C22⋊C4—342no—
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—
1417C42—41no—
1418C42—681no—
1419C42—681no—
1420C42—681no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—172no—
1435C23—172no—
1436C23—172no—
1437C23—172no—
1438C23—348no—
1439C23—341no—
1440C23—341no—
1441C23—341no—
1442C23—341no—
1443C23—341no—
1444C23—341no—
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—684no—
1471C23—684no—
1472C23—684no—
1473C23—684no—
1474C23—684no—
1475C23—684no—
1476C23#1058769612yes—
1477C23C24×D1711yescharacteristic
1478D4—82no—
1479D4—684no—
1480D4—684no—
1481D4—684no—
1482D4—684no—
1483D4—1362no—
1484D4—1362no—
1485D4—1362no—
1486D4—1362no—
1487D4—1362no—
1488D4—1362no—
1489D4—1362no—
1490D4—1362no—
1491D4—1362no—
1492D4—1362no—
1493D4—1362no—
1494D4—1362no—
1495D4—1362no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
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—44no—
1535C2×C4—82no—
1536C2×C4—172no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
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—684no—
1570C2×C4—684no—
1571C2×C4—684no—
1572C2×C4—684no—
1573C2×C4—684no—
1574C2×C4—1362no—
1575C2×C4—1362no—
1576C2×C4—1362no—
1577C2×C4—1362no—
1578C2×C4—1362no—
1579C2×C4—1362no—
1580C2×C4—1362no—
1581C2×C4#41×D1712yes—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—174no—
1597C22—342no—
1598C22—342no—
1599C22—342no—
1600C22—342no—
1601C22—342no—
1602C22—342no—
1603C22—342no—
1604C22—342no—
1605C22—342no—
1606C22—6816no—
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—
1632C22C2×#41×D1711yescharacteristic
1633C22H(5,𝔽2)×D1711yescharacteristic
1634C22H(5,𝔽2)×D1711yescharacteristic
1635C22H(5,𝔽2)×D1711yescharacteristic
1636C22C2×#1058769611yescharacteristic
1637C22#1176364511yescharacteristic
1638C22#1176364611yescharacteristic
1639C4—22no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—342no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C4—681no—
1659C4—681no—
1660C4—681no—
1661C4—681no—
1662C4—681no—
1663C2—42no—
1664C2—81no—
1665C2—344no—
1666C2—682no—
1667C2—1361no—
1668C2—1361no—
1669C2—1361no—
1670C2D17×#54011yescharacteristic
1671C2#1454246811yescharacteristic
1672C2#1454250211yescharacteristic
1673C2#1454297211yescharacteristic
1674C2#1454297311yescharacteristic
1675C2#1454297611yescharacteristic
1676C2#1454297711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2743C2
hypercenter#2743D17
hypocenterC17#36731
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2743

Complements

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

NH ≅ G/Ntype
1. #14537067C2semidirect
2. #14537065C2semidirect
3. #14535928C2semidirect
4. #14535919C2semidirect
5. #14535916C2semidirect
6. #14535890C2semidirect
7. #14535883C2semidirect
8. #14535879C2semidirect
9. #14535878C2semidirect
10. #14535373C2semidirect
11. #14535371C2semidirect
12. #14535371C2semidirect
13. #14535368C2semidirect
14. #14535227C2semidirect
15. #14535223C2semidirect
16. #14535222C2semidirect
17. #14535218C2semidirect
18. #14534887C2semidirect
19. #14534755C2semidirect
20. #14532541C2semidirect
21. #14532535C2semidirect
22. #14532535C2semidirect
23. #14532533C2semidirect
24. #14532325C2semidirect
25. #14532319C2semidirect
26. #14532315C2semidirect
27. #14532313C2semidirect
28. #14531483C2semidirect
29. #14531481C2semidirect
30. D17×#381C2semidirect
31. C17×#2743C2semidirect
57. #11762750C22semidirect
58. #11762750C22semidirect
59. #11762749C22semidirect
60. #11762749C22semidirect
61. #11762748C22semidirect
62. #11762744C22semidirect
63. #11762744C22semidirect
64. #11762744C22semidirect
65. #11762743C22semidirect
66. #11762743C22semidirect
67. #11762742C22semidirect
68. #11762741C22semidirect
69. #11762738C22semidirect
70. #11762737C22semidirect
71. #11762736C22semidirect
72. #11762736C22semidirect
73. #11762735C22semidirect
74. #11762735C22semidirect
75. #11762735C22semidirect
76. #11762734C22semidirect
82. #11762727C22semidirect
83. #11762727C22semidirect
87. #11762725C22semidirect
90. #11762724C22semidirect
92. #11762719C22semidirect
95. #11762718C22semidirect
96. #11762718C22semidirect
97. #11762718C22semidirect
104. #11762702C22semidirect
105. #11762701C22semidirect
106. #11762701C22semidirect
107. #11762701C22semidirect
108. #11762700C22semidirect
111. #11762698C22semidirect
112. #11762698C22semidirect
113. #11762695C22semidirect
114. #11762693C22semidirect
115. #11762692C22semidirect
116. #11762691C22semidirect
117. #11762690C22semidirect
118. #11762690C22semidirect
119. #11762690C22semidirect
121. #11762688C22semidirect
122. #11762688C22semidirect
134. #11762687C22semidirect
135. #11762687C22semidirect
136. #11762687C22semidirect
137. #11762687C22semidirect
144. #11762685C22semidirect
145. #11762685C22semidirect
149. #11762683C22semidirect
151. #11762680C22semidirect
152. #11762680C22semidirect
158. #11762671C22semidirect
159. #11762671C22semidirect
160. #11762671C22semidirect
172. C17×#400C22semidirect
173. C17×#400C22semidirect
174. C17×#400C22semidirect
175. C17×#399C22semidirect
179. C17×#388C22semidirect
180. C17×#387C22semidirect
183. C17×#385C22semidirect
185. C17×#381C22semidirect
749. #2743D17semidirect
886. #400C2×D17semidirect
887. #400C2×D17semidirect
888. #400C2×D17semidirect
892. #399C2×D17semidirect
944. #388C2×D17semidirect
952. #387C2×D17semidirect
988. #385C2×D17semidirect
1000. #381C2×D17semidirect
1207. C17#36731semidirect

Maximal subgroups

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

subgroupindex
#145370672
#145370652
#145359282
#145359192
#145359162
#145358902
#145358832
#145358792
#145358782
#145353732
#145353712
#145353682
#145352272
#145352232
#145352222
#145352182
#145348872
#145347552
#145325412
#145325352
#145325332
#145323252
#145323192
#145323152
#145323132
#145314832
#145314812
D17×#3812
C17×#27432
#3673117