Finite Group Databasebeta

← #17243124

Subgroups — #17243124

Order 4352.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537076C211yesmaximal, characteristic, complemented
2#14537066C211yesmaximal, characteristic, complemented
3#14536726C211yesmaximal, characteristic, complemented
4#14536645C211yesmaximal, characteristic, complemented
5#14536530C211yesmaximal, characteristic, complemented
6#14536483C211yesmaximal, characteristic, complemented
7#14536430C211yesmaximal, characteristic, complemented
8#14536396C211yesmaximal, characteristic, complemented
9#14536041C211yesmaximal, characteristic, complemented
10#14536026C211yesmaximal, characteristic, complemented
11#14535957C211yesmaximal, characteristic, complemented
12#14535581C211yesmaximal, characteristic, complemented
13#14535530C211yesmaximal, characteristic, complemented
14#14535506C211yesmaximal, characteristic, complemented
15#14535503C211yesmaximal, characteristic, complemented
16#14535323C211yesmaximal, characteristic, complemented
17#14535194C211yesmaximal, characteristic, complemented
18#14535150C211yesmaximal, characteristic, complemented
19#14534737C211yesmaximal, characteristic, complemented
20#14534712C211yesmaximal, characteristic, complemented
21#14533039C211yesmaximal, characteristic, complemented
22#14532904C211yesmaximal, characteristic, complemented
23#14532519C211yesmaximal, characteristic, complemented
24#14532460C211yesmaximal, characteristic, complemented
25#14532394C211yesmaximal, characteristic, complemented
26#14532320C211yesmaximal, characteristic, complemented
27#14532169C211yesmaximal, characteristic, complemented
28#14532103C211yesmaximal, characteristic, complemented
29#14531453C211yesmaximal, characteristic, complemented
30#14531377C211yesmaximal, characteristic, complemented
31C2×C17×#385C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C2×#10587584C2211yescharacteristic, complemented
34C2×#10587571C2211yescharacteristic
35C2×#10587580C2211yescharacteristic, complemented
36C2×#10587615C2211yescharacteristic
37C2×#10587615C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587610C2211yescharacteristic
40C2×#10587616C2211yescharacteristic
41C2×#10587616C2211yescharacteristic
42C2×#10587616C2211yescharacteristic
43C2×#10587616C2211yescharacteristic
44C2×#10587570C2211yescharacteristic
45C2×#10587639C2211yescharacteristic
46C2×#10587639C2211yescharacteristic
47C2×#10587639C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×#10587612C2211yescharacteristic
50C17⋊#401C2211yescharacteristic, complemented
51#11762751C2211yescharacteristic, complemented
52#11762750C2211yescharacteristic, complemented
53#11762750C2211yescharacteristic, complemented
54#11762750C2211yescharacteristic, complemented
55#11762749C2211yescharacteristic, complemented
56#11762749C2211yescharacteristic, complemented
57#11762748C2211yescharacteristic, complemented
58#11762747C2211yescharacteristic, complemented
59#11762744C2211yescharacteristic, complemented
60#11762743C2211yescharacteristic, complemented
61#11762742C2211yescharacteristic, complemented
62#11762741C2211yescharacteristic, complemented
63#11762738C2211yescharacteristic, complemented
64#11762738C2211yescharacteristic, complemented
65#11762738C2211yescharacteristic, complemented
66#11762737C2211yescharacteristic
67#11762736C2211yescharacteristic, complemented
68#11762736C2211yescharacteristic, complemented
69#11762735C2211yescharacteristic, complemented
70#11762735C2211yescharacteristic, complemented
71#11762733C2211yescharacteristic, complemented
72#11762732C2211yescharacteristic
73#11762732C2211yescharacteristic
74#11762732C2211yescharacteristic
75#11762731C2211yescharacteristic, complemented
76#11762730C2211yescharacteristic, complemented
77#11762730C2211yescharacteristic, complemented
78#11762727C2211yescharacteristic, complemented
79#11762727C2211yescharacteristic, complemented
80#11762727C2211yescharacteristic, complemented
81#11762726C2211yescharacteristic, complemented
82#11762725C2211yescharacteristic
83#11762725C2211yescharacteristic
84#11762725C2211yescharacteristic
85#11762724C2211yescharacteristic
86#11762724C2211yescharacteristic
87#11762724C2211yescharacteristic
88#11762722C2211yescharacteristic, complemented
89#11762722C2211yescharacteristic, complemented
90#11762722C2211yescharacteristic, complemented
91#11762721C2211yescharacteristic
92#11762721C2211yescharacteristic
93#11762721C2211yescharacteristic
94#11762719C2211yescharacteristic, complemented
95#11762718C2211yescharacteristic
96#11762718C2211yescharacteristic
97#11762718C2211yescharacteristic
98#11762714C2211yescharacteristic, complemented
99#11762714C2211yescharacteristic, complemented
100#11762713C2211yescharacteristic, complemented
101#11762710C2211yescharacteristic, complemented
102#11762710C2211yescharacteristic, complemented
103#11762709C2211yescharacteristic
104#11762709C2211yescharacteristic
105#11762709C2211yescharacteristic
106#11762709C2211yescharacteristic
107#11762706C2211yescharacteristic, complemented
108#11762704C2211yescharacteristic, complemented
109#11762704C2211yescharacteristic, complemented
110#11762703C2211yescharacteristic
111#11762703C2211yescharacteristic
112#11762702C2211yescharacteristic
113#11762702C2211yescharacteristic
114#11762699C2211yescharacteristic, complemented
115#11762699C2211yescharacteristic, complemented
116#11762699C2211yescharacteristic, complemented
117#11762699C2211yescharacteristic, complemented
118#11762697C2211yescharacteristic
119#11762696C2211yescharacteristic, complemented
120#11762695C2211yescharacteristic, complemented
121#11762695C2211yescharacteristic, complemented
122#11762692C2211yescharacteristic, complemented
123#11762690C2211yescharacteristic, complemented
124#11762690C2211yescharacteristic, complemented
125#11762690C2211yescharacteristic, complemented
126#11762688C2211yescharacteristic
127#11762688C2211yescharacteristic
128#11762688C2211yescharacteristic
129#11762688C2211yescharacteristic
130#11762688C2211yescharacteristic
131#11762688C2211yescharacteristic
132#11762688C2211yescharacteristic
133#11762688C2211yescharacteristic
134#11762688C2211yescharacteristic
135#11762688C2211yescharacteristic
136#11762688C2211yescharacteristic
137#11762688C2211yescharacteristic
138#11762688C2211yescharacteristic
139#11762688C2211yescharacteristic
140#11762688C2211yescharacteristic
141#11762688C2211yescharacteristic
142#11762687C2211yescharacteristic, complemented
143#11762687C2211yescharacteristic, complemented
144#11762685C2211yescharacteristic
145#11762685C2211yescharacteristic
146#11762685C2211yescharacteristic
147#11762685C2211yescharacteristic
148#11762685C2211yescharacteristic
149#11762683C2211yescharacteristic, complemented
150#11762683C2211yescharacteristic, complemented
151#11762682C2211yescharacteristic
152#11762682C2211yescharacteristic
153#11762682C2211yescharacteristic
154#11762682C2211yescharacteristic
155#11762682C2211yescharacteristic
156#11762682C2211yescharacteristic
157#11762680C2211yescharacteristic, complemented
158#11762680C2211yescharacteristic, complemented
159#11762680C2211yescharacteristic, complemented
160#11762672C2211yescharacteristic
161#11762672C2211yescharacteristic
162#11762672C2211yescharacteristic
163#11762669C2211yescharacteristic
164#11762669C2211yescharacteristic
165#11762669C2211yescharacteristic
166#11762666C2211yescharacteristic, complemented
167#11762666C2211yescharacteristic, complemented
168#11762666C2211yescharacteristic, complemented
169#11762666C2211yescharacteristic, complemented
170#11762665C2211yescharacteristic
171C4×C22⋊Dic17C2211yescharacteristic
172C24×C4×C17C2211yescharacteristic
173C22×C4⋊C4×C17C2211yescharacteristic
174C22×C4⋊C4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C22×C22⋊C4×C17C2211yescharacteristic
177C17×#385C2211yescharacteristic
178C17×#385C2211yescharacteristic
179C17×#385C2211yescharacteristic
180C17×#385C2211yescharacteristic
181C17×#385C2211yescharacteristic
182C17×#385C2211yescharacteristic
183C17×#385C2211yescharacteristic
184C17×#385C2211yescharacteristic
185C2×C17×#95C2211yescharacteristic
186C2×C17×#95C2211yescharacteristic
187C25×C17C2311yescharacteristic
188C23×C4×C17—42no—
189C23×C4×C17—42no—
190C23×C4×C17—42no—
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C22×C22⋊D17C2311yescharacteristic
209C22×C22⋊D17C2311yescharacteristic
210C2×#63252—24no—
211C2×#63252—42no—
212C2×#63252—42no—
213C22×D68C2311yescharacteristic
214C22×D68C2311yescharacteristic
215C22×D68C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×Dic34C2311yescharacteristic
220C22×Dic34C2311yescharacteristic
221C2×C4⋊C4×C17—42no—
222C2×C4⋊C4×C17—42no—
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×C4⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17—24no—
232C2×C22⋊C4×C17—42no—
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×C22⋊C4×C17C2311yescharacteristic
241#10587639—42no—
242#10587639—42no—
243#10587639—42no—
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259#10587616—42no—
260#10587616—42no—
261#10587616—42no—
262#10587616—42no—
263#10587615—24no—
264#10587615—42no—
265#10587615—42no—
266C4×C22⋊D17—42no—
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
294#10587612—42no—
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302#10587610—42no—
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321#10587584—42no—
322#10587580—42no—
323#10587571—42no—
324#10587570—42no—
325C17×#95C2311yescharacteristic
326C17×#95C2311yescharacteristic
327C17×#95C2311yescharacteristic
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
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×C17—22no—
370C24×C17—22no—
371C24×C17—22no—
372C24×C17—22no—
373C24×C17—22no—
374C24×C17—41no—
375C24×C17—41no—
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C22×C4×C17—22no—
383C22×C4×C17—22no—
384C22×C4×C17—22no—
385C22×C4×C17—22no—
386C22×C4×C17—22no—
387C22×C4×C17—22no—
388C22×C4×C17—22no—
389C22×C4×C17—22no—
390C22×C4×C17—22no—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—22no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—416no—
412C22×C4×C17#4114yes—
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—22no—
429C2×C22⋊D17—22no—
430C2×C22⋊D17—22no—
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—41no—
450C2×C22⋊D17—41no—
451C2×C22⋊D17—41no—
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465#63252—416no—
466C2×D68—22no—
467C2×D68—22no—
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—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×Dic34—22no—
485C2×Dic34—41no—
486C2×Dic34—41no—
487C2×Dic34—41no—
488C2×Dic34—41no—
489C2×Dic34—41no—
490C4⋊C4×C17—22no—
491C4⋊C4×C17—22no—
492C4⋊C4×C17—41no—
493C4⋊C4×C17—41no—
494C4⋊C4×C17—41no—
495C4⋊C4×C17—41no—
496C4⋊C4×C17—41no—
497C4⋊C4×C17—41no—
498C22⋊C4×C17—22no—
499C22⋊C4×C17—22no—
500C22⋊C4×C17—22no—
501C22⋊C4×C17—22no—
502C22⋊C4×C17—22no—
503C22⋊C4×C17—22no—
504C22⋊C4×C17—41no—
505C22⋊C4×C17—41no—
506C22⋊Dic17—22no—
507C22⋊Dic17—22no—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—22no—
512C22⋊Dic17—22no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17—41no—
519C22⋊Dic17—41no—
520C22⋊Dic17—41no—
521#63227—22no—
522#63227—22no—
523#63227—22no—
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—
548C4⋊Dic17—22no—
549C4⋊Dic17—41no—
550C4⋊Dic17—41no—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17—41no—
554C4⋊Dic17—41no—
555#63225—22no—
556#63225—22no—
557#63225—22no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573#36791—171nomaximal, Sylow
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—28no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
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—44no—
592C23×C17—44no—
593C23×C17—44no—
594C23×C17—44no—
595C23×C17—44no—
596C23×C17—44no—
597C23×C17C2×#4112yes—
598C23×C17H(5,𝔽2)12yes—
599C23×C17H(5,𝔽2)12yes—
600C23×C17H(5,𝔽2)12yes—
601C23×C172−1+412yes—
602C23×C17C2511yescharacteristic
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—
624C2×C4×C17—28no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
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—44no—
659C2×C4×C17—44no—
660C2×C4×C17—44no—
661C2×C4×C17—44no—
662C2×C4×C17—44no—
663C2×C4×C17—44no—
664C2×C4×C17—44no—
665C2×C4×C17—82no—
666C2×C4×C17—82no—
667C2×C4×C17C2×#4112yes—
668C2×C4×C17C2×#4112yes—
669C2×C4×C17H(5,𝔽2)12yes—
670C22⋊D17—44no—
671C22⋊D17—44no—
672C22⋊D17—44no—
673C22⋊D17—82no—
674C22⋊D17—82no—
675C22⋊D17—82no—
676C22⋊D17—82no—
677C22⋊D17—82no—
678C22⋊D17—82no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
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—
718D68—44no—
719D68—82no—
720D68—82no—
721C4×D17—44no—
722C4×D17—44no—
723C4×D17—82no—
724Dic34—44no—
725Dic34—82no—
726#2849—171no—
727#2847—171no—
728#2804—171no—
729#2797—171no—
730#2788—171no—
731#2784—171no—
732#2780—171no—
733#2778—171no—
734#2751—171no—
735#2750—171no—
736#2745—171no—
737#2714—171no—
738#2710—171no—
739#2708—171no—
740#2708—171no—
741#2695—171no—
742#2686—171no—
743#2682—171no—
744#2643—171no—
745#2639—171no—
746#2481—171no—
747#2472—171no—
748#2443—171no—
749#2438—171no—
750#2430—171no—
751#2424—171no—
752#2411—171no—
753#2404—171no—
754#2322—171no—
755#2311—171no—
756C2×#385D1711yescharacteristic, complemented
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—22no—
767C22×C17—22no—
768C22×C17—22no—
769C22×C17—416no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17#53814yes—
779C22×C17C22×#4111yescharacteristic
780C22×C17C2×H(5,𝔽2)11yescharacteristic
781C22×C17C2×H(5,𝔽2)11yescharacteristic
782C22×C17C2×H(5,𝔽2)11yescharacteristic
783C22×C17C2×H(5,𝔽2)11yescharacteristic
784C22×C17C2×2−1+411yescharacteristic
785C22×C17#58511yescharacteristic
786C2×D17—41no—
787C2×D17—41no—
788C2×D17—41no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C4×C17—22no—
808C4×C17—22no—
809C4×C17—22no—
810C4×C17—41no—
811C4×C17—41no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823Dic17—41no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832C22×#41—171no—
833C24×C4C2×D1711yescharacteristic
834C2×#126—171no—
835C2×#124—171no—
836C2×#123—171no—
837C2×#123—171no—
838C2×#123—171no—
839C2×#123—171no—
840C2×C22⋊Q8—171no—
841C2×#121—171no—
842C2×#121—171no—
843C2×#121—171no—
844C2×#121—171no—
845C2×#121—171no—
846C2×#120—171no—
847C2×#120—171no—
848C2×#120—171no—
849C2×C4×D4—171no—
850C2×#117—171no—
851C22×C4⋊C4C2×D1711yescharacteristic
852C22×C4⋊C4C2×D1711yescharacteristic
853C22×C22⋊C4C2×D1711yescharacteristic
854C22×C22⋊C4C2×D1711yescharacteristic
855#401—171no—
856#400—171no—
857#400—171no—
858#400—171no—
859#400—171no—
860#400—171no—
861#400—171no—
862#400—171no—
863#400—171no—
864#399—171no—
865#398—171no—
866#398—171no—
867#398—171no—
868#397—171no—
869#397—171no—
870#397—171no—
871#397—171no—
872#397—171no—
873#397—171no—
874#397—171no—
875#397—171no—
876#396—171no—
877#396—171no—
878#396—171no—
879#396—171no—
880#396—171no—
881#395—171no—
882#395—171no—
883#394—171no—
884#394—171no—
885#394—171no—
886#394—171no—
887#394—171no—
888#394—171no—
889#394—171no—
890#394—171no—
891#394—171no—
892#394—171no—
893#393—171no—
894#393—171no—
895#393—171no—
896#393—171no—
897#393—171no—
898#393—171no—
899#392—171no—
900#392—171no—
901#392—171no—
902#392—171no—
903#391—171no—
904#391—171no—
905#391—171no—
906#390—171no—
907#390—171no—
908#390—171no—
909#390—171no—
910#390—171no—
911#390—171no—
912#389—171no—
913#389—171no—
914#389—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388—171no—
921#388—171no—
922#388—171no—
923#388—171no—
924#387—171no—
925#387—171no—
926#387—171no—
927#387—171no—
928#387—171no—
929#387—171no—
930#387—171no—
931#386—171no—
932#386—171no—
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386—171no—
954#385—171no—
955#385—171no—
956#385—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385C2×D1711yescharacteristic
966#385C2×D1711yescharacteristic
967#385C2×D1711yescharacteristic
968#385C2×D1711yescharacteristic
969#385C2×D1711yescharacteristic
970#385C2×D1711yescharacteristic
971#385C2×D1711yescharacteristic
972#385C2×D1711yescharacteristic
973#381—171no—
974#381—171no—
975#381—171no—
976#380—171no—
977#380—171no—
978#380—171no—
979#380—171no—
980#380—171no—
981#380—171no—
982#380—171no—
983#379—171no—
984C4×C22⋊C4—171no—
985C2×#95C2×D1711yescharacteristic
986C2×#95C2×D1711yescharacteristic
987C2×C17—24no—
988C2×C17—42no—
989C2×C17—42no—
990C2×C17C2×#53811yescharacteristic
991C2×C17#349211yescharacteristic
992C2×C17#350611yescharacteristic
993C2×C17#353211yescharacteristic
994C2×C17#353411yescharacteristic
995C2×C17#353511yescharacteristic
996C2×C17#353611yescharacteristic
997D17—81no—
998D17—81no—
999D17—81no—
1000C25C22×D1711yescharacteristic
1001C2×#41—344no—
1002C2×#41—682no—
1003C2×#41—682no—
1004C22×Q8—171no—
1005C22×Q8—171no—
1006C22×D4—171no—
1007C22×D4—171no—
1008C22×D4—171no—
1009C22×D4—171no—
1010C22×D4—171no—
1011C22×D4—171no—
1012C22×D4—171no—
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4—171no—
1016C22×D4—171no—
1017C22×D4—171no—
1018C23×C4—42no—
1019C23×C4—42no—
1020C23×C4—42no—
1021C23×C4—171no—
1022C23×C4—171no—
1023C23×C4—171no—
1024C23×C4C22×D1711yescharacteristic
1025C23×C4C22×D1711yescharacteristic
1026C23×C4C22×D1711yescharacteristic
1027C23×C4C22×D1711yescharacteristic
1028C23×C4C22×D1711yescharacteristic
1029C23×C4C22×D1711yescharacteristic
1030C23×C4C22×D1711yescharacteristic
1031C23×C4C22×D1711yescharacteristic
1032C23×C4C22×D1711yescharacteristic
1033C23×C4C22×D1711yescharacteristic
1034#126—682no—
1035#124—682no—
1036#123—344no—
1037#123—682no—
1038#123—682no—
1039#123—682no—
1040C22⋊Q8—682no—
1041#121—682no—
1042#121—682no—
1043#121—682no—
1044#121—682no—
1045#121—682no—
1046#120—682no—
1047#120—682no—
1048#120—682no—
1049C4×D4—682no—
1050#117—682no—
1051C2×C4⋊C4—42no—
1052C2×C4⋊C4—42no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4C22×D1711yescharacteristic
1074C2×C4⋊C4C22×D1711yescharacteristic
1075C2×C4⋊C4C22×D1711yescharacteristic
1076C2×C4⋊C4C22×D1711yescharacteristic
1077C2×C4⋊C4C22×D1711yescharacteristic
1078C2×C4⋊C4C22×D1711yescharacteristic
1079C2×C4⋊C4C22×D1711yescharacteristic
1080C2×C4⋊C4C22×D1711yescharacteristic
1081C2×C22⋊C4—24no—
1082C2×C22⋊C4—42no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1126C2×C22⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4C22×D1711yescharacteristic
1128C2×C22⋊C4C22×D1711yescharacteristic
1129C2×C22⋊C4C22×D1711yescharacteristic
1130C2×C22⋊C4C22×D1711yescharacteristic
1131C2×C22⋊C4C22×D1711yescharacteristic
1132C2×C22⋊C4C22×D1711yescharacteristic
1133C2×C42—171no—
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42—171no—
1137C2×C42—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
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#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179#95C22×D1711yescharacteristic
1180#95C22×D1711yescharacteristic
1181#95C22×D1711yescharacteristic
1182C17#3679111yescharacteristic, complemented, Sylow
1183C24—22no—
1184C24—22no—
1185C24—22no—
1186C24—22no—
1187C24—22no—
1188C24—41no—
1189C24—41no—
1190C24—171no—
1191C24—171no—
1192C24—171no—
1193C24C23×D1711yescharacteristic
1194C24C23×D1711yescharacteristic
1195C24C23×D1711yescharacteristic
1196#41—6816no—
1197C2×Q8—342no—
1198C2×Q8—681no—
1199C2×Q8—681no—
1200C2×Q8—681no—
1201C2×Q8—681no—
1202C2×Q8—681no—
1203C2×D4—342no—
1204C2×D4—342no—
1205C2×D4—342no—
1206C2×D4—342no—
1207C2×D4—342no—
1208C2×D4—342no—
1209C2×D4—342no—
1210C2×D4—342no—
1211C2×D4—342no—
1212C2×D4—342no—
1213C2×D4—342no—
1214C2×D4—342no—
1215C2×D4—342no—
1216C2×D4—342no—
1217C2×D4—342no—
1218C2×D4—342no—
1219C2×D4—342no—
1220C2×D4—681no—
1221C2×D4—681no—
1222C2×D4—681no—
1223C2×D4—681no—
1224C2×D4—681no—
1225C2×D4—681no—
1226C2×D4—681no—
1227C2×D4—681no—
1228C2×D4—681no—
1229C2×D4—681no—
1230C2×D4—681no—
1231C2×D4—681no—
1232C2×D4—681no—
1233C2×D4—681no—
1234C2×D4—681no—
1235C2×D4—681no—
1236C2×D4—681no—
1237C2×D4—681no—
1238C2×D4—681no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—416no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—171no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—171no—
1282C22×C4—342no—
1283C22×C4—342no—
1284C22×C4—681no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4#6325214yes—
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C22×C4C23×D1711yescharacteristic
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C22×C4C23×D1711yescharacteristic
1300C22×C4C23×D1711yescharacteristic
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
1311C4⋊C4—41no—
1312C4⋊C4—342no—
1313C4⋊C4—342no—
1314C4⋊C4—342no—
1315C4⋊C4—342no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4—681no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—342no—
1341C22⋊C4—342no—
1342C22⋊C4—342no—
1343C22⋊C4—342no—
1344C22⋊C4—342no—
1345C22⋊C4—342no—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4—681no—
1360C22⋊C4—681no—
1361C22⋊C4—681no—
1362C22⋊C4—681no—
1363C22⋊C4—681no—
1364C22⋊C4—681no—
1365C22⋊C4—681no—
1366C22⋊C4—681no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C42—681no—
1383C42—681no—
1384C42—681no—
1385C42—681no—
1386C42—681no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—28no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—44no—
1405C23—44no—
1406C23—44no—
1407C23—44no—
1408C23—44no—
1409C23—44no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—341no—
1424C23—341no—
1425C23—341no—
1426C23—341no—
1427C23—341no—
1428C23—341no—
1429C23—341no—
1430C23—341no—
1431C23C2×#6325212yes—
1432C23#1058769112yes—
1433C23#1058769112yes—
1434C23#1058769412yes—
1435C23#1058769612yes—
1436C23C24×D1711yescharacteristic
1437Q8—684no—
1438Q8—1362no—
1439D4—684no—
1440D4—684no—
1441D4—684no—
1442D4—684no—
1443D4—1362no—
1444D4—1362no—
1445D4—1362no—
1446D4—1362no—
1447D4—1362no—
1448D4—1362no—
1449D4—1362no—
1450D4—1362no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—28no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—44no—
1486C2×C4—44no—
1487C2×C4—44no—
1488C2×C4—44no—
1489C2×C4—44no—
1490C2×C4—44no—
1491C2×C4—44no—
1492C2×C4—82no—
1493C2×C4—82no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—684no—
1534C2×C4—684no—
1535C2×C4—1362no—
1536C2×C4C2×#6325212yes—
1537C2×C4C2×#6325212yes—
1538C2×C4#1058769112yes—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—416no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—681no—
1561C22—681no—
1562C22—681no—
1563C22—681no—
1564C22—681no—
1565C22—681no—
1566C22—681no—
1567C22—681no—
1568C22—681no—
1569C22—681no—
1570C22—681no—
1571C22—681no—
1572C22—681no—
1573C22—681no—
1574C22—681no—
1575C22—681no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—681no—
1581C22#1176339214yes—
1582C22C22×#6325211yescharacteristic
1583C22C2×#1058769111yescharacteristic
1584C22C2×#1058769111yescharacteristic
1585C22C2×#1058769111yescharacteristic
1586C22C2×#1058769611yescharacteristic
1587C22C2×#1058769411yescharacteristic
1588C22#1176364511yescharacteristic
1589C4—22no—
1590C4—22no—
1591C4—22no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—681no—
1602C4—681no—
1603C4—681no—
1604C4—681no—
1605C4—681no—
1606C4—681no—
1607C4—681no—
1608C4—681no—
1609C4—681no—
1610C4—681no—
1611C4—681no—
1612C4—681no—
1613C4—681no—
1614C2—24no—
1615C2—42no—
1616C2—42no—
1617C2—1361no—
1618C2—1361no—
1619C2—1361no—
1620C2C2×#1176339211yescharacteristic
1621C2#1454249311yescharacteristic
1622C2#1454263611yescharacteristic
1623C2#1454293911yescharacteristic
1624C2#1454297811yescharacteristic
1625C2#1454299311yescharacteristic
1626C2#1454301311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC2×C17×#385C2
hypercenterC2×#385D17
hypocenterC17#36791
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #14537076C2semidirect
2. #14537066C2semidirect
3. #14536726C2semidirect
4. #14536645C2semidirect
5. #14536530C2semidirect
6. #14536483C2semidirect
7. #14536430C2semidirect
8. #14536396C2semidirect
9. #14536041C2semidirect
10. #14536026C2semidirect
11. #14535957C2semidirect
12. #14535581C2semidirect
13. #14535530C2semidirect
14. #14535506C2semidirect
15. #14535503C2semidirect
16. #14535323C2semidirect
17. #14535194C2semidirect
18. #14535150C2semidirect
19. #14534737C2semidirect
20. #14534712C2semidirect
21. #14533039C2semidirect
22. #14532904C2semidirect
23. #14532519C2semidirect
24. #14532460C2semidirect
25. #14532394C2semidirect
26. #14532320C2semidirect
27. #14532169C2semidirect
28. #14532103C2semidirect
29. #14531453C2semidirect
30. #14531377C2semidirect
31. C2×C17×#385C2semidirect
33. C2×#10587584C22semidirect
35. C2×#10587580C22semidirect
50. C17⋊#401C22semidirect
51. #11762751C22semidirect
52. #11762750C22semidirect
53. #11762750C22semidirect
54. #11762750C22semidirect
55. #11762749C22semidirect
56. #11762749C22semidirect
57. #11762748C22semidirect
58. #11762747C22semidirect
59. #11762744C22semidirect
60. #11762743C22semidirect
61. #11762742C22semidirect
62. #11762741C22semidirect
63. #11762738C22semidirect
64. #11762738C22semidirect
65. #11762738C22semidirect
67. #11762736C22semidirect
68. #11762736C22semidirect
69. #11762735C22semidirect
70. #11762735C22semidirect
71. #11762733C22semidirect
75. #11762731C22semidirect
76. #11762730C22semidirect
77. #11762730C22semidirect
78. #11762727C22semidirect
79. #11762727C22semidirect
80. #11762727C22semidirect
81. #11762726C22semidirect
88. #11762722C22semidirect
89. #11762722C22semidirect
90. #11762722C22semidirect
94. #11762719C22semidirect
98. #11762714C22semidirect
99. #11762714C22semidirect
100. #11762713C22semidirect
101. #11762710C22semidirect
102. #11762710C22semidirect
107. #11762706C22semidirect
108. #11762704C22semidirect
109. #11762704C22semidirect
114. #11762699C22semidirect
115. #11762699C22semidirect
116. #11762699C22semidirect
117. #11762699C22semidirect
119. #11762696C22semidirect
120. #11762695C22semidirect
121. #11762695C22semidirect
122. #11762692C22semidirect
123. #11762690C22semidirect
124. #11762690C22semidirect
125. #11762690C22semidirect
142. #11762687C22semidirect
143. #11762687C22semidirect
149. #11762683C22semidirect
150. #11762683C22semidirect
157. #11762680C22semidirect
158. #11762680C22semidirect
159. #11762680C22semidirect
166. #11762666C22semidirect
167. #11762666C22semidirect
168. #11762666C22semidirect
169. #11762666C22semidirect
756. C2×#385D17semidirect
1182. C17#36791semidirect

Maximal subgroups

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

subgroupindex
#145370762
#145370662
#145367262
#145366452
#145365302
#145364832
#145364302
#145363962
#145360412
#145360262
#145359572
#145355812
#145355302
#145355062
#145355032
#145353232
#145351942
#145351502
#145347372
#145347122
#145330392
#145329042
#145325192
#145324602
#145323942
#145323202
#145321692
#145321032
#145314532
#145313772
C2×C17×#3852
#3679117