Finite Group Databasebeta

← #15791498

Subgroups — #15791498

Order 3328.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718871C211yesmaximal, characteristic
2#13113102C211yesmaximal, characteristic, complemented
3#13113096C211yesmaximal, characteristic, complemented
4#13113087C211yesmaximal, characteristic, complemented
5#13113087C211yesmaximal, characteristic, complemented
6#13113079C211yesmaximal, characteristic
7#13113079C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113071C211yesmaximal, characteristic, complemented
11#13113064C211yesmaximal, characteristic, complemented
12#13113060C211yesmaximal, characteristic, complemented
13#13113060C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33#11718871C418yescomplemented
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C25×C13C2311yescharacteristic
53C23×C4×C13—41no—
54C23×C4×C13—41no—
55C23×C4×C13—41no—
56C23×C4×C13—41no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13C2×C414yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—41no—
79C2×C13×C22⋊C4—41no—
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—41no—
84C2×C22⋊Dic13—41no—
85C2×C22⋊Dic13—41no—
86C2×C22⋊Dic13—41no—
87C2×C22⋊Dic13—41no—
88C2×C22⋊Dic13—41no—
89C2×C22⋊Dic13C2×C414yes—
90C2×C22⋊Dic13C2×C414yes—
91C2×C22⋊Dic13Q814yes—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101—41no—
95C2×#6101—41no—
96C2×#6101—41no—
97C2×#6101—41no—
98C2×#6101—41no—
99C2×#6101—41no—
100C2×#6101—41no—
101C2×#6101—41no—
102C2×#6101C2×C414yes—
103C2×#6101C2×C414yes—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—41no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C13×#95—41no—
111C13×#95—41no—
112C13×#95—41no—
113C13×#95—41no—
114#88071—22no—
115#88071—22no—
116#88071—22no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071C2×C414yes—
131#88071C2×C414yes—
132#14456—131nomaximal, Sylow
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13C22×C412yes—
146C24×C13C2×Q812yes—
147C24×C13#4112yes—
148C24×C13C2411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—44no—
188C22×C4×C13—44no—
189C22×C4×C13—44no—
190C22×C4×C13—44no—
191C22×C4×C13—44no—
192C22×C4×C13—44no—
193C22×C4×C13—44no—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13#4112yes—
197C22×C4×C13#4112yes—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C412yes—
250C22×Dic13C2×Q812yes—
251C22×Dic13C2×Q812yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C13×C22⋊C4—44no—
255C13×C22⋊C4—44no—
256C22⋊Dic13—28no—
257C22⋊Dic13—44no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260#6101—44no—
261#6101—44no—
262#6101—44no—
263#6101—44no—
264C4×Dic13—44no—
265C4×Dic13—44no—
266C2×#385—131no—
267#1445—131no—
268#1443—131no—
269#1441—131no—
270#1441—131no—
271#1439—131no—
272#1439—131no—
273#1437—131no—
274#1437—131no—
275#1436—131no—
276C4⋊#95—131no—
277#1434—131no—
278#1434—131no—
279C22⋊#95—131no—
280C22⋊#95D1311yescharacteristic
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13C4×Q814yes—
316C23×C13C23×C411yescharacteristic
317C23×C13C22×Q811yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C13H(5,𝔽2)11yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C13H(5,𝔽2)11yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C132−1+411yescharacteristic
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—416no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13#11714yes—
430C24×C4C2×D1311yescharacteristic
431C22×C4⋊C4—131no—
432C22×C4⋊C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4C2×D1311yescharacteristic
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C42—131no—
442C22×C42—131no—
443#385—138no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95C2×D1311yescharacteristic
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C2×#95C2×D1311yescharacteristic
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—24no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13C2×#11711yescharacteristic
482C22×C13C2×C4×Q811yescharacteristic
483C22×C13C4×#4111yescharacteristic
484C22×C13#51811yescharacteristic
485C22×C13#51811yescharacteristic
486C22×C13#51811yescharacteristic
487C22×C13#52011yescharacteristic
488C22×C13#53811yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53911yescharacteristic
491C22×C13#53911yescharacteristic
492C22×C13#54011yescharacteristic
493C22×C13#54011yescharacteristic
494C22×C13#54011yescharacteristic
495C22×C13#54211yescharacteristic
496C22×C13#54211yescharacteristic
497C22×C13#54211yescharacteristic
498C22×C13#54311yescharacteristic
499C22×C13#54411yescharacteristic
500C22×C13#55111yescharacteristic
501C22×C13#55111yescharacteristic
502C22×C13#55111yescharacteristic
503C22×C13#55111yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55311yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55311yescharacteristic
508C22×C13#55411yescharacteristic
509C22×C13#55411yescharacteristic
510C22×C13#55411yescharacteristic
511C22×C13#55411yescharacteristic
512C22×C13#56011yescharacteristic
513C22×C13#56011yescharacteristic
514C22×C13#56011yescharacteristic
515C22×C13H(3,𝔽4)11yescharacteristic
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—81no—
521C4×C13—81no—
522Dic13—24no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—42no—
527Dic13—42no—
528Dic13—81no—
529Dic13—81no—
530C25C22×D1311yescharacteristic
531C23×C4—41no—
532C23×C4—41no—
533C23×C4—41no—
534C23×C4—41no—
535C23×C4—41no—
536C23×C4—41no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4C4×D1314yes—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C2×C4⋊C4—134no—
553C2×C4⋊C4—134no—
554C2×C4⋊C4—262no—
555C2×C4⋊C4—262no—
556C2×C4⋊C4—521no—
557C2×C4⋊C4—521no—
558C2×C4⋊C4—521no—
559C2×C4⋊C4—521no—
560C2×C4⋊C4—521no—
561C2×C4⋊C4—521no—
562C2×C4⋊C4—521no—
563C2×C4⋊C4—521no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—134no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—521no—
577C2×C22⋊C4—521no—
578C2×C22⋊C4—521no—
579C2×C22⋊C4—521no—
580C2×C22⋊C4—521no—
581C2×C22⋊C4—521no—
582C2×C42—262no—
583C2×C42—262no—
584C2×C42—262no—
585C2×C42—521no—
586C2×C42—521no—
587C2×C42—521no—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—134no—
593#95—134no—
594#95—262no—
595#95—262no—
596#95—262no—
597#95—521no—
598#95—521no—
599#95—521no—
600#95—521no—
601#95—521no—
602#95—521no—
603#95—521no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610C2×C13—44no—
611C2×C13#231911yescharacteristic
612C2×C13#232911yescharacteristic
613C2×C13#233511yescharacteristic
614C2×C13#234511yescharacteristic
615C2×C13#235311yescharacteristic
616C2×C13#236811yescharacteristic
617C2×C13#237511yescharacteristic
618C2×C13#274611yescharacteristic
619C2×C13#274811yescharacteristic
620C2×C13#274911yescharacteristic
621C2×C13#275311yescharacteristic
622C2×C13#275711yescharacteristic
623C2×C13#276311yescharacteristic
624C2×C13#278011yescharacteristic
625C2×C13#279011yescharacteristic
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24C2×C4×D1312yes—
639C24#612912yes—
640C24Q8×D1312yes—
641C24C23×D1311yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4C2×C4×D1312yes—
744C22×C4C2×C4×D1312yes—
745C22×C4#612712yes—
746C22×C4#612712yes—
747C4⋊C4—524no—
748C4⋊C4—524no—
749C4⋊C4—524no—
750C4⋊C4—524no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—268no—
754C22⋊C4—524no—
755C22⋊C4—524no—
756C22⋊C4—524no—
757C42—524no—
758C42—524no—
759C13#1445611yescharacteristic, complemented, Sylow
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23#8814114yes—
795C23C22×C4×D1311yescharacteristic
796C23C2×#612711yescharacteristic
797C23C2×#612711yescharacteristic
798C23C2×#612911yescharacteristic
799C23#8825111yescharacteristic
800C23#8825111yescharacteristic
801C23#8825111yescharacteristic
802C23#8825111yescharacteristic
803C23#8825111yescharacteristic
804C23#8825111yescharacteristic
805C23C2×Q8×D1311yescharacteristic
806C23#41×D1311yescharacteristic
807C23#41×D1311yescharacteristic
808C23#8825611yescharacteristic
809C23#8825711yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—416no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—134no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22C4×#612711yescharacteristic
925C22#1171919111yescharacteristic
926C22#1171919111yescharacteristic
927C22#1171919111yescharacteristic
928C22#1171920011yescharacteristic
929C22#1171920011yescharacteristic
930C22C2×#8814111yescharacteristic
931C22#1171921611yescharacteristic
932C22#1171921611yescharacteristic
933C22D13×#11711yescharacteristic
934C22#1171922811yescharacteristic
935C22#1171926111yescharacteristic
936C22#1171926111yescharacteristic
937C22#1171926311yescharacteristic
938C22#1171926311yescharacteristic
939C22#1171926511yescharacteristic
940C22#1171926611yescharacteristic
941C22#1171926711yescharacteristic
942C22#1171926911yescharacteristic
943C22#1171929911yescharacteristic
944C22#1171930011yescharacteristic
945C22#1171930011yescharacteristic
946C22#1171930011yescharacteristic
947C22#1171930611yescharacteristic
948C22#1171930611yescharacteristic
949C22#1171930711yescharacteristic
950C22#1171932211yescharacteristic
951C22#1171932811yescharacteristic
952C22#1171933911yescharacteristic
953C22#1171934111yescharacteristic
954C22#1171934111yescharacteristic
955C22#1171936711yescharacteristic
956C22#1171936711yescharacteristic
957C22#1171936811yescharacteristic
958C22#1171936811yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—81no—
964C4—81no—
965C4—264no—
966C4—522no—
967C4—522no—
968C4—522no—
969C4—522no—
970C4—522no—
971C4—1041no—
972C4—1041no—
973C2—44no—
974C2#1311747611yescharacteristic
975C2#1311756611yescharacteristic
976C2#1311762611yescharacteristic
977C2#1311770811yescharacteristic
978C2#1311777911yescharacteristic
979C2#1311791611yescharacteristic
980C2#1311797511yescharacteristic
981C2#1312201811yescharacteristic
982C2#1312204511yescharacteristic
983C2#1312205311yescharacteristic
984C2#1312210711yescharacteristic
985C2#1312216711yescharacteristic
986C2#1312224811yescharacteristic
987C2#1312248211yescharacteristic
988C2#1312260011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#14456
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #13113102C2semidirect
3. #13113096C2semidirect
4. #13113087C2semidirect
5. #13113087C2semidirect
10. #13113071C2semidirect
11. #13113064C2semidirect
12. #13113060C2semidirect
13. #13113060C2semidirect
33. #11718871C4semidirect
759. C13#14456semidirect

Maximal subgroups

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

subgroupindex
C2×#117188712
#131131022
#131130962
#131130872
#131130792
#131130732
#131130712
#131130642
#131130602
#131130592
C13×C22⋊#952
#1445613