Finite Group Databasebeta

← #15793221

Subgroups — #15793221

Order 3328.

1442 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
1#13113104C211yesmaximal, characteristic, complemented
2#13113104C211yesmaximal, characteristic, complemented
3#13113104C211yesmaximal, characteristic, complemented
4#13113089C211yesmaximal, characteristic, complemented
5#13113081C211yesmaximal, characteristic
6#13113073C211yesmaximal, characteristic
7#13113073C211yesmaximal, characteristic
8#13113070C211yesmaximal, characteristic, complemented
9#13113068C211yesmaximal, characteristic, complemented
10#13113068C211yesmaximal, characteristic, complemented
11#13113061C211yesmaximal, characteristic, complemented
12#13113058C211yesmaximal, characteristic
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C2×C13×#396C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C13×#396C418yescomplemented
30C2×C13×#95C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
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×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—22no—
60C23×Dic13—22no—
61C23×Dic13—22no—
62C23×Dic13—41no—
63C23×Dic13—41no—
64C23×Dic13—41no—
65C23×Dic13—41no—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C4⋊C4—41no—
80C2×C13×C4⋊C4C2×C414yescomplemented
81C2×C13×C4⋊C4C2×C414yescomplemented
82C2×C13×C4⋊C4C2×C414yescomplemented
83C2×C13×C22⋊C4—41no—
84C2×C13×C22⋊C4—41no—
85C2×C13×C22⋊C4—41no—
86C2×C13×C22⋊C4—41no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C13×C22⋊C4C2×C414yes—
91C2×C13×C22⋊C4C2×C414yes—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13—41no—
99C2×C22⋊Dic13—41no—
100C2×C22⋊Dic13Q814yes—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—41no—
103C2×C4⋊Dic13—41no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—41no—
106C2×C4×Dic13—41no—
107C2×C4×Dic13—41no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C13×#95C2×C414yescomplemented
111#88071—22no—
112#88071—22no—
113#88071—22no—
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#88071—41no—
131#88071—41no—
132#14591—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×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13C22×C412yes—
189C22×C4×C13C22×C412yes—
190C22×C4×C13C22×C412yes—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
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—44no—
242C22×Dic13—44no—
243C22×Dic13—44no—
244C22×Dic13—44no—
245C22×Dic13—44no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13C2×Q812yes—
249C22×Dic13C2×Q812yes—
250C22×Dic13#4112yes—
251C22×Dic13#4112yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C13×C4⋊C4—44no—
255C13×C4⋊C4—44no—
256C13×C4⋊C4—44no—
257C13×C22⋊C4—44no—
258C13×C22⋊C4—44no—
259C13×C22⋊C4—44no—
260C22⋊Dic13—44no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263C4⋊Dic13—44no—
264C4×Dic13—44no—
265C4×Dic13—44no—
266C2×#396D1311yescharacteristic
267#1445—131no—
268#1445—131no—
269#1445—131no—
270#1441—131no—
271#1439—131no—
272#1437—131no—
273#1437—131no—
274#1436—131no—
275#1436—131no—
276#1436—131no—
277#1434—131no—
278C22⋊#95—131no—
279C22⋊#95—131no—
280C22⋊#95—131no—
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—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
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×Dic13—22no—
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—416no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
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—41no—
430C24×C4—131no—
431C22×C4⋊C4—131no—
432C22×C4⋊C4C2×D1311yescharacteristic
433C22×C4⋊C4C2×D1311yescharacteristic
434C22×C4⋊C4C2×D1311yescharacteristic
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4C2×D1311yescharacteristic
439C22×C22⋊C4C2×D1311yescharacteristic
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C42—131no—
442C22×C42—131no—
443#396Dic1318yescomplemented
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×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
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×C4×Q811yescharacteristic
482C22×C13C4×#4111yescharacteristic
483C22×C13C4×#4111yescharacteristic
484C22×C13#51811yescharacteristic
485C22×C13#51811yescharacteristic
486C22×C13#51811yescharacteristic
487C22×C13#52011yescharacteristic
488C22×C13#53811yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53811yescharacteristic
492C22×C13#53811yescharacteristic
493C22×C13#53911yescharacteristic
494C22×C13#54011yescharacteristic
495C22×C13#54011yescharacteristic
496C22×C13#54011yescharacteristic
497C22×C13#54011yescharacteristic
498C22×C13#54311yescharacteristic
499C22×C13#54411yescharacteristic
500C22×C13#55111yescharacteristic
501C22×C13#55111yescharacteristic
502C22×C13#55111yescharacteristic
503C22×C13#55111yescharacteristic
504C22×C13#55111yescharacteristic
505C22×C13#55211yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55411yescharacteristic
508C22×C13#55411yescharacteristic
509C22×C13#55411yescharacteristic
510C22×C13#55411yescharacteristic
511C22×C13#55611yescharacteristic
512C22×C13#56011yescharacteristic
513C22×C13#56011yescharacteristic
514C22×C13#56211yescharacteristic
515C22×C13#56211yescharacteristic
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—42no—
521C4×C13—42no—
522Dic13—42no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—42no—
527Dic13—42no—
528Dic13—81no—
529Dic13—81no—
530C25C22×D1311yescharacteristic
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—262no—
540C23×C4—262no—
541C23×C4—262no—
542C23×C4—521no—
543C23×C4—521no—
544C23×C4—521no—
545C23×C4—521no—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—521no—
560C2×C4⋊C4—521no—
561C2×C4⋊C4C2×Dic1314yescomplemented
562C2×C4⋊C4C2×Dic1314yescomplemented
563C2×C4⋊C4C2×Dic1314yescomplemented
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—262no—
572C2×C22⋊C4—262no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—521no—
576C2×C22⋊C4—521no—
577C2×C22⋊C4—521no—
578C2×C22⋊C4—521no—
579C2×C22⋊C4C2×Dic1314yes—
580C2×C22⋊C4C2×Dic1314yes—
581C2×C22⋊C4C2×Dic1314yes—
582C2×C42—262no—
583C2×C42—521no—
584C2×C42—521no—
585C2×C42—521no—
586C2×C42—521no—
587C2×C42—521no—
588#95—262no—
589#95—262no—
590#95—262no—
591#95—262no—
592#95—262no—
593#95—262no—
594#95—521no—
595#95—521no—
596#95—521no—
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#95C2×Dic1314yescomplemented
610C2×C13—44no—
611C2×C13#232911yescharacteristic
612C2×C13#233311yescharacteristic
613C2×C13#233311yescharacteristic
614C2×C13#236811yescharacteristic
615C2×C13#236811yescharacteristic
616C2×C13#237311yescharacteristic
617C2×C13#237711yescharacteristic
618C2×C13#273511yescharacteristic
619C2×C13#274011yescharacteristic
620C2×C13#274311yescharacteristic
621C2×C13#274811yescharacteristic
622C2×C13#274911yescharacteristic
623C2×C13#276811yescharacteristic
624C2×C13#278011yescharacteristic
625C2×C13#278811yescharacteristic
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24Q8×D1312yes—
639C24#613112yes—
640C24C22×Dic1312yes—
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—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
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—524no—
735C22×C4—524no—
736C22×C4—524no—
737C22×C4—524no—
738C22×C4—524no—
739C22×C4—524no—
740C22×C4—524no—
741C22×C4C22×Dic1312yes—
742C22×C4C22×Dic1312yes—
743C22×C4C22×Dic1312yes—
744C22×C4C22×Dic1312yes—
745C22×C4C22×Dic1312yes—
746C22×C4C22×Dic1312yes—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—524no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—524no—
755C22⋊C4—524no—
756C22⋊C4—524no—
757C42—524no—
758C42—524no—
759C13#1459111yescharacteristic, 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—
794C23Q8×Dic1314yes—
795C23#8825111yescharacteristic
796C23#8825111yescharacteristic
797C23#8825111yescharacteristic
798C23#8825111yescharacteristic
799C23#8825111yescharacteristic
800C23#8825111yescharacteristic
801C23C2×Q8×D1311yescharacteristic
802C23C2×#613111yescharacteristic
803C23#41×D1311yescharacteristic
804C23#41×D1311yescharacteristic
805C23#41×D1311yescharacteristic
806C23#41×D1311yescharacteristic
807C23#8825611yescharacteristic
808C23#8825711yescharacteristic
809C23C23×Dic1311yescharacteristic
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—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
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—262no—
853C2×C4—262no—
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—5216no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
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—
924C22#1171931811yescharacteristic
925C22#1171931811yescharacteristic
926C22#1171931811yescharacteristic
927C22#1171931811yescharacteristic
928C22#1171932011yescharacteristic
929C22#1171932011yescharacteristic
930C22#1171932011yescharacteristic
931C22#1171932011yescharacteristic
932C22#1171932511yescharacteristic
933C22#1171932511yescharacteristic
934C22#1171932611yescharacteristic
935C22#1171932611yescharacteristic
936C22#1171932811yescharacteristic
937C22#1171933911yescharacteristic
938C22#1171934111yescharacteristic
939C22#1171934111yescharacteristic
940C22#1171934111yescharacteristic
941C22#1171934111yescharacteristic
942C22#1171934211yescharacteristic
943C22#1171934211yescharacteristic
944C22#1171934211yescharacteristic
945C22#1171934211yescharacteristic
946C22#1171934911yescharacteristic
947C22#1171935011yescharacteristic
948C22#1171940711yescharacteristic
949C22#1171941011yescharacteristic
950C22#1171941311yescharacteristic
951C22#1171941411yescharacteristic
952C22#1171950311yescharacteristic
953C22#1171950311yescharacteristic
954C22#1171950311yescharacteristic
955C22C2×Q8×Dic1311yescharacteristic
956C22#41×Dic1311yescharacteristic
957C22#41×Dic1311yescharacteristic
958C22#1171953211yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—522no—
966C4—522no—
967C4—522no—
968C4—522no—
969C4—522no—
970C4—522no—
971C4—1041no—
972C4—1041no—
973C2—44no—
974C2#1311757111yescharacteristic
975C2#1311760311yescharacteristic
976C2#1311760311yescharacteristic
977C2#1311792111yescharacteristic
978C2#1311792111yescharacteristic
979C2#1311796011yescharacteristic
980C2#1311799311yescharacteristic
981C2#1312187911yescharacteristic
982C2#1312194211yescharacteristic
983C2#1312198111yescharacteristic
984C2#1312204311yescharacteristic
985C2#1312206511yescharacteristic
986C2#1312232311yescharacteristic
987C2#1312249111yescharacteristic
988C2#1312257511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#396C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#396D13
hypocenterC13#14591
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #13113104C2semidirect
2. #13113104C2semidirect
3. #13113104C2semidirect
4. #13113089C2semidirect
8. #13113070C2semidirect
9. #13113068C2semidirect
10. #13113068C2semidirect
11. #13113061C2semidirect
29. C13×#396C4semidirect
80. C2×C13×C4⋊C4C2×C4semidirect
81. C2×C13×C4⋊C4C2×C4semidirect
82. C2×C13×C4⋊C4C2×C4semidirect
110. C13×#95C2×C4semidirect
443. #396Dic13semidirect
561. C2×C4⋊C4C2×Dic13semidirect
562. C2×C4⋊C4C2×Dic13semidirect
563. C2×C4⋊C4C2×Dic13semidirect
609. #95C2×Dic13semidirect
759. C13#14591semidirect

Maximal subgroups

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

subgroupindex
#131131042
#131130892
#131130812
#131130732
#131130702
#131130682
#131130612
#131130582
C2×C13×#3962
#1459113