Finite Group Databasebeta

← #15786938

Subgroups — #15786938

Order 3328.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718650C211yesmaximal, characteristic
2C2×#11718310C211yesmaximal, characteristic, complemented
3C2×#11718327C211yesmaximal, characteristic
4#13113094C211yesmaximal, characteristic, complemented
5#13113080C211yesmaximal, characteristic
6#13113080C211yesmaximal, characteristic
7#13113072C211yesmaximal, characteristic
8#13113072C211yesmaximal, characteristic
9#13113071C211yesmaximal, characteristic, complemented
10#13113068C211yesmaximal, characteristic, complemented
11#13113067C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113060C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C13×#1445C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
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
51#11718650C418yescomplemented
52#11718327—24no—
53#11718310—24no—
54C24×D13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×C4×D13—22no—
70C22×C4×D13—22no—
71C22×C4×D13—41no—
72C22×C4×D13—41no—
73C22×C4×D13—41no—
74C22×C4×D13—41no—
75C22×C4×D13C2×C414yes—
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4C2×C414yes—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×#6103—22no—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103C2×C414yes—
95C2×#6103C2×C414yes—
96C2×#6103Q814yes—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—41no—
105C2×#6101C2×C414yes—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—41no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13—41no—
114C2×C4×Dic13—41no—
115C2×C4×Dic13—41no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13D414yes—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—41no—
121C13×#95—41no—
122C13×#95—41no—
123C13×#95—41no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071C2×C414yes—
137#88071C2×C414yes—
138#14067—131nomaximal, Sylow
139C24×C13C2411yescharacteristic
140C23×D13—21no—
141C23×D13—21no—
142C23×D13—21no—
143C23×D13—21no—
144C23×D13—21no—
145C23×D13—21no—
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13C22×C412yes—
153C23×D13C2×Q812yes—
154C23×D13#4112yes—
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—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×Q812yes—
203C22×C4×C13#4112yes—
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×Dic13C22×C412yes—
242C22×Dic13C22×C412yes—
243C22×Dic13C22×C412yes—
244C22×Dic13C2×D412yes—
245C22×Dic13C2×D412yes—
246C22×Dic13C2×Q812yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C22×Dic13#4112yes—
250C22×Dic13#4112yes—
251C22×Dic13#4112yes—
252C22×Dic13#4112yes—
253C2×C4×D13—28no—
254C2×C4×D13—44no—
255C2×C4×D13—44no—
256C2×C4×D13—44no—
257C2×C4×D13—44no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C13×C4⋊C4—44no—
261#6103—28no—
262#6103—28no—
263#6103—28no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267#6101—28no—
268#6101—28no—
269#6101—44no—
270C4×Dic13—28no—
271C4×Dic13—44no—
272C4×Dic13—44no—
273C4×Dic13—44no—
274C2×#385—131no—
275C2×C4×C4⋊C4—131no—
276C2×C4×C22⋊C4—131no—
277#1445D1311yescharacteristic, complemented
278#1442—131no—
279#1439—131no—
280#1439—131no—
281#1437—131no—
282#1437—131no—
283#1436—131no—
284#1436—131no—
285#1436—131no—
286#1436—131no—
287#1434—131no—
288C22⋊#95—131no—
289C23×C13C23×C411yescharacteristic
290C23×C13C22×D411yescharacteristic
291C23×C13C22×Q811yescharacteristic
292C23×C13C2×#4111yescharacteristic
293C23×C13C2×#4111yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
298C23×C13C2×#4111yescharacteristic
299C23×C13C2×#4111yescharacteristic
300C23×C13H(5,𝔽2)11yescharacteristic
301C23×C13H(5,𝔽2)11yescharacteristic
302C23×C13H(5,𝔽2)11yescharacteristic
303C23×C13H(5,𝔽2)11yescharacteristic
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13—41no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—41no—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13C4×Q814yes—
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—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
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×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
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—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13#11714yes—
435C2×Dic13C4×D414yes—
436C2×Dic13C22⋊Q814yes—
437C4×D13—416no—
438C24×C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4C2×D1311yescharacteristic
443C22×C22⋊C4—131no—
444C22×C22⋊C4—131no—
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C42—131no—
450C22×C42—131no—
451C22×C42—131no—
452C22×C42—131no—
453#385—138no—
454C4×C4⋊C4—264no—
455C4×C22⋊C4—264no—
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×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95C2×D1311yescharacteristic
471C2×#95C2×D1311yescharacteristic
472C2×#95C2×D1311yescharacteristic
473C2×#95C2×D1311yescharacteristic
474C2×#95C2×D1311yescharacteristic
475C2×#95C2×D1311yescharacteristic
476C22×C13C2×#11711yescharacteristic
477C22×C13C2×C4×D411yescharacteristic
478C22×C13C2×C4×Q811yescharacteristic
479C22×C13C4×#4111yescharacteristic
480C22×C13C4×#4111yescharacteristic
481C22×C13#51811yescharacteristic
482C22×C13#51811yescharacteristic
483C22×C13C2×C22⋊Q811yescharacteristic
484C22×C13#52511yescharacteristic
485C22×C13#52511yescharacteristic
486C22×C13#52511yescharacteristic
487C22×C13#52911yescharacteristic
488C22×C13#52911yescharacteristic
489C22×C13#52911yescharacteristic
490C22×C13#53311yescharacteristic
491C22×C13#53411yescharacteristic
492C22×C13#53511yescharacteristic
493C22×C13#53811yescharacteristic
494C22×C13#53811yescharacteristic
495C22×C13#55111yescharacteristic
496C22×C13#55111yescharacteristic
497C22×C13#55111yescharacteristic
498C22×C13#55311yescharacteristic
499C22×C13#55311yescharacteristic
500C22×C13#55311yescharacteristic
501C22×C13#55311yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55411yescharacteristic
505C22×C13#55411yescharacteristic
506C22×C13#55411yescharacteristic
507C22×C13#55411yescharacteristic
508C22×C13#55911yescharacteristic
509C22×C13#55911yescharacteristic
510C22×C13#55911yescharacteristic
511C2×D13—24no—
512C2×D13—24no—
513C2×D13—24no—
514C2×D13—42no—
515C2×D13—42no—
516C2×D13—42no—
517C2×D13—42no—
518C2×D13—42no—
519C2×D13—42no—
520C2×D13—42no—
521C2×D13—42no—
522C2×D13—42no—
523C2×D13—42no—
524C2×D13—42no—
525C2×D13—42no—
526C4×C13—42no—
527C4×C13—42no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—81no—
533Dic13—24no—
534Dic13—24no—
535Dic13—24no—
536Dic13—42no—
537Dic13—42no—
538Dic13—42no—
539Dic13—81no—
540C25—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—134no—
548C23×C4—131no—
549C23×C4—262no—
550C23×C4—262no—
551C23×C4—521no—
552C23×C4—521no—
553C23×C4—521no—
554C23×C4—521no—
555C23×C4C22×D1311yescharacteristic
556C23×C4C22×D1311yescharacteristic
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1311yescharacteristic
559C23×C4C22×D1311yescharacteristic
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—262no—
566C2×C4⋊C4—262no—
567C2×C4⋊C4—262no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—262no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—521no—
573C2×C4⋊C4C4×D1314yes—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—262no—
582C2×C22⋊C4—262no—
583C2×C22⋊C4—262no—
584C2×C22⋊C4—262no—
585C2×C22⋊C4—262no—
586C2×C22⋊C4—262no—
587C2×C22⋊C4—262no—
588C2×C22⋊C4—521no—
589C2×C22⋊C4—521no—
590C2×C22⋊C4—521no—
591C2×C22⋊C4—521no—
592C2×C42—134no—
593C2×C42—262no—
594C2×C42—262no—
595C2×C42—262no—
596C2×C42—262no—
597C2×C42—262no—
598C2×C42—521no—
599C2×C42—521no—
600C2×C42—521no—
601C2×C42—521no—
602C2×C42—521no—
603C2×C42—521no—
604#95—22no—
605#95—22no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—41no—
610#95—134no—
611#95—134no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—521no—
622#95—521no—
623#95—521no—
624C2×C13#229011yescharacteristic
625C2×C13C4×C22⋊Q811yescharacteristic
626C2×C13#232111yescharacteristic
627C2×C13#234511yescharacteristic
628C2×C13#235711yescharacteristic
629C2×C13#236811yescharacteristic
630C2×C13#237411yescharacteristic
631C2×C13#257911yescharacteristic
632C2×C13#258011yescharacteristic
633C2×C13#258711yescharacteristic
634C2×C13#258911yescharacteristic
635C2×C13#259511yescharacteristic
636C2×C13#259711yescharacteristic
637C2×C13#259811yescharacteristic
638C2×C13#260011yescharacteristic
639D13—44no—
640C24—132no—
641C24—132no—
642C24—132no—
643C24—261no—
644C24—261no—
645C24—261no—
646C24—261no—
647C24—261no—
648C24—261no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24—261no—
655C24C23×D1311yescharacteristic
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—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—268no—
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×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—524no—
750C22×C4—524no—
751C22×C4—524no—
752C22×C4—524no—
753C22×C4—524no—
754C22×C4—524no—
755C22×C4C2×C4×D1312yes—
756C22×C4C2×C4×D1312yes—
757C22×C4C2×C4×D1312yes—
758C22×C4D4×D1312yes—
759C22×C4Q8×D1312yes—
760C22×C4#613112yes—
761C4⋊C4—44no—
762C4⋊C4—268no—
763C4⋊C4—268no—
764C4⋊C4—524no—
765C22⋊C4—268no—
766C22⋊C4—268no—
767C22⋊C4—268no—
768C22⋊C4—524no—
769C22⋊C4—524no—
770C22⋊C4—524no—
771C42—268no—
772C42—524no—
773C42—524no—
774C42—524no—
775C13#1406711yescharacteristic, complemented, Sylow
776C23—134no—
777C23—262no—
778C23—262no—
779C23—262no—
780C23—262no—
781C23—262no—
782C23—262no—
783C23—262no—
784C23—262no—
785C23—262no—
786C23—262no—
787C23—262no—
788C23—262no—
789C23—262no—
790C23—262no—
791C23—262no—
792C23—262no—
793C23—262no—
794C23—262no—
795C23—521no—
796C23—521no—
797C23—521no—
798C23—521no—
799C23—521no—
800C23—521no—
801C23—521no—
802C23—521no—
803C23—521no—
804C23—521no—
805C23—521no—
806C23—521no—
807C23—521no—
808C23—521no—
809C23—521no—
810C23—521no—
811C23C22×C4×D1311yescharacteristic
812C23C2×D4×D1311yescharacteristic
813C23#8825111yescharacteristic
814C23#8825111yescharacteristic
815C23#8825111yescharacteristic
816C23C2×Q8×D1311yescharacteristic
817C23C2×#613111yescharacteristic
818C23#41×D1311yescharacteristic
819C23#41×D1311yescharacteristic
820C23#41×D1311yescharacteristic
821C23#41×D1311yescharacteristic
822C23#41×D1311yescharacteristic
823C23#41×D1311yescharacteristic
824C23#41×D1311yescharacteristic
825C23#8825611yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
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—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—134no—
876C2×C4—134no—
877C2×C4—134no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—5216no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C22—264no—
926C22—264no—
927C22—264no—
928C22—522no—
929C22—522no—
930C22—522no—
931C22—522no—
932C22—522no—
933C22—522no—
934C22—522no—
935C22—522no—
936C22—522no—
937C22—522no—
938C22—522no—
939C22—522no—
940C22#1171919111yescharacteristic
941C22D13×#11711yescharacteristic
942C22#1171922711yescharacteristic
943C22C4×D4×D1311yescharacteristic
944C22#1171925011yescharacteristic
945C22C4×Q8×D1311yescharacteristic
946C22C4×#613111yescharacteristic
947C22#1171931011yescharacteristic
948C22#1171931811yescharacteristic
949C22D13×C22⋊Q811yescharacteristic
950C22#1171933211yescharacteristic
951C22#1171934111yescharacteristic
952C22#1171934111yescharacteristic
953C22#1171934211yescharacteristic
954C22#1171934211yescharacteristic
955C22#1171936111yescharacteristic
956C22#1171936111yescharacteristic
957C22#1171936611yescharacteristic
958C22#1171936611yescharacteristic
959C22#1171936611yescharacteristic
960C22#1171936911yescharacteristic
961C22#1171936911yescharacteristic
962C22#1171936911yescharacteristic
963C22#1171938311yescharacteristic
964C22#1171938411yescharacteristic
965C22#1171939311yescharacteristic
966C22#1171939511yescharacteristic
967C22#1171939611yescharacteristic
968C22#1171940011yescharacteristic
969C22#1171941111yescharacteristic
970C22#1171941111yescharacteristic
971C22#1171941411yescharacteristic
972C22#1171941411yescharacteristic
973C22#1171942011yescharacteristic
974C22#1171943511yescharacteristic
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—81no—
982C4—264no—
983C4—264no—
984C4—264no—
985C4—522no—
986C4—522no—
987C4—522no—
988C4—1041no—
989C2—524no—
990C2#1311727411yescharacteristic
991C2#1311737011yescharacteristic
992C2#1311749511yescharacteristic
993C2#1311771011yescharacteristic
994C2#1311780411yescharacteristic
995C2#1311791511yescharacteristic
996C2#1311796811yescharacteristic
997C2#1312018411yescharacteristic
998C2#1312019111yescharacteristic
999C2#1312026011yescharacteristic
1000C2#1312029011yescharacteristic
1001C2#1312035211yescharacteristic
1002C2#1312038211yescharacteristic
1003C2#1312040311yescharacteristic
1004C2#1312042411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1445C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1445D13
hypocenterC13#14067
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#11718310C2semidirect
4. #13113094C2semidirect
9. #13113071C2semidirect
10. #13113068C2semidirect
11. #13113067C2semidirect
12. #13113067C2semidirect
13. #13113060C2semidirect
15. C13×#1445C2semidirect
51. #11718650C4semidirect
277. #1445D13semidirect
775. C13#14067semidirect

Maximal subgroups

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

subgroupindex
C2×#117186502
C2×#117183102
C2×#117183272
#131130942
#131130802
#131130722
#131130712
#131130682
#131130672
#131130602
#131130572
C13×#14452
#1406713