Finite Group Databasebeta

← #15786929

Subgroups — #15786929

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×C4×#6103C211yesmaximal, characteristic
3#13113102C211yesmaximal, characteristic, complemented
4#13113095C211yesmaximal, characteristic, complemented
5#13113080C211yesmaximal, characteristic
6#13113078C211yesmaximal, characteristic
7#13113074C211yesmaximal, characteristic
8#13113074C211yesmaximal, characteristic
9#13113069C211yesmaximal, characteristic, complemented
10#13113069C211yesmaximal, characteristic, complemented
11#13113068C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113063C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C4×C13×C4⋊C4—24no—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
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
52#11718650C418yescomplemented
53C4×#6103—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—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4C2×C414yes—
82C2×C42×C13—22no—
83C2×C42×C13—22no—
84C2×C42×C13—22no—
85C2×C42×C13—22no—
86C2×C42×C13—41no—
87C2×C42×C13—41no—
88C2×C42×C13—41no—
89C2×C42×C13—41no—
90C2×C42×C13D414yes—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103—41no—
103C2×#6103—41no—
104C2×#6103—41no—
105C2×#6103—41no—
106C2×#6103C2×C414yes—
107C2×#6103C2×C414yes—
108C2×#6103Q814yes—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—41no—
112C2×#6101—41no—
113C2×#6101—41no—
114C2×#6101C2×C414yes—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13—41no—
118C13×#95—22no—
119C13×#95—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
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×C13C22×C412yes—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×Q812yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
200C22×C4×C13#4112yes—
201C22×C4×C13#4112yes—
202C22×C4×C13#4112yes—
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×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C412yes—
250C22×Dic13C22×C412yes—
251C22×Dic13C2×Q812yes—
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—28no—
261C13×C4⋊C4—28no—
262C42×C13—28no—
263C42×C13—44no—
264C42×C13—44no—
265#6103—28no—
266#6103—28no—
267#6103—28no—
268#6103—44no—
269#6103—44no—
270#6103—44no—
271#6101—44no—
272#6101—44no—
273C4×Dic13—44no—
274C2×#385—131no—
275C2×C4×C4⋊C4D1311yescharacteristic, complemented
276C2×C4×C22⋊C4—131no—
277#1445—131no—
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—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
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#11714yes—
386C2×C4×C13C4×D414yes—
387C2×C4×C13C22⋊Q814yes—
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—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—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C4×D13—416no—
438C24×C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4C2×D1311yescharacteristic
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×C42C2×D1311yescharacteristic
451C22×C42C2×D1311yescharacteristic
452C22×C42C2×D1311yescharacteristic
453#385—138no—
454C4×C4⋊C4—24no—
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×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
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—24no—
527C4×C13—24no—
528C4×C13—24no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—42no—
533Dic13—42no—
534Dic13—42no—
535Dic13—42no—
536Dic13—42no—
537Dic13—42no—
538Dic13—81no—
539Dic13—81no—
540C25—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—134no—
547C23×C4—131no—
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—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—521no—
571C2×C4⋊C4—521no—
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—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—41no—
597C2×C42—41no—
598C2×C42—41no—
599C2×C42—41no—
600C2×C42—262no—
601C2×C42—521no—
602C2×C42—521no—
603C2×C42C22⋊D1314yes—
604#95—22no—
605#95—22no—
606#95—134no—
607#95—134no—
608#95—262no—
609#95—262no—
610#95—262no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—521no—
618#95—521no—
619#95—521no—
620#95—521no—
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—132no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
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—268no—
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—524no—
743C22×C4—524no—
744C22×C4—524no—
745C22×C4—524no—
746C22×C4—524no—
747C22×C4—524no—
748C22×C4C2×C4×D1312yes—
749C22×C4C2×C4×D1312yes—
750C22×C4C2×C4×D1312yes—
751C22×C4#612712yes—
752C22×C4#612712yes—
753C22×C4#612712yes—
754C22×C4#612712yes—
755C22×C4#612712yes—
756C22×C4Q8×D1312yes—
757C22×C4#613112yes—
758C22×C4C2×C22⋊D1312yes—
759C22×C4C2×C22⋊D1312yes—
760C22×C4C2×C22⋊D1312yes—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—524no—
764C4⋊C4—524no—
765C22⋊C4—268no—
766C22⋊C4—268no—
767C22⋊C4—268no—
768C22⋊C4—524no—
769C22⋊C4—524no—
770C22⋊C4—524no—
771C42—28no—
772C42—44no—
773C42—44no—
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×#612711yescharacteristic
813C23C2×#612711yescharacteristic
814C23C2×#612711yescharacteristic
815C23C2×#612711yescharacteristic
816C23C2×#612711yescharacteristic
817C23#8825111yescharacteristic
818C23#8825111yescharacteristic
819C23C2×Q8×D1311yescharacteristic
820C23C2×#613111yescharacteristic
821C23#41×D1311yescharacteristic
822C23#41×D1311yescharacteristic
823C23#8825611yescharacteristic
824C23#8825611yescharacteristic
825C23C22×C22⋊D1311yescharacteristic
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—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
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—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
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—5216no—
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—
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#8812614yes—
923C2×C4C4×C22⋊D1314yes—
924C2×C4#8820014yes—
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—
940C22C2×#8812611yescharacteristic
941C22C4×#612711yescharacteristic
942C22#1171918411yescharacteristic
943C22#1171918411yescharacteristic
944C22#1171921611yescharacteristic
945C22#1171921611yescharacteristic
946C22#1171921911yescharacteristic
947C22#1171921911yescharacteristic
948C22#1171923211yescharacteristic
949C22#1171923211yescharacteristic
950C22#1171923511yescharacteristic
951C22#1171923511yescharacteristic
952C22#1171924511yescharacteristic
953C22#1171925011yescharacteristic
954C22#1171925011yescharacteristic
955C22#1171926111yescharacteristic
956C22#1171926311yescharacteristic
957C22#1171926411yescharacteristic
958C22#1171926511yescharacteristic
959C22#1171926511yescharacteristic
960C22C4×Q8×D1311yescharacteristic
961C22C4×#613111yescharacteristic
962C22#1171928311yescharacteristic
963C22#1171928411yescharacteristic
964C22#1171928411yescharacteristic
965C22#1171928511yescharacteristic
966C22#1171929011yescharacteristic
967C22#1171929011yescharacteristic
968C22C2×C4×C22⋊D1311yescharacteristic
969C22#1171949611yescharacteristic
970C22#1171949611yescharacteristic
971C22#1171950911yescharacteristic
972C22C2×#8820011yescharacteristic
973C22#1171953311yescharacteristic
974C22#1171953511yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—522no—
983C4—522no—
984C4—522no—
985C4—522no—
986C4—522no—
987C4—1041no—
988C4—1041no—
989C2—524no—
990C2#1311727911yescharacteristic
991C2C4×#8820011yescharacteristic
992C2#1311749011yescharacteristic
993C2#1311770911yescharacteristic
994C2#1311780511yescharacteristic
995C2#1311792011yescharacteristic
996C2#1311796511yescharacteristic
997C2#1312018311yescharacteristic
998C2#1312019411yescharacteristic
999C2#1312025711yescharacteristic
1000C2#1312028711yescharacteristic
1001C2#1312035711yescharacteristic
1002C2#1312038711yescharacteristic
1003C2#1312040211yescharacteristic
1004C2#1312041811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#14067
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13113102C2semidirect
4. #13113095C2semidirect
9. #13113069C2semidirect
10. #13113069C2semidirect
11. #13113068C2semidirect
12. #13113067C2semidirect
13. #13113063C2semidirect
15. C2×C4×C13×C4⋊C4C2semidirect
52. #11718650C4semidirect
275. C2×C4×C4⋊C4D13semidirect
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×C4×#61032
#131131022
#131130952
#131130802
#131130782
#131130742
#131130692
#131130682
#131130672
#131130632
#131130572
C2×C4×C13×C4⋊C42
#1406713