Finite Group Databasebeta

← #15785929

Subgroups — #15785929

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718315C211yesmaximal, characteristic, complemented
2C2×#11718329C211yesmaximal, characteristic
3C2×#11718328C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic, complemented
5C2×C4×#6103C211yesmaximal, characteristic
6#13113099C211yesmaximal, characteristic, complemented
7#13113088C211yesmaximal, characteristic, complemented
8#13113080C211yesmaximal, characteristic
9#13113078C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113072C211yesmaximal, characteristic
12#13113071C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113061C211yesmaximal, characteristic, complemented
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
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
51C4×#6103—24no—
52C4×#6101—24no—
53#11718329C418yescomplemented
54#11718328—24no—
55#11718315—24no—
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—41no—
80C2×C13×C4⋊C4—41no—
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C42×C13—41no—
84C2×#6103—22no—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—22no—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—41no—
96C2×#6103—41no—
97C2×#6103—41no—
98C2×#6103—41no—
99C2×#6103C2×C414yes—
100C2×#6103C2×C414yes—
101C2×#6103Q814yes—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13C2×C414yes—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—41no—
115C2×#6101—41no—
116C2×#6101C2×C414yes—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13—41no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—41no—
130C13×#95C2×C414yes—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071C2×C414yes—
142#88071D414yes—
143#88071D414yes—
144#13987—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C2×Q812yes—
160C23×D13#4112yes—
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×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×Q812yes—
207C22×C4×C13#4112yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
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×D412yes—
252C22×Dic13C2×D412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13C2×D412yes—
255C22×Dic13C2×Q812yes—
256C22×Dic13#4112yes—
257C22×Dic13#4112yes—
258C22×Dic13#4112yes—
259C2×C4×D13—28no—
260C2×C4×D13—28no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C13×C4⋊C4—44no—
267C42×C13—44no—
268#6103—28no—
269#6103—28no—
270#6103—28no—
271#6103—44no—
272#6103—44no—
273#6103—44no—
274C4⋊Dic13—28no—
275#6101—28no—
276#6101—28no—
277#6101—44no—
278#6101—44no—
279C4×Dic13—28no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#387—131no—
283C2×#385—131no—
284C2×#380—131no—
285C2×C4×C4⋊C4—131no—
286C2×C4×C22⋊C4—131no—
287#1444—131no—
288#1441—131no—
289#1439—131no—
290#1439—131no—
291#1437—131no—
292#1437—131no—
293#1436—131no—
294#1436—131no—
295#1436D1311yescharacteristic, complemented
296#1434—131no—
297C23×C13C23×C411yescharacteristic
298C23×C13C22×D411yescharacteristic
299C23×C13C22×D411yescharacteristic
300C23×C13C22×Q811yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13C2×#4111yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C13H(5,𝔽2)11yescharacteristic
310C23×C13H(5,𝔽2)11yescharacteristic
311C23×C132−1+411yescharacteristic
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—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
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×D13—41no—
339C22×D13—41no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13C4×Q814yes—
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—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×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13C4×D414yes—
395C2×C4×C13C22⋊Q814yes—
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—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
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—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13#11714yes—
444C2×Dic13C4×D414yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4—131no—
452C22×C4⋊C4C2×D1311yescharacteristic
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C42—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42C2×D1311yescharacteristic
463#387—264no—
464#385—138no—
465#380—264no—
466C4×C4⋊C4—264no—
467C4×C22⋊C4—264no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95C2×D1311yescharacteristic
482C2×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C2×#11711yescharacteristic
487C22×C13C2×C4×D411yescharacteristic
488C22×C13C2×C4×D411yescharacteristic
489C22×C13C2×C4×Q811yescharacteristic
490C22×C13C4×#4111yescharacteristic
491C22×C13#51811yescharacteristic
492C22×C13#52011yescharacteristic
493C22×C13C2×C22⋊Q811yescharacteristic
494C22×C13#52511yescharacteristic
495C22×C13#52511yescharacteristic
496C22×C13#52511yescharacteristic
497C22×C13#52911yescharacteristic
498C22×C13#52911yescharacteristic
499C22×C13#52911yescharacteristic
500C22×C13#53311yescharacteristic
501C22×C13#53811yescharacteristic
502C22×C13#53911yescharacteristic
503C22×C13#54011yescharacteristic
504C22×C13#54211yescharacteristic
505C22×C13D4211yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54611yescharacteristic
509C22×C13#54711yescharacteristic
510C22×C13D4×Q811yescharacteristic
511C22×C13#55011yescharacteristic
512C22×C13#55111yescharacteristic
513C22×C13#55211yescharacteristic
514C22×C13#55311yescharacteristic
515C22×C13#55311yescharacteristic
516C22×C13#55411yescharacteristic
517C22×C13#55411yescharacteristic
518C22×C13#55411yescharacteristic
519C22×C13#55511yescharacteristic
520C22×C13#55611yescharacteristic
521C2×D13—24no—
522C2×D13—24no—
523C2×D13—24no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C2×D13—42no—
531C2×D13—42no—
532C2×D13—42no—
533C2×D13—42no—
534C2×D13—42no—
535C2×D13—42no—
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—81no—
542C4×C13—81no—
543Dic13—24no—
544Dic13—24no—
545Dic13—42no—
546Dic13—42no—
547Dic13—42no—
548Dic13—42no—
549Dic13—42no—
550C25—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—134no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4—262no—
562C23×C4—262no—
563C23×C4—521no—
564C23×C4—521no—
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—134no—
576C2×C4⋊C4—134no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4—521no—
590C2×C22⋊C4—134no—
591C2×C22⋊C4—134no—
592C2×C22⋊C4—134no—
593C2×C22⋊C4—262no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—262no—
597C2×C22⋊C4—262no—
598C2×C22⋊C4—262no—
599C2×C22⋊C4—262no—
600C2×C22⋊C4—262no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—521no—
605C2×C22⋊C4—521no—
606C2×C22⋊C4—521no—
607C2×C22⋊C4—521no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—41no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—262no—
614C2×C42—262no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—262no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—134no—
625#95—134no—
626#95—134no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—521no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95C4×D1314yes—
638C2×C13#229011yescharacteristic
639C2×C13C4×C22⋊Q811yescharacteristic
640C2×C13#233511yescharacteristic
641C2×C13#234511yescharacteristic
642C2×C13#235411yescharacteristic
643C2×C13#235811yescharacteristic
644C2×C13#236011yescharacteristic
645C2×C13#244911yescharacteristic
646C2×C13#245411yescharacteristic
647C2×C13#245611yescharacteristic
648C2×C13#246511yescharacteristic
649C2×C13#246811yescharacteristic
650C2×C13#247611yescharacteristic
651C2×C13#257411yescharacteristic
652C2×C13#257711yescharacteristic
653D13—44no—
654C24—132no—
655C24—132no—
656C24—132no—
657C24—261no—
658C24—261no—
659C24—261no—
660C24—261no—
661C24—261no—
662C24—261no—
663C24—261no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
669C24C23×D1311yescharacteristic
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—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
719C22×C4—132no—
720C22×C4—132no—
721C22×C4—268no—
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—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—268no—
761C22×C4—524no—
762C22×C4—524no—
763C22×C4—524no—
764C22×C4—524no—
765C22×C4—524no—
766C22×C4C2×C4×D1312yes—
767C22×C4C2×C4×D1312yes—
768C22×C4C2×C4×D1312yes—
769C22×C4#612712yes—
770C22×C4#612712yes—
771C22×C4D4×D1312yes—
772C22×C4D4×D1312yes—
773C22×C4Q8×D1312yes—
774C22×C4#613112yes—
775C4⋊C4—44no—
776C4⋊C4—268no—
777C4⋊C4—268no—
778C4⋊C4—268no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C22⋊C4—268no—
782C22⋊C4—268no—
783C22⋊C4—268no—
784C22⋊C4—524no—
785C22⋊C4—524no—
786C22⋊C4—524no—
787C42—44no—
788C42—268no—
789C42—524no—
790C42—524no—
791C13#1398711yescharacteristic, complemented, Sylow
792C23—134no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—262no—
801C23—262no—
802C23—262no—
803C23—262no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23—521no—
816C23—521no—
817C23—521no—
818C23—521no—
819C23—521no—
820C23—521no—
821C23—521no—
822C23—521no—
823C23—521no—
824C23—521no—
825C23—521no—
826C23—521no—
827C23C22×C4×D1311yescharacteristic
828C23C2×#612711yescharacteristic
829C23C2×#612711yescharacteristic
830C23C2×D4×D1311yescharacteristic
831C23C2×D4×D1311yescharacteristic
832C23#8825111yescharacteristic
833C23#8825111yescharacteristic
834C23C2×Q8×D1311yescharacteristic
835C23C2×#613111yescharacteristic
836C23#41×D1311yescharacteristic
837C23#41×D1311yescharacteristic
838C23#41×D1311yescharacteristic
839C23#41×D1311yescharacteristic
840C23#8825611yescharacteristic
841C23#8825711yescharacteristic
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—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
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—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—134no—
890C2×C4—134no—
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—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—5216no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4#8814714yes—
940C2×C4#8815014yes—
941C22—264no—
942C22—264no—
943C22—264no—
944C22—522no—
945C22—522no—
946C22—522no—
947C22—522no—
948C22—522no—
949C22—522no—
950C22—522no—
951C22—522no—
952C22—522no—
953C22—522no—
954C22—522no—
955C22—522no—
956C22C4×#612711yescharacteristic
957C22#1171919911yescharacteristic
958C22C2×#8814711yescharacteristic
959C22C2×#8815011yescharacteristic
960C22D13×#11711yescharacteristic
961C22#1171923311yescharacteristic
962C22#1171923911yescharacteristic
963C22C4×D4×D1311yescharacteristic
964C22#1171925011yescharacteristic
965C22#1171925111yescharacteristic
966C22#1171925211yescharacteristic
967C22#1171925211yescharacteristic
968C22#1171925211yescharacteristic
969C22#1171926711yescharacteristic
970C22#1171926911yescharacteristic
971C22C4×Q8×D1311yescharacteristic
972C22#1171928311yescharacteristic
973C22#1171928511yescharacteristic
974C22#1171928511yescharacteristic
975C22#1171929511yescharacteristic
976C22#1171930411yescharacteristic
977C22#1171931711yescharacteristic
978C22#1171933511yescharacteristic
979C22#1171933711yescharacteristic
980C22#1171934111yescharacteristic
981C22#1171934211yescharacteristic
982C22#1171935911yescharacteristic
983C22#1171936011yescharacteristic
984C22#1171936611yescharacteristic
985C22#1171937511yescharacteristic
986C22#1171939511yescharacteristic
987C22#1171939911yescharacteristic
988C22#1171940711yescharacteristic
989C22#1171941411yescharacteristic
990C22#1171943511yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—81no—
997C4—81no—
998C4—264no—
999C4—264no—
1000C4—522no—
1001C4—522no—
1002C4—522no—
1003C4—522no—
1004C4—522no—
1005C2—524no—
1006C2#1311727711yescharacteristic
1007C2C4×#8815011yescharacteristic
1008C2#1311762811yescharacteristic
1009C2#1311771011yescharacteristic
1010C2#1311778211yescharacteristic
1011C2#1311781211yescharacteristic
1012C2#1311784011yescharacteristic
1013C2#1311864711yescharacteristic
1014C2#1311870911yescharacteristic
1015C2#1311873011yescharacteristic
1016C2#1311885911yescharacteristic
1017C2#1311890411yescharacteristic
1018C2#1311902411yescharacteristic
1019C2#1312011211yescharacteristic
1020C2#1312015711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1436D13
hypocenterC13#13987
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#11718315C2semidirect
4. C2×C4×#6101C2semidirect
6. #13113099C2semidirect
7. #13113088C2semidirect
12. #13113071C2semidirect
13. #13113067C2semidirect
14. #13113061C2semidirect
15. C13×#1436C2semidirect
53. #11718329C4semidirect
295. #1436D13semidirect
791. C13#13987semidirect

Maximal subgroups

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

subgroupindex
C2×#117183152
C2×#117183292
C2×#117183282
C2×C4×#61012
C2×C4×#61032
#131130992
#131130882
#131130802
#131130782
#131130722
#131130712
#131130672
#131130612
C13×#14362
#1398713