Finite Group Databasebeta

← #15791399

Subgroups — #15791399

Order 3328.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718651C211yesmaximal, characteristic
2C2×#11718651C211yesmaximal, characteristic
3#13113097C211yesmaximal, characteristic, complemented
4#13113089C211yesmaximal, characteristic, complemented
5#13113084C211yesmaximal, characteristic
6#13113082C211yesmaximal, characteristic
7#13113080C211yesmaximal, characteristic
8#13113080C211yesmaximal, characteristic
9#13113074C211yesmaximal, characteristic
10#13113069C211yesmaximal, characteristic, complemented
11#13113067C211yesmaximal, characteristic, complemented
12#13113065C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113060C211yesmaximal, characteristic, complemented
15C2×C13×#387C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#387—24no—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
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#11718651—24no—
53#11718651C418yescomplemented
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
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4—41no—
73C2×C13×C4⋊C4C2×C414yes—
74C2×C13×C4⋊C4D414yes—
75C2×C42×C13—22no—
76C2×C42×C13—41no—
77C2×C42×C13—41no—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×#6103—22no—
85C2×#6103—22no—
86C2×#6103—41no—
87C2×#6103—41no—
88C2×#6103—41no—
89C2×#6103—41no—
90C2×#6103—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103C2×C414yes—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13—41no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13—41no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13C2×C414yes—
114C13×#95—22no—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
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#88071C2×C414yes—
133#88071C2×C414yes—
134#14447—131nomaximal, Sylow
135C24×C13C2411yescharacteristic
136C23×D13—21no—
137C23×D13—21no—
138C23×D13—21no—
139C23×D13—21no—
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×D13C22×C412yes—
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—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
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×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C13×C4⋊C4—28no—
250C13×C4⋊C4—44no—
251C42×C13—44no—
252#6103—28no—
253#6103—28no—
254#6103—44no—
255#6103—44no—
256#6103—44no—
257#6103—44no—
258#6103—44no—
259C4⋊Dic13—44no—
260#6101—44no—
261#6101—44no—
262C4×Dic13—44no—
263C4×Dic13—44no—
264C2×#388—131no—
265C2×#388—131no—
266C2×#387D1311yescharacteristic, complemented
267#1443—131no—
268#1441—131no—
269#1440—131no—
270#1439—131no—
271#1439—131no—
272#1439—131no—
273#1437—131no—
274#1436—131no—
275#1436—131no—
276C4⋊#95—131no—
277C4⋊#95—131no—
278#1434—131no—
279C23×C13C23×C411yescharacteristic
280C23×C13C22×D411yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13C2×#4111yescharacteristic
284C23×C13C2×#4111yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13H(5,𝔽2)11yescharacteristic
287C23×C13H(5,𝔽2)11yescharacteristic
288C23×C13H(5,𝔽2)11yescharacteristic
289C23×C13H(5,𝔽2)11yescharacteristic
290C23×C13H(5,𝔽2)11yescharacteristic
291C23×C132−1+411yescharacteristic
292C23×C132−1+411yescharacteristic
293C23×C132−1+411yescharacteristic
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—41no—
302C22×D13—41no—
303C22×D13—41no—
304C22×D13—41no—
305C22×D13—41no—
306C22×D13—41no—
307C22×D13—41no—
308C22×D13—41no—
309C22×D13—41no—
310C22×D13—41no—
311C22×D13—41no—
312C22×D13—41no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
316C22×D13—41no—
317C22×D13—41no—
318C22×D13—41no—
319C22×D13—41no—
320C22×D13—41no—
321C22×D13—41no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
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—22no—
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×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13C4×D414yes—
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—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#11714yes—
427C22×C4⋊C4—131no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4—131no—
430C22×C4⋊C4C2×D1311yescharacteristic
431C22×C4⋊C4C2×D1311yescharacteristic
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C42—131no—
440C22×C42—131no—
441C22×C42C2×D1311yescharacteristic
442#388—138no—
443#388—264no—
444#387—24no—
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×#95C2×D1311yescharacteristic
462C2×#95C2×D1311yescharacteristic
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C22×C13C2×#11711yescharacteristic
466C22×C13C2×C4×D411yescharacteristic
467C22×C13C4×#4111yescharacteristic
468C22×C13#51811yescharacteristic
469C22×C13#52011yescharacteristic
470C22×C13#52011yescharacteristic
471C22×C13#52011yescharacteristic
472C22×C13#53411yescharacteristic
473C22×C13#53711yescharacteristic
474C22×C13#53811yescharacteristic
475C22×C13#53811yescharacteristic
476C22×C13#53911yescharacteristic
477C22×C13#53911yescharacteristic
478C22×C13#54011yescharacteristic
479C22×C13#54111yescharacteristic
480C22×C13#54111yescharacteristic
481C22×C13#54211yescharacteristic
482C22×C13#54211yescharacteristic
483C22×C13#54211yescharacteristic
484C22×C13#54611yescharacteristic
485C22×C13#54711yescharacteristic
486C22×C13#54811yescharacteristic
487C22×C13#55011yescharacteristic
488C22×C13#55111yescharacteristic
489C22×C13#55111yescharacteristic
490C22×C13#55311yescharacteristic
491C22×C13#55311yescharacteristic
492C22×C13#55511yescharacteristic
493C22×C13#55611yescharacteristic
494C22×C13#55611yescharacteristic
495C22×C13#55911yescharacteristic
496C22×C13#56011yescharacteristic
497C22×C13#56211yescharacteristic
498C22×C13#56211yescharacteristic
499C22×C13#56311yescharacteristic
500C2×D13—42no—
501C2×D13—42no—
502C2×D13—42no—
503C2×D13—42no—
504C2×D13—42no—
505C2×D13—42no—
506C2×D13—42no—
507C2×D13—81no—
508C2×D13—81no—
509C2×D13—81no—
510C2×D13—81no—
511C2×D13—81no—
512C2×D13—81no—
513C2×D13—81no—
514C2×D13—81no—
515C4×C13—24no—
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—42no—
521C4×C13—81no—
522Dic13—24no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—81no—
527Dic13—81no—
528Dic13—81no—
529C25—131no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—262no—
549C2×C4⋊C4—262no—
550C2×C4⋊C4—262no—
551C2×C4⋊C4—262no—
552C2×C4⋊C4—262no—
553C2×C4⋊C4—521no—
554C2×C4⋊C4—521no—
555C2×C4⋊C4—521no—
556C2×C4⋊C4—521no—
557C2×C4⋊C4C4×D1314yes—
558C2×C4⋊C4C22⋊D1314yes—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—134no—
562C2×C22⋊C4—262no—
563C2×C22⋊C4—262no—
564C2×C22⋊C4—262no—
565C2×C22⋊C4—262no—
566C2×C22⋊C4—262no—
567C2×C22⋊C4—262no—
568C2×C22⋊C4—262no—
569C2×C22⋊C4—262no—
570C2×C22⋊C4—521no—
571C2×C22⋊C4—521no—
572C2×C22⋊C4—521no—
573C2×C22⋊C4—521no—
574C2×C22⋊C4—521no—
575C2×C22⋊C4—521no—
576C2×C22⋊C4—521no—
577C2×C22⋊C4—521no—
578C2×C22⋊C4—521no—
579C2×C22⋊C4—521no—
580C2×C42—22no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—134no—
584C2×C42—262no—
585C2×C42—262no—
586C2×C42—521no—
587C2×C42—521no—
588C2×C42—521no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—134no—
594#95—134no—
595#95—262no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
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—
609C2×C13#231411yescharacteristic
610C2×C13#232511yescharacteristic
611C2×C13#233411yescharacteristic
612C2×C13#235311yescharacteristic
613C2×C13#235411yescharacteristic
614C2×C13#236711yescharacteristic
615C2×C13#237611yescharacteristic
616C2×C13#270111yescharacteristic
617C2×C13#270511yescharacteristic
618C2×C13#272511yescharacteristic
619C2×C13#273011yescharacteristic
620C2×C13#275911yescharacteristic
621C2×C13#278311yescharacteristic
622C2×C13#279811yescharacteristic
623C2×C13#280311yescharacteristic
624D13—82no—
625C24—132no—
626C24—261no—
627C24—261no—
628C24—261no—
629C24—261no—
630C24—261no—
631C24—261no—
632C24—261no—
633C24—261no—
634C24—261no—
635C24—261no—
636C24—261no—
637C24—261no—
638C24—261no—
639C24—261no—
640C24C23×D1311yescharacteristic
641C22×C4—21no—
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—21no—
681C22×C4—21no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
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×C4C2×C4×D1312yes—
732C22×C4C2×C4×D1312yes—
733C22×C4C2×C4×D1312yes—
734C22×C4#612712yes—
735C22×C4#613112yes—
736C22×C4C2×C22⋊D1312yes—
737C22×C4C2×C22⋊D1312yes—
738C22×C4C2×C22⋊D1312yes—
739C4⋊C4—28no—
740C4⋊C4—44no—
741C4⋊C4—524no—
742C4⋊C4—524no—
743C4⋊C4—524no—
744C22⋊C4—268no—
745C22⋊C4—268no—
746C22⋊C4—524no—
747C22⋊C4—524no—
748C22⋊C4—524no—
749C22⋊C4—524no—
750C22⋊C4—524no—
751C42—44no—
752C42—524no—
753C42—524no—
754C13#1444711yescharacteristic, complemented, Sylow
755C23—262no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—521no—
763C23—521no—
764C23—521no—
765C23—521no—
766C23—521no—
767C23—521no—
768C23—521no—
769C23—521no—
770C23—521no—
771C23—521no—
772C23—521no—
773C23—521no—
774C23—521no—
775C23—521no—
776C23—521no—
777C23—521no—
778C23—521no—
779C23—521no—
780C23—521no—
781C23—521no—
782C23—521no—
783C23—521no—
784C23—521no—
785C23—521no—
786C23—521no—
787C23—521no—
788C23—521no—
789C23—521no—
790C23C22×C4×D1311yescharacteristic
791C23C2×#612711yescharacteristic
792C23#8825111yescharacteristic
793C23#8825111yescharacteristic
794C23C2×#613111yescharacteristic
795C23#8825411yescharacteristic
796C23#41×D1311yescharacteristic
797C23#41×D1311yescharacteristic
798C23#41×D1311yescharacteristic
799C23#8825611yescharacteristic
800C23#8825611yescharacteristic
801C23#8825611yescharacteristic
802C23#8825711yescharacteristic
803C23#8825711yescharacteristic
804C23C22×C22⋊D1311yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
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—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—521no—
870C2×C4—521no—
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×C4C4×C22⋊D1314yes—
903C22—522no—
904C22—522no—
905C22—522no—
906C22—522no—
907C22—522no—
908C22—522no—
909C22—522no—
910C22—1041no—
911C22—1041no—
912C22—1041no—
913C22—1041no—
914C22—1041no—
915C22—1041no—
916C22—1041no—
917C22—1041no—
918C22D13×#11711yescharacteristic
919C22#1171922811yescharacteristic
920C22#1171923711yescharacteristic
921C22#1171923811yescharacteristic
922C22#1171925011yescharacteristic
923C22#1171925111yescharacteristic
924C22#1171926511yescharacteristic
925C22#1171926911yescharacteristic
926C22#1171927311yescharacteristic
927C22C4×#613111yescharacteristic
928C22#1171927911yescharacteristic
929C22#1171929011yescharacteristic
930C22#1171934211yescharacteristic
931C22#1171934511yescharacteristic
932C22#1171934911yescharacteristic
933C22#1171935211yescharacteristic
934C22#1171936611yescharacteristic
935C22#1171936711yescharacteristic
936C22#1171936811yescharacteristic
937C22#1171937211yescharacteristic
938C22#1171940011yescharacteristic
939C22#1171940111yescharacteristic
940C22#1171940211yescharacteristic
941C22#1171940411yescharacteristic
942C22#1171941011yescharacteristic
943C22#1171941211yescharacteristic
944C22#1171941511yescharacteristic
945C22#1171941611yescharacteristic
946C22C2×C4×C22⋊D1311yescharacteristic
947C22#1171950911yescharacteristic
948C22#1171952211yescharacteristic
949C22#1171952911yescharacteristic
950C22#1171953411yescharacteristic
951C22#1171953811yescharacteristic
952C22#1171953911yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—81no—
960C4—264no—
961C4—522no—
962C4—522no—
963C4—522no—
964C4—1041no—
965C4—1041no—
966C4—1041no—
967C2—1042no—
968C2#1311744211yescharacteristic
969C2#1311753411yescharacteristic
970C2#1311761411yescharacteristic
971C2#1311777511yescharacteristic
972C2#1311778611yescharacteristic
973C2#1311790311yescharacteristic
974C2#1311798311yescharacteristic
975C2#1312144311yescharacteristic
976C2#1312150311yescharacteristic
977C2#1312177211yescharacteristic
978C2#1312182711yescharacteristic
979C2#1312220011yescharacteristic
980C2#1312252011yescharacteristic
981C2#1312270911yescharacteristic
982C2#1312277311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#387C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#387D13
hypocenterC13#14447
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #13113097C2semidirect
4. #13113089C2semidirect
10. #13113069C2semidirect
11. #13113067C2semidirect
12. #13113065C2semidirect
13. #13113064C2semidirect
14. #13113060C2semidirect
15. C2×C13×#387C2semidirect
53. #11718651C4semidirect
266. C2×#387D13semidirect
754. C13#14447semidirect

Maximal subgroups

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

subgroupindex
C2×#117186512
#131130972
#131130892
#131130842
#131130822
#131130802
#131130742
#131130692
#131130672
#131130652
#131130642
#131130602
C2×C13×#3872
#1444713