Finite Group Databasebeta

← #15860722

Subgroups — #15860722

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719279C211yesmaximal, characteristic
2C2×#11718464C211yesmaximal, characteristic
3C2×#11718465C211yesmaximal, characteristic
4C2×#11718369C211yesmaximal, characteristic, complemented
5#13117190C211yesmaximal, characteristic, complemented
6#13114668C211yesmaximal, characteristic, complemented
7#13114662C211yesmaximal, characteristic, complemented
8#13114660C211yesmaximal, characteristic, complemented
9#103×Dic13C211yesmaximal, characteristic, complemented
10C4×#88075C211yesmaximal, characteristic, complemented
11C4×#88049C211yesmaximal, characteristic, complemented
12#13114650C211yesmaximal, characteristic, complemented
13#13114554C211yesmaximal, characteristic, complemented
14D13×#340C211yesmaximal, characteristic, complemented
15C13×#1763C211yesmaximal, characteristic, complemented
16C22×#6131C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×#6094C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21#11719279—24no—
22#11719279C418yescomplemented
23C2×#88147—21no—
24C2×#88147C2211yescharacteristic
25C2×#88146C2211yescharacteristic
26C2×C4⋊C4×D13—21no—
27C2×C4⋊C4×D13C2211yescharacteristic
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×C4×D52—21no—
30C2×C4×D52C2211yescharacteristic
31C2×#88126—21no—
32C2×#88126C2211yescharacteristic
33C2×C13×#103C2211yescharacteristic
34C2×C13×#103C2211yescharacteristic
35C2×C13×#97C2211yescharacteristic
36C4×C13×C4⋊C4C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88061C2211yescharacteristic
40C2×#88061C2211yescharacteristic
41C2×#88055C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C4⋊C4×Dic13C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C4×#6103—21no—
48C4×C4⋊Dic13C2211yescharacteristic
49C4×#6101—21no—
50C2×C4×#1055C2211yescharacteristic
51#11718465C418yescomplemented
52#11718464C418yescomplemented
53#11718369—24no—
54#11718327—21no—
55#11718310—21no—
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63#11718121C2211yescharacteristic
64C22×Q8×C13C2311yescharacteristic
65C2×#6131—22no—
66C2×#6131—22no—
67C2×#6131—22no—
68C2×#6131C2×C414yes—
69C2×#6131C2×C414yes—
70C2×#6131C2×C414yes—
71C22×D52—21no—
72C22×D52C2311yescharacteristic
73C22×C4×D13—21no—
74C22×C4×D13—21no—
75C22×C4×D13—21no—
76C22×C4×D13—21no—
77C22×C4×D13—21no—
78C22×C4×D13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C4×Q8×C13—22no—
82C4×Q8×C13C2×C414yescomplemented
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C42×C13—21no—
88C2×C42×C13—21no—
89C2×C42×C13C2311yescharacteristic
90Q8×Dic13—22no—
91Q8×Dic13C2×C414yescomplemented
92C2×#6103—21no—
93C2×#6103—21no—
94C2×#6103—21no—
95C2×#6103D411yescharacteristic
96C2×#6103D411yescharacteristic
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×#6101—21no—
102C2×#6101—21no—
103C2×#6101D411yescharacteristic
104C2×#6101D411yescharacteristic
105C2×C4×Dic13—21no—
106C2×C4×Dic13—21no—
107C2×C4×Dic13—21no—
108C2×C4×Dic13—21no—
109C2×C4×Dic13—21no—
110C2×C4×Dic13C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C2×#6094—22no—
114C2×#6094—22no—
115C2×#6094C2×C414yescomplemented
116C2×C8×D13—22no—
117C2×C8×D13—22no—
118C2×C8×D13C2×C414yescomplemented
119#88147—28no—
120#88147—22no—
121#88147C2×C414yescomplemented
122#88146—22no—
123#88146C2×C414yescomplemented
124C4⋊C4×D13—22no—
125C4⋊C4×D13—22no—
126C4⋊C4×D13—28no—
127C4⋊C4×D13C2×C414yes—
128C4⋊C4×D13C2×C414yescomplemented
129C4×D52—22no—
130C4×D52—28no—
131C4×D52C2×C414yescomplemented
132#88126—28no—
133#88126C2×C414yes—
134#88126D414yes—
135C13×#103C2×C414yescomplemented
136C13×#103C2×C414yescomplemented
137C13×#97—22no—
138C13×#95—21no—
139#88075C2×C414yescomplemented
140#88075C2×C414yescomplemented
141#88071—21no—
142#88071—21no—
143#88071—21no—
144#88061C2×C414yescomplemented
145#88061C2×C414yescomplemented
146#88055—22no—
147C8×Dic13—22no—
148#88049C2×C414yescomplemented
149#88049C2×C414yescomplemented
150C4×#1055—22no—
151#20415—131nomaximal, Sylow
152C23×D13—21no—
153C23×D13C2×D411yescharacteristic
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13C22×C412yes—
158C2×Q8×C13C22×C412yes—
159C2×Q8×C13C22×C412yes—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2411yescharacteristic
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13C2×D411yescharacteristic
171C22×Dic13C2×D411yescharacteristic
172C22×Dic13C2×D411yescharacteristic
173#6131—28no—
174#6131—28no—
175#6131—28no—
176#6131C42116yescomplemented
177C2×D52—24no—
178C2×D52—24no—
179C2×D52—24no—
180C2×D52—21no—
181C2×D52—21no—
182C2×D52—21no—
183C2×D52C22×C412yes—
184C2×D52C22×C412yes—
185C2×D52C22×C412yes—
186C2×C4×D13—24no—
187C2×C4×D13—24no—
188C2×C4×D13—24no—
189C2×C4×D13—24no—
190C2×C4×D13—24no—
191C2×C4×D13—24no—
192C2×C4×D13—24no—
193C2×C4×D13—81no—
194C2×C4×D13—81no—
195C2×C4×D13—81no—
196C2×C4×D13—81no—
197C2×C4×D13—81no—
198C2×C4×D13—81no—
199C2×C4×D13—81no—
200C2×C4×D13—81no—
201C2×C4×D13C22×C412yes—
202C2×C4×D13C22×C412yes—
203C2×C4×D13C22×C412yes—
204C2×C4×D13C2×D412yes—
205C2×C4×D13#4112yes—
206C2×C4×D13#4112yes—
207C2×C8×C13—21no—
208C2×C8×C13—21no—
209C2×C8×C13—21no—
210C2×C8×C13—21no—
211C2×C8×C13C22×C412yes—
212C2×C8×C13C22×C412yes—
213C13×C4⋊C4—24no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4C22×C412yes—
218C13×C4⋊C4C22×C412yes—
219C13×C4⋊C4C22×C412yes—
220C42×C13—24no—
221C42×C13—81no—
222C42×C13C22×C412yes—
223C42×C13C2×D412yes—
224#6103—24no—
225#6103—24no—
226#6103—24no—
227#6103C22⋊C414yes—
228#6103C22⋊C414yes—
229C4⋊Dic13—21no—
230C4⋊Dic13—21no—
231C4⋊Dic13—21no—
232C4⋊Dic13—24no—
233C4⋊Dic13C22×C412yes—
234C4⋊Dic13C22×C412yes—
235C4⋊Dic13C22×C412yes—
236#6101—24no—
237#6101—24no—
238#6101C22⋊C414yes—
239#6101C22⋊C414yes—
240C4×Dic13—24no—
241C4×Dic13—24no—
242C4×Dic13—81no—
243C4×Dic13—81no—
244C4×Dic13—81no—
245C4×Dic13C22×C412yes—
246C4×Dic13C2×D412yes—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—21no—
251C2×#1055C22×C412yes—
252C2×#1055C22×C412yes—
253#6094—28no—
254C8×D13—28no—
255C2×#520—131no—
256C2×#417—131no—
257C2×#416—131no—
258C2×#405—131no—
259#2274—131no—
260#1763—131no—
261#1763D1311yescharacteristic, complemented
262#1762—131no—
263#1762—131no—
264C4×#103—131no—
265C4×#103—131no—
266C4×#102—131no—
267C4×#102—131no—
268#1736—131no—
269C2×#340—131no—
270C23×C13C22×D411yescharacteristic
271C22×D13—21no—
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—41no—
282C22×D13C2×C22⋊C412yes—
283C22×D13C4×D412yes—
284C22×D13C4×D412yes—
285Q8×C13—22no—
286Q8×C13—22no—
287Q8×C13—22no—
288Q8×C13C2×C4214yes—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13C2×C22⋊C412yes—
306C2×C4×C13C2×C22⋊C412yes—
307C2×C4×C13C23×C411yescharacteristic
308C2×C4×C13C23×C411yescharacteristic
309C2×C4×C13C23×C411yescharacteristic
310C2×C4×C13C22×D411yescharacteristic
311C2×C4×C13C2×#4111yescharacteristic
312C2×C4×C13C2×#4111yescharacteristic
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13C2×C22⋊C412yes—
327C2×Dic13C2×C22⋊C412yes—
328C2×Dic13C2×C22⋊C412yes—
329C2×Dic13C4×D412yes—
330C2×Dic13C4×D412yes—
331D52—216no—
332D52—22no—
333D52—22no—
334D52—22no—
335D52C2×C4214yes—
336C4×D13—216no—
337C4×D13—84no—
338C4×D13—84no—
339C4×D13—84no—
340C4×D13—84no—
341C4×D13C2×C4214yes—
342C4×D13#11714yes—
343C4×D13C4×D414yes—
344C4×D13C4×D414yes—
345C8×C13—22no—
346C8×C13—22no—
347#1055—22no—
348#1055—22no—
349C22×#41—131no—
350C22×M16—131no—
351C23×C8—131no—
352#520—138no—
353#520—264no—
354C2×C4×Q8—131no—
355C2×C4×Q8C2×D1311yescharacteristic
356C2×C4×D4—131no—
357C2×C4×D4—131no—
358C2×C4×D4—261no—
359C2×C4×D4—261no—
360C2×#117—131no—
361C2×#117—131no—
362C2×#117—261no—
363C22×C4⋊C4—131no—
364C22×C4⋊C4—131no—
365C22×C4⋊C4—261no—
366#417—138no—
367#416—138no—
368C2×#103—131no—
369C2×#103—131no—
370C2×#103C2×D1311yescharacteristic
371C2×#103C2×D1311yescharacteristic
372C2×#102—131no—
373C2×#102—131no—
374C2×#102—131no—
375C2×#102—131no—
376#405—264no—
377C2×#97—131no—
378C2×#97C2×D1311yescharacteristic
379C2×C4×C8—131no—
380C2×C4×C8—131no—
381C4×C4⋊C4—131no—
382C4×C4⋊C4—131no—
383C4×C4⋊C4—131no—
384C4×C4⋊C4—261no—
385C4×C4⋊C4—261no—
386C4×C4⋊C4C2×D1311yescharacteristic
387C4×C22⋊C4—261no—
388C4×C22⋊C4—261no—
389#340—131no—
390#340—131no—
391#340—131no—
392#340—131no—
393#340—131no—
394#340—131no—
395#340C2×D1311yescharacteristic
396#340C2×D1311yescharacteristic
397C22×C13C22×C22⋊C411yescharacteristic
398C22×C13C2×C4×D411yescharacteristic
399C22×C13C2×C4×D411yescharacteristic
400C22×C13#57611yescharacteristic
401C22×C13#57711yescharacteristic
402C22×C13#57711yescharacteristic
403C22×C13#57811yescharacteristic
404C2×D13—22no—
405C2×D13—22no—
406C2×D13—22no—
407C2×D13—22no—
408C2×D13—22no—
409C2×D13—22no—
410C2×D13—24no—
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13C4×C22⋊C414yes—
418C4×C13—22no—
419C4×C13—22no—
420C4×C13—24no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—42no—
424C4×C13C22×C4211yescharacteristic
425C4×C13C2×#11711yescharacteristic
426C4×C13C2×C4×D411yescharacteristic
427C4×C13C2×C4×D411yescharacteristic
428Dic13—22no—
429Dic13—22no—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13C4×C22⋊C414yes—
434C2×#41—134no—
435C2×#41—134no—
436C2×#41—134no—
437C2×#41—262no—
438C2×#41—262no—
439C2×#41—262no—
440C22×Q8C22×D1311yescharacteristic
441C22×D4—131no—
442C22×D4—261no—
443C23×C4—131no—
444C23×C4—261no—
445C23×C4—261no—
446C23×C4—261no—
447C23×C4—261no—
448C23×C4—261no—
449C2×M16—134no—
450C2×M16—262no—
451C2×M16—262no—
452C22×C8—131no—
453C22×C8—131no—
454C22×C8—134no—
455C22×C8—262no—
456C22×C8—262no—
457C22×C8C22×D1311yescharacteristic
458C22×C8C22×D1311yescharacteristic
459C4×Q8—22no—
460C4×Q8—134no—
461C4×Q8—262no—
462C4×Q8C4×D1314yescomplemented
463C4×D4—134no—
464C4×D4—134no—
465C4×D4—268no—
466C4×D4—262no—
467C4×D4—268no—
468C4×D4—262no—
469#117—134no—
470#117—134no—
471#117—134no—
472#117—268no—
473#117—262no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—131no—
476C2×C4⋊C4—131no—
477C2×C4⋊C4—131no—
478C2×C4⋊C4—131no—
479C2×C4⋊C4—131no—
480C2×C4⋊C4—134no—
481C2×C4⋊C4—134no—
482C2×C4⋊C4—268no—
483C2×C4⋊C4—262no—
484C2×C4⋊C4—262no—
485C2×C4⋊C4—261no—
486C2×C4⋊C4—261no—
487C2×C4⋊C4—261no—
488C2×C4⋊C4C22×D1311yescharacteristic
489C2×C4⋊C4C22×D1311yescharacteristic
490C2×C4⋊C4C22×D1311yescharacteristic
491C2×C22⋊C4—131no—
492C2×C22⋊C4—131no—
493C2×C22⋊C4—261no—
494C2×C22⋊C4—261no—
495C2×C22⋊C4—261no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—131no—
499C2×C42—261no—
500C2×C42—261no—
501C2×C42—261no—
502C2×C42—261no—
503C2×C42—261no—
504C2×C42C22×D1311yescharacteristic
505#103—134no—
506#103—134no—
507#103C4×D1314yescomplemented
508#103C4×D1314yescomplemented
509#102—134no—
510#102—134no—
511#102—134no—
512#102—134no—
513#97—22no—
514#97—262no—
515C4×C8—262no—
516C4×C8—262no—
517#95—21no—
518#95—261no—
519#95—261no—
520#95—261no—
521C2×C13C2×C4×C22⋊C411yescharacteristic
522C2×C13#289711yescharacteristic
523C2×C13#289811yescharacteristic
524C2×C13#294611yescharacteristic
525C2×C13#294711yescharacteristic
526C2×C13#295111yescharacteristic
527C2×C13#295211yescharacteristic
528D13—24no—
529D13—44no—
530C24—131no—
531C24—261no—
532#41—1316no—
533#41—268no—
534#41—268no—
535#41—268no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8C2×C4×D1312yes—
540C2×Q8C2×C4×D1312yes—
541C2×Q8C2×C4×D1312yes—
542C2×D4—132no—
543C2×D4—132no—
544C2×D4—132no—
545C2×D4—264no—
546C2×D4—264no—
547C2×D4—264no—
548C2×D4—261no—
549C2×D4—261no—
550C2×D4—261no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—131no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—131no—
563C22×C4—131no—
564C22×C4—264no—
565C22×C4—264no—
566C22×C4—264no—
567C22×C4—264no—
568C22×C4—264no—
569C22×C4—264no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—264no—
574C22×C4—1041no—
575C22×C4—1041no—
576C22×C4—1041no—
577C22×C4—1041no—
578C22×C4—1041no—
579C22×C4—1041no—
580C22×C4—1041no—
581C22×C4—1041no—
582C22×C4D4×D1311yescharacteristic
583C22×C4D4×D1311yescharacteristic
584C22×C4C23×D1311yescharacteristic
585M16—268no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—132no—
591C2×C8—132no—
592C2×C8—268no—
593C2×C8—261no—
594C2×C8—261no—
595C2×C8—261no—
596C2×C8—261no—
597C2×C8C2×C4×D1312yes—
598C2×C8C2×C4×D1312yes—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—134no—
604C4⋊C4—134no—
605C4⋊C4—132no—
606C4⋊C4—132no—
607C4⋊C4—132no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4—264no—
611C4⋊C4—261no—
612C4⋊C4—261no—
613C4⋊C4—261no—
614C4⋊C4C2×C4×D1312yes—
615C4⋊C4C2×C4×D1312yes—
616C4⋊C4C2×C4×D1312yes—
617C22⋊C4—134no—
618C22⋊C4—134no—
619C22⋊C4—264no—
620C22⋊C4—264no—
621C22⋊C4—264no—
622C42—24no—
623C42—81no—
624C42—132no—
625C42—132no—
626C42—264no—
627C42—264no—
628C42—1041no—
629C42—1041no—
630C42—1041no—
631C42C2×C4×D1312yes—
632C42D4×D1312yes—
633C13#2041511yescharacteristic, complemented, Sylow
634C23—132no—
635C23—132no—
636C23—132no—
637C23—261no—
638C23—261no—
639C23—261no—
640C23—261no—
641C23—262no—
642C23—262no—
643C23—262no—
644C23—521no—
645C23—521no—
646C23—521no—
647C23—521no—
648C23C2×D4×D1311yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8C42×D1314yes—
653D4—134no—
654D4—2616no—
655D4—262no—
656D4—262no—
657D4—262no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—132no—
675C2×C4—132no—
676C2×C4—132no—
677C2×C4—134no—
678C2×C4—134no—
679C2×C4—134no—
680C2×C4—134no—
681C2×C4—132no—
682C2×C4—132no—
683C2×C4—2616no—
684C2×C4—261no—
685C2×C4—261no—
686C2×C4—261no—
687C2×C4—261no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4—521no—
696C2×C4—521no—
697C2×C4—1044no—
698C2×C4—1044no—
699C2×C4—1044no—
700C2×C4—1044no—
701C2×C4C22⋊C4×D1312yes—
702C2×C4C22⋊C4×D1312yes—
703C2×C4C22×C4×D1311yescharacteristic
704C2×C4C22×C4×D1311yescharacteristic
705C2×C4C22×C4×D1311yescharacteristic
706C2×C4C2×D4×D1311yescharacteristic
707C2×C4#41×D1311yescharacteristic
708C2×C4#41×D1311yescharacteristic
709C8—22no—
710C8—22no—
711C8—262no—
712C8—262no—
713C22—134no—
714C22—262no—
715C22—262no—
716C22—262no—
717C22—262no—
718C22—262no—
719C22—262no—
720C22—264no—
721C22—522no—
722C22—522no—
723C22—522no—
724C22—522no—
725C22—522no—
726C22—522no—
727C22C2×C22⋊C4×D1311yescharacteristic
728C22C4×D4×D1311yescharacteristic
729C22C4×D4×D1311yescharacteristic
730C22#1171947911yescharacteristic
731C22#1171948311yescharacteristic
732C22#1171948311yescharacteristic
733C22#1171948411yescharacteristic
734C4—22no—
735C4—22no—
736C4—24no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—134no—
741C4—262no—
742C4—262no—
743C4—522no—
744C4—522no—
745C4—522no—
746C4C2×C42×D1311yescharacteristic
747C4D13×#11711yescharacteristic
748C4C4×D4×D1311yescharacteristic
749C4C4×D4×D1311yescharacteristic
750C2—264no—
751C2—524no—
752C2C4×C22⋊C4×D1311yescharacteristic
753C2#1312336011yescharacteristic
754C2#1312336811yescharacteristic
755C2#1312366711yescharacteristic
756C2#1312367811yescharacteristic
757C2#1312370811yescharacteristic
758C2#1312371611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1763C2
socleC23×C13C22×D4
prime radicalC22×#6131C22
cosocleC22×C4×C13C24
hypercenter#1763D13
hypocenterC13#20415
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
4. C2×#11718369C2semidirect
5. #13117190C2semidirect
6. #13114668C2semidirect
7. #13114662C2semidirect
8. #13114660C2semidirect
9. #103×Dic13C2semidirect
10. C4×#88075C2semidirect
11. C4×#88049C2semidirect
12. #13114650C2semidirect
13. #13114554C2semidirect
14. D13×#340C2semidirect
15. C13×#1763C2semidirect
22. #11719279C4semidirect
51. #11718465C4semidirect
52. #11718464C4semidirect
82. C4×Q8×C13C2×C4semidirect
91. Q8×Dic13C2×C4semidirect
115. C2×#6094C2×C4semidirect
118. C2×C8×D13C2×C4semidirect
121. #88147C2×C4semidirect
123. #88146C2×C4semidirect
128. C4⋊C4×D13C2×C4semidirect
131. C4×D52C2×C4semidirect
135. C13×#103C2×C4semidirect
136. C13×#103C2×C4semidirect
139. #88075C2×C4semidirect
140. #88075C2×C4semidirect
144. #88061C2×C4semidirect
145. #88061C2×C4semidirect
148. #88049C2×C4semidirect
149. #88049C2×C4semidirect
176. #6131C42semidirect
261. #1763D13semidirect
462. C4×Q8C4×D13semidirect
507. #103C4×D13semidirect
508. #103C4×D13semidirect
633. C13#20415semidirect

Maximal subgroups

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

subgroupindex
C2×#117192792
C2×#117184642
C2×#117184652
C2×#117183692
#131171902
#131146682
#131146622
#131146602
#103×Dic132
C4×#880752
C4×#880492
#131146502
#131145542
D13×#3402
C13×#17632
#2041513