Finite Group Databasebeta

← #16023416

Subgroups — #16023416

Order 3328.

2230 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719396C211yesmaximal, characteristic
2#13117962C212yesmaximal, complemented
3#13117950C212yesmaximal, complemented
4#13117946C211yesmaximal, characteristic, complemented
5#13117946C211yesmaximal, characteristic, complemented
6#13117942C211yesmaximal, characteristic, complemented
7#13117798C212yesmaximal, complemented
8#13117775C212yesmaximal, complemented
9#13117717C212yesmaximal, complemented
10#13117691C212yesmaximal, complemented
11#13117565C212yesmaximal, complemented
12#13117535C212yesmaximal
13#13117468C212yesmaximal, complemented
14C4×#88148C212yesmaximal, complemented
15#13117357C212yesmaximal, complemented
16#13117228C211yesmaximal, characteristic, complemented
17#13117196C212yesmaximal, complemented
18D13×#376C211yesmaximal, characteristic, complemented
19C13×#2371C211yesmaximal, characteristic, complemented
20C2×C13×#125C2211yescharacteristic
21#11719396C4116yescomplemented
22C2×#88152C2212yes—
23C2×#88151C2211yescharacteristic
24C2×#88149C2211yescharacteristic
25C2×#88148C2212yes—
26C2×#88147C2212yes—
27C2×#88147C2212yes—
28C2×#88147C2211yescharacteristic
29C2×#88146C2212yes—
30C2×#88141C2211yescharacteristic
31C2×#88129C2211yescharacteristic
32C2×C4×D52C2212yes—
33C2×C42×D13C2212yes—
34C2×C42×D13C2211yescharacteristic
35C13×#387C2212yes—
36C13×#387C2212yes—
37C13×#387C2212yes—
38C13×#387C2212yes—
39C4×C13×C4⋊C4C2212yes—
40C4×C13×C4⋊C4C2212yes—
41C13×#376C2211yescharacteristic
42C13×#376C2211yescharacteristic
43#11718651C2212yes—
44#11718650C2212yes—
45#11718650C2212yes—
46#11718648C2212yes—
47#11718642C2212yes—
48#11718642C2212yes—
49#11718642C2212yes—
50#11718642C2212yes—
51#11718639C2212yes—
52C4⋊C4×Dic13C2212yes—
53C4⋊C4×Dic13C2212yes—
54C4⋊C4×Dic13C2212yes—
55#11718634C2212yes—
56#11718601C2212yes—
57#11718601C2212yes—
58#11718601C2212yes—
59C4×#6103C2212yes—
60C4×#6103C2212yes—
61C4×#6103C2212yes—
62C4×#6103C2212yes—
63C4×#6103C2212yes—
64C4×#6103C2212yes—
65#11718593C2212yes—
66#11718593C2212yes—
67#11718593C2211yescharacteristic
68#11718593C2211yescharacteristic
69C4×#6101C2212yes—
70C4×#6101C2212yes—
71#11718589C2212yes—
72#11718331C2212yes—
73#11718330C2212yes—
74#11718330C2212yes—
75#11718330C2212yes—
76#11718329C2212yes—
77#11718329C2212yes—
78#11718328C2212yes—
79#11718327C2212yes—
80#11718327C2212yes—
81#11718327C2212yes—
82#11718327C2212yes—
83#11718326C2212yes—
84#11718326C2212yes—
85#11718326C2212yes—
86#11718326C2212yes—
87#11718325C2212yes—
88#11718325C2211yescharacteristic
89#11718325C2211yescharacteristic
90D13×#95C2211yescharacteristic
91D13×#95C2212yes—
92D13×#95C2211yescharacteristic
93D13×#95C2212yes—
94#11718316C2212yes—
95#11718315C2212yes—
96#11718314C2212yes—
97#11718312C2212yes—
98#11718312C2212yes—
99#11718311C2211yescharacteristic
100#11718311C2212yes—
101#11718311C2211yescharacteristic
102#11718310C2212yes—
103#11718309C2211yescharacteristic
104#11718309C2212yes—
105#11718309C2211yescharacteristic
106#11718307C2212yes—
107#11718307C2212yes—
108C22×D52C2312yes—
109C22×D52C2311yescharacteristic
110C22×C4×D13C2311yescharacteristic
111C22×C4×D13C2312yes—
112C22×C4×D13C2312yes—
113C22×C4×D13C2312yes—
114C22×C4×D13C2311yescharacteristic
115C22×C4×D13C2311yescharacteristic
116C22×C4×D13C2312yes—
117C22×C4×D13C2312yes—
118C22×Dic26C2311yescharacteristic
119C13×#125C2×C418yescomplemented
120C2×C13×C4⋊C4C2312yes—
121C2×C13×C4⋊C4C2312yes—
122C2×C13×C4⋊C4C2312yes—
123C2×C13×C4⋊C4C2312yes—
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C42×C13C2312yes—
127C2×C42×C13C2312yes—
128C2×C42×C13C2312yes—
129C2×C42×C13C2312yes—
130C2×C42×C13C2311yescharacteristic
131C2×#6103C2312yes—
132C2×#6103C2312yes—
133C2×#6103C2312yes—
134C2×#6103C2312yes—
135C2×#6103C2312yes—
136C2×#6103C2312yes—
137C2×#6103C2312yes—
138C2×#6103C2312yes—
139C2×#6103C2312yes—
140C2×#6103C2312yes—
141C2×#6103C2312yes—
142C2×#6103C2312yes—
143C2×#6103C2312yes—
144C2×C4⋊Dic13C2312yes—
145C2×C4⋊Dic13C2312yes—
146C2×C4⋊Dic13C2312yes—
147C2×#6101C2312yes—
148C2×#6101C2312yes—
149C2×#6101C2312yes—
150C2×#6101C2312yes—
151C2×#6101C2312yes—
152C2×C4×Dic13C2312yes—
153C2×C4×Dic13C2312yes—
154C2×C4×Dic13C2312yes—
155C2×C4×Dic13C2312yes—
156C2×C4×Dic13C2312yes—
157C2×C4×Dic13C2312yes—
158C2×C4×Dic13C2312yes—
159C2×C4×Dic13C2312yes—
160C2×C4×Dic13C2311yescharacteristic
161C2×C4×Dic13C2311yescharacteristic
162C2×C4×Dic13C2311yescharacteristic
163C2×C4×Dic13C2312yes—
164#88152C2×C4116yescomplemented
165#88151C2×C418yescomplemented
166#88149C2×C418yes—
167#88148C2×C4116yescomplemented
168#88147—28no—
169#88147C2×C418yescomplemented
170#88147C2×C4116yescomplemented
171#88146C2×C4116yescomplemented
172#88141C2×C418yescomplemented
173#88129C2×C418yescomplemented
174C4×D52—28no—
175C42×D13—28no—
176C42×D13C2×C418yescomplemented
177C13×#95C2311yescharacteristic
178C13×#95C2311yescharacteristic
179C13×#95C2312yes—
180C13×#95C2312yes—
181C13×#95C2312yes—
182C13×#95C2312yes—
183C13×#95C2312yes—
184C13×#95C2312yes—
185C13×#95C2311yescharacteristic
186C13×#95C2311yescharacteristic
187#88071C2312yes—
188#88071C2312yes—
189#88071C2312yes—
190#88071C2312yes—
191#88071C2312yes—
192#88071C2312yes—
193#88071C2312yes—
194#88071C2312yes—
195#88071C2312yes—
196#88071C2312yes—
197#88071C2311yescharacteristic
198#88071C2311yescharacteristic
199#88071C2312yes—
200#88071C2312yes—
201#88071C2312yes—
202#88071C2311yescharacteristic
203#88071C2311yescharacteristic
204#88071C2312yes—
205#88071C2312yes—
206#88071C2312yes—
207#88071C2312yes—
208#88071C2312yes—
209#34219—131nomaximal, Sylow
210C23×D13C2412yes—
211C23×D13C2411yescharacteristic
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2411yescharacteristic
216C22×C4×C13C2411yescharacteristic
217C22×C4×C13C2411yescharacteristic
218C22×C4×C13C2412yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C22×Dic13C2411yescharacteristic
225C22×Dic13C2411yescharacteristic
226C22×Dic13C2412yes—
227C22×Dic13C2411yescharacteristic
228C22×Dic13C2412yes—
229C2×D52—24no—
230C2×D52—24no—
231C2×D52—41no—
232C2×D52—41no—
233C2×D52C22×C418yes—
234C2×D52C22×C414yes—
235C2×C4×D13—24no—
236C2×C4×D13—24no—
237C2×C4×D13—24no—
238C2×C4×D13—24no—
239C2×C4×D13—41no—
240C2×C4×D13—41no—
241C2×C4×D13—42no—
242C2×C4×D13—42no—
243C2×C4×D13—42no—
244C2×C4×D13—42no—
245C2×C4×D13—42no—
246C2×C4×D13—42no—
247C2×C4×D13—42no—
248C2×C4×D13—42no—
249C2×C4×D13—42no—
250C2×C4×D13—42no—
251C2×C4×D13—42no—
252C2×C4×D13C22×C414yes—
253C2×C4×D13C22×C414yes—
254C2×C4×D13C22×C414yes—
255C2×C4×D13C22×C418yes—
256C2×C4×D13#4118yes—
257C2×Dic26—41no—
258C2×Dic26—41no—
259C2×Dic26C22×C414yes—
260C13×C4⋊C4—24no—
261C13×C4⋊C4—42no—
262C13×C4⋊C4C22×C414yes—
263C13×C4⋊C4C22×C418yes—
264C13×C4⋊C4C22×C414yes—
265C13×C4⋊C4C22×C418yes—
266C42×C13—24no—
267C42×C13—24no—
268C42×C13—42no—
269C42×C13—42no—
270C42×C13C22×C414yes—
271#6103—24no—
272#6103—24no—
273#6103—24no—
274#6103—24no—
275#6103—42no—
276#6103—42no—
277#6103—42no—
278#6103—42no—
279#6103C22×C418yes—
280#6103C22×C418yes—
281#6103C22×C418yes—
282#6103C22×C418yes—
283#6103C22×C418yes—
284C4⋊Dic13—24no—
285C4⋊Dic13—42no—
286C4⋊Dic13C22×C418yes—
287#6101—42no—
288#6101—42no—
289#6101—42no—
290#6101—42no—
291#6101C22×C418yes—
292C4×Dic13—24no—
293C4×Dic13—24no—
294C4×Dic13—24no—
295C4×Dic13—24no—
296C4×Dic13—42no—
297C4×Dic13—42no—
298C4×Dic13—42no—
299C4×Dic13—42no—
300C4×Dic13C22×C414yes—
301C4×Dic13C22×C414yes—
302C4×Dic13C22×C414yes—
303C4×Dic13C22×C418yes—
304C2×#529—131no—
305#2373—132no—
306#2373—132no—
307#2372—131no—
308#2372—131no—
309#2371—131no—
310#2371D1311yescharacteristic, complemented
311#2356—132no—
312#2353—132no—
313#2346—132no—
314#2343—132no—
315#2329—132no—
316#2325—132no—
317#2318—132no—
318C4×#123—132no—
319C4×#123—132no—
320#2283—131no—
321#2275—132no—
322C2×#376—131no—
323C23×C13C2511yescharacteristic
324C22×D13—21no—
325C22×D13—22no—
326C22×D13—21no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13C23×C414yes—
334C22×D13C23×C412yes—
335C22×D13C2×#4114yes—
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—21no—
345C2×C4×C13—21no—
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×C13C23×C414yes—
356C2×C4×C13C23×C412yes—
357C2×C4×C13C23×C412yes—
358C2×C4×C13C23×C412yes—
359C2×C4×C13C23×C414yes—
360C2×C4×C13C2×#4114yes—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—21no—
367C2×Dic13—21no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13C23×C412yes—
379C2×Dic13C23×C412yes—
380C2×Dic13C23×C412yes—
381C2×Dic13C23×C414yes—
382C2×Dic13C2×#4114yes—
383D52—216no—
384D52—44no—
385C4×D13—28no—
386C4×D13—44no—
387C4×D13—48no—
388C4×D13—44no—
389C4×D13—48no—
390C4×D13—48no—
391C4×D13—84no—
392C4×D13—84no—
393Dic26—44no—
394#529—1316no—
395C2×#126—132no—
396C2×#125C2×D1311yescharacteristic
397C2×#124—131no—
398C2×#123—132no—
399C2×C22⋊Q8—131no—
400C2×#121—131no—
401C2×C4×Q8—131no—
402C2×C4×D4—132no—
403C2×C4×D4—131no—
404C2×C4×D4—132no—
405C2×C4×D4—132no—
406C2×#117—132no—
407C22×C42—131no—
408C22×C42—132no—
409#391—132no—
410#391—132no—
411#389—132no—
412#389—132no—
413#388—132no—
414#388—132no—
415#388—132no—
416#388—132no—
417#388—132no—
418#388—132no—
419#388—132no—
420#388—132no—
421#387—132no—
422#387—132no—
423#387—132no—
424#387—132no—
425#387—132no—
426#387—132no—
427#387—132no—
428#387—132no—
429#387C2×D1312yes—
430#387C2×D1312yes—
431#387C2×D1312yes—
432#387C2×D1312yes—
433#386—132no—
434#386—132no—
435#386—132no—
436#386—132no—
437#385—132no—
438#385—132no—
439#385—132no—
440#385—132no—
441#383—132no—
442#383—132no—
443#382—132no—
444#382—131no—
445#382—131no—
446#381—132no—
447#381—131no—
448#381—131no—
449#380—132no—
450#380—132no—
451C4×C4⋊C4—132no—
452C4×C4⋊C4—132no—
453C4×C4⋊C4—132no—
454C4×C4⋊C4—132no—
455C4×C4⋊C4—132no—
456C4×C4⋊C4—132no—
457C4×C4⋊C4C2×D1312yes—
458C4×C4⋊C4C2×D1312yes—
459C4×C22⋊C4—132no—
460C4×C22⋊C4—132no—
461C4×C22⋊C4—132no—
462C4×C22⋊C4—132no—
463C4×C22⋊C4—132no—
464C4×C22⋊C4—132no—
465C4×C22⋊C4—132no—
466C4×C22⋊C4—132no—
467C4×C22⋊C4—132no—
468C4×C22⋊C4—132no—
469#376—132no—
470#376—132no—
471#376—131no—
472#376—131no—
473#376—132no—
474#376—131no—
475#376—131no—
476#376C2×D1311yescharacteristic
477#376C2×D1311yescharacteristic
478C2×#95—131no—
479C2×#95—132no—
480C2×#95—132no—
481C2×#95—131no—
482C22×C13C24×C411yescharacteristic
483C22×C13C22×#4112yes—
484C22×C13#58512yes—
485C22×C13#58511yescharacteristic
486C22×C13#58511yescharacteristic
487C2×D13—22no—
488C2×D13—22no—
489C2×D13—24no—
490C2×D13—24no—
491C2×D13—24no—
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13C4×#4114yes—
499C4×C13—22no—
500C4×C13—24no—
501C4×C13—22no—
502C4×C13—22no—
503C4×C13—24no—
504C4×C13—24no—
505C4×C13—42no—
506C4×C13—42no—
507C4×C13—42no—
508Dic13—22no—
509Dic13—24no—
510Dic13—22no—
511Dic13—22no—
512Dic13—24no—
513Dic13—42no—
514Dic13—42no—
515Dic13—42no—
516C22×Q8—131no—
517C22×D4—132no—
518C22×D4—131no—
519C23×C4—131no—
520C23×C4—132no—
521C23×C4—131no—
522C23×C4—132no—
523C23×C4—131no—
524C23×C4—132no—
525C23×C4—132no—
526C23×C4—132no—
527#126—1316no—
528#125C4×D1318yescomplemented
529#124—138no—
530#123—1316no—
531C22⋊Q8—138no—
532#121—138no—
533C4×Q8—138no—
534C4×D4—138no—
535C4×D4—1316no—
536C4×D4—268no—
537C4×D4—268no—
538#117—1316no—
539C2×C4⋊C4—132no—
540C2×C4⋊C4—132no—
541C2×C4⋊C4—132no—
542C2×C4⋊C4—132no—
543C2×C4⋊C4—132no—
544C2×C4⋊C4—132no—
545C2×C4⋊C4—132no—
546C2×C4⋊C4—132no—
547C2×C4⋊C4C22×D1312yes—
548C2×C4⋊C4C22×D1312yes—
549C2×C4⋊C4C22×D1312yes—
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1312yes—
552C2×C4⋊C4C22×D1311yescharacteristic
553C2×C22⋊C4—132no—
554C2×C22⋊C4—132no—
555C2×C22⋊C4—132no—
556C2×C22⋊C4—132no—
557C2×C22⋊C4—132no—
558C2×C22⋊C4—132no—
559C2×C22⋊C4—132no—
560C2×C22⋊C4—132no—
561C2×C22⋊C4—132no—
562C2×C22⋊C4—132no—
563C2×C22⋊C4—132no—
564C2×C22⋊C4—132no—
565C2×C22⋊C4—132no—
566C2×C42—131no—
567C2×C42—132no—
568C2×C42—131no—
569C2×C42—131no—
570C2×C42—138no—
571C2×C42—132no—
572C2×C42—132no—
573C2×C42—132no—
574C2×C42—132no—
575C2×C42—132no—
576C2×C42—132no—
577C2×C42—132no—
578C2×C42—132no—
579C2×C42—268no—
580C2×C42C22×D1312yes—
581C2×C42C22×D1312yes—
582C2×C42C22×D1312yes—
583C2×C42C22×D1312yes—
584C2×C42C22×D1311yescharacteristic
585#95—132no—
586#95—131no—
587#95—132no—
588#95—132no—
589#95—132no—
590#95—132no—
591#95—131no—
592#95—132no—
593#95—132no—
594#95—132no—
595#95—131no—
596#95—132no—
597#95—132no—
598#95—131no—
599#95—132no—
600#95—132no—
601#95—132no—
602#95—132no—
603#95—132no—
604#95—132no—
605#95—132no—
606#95—132no—
607#95C22×D1311yescharacteristic
608#95C22×D1312yes—
609#95C22×D1311yescharacteristic
610#95C22×D1312yes—
611#95C22×D1311yescharacteristic
612#95C22×D1311yescharacteristic
613#95C22×D1312yes—
614#95C22×D1312yes—
615#95C22×D1312yes—
616#95C22×D1312yes—
617C2×C13C2×C4×#4111yescharacteristic
618C2×C13#342811yescharacteristic
619C2×C13#342811yescharacteristic
620C2×C13#349112yes—
621C2×C13#349312yes—
622D13—24no—
623D13—44no—
624C24—131no—
625C24—132no—
626C2×Q8—134no—
627C2×Q8—521no—
628C2×Q8—521no—
629C2×D4—138no—
630C2×D4—134no—
631C2×D4—264no—
632C2×D4—264no—
633C2×D4—521no—
634C2×D4—521no—
635C22×C4—131no—
636C22×C4—132no—
637C22×C4—131no—
638C22×C4—132no—
639C22×C4—131no—
640C22×C4—134no—
641C22×C4—134no—
642C22×C4—134no—
643C22×C4—138no—
644C22×C4—138no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—264no—
649C22×C4—264no—
650C22×C4—264no—
651C22×C4—264no—
652C22×C4—522no—
653C22×C4—522no—
654C22×C4—522no—
655C22×C4—522no—
656C22×C4—522no—
657C22×C4—521no—
658C22×C4—521no—
659C22×C4—522no—
660C22×C4—522no—
661C22×C4—522no—
662C22×C4—522no—
663C22×C4—522no—
664C22×C4—522no—
665C22×C4C23×D1312yes—
666C22×C4C23×D1312yes—
667C22×C4C23×D1312yes—
668C22×C4C23×D1311yescharacteristic
669C22×C4C23×D1311yescharacteristic
670C22×C4C23×D1311yescharacteristic
671C22×C4C23×D1312yes—
672C22×C4C23×D1312yes—
673C22×C4C23×D1312yes—
674C4⋊C4—24no—
675C4⋊C4—42no—
676C4⋊C4—138no—
677C4⋊C4—138no—
678C4⋊C4—264no—
679C4⋊C4—522no—
680C4⋊C4—522no—
681C4⋊C4—522no—
682C4⋊C4—522no—
683C4⋊C4—522no—
684C4⋊C4C2×C4×D1318yes—
685C4⋊C4C2×C4×D1314yes—
686C4⋊C4C2×C4×D1318yes—
687C4⋊C4C2×C4×D1314yes—
688C22⋊C4—138no—
689C22⋊C4—138no—
690C22⋊C4—138no—
691C22⋊C4—138no—
692C22⋊C4—138no—
693C22⋊C4—264no—
694C22⋊C4—264no—
695C22⋊C4—264no—
696C22⋊C4—264no—
697C22⋊C4—522no—
698C22⋊C4—522no—
699C22⋊C4—522no—
700C22⋊C4—522no—
701C42—24no—
702C42—24no—
703C42—42no—
704C42—42no—
705C42—134no—
706C42—134no—
707C42—134no—
708C42—138no—
709C42—264no—
710C42—264no—
711C42—264no—
712C42—264no—
713C42—522no—
714C42—522no—
715C42—522no—
716C42—522no—
717C42C2×C4×D1314yes—
718C13#3421911yescharacteristic, complemented, Sylow
719C23—132no—
720C23—134no—
721C23—134no—
722C23—262no—
723C23—261no—
724C23—261no—
725C23—262no—
726C23—262no—
727C23—262no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23C24×D1311yescharacteristic
732Q8—524no—
733D4—2616no—
734D4—524no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—132no—
755C2×C4—132no—
756C2×C4—132no—
757C2×C4—134no—
758C2×C4—134no—
759C2×C4—268no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—261no—
766C2×C4—261no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—528no—
778C2×C4—524no—
779C2×C4—528no—
780C2×C4—524no—
781C2×C4—528no—
782C2×C4—1044no—
783C2×C4—1044no—
784C2×C4C22×C4×D1312yes—
785C2×C4C22×C4×D1312yes—
786C2×C4C22×C4×D1312yes—
787C2×C4C22×C4×D1314yes—
788C2×C4C22×C4×D1314yes—
789C2×C4#41×D1314yes—
790C22—134no—
791C22—264no—
792C22—262no—
793C22—262no—
794C22—264no—
795C22—264no—
796C22—264no—
797C22—264no—
798C22—522no—
799C22—522no—
800C22—522no—
801C22—522no—
802C22C23×C4×D1311yescharacteristic
803C22C2×#41×D1312yes—
804C22#1171964812yes—
805C22#1171965211yescharacteristic
806C22#1171965211yescharacteristic
807C4—22no—
808C4—24no—
809C4—24no—
810C4—22no—
811C4—24no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—262no—
817C4—264no—
818C4—262no—
819C4—262no—
820C4—264no—
821C4—522no—
822C4—522no—
823C4—522no—
824C2—264no—
825C2—524no—
826C2C4×#41×D1311yescharacteristic
827C2#1312803511yescharacteristic
828C2#1312803811yescharacteristic
829C2#1312853112yes—
830C2#1312855412yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2371C2
socle, cosocleC23×C13C25
prime radicalC2×#88149C22
hypercenter#2371D13
hypocenterC13#34219
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #13117962C2semidirect
3. #13117950C2semidirect
4. #13117946C2semidirect
5. #13117946C2semidirect
6. #13117942C2semidirect
7. #13117798C2semidirect
8. #13117775C2semidirect
9. #13117717C2semidirect
10. #13117691C2semidirect
11. #13117565C2semidirect
13. #13117468C2semidirect
14. C4×#88148C2semidirect
15. #13117357C2semidirect
16. #13117228C2semidirect
17. #13117196C2semidirect
18. D13×#376C2semidirect
19. C13×#2371C2semidirect
21. #11719396C4semidirect
119. C13×#125C2×C4semidirect
164. #88152C2×C4semidirect
165. #88151C2×C4semidirect
167. #88148C2×C4semidirect
169. #88147C2×C4semidirect
170. #88147C2×C4semidirect
171. #88146C2×C4semidirect
172. #88141C2×C4semidirect
173. #88129C2×C4semidirect
176. C42×D13C2×C4semidirect
310. #2371D13semidirect
528. #125C4×D13semidirect
718. C13#34219semidirect

Maximal subgroups

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

subgroupindex
C2×#117193962
#131179622
#131179502
#131179462
#131179422
#131177982
#131177752
#131177172
#131176912
#131175652
#131175352
#131174682
C4×#881482
#131173572
#131172282
#131171962
D13×#3762
C13×#23712
#3421913