Finite Group Databasebeta

← #16727907

Subgroups — #16727907

Order 3328.

1748 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#533C211yesmaximal, characteristic
2#13123936C212yesmaximal, complemented
3#13123934C212yesmaximal, complemented
4#13123929C214yesmaximal, complemented
5#13123922C214yesmaximal, complemented
6#13123918C212yesmaximal, complemented
7#13123915C212yesmaximal, complemented
8#13123785C211yesmaximal, characteristic, complemented
9#13123783C211yesmaximal, characteristic, complemented
10#13123779C211yesmaximal, characteristic, complemented
11#13123769C212yesmaximal, complemented
12#13123768C212yesmaximal, complemented
13#13123493C212yesmaximal
14#13123491C212yesmaximal
15#13123467C211yesmaximal, characteristic
16C2×#11718494C211yesmaximal, characteristic
17C13×#2962C211yesmaximal, characteristic, complemented
18C13×#533C2211yescharacteristic
19#11719433C411yescharacteristic
20#11719433C411yescharacteristic
21D13×C4⋊Q8C411yescharacteristic
22D13×C4⋊Q8C411yescharacteristic
23#11719393C412yes—
24D13×#125C412yes—
25D13×C22⋊Q8C412yes—
26D13×C22⋊Q8C412yes—
27#11719327C412yes—
28#11719327C412yes—
29#11719283C2212yes—
30#11719283C2212yes—
31C4×Q8×D13C2212yes—
32C4×Q8×D13C2212yes—
33D13×#117C2212yes—
34#11719222C2212yes—
35C2×C42×D13C2211yescharacteristic
36#11719175C2211yescharacteristic
37C13×#446C2212yescomplemented
38C13×#446C2214yescomplemented
39C8×Q8×C13C2212yescomplemented
40C13×#424C2212yes—
41C2×C13×C4⋊C8C2211yescharacteristic
42C13×#405C2212yes—
43C4×C13×M16C2211yescharacteristic
44#11718787C2211yescharacteristic
45#11718787C2211yescharacteristic
46#11718783C2212yes—
47#11718780C2212yes—
48#11718779C2211yescharacteristic
49#11718779C2211yescharacteristic
50C2×#88060C2212yes—
51#11718763C2212yes—
52#11718762C2212yes—
53C2×C8×Dic13C2212yes—
54#11718685C2212yescomplemented
55#11718685C2214yescomplemented
56Q8×#1055C2212yescomplemented
57#11718660C2212yes—
58#11718658C2212yes—
59C2×C4⋊#1055C2211yescharacteristic
60C4×#6099C2211yescharacteristic
61#11718501C2214yes—
62#11718501C2214yes—
63#11718496C2214yes—
64#11718494C2211yescharacteristic
65#11718494C2214yes—
66#11718494C2211yescharacteristic
67#11718494C2212yes—
68#11718494C2212yes—
69#11718494C2211yescharacteristic
70#11718494C2211yescharacteristic
71#11718492C2212yescomplemented
72#11718491C2214yescomplemented
73#11718491C2212yescomplemented
74#11718491C2214yescomplemented
75#11718489C2214yescomplemented
76#11718489C2214yescomplemented
77#11718489C2214yescomplemented
78#11718370C2214yes—
79#11718366C2214yes—
80#11718366C2212yes—
81#11718366C2212yes—
82#11718362C2214yescomplemented
83#11718362C2214yescomplemented
84#11718362C2214yescomplemented
85#11718351C2214yes—
86#11718346C2212yes—
87#11718346C2214yes—
88#11718346C2212yes—
89#11718340C2212yescomplemented
90C8×Dic26C2214yescomplemented
91C8×Dic26C2212yescomplemented
92C8×Dic26C2214yescomplemented
93C2×Q8×D13C2×C412yes—
94C2×Q8×D13C2×C412yes—
95C22×C4×D13C2×C411yescharacteristic
96C22×C4×D13C2×C411yescharacteristic
97C22×C4×D13C2311yescharacteristic
98C2×C13×M16C2311yescharacteristic
99C2×C13×M16C2311yescharacteristic
100C22×C8×C13C2312yes—
101C13×C4⋊Q8C2×C411yescharacteristic
102C13×C4⋊Q8C2×C411yescharacteristic
103C13×#125C2×C412yes—
104C13×C22⋊Q8C2×C412yes—
105C13×C22⋊Q8C2×C412yes—
106C4×Q8×C13C2312yes—
107C4×Q8×C13C2312yes—
108C13×#117C2312yes—
109C2×C42×C13C2311yescharacteristic
110#88200C2×C412yes—
111#88200C2×C412yes—
112Q8×Dic13C2×C412yes—
113Q8×Dic13C2×C412yes—
114#88198C2×C412yes—
115#88198C2×C412yes—
116#88180C2312yes—
117#88178C2×C412yes—
118#88178C2×C412yes—
119C2×C4×Dic13C2×C411yescharacteristic
120C2×C4×Dic13C2×C411yescharacteristic
121C2×C4×Dic13C2311yescharacteristic
122C2×#6099C2311yescharacteristic
123C2×#6099C2311yescharacteristic
124C22×#1055C2312yes—
125#88151C2×C412yes—
126#88151C2×C412yes—
127#88150C2×C414yes—
128#88150C2×C414yes—
129#88146C2×C412yes—
130#88146C2×C412yes—
131C4⋊C4×D13C2×C412yes—
132C4⋊C4×D13C2×C412yes—
133C4⋊C4×D13C2×C412yes—
134C4⋊C4×D13C2×C412yes—
135C4⋊C4×D13C2×C414yes—
136C4⋊C4×D13C2×C414yes—
137#88144C2×C412yes—
138#88144C2×C412yes—
139#88143C2×C414yes—
140#88143C2×C414yes—
141#88142C2×C412yes—
142#88142C2×C412yes—
143#88142C2×C412yes—
144#88142C2×C412yes—
145#88141C2×C412yes—
146#88141C2×C412yes—
147#88141C2×C414yes—
148#88141C2×C414yes—
149C22⋊C4×D13C2×C414yes—
150#88132C2×C414yes—
151#88132C2×C414yes—
152#88131C2×C414yes—
153#88126C2314yes—
154C42×D13C2×C411yescharacteristic
155C42×D13C2×C411yescharacteristic
156C42×D13C2×C411yescharacteristic
157C42×D13C2×C411yescharacteristic
158C42×D13C2311yescharacteristic
159C42×D13C2311yescharacteristic
160C42×D13C2311yescharacteristic
161C42×D13C2311yescharacteristic
162C42×D13C2314yes—
163#88124C2×C412yes—
164#88123C2×C411yescharacteristic
165#88123C2×C411yescharacteristic
166C4×Dic26C2312yes—
167C4×Dic26C2312yes—
168C4×Dic26C2314yes—
169C4×Dic26C2314yes—
170C13×C4⋊C8C2311yescharacteristic
171C13×C4⋊C8C2312yes—
172C13×C4⋊C8C2311yescharacteristic
173C13×C4⋊C8C2314yes—
174C13×C4⋊C8C2314yes—
175C13×#97C2312yes—
176C13×#97C2314yes—
177C4×C8×C13C2312yes—
178C4×C8×C13C2314yes—
179#88060C2312yes—
180#88060C2312yes—
181#88060C2312yes—
182#88060C2312yes—
183#88060C2312yes—
184#88060C2312yes—
185#88060C2312yes—
186#88060C2312yes—
187#88055C2314yes—
188#88055C2314yes—
189#88054C2314yes—
190#88054C2312yes—
191#88054C2312yes—
192#88054C2314yes—
193#88054C2312yes—
194#88054C2312yes—
195#88054C2314yes—
196#88054C2314yes—
197C8×Dic13C2312yes—
198C8×Dic13C2312yes—
199C8×Dic13C2314yes—
200C8×Dic13C2312yes—
201C8×Dic13C2312yes—
202C8×Dic13C2314yes—
203C4⋊#1055C2314yes—
204C4⋊#1055C2314yes—
205C4⋊#1055C2311yescharacteristic
206C4⋊#1055C2311yescharacteristic
207C4⋊#1055C2312yes—
208#88043C2314yes—
209#88043C2312yes—
210C4×#1055C2314yes—
211C4×#1055C2312yes—
212#60250—131nomaximal, Sylow
213C23×D13C22×C411yescharacteristic
214C2×Q8×C13C22×C412yes—
215C2×Q8×C13C22×C412yes—
216C22×C4×C13C22×C411yescharacteristic
217C22×C4×C13C22×C411yescharacteristic
218C22×C4×C13C2411yescharacteristic
219C22×Dic13C22×C411yescharacteristic
220C22×Dic13C22×C411yescharacteristic
221C22×Dic13C22×C411yescharacteristic
222Q8×D13—28no—
223Q8×D13—44no—
224C2×C4×D13—22no—
225C2×C4×D13—22no—
226C2×C4×D13—24no—
227C2×C4×D13—42no—
228C2×C4×D13C22×C411yescharacteristic
229C2×C4×D13C22×C411yescharacteristic
230C2×C4×D13C22×C411yescharacteristic
231C2×C4×D13C22×C411yescharacteristic
232C2×C4×D13C22×C411yescharacteristic
233C2×C4×D13C22×C411yescharacteristic
234C2×C4×D13C22×C411yescharacteristic
235C2×C4×D13C22×C414yes—
236C2×C4×D13C22×C411yescharacteristic
237C2×C4×D13C22×C411yescharacteristic
238C2×C4×D13C22×C414yes—
239C2×C4×D13C22×C411yescharacteristic
240C2×C4×D13C2411yescharacteristic
241C2×C4×D13C2411yescharacteristic
242C2×Dic26C22×C412yes—
243C2×Dic26C22×C414yes—
244C2×Dic26C22×C414yes—
245C2×Dic26C22×C412yes—
246C13×M16—22no—
247C13×M16—22no—
248C2×C8×C13—24no—
249C2×C8×C13C2412yes—
250C2×C8×C13C2412yes—
251C2×C8×C13C2412yes—
252C2×C8×C13C2412yes—
253C13×C4⋊C4C22×C412yes—
254C13×C4⋊C4C22×C412yes—
255C13×C4⋊C4C22×C414yes—
256C13×C4⋊C4C22×C414yes—
257C13×C4⋊C4C22×C412yes—
258C13×C4⋊C4C22×C412yes—
259C13×C22⋊C4C22×C414yes—
260C42×C13C22×C411yescharacteristic
261C42×C13C22×C411yescharacteristic
262C42×C13C2411yescharacteristic
263C42×C13C2414yes—
264C42×C13C2411yescharacteristic
265C22⋊Dic13C22×C414yes—
266#6103C22×C414yes—
267#6103C22×C414yes—
268C4⋊Dic13C22×C412yes—
269C4⋊Dic13C22×C412yes—
270C4⋊Dic13C22×C414yes—
271C4⋊Dic13C22×C414yes—
272C4⋊Dic13C22×C412yes—
273C4⋊Dic13C22×C412yes—
274#6101C22×C414yes—
275#6101C22×C414yes—
276#6101C22×C414yes—
277#6101C22×C414yes—
278#6101C22×C414yes—
279#6101C22×C414yes—
280#6101C22×C414yes—
281#6101C22×C414yes—
282C4×Dic13C22×C411yescharacteristic
283C4×Dic13C22×C411yescharacteristic
284C4×Dic13C22×C411yescharacteristic
285C4×Dic13C22×C411yescharacteristic
286C4×Dic13C22×C411yescharacteristic
287C4×Dic13C22×C411yescharacteristic
288C4×Dic13C22×C411yescharacteristic
289C4×Dic13C22×C411yescharacteristic
290C4×Dic13C22×C411yescharacteristic
291C4×Dic13C22×C411yescharacteristic
292C4×Dic13C22×C414yes—
293C4×Dic13C22×C414yes—
294C4×Dic13C2411yescharacteristic
295C4×Dic13C2411yescharacteristic
296C4×Dic13C2414yes—
297#6099—22no—
298#6099—22no—
299C2×#1055—24no—
300C2×#1055C2412yes—
301C2×#1055C2412yes—
302C2×#1055C2412yes—
303C2×#1055C2412yes—
304C2×#533—131no—
305#2986—132no—
306#2986—132no—
307#2985—134no—
308#2984—134no—
309#2983—132no—
310#2982—132no—
311#2962—131no—
312#2962—131no—
313#2962—131no—
314#2962D1311yescharacteristic, complemented
315#2960—132no—
316#2960—132no—
317#2924—132no—
318#2924—132no—
319#2920—131no—
320C2×#431—131no—
321C23×C13C23×C411yescharacteristic
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—41no—
325C22×D13C23×C411yescharacteristic
326C22×D13C23×C411yescharacteristic
327Q8×C13—24no—
328Q8×C13—42no—
329C2×C4×C13—22no—
330C2×C4×C13—41no—
331C2×C4×C13C23×C411yescharacteristic
332C2×C4×C13C23×C411yescharacteristic
333C2×C4×C13C23×C411yescharacteristic
334C2×C4×C13C23×C414yes—
335C2×C4×C13C23×C414yes—
336C2×C4×C13C23×C411yescharacteristic
337C2×C4×C13C23×C411yescharacteristic
338C2×C4×C132−1+412yes—
339C2×C4×C132−1+412yes—
340C2×C4×C13C2511yescharacteristic
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13C23×C411yescharacteristic
345C2×Dic13C23×C411yescharacteristic
346C2×Dic13C23×C411yescharacteristic
347C2×Dic13C23×C411yescharacteristic
348C2×Dic13C23×C414yes—
349C2×Dic13C23×C414yes—
350C2×Dic13C23×C411yescharacteristic
351C2×Dic13C23×C411yescharacteristic
352C4×D13—22no—
353C4×D13—28no—
354C4×D13—22no—
355C4×D13—22no—
356C4×D13—22no—
357C4×D13—21no—
358C4×D13—21no—
359C4×D13—21no—
360C4×D13—21no—
361C4×D13—22no—
362C4×D13—22no—
363C4×D13—22no—
364C4×D13—41no—
365C4×D13—41no—
366C4×D13—44no—
367C4×D13#13114yes—
368Dic26—24no—
369Dic26—28no—
370Dic26—28no—
371Dic26—42no—
372C8×C13—22no—
373C8×C13—22no—
374C8×C13—22no—
375C8×C13—22no—
376#1055—22no—
377#1055—22no—
378#1055—22no—
379#1055—22no—
380#533—131no—
381#533—131no—
382#533—132no—
383#533—132no—
384#533—132no—
385#533—132no—
386#533—132no—
387#533—132no—
388#533—131no—
389#533C2×D1311yescharacteristic
390C2×C4⋊Q8—131no—
391C2×C4⋊Q8—131no—
392C2×#125—132no—
393C2×C22⋊Q8—132no—
394C2×C22⋊Q8—132no—
395C2×C4×Q8—132no—
396C2×C4×Q8—132no—
397C2×#117—132no—
398C22×C42—131no—
399#446—132no—
400#446—134no—
401#446—134no—
402#446—134no—
403#446—134no—
404#446—132no—
405#446—134no—
406#446—134no—
407#446—134no—
408#446—132no—
409#446C2×D1312yescomplemented
410#446C2×D1314yescomplemented
411C8×Q8—132no—
412C8×Q8—134no—
413C8×Q8—134no—
414C8×Q8—132no—
415C8×Q8—134no—
416C8×Q8—134no—
417C8×Q8—132no—
418C8×Q8C2×D1312yescomplemented
419#433—134no—
420#433—134no—
421#433—134no—
422#433—134no—
423#432—134no—
424#432—132no—
425#432—132no—
426#432—134no—
427#431—131no—
428#431—131no—
429#431—132no—
430#431—132no—
431#431—131no—
432#431—131no—
433#431—134no—
434#431—132no—
435#431—132no—
436#431—134no—
437#424—132no—
438#424—132no—
439#424—132no—
440#424C2×D1312yes—
441#423—131no—
442#423—131no—
443C2×C4⋊C8—131no—
444C2×C4⋊C8C2×D1311yescharacteristic
445#407—131no—
446#407—131no—
447C2×C22⋊C8—132no—
448#405—132no—
449#405—132no—
450#405—132no—
451#405C2×D1312yes—
452C4×M16—131no—
453C4×M16C2×D1311yescharacteristic
454C2×C4×C8—132no—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13#51912yes—
458C22×C13C24×C411yescharacteristic
459C2×D13—21no—
460C2×D13—21no—
461C2×D13—21no—
462C2×D13—21no—
463C2×D13—21no—
464C2×D13—44no—
465C2×D13C2×#13112yes—
466C4×C13—24no—
467C4×C13—21no—
468C4×C13—24no—
469C4×C13—21no—
470C4×C13—21no—
471C4×C13#51912yes—
472C4×C13C2×#13112yes—
473C4×C13C2×2−1+411yescharacteristic
474C4×C13C2×2−1+411yescharacteristic
475Dic13—21no—
476Dic13—21no—
477Dic13—24no—
478Dic13—21no—
479Dic13—24no—
480Dic13—21no—
481Dic13C2×#13112yes—
482Dic13#56812yes—
483C22×Q8—132no—
484C22×Q8—132no—
485C23×C4—131no—
486C23×C4—131no—
487C23×C4—131no—
488C2×M16—131no—
489C2×M16—131no—
490C2×M16C22×D1311yescharacteristic
491C2×M16C22×D1311yescharacteristic
492C22×C8—132no—
493C22×C8C22×D1312yes—
494C4⋊Q8—132no—
495C4⋊Q8—132no—
496C4⋊Q8—132no—
497C4⋊Q8—132no—
498C4⋊Q8—132no—
499C4⋊Q8—132no—
500C4⋊Q8—131no—
501C4⋊Q8—131no—
502C4⋊Q8C4×D1311yescharacteristic
503C4⋊Q8C4×D1311yescharacteristic
504#125—134no—
505#125—134no—
506#125—132no—
507#125—132no—
508#125—132no—
509#125C4×D1312yes—
510C22⋊Q8—132no—
511C22⋊Q8—132no—
512C22⋊Q8—132no—
513C22⋊Q8—132no—
514C22⋊Q8—134no—
515C22⋊Q8—134no—
516C22⋊Q8—132no—
517C22⋊Q8—132no—
518C22⋊Q8—134no—
519C22⋊Q8—134no—
520C22⋊Q8C4×D1312yes—
521C22⋊Q8C4×D1312yes—
522C4×Q8—132no—
523C4×Q8—132no—
524C4×Q8—132no—
525C4×Q8—132no—
526C4×Q8—134no—
527C4×Q8—134no—
528C4×Q8—134no—
529C4×Q8—134no—
530C4×Q8—132no—
531C4×Q8—132no—
532C4×Q8C22×D1312yes—
533C4×Q8C22×D1312yes—
534#117—132no—
535#117—132no—
536#117—132no—
537#117—134no—
538#117—134no—
539#117C22×D1312yes—
540C2×C4⋊C4—132no—
541C2×C4⋊C4—132no—
542C2×C4⋊C4—134no—
543C2×C4⋊C4—134no—
544C2×C4⋊C4—132no—
545C2×C4⋊C4—132no—
546C2×C22⋊C4—134no—
547C2×C42—131no—
548C2×C42—131no—
549C2×C42—131no—
550C2×C42—131no—
551C2×C42—131no—
552C2×C42—131no—
553C2×C42—131no—
554C2×C42—134no—
555C2×C42—131no—
556C2×C42—131no—
557C2×C42—131no—
558C2×C42—131no—
559C2×C42C22×D1311yescharacteristic
560C4⋊C8—132no—
561C4⋊C8—132no—
562C4⋊C8—132no—
563C4⋊C8—132no—
564C4⋊C8—134no—
565C4⋊C8—134no—
566C4⋊C8—134no—
567C4⋊C8—134no—
568C4⋊C8—131no—
569C4⋊C8—131no—
570C4⋊C8—132no—
571C4⋊C8—134no—
572C4⋊C8—134no—
573C4⋊C8C22×D1311yescharacteristic
574C4⋊C8C22×D1311yescharacteristic
575C4⋊C8C22×D1312yes—
576C4⋊C8C22×D1314yes—
577C4⋊C8C22×D1314yes—
578C22⋊C8—132no—
579C22⋊C8—132no—
580C22⋊C8—132no—
581C22⋊C8—132no—
582C22⋊C8—132no—
583C22⋊C8—132no—
584C22⋊C8—132no—
585C22⋊C8—132no—
586#97—134no—
587#97—134no—
588#97—132no—
589#97—134no—
590#97C22×D1312yes—
591#97C22×D1314yes—
592C4×C8—132no—
593C4×C8—132no—
594C4×C8—132no—
595C4×C8—132no—
596C4×C8—134no—
597C4×C8—134no—
598C4×C8—132no—
599C4×C8—134no—
600C4×C8C22×D1312yes—
601C4×C8C22×D1314yes—
602C2×C13—22no—
603C2×C13C2×#51911yescharacteristic
604C2×C13C22×#13111yescharacteristic
605C2×C13C2×#56811yescharacteristic
606D13—22no—
607D13—41no—
608C24—131no—
609C2×Q8—134no—
610C2×Q8—134no—
611C2×Q8—132no—
612C2×Q8—132no—
613C2×Q8—268no—
614C2×Q8—524no—
615C2×Q8C2×C4×D1312yes—
616C2×Q8C2×C4×D1312yes—
617C22×C4—131no—
618C22×C4—131no—
619C22×C4—131no—
620C22×C4—131no—
621C22×C4—131no—
622C22×C4—131no—
623C22×C4—131no—
624C22×C4—131no—
625C22×C4—131no—
626C22×C4—131no—
627C22×C4—131no—
628C22×C4—134no—
629C22×C4—131no—
630C22×C4—131no—
631C22×C4—131no—
632C22×C4—131no—
633C22×C4—134no—
634C22×C4—264no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—522no—
638C22×C4C2×C4×D1311yescharacteristic
639C22×C4C2×C4×D1311yescharacteristic
640C22×C4C23×D1311yescharacteristic
641M16—22no—
642M16—22no—
643M16—262no—
644M16—262no—
645C2×C8—24no—
646C2×C8—132no—
647C2×C8—132no—
648C2×C8—132no—
649C2×C8—132no—
650C2×C8—264no—
651C2×C8C23×D1312yes—
652C2×C8C23×D1312yes—
653C2×C8C23×D1312yes—
654C2×C8C23×D1312yes—
655C4⋊C4—134no—
656C4⋊C4—134no—
657C4⋊C4—132no—
658C4⋊C4—132no—
659C4⋊C4—134no—
660C4⋊C4—134no—
661C4⋊C4—134no—
662C4⋊C4—134no—
663C4⋊C4—134no—
664C4⋊C4—134no—
665C4⋊C4—134no—
666C4⋊C4—134no—
667C4⋊C4—132no—
668C4⋊C4—132no—
669C4⋊C4C2×C4×D1312yes—
670C4⋊C4C2×C4×D1312yes—
671C4⋊C4C2×C4×D1314yes—
672C4⋊C4C2×C4×D1314yes—
673C4⋊C4C2×C4×D1312yes—
674C4⋊C4C2×C4×D1312yes—
675C22⋊C4—134no—
676C22⋊C4—134no—
677C22⋊C4—134no—
678C22⋊C4C2×C4×D1314yes—
679C42—131no—
680C42—131no—
681C42—131no—
682C42—131no—
683C42—131no—
684C42—131no—
685C42—131no—
686C42—131no—
687C42—131no—
688C42—131no—
689C42—134no—
690C42—134no—
691C42—131no—
692C42—131no—
693C42—134no—
694C42C2×C4×D1311yescharacteristic
695C42C2×C4×D1311yescharacteristic
696C42C23×D1311yescharacteristic
697C42C23×D1314yes—
698C42C23×D1311yescharacteristic
699C13#6025011yescharacteristic, complemented, Sylow
700C23—131no—
701C23—131no—
702C23—262no—
703C23—262no—
704C23—521no—
705C23C22×C4×D1311yescharacteristic
706Q8—24no—
707Q8—42no—
708Q8—268no—
709Q8—268no—
710Q8—264no—
711Q8—522no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—131no—
715C2×C4—131no—
716C2×C4—134no—
717C2×C4—131no—
718C2×C4—131no—
719C2×C4—131no—
720C2×C4—131no—
721C2×C4—134no—
722C2×C4—134no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—268no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—261no—
735C2×C4—261no—
736C2×C4—261no—
737C2×C4—261no—
738C2×C4—521no—
739C2×C4—521no—
740C2×C4—524no—
741C2×C4C22×C4×D1311yescharacteristic
742C2×C4C22×C4×D1311yescharacteristic
743C2×C4C22×C4×D1311yescharacteristic
744C2×C4C22×C4×D1314yes—
745C2×C4C22×C4×D1314yes—
746C2×C4C22×C4×D1311yescharacteristic
747C2×C4C22×C4×D1311yescharacteristic
748C2×C4#8825412yes—
749C2×C4#8825712yes—
750C2×C4C24×D1311yescharacteristic
751C8—22no—
752C8—22no—
753C8—22no—
754C8—22no—
755C8—262no—
756C8—262no—
757C8—262no—
758C8—262no—
759C22—21no—
760C22—21no—
761C22—132no—
762C22—261no—
763C22—261no—
764C22—261no—
765C22—261no—
766C22—261no—
767C22—524no—
768C22#1171927712yes—
769C22C23×C4×D1311yescharacteristic
770C4—21no—
771C4—24no—
772C4—21no—
773C4—21no—
774C4—24no—
775C4—132no—
776C4—132no—
777C4—261no—
778C4—264no—
779C4—261no—
780C4—264no—
781C4—261no—
782C4—261no—
783C4#1171927712yes—
784C4D13×#13112yes—
785C4C2×#8825411yescharacteristic
786C4C2×#8825711yescharacteristic
787C2—22no—
788C2—262no—
789C2—521no—
790C2C2×#1171927711yescharacteristic
791C2C2×D13×#13111yescharacteristic
792C2D13×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC13×#2962C2
prime radicalC23×D13C22×C4
cosocleC2×C4×C13C25
hypercenter#2962D13
hypocenterC13#60250
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #2962

Complements

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

NH ≅ G/Ntype
2. #13123936C2semidirect
3. #13123934C2semidirect
4. #13123929C2semidirect
5. #13123922C2semidirect
6. #13123918C2semidirect
7. #13123915C2semidirect
8. #13123785C2semidirect
9. #13123783C2semidirect
10. #13123779C2semidirect
11. #13123769C2semidirect
12. #13123768C2semidirect
17. C13×#2962C2semidirect
37. C13×#446C22semidirect
38. C13×#446C22semidirect
39. C8×Q8×C13C22semidirect
54. #11718685C22semidirect
55. #11718685C22semidirect
56. Q8×#1055C22semidirect
71. #11718492C22semidirect
72. #11718491C22semidirect
73. #11718491C22semidirect
74. #11718491C22semidirect
75. #11718489C22semidirect
76. #11718489C22semidirect
77. #11718489C22semidirect
82. #11718362C22semidirect
83. #11718362C22semidirect
84. #11718362C22semidirect
89. #11718340C22semidirect
90. C8×Dic26C22semidirect
91. C8×Dic26C22semidirect
92. C8×Dic26C22semidirect
314. #2962D13semidirect
409. #446C2×D13semidirect
410. #446C2×D13semidirect
418. C8×Q8C2×D13semidirect
699. C13#60250semidirect

Maximal subgroups

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

subgroupindex
D13×#5332
#131239362
#131239342
#131239292
#131239222
#131239182
#131239152
#131237852
#131237832
#131237792
#131237692
#131237682
#131234932
#131234912
#131234672
C2×#117184942
C13×#29622
#6025013