Finite Group Databasebeta

← #16727955

Subgroups — #16727955

Order 3328.

1658 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123942C214yesmaximal, complemented
2#13123938C212yesmaximal, complemented
3#13123931C214yesmaximal, complemented
4#13123931C212yesmaximal, complemented
5#13123925C212yesmaximal, complemented
6#13123921C212yesmaximal, complemented
7Q8×#6099C211yesmaximal, characteristic, complemented
8#13123785C212yesmaximal, complemented
9#13123785C211yesmaximal, characteristic, complemented
10#13123777C212yesmaximal, complemented
11#13123771C211yesmaximal, characteristic, complemented
12C2×#11718685C211yesmaximal, characteristic, complemented
13#13123502C212yesmaximal
14#13123502C211yesmaximal, characteristic
15#13123487C212yesmaximal
16#13123480C211yesmaximal, characteristic
17Q8×C13×#41C211yesmaximal, characteristic
18Q82×C13C411yescharacteristic
19C13×#557C411yescharacteristic
20C13×#557C412yes—
21C13×#554C411yescharacteristic
22C13×#554C412yes—
23C13×#554C412yes—
24C13×#554C414yes—
25D4×Q8×C13C412yes—
26D4×Q8×C13C411yescharacteristic
27C13×#533C2212yes—
28C13×#533C2214yes—
29C13×#533C2211yescharacteristic
30C13×#533C2212yes—
31C4×C13×#41C2211yescharacteristic
32C4×C13×#41C2212yes—
33C2×C4×Q8×C13C2212yes—
34C2×C4×Q8×C13C2211yescharacteristic
35#11718895C2211yescharacteristic
36#11718895C2211yescharacteristic
37#11718895C2212yes—
38#11718685C2211yescharacteristic
39#11718685C2212yes—
40#11718685C2212yes—
41#11718685C2214yes—
42#11718685C2212yes—
43#11718685C2214yes—
44#11718685C2211yescharacteristic
45#11718685C2214yes—
46#11718685C2214yes—
47#11718685C2211yescharacteristic
48#11718685C2212yes—
49#11718685C2214yes—
50#11718685C2214yes—
51#11718685C2214yes—
52#11718685C2214yes—
53#11718685C2211yescharacteristic
54#11718685C2214yes—
55#11718685C2212yes—
56#11718685C2212yes—
57Q8×#1055C2212yes—
58Q8×#1055C2212yes—
59Q8×#1055C2212yes—
60Q8×#1055C2214yes—
61Q8×#1055C2212yes—
62#11718661C2212yes—
63#11718661C2214yes—
64#11718661C2214yes—
65#11718661C2214yes—
66#11718661C2214yes—
67#11718661C2214yes—
68#11718661C2212yes—
69#11718660C2211yescharacteristic
70#11718660C2211yescharacteristic
71#11718660C2212yes—
72#11718660C2212yes—
73#11718658C2212yes—
74#11718658C2212yes—
75#11718658C2212yes—
76#11718587C2214yes—
77#11718587C2214yes—
78#11718587C2212yes—
79#11718587C2214yes—
80#11718586C2212yes—
81#11718586C2212yes—
82#11718586C2214yes—
83#11718586C2212yes—
84#11718585C2211yescharacteristic
85#11718585C2212yes—
86C2×C4⋊#1055C2212yes—
87C2×C4⋊#1055C2211yescharacteristic
88C4×#6099C2211yescharacteristic
89C4×#6099C2212yes—
90C2×#88043C2212yes—
91C2×C4×#1055C2211yescharacteristic
92C2×C13×#41C2311yescharacteristic
93C22×Q8×C13C2×C412yes—
94C22×Q8×C13C2×C411yescharacteristic
95C13×C4⋊Q8C2×C412yes—
96C13×C4⋊Q8C2×C411yescharacteristic
97C13×C4⋊Q8C2×C414yes—
98C13×C4⋊Q8C2×C412yes—
99C13×C4⋊Q8C2×C412yes—
100C13×C4⋊Q8C2×C414yes—
101C13×C4⋊Q8C2×C411yescharacteristic
102C13×C4⋊Q8C2×C412yes—
103C13×#125C2×C414yes—
104C13×#125C2×C414yes—
105C13×#125C2×C414yes—
106C13×#125C2×C412yes—
107C13×#125C2×C412yes—
108C13×#125C2×C412yes—
109C13×C22⋊Q8C2×C412yes—
110C13×C22⋊Q8C2×C412yes—
111C13×C22⋊Q8C2×C412yes—
112C13×C22⋊Q8C2×C414yes—
113C13×C22⋊Q8C2×C414yes—
114C13×C22⋊Q8C2×C414yes—
115C13×C22⋊Q8C2×C414yes—
116C13×C22⋊Q8C2×C414yes—
117C13×C22⋊Q8C2×C414yes—
118C13×C22⋊Q8C2×C412yes—
119C13×C22⋊Q8C2×C414yes—
120C4×Q8×C13C2×C412yes—
121C4×Q8×C13C2×C411yescharacteristic
122C4×Q8×C13C2×C412yes—
123C4×Q8×C13C2×C411yescharacteristic
124C4×Q8×C13C2×C414yes—
125C4×Q8×C13C2×C412yes—
126C4×Q8×C13C2×C411yescharacteristic
127C4×Q8×C13C2×C412yes—
128C4×Q8×C13C2×C411yescharacteristic
129C4×Q8×C13C2×C412yes—
130C4×Q8×C13C2312yes—
131C4×Q8×C13C2311yescharacteristic
132C4×Q8×C13C2312yes—
133C4×Q8×C13C2314yes—
134C4×Q8×C13C2311yescharacteristic
135C4×Q8×C13C2314yes—
136C4×Q8×C13C2312yes—
137C4×D4×C13C2×C412yes—
138C4×D4×C13C2×C411yescharacteristic
139C4×D4×C13C2×C414yes—
140C4×D4×C13C2×C412yes—
141C4×D4×C13C2×C412yes—
142C4×D4×C13C2×C411yescharacteristic
143C4×D4×C13C2×C414yes—
144C4×D4×C13C2×C412yes—
145C13×#117C2312yes—
146C13×#117C2311yescharacteristic
147C13×#117C2312yes—
148C13×#117C2314yes—
149C2×C13×C4⋊C4C2×C412yes—
150C2×C13×C4⋊C4C2×C411yescharacteristic
151C2×C13×C4⋊C4C2×C414yes—
152C2×C13×C4⋊C4C2×C412yes—
153C2×C42×C13C2311yescharacteristic
154C2×C42×C13C2312yes—
155C2×C42×C13C2312yes—
156C2×C42×C13C2314yes—
157C2×#6099C2312yes—
158C2×#6099C2311yescharacteristic
159C2×#6099C2311yescharacteristic
160C22×#1055C2311yescharacteristic
161C22×#1055C2312yes—
162C22×#1055C2311yescharacteristic
163C22⋊#1055C2312yes—
164C22⋊#1055C2312yes—
165C22⋊#1055C2314yes—
166C22⋊#1055C2314yes—
167C22⋊#1055C2312yes—
168C22⋊#1055C2312yes—
169C4⋊#1055C2312yes—
170C4⋊#1055C2314yes—
171C4⋊#1055C2314yes—
172C4⋊#1055C2314yes—
173C4⋊#1055C2314yes—
174C4⋊#1055C2312yes—
175C4⋊#1055C2312yes—
176C4⋊#1055C2312yes—
177C4⋊#1055C2312yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2312yes—
180C4⋊#1055C2312yes—
181C4⋊#1055C2312yes—
182C4⋊#1055C2311yescharacteristic
183C4⋊#1055C2312yes—
184C4⋊#1055C2312yes—
185C4⋊#1055C2311yescharacteristic
186C4⋊#1055C2312yes—
187C4⋊#1055C2314yes—
188#88043C2314yes—
189#88043C2314yes—
190#88043C2314yes—
191#88043C2312yes—
192#88043C2312yes—
193#88043C2312yes—
194#88043C2312yes—
195#88043C2312yes—
196#88043C2314yes—
197C4×#1055C2314yes—
198C4×#1055C2314yes—
199C4×#1055C2314yes—
200C4×#1055C2311yescharacteristic
201C4×#1055C2314yes—
202C4×#1055C2311yescharacteristic
203C4×#1055C2311yescharacteristic
204C4×#1055C2312yes—
205C4×#1055C2311yescharacteristic
206#60254—131nomaximal, Sylow
207C13×#41—22no—
208C13×#41—22no—
209C2×Q8×C13—42no—
210C2×Q8×C13—44no—
211C2×Q8×C13C22×C411yescharacteristic
212C2×Q8×C13C22×C411yescharacteristic
213C2×Q8×C13C22×C412yes—
214C2×Q8×C13C22×C411yescharacteristic
215C2×Q8×C13C22×C414yes—
216C2×Q8×C13C22×C412yes—
217C2×Q8×C13C22×C412yes—
218C2×Q8×C13C22×C414yes—
219C2×D4×C13C22×C412yes—
220C2×D4×C13C22×C411yescharacteristic
221C22×C4×C13C22×C412yes—
222C22×C4×C13C22×C411yescharacteristic
223C22×C4×C13C22×C412yes—
224C22×C4×C13C22×C414yes—
225C22×C4×C13C22×C411yescharacteristic
226C22×C4×C13C22×C412yes—
227C22×C4×C13C22×C414yes—
228C22×C4×C13C22×C412yes—
229C22×C4×C13C2412yes—
230C22×C4×C13C2411yescharacteristic
231C13×C4⋊C4C22×C412yes—
232C13×C4⋊C4C22×C411yescharacteristic
233C13×C4⋊C4C22×C414yes—
234C13×C4⋊C4C22×C412yes—
235C13×C4⋊C4C22×C414yes—
236C13×C4⋊C4C22×C412yes—
237C13×C4⋊C4C22×C414yes—
238C13×C4⋊C4C22×C412yes—
239C13×C4⋊C4C22×C414yes—
240C13×C4⋊C4C22×C412yes—
241C13×C4⋊C4C22×C412yes—
242C13×C4⋊C4C22×C411yescharacteristic
243C13×C4⋊C4C22×C412yes—
244C13×C4⋊C4C22×C414yes—
245C13×C4⋊C4C22×C412yes—
246C13×C4⋊C4C22×C414yes—
247C13×C4⋊C4C22×C411yescharacteristic
248C13×C4⋊C4C22×C412yes—
249C13×C4⋊C4C22×C412yes—
250C13×C4⋊C4C22×C411yescharacteristic
251C13×C4⋊C4C22×C414yes—
252C13×C4⋊C4C22×C414yes—
253C13×C4⋊C4C22×C414yes—
254C13×C4⋊C4C22×C412yes—
255C13×C4⋊C4C22×C414yes—
256C13×C22⋊C4C22×C412yes—
257C13×C22⋊C4C22×C412yes—
258C13×C22⋊C4C22×C414yes—
259C13×C22⋊C4C22×C414yes—
260C13×C22⋊C4C22×C412yes—
261C13×C22⋊C4C22×C414yes—
262C42×C13C22×C412yes—
263C42×C13C22×C414yes—
264C42×C13C22×C411yescharacteristic
265C42×C13C22×C412yes—
266C42×C13C22×C414yes—
267C42×C13C22×C412yes—
268C42×C13C22×C412yes—
269C42×C13C22×C411yescharacteristic
270C42×C13C2411yescharacteristic
271C42×C13C2412yes—
272C42×C13C2411yescharacteristic
273C42×C13C2412yes—
274C42×C13C2412yes—
275C42×C13C2414yes—
276#6099—22no—
277#6099—24no—
278#6099—22no—
279C2×#1055—22no—
280C2×#1055—24no—
281C2×#1055—22no—
282C2×#1055C2411yescharacteristic
283C2×#1055C2411yescharacteristic
284C2×#1055C2412yes—
285C2×#1055C2412yes—
286C2×#1055C2411yescharacteristic
287C2×#1055C2411yescharacteristic
288C2×#1055C2412yes—
289C2×#1055C2414yes—
290C2×#1055C2412yes—
291Q8×#41D1311yescharacteristic
292#2987—134no—
293#2986—132no—
294#2985—132no—
295#2985—134no—
296#2984—132no—
297#2983—132no—
298Q8×M16—131no—
299#2962—131no—
300#2962—132no—
301#2961—132no—
302#2960—131no—
303C2×#446—131no—
304#2925—131no—
305#2925—132no—
306#2923—132no—
307#2922—131no—
308C23×C13C23×C412yes—
309C23×C13C23×C411yescharacteristic
310Q8×C13—22no—
311Q8×C13—22no—
312Q8×C13—22no—
313Q8×C13—24no—
314Q8×C13—42no—
315Q8×C13—44no—
316Q8×C13—42no—
317Q8×C13—44no—
318D4×C13—24no—
319D4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—24no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—41no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—44no—
328C2×C4×C13—42no—
329C2×C4×C13—44no—
330C2×C4×C13C23×C412yes—
331C2×C4×C13C23×C411yescharacteristic
332C2×C4×C13C23×C412yes—
333C2×C4×C13C23×C412yes—
334C2×C4×C13C23×C412yes—
335C2×C4×C13C23×C411yescharacteristic
336C2×C4×C13C23×C414yes—
337C2×C4×C13C23×C412yes—
338C2×C4×C13C23×C414yes—
339C2×C4×C13C23×C412yes—
340C2×C4×C13C23×C412yes—
341C2×C4×C13C23×C411yescharacteristic
342C2×C4×C13C23×C411yescharacteristic
343C2×C4×C13C23×C411yescharacteristic
344C2×C4×C132−1+412yes—
345C2×C4×C132−1+412yes—
346C2×C4×C13C2511yescharacteristic
347#1055—21no—
348#1055—21no—
349#1055—22no—
350#1055—22no—
351#1055—21no—
352#1055—21no—
353#1055—22no—
354#1055—22no—
355#1055—24no—
356Q82Dic1311yescharacteristic
357#557Dic1311yescharacteristic
358#557Dic1312yes—
359#554Dic1312yes—
360#554Dic1311yescharacteristic
361#554Dic1314yes—
362#554Dic1312yes—
363D4×Q8Dic1311yescharacteristic
364D4×Q8Dic1312yes—
365#533C2×D1311yescharacteristic
366#533C2×D1312yes—
367#533C2×D1312yes—
368#533C2×D1314yes—
369C4×#41C2×D1311yescharacteristic
370C4×#41C2×D1312yes—
371C2×C4×Q8C2×D1311yescharacteristic
372C2×C4×Q8C2×D1312yes—
373#446—131no—
374#446—131no—
375#446—131no—
376#446—132no—
377#446—131no—
378#446—132no—
379#446—132no—
380#446—132no—
381#446—134no—
382#446—134no—
383#446—134no—
384#446—134no—
385#446—132no—
386#446—134no—
387#446—134no—
388#446—134no—
389#446—134no—
390#446—132no—
391#446—134no—
392C8×Q8—132no—
393C8×Q8—132no—
394C8×Q8—132no—
395C8×Q8—134no—
396C8×Q8—132no—
397#433—132no—
398#433—132no—
399#433—134no—
400#433—134no—
401#433—134no—
402#433—134no—
403#433—134no—
404#432—134no—
405#432—134no—
406#432—134no—
407#432—132no—
408#431—132no—
409#431—132no—
410#431—132no—
411#431—134no—
412#424—131no—
413#424—131no—
414#424—132no—
415#424—132no—
416#423—131no—
417#423—132no—
418C2×C4⋊C8—131no—
419C2×C4⋊C8—132no—
420#408—131no—
421#408—131no—
422#408—132no—
423#405—132no—
424#405—132no—
425#405—132no—
426C4×M16—131no—
427C4×M16—132no—
428C2×#97—132no—
429C2×C4×C8—131no—
430C22×C13—21no—
431C22×C13—21no—
432C22×C13—22no—
433C22×C13—22no—
434C22×C13—22no—
435C22×C13#51912yes—
436C22×C13C24×C411yescharacteristic
437C4×C13—22no—
438C4×C13—21no—
439C4×C13—22no—
440C4×C13—22no—
441C4×C13—22no—
442C4×C13—24no—
443C4×C13—21no—
444C4×C13—22no—
445C4×C13—21no—
446C4×C13—22no—
447C4×C13—22no—
448C4×C13—24no—
449C4×C13#51912yes—
450C4×C13#56812yes—
451C4×C13C2×2−1+411yescharacteristic
452C4×C13C2×2−1+411yescharacteristic
453C2×#41C22×D1311yescharacteristic
454C22×Q8C2×Dic1311yescharacteristic
455C22×Q8C2×Dic1312yes—
456C2×M16—131no—
457C2×M16—131no—
458C2×M16—132no—
459C22×C8—131no—
460C22×C8—131no—
461C22×C8—132no—
462C4⋊Q8C2×Dic1311yescharacteristic
463C4⋊Q8C2×Dic1312yes—
464C4⋊Q8C2×Dic1312yes—
465C4⋊Q8C2×Dic1314yes—
466C4⋊Q8C2×Dic1311yescharacteristic
467C4⋊Q8C2×Dic1312yes—
468C4⋊Q8C2×Dic1312yes—
469C4⋊Q8C2×Dic1314yes—
470#125C2×Dic1312yes—
471#125C2×Dic1312yes—
472#125C2×Dic1312yes—
473#125C2×Dic1314yes—
474#125C2×Dic1314yes—
475#125C2×Dic1314yes—
476C22⋊Q8C2×Dic1312yes—
477C22⋊Q8C2×Dic1312yes—
478C22⋊Q8C2×Dic1312yes—
479C22⋊Q8C2×Dic1314yes—
480C22⋊Q8C2×Dic1314yes—
481C22⋊Q8C2×Dic1314yes—
482C22⋊Q8C2×Dic1312yes—
483C22⋊Q8C2×Dic1314yes—
484C22⋊Q8C2×Dic1314yes—
485C22⋊Q8C2×Dic1314yes—
486C22⋊Q8C2×Dic1314yes—
487C4×Q8C2×Dic1311yescharacteristic
488C4×Q8C2×Dic1312yes—
489C4×Q8C2×Dic1311yescharacteristic
490C4×Q8C2×Dic1312yes—
491C4×Q8C2×Dic1312yes—
492C4×Q8C2×Dic1314yes—
493C4×Q8C2×Dic1311yescharacteristic
494C4×Q8C2×Dic1312yes—
495C4×Q8C2×Dic1311yescharacteristic
496C4×Q8C2×Dic1312yes—
497C4×Q8C22×D1311yescharacteristic
498C4×Q8C22×D1311yescharacteristic
499C4×Q8C22×D1312yes—
500C4×Q8C22×D1312yes—
501C4×Q8C22×D1314yes—
502C4×Q8C22×D1312yes—
503C4×Q8C22×D1314yes—
504C4×D4C2×Dic1312yes—
505C4×D4C2×Dic1311yescharacteristic
506C4×D4C2×Dic1314yes—
507C4×D4C2×Dic1312yes—
508C4×D4C2×Dic1312yes—
509C4×D4C2×Dic1311yescharacteristic
510C4×D4C2×Dic1314yes—
511C4×D4C2×Dic1312yes—
512#117C22×D1311yescharacteristic
513#117C22×D1312yes—
514#117C22×D1312yes—
515#117C22×D1314yes—
516C2×C4⋊C4C2×Dic1311yescharacteristic
517C2×C4⋊C4C2×Dic1312yes—
518C2×C4⋊C4C2×Dic1312yes—
519C2×C4⋊C4C2×Dic1314yes—
520C2×C42C22×D1311yescharacteristic
521C2×C42C22×D1312yes—
522C2×C42C22×D1312yes—
523C2×C42C22×D1314yes—
524C4⋊C8—131no—
525C4⋊C8—132no—
526C4⋊C8—131no—
527C4⋊C8—132no—
528C4⋊C8—132no—
529C4⋊C8—132no—
530C4⋊C8—132no—
531C4⋊C8—132no—
532C4⋊C8—134no—
533C4⋊C8—132no—
534C4⋊C8—134no—
535C4⋊C8—132no—
536C4⋊C8—132no—
537C4⋊C8—132no—
538C4⋊C8—132no—
539C4⋊C8—134no—
540C4⋊C8—134no—
541C4⋊C8—134no—
542C4⋊C8—134no—
543C22⋊C8—132no—
544C22⋊C8—132no—
545C22⋊C8—132no—
546C22⋊C8—132no—
547C22⋊C8—134no—
548C22⋊C8—134no—
549#97—132no—
550#97—132no—
551#97—132no—
552#97—132no—
553#97—134no—
554#97—132no—
555#97—134no—
556#97—134no—
557#97—134no—
558C4×C8—131no—
559C4×C8—131no—
560C4×C8—131no—
561C4×C8—131no—
562C4×C8—132no—
563C4×C8—134no—
564C4×C8—134no—
565C4×C8—134no—
566C4×C8—134no—
567C2×C13—22no—
568C2×C13—42no—
569C2×C13C2×#51911yescharacteristic
570C2×C13C2×#56811yescharacteristic
571C2×C13#357311yescharacteristic
572#41—22no—
573#41—22no—
574C2×Q8—42no—
575C2×Q8—44no—
576C2×Q8C22×Dic1311yescharacteristic
577C2×Q8C22×Dic1311yescharacteristic
578C2×Q8C22×Dic1311yescharacteristic
579C2×Q8C22×Dic1312yes—
580C2×Q8C22×Dic1312yes—
581C2×Q8C22×Dic1314yes—
582C2×Q8C22×Dic1312yes—
583C2×Q8C22×Dic1314yes—
584C2×D4C22×Dic1312yes—
585C2×D4C22×Dic1311yescharacteristic
586C22×C4C22×Dic1312yes—
587C22×C4C22×Dic1311yescharacteristic
588C22×C4C22×Dic1312yes—
589C22×C4C22×Dic1314yes—
590C22×C4C22×Dic1311yescharacteristic
591C22×C4C22×Dic1312yes—
592C22×C4C22×Dic1314yes—
593C22×C4C22×Dic1312yes—
594C22×C4C23×D1312yes—
595C22×C4C23×D1311yescharacteristic
596M16—262no—
597M16—262no—
598M16—264no—
599C2×C8—131no—
600C2×C8—132no—
601C2×C8—132no—
602C2×C8—134no—
603C2×C8—131no—
604C2×C8—131no—
605C2×C8—131no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—262no—
609C2×C8—264no—
610C2×C8—262no—
611C4⋊C4C22×Dic1312yes—
612C4⋊C4C22×Dic1311yescharacteristic
613C4⋊C4C22×Dic1312yes—
614C4⋊C4C22×Dic1314yes—
615C4⋊C4C22×Dic1312yes—
616C4⋊C4C22×Dic1314yes—
617C4⋊C4C22×Dic1312yes—
618C4⋊C4C22×Dic1314yes—
619C4⋊C4C22×Dic1312yes—
620C4⋊C4C22×Dic1314yes—
621C4⋊C4C22×Dic1311yescharacteristic
622C4⋊C4C22×Dic1312yes—
623C4⋊C4C22×Dic1312yes—
624C4⋊C4C22×Dic1314yes—
625C4⋊C4C22×Dic1312yes—
626C4⋊C4C22×Dic1314yes—
627C4⋊C4C22×Dic1311yescharacteristic
628C4⋊C4C22×Dic1312yes—
629C4⋊C4C22×Dic1311yescharacteristic
630C4⋊C4C22×Dic1312yes—
631C4⋊C4C22×Dic1314yes—
632C4⋊C4C22×Dic1314yes—
633C4⋊C4C22×Dic1314yes—
634C4⋊C4C22×Dic1312yes—
635C4⋊C4C22×Dic1314yes—
636C22⋊C4C22×Dic1312yes—
637C22⋊C4C22×Dic1312yes—
638C22⋊C4C22×Dic1314yes—
639C22⋊C4C22×Dic1314yes—
640C22⋊C4C22×Dic1312yes—
641C22⋊C4C22×Dic1314yes—
642C42C22×Dic1312yes—
643C42C22×Dic1314yes—
644C42C22×Dic1311yescharacteristic
645C42C22×Dic1312yes—
646C42C22×Dic1314yes—
647C42C22×Dic1312yes—
648C42C22×Dic1312yes—
649C42C22×Dic1311yescharacteristic
650C42C23×D1311yescharacteristic
651C42C23×D1311yescharacteristic
652C42C23×D1312yes—
653C42C23×D1314yes—
654C42C23×D1312yes—
655C42C23×D1312yes—
656C13#6025411yescharacteristic, complemented, Sylow
657C23C23×Dic1312yes—
658C23C23×Dic1311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—24no—
663Q8—42no—
664Q8—44no—
665Q8—42no—
666Q8—44no—
667D4—24no—
668D4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4#8825412yes—
680C2×C4#8825412yes—
681C2×C4C23×Dic1312yes—
682C2×C4C23×Dic1311yescharacteristic
683C2×C4C23×Dic1312yes—
684C2×C4C23×Dic1312yes—
685C2×C4C23×Dic1312yes—
686C2×C4C23×Dic1311yescharacteristic
687C2×C4C23×Dic1314yes—
688C2×C4C23×Dic1312yes—
689C2×C4C23×Dic1314yes—
690C2×C4C23×Dic1312yes—
691C2×C4C23×Dic1312yes—
692C2×C4C23×Dic1311yescharacteristic
693C2×C4C23×Dic1311yescharacteristic
694C2×C4C23×Dic1311yescharacteristic
695C2×C4C24×D1311yescharacteristic
696C8—261no—
697C8—261no—
698C8—262no—
699C8—262no—
700C8—261no—
701C8—261no—
702C8—262no—
703C8—262no—
704C8—264no—
705C22—21no—
706C22—21no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22#1171951712yes—
711C22C24×Dic1311yescharacteristic
712C4—21no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—24no—
717C4—21no—
718C4—22no—
719C4—21no—
720C4—22no—
721C4—22no—
722C4—24no—
723C4—22no—
724C4#1171951712yes—
725C4#1171952412yes—
726C4C2×#8825411yescharacteristic
727C4C2×#8825411yescharacteristic
728C2—22no—
729C2—42no—
730C2C2×#1171951711yescharacteristic
731C2C2×#1171952411yescharacteristic
732C2#1312954811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingQ8×C13×#41C2
prime radicalC2×C13×#41C23
cosocleC2×C4×C13C25
hypercenterQ8×#41D13
hypocenterC13#60254
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #13123942C2semidirect
2. #13123938C2semidirect
3. #13123931C2semidirect
4. #13123931C2semidirect
5. #13123925C2semidirect
6. #13123921C2semidirect
7. Q8×#6099C2semidirect
8. #13123785C2semidirect
9. #13123785C2semidirect
10. #13123777C2semidirect
11. #13123771C2semidirect
12. C2×#11718685C2semidirect
656. C13#60254semidirect

Maximal subgroups

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

subgroupindex
#131239422
#131239382
#131239312
#131239252
#131239212
Q8×#60992
#131237852
#131237772
#131237712
C2×#117186852
#131235022
#131234872
#131234802
Q8×C13×#412
#6025413