Finite Group Databasebeta

← #16807790

Subgroups — #16807790

Order 3328.

2036 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131371C214yesmaximal
2#13131370C212yesmaximal
3#13131365C211yesmaximal, characteristic
4#13131365C212yesmaximal
5#13131356C212yesmaximal
6#13131356C212yesmaximal
7#13131355C211yesmaximal, characteristic
8#13131355C211yesmaximal, characteristic
9#13131336C214yesmaximal
10#13131327C212yesmaximal
11C4⋊Q8×#261C211yesmaximal, characteristic
12#125×#261C212yesmaximal
13#13131295C211yesmaximal, characteristic
14#13131295C212yesmaximal
15#13131276C212yesmaximal
16C4×Q8×#261C211yesmaximal, characteristic
17D13×#557C211yesmaximal, characteristic
18C2×Q8×#261C2211yescharacteristic
19C2×Q8×#261C2211yescharacteristic
20C2×Q8×#261C2212yes—
21C2×Q8×#261C2212yes—
22C13×#557C411yescharacteristic, complemented
23D13×C4⋊Q8C2211yescharacteristic
24D13×C4⋊Q8C2212yes—
25#11719426C411yescharacteristic, complemented
26#11719426C412yescomplemented
27D13×#125C2212yes—
28D13×#125C2214yes—
29#11719390C412yescomplemented
30#11719390C414yescomplemented
31C4×Q8×D13C2211yescharacteristic
32C4×Q8×D13C2212yes—
33C4×Q8×D13C2211yescharacteristic
34C4×Q8×D13C2212yes—
35#11719275C411yescharacteristic, complemented
36#11719274C412yescomplemented
37#11719272C411yescharacteristic, complemented
38#11719272C412yescomplemented
39(C2×#261)⋊Q8C2211yescharacteristic
40(C2×#261)⋊Q8C2212yes—
41(C2×#261)⋊Q8C2211yescharacteristic
42(C2×#261)⋊Q8C2212yes—
43(C2×#261)⋊Q8C2212yes—
44(C2×#261)⋊Q8C2212yes—
45#11719083C2211yescharacteristic
46#11719083C2212yes—
47#11719083C2212yes—
48#11719083C2211yescharacteristic
49#11719083C2212yes—
50#11719083C2214yes—
51#11719082C2214yes—
52#11719082C2212yes—
53#11719082C2214yes—
54#11719082C2212yes—
55#11719082C2214yes—
56#11719082C2214yes—
57#11719082C2214yes—
58#11719082C2214yes—
59#11719082C2214yes—
60#11719082C2214yes—
61#11719082C2214yes—
62#11719082C2214yes—
63#11719082C2214yes—
64C4⋊C4×#261C2211yescharacteristic
65C4⋊C4×#261C2212yes—
66C4⋊C4×#261C2211yescharacteristic
67C4⋊C4×#261C2212yes—
68C4⋊C4×#261C2214yes—
69C4⋊C4×#261C2212yes—
70C4⋊C4×#261C2214yes—
71C4⋊C4×#261C2212yes—
72C4⋊C4×#261C2212yes—
73C4⋊C4×#261C2214yes—
74C4⋊C4×#261C2212yes—
75C4⋊C4×#261C2212yes—
76#11719061C2214yes—
77#11719060C2212yes—
78#11719060C2212yes—
79#11719059C2211yescharacteristic
80C4×C4⋊#261C2211yescharacteristic
81C4×C4⋊#261C2212yes—
82C4×C4⋊#261C2214yes—
83C4×C4⋊#261C2212yes—
84C4×C4⋊#261C2211yescharacteristic
85C4×C4⋊#261C2212yes—
86C4×C4⋊#261C2212yes—
87#11719057C2212yes—
88#11719057C2214yes—
89#11719057C2214yes—
90C42×#261C2212yes—
91C42×#261C2211yescharacteristic
92C2×Q8×D13C2312yes—
93C2×Q8×D13C2311yescharacteristic
94C2×Q8×D13C2311yescharacteristic
95Q8×#261—24no—
96Q8×#261—28no—
97Q8×#261—24no—
98Q8×#261—28no—
99C2×C4⋊#261C2311yescharacteristic
100C2×C4⋊#261C2312yes—
101C2×C4⋊#261C2312yes—
102C2×C4⋊#261C2311yescharacteristic
103C2×C4⋊#261C2311yescharacteristic
104C2×C4⋊#261C2312yes—
105C2×C4⋊#261C2312yes—
106C2×C4⋊#261C2312yes—
107C2×C4⋊#261C2314yes—
108C2×C4⋊#261C2314yes—
109C2×C4⋊#261C2312yes—
110C2×C4⋊#261C2312yes—
111C2×C4⋊#261C2311yescharacteristic
112C2×C4×#261C2311yescharacteristic
113C2×C4×#261C2312yes—
114C2×C4×#261C2312yes—
115C2×C4×#261C2311yescharacteristic
116C2×C4×#261C2311yescharacteristic
117C2×C4×#261C2311yescharacteristic
118C2×C4×#261C2312yes—
119C2×C4×#261C2312yes—
120C2×C4×#261C2312yes—
121C2×C4×#261C2314yes—
122C2×C4×#261C2314yes—
123C2×C4×#261C2312yes—
124C2×C4×#261C2311yescharacteristic
125C2×C4×#261C2314yes—
126C2×C4×#261C2314yes—
127C2×C4×#261C2311yescharacteristic
128C13×C4⋊Q8C2×C411yescharacteristic
129C13×C4⋊Q8C2×C412yes—
130C13×#125C2×C412yes—
131C13×#125C2×C414yes—
132C4×Q8×C13C2×C411yescharacteristic
133C4×Q8×C13C2×C412yes—
134C4×Q8×C13C2×C412yes—
135C4×Q8×C13C2×C411yescharacteristic
136Q8×Dic13C2×C411yescharacteristic
137Q8×Dic13C2×C412yes—
138Q8×Dic13C2×C411yescharacteristic
139Q8×Dic13C2×C412yes—
140#88198C2×C412yes—
141#88198C2×C412yes—
142#88198C2×C412yes—
143C4⋊C4×D13C2312yes—
144C4⋊C4×D13C2314yes—
145C4⋊C4×D13C2312yes—
146C4⋊C4×D13C2314yes—
147C4⋊C4×D13C2311yescharacteristic
148C4⋊C4×D13C2312yes—
149C4⋊C4×D13C2314yes—
150C4⋊C4×D13C2311yescharacteristic
151C4⋊C4×D13C2312yes—
152#88144C2×C412yes—
153#88144C2×C414yes—
154#88144C2×C412yes—
155#88144C2×C414yes—
156#88143C2×C414yes—
157#88143C2×C414yes—
158#88143C2×C414yes—
159#88143C2×C414yes—
160#88143C2×C414yes—
161#88143C2×C414yes—
162#88142C2×C412yes—
163#88142C2×C414yes—
164#88142C2×C412yes—
165#88142C2×C414yes—
166#88141C2×C414yes—
167#88141C2×C412yes—
168#88141C2×C411yescharacteristic
169#88141C2×C412yes—
170#88141C2×C412yes—
171#88141C2×C414yes—
172#88141C2×C412yes—
173#88141C2×C411yescharacteristic
174C42×D13C2311yescharacteristic
175C42×D13C2312yes—
176C42×D13C2312yes—
177C42×D13C2314yes—
178#88124C2×C412yes—
179#88124C2×C414yes—
180#88123C2×C411yescharacteristic
181#88123C2×C412yes—
182C4×Dic26C2×C411yescharacteristic
183C4×Dic26C2×C412yes—
184C4×Dic26C2×C411yescharacteristic
185C4×Dic26C2×C412yes—
186C4×Dic26C2×C412yes—
187C4×Dic26C2×C414yes—
188C4×Dic26C2×C412yes—
189C4×Dic26C2×C414yes—
190(C2×#261)⋊C4C2312yes—
191(C2×#261)⋊C4C2312yes—
192(C2×#261)⋊C4C2312yes—
193(C2×#261)⋊C4C2312yes—
194(C2×#261)⋊C4C2314yes—
195(C2×#261)⋊C4C2314yes—
196(C2×#261)⋊C4C2314yes—
197(C2×#261)⋊C4C2312yes—
198(C2×#261)⋊C4C2312yes—
199(C2×#261)⋊C4C2314yes—
200(C2×#261)⋊C4C2314yes—
201(C2×#261)⋊C4C2312yes—
202(C2×#261)⋊C4C2312yes—
203(C2×#261)⋊C4C2312yes—
204(C2×#261)⋊C4C2312yes—
205(C2×#261)⋊C4C2314yes—
206(C2×#261)⋊C4C2314yes—
207(C2×#261)⋊C4C2314yes—
208(C2×#261)⋊C4C2314yes—
209(C2×#261)⋊C4C2314yes—
210#34328—131nomaximal, Sylow
211C22×#261C2412yes—
212C22×#261C2412yes—
213C22×#261C2411yescharacteristic
214C22×#261C2412yes—
215C22×#261C2414yes—
216C22×#261C2411yescharacteristic
217C22×#261C2412yes—
218C22×#261C2411yescharacteristic
219C22×#261C2411yescharacteristic
220C2×Q8×C13C22×C412yes—
221C2×Q8×C13C22×C411yescharacteristic
222C2×Q8×C13C22×C411yescharacteristic
223Q8×D13—22no—
224Q8×D13—24no—
225Q8×D13—22no—
226Q8×D13—24no—
227Q8×D13—22no—
228Q8×D13—22no—
229C2×C4×D13C2412yes—
230C2×C4×D13C2412yes—
231C2×C4×D13C2411yescharacteristic
232C2×C4×D13C2412yes—
233C2×C4×D13C2414yes—
234C2×C4×D13C2412yes—
235C2×C4×D13C2411yescharacteristic
236C2×C4×D13C2411yescharacteristic
237C2×Dic26C22×C411yescharacteristic
238C2×Dic26C22×C412yes—
239C2×Dic26C22×C411yescharacteristic
240C2×Dic26C22×C412yes—
241C2×Dic26C22×C412yes—
242C2×Dic26C22×C414yes—
243C4⋊#261—24no—
244C4⋊#261—24no—
245C4⋊#261—28no—
246C4⋊#261—28no—
247C4⋊#261—24no—
248C4⋊#261—24no—
249C4⋊#261—22no—
250C4⋊#261—22no—
251C4⋊#261—24no—
252C4⋊#261—22no—
253C4⋊#261—42no—
254C4⋊#261—42no—
255C4⋊#261#4114yes—
256C4×#261—24no—
257C4×#261—28no—
258C4×#261—28no—
259C4×#261—24no—
260C4×#261—22no—
261C4×#261—24no—
262C4×#261—22no—
263C4×#261—24no—
264C4×#261—22no—
265C4×#261—24no—
266C4×#261—22no—
267C4×#261—42no—
268C4×#261—44no—
269C4×#261—44no—
270C4×#261—41no—
271C4×#261#4114yes—
272C13×C4⋊C4C22×C411yescharacteristic
273C13×C4⋊C4C22×C414yes—
274C13×C4⋊C4C22×C412yes—
275C13×C4⋊C4C22×C412yes—
276C13×C4⋊C4C22×C414yes—
277C13×C4⋊C4C22×C412yes—
278C13×C4⋊C4C22×C411yescharacteristic
279C13×C4⋊C4C22×C412yes—
280C13×C4⋊C4C22×C414yes—
281C42×C13C22×C412yes—
282C42×C13C22×C411yescharacteristic
283C42×C13C22×C414yes—
284C42×C13C22×C412yes—
285C4⋊Dic13C22×C411yescharacteristic
286C4⋊Dic13C22×C414yes—
287C4⋊Dic13C22×C412yes—
288C4⋊Dic13C22×C412yes—
289C4⋊Dic13C22×C411yescharacteristic
290C4⋊Dic13C22×C412yes—
291C4⋊Dic13C22×C414yes—
292C4⋊Dic13C22×C412yes—
293C4⋊Dic13C22×C414yes—
294#6101C22×C412yes—
295#6101C22×C412yes—
296#6101C22×C414yes—
297#6101C22×C414yes—
298#6101C22×C414yes—
299#6101C22×C414yes—
300#6101C22×C412yes—
301#6101C22×C412yes—
302#6101C22×C412yes—
303#6101C22×C412yes—
304#6101C22×C414yes—
305#6101C22×C414yes—
306#6101C22×C414yes—
307#6101C22×C414yes—
308C4×Dic13C22×C414yes—
309C4×Dic13C22×C412yes—
310C4×Dic13C22×C412yes—
311C4×Dic13C22×C411yescharacteristic
312C4×Dic13C22×C414yes—
313C4×Dic13C22×C412yes—
314C4×Dic13C22×C412yes—
315C4×Dic13C22×C411yescharacteristic
316C4×Dic13C22×C412yes—
317C4×Dic13C22×C411yescharacteristic
318C4×Dic13C22×C414yes—
319C4×Dic13C22×C412yes—
320C2×#557—131no—
321#2371—134no—
322#2370—132no—
323#2365—132no—
324#2365—131no—
325#2356—132no—
326#2356—132no—
327#2355—131no—
328#2355—131no—
329#2336—134no—
330#2327—132no—
331C4×C4⋊Q8—131no—
332C4×#125—132no—
333#2295—131no—
334#2295—132no—
335#2276—132no—
336C42×Q8—131no—
337C22×D13C2511yescharacteristic
338C2×#261—21no—
339C2×#261—21no—
340C2×#261—21no—
341C2×#261—21no—
342C2×#261—22no—
343C2×#261—21no—
344C2×#261—21no—
345C2×#261—22no—
346C2×#261—22no—
347C2×#261—24no—
348C2×#261—22no—
349C2×#261—21no—
350C2×#261—22no—
351C2×#261—22no—
352C2×#261—22no—
353C2×#261—21no—
354C2×#261—24no—
355C2×#261—22no—
356C2×#261—22no—
357C2×#261—22no—
358C2×#261—24no—
359C2×#261—22no—
360C2×#261—21no—
361C2×#261C2×#4112yes—
362C2×#261C2×#4114yes—
363C2×#261C2×#4112yes—
364C2×#2612−1+412yes—
365Q8×C13—22no—
366Q8×C13—24no—
367Q8×C13—22no—
368C2×C4×C13C23×C412yes—
369C2×C4×C13C23×C412yes—
370C2×C4×C13C23×C411yescharacteristic
371C2×C4×C13C23×C412yes—
372C2×C4×C13C23×C414yes—
373C2×C4×C13C23×C412yes—
374C2×C4×C13C23×C411yescharacteristic
375C2×C4×C13C23×C411yescharacteristic
376C2×Dic13C23×C412yes—
377C2×Dic13C23×C412yes—
378C2×Dic13C23×C411yescharacteristic
379C2×Dic13C23×C412yes—
380C2×Dic13C23×C414yes—
381C2×Dic13C23×C412yes—
382C2×Dic13C23×C411yescharacteristic
383C2×Dic13C23×C411yescharacteristic
384C4×D13—24no—
385C4×D13—22no—
386C4×D13—22no—
387C4×D13—24no—
388C4×D13—22no—
389C4×D13—21no—
390C4×D13—22no—
391C4×D13—22no—
392C4×D13—22no—
393C4×D13—22no—
394C4×D13—22no—
395C4×D13—21no—
396C4×D13C2×#4112yes—
397C4×D13C2×#4112yes—
398C4×D132−1+412yes—
399C4×D132−1+412yes—
400Dic26—22no—
401Dic26—24no—
402Dic26—22no—
403Dic26—24no—
404Dic26—28no—
405Dic26—24no—
406#557—132no—
407#557—131no—
408#557—134no—
409#557—132no—
410#557—132no—
411#557—131no—
412#557—132no—
413#557—131no—
414#557#26111yescharacteristic, complemented
415C2×C4⋊Q8—131no—
416C2×C4⋊Q8—132no—
417C2×#125—132no—
418C2×#125—134no—
419C2×C4×Q8—131no—
420C2×C4×Q8—131no—
421C2×C4×Q8—132no—
422C2×C4×Q8—132no—
423C2×C4×Q8—132no—
424C2×C4×Q8—131no—
425C2×C4×Q8—131no—
426C2×C4×Q8—132no—
427#391—132no—
428#391—132no—
429#391—132no—
430#391—132no—
431#391—131no—
432#391—131no—
433#389—131no—
434#389—132no—
435#389—132no—
436#389—134no—
437#389—132no—
438#389—131no—
439#387—134no—
440#387—134no—
441#387—134no—
442#387—134no—
443#387—134no—
444#387—132no—
445#387—134no—
446#387—134no—
447#387—134no—
448#387—134no—
449#387—134no—
450#387—134no—
451#387—132no—
452#384—131no—
453#383—134no—
454#382—132no—
455#382—132no—
456C4×C4⋊C4—134no—
457C4×C4⋊C4—132no—
458C4×C4⋊C4—132no—
459C4×C4⋊C4—134no—
460C4×C4⋊C4—132no—
461C4×C4⋊C4—132no—
462C4×C4⋊C4—132no—
463C4×C4⋊C4—134no—
464C4×C4⋊C4—132no—
465C4×C4⋊C4—131no—
466C4×C4⋊C4—132no—
467C4×C4⋊C4—131no—
468C4×C4⋊C4—132no—
469C4×C4⋊C4—131no—
470C4×C4⋊C4—132no—
471C4×C4⋊C4—132no—
472C4×C4⋊C4—134no—
473C4×C4⋊C4—132no—
474C4×C4⋊C4—131no—
475#376—132no—
476#376—134no—
477#376—134no—
478C43—132no—
479C43—131no—
480C22×C13C24×C411yescharacteristic
481C2×D13C22×#4111yescharacteristic
482C2×D13C22×#4111yescharacteristic
483C2×D13C2×2−1+411yescharacteristic
484C2×D13C2×2−1+411yescharacteristic
485C2×D13C2×2−1+411yescharacteristic
486C2×D13#58511yescharacteristic
487#261—22no—
488#261—22no—
489#261—24no—
490#261—22no—
491#261—44no—
492#261—42no—
493#261—41no—
494#261—42no—
495#261—42no—
496C4×C13—24no—
497C4×C13—22no—
498C4×C13—22no—
499C4×C13—22no—
500C4×C13—21no—
501C4×C13—22no—
502C4×C13C4×#4112yes—
503C4×C13#51912yes—
504Dic13—24no—
505Dic13—22no—
506Dic13—22no—
507Dic13—22no—
508Dic13—21no—
509Dic13—22no—
510Dic13C4×#4112yes—
511Dic13#51912yes—
512C22×Q8—131no—
513C22×Q8—132no—
514C22×Q8—131no—
515C4⋊Q8—132no—
516C4⋊Q8—132no—
517C4⋊Q8—132no—
518C4⋊Q8—132no—
519C4⋊Q8—134no—
520C4⋊Q8—132no—
521C4⋊Q8—134no—
522C4⋊Q8—131no—
523C4⋊Q8—132no—
524C4⋊Q8C2×#26111yescharacteristic
525C4⋊Q8C2×#26112yes—
526#125—134no—
527#125—134no—
528#125—134no—
529#125—134no—
530#125—134no—
531#125—134no—
532#125—132no—
533#125—134no—
534#125—132no—
535#125—134no—
536#125—132no—
537#125—134no—
538#125C2×#26112yes—
539#125C2×#26114yes—
540C4×Q8—132no—
541C4×Q8—131no—
542C4×Q8—132no—
543C4×Q8—131no—
544C4×Q8—134no—
545C4×Q8—132no—
546C4×Q8—132no—
547C4×Q8—134no—
548C4×Q8—131no—
549C4×Q8—132no—
550C4×Q8—132no—
551C4×Q8—131no—
552C4×Q8—134no—
553C4×Q8—132no—
554C4×Q8—131no—
555C4×Q8—132no—
556C4×Q8—132no—
557C4×Q8—134no—
558C4×Q8—132no—
559C4×Q8—131no—
560C4×Q8—268no—
561C4×Q8—264no—
562C4×Q8—264no—
563C4×Q8—268no—
564C4×Q8C2×#26112yes—
565C4×Q8C2×#26111yescharacteristic
566C4×Q8C2×#26112yes—
567C4×Q8C2×#26111yescharacteristic
568C2×C4⋊C4—131no—
569C2×C4⋊C4—131no—
570C2×C4⋊C4—132no—
571C2×C4⋊C4—134no—
572C2×C4⋊C4—131no—
573C2×C4⋊C4—132no—
574C2×C4⋊C4—132no—
575C2×C4⋊C4—134no—
576C2×C4⋊C4—134no—
577C2×C4⋊C4—132no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—132no—
580C2×C4⋊C4—132no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—132no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—131no—
585C2×C4⋊C4—132no—
586C2×C4⋊C4—132no—
587C2×C4⋊C4—131no—
588C2×C4⋊C4—132no—
589C2×C4⋊C4—132no—
590C2×C42—131no—
591C2×C42—132no—
592C2×C42—134no—
593C2×C42—131no—
594C2×C42—132no—
595C2×C42—132no—
596C2×C42—131no—
597C2×C42—132no—
598C2×C42—134no—
599C2×C42—134no—
600C2×C42—132no—
601C2×C42—131no—
602C2×C42—132no—
603C2×C42—131no—
604C2×C42—131no—
605C2×C42—132no—
606C2×C42—132no—
607C2×C42—131no—
608C2×C42—134no—
609C2×C42—134no—
610#95—132no—
611#95—132no—
612#95—132no—
613#95—134no—
614#95—132no—
615#95—132no—
616#95—132no—
617#95—134no—
618#95—134no—
619#95—134no—
620#95—134no—
621#95—132no—
622#95—132no—
623#95—134no—
624#95—134no—
625#95—132no—
626#95—134no—
627#95—134no—
628#95—132no—
629#95—134no—
630C2×C13C2×C4×#4111yescharacteristic
631C2×C13C2×#51911yescharacteristic
632C2×C13C4×2−1+411yescharacteristic
633D13#350711yescharacteristic
634D13#350911yescharacteristic
635D13#351511yescharacteristic
636D13#352311yescharacteristic
637C2×Q8—132no—
638C2×Q8—131no—
639C2×Q8—132no—
640C2×Q8—134no—
641C2×Q8—131no—
642C2×Q8—132no—
643C2×Q8—264no—
644C2×Q8—262no—
645C2×Q8—262no—
646C2×Q8—264no—
647C2×Q8—262no—
648C2×Q8—262no—
649C2×Q8C22×#26111yescharacteristic
650C2×Q8C22×#26111yescharacteristic
651C2×Q8C22×#26112yes—
652C22×C4—131no—
653C22×C4—131no—
654C22×C4—131no—
655C22×C4—131no—
656C22×C4—131no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—131no—
661C22×C4—132no—
662C22×C4—134no—
663C22×C4—132no—
664C22×C4—132no—
665C22×C4—132no—
666C22×C4—131no—
667C22×C4—132no—
668C22×C4—134no—
669C4⋊C4—134no—
670C4⋊C4—132no—
671C4⋊C4—131no—
672C4⋊C4—132no—
673C4⋊C4—132no—
674C4⋊C4—134no—
675C4⋊C4—132no—
676C4⋊C4—132no—
677C4⋊C4—132no—
678C4⋊C4—134no—
679C4⋊C4—132no—
680C4⋊C4—134no—
681C4⋊C4—132no—
682C4⋊C4—131no—
683C4⋊C4—134no—
684C4⋊C4—134no—
685C4⋊C4—134no—
686C4⋊C4—134no—
687C4⋊C4—132no—
688C4⋊C4—134no—
689C4⋊C4—134no—
690C4⋊C4—134no—
691C4⋊C4—134no—
692C4⋊C4—132no—
693C4⋊C4—262no—
694C4⋊C4—264no—
695C4⋊C4—264no—
696C4⋊C4—268no—
697C4⋊C4—264no—
698C4⋊C4—268no—
699C4⋊C4—262no—
700C4⋊C4—262no—
701C4⋊C4—264no—
702C4⋊C4—264no—
703C4⋊C4—522no—
704C4⋊C4—522no—
705C4⋊C4C22×#26111yescharacteristic
706C4⋊C4C22×#26112yes—
707C4⋊C4C22×#26114yes—
708C4⋊C4C22×#26112yes—
709C4⋊C4C22×#26111yescharacteristic
710C4⋊C4C22×#26114yes—
711C4⋊C4C22×#26112yes—
712C4⋊C4C22×#26114yes—
713C4⋊C4C22×#26112yes—
714C42—134no—
715C42—132no—
716C42—132no—
717C42—134no—
718C42—134no—
719C42—132no—
720C42—134no—
721C42—131no—
722C42—131no—
723C42—132no—
724C42—132no—
725C42—131no—
726C42—132no—
727C42—262no—
728C42—264no—
729C42—268no—
730C42—264no—
731C42—264no—
732C42—268no—
733C42—262no—
734C42—264no—
735C42—262no—
736C42—262no—
737C42—264no—
738C42—522no—
739C42—524no—
740C42—524no—
741C42—521no—
742C42C22×#26114yes—
743C42C22×#26112yes—
744C42C22×#26112yes—
745C42C22×#26111yescharacteristic
746C13#3432811yescharacteristic, complemented, Sylow
747C23—131no—
748Q8—22no—
749Q8—24no—
750Q8—22no—
751Q8—264no—
752Q8—268no—
753Q8—264no—
754Q8—262no—
755Q8—262no—
756Q8—264no—
757C2×C4—131no—
758C2×C4—131no—
759C2×C4—132no—
760C2×C4—132no—
761C2×C4—132no—
762C2×C4—132no—
763C2×C4—132no—
764C2×C4—132no—
765C2×C4—134no—
766C2×C4—132no—
767C2×C4—132no—
768C2×C4—132no—
769C2×C4—131no—
770C2×C4—132no—
771C2×C4—132no—
772C2×C4—134no—
773C2×C4—262no—
774C2×C4—264no—
775C2×C4—264no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—261no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—261no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—261no—
786C2×C4—261no—
787C2×C4—261no—
788C2×C4—262no—
789C2×C4—261no—
790C2×C4—261no—
791C2×C4—262no—
792C2×C4—261no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—261no—
796C2×C4—262no—
797C2×C4—264no—
798C2×C4—262no—
799C2×C4—261no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—264no—
803C2×C4—261no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4—264no—
807C2×C4—262no—
808C2×C4C23×#26112yes—
809C2×C4C23×#26112yes—
810C2×C4C23×#26111yescharacteristic
811C2×C4C23×#26112yes—
812C2×C4C23×#26112yes—
813C2×C4C23×#26114yes—
814C2×C4C23×#26111yescharacteristic
815C2×C4C23×#26111yescharacteristic
816C22—131no—
817C22—131no—
818C22—131no—
819C22—131no—
820C22—131no—
821C22—131no—
822C22C24×#26111yescharacteristic
823C4—22no—
824C4—24no—
825C4—22no—
826C4—22no—
827C4—21no—
828C4—22no—
829C4—132no—
830C4—132no—
831C4—264no—
832C4—262no—
833C4—262no—
834C4—262no—
835C4—262no—
836C4—264no—
837C4—262no—
838C4—262no—
839C4—261no—
840C4—262no—
841C4—521no—
842C4—522no—
843C4—524no—
844C4—522no—
845C4—522no—
846C4#1171962712yes—
847C4#41×#26112yes—
848C2—131no—
849C2—131no—
850C2—131no—
851C2—131no—
852C2C2×#41×#26111yescharacteristic
853C2C2×#1171962711yescharacteristic
854C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#557C4
prime radical, cosocleC22×D13C25
hypercenter#557#261
hypocenterC13#34328
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
22. C13×#557C4semidirect
25. #11719426C4semidirect
26. #11719426C4semidirect
29. #11719390C4semidirect
30. #11719390C4semidirect
35. #11719275C4semidirect
36. #11719274C4semidirect
37. #11719272C4semidirect
38. #11719272C4semidirect
414. #557#261semidirect
746. C13#34328semidirect

Maximal subgroups

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

subgroupindex
#131313712
#131313702
#131313652
#131313562
#131313552
#131313362
#131313272
C4⋊Q8×#2612
#125×#2612
#131312952
#131312762
C4×Q8×#2612
D13×#5572
#3432813