Finite Group Databasebeta

← #16807950

Subgroups — #16807950

Order 3328.

1940 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131382C214yesmaximal
2#13131370C212yesmaximal
3#13131365C211yesmaximal, characteristic
4#13131365C212yesmaximal
5#13131355C211yesmaximal, characteristic
6#13131355C212yesmaximal
7#13131351C212yesmaximal
8Q8×C4⋊#261C211yesmaximal, characteristic
9#13131336C214yesmaximal
10#13131330C212yesmaximal
11#13131327C212yesmaximal
12#13131320C212yesmaximal
13#13131320C212yesmaximal
14C4⋊Q8×#261C211yesmaximal, characteristic
15#13131295C211yesmaximal, characteristic
16#13131295C211yesmaximal, characteristic
17D13×#557C211yesmaximal, characteristic
18C2×Q8×#261C2212yes—
19C2×Q8×#261C2212yes—
20C2×Q8×#261C2212yes—
21C13×#557C411yescharacteristic, complemented
22D13×C4⋊Q8C2211yescharacteristic
23D13×C4⋊Q8C2212yes—
24#11719426C411yescharacteristic, complemented
25#11719426C412yescomplemented
26D13×#125C2212yes—
27D13×#125C2214yes—
28#11719390C412yescomplemented
29#11719390C414yescomplemented
30C4×Q8×D13C2211yescharacteristic
31C4×Q8×D13C2211yescharacteristic
32C4×Q8×D13C2212yes—
33C4×Q8×D13C2212yes—
34#11719275C411yescharacteristic, complemented
35#11719274C412yescomplemented
36#11719272C411yescharacteristic, complemented
37#11719272C412yescomplemented
38(C2×#261)⋊Q8C2211yescharacteristic
39(C2×#261)⋊Q8C2211yescharacteristic
40(C2×#261)⋊Q8C2211yescharacteristic
41(C2×#261)⋊Q8C2211yescharacteristic
42(C2×#261)⋊Q8C2212yes—
43(C2×#261)⋊Q8C2212yes—
44(C2×#261)⋊Q8C2212yes—
45#11719083C2211yescharacteristic
46#11719083C2211yescharacteristic
47#11719083C2211yescharacteristic
48#11719083C2211yescharacteristic
49#11719083C2212yes—
50#11719083C2212yes—
51#11719083C2212yes—
52#11719083C2212yes—
53#11719083C2214yes—
54#11719083C2214yes—
55#11719083C2214yes—
56#11719083C2214yes—
57#11719082C2212yes—
58#11719082C2212yes—
59#11719082C2212yes—
60#11719082C2212yes—
61#11719082C2214yes—
62#11719082C2214yes—
63#11719082C2214yes—
64#11719082C2214yes—
65#11719082C2214yes—
66#11719082C2214yes—
67#11719082C2214yes—
68#11719082C2214yes—
69#11719082C2214yes—
70#11719082C2214yes—
71C4⋊C4×#261C2212yes—
72C4⋊C4×#261C2212yes—
73C4⋊C4×#261C2212yes—
74C4⋊C4×#261C2212yes—
75C4⋊C4×#261C2214yes—
76#11719061C2214yes—
77#11719060C2214yes—
78#11719060C2214yes—
79#11719060C2212yes—
80#11719059C2211yescharacteristic
81#11719059C2212yes—
82C4×C4⋊#261C2211yescharacteristic
83C4×C4⋊#261C2212yes—
84C4×C4⋊#261C2211yescharacteristic
85C4×C4⋊#261C2212yes—
86C4×C4⋊#261C2212yes—
87C4×C4⋊#261C2212yes—
88C4×C4⋊#261C2214yes—
89#11719057C2212yes—
90#11719057C2212yes—
91C42×#261C2211yescharacteristic
92C2×Q8×D13C2312yes—
93C2×Q8×D13C2311yescharacteristic
94C2×Q8×D13C2311yescharacteristic
95Q8×#261—44no—
96Q8×#261—44no—
97Q8×#261—44no—
98C2×C4⋊#261C2312yes—
99C2×C4⋊#261C2311yescharacteristic
100C2×C4⋊#261C2311yescharacteristic
101C2×C4⋊#261C2311yescharacteristic
102C2×C4⋊#261C2312yes—
103C2×C4⋊#261C2312yes—
104C2×C4⋊#261C2311yescharacteristic
105C2×C4⋊#261C2312yes—
106C2×C4⋊#261C2314yes—
107C2×C4⋊#261C2312yes—
108C2×C4⋊#261C2312yes—
109C2×C4⋊#261C2312yes—
110C2×C4⋊#261C2314yes—
111C2×C4⋊#261C2314yes—
112C2×C4⋊#261C2314yes—
113C2×C4×#261C2311yescharacteristic
114C2×C4×#261C2311yescharacteristic
115C2×C4×#261C2311yescharacteristic
116C2×C4×#261C2311yescharacteristic
117C2×C4×#261C2311yescharacteristic
118C2×C4×#261C2312yes—
119C2×C4×#261C2312yes—
120C2×C4×#261C2311yescharacteristic
121C2×C4×#261C2314yes—
122C2×C4×#261C2314yes—
123C2×C4×#261C2314yes—
124C2×C4×#261C2314yes—
125C13×C4⋊Q8C2×C411yescharacteristic
126C13×C4⋊Q8C2×C412yes—
127C13×#125C2×C412yes—
128C13×#125C2×C414yes—
129C4×Q8×C13C2×C411yescharacteristic
130C4×Q8×C13C2×C412yes—
131C4×Q8×C13C2×C412yes—
132C4×Q8×C13C2×C411yescharacteristic
133Q8×Dic13C2×C411yescharacteristic
134Q8×Dic13C2×C412yes—
135Q8×Dic13C2×C411yescharacteristic
136Q8×Dic13C2×C412yes—
137#88198C2×C412yes—
138#88198C2×C412yes—
139#88198C2×C412yes—
140C4⋊C4×D13C2312yes—
141C4⋊C4×D13C2314yes—
142C4⋊C4×D13C2312yes—
143C4⋊C4×D13C2314yes—
144C4⋊C4×D13C2311yescharacteristic
145C4⋊C4×D13C2311yescharacteristic
146C4⋊C4×D13C2312yes—
147C4⋊C4×D13C2312yes—
148C4⋊C4×D13C2314yes—
149#88144C2×C412yes—
150#88144C2×C414yes—
151#88144C2×C412yes—
152#88144C2×C414yes—
153#88143C2×C414yes—
154#88143C2×C414yes—
155#88143C2×C414yes—
156#88143C2×C414yes—
157#88143C2×C414yes—
158#88143C2×C414yes—
159#88142C2×C412yes—
160#88142C2×C414yes—
161#88142C2×C412yes—
162#88142C2×C414yes—
163#88141C2×C414yes—
164#88141C2×C412yes—
165#88141C2×C411yescharacteristic
166#88141C2×C412yes—
167#88141C2×C412yes—
168#88141C2×C414yes—
169#88141C2×C412yes—
170#88141C2×C411yescharacteristic
171C42×D13C2311yescharacteristic
172C42×D13C2312yes—
173C42×D13C2312yes—
174C42×D13C2314yes—
175#88124C2×C412yes—
176#88124C2×C414yes—
177#88123C2×C411yescharacteristic
178#88123C2×C412yes—
179C4×Dic26C2×C411yescharacteristic
180C4×Dic26C2×C412yes—
181C4×Dic26C2×C411yescharacteristic
182C4×Dic26C2×C412yes—
183C4×Dic26C2×C412yes—
184C4×Dic26C2×C414yes—
185C4×Dic26C2×C412yes—
186C4×Dic26C2×C414yes—
187(C2×#261)⋊C4C2312yes—
188(C2×#261)⋊C4C2312yes—
189(C2×#261)⋊C4C2312yes—
190(C2×#261)⋊C4C2312yes—
191(C2×#261)⋊C4C2312yes—
192(C2×#261)⋊C4C2312yes—
193(C2×#261)⋊C4C2312yes—
194(C2×#261)⋊C4C2312yes—
195(C2×#261)⋊C4C2312yes—
196(C2×#261)⋊C4C2312yes—
197(C2×#261)⋊C4C2314yes—
198(C2×#261)⋊C4C2314yes—
199(C2×#261)⋊C4C2314yes—
200(C2×#261)⋊C4C2312yes—
201(C2×#261)⋊C4C2312yes—
202(C2×#261)⋊C4C2312yes—
203(C2×#261)⋊C4C2312yes—
204(C2×#261)⋊C4C2314yes—
205(C2×#261)⋊C4C2314yes—
206(C2×#261)⋊C4C2314yes—
207(C2×#261)⋊C4C2314yes—
208(C2×#261)⋊C4C2314yes—
209#34488—131nomaximal, Sylow
210C22×#261C2411yescharacteristic
211C22×#261C2411yescharacteristic
212C22×#261C2412yes—
213C22×#261C2412yes—
214C22×#261C2412yes—
215C22×#261C2412yes—
216C22×#261C2411yescharacteristic
217C22×#261C2414yes—
218C22×#261C2411yescharacteristic
219C2×Q8×C13C22×C412yes—
220C2×Q8×C13C22×C411yescharacteristic
221C2×Q8×C13C22×C411yescharacteristic
222Q8×D13—24no—
223Q8×D13—22no—
224Q8×D13—22no—
225Q8×D13—22no—
226Q8×D13—24no—
227Q8×D13—22no—
228C2×C4×D13C2412yes—
229C2×C4×D13C2412yes—
230C2×C4×D13C2411yescharacteristic
231C2×C4×D13C2412yes—
232C2×C4×D13C2412yes—
233C2×C4×D13C2414yes—
234C2×C4×D13C2411yescharacteristic
235C2×C4×D13C2411yescharacteristic
236C2×Dic26C22×C411yescharacteristic
237C2×Dic26C22×C412yes—
238C2×Dic26C22×C411yescharacteristic
239C2×Dic26C22×C412yes—
240C2×Dic26C22×C412yes—
241C2×Dic26C22×C414yes—
242C4⋊#261—24no—
243C4⋊#261—24no—
244C4⋊#261—24no—
245C4⋊#261—22no—
246C4⋊#261—22no—
247C4⋊#261—22no—
248C4⋊#261—24no—
249C4⋊#261—22no—
250C4⋊#261—42no—
251C4⋊#261—42no—
252C4⋊#261—42no—
253C4⋊#261—44no—
254C4⋊#261—44no—
255C4⋊#261—44no—
256C4⋊#261—44no—
257C4×#261—22no—
258C4×#261—22no—
259C4×#261—24no—
260C4×#261—22no—
261C4×#261—24no—
262C4×#261—22no—
263C4×#261—22no—
264C4×#261—44no—
265C4×#261—41no—
266C4×#261—44no—
267C4×#261—44no—
268C4×#261—44no—
269C13×C4⋊C4C22×C411yescharacteristic
270C13×C4⋊C4C22×C414yes—
271C13×C4⋊C4C22×C412yes—
272C13×C4⋊C4C22×C412yes—
273C13×C4⋊C4C22×C414yes—
274C13×C4⋊C4C22×C412yes—
275C13×C4⋊C4C22×C411yescharacteristic
276C13×C4⋊C4C22×C412yes—
277C13×C4⋊C4C22×C414yes—
278C42×C13C22×C412yes—
279C42×C13C22×C411yescharacteristic
280C42×C13C22×C414yes—
281C42×C13C22×C412yes—
282C4⋊Dic13C22×C411yescharacteristic
283C4⋊Dic13C22×C414yes—
284C4⋊Dic13C22×C412yes—
285C4⋊Dic13C22×C412yes—
286C4⋊Dic13C22×C411yescharacteristic
287C4⋊Dic13C22×C412yes—
288C4⋊Dic13C22×C414yes—
289C4⋊Dic13C22×C412yes—
290C4⋊Dic13C22×C414yes—
291#6101C22×C412yes—
292#6101C22×C412yes—
293#6101C22×C414yes—
294#6101C22×C414yes—
295#6101C22×C414yes—
296#6101C22×C414yes—
297#6101C22×C412yes—
298#6101C22×C412yes—
299#6101C22×C412yes—
300#6101C22×C412yes—
301#6101C22×C414yes—
302#6101C22×C414yes—
303#6101C22×C414yes—
304#6101C22×C414yes—
305C4×Dic13C22×C414yes—
306C4×Dic13C22×C412yes—
307C4×Dic13C22×C412yes—
308C4×Dic13C22×C411yescharacteristic
309C4×Dic13C22×C414yes—
310C4×Dic13C22×C412yes—
311C4×Dic13C22×C412yes—
312C4×Dic13C22×C411yescharacteristic
313C4×Dic13C22×C412yes—
314C4×Dic13C22×C411yescharacteristic
315C4×Dic13C22×C414yes—
316C4×Dic13C22×C412yes—
317C2×#557—131no—
318#2382—134no—
319#2370—132no—
320#2365—132no—
321#2365—131no—
322#2355—132no—
323#2355—131no—
324#2351—132no—
325Q8×C4⋊C4—131no—
326#2336—134no—
327#2330—132no—
328#2327—132no—
329#2320—132no—
330#2320—132no—
331C4×C4⋊Q8—131no—
332#2295—131no—
333#2295—131no—
334C22×D13C2511yescharacteristic
335C2×#261—21no—
336C2×#261—21no—
337C2×#261—22no—
338C2×#261—22no—
339C2×#261—21no—
340C2×#261—22no—
341C2×#261—24no—
342C2×#261—22no—
343C2×#261—21no—
344C2×#261—21no—
345C2×#261—22no—
346C2×#261—21no—
347C2×#261—21no—
348C2×#261—21no—
349C2×#261—21no—
350C2×#261—22no—
351C2×#261—22no—
352C2×#261—22no—
353C2×#261—22no—
354C2×#261—24no—
355C2×#261—22no—
356C2×#261—22no—
357C2×#261—21no—
358C2×#261—24no—
359C2×#261—21no—
360C2×#261—22no—
361C2×#2612−1+412yes—
362Q8×C13—22no—
363Q8×C13—24no—
364Q8×C13—22no—
365C2×C4×C13C23×C412yes—
366C2×C4×C13C23×C412yes—
367C2×C4×C13C23×C411yescharacteristic
368C2×C4×C13C23×C412yes—
369C2×C4×C13C23×C414yes—
370C2×C4×C13C23×C412yes—
371C2×C4×C13C23×C411yescharacteristic
372C2×C4×C13C23×C411yescharacteristic
373C2×Dic13C23×C412yes—
374C2×Dic13C23×C412yes—
375C2×Dic13C23×C411yescharacteristic
376C2×Dic13C23×C412yes—
377C2×Dic13C23×C414yes—
378C2×Dic13C23×C412yes—
379C2×Dic13C23×C411yescharacteristic
380C2×Dic13C23×C411yescharacteristic
381C4×D13—24no—
382C4×D13—22no—
383C4×D13—21no—
384C4×D13—22no—
385C4×D13—22no—
386C4×D13—22no—
387C4×D13—22no—
388C4×D13—22no—
389C4×D13—24no—
390C4×D13—22no—
391C4×D13—21no—
392C4×D13—22no—
393C4×D13H(5,𝔽2)12yes—
394C4×D132−1+412yes—
395C4×D132−1+412yes—
396C4×D132−1+412yes—
397Dic26—22no—
398Dic26—22no—
399Dic26—24no—
400Dic26—24no—
401Dic26—24no—
402Dic26—28no—
403#557—131no—
404#557—132no—
405#557—132no—
406#557—134no—
407#557—131no—
408#557—132no—
409#557—132no—
410#557—131no—
411#557#26111yescharacteristic, complemented
412C2×C4⋊Q8—131no—
413C2×C4⋊Q8—132no—
414C2×#125—132no—
415C2×#125—134no—
416C2×C4×Q8—132no—
417C2×C4×Q8—132no—
418C2×C4×Q8—131no—
419C2×C4×Q8—131no—
420C2×C4×Q8—132no—
421C2×C4×Q8—132no—
422C2×C4×Q8—132no—
423#391—132no—
424#391—131no—
425#391—132no—
426#391—132no—
427#391—131no—
428#391—131no—
429#391—131no—
430#389—132no—
431#389—132no—
432#389—131no—
433#389—132no—
434#389—132no—
435#389—131no—
436#389—134no—
437#389—134no—
438#389—134no—
439#389—134no—
440#389—131no—
441#389—131no—
442#387—134no—
443#387—134no—
444#387—134no—
445#387—134no—
446#387—134no—
447#387—134no—
448#387—134no—
449#387—132no—
450#387—132no—
451#387—134no—
452#387—134no—
453#387—134no—
454#387—132no—
455#387—132no—
456#384—131no—
457#384—132no—
458#383—134no—
459#382—134no—
460#382—134no—
461#382—132no—
462C4×C4⋊C4—132no—
463C4×C4⋊C4—132no—
464C4×C4⋊C4—132no—
465C4×C4⋊C4—132no—
466C4×C4⋊C4—132no—
467C4×C4⋊C4—132no—
468C4×C4⋊C4—134no—
469C4×C4⋊C4—134no—
470C4×C4⋊C4—131no—
471C4×C4⋊C4—132no—
472C4×C4⋊C4—131no—
473C4×C4⋊C4—132no—
474#376—132no—
475#376—132no—
476C43—131no—
477C22×C13C24×C411yescharacteristic
478C2×D13C2×H(5,𝔽2)11yescharacteristic
479C2×D13C2×2−1+411yescharacteristic
480C2×D13C2×2−1+411yescharacteristic
481C2×D13C2×2−1+411yescharacteristic
482C2×D13C2×2−1+411yescharacteristic
483C2×D13#58511yescharacteristic
484#261—22no—
485#261—42no—
486#261—42no—
487#261—42no—
488#261—41no—
489#261—44no—
490#261—41no—
491#261—42no—
492#261—41no—
493C4×C13—22no—
494C4×C13—24no—
495C4×C13—22no—
496C4×C13—21no—
497C4×C13—22no—
498C4×C13—22no—
499C4×C13#51912yes—
500C4×C13#52012yes—
501Dic13—22no—
502Dic13—24no—
503Dic13—22no—
504Dic13—21no—
505Dic13—22no—
506Dic13—22no—
507Dic13#51912yes—
508Dic13#52012yes—
509C22×Q8—132no—
510C22×Q8—131no—
511C22×Q8—131no—
512C4⋊Q8—132no—
513C4⋊Q8—132no—
514C4⋊Q8—132no—
515C4⋊Q8—132no—
516C4⋊Q8—134no—
517C4⋊Q8—132no—
518C4⋊Q8—134no—
519C4⋊Q8—131no—
520C4⋊Q8—132no—
521C4⋊Q8C2×#26111yescharacteristic
522C4⋊Q8C2×#26112yes—
523#125—134no—
524#125—134no—
525#125—134no—
526#125—134no—
527#125—134no—
528#125—134no—
529#125—132no—
530#125—134no—
531#125—132no—
532#125—134no—
533#125—132no—
534#125—134no—
535#125C2×#26112yes—
536#125C2×#26114yes—
537C4×Q8—132no—
538C4×Q8—132no—
539C4×Q8—131no—
540C4×Q8—131no—
541C4×Q8—134no—
542C4×Q8—132no—
543C4×Q8—134no—
544C4×Q8—132no—
545C4×Q8—132no—
546C4×Q8—131no—
547C4×Q8—132no—
548C4×Q8—131no—
549C4×Q8—134no—
550C4×Q8—132no—
551C4×Q8—132no—
552C4×Q8—131no—
553C4×Q8—134no—
554C4×Q8—132no—
555C4×Q8—132no—
556C4×Q8—131no—
557C4×Q8—524no—
558C4×Q8—524no—
559C4×Q8—524no—
560C4×Q8C2×#26112yes—
561C4×Q8C2×#26112yes—
562C4×Q8C2×#26111yescharacteristic
563C4×Q8C2×#26111yescharacteristic
564C2×C4⋊C4—131no—
565C2×C4⋊C4—131no—
566C2×C4⋊C4—132no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—132no—
569C2×C4⋊C4—132no—
570C2×C4⋊C4—134no—
571C2×C4⋊C4—134no—
572C2×C4⋊C4—132no—
573C2×C4⋊C4—131no—
574C2×C4⋊C4—132no—
575C2×C4⋊C4—132no—
576C2×C4⋊C4—131no—
577C2×C4⋊C4—132no—
578C2×C4⋊C4—132no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—131no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—132no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—132no—
587C2×C4⋊C4—132no—
588C2×C42—132no—
589C2×C42—134no—
590C2×C42—131no—
591C2×C42—132no—
592C2×C42—131no—
593C2×C42—132no—
594C2×C42—131no—
595C2×C42—131no—
596C2×C42—131no—
597C2×C42—131no—
598C2×C42—132no—
599C2×C42—134no—
600C2×C42—134no—
601C2×C42—134no—
602C2×C42—131no—
603C2×C42—134no—
604#95—132no—
605#95—132no—
606#95—132no—
607#95—132no—
608#95—132no—
609#95—132no—
610#95—132no—
611#95—132no—
612#95—132no—
613#95—132no—
614#95—134no—
615#95—132no—
616#95—134no—
617#95—134no—
618#95—134no—
619#95—134no—
620#95—134no—
621#95—134no—
622#95—134no—
623#95—132no—
624#95—132no—
625#95—132no—
626C2×C13C2×#51911yescharacteristic
627C2×C13C2×#52011yescharacteristic
628C2×C13C4×2−1+411yescharacteristic
629D13#355211yescharacteristic
630D13#355411yescharacteristic
631D13#355511yescharacteristic
632D13#355611yescharacteristic
633C2×Q8—132no—
634C2×Q8—131no—
635C2×Q8—134no—
636C2×Q8—132no—
637C2×Q8—132no—
638C2×Q8—131no—
639C2×Q8—264no—
640C2×Q8—262no—
641C2×Q8—262no—
642C2×Q8—262no—
643C2×Q8—264no—
644C2×Q8—262no—
645C2×Q8C22×#26111yescharacteristic
646C2×Q8C22×#26112yes—
647C2×Q8C22×#26111yescharacteristic
648C22×C4—131no—
649C22×C4—131no—
650C22×C4—131no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—131no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—134no—
657C22×C4—131no—
658C22×C4—131no—
659C22×C4—132no—
660C22×C4—132no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—131no—
664C22×C4—134no—
665C4⋊C4—132no—
666C4⋊C4—131no—
667C4⋊C4—132no—
668C4⋊C4—134no—
669C4⋊C4—132no—
670C4⋊C4—132no—
671C4⋊C4—132no—
672C4⋊C4—134no—
673C4⋊C4—132no—
674C4⋊C4—134no—
675C4⋊C4—132no—
676C4⋊C4—132no—
677C4⋊C4—131no—
678C4⋊C4—134no—
679C4⋊C4—134no—
680C4⋊C4—134no—
681C4⋊C4—134no—
682C4⋊C4—132no—
683C4⋊C4—134no—
684C4⋊C4—134no—
685C4⋊C4—134no—
686C4⋊C4—134no—
687C4⋊C4—132no—
688C4⋊C4—262no—
689C4⋊C4—264no—
690C4⋊C4—262no—
691C4⋊C4—264no—
692C4⋊C4—262no—
693C4⋊C4—262no—
694C4⋊C4—264no—
695C4⋊C4—264no—
696C4⋊C4—524no—
697C4⋊C4—524no—
698C4⋊C4—524no—
699C4⋊C4—522no—
700C4⋊C4—522no—
701C4⋊C4—522no—
702C4⋊C4—524no—
703C4⋊C4C22×#26111yescharacteristic
704C4⋊C4C22×#26114yes—
705C4⋊C4C22×#26112yes—
706C4⋊C4C22×#26112yes—
707C4⋊C4C22×#26111yescharacteristic
708C4⋊C4C22×#26114yes—
709C4⋊C4C22×#26112yes—
710C4⋊C4C22×#26114yes—
711C4⋊C4C22×#26112yes—
712C42—132no—
713C42—132no—
714C42—134no—
715C42—134no—
716C42—132no—
717C42—134no—
718C42—131no—
719C42—131no—
720C42—132no—
721C42—132no—
722C42—131no—
723C42—132no—
724C42—262no—
725C42—264no—
726C42—262no—
727C42—264no—
728C42—262no—
729C42—262no—
730C42—262no—
731C42—524no—
732C42—524no—
733C42—524no—
734C42—524no—
735C42—521no—
736C42C22×#26114yes—
737C42C22×#26112yes—
738C42C22×#26112yes—
739C42C22×#26111yescharacteristic
740C13#3448811yescharacteristic, complemented, Sylow
741C23—131no—
742Q8—22no—
743Q8—24no—
744Q8—22no—
745Q8—264no—
746Q8—268no—
747Q8—264no—
748Q8—262no—
749Q8—264no—
750Q8—262no—
751C2×C4—131no—
752C2×C4—131no—
753C2×C4—132no—
754C2×C4—132no—
755C2×C4—132no—
756C2×C4—132no—
757C2×C4—132no—
758C2×C4—132no—
759C2×C4—132no—
760C2×C4—131no—
761C2×C4—132no—
762C2×C4—132no—
763C2×C4—134no—
764C2×C4—261no—
765C2×C4—264no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—261no—
769C2×C4—262no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—264no—
776C2×C4—261no—
777C2×C4—261no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—261no—
781C2×C4—261no—
782C2×C4—261no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—261no—
786C2×C4—261no—
787C2×C4—261no—
788C2×C4—261no—
789C2×C4—262no—
790C2×C4—264no—
791C2×C4—262no—
792C2×C4—261no—
793C2×C4—261no—
794C2×C4—264no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—264no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4C23×#26112yes—
803C2×C4C23×#26112yes—
804C2×C4C23×#26111yescharacteristic
805C2×C4C23×#26112yes—
806C2×C4C23×#26112yes—
807C2×C4C23×#26114yes—
808C2×C4C23×#26111yescharacteristic
809C2×C4C23×#26111yescharacteristic
810C22—131no—
811C22—131no—
812C22—131no—
813C22—131no—
814C22—131no—
815C22—131no—
816C22C24×#26111yescharacteristic
817C4—22no—
818C4—24no—
819C4—22no—
820C4—21no—
821C4—22no—
822C4—22no—
823C4—132no—
824C4—132no—
825C4—262no—
826C4—262no—
827C4—262no—
828C4—264no—
829C4—262no—
830C4—261no—
831C4—262no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—521no—
836C4—524no—
837C4—521no—
838C4—522no—
839C4—521no—
840C4#1171962712yes—
841C4#1171963112yes—
842C2—131no—
843C2—131no—
844C2—131no—
845C2—131no—
846C2C2×#1171962711yescharacteristic
847C2C2×#1171963111yescharacteristic
848C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#557C4
prime radical, cosocleC22×D13C25
hypercenter#557#261
hypocenterC13#34488
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
21. C13×#557C4semidirect
24. #11719426C4semidirect
25. #11719426C4semidirect
28. #11719390C4semidirect
29. #11719390C4semidirect
34. #11719275C4semidirect
35. #11719274C4semidirect
36. #11719272C4semidirect
37. #11719272C4semidirect
411. #557#261semidirect
740. C13#34488semidirect

Maximal subgroups

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

subgroupindex
#131313822
#131313702
#131313652
#131313552
#131313512
Q8×C4⋊#2612
#131313362
#131313302
#131313272
#131313202
C4⋊Q8×#2612
#131312952
D13×#5572
#3448813