Finite Group Databasebeta

← #16029070

Subgroups — #16029070

Order 3328.

2008 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719377C211yesmaximal, characteristic
2#13118021C211yesmaximal, characteristic, complemented
3#13118021C211yesmaximal, characteristic, complemented
4#13117954C212yesmaximal, complemented
5#13117951C212yesmaximal, complemented
6#13117917C212yesmaximal, complemented
7#13117893C212yesmaximal, complemented
8#13117866C212yesmaximal, complemented
9#13117834C212yesmaximal
10#13117627C212yesmaximal
11#13117612C212yesmaximal, complemented
12#13117609C212yesmaximal, complemented
13#13117579C212yesmaximal, complemented
14#13117567C212yesmaximal, complemented
15#13117515C212yesmaximal, complemented
16#13117391C211yesmaximal, characteristic, complemented
17#13117391C211yesmaximal, characteristic, complemented
18#124×Dic13C211yesmaximal, characteristic
19C13×#2379C211yesmaximal, characteristic
20C2×C13×#124C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C2×#88198C2212yes—
23C2×#88189C2212yes—
24C2×D4×Dic13C2211yescharacteristic
25#11719377C4116yescomplemented
26C2×#88133C2212yes—
27C2×#88133C2212yes—
28C2×#88132C2212yes—
29C2×#88132C2212yes—
30C2×#88131C2212yes—
31C2×#88124C2211yescharacteristic
32C2×#88124C2211yescharacteristic
33C2×C4×Dic26C2212yes—
34C13×#391C2212yes—
35C13×#388C2212yes—
36C13×#388C2212yes—
37C13×#386C2212yes—
38C13×#385C2212yes—
39C13×#385C2212yes—
40C13×#382C2211yescharacteristic
41C13×#382C2211yescharacteristic
42#11718891C2211yescharacteristic
43#11718882C2211yescharacteristic
44#11718871C2212yes—
45C4×C22⋊Dic13C2212yes—
46C4×C22⋊Dic13C2212yes—
47C2×#88071C2212yes—
48#11718639C2212yes—
49#11718639C2212yes—
50#11718639C2212yes—
51C4⋊C4×Dic13C2211yescharacteristic
52C4⋊C4×Dic13C2211yescharacteristic
53C4⋊C4×Dic13C2212yes—
54C4⋊C4×Dic13C2211yescharacteristic
55C4⋊C4×Dic13C2211yescharacteristic
56#11718635C2212yes—
57#11718634C2211yescharacteristic
58#11718634C2211yescharacteristic
59#11718634C2211yescharacteristic
60#11718634C2211yescharacteristic
61#11718633C2212yes—
62#11718633C2212yes—
63#11718633C2212yes—
64#11718612C2212yes—
65#11718612C2212yes—
66#11718607C2212yes—
67#11718607C2212yes—
68#11718606C2212yes—
69#11718606C2212yes—
70#11718606C2212yes—
71#11718606C2212yes—
72#11718605C2212yes—
73#11718605C2212yes—
74#11718603C2212yes—
75C22⋊C4×Dic13C2212yes—
76C22⋊C4×Dic13C2212yes—
77C22⋊C4×Dic13C2212yes—
78C22⋊C4×Dic13C2212yes—
79#11718597C2211yescharacteristic
80#11718594C2212yes—
81C4×#6101C2212yes—
82C4×#6101C2212yes—
83C42×Dic13C2211yescharacteristic
84#11718316C2212yes—
85#11718316C2212yes—
86#11718316C2212yes—
87#11718315C2212yes—
88#11718315C2212yes—
89#11718314C2212yes—
90#11718314C2212yes—
91#11718313C2212yes—
92#11718313C2212yes—
93#11718313C2212yes—
94#11718313C2212yes—
95#11718313C2212yes—
96#11718311C2212yes—
97#11718310C2212yes—
98#11718310C2212yes—
99#11718310C2212yes—
100#11718310C2212yes—
101#11718310C2212yes—
102#11718309C2212yes—
103#11718308C2212yes—
104#11718308C2212yes—
105#11718308C2212yes—
106#11718307C2212yes—
107#11718307C2212yes—
108C22×Q8×C13C2311yescharacteristic
109C22×D4×C13C2311yescharacteristic
110C23×C4×C13C2312yes—
111C23×Dic13C2312yes—
112C23×Dic13C2312yes—
113C22×Dic26C2312yes—
114C13×#124C2×C418yes—
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C4⋊C4C2311yescharacteristic
117C2×C13×C4⋊C4C2311yescharacteristic
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C4⋊C4C2312yes—
120C2×C13×C22⋊C4C2312yes—
121C2×C13×C22⋊C4C2312yes—
122C2×C13×C22⋊C4C2312yes—
123C2×C13×C22⋊C4C2312yes—
124C2×C13×C22⋊C4C2312yes—
125C2×C42×C13C2312yes—
126C2×C42×C13C2311yescharacteristic
127C2×C22⋊Dic13C2312yes—
128C2×C22⋊Dic13C2312yes—
129C2×C22⋊Dic13C2312yes—
130C2×C22⋊Dic13C2312yes—
131C2×C22⋊Dic13C2312yes—
132C2×C22⋊Dic13C2312yes—
133Q8×Dic13—42no—
134#88198C2×C4116yescomplemented
135#88189C2×C4116yes—
136D4×Dic13—42no—
137C2×C4⋊Dic13C2312yes—
138C2×C4⋊Dic13C2311yescharacteristic
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2311yescharacteristic
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4⋊Dic13C2311yescharacteristic
144C2×#6101C2312yes—
145C2×#6101C2312yes—
146C2×#6101C2312yes—
147C2×#6101C2312yes—
148C2×#6101C2312yes—
149C2×#6101C2312yes—
150C2×#6101C2312yes—
151C2×#6101C2312yes—
152C2×#6101C2312yes—
153C2×#6101C2312yes—
154C2×#6101C2312yes—
155C2×#6101C2312yes—
156C2×#6101C2312yes—
157C2×#6101C2312yes—
158C2×C4×Dic13C2312yes—
159C2×C4×Dic13C2311yescharacteristic
160C2×C4×Dic13C2312yes—
161C2×C4×Dic13C2311yescharacteristic
162C2×C4×Dic13C2311yescharacteristic
163C2×C4×Dic13C2312yes—
164C2×C4×Dic13C2312yes—
165C2×C4×Dic13C2312yes—
166C2×C4×Dic13C2312yes—
167C2×C4×Dic13C2312yes—
168C2×C4×Dic13C2312yes—
169C2×C4×Dic13C2312yes—
170C2×C4×Dic13C2311yescharacteristic
171C2×C4×Dic13C2311yescharacteristic
172C2×C4×Dic13C2311yescharacteristic
173C2×C4×Dic13C2312yes—
174#88133C2×C4116yescomplemented
175#88133C2×C4116yescomplemented
176#88132C2×C4116yescomplemented
177#88132C2×C4116yescomplemented
178#88131—44no—
179#88124C2×C418yescomplemented
180#88124C2×C418yescomplemented
181C4×Dic26—44no—
182C13×#95C2312yes—
183C13×#95C2312yes—
184C13×#95C2312yes—
185C13×#95C2312yes—
186C13×#95C2312yes—
187C13×#95C2312yes—
188#88071C2312yes—
189#88071C2312yes—
190#88071C2312yes—
191#88071C2312yes—
192#88071C2312yes—
193#88071C2312yes—
194#88071C2312yes—
195#88071C2312yes—
196#88071C2312yes—
197#88071C2312yes—
198#88071C2312yes—
199#88071C2312yes—
200#88071C2312yes—
201#88071C2312yes—
202#88071C2312yes—
203#88071C2312yes—
204#88071C2312yes—
205#88071C2312yes—
206#88071C2312yes—
207#88071C2312yes—
208#34528—131nomaximal, Sylow
209C24×C13C2412yes—
210C2×Q8×C13—41no—
211C2×Q8×C13—41no—
212C2×Q8×C13C22×C414yes—
213C2×D4×C13—41no—
214C2×D4×C13—41no—
215C2×D4×C13C22×C414yes—
216C22×C4×C13—42no—
217C22×C4×C13—42no—
218C22×C4×C13—42no—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2411yescharacteristic
224C22×C4×C13C2411yescharacteristic
225C22×C4×C13C2412yes—
226C22×C4×C13C2411yescharacteristic
227C22×Dic13—24no—
228C22×Dic13—42no—
229C22×Dic13—42no—
230C22×Dic13—42no—
231C22×Dic13—42no—
232C22×Dic13C22×C418yes—
233C22×Dic13C2412yes—
234C22×Dic13C2411yescharacteristic
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2411yescharacteristic
241C22×Dic13C2411yescharacteristic
242C22×Dic13C2411yescharacteristic
243C2×Dic26—42no—
244C2×Dic26—42no—
245C2×Dic26C22×C418yes—
246C13×C4⋊C4—41no—
247C13×C4⋊C4—41no—
248C13×C4⋊C4—41no—
249C13×C4⋊C4—41no—
250C13×C4⋊C4—42no—
251C13×C22⋊C4—42no—
252C13×C22⋊C4—42no—
253C13×C22⋊C4—42no—
254C13×C22⋊C4C22×C418yes—
255C13×C22⋊C4C22×C418yes—
256C42×C13—42no—
257C42×C13C22×C414yes—
258C22⋊Dic13—24no—
259C22⋊Dic13—24no—
260C22⋊Dic13—42no—
261C22⋊Dic13C22×C418yes—
262C22⋊Dic13C22×C418yes—
263C22⋊Dic13C22×C418yes—
264C4⋊Dic13—24no—
265C4⋊Dic13—41no—
266C4⋊Dic13—41no—
267C4⋊Dic13C22×C414yes—
268C4⋊Dic13C22×C414yes—
269C4⋊Dic13C22×C414yes—
270C4⋊Dic13C22×C414yes—
271#6101—24no—
272#6101—24no—
273#6101—42no—
274#6101—42no—
275#6101—42no—
276#6101—42no—
277#6101—42no—
278#6101—42no—
279#6101C22×C418yes—
280#6101C22×C418yes—
281#6101C22×C418yes—
282#6101C22×C418yes—
283#6101C22×C418yes—
284#6101C22×C418yes—
285C4×Dic13—24no—
286C4×Dic13—22no—
287C4×Dic13—22no—
288C4×Dic13—24no—
289C4×Dic13—22no—
290C4×Dic13—42no—
291C4×Dic13—42no—
292C4×Dic13—42no—
293C4×Dic13—42no—
294C4×Dic13—41no—
295C4×Dic13—41no—
296C4×Dic13—42no—
297C4×Dic13—42no—
298C4×Dic13—41no—
299C4×Dic13—42no—
300C4×Dic13C22×C418yes—
301C2×#563—131no—
302#2382—131no—
303#2382—131no—
304#2379D1311yescharacteristic
305#2373—132no—
306#2373—132no—
307#2368—132no—
308#2365—132no—
309#2362—132no—
310#2359—132no—
311#2335—132no—
312#2334—132no—
313#2334—132no—
314#2331—132no—
315#2329—132no—
316#2323—132no—
317C4×#125—131no—
318C4×#125—131no—
319C4×#124—131no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13C23×C414yes—
327C23×C13C2511yescharacteristic
328Q8×C13—44no—
329D4×C13—44no—
330C2×C4×C13—21no—
331C2×C4×C13—22no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—21no—
336C2×C4×C13—21no—
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—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—84no—
351C2×C4×C13C23×C414yes—
352C2×C4×C13C23×C412yes—
353C2×C4×C13C23×C412yes—
354C2×C4×C13C23×C412yes—
355C2×Dic13—21no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—21no—
360C2×Dic13—21no—
361C2×Dic13—22no—
362C2×Dic13—21no—
363C2×Dic13—21no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—21no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—21no—
374C2×Dic13—21no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—21no—
378C2×Dic13—48no—
379C2×Dic13—84no—
380C2×Dic13C23×C414yes—
381C2×Dic13C23×C414yes—
382C2×Dic13C23×C414yes—
383C2×Dic13C23×C414yes—
384C2×Dic13H(5,𝔽2)12yes—
385C2×Dic132−1+412yes—
386C2×Dic132−1+412yes—
387Dic26—48no—
388#563—1316no—
389C2×C4⋊Q8—132no—
390C2×#126—132no—
391C2×#126—132no—
392C2×#125—131no—
393C2×#125—131no—
394C2×#124C2×D1311yescharacteristic
395C2×#123—132no—
396C2×C22⋊Q8—132no—
397C2×C22⋊Q8—132no—
398C2×C4×Q8—131no—
399C2×C4×Q8—132no—
400C2×C4×D4—131no—
401C2×#117—132no—
402#391—131no—
403#391—132no—
404#391—132no—
405#391—132no—
406#391C2×D1312yes—
407#390—131no—
408#389—131no—
409#389—131no—
410#389—131no—
411#389—131no—
412#389—132no—
413#389—132no—
414#389—132no—
415#389—132no—
416#389—132no—
417#389—132no—
418#388—132no—
419#388—132no—
420#388—132no—
421#388—132no—
422#388—132no—
423#388—132no—
424#388—132no—
425#388—132no—
426#388C2×D1312yes—
427#388C2×D1312yes—
428#387—132no—
429#387—132no—
430#387—132no—
431#387—132no—
432#387—132no—
433#387—132no—
434#387—132no—
435#387—132no—
436#387—132no—
437#387—132no—
438#387—132no—
439#387—132no—
440#387—132no—
441#387—132no—
442#387—132no—
443#387—132no—
444#386C2×D1312yes—
445#385—132no—
446#385—132no—
447#385—132no—
448#385C2×D1312yes—
449#385C2×D1312yes—
450#382—131no—
451#382—132no—
452#382C2×D1311yescharacteristic
453#382C2×D1311yescharacteristic
454#380—132no—
455C4×C4⋊C4—131no—
456C4×C4⋊C4—131no—
457C4×C4⋊C4—131no—
458C4×C4⋊C4—131no—
459C4×C4⋊C4—132no—
460C4×C4⋊C4—132no—
461C4×C4⋊C4—132no—
462C4×C4⋊C4—132no—
463C4×C4⋊C4—132no—
464C4×C4⋊C4—132no—
465C4×C4⋊C4—132no—
466C4×C4⋊C4—132no—
467C4×C22⋊C4—132no—
468C4×C22⋊C4—132no—
469C4×C22⋊C4—132no—
470C4×C22⋊C4—132no—
471C4×C22⋊C4—132no—
472C4×C22⋊C4—132no—
473#376—132no—
474C2×#95—132no—
475C43—131no—
476C22×C13—24no—
477C22×C13—24no—
478C22×C13—24no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13C24×C411yescharacteristic
484C22×C13C2×H(5,𝔽2)11yescharacteristic
485C22×C13C2×2−1+411yescharacteristic
486C22×C13C2×2−1+411yescharacteristic
487C22×C13#58511yescharacteristic
488C22×C13#58511yescharacteristic
489C22×C13#58511yescharacteristic
490C4×C13—24no—
491C4×C13—22no—
492C4×C13—22no—
493C4×C13—22no—
494C4×C13—42no—
495C4×C13—42no—
496C4×C13—42no—
497C4×C13—42no—
498Dic13—24no—
499Dic13—24no—
500Dic13—24no—
501Dic13—24no—
502Dic13—22no—
503Dic13—22no—
504Dic13—22no—
505Dic13—42no—
506Dic13—42no—
507Dic13—41no—
508C22×Q8—132no—
509C22×Q8C22×D1311yescharacteristic
510C22×D4C22×D1311yescharacteristic
511C23×C4—132no—
512C23×C4—132no—
513C23×C4C22×D1312yes—
514C4⋊Q8—1316no—
515#126—1316no—
516#126—1316no—
517#125—138no—
518#125—138no—
519#124C4×D1318yes—
520#123—1316no—
521C22⋊Q8—1316no—
522C22⋊Q8—1316no—
523C4×Q8—524no—
524C4×Q8—522no—
525C4×D4—522no—
526#117—524no—
527C2×C4⋊C4—131no—
528C2×C4⋊C4—131no—
529C2×C4⋊C4—132no—
530C2×C4⋊C4—132no—
531C2×C4⋊C4—132no—
532C2×C4⋊C4—132no—
533C2×C4⋊C4—132no—
534C2×C4⋊C4—132no—
535C2×C4⋊C4—131no—
536C2×C4⋊C4—131no—
537C2×C4⋊C4—132no—
538C2×C4⋊C4—132no—
539C2×C4⋊C4—132no—
540C2×C4⋊C4—132no—
541C2×C4⋊C4—131no—
542C2×C4⋊C4—132no—
543C2×C4⋊C4—131no—
544C2×C4⋊C4—132no—
545C2×C4⋊C4—132no—
546C2×C4⋊C4—132no—
547C2×C4⋊C4—132no—
548C2×C4⋊C4C22×D1311yescharacteristic
549C2×C4⋊C4C22×D1311yescharacteristic
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1312yes—
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⋊C4C22×D1312yes—
560C2×C22⋊C4C22×D1312yes—
561C2×C22⋊C4C22×D1312yes—
562C2×C22⋊C4C22×D1312yes—
563C2×C22⋊C4C22×D1312yes—
564C2×C42—132no—
565C2×C42—132no—
566C2×C42—131no—
567C2×C42—131no—
568C2×C42—131no—
569C2×C42—132no—
570C2×C42—132no—
571C2×C42—132no—
572C2×C42—132no—
573C2×C42—131no—
574C2×C42—131no—
575C2×C42—131no—
576C2×C42—132no—
577C2×C42—132no—
578C2×C42—132no—
579C2×C42—132no—
580C2×C42C22×D1312yes—
581C2×C42C22×D1311yescharacteristic
582#95—132no—
583#95—132no—
584#95—132no—
585#95—132no—
586#95—132no—
587#95—132no—
588#95—132no—
589#95—132no—
590#95—132no—
591#95—132no—
592#95—132no—
593#95—132no—
594#95—132no—
595#95—132no—
596#95—132no—
597#95—132no—
598#95—132no—
599#95—132no—
600#95—132no—
601#95—132no—
602#95C22×D1312yes—
603#95C22×D1312yes—
604#95C22×D1312yes—
605#95C22×D1312yes—
606#95C22×D1312yes—
607#95C22×D1312yes—
608C2×C13—44no—
609C2×C13C4×H(5,𝔽2)11yescharacteristic
610C2×C13C4×2−1+411yescharacteristic
611C2×C13C4×2−1+411yescharacteristic
612C2×C13#355911yescharacteristic
613C2×C13#356111yescharacteristic
614C2×C13#356311yescharacteristic
615C2×C13#356811yescharacteristic
616C24C23×D1312yes—
617C2×Q8—41no—
618C2×Q8—41no—
619C2×Q8—138no—
620C2×Q8—522no—
621C2×Q8—522no—
622C2×Q8C2×C4×D1314yes—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4C2×C4×D1314yes—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—131no—
630C22×C4—131no—
631C22×C4—132no—
632C22×C4—132no—
633C22×C4—132no—
634C22×C4—132no—
635C22×C4—131no—
636C22×C4—138no—
637C22×C4—132no—
638C22×C4—132no—
639C22×C4—131no—
640C22×C4—264no—
641C22×C4—522no—
642C22×C4—522no—
643C22×C4—522no—
644C22×C4—522no—
645C22×C4C23×D1312yes—
646C22×C4C23×D1312yes—
647C22×C4C23×D1312yes—
648C22×C4C23×D1312yes—
649C22×C4C23×D1311yescharacteristic
650C22×C4C23×D1311yescharacteristic
651C22×C4C23×D1312yes—
652C22×C4C23×D1311yescharacteristic
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—42no—
658C4⋊C4—134no—
659C4⋊C4—134no—
660C4⋊C4—138no—
661C4⋊C4—138no—
662C4⋊C4—138no—
663C4⋊C4—138no—
664C4⋊C4—138no—
665C4⋊C4—138no—
666C4⋊C4—134no—
667C4⋊C4—134no—
668C4⋊C4—264no—
669C4⋊C4—264no—
670C4⋊C4—264no—
671C4⋊C4—522no—
672C4⋊C4—521no—
673C4⋊C4—522no—
674C4⋊C4—521no—
675C4⋊C4—522no—
676C4⋊C4—522no—
677C4⋊C4—522no—
678C4⋊C4—522no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—138no—
683C22⋊C4—138no—
684C22⋊C4—138no—
685C22⋊C4—264no—
686C22⋊C4—264no—
687C22⋊C4—522no—
688C22⋊C4C2×C4×D1318yes—
689C22⋊C4C2×C4×D1318yes—
690C42—42no—
691C42—138no—
692C42—264no—
693C42—262no—
694C42—262no—
695C42—262no—
696C42—264no—
697C42—522no—
698C42—522no—
699C42—522no—
700C42—521no—
701C42—521no—
702C42—521no—
703C42—522no—
704C42—522no—
705C42—522no—
706C42—522no—
707C42C2×C4×D1314yes—
708C13#3452811yescharacteristic, complemented, Sylow
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23C22×C4×D1314yes—
716C23C24×D1311yescharacteristic
717Q8—44no—
718Q8—528no—
719D4—44no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—84no—
741C2×C4—134no—
742C2×C4—134no—
743C2×C4—134no—
744C2×C4—134no—
745C2×C4—132no—
746C2×C4—132no—
747C2×C4—132no—
748C2×C4—261no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—261no—
752C2×C4—261no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—261no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—261no—
760C2×C4—261no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—261no—
765C2×C4—262no—
766C2×C4—261no—
767C2×C4—261no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—262no—
771C2×C4—528no—
772C2×C4—1044no—
773C2×C4C22×C4×D1314yes—
774C2×C4C22×C4×D1312yes—
775C2×C4C22×C4×D1312yes—
776C2×C4C22×C4×D1312yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22C23×C4×D1311yescharacteristic
785C22D13×H(5,𝔽2)11yescharacteristic
786C22#1171965011yescharacteristic
787C22#1171965011yescharacteristic
788C22#1171965011yescharacteristic
789C22D13×2−1+411yescharacteristic
790C22D13×2−1+411yescharacteristic
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—264no—
800C4—264no—
801C4—264no—
802C4—264no—
803C4—262no—
804C4—262no—
805C4—262no—
806C4—521no—
807C4—522no—
808C4—522no—
809C2—44no—
810C2#1312804011yescharacteristic
811C2#1312804711yescharacteristic
812C2#1312804711yescharacteristic
813C2#1312936411yescharacteristic
814C2#1312939811yescharacteristic
815C2#1312943611yescharacteristic
816C2#1312953011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2379C2
socle, cosocleC23×C13C25
prime radicalC22×D4×C13C23
hypercenter#2379D13
hypocenterC13#34528
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2379

Complements

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

NH ≅ G/Ntype
2. #13118021C2semidirect
3. #13118021C2semidirect
4. #13117954C2semidirect
5. #13117951C2semidirect
6. #13117917C2semidirect
7. #13117893C2semidirect
8. #13117866C2semidirect
11. #13117612C2semidirect
12. #13117609C2semidirect
13. #13117579C2semidirect
14. #13117567C2semidirect
15. #13117515C2semidirect
16. #13117391C2semidirect
17. #13117391C2semidirect
25. #11719377C4semidirect
134. #88198C2×C4semidirect
174. #88133C2×C4semidirect
175. #88133C2×C4semidirect
176. #88132C2×C4semidirect
177. #88132C2×C4semidirect
179. #88124C2×C4semidirect
180. #88124C2×C4semidirect
708. C13#34528semidirect

Maximal subgroups

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

subgroupindex
C2×#117193772
#131180212
#131179542
#131179512
#131179172
#131178932
#131178662
#131178342
#131176272
#131176122
#131176092
#131175792
#131175672
#131175152
#131173912
#124×Dic132
C13×#23792
#3452813