Finite Group Databasebeta

← C113×#18962 #43286982

Subgroups — C113×#18962 #43286982

Order 28928.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3546C211yesmaximal, characteristic, complemented
2C113×#3253C211yesmaximal, characteristic, complemented
3C113×#3247C211yesmaximal, characteristic, complemented
4C113×#3207C211yesmaximal, characteristic, complemented
5C113×#1638C211yesmaximal, characteristic, complemented
6C113×#1635C211yesmaximal, characteristic, complemented
7C113×#1631C211yesmaximal, characteristic, complemented
8C113×#1629C211yesmaximal, characteristic, complemented
9C113×#1628C211yesmaximal, characteristic, complemented
10C113×#1625C211yesmaximal, characteristic, complemented
11C113×#1621C211yesmaximal, characteristic, complemented
12C113×#1619C211yesmaximal, characteristic, complemented
13C113×#1547C211yesmaximal, characteristic, complemented
14C113×#1495C211yesmaximal, characteristic, complemented
15C113×#1480C211yesmaximal, characteristic, complemented
16#560×C113—22no—
17#556×C113C2211yescharacteristic
18#553×C113—21no—
19#550×C113—21no—
20#550×C113C2211yescharacteristic
21#547×C113C2211yescharacteristic
22#546×C113—21no—
23#546×C113—21no—
24D42×C113C2211yescharacteristic
25#542×C113—21no—
26#538×C113—22no—
27#537×C113—21no—
28#535×C113—21no—
29#535×C113—21no—
30#532×C113C2211yescharacteristic
31#532×C113C2211yescharacteristic
32#532×C113C2211yescharacteristic, complemented
33#529×C113C2211yescharacteristic
34#493×C113C2211yescharacteristic
35#492×C113C2211yescharacteristic
36#487×C113C2211yescharacteristic, complemented
37#486×C113C2211yescharacteristic, complemented
38#478×C113—21no—
39#477×C113C2211yescharacteristic, complemented
40#476×C113—21no—
41#476×C113C2211yescharacteristic
42#476×C113C2211yescharacteristic
43#476×C113C2211yescharacteristic, complemented
44#469×C113—21no—
45#469×C113—21no—
46#466×C113—21no—
47#465×C113—21no—
48#463×C113—21no—
49#463×C113—22no—
50#460×C113C2211yescharacteristic, complemented
51#459×C113—21no—
52#459×C113C2211yescharacteristic
53#459×C113C2211yescharacteristic
54#459×C113C2211yescharacteristic, complemented
55#449×C113—22no—
56#431×C113C2211yescharacteristic, complemented
57#423×C113C2211yescharacteristic, complemented
58C2×C4⋊C8×C113C2211yescharacteristic, complemented
59#332×C113C2211yescharacteristic, complemented
60#332×C113C2211yescharacteristic, complemented
61#331×C113C2211yescharacteristic
62#331×C113C2211yescharacteristic
63Q8⋊C8×C113C2211yescharacteristic, complemented
64Q8⋊C8×C113C2211yescharacteristic, complemented
65D4⋊C8×C113C2211yescharacteristic
66D4⋊C8×C113C2211yescharacteristic
67D4⋊C8×C113C2211yescharacteristic
68D4⋊C8×C113C2211yescharacteristic
69D4⋊C8×C113C2211yescharacteristic, complemented
70D4⋊C8×C113C2211yescharacteristic, complemented
71C2×#41×C113—21no—
72C2×#41×C113—21no—
73C2×#41×C113—21no—
74C2×#41×C113—21no—
75C2×#41×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C2×SD16×C113—21no—
79C2×SD16×C113—22no—
80C2×D8×C113—22no—
81C2×D8×C113—21no—
82C2×D8×C113—21no—
83C2×D8×C113—21no—
84C2×M16×C113—21no—
85C22×C8×C113—21no—
86C4⋊Q8×C113D411yescharacteristic
87C4⋊Q8×C113C2311yescharacteristic
88C4⋊Q8×C113C2311yescharacteristic
89#127×C113—22no—
90#127×C113—21no—
91#127×C113D411yescharacteristic
92#127×C113C2311yescharacteristic
93#127×C113C2311yescharacteristic
94#126×C113—22no—
95#126×C113—22no—
96#126×C113—21no—
97#125×C113D411yescharacteristic
98#124×C113—22no—
99#124×C113—21no—
100#124×C113—21no—
101#124×C113—21no—
102#124×C113—21no—
103#124×C113D411yescharacteristic
104#123×C113—22no—
105#123×C113—22no—
106#123×C113—21no—
107#123×C113—22no—
108C22⋊Q8×C113—22no—
109C22⋊Q8×C113—21no—
110C22⋊Q8×C113—21no—
111C22⋊Q8×C113D411yescharacteristic
112#121×C113—22no—
113#121×C113—22no—
114#121×C113—22no—
115#121×C113—22no—
116#121×C113—22no—
117#121×C113—21no—
118#121×C113—22no—
119#121×C113—21no—
120#121×C113—21no—
121#121×C113—21no—
122#121×C113—21no—
123#121×C113—21no—
124#121×C113—21no—
125#121×C113—21no—
126#121×C113D411yescharacteristic
127#121×C113D411yescharacteristic
128#121×C113D411yescharacteristic
129#121×C113D412yes—
130#120×C113—22no—
131#120×C113—22no—
132#120×C113—22no—
133#120×C113—22no—
134C4×Q8×C113—21no—
135C4×Q8×C113C2311yescharacteristic
136C4×D4×C113—22no—
137C4×D4×C113—21no—
138C4×D4×C113—21no—
139C4×D4×C113—21no—
140C4×D4×C113—21no—
141C4×D4×C113—21no—
142C4×D4×C113—21no—
143C4×D4×C113D412yes—
144C4×D4×C113C2311yescharacteristic
145C4×D4×C113C2311yescharacteristic
146C4×D4×C113C2311yescharacteristic
147#117×C113—21no—
148#117×C113—21no—
149C2×C4⋊C4×C113—21no—
150C2×C22⋊C4×C113—22no—
151C2×C42×C113C2311yescharacteristic
152#107×C113—21no—
153#106×C113—21no—
154#106×C113—21no—
155#106×C113—21no—
156C4⋊C8×C113—21no—
157C4⋊C8×C113—21no—
158C4⋊C8×C113—21no—
159C4⋊C8×C113C2311yescharacteristic
160C4⋊C8×C113C2311yescharacteristic
161C4⋊C8×C113C2311yescharacteristic
162C4⋊C8×C113C2311yescharacteristic
163#103×C113—21no—
164#103×C113—22no—
165#102×C113—21no—
166#102×C113—21no—
167#102×C113—21no—
168#102×C113—22no—
169#102×C113—21no—
170#102×C113—21no—
171#102×C113—21no—
172#102×C113—21no—
173C22⋊C8×C113—21no—
174C4×C8×C113C2311yescharacteristic
175C4×C8×C113C2311yescharacteristic
176C24×C113—22no—
177#41×C113—81no—
178#41×C113—81no—
179#41×C113—81no—
180#41×C113—81no—
181#41×C113—81no—
182#41×C113—81no—
183#41×C113—81no—
184#41×C113—81no—
185#41×C113—82no—
186C2×Q8×C113—21no—
187C2×Q8×C113—21no—
188C2×Q8×C113—21no—
189C2×Q8×C113C2×D411yescharacteristic
190C2×D4×C113—22no—
191C2×D4×C113—22no—
192C2×D4×C113—22no—
193C2×D4×C113—22no—
194C2×D4×C113—22no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—22no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—41no—
207C2×D4×C113—81no—
208C2×D4×C113—81no—
209C2×D4×C113—81no—
210C2×D4×C113—81no—
211C2×D4×C113C2×D411yescharacteristic
212C2×D4×C113C2×D411yescharacteristic
213C2×D4×C113C2×D411yescharacteristic
214C2×D4×C113C2×D412yes—
215C22×C4×C113—22no—
216C22×C4×C113—22no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—22no—
221C22×C4×C113—41no—
222C22×C4×C113C2×D411yescharacteristic
223C22×C4×C113C2×D411yescharacteristic
224C22×C4×C113C2×D411yescharacteristic
225SD16×C113—81no—
226SD16×C113—82no—
227D8×C113—81no—
228D8×C113—81no—
229D8×C113—81no—
230D8×C113—82no—
231M16×C113—81no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
234C2×C8×C113—21no—
235C2×C8×C113—21no—
236C2×C8×C113—21no—
237C2×C8×C113—21no—
238C2×C8×C113—81no—
239C4⋊C4×C113—22no—
240C4⋊C4×C113—22no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—21no—
244C4⋊C4×C113—21no—
245C4⋊C4×C113—21no—
246C4⋊C4×C113—21no—
247C4⋊C4×C113—21no—
248C4⋊C4×C113—21no—
249C4⋊C4×C113C2×D412yes—
250C4⋊C4×C113C2×D411yescharacteristic
251C4⋊C4×C113C2×D411yescharacteristic
252C4⋊C4×C113C2×D411yescharacteristic
253C4⋊C4×C113C2×D411yescharacteristic
254C22⋊C4×C113—22no—
255C22⋊C4×C113—22no—
256C22⋊C4×C113—22no—
257C22⋊C4×C113—22no—
258C22⋊C4×C113—22no—
259C22⋊C4×C113—21no—
260C22⋊C4×C113—21no—
261C22⋊C4×C113—21no—
262C22⋊C4×C113—21no—
263C22⋊C4×C113—21no—
264C22⋊C4×C113—21no—
265C22⋊C4×C113—22no—
266C22⋊C4×C113—22no—
267C22⋊C4×C113—21no—
268C22⋊C4×C113—21no—
269C22⋊C4×C113—21no—
270C22⋊C4×C113—41no—
271C22⋊C4×C113—41no—
272C42×C113—22no—
273C42×C113—21no—
274C42×C113C2×D411yescharacteristic
275C42×C113C2×D411yescharacteristic
276C42×C113C2×D411yescharacteristic
277C42×C113C2411yescharacteristic
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—22no—
281C23×C113—21no—
282C23×C113—41no—
283C23×C113—82no—
284C23×C113—82no—
285C23×C113—82no—
286C23×C113#12011yescharacteristic
287Q8×C113—21no—
288Q8×C113—21no—
289Q8×C113—42no—
290Q8×C113—41no—
291Q8×C113—41no—
292Q8×C113—81no—
293D4×C113—21no—
294D4×C113—21no—
295D4×C113—21no—
296D4×C113—21no—
297D4×C113—21no—
298D4×C113—21no—
299D4×C113—42no—
300D4×C113—42no—
301D4×C113—41no—
302D4×C113—41no—
303D4×C113—41no—
304D4×C113—41no—
305D4×C113—41no—
306D4×C113—41no—
307D4×C113—41no—
308D4×C113—41no—
309D4×C113—81no—
310D4×C113—81no—
311D4×C113—81no—
312D4×C113—81no—
313D4×C113—81no—
314D4×C113—82no—
315D4×C113—82no—
316D4×C113—82no—
317D4×C113—82no—
318D4×C113—82no—
319D4×C113—82no—
320D4×C113—82no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—21no—
325C2×C4×C113—21no—
326C2×C4×C113—21no—
327C2×C4×C113—21no—
328C2×C4×C113—22no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—82no—
340C2×C4×C113—82no—
341C2×C4×C113—82no—
342C2×C4×C113—82no—
343C2×C4×C113#12011yescharacteristic
344C2×C4×C113#12011yescharacteristic
345C2×C4×C113#12011yescharacteristic
346C2×C4×C113C22×D411yescharacteristic
347C2×C4×C113C22×D411yescharacteristic
348C2×C4×C113C22×D411yescharacteristic
349C8×C113—41no—
350C8×C113—41no—
351C8×C113—41no—
352C8×C113—41no—
353C8×C113—41no—
354C8×C113—41no—
355C22×C113—21no—
356C22×C113—21no—
357C22×C113—21no—
358C22×C113—41no—
359C22×C113—41no—
360C22×C113—41no—
361C22×C113—41no—
362C22×C113—42no—
363C22×C113—42no—
364C22×C113—41no—
365C22×C113—41no—
366C22×C113—42no—
367C22×C113—41no—
368C22×C113—41no—
369C22×C113—41no—
370C22×C113—81no—
371C22×C113—81no—
372C22×C113—81no—
373C22×C113—164no—
374C22×C113C2×#12011yescharacteristic
375C4×C113—21no—
376C4×C113—21no—
377C4×C113—21no—
378C4×C113—21no—
379C4×C113—41no—
380C4×C113—41no—
381C4×C113—41no—
382C4×C113—41no—
383C4×C113—42no—
384C4×C113—41no—
385C4×C113—81no—
386C4×C113#57611yescharacteristic
387C4×C113#57611yescharacteristic
388C4×C113#57711yescharacteristic
389C4×C113#57711yescharacteristic
390#18962C11311yesmaximal, characteristic, direct product factor, Sylow
391C2×C113—41no—
392C2×C113—81no—
393C2×C113—82no—
394C2×C113—81no—
395C2×C113—81no—
396C2×C113—161no—
397C2×C113#301211yescharacteristic
398C2×C113#301211yescharacteristic
399C2×C113#302111yescharacteristic
400#3546C2×C11311yescharacteristic, complemented
401#3253C2×C11311yescharacteristic, complemented
402#3247C2×C11311yescharacteristic, complemented
403#3207C2×C11311yescharacteristic, complemented
404#1638C2×C11311yescharacteristic, complemented
405#1635C2×C11311yescharacteristic, complemented
406#1631C2×C11311yescharacteristic, complemented
407#1629C2×C11311yescharacteristic, complemented
408#1628C2×C11311yescharacteristic, complemented
409#1625C2×C11311yescharacteristic, complemented
410#1621C2×C11311yescharacteristic, complemented
411#1619C2×C11311yescharacteristic, complemented
412#1547C2×C11311yescharacteristic, complemented
413#1495C2×C11311yescharacteristic, complemented
414#1480C2×C11311yescharacteristic, complemented
415C113#1896211yescharacteristic, direct product factor, Sylow
416#560—22no—
417#556C22×C11311yescharacteristic
418#553—21no—
419#550—21no—
420#550C22×C11311yescharacteristic
421#547C22×C11311yescharacteristic
422#546—21no—
423#546—21no—
424D42C22×C11311yescharacteristic
425#542—21no—
426#538—22no—
427#537—21no—
428#535—21no—
429#535—21no—
430#532C22×C11311yescharacteristic
431#532C22×C11311yescharacteristic
432#532C22×C11311yescharacteristic, complemented
433#529C22×C11311yescharacteristic
434#493C22×C11311yescharacteristic
435#492C22×C11311yescharacteristic
436#487C22×C11311yescharacteristic, complemented
437#486C22×C11311yescharacteristic, complemented
438#478—21no—
439#477C22×C11311yescharacteristic, complemented
440#476—21no—
441#476C22×C11311yescharacteristic
442#476C22×C11311yescharacteristic
443#476C22×C11311yescharacteristic, complemented
444#469—21no—
445#469—21no—
446#466—21no—
447#465—21no—
448#463—21no—
449#463—22no—
450#460C22×C11311yescharacteristic, complemented
451#459—21no—
452#459C22×C11311yescharacteristic
453#459C22×C11311yescharacteristic
454#459C22×C11311yescharacteristic, complemented
455#449—22no—
456#431C22×C11311yescharacteristic, complemented
457#423C22×C11311yescharacteristic, complemented
458C2×C4⋊C8C22×C11311yescharacteristic, complemented
459#332C22×C11311yescharacteristic, complemented
460#332C22×C11311yescharacteristic, complemented
461#331C22×C11311yescharacteristic
462#331C22×C11311yescharacteristic
463Q8⋊C8C22×C11311yescharacteristic, complemented
464Q8⋊C8C22×C11311yescharacteristic, complemented
465D4⋊C8C22×C11311yescharacteristic
466D4⋊C8C22×C11311yescharacteristic
467D4⋊C8C22×C11311yescharacteristic
468D4⋊C8C22×C11311yescharacteristic
469D4⋊C8C22×C11311yescharacteristic, complemented
470D4⋊C8C22×C11311yescharacteristic, complemented
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C11311yescharacteristic
487C4⋊Q8C23×C11311yescharacteristic
488C4⋊Q8C23×C11311yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C11311yescharacteristic
492#127C23×C11311yescharacteristic
493#127C23×C11311yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C11311yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C11311yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C11311yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C11311yescharacteristic
527#121D4×C11311yescharacteristic
528#121D4×C11311yescharacteristic
529#121D4×C11312yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C11311yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C11312yes—
544C4×D4C23×C11311yescharacteristic
545C4×D4C23×C11311yescharacteristic
546C4×D4C23×C11311yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C11311yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C11311yescharacteristic
560C4⋊C8C23×C11311yescharacteristic
561C4⋊C8C23×C11311yescharacteristic
562C4⋊C8C23×C11311yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C11311yescharacteristic
575C4×C8C23×C11311yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C11311yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C11311yescharacteristic
612C2×D4C2×D4×C11311yescharacteristic
613C2×D4C2×D4×C11311yescharacteristic
614C2×D4C2×D4×C11312yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C11311yescharacteristic
623C22×C4C2×D4×C11311yescharacteristic
624C22×C4C2×D4×C11311yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C11312yes—
650C4⋊C4C2×D4×C11311yescharacteristic
651C4⋊C4C2×D4×C11311yescharacteristic
652C4⋊C4C2×D4×C11311yescharacteristic
653C4⋊C4C2×D4×C11311yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C11311yescharacteristic
675C42C2×D4×C11311yescharacteristic
676C42C2×D4×C11311yescharacteristic
677C42C24×C11311yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C11311yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C11311yescharacteristic
744C2×C4#120×C11311yescharacteristic
745C2×C4#120×C11311yescharacteristic
746C2×C4C22×D4×C11311yescharacteristic
747C2×C4C22×D4×C11311yescharacteristic
748C2×C4C22×D4×C11311yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C11311yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4#576×C11311yescharacteristic
787C4#576×C11311yescharacteristic
788C4#577×C11311yescharacteristic
789C4#577×C11311yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C113×#301211yescharacteristic
797C2C113×#301211yescharacteristic
798C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3546C2semidirect
2. C113×#3253C2semidirect
3. C113×#3247C2semidirect
4. C113×#3207C2semidirect
5. C113×#1638C2semidirect
6. C113×#1635C2semidirect
7. C113×#1631C2semidirect
8. C113×#1629C2semidirect
9. C113×#1628C2semidirect
10. C113×#1625C2semidirect
11. C113×#1621C2semidirect
12. C113×#1619C2semidirect
13. C113×#1547C2semidirect
14. C113×#1495C2semidirect
15. C113×#1480C2semidirect
32. #532×C113C22semidirect
36. #487×C113C22semidirect
37. #486×C113C22semidirect
39. #477×C113C22semidirect
43. #476×C113C22semidirect
50. #460×C113C22semidirect
54. #459×C113C22semidirect
56. #431×C113C22semidirect
57. #423×C113C22semidirect
58. C2×C4⋊C8×C113C22semidirect
59. #332×C113C22semidirect
60. #332×C113C22semidirect
63. Q8⋊C8×C113C22semidirect
64. Q8⋊C8×C113C22semidirect
69. D4⋊C8×C113C22semidirect
70. D4⋊C8×C113C22semidirect
390. #18962C113direct (N × H)
400. #3546C2×C113semidirect
401. #3253C2×C113semidirect
402. #3247C2×C113semidirect
403. #3207C2×C113semidirect
404. #1638C2×C113semidirect
405. #1635C2×C113semidirect
406. #1631C2×C113semidirect
407. #1629C2×C113semidirect
408. #1628C2×C113semidirect
409. #1625C2×C113semidirect
410. #1621C2×C113semidirect
411. #1619C2×C113semidirect
412. #1547C2×C113semidirect
413. #1495C2×C113semidirect
414. #1480C2×C113semidirect
415. C113#18962direct (N × H)
432. #532C22×C113semidirect
436. #487C22×C113semidirect
437. #486C22×C113semidirect
439. #477C22×C113semidirect
443. #476C22×C113semidirect
450. #460C22×C113semidirect
454. #459C22×C113semidirect
456. #431C22×C113semidirect
457. #423C22×C113semidirect
458. C2×C4⋊C8C22×C113semidirect
459. #332C22×C113semidirect
460. #332C22×C113semidirect
463. Q8⋊C8C22×C113semidirect
464. Q8⋊C8C22×C113semidirect
469. D4⋊C8C22×C113semidirect
470. D4⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35462
C113×#32532
C113×#32472
C113×#32072
C113×#16382
C113×#16352
C113×#16312
C113×#16292
C113×#16282
C113×#16252
C113×#16212
C113×#16192
C113×#15472
C113×#14952
C113×#14802
#18962113