Finite Group Databasebeta

← C113×#18974 #43286994

Subgroups — C113×#18974 #43286994

Order 28928.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3546C211yesmaximal, characteristic
2C113×#3254C211yesmaximal, characteristic, complemented
3C113×#3248C211yesmaximal, characteristic, complemented
4C113×#3228C211yesmaximal, characteristic, complemented
5C113×#1654C211yesmaximal, characteristic, complemented
6C113×#1652C211yesmaximal, characteristic, complemented
7C113×#1650C211yesmaximal, characteristic, complemented
8C113×#1647C211yesmaximal, characteristic, complemented
9C113×#1642C211yesmaximal, characteristic, complemented
10C113×#1641C211yesmaximal, characteristic, complemented
11C113×#1639C211yesmaximal, characteristic, complemented
12C113×#1639C211yesmaximal, 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#533×C113C2211yescharacteristic, complemented
31#532×C113C2211yescharacteristic
32#532×C113C2211yescharacteristic
33#529×C113C2211yescharacteristic
34#500×C113C2211yescharacteristic, complemented
35#498×C113C2211yescharacteristic, complemented
36#486×C113C2211yescharacteristic
37#486×C113C2211yescharacteristic
38#482×C113—22no—
39#479×C113—21no—
40#478×C113—22no—
41#477×C113—21no—
42#475×C113C2211yescharacteristic, complemented
43#474×C113C2211yescharacteristic
44#474×C113C2211yescharacteristic
45#474×C113C2211yescharacteristic, complemented
46#468×C113—21no—
47#468×C113—21no—
48#467×C113—21no—
49#465×C113—21no—
50#464×C113—21no—
51#462×C113C2211yescharacteristic, complemented
52#461×C113C2211yescharacteristic
53#461×C113C2211yescharacteristic
54#461×C113C2211yescharacteristic, complemented
55#460×C113—21no—
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—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C2×Q16×C113—21no—
78C2×SD16×C113—21no—
79C2×SD16×C113—21no—
80C2×SD16×C113—21no—
81C2×M16×C113—21no—
82C22×C8×C113—21no—
83C4⋊Q8×C113D411yescharacteristic
84C4⋊Q8×C113C2311yescharacteristic
85C4⋊Q8×C113C2311yescharacteristic
86C4⋊Q8×C113C2311yescharacteristic
87#127×C113—22no—
88#127×C113—21no—
89#127×C113D411yescharacteristic
90#127×C113C2311yescharacteristic
91#126×C113—22no—
92#126×C113—22no—
93#126×C113—21no—
94#125×C113—21no—
95#125×C113D411yescharacteristic
96#124×C113—22no—
97#124×C113—21no—
98#124×C113—21no—
99#124×C113—21no—
100#124×C113D411yescharacteristic
101#123×C113—22no—
102#123×C113—22no—
103#123×C113—21no—
104#123×C113—22no—
105C22⋊Q8×C113—22no—
106C22⋊Q8×C113—21no—
107C22⋊Q8×C113—21no—
108C22⋊Q8×C113—21no—
109C22⋊Q8×C113—21no—
110C22⋊Q8×C113D411yescharacteristic
111#121×C113—22no—
112#121×C113—22no—
113#121×C113—22no—
114#121×C113—22no—
115#121×C113—22no—
116#121×C113—21no—
117#121×C113—22no—
118#121×C113—21no—
119#121×C113—21no—
120#121×C113—21no—
121#121×C113—21no—
122#121×C113—21no—
123#121×C113D411yescharacteristic
124#121×C113D411yescharacteristic
125#121×C113D411yescharacteristic
126#121×C113D412yes—
127#120×C113—22no—
128#120×C113—22no—
129#120×C113—22no—
130#120×C113—22no—
131C4×Q8×C113—21no—
132C4×Q8×C113—21no—
133C4×Q8×C113—21no—
134C4×Q8×C113C2311yescharacteristic
135C4×D4×C113—22no—
136C4×D4×C113—21no—
137C4×D4×C113—21no—
138C4×D4×C113—21no—
139C4×D4×C113—21no—
140C4×D4×C113D412yes—
141C4×D4×C113C2311yescharacteristic
142C4×D4×C113C2311yescharacteristic
143C4×D4×C113C2311yescharacteristic
144#117×C113—21no—
145#117×C113—21no—
146#117×C113—21no—
147C2×C4⋊C4×C113—21no—
148C2×C22⋊C4×C113—22no—
149C2×C42×C113C2311yescharacteristic
150#107×C113—21no—
151#107×C113—21no—
152#107×C113—21no—
153#107×C113—22no—
154#106×C113—21no—
155#106×C113—22no—
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—21no—
165#103×C113—21no—
166#103×C113—21no—
167#103×C113—21no—
168#102×C113—21no—
169#102×C113—21no—
170#102×C113—21no—
171#102×C113—22no—
172#102×C113—22no—
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—
185C2×Q8×C113—21no—
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—81no—
204C2×D4×C113—81no—
205C2×D4×C113—81no—
206C2×D4×C113—81no—
207C2×D4×C113C2×D411yescharacteristic
208C2×D4×C113C2×D411yescharacteristic
209C2×D4×C113C2×D411yescharacteristic
210C2×D4×C113C2×D412yes—
211C22×C4×C113—22no—
212C22×C4×C113—22no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—22no—
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113C2×D411yescharacteristic
219C22×C4×C113C2×D411yescharacteristic
220Q16×C113—81no—
221SD16×C113—81no—
222SD16×C113—81no—
223SD16×C113—81no—
224M16×C113—81no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—81no—
232C4⋊C4×C113—22no—
233C4⋊C4×C113—22no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—21no—
244C4⋊C4×C113—41no—
245C4⋊C4×C113—41no—
246C4⋊C4×C113C2×D411yescharacteristic
247C4⋊C4×C113C2×D411yescharacteristic
248C4⋊C4×C113C2×D411yescharacteristic
249C4⋊C4×C113C2×D411yescharacteristic
250C4⋊C4×C113C2×D412yes—
251C22⋊C4×C113—22no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—22no—
255C22⋊C4×C113—22no—
256C22⋊C4×C113—21no—
257C22⋊C4×C113—21no—
258C22⋊C4×C113—21no—
259C22⋊C4×C113—21no—
260C22⋊C4×C113—21no—
261C22⋊C4×C113—21no—
262C22⋊C4×C113—22no—
263C22⋊C4×C113—22no—
264C22⋊C4×C113—21no—
265C22⋊C4×C113—21no—
266C22⋊C4×C113—21no—
267C22⋊C4×C113—41no—
268C42×C113—22no—
269C42×C113—21no—
270C42×C113—41no—
271C42×C113C2×D411yescharacteristic
272C42×C113C2×D411yescharacteristic
273C42×C113C2×D411yescharacteristic
274C42×C113C2411yescharacteristic
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—22no—
278C23×C113—21no—
279C23×C113—82no—
280C23×C113—82no—
281C23×C113—82no—
282C23×C113#12011yescharacteristic
283Q8×C113—21no—
284Q8×C113—21no—
285Q8×C113—41no—
286Q8×C113—41no—
287Q8×C113—41no—
288Q8×C113—41no—
289Q8×C113—41no—
290Q8×C113—41no—
291Q8×C113—81no—
292D4×C113—21no—
293D4×C113—21no—
294D4×C113—21no—
295D4×C113—21no—
296D4×C113—21no—
297D4×C113—21no—
298D4×C113—42no—
299D4×C113—41no—
300D4×C113—41no—
301D4×C113—41no—
302D4×C113—41no—
303D4×C113—81no—
304D4×C113—81no—
305D4×C113—81no—
306D4×C113—81no—
307D4×C113—81no—
308D4×C113—82no—
309D4×C113—82no—
310D4×C113—82no—
311D4×C113—82no—
312D4×C113—82no—
313D4×C113—82no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—21no—
318C2×C4×C113—21no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—22no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—41no—
325C2×C4×C113—41no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
328C2×C4×C113—41no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—82no—
334C2×C4×C113—82no—
335C2×C4×C113—82no—
336C2×C4×C113#12011yescharacteristic
337C2×C4×C113#12011yescharacteristic
338C2×C4×C113#12011yescharacteristic
339C2×C4×C113C22×D411yescharacteristic
340C2×C4×C113C22×D411yescharacteristic
341C2×C4×C113C22×D411yescharacteristic
342C8×C113—41no—
343C8×C113—41no—
344C8×C113—41no—
345C8×C113—41no—
346C8×C113—41no—
347C8×C113—41no—
348C22×C113—21no—
349C22×C113—21no—
350C22×C113—21no—
351C22×C113—41no—
352C22×C113—41no—
353C22×C113—41no—
354C22×C113—41no—
355C22×C113—42no—
356C22×C113—42no—
357C22×C113—41no—
358C22×C113—41no—
359C22×C113—42no—
360C22×C113—41no—
361C22×C113—41no—
362C22×C113—41no—
363C22×C113—164no—
364C22×C113C2×#12011yescharacteristic
365C4×C113—21no—
366C4×C113—21no—
367C4×C113—21no—
368C4×C113—21no—
369C4×C113—41no—
370C4×C113—41no—
371C4×C113—41no—
372C4×C113—41no—
373C4×C113—42no—
374C4×C113—41no—
375C4×C113—81no—
376C4×C113—81no—
377C4×C113#57611yescharacteristic
378C4×C113#57611yescharacteristic
379C4×C113#57711yescharacteristic
380C4×C113#57711yescharacteristic
381#18974C11311yesmaximal, characteristic, direct product factor, Sylow
382C2×C113—41no—
383C2×C113—81no—
384C2×C113—82no—
385C2×C113—81no—
386C2×C113—81no—
387C2×C113#301211yescharacteristic
388C2×C113#301211yescharacteristic
389C2×C113#302211yescharacteristic
390#3546C2×C11311yescharacteristic
391#3254C2×C11311yescharacteristic, complemented
392#3248C2×C11311yescharacteristic, complemented
393#3228C2×C11311yescharacteristic, complemented
394#1654C2×C11311yescharacteristic, complemented
395#1652C2×C11311yescharacteristic, complemented
396#1650C2×C11311yescharacteristic, complemented
397#1647C2×C11311yescharacteristic, complemented
398#1642C2×C11311yescharacteristic, complemented
399#1641C2×C11311yescharacteristic, complemented
400#1639C2×C11311yescharacteristic, complemented
401#1639C2×C11311yescharacteristic, complemented
402#1547C2×C11311yescharacteristic, complemented
403#1495C2×C11311yescharacteristic, complemented
404#1480C2×C11311yescharacteristic, complemented
405C113#1897411yescharacteristic, direct product factor, Sylow
406#560—22no—
407#556C22×C11311yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C11311yescharacteristic
411#547C22×C11311yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C11311yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C11311yescharacteristic, complemented
421#532C22×C11311yescharacteristic
422#532C22×C11311yescharacteristic
423#529C22×C11311yescharacteristic
424#500C22×C11311yescharacteristic, complemented
425#498C22×C11311yescharacteristic, complemented
426#486C22×C11311yescharacteristic
427#486C22×C11311yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C11311yescharacteristic, complemented
433#474C22×C11311yescharacteristic
434#474C22×C11311yescharacteristic
435#474C22×C11311yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C11311yescharacteristic, complemented
442#461C22×C11311yescharacteristic
443#461C22×C11311yescharacteristic
444#461C22×C11311yescharacteristic, complemented
445#460—21no—
446#431C22×C11311yescharacteristic, complemented
447#423C22×C11311yescharacteristic, complemented
448C2×C4⋊C8C22×C11311yescharacteristic, complemented
449#332C22×C11311yescharacteristic, complemented
450#332C22×C11311yescharacteristic, complemented
451#331C22×C11311yescharacteristic
452#331C22×C11311yescharacteristic
453Q8⋊C8C22×C11311yescharacteristic, complemented
454Q8⋊C8C22×C11311yescharacteristic, complemented
455D4⋊C8C22×C11311yescharacteristic
456D4⋊C8C22×C11311yescharacteristic
457D4⋊C8C22×C11311yescharacteristic
458D4⋊C8C22×C11311yescharacteristic
459D4⋊C8C22×C11311yescharacteristic, complemented
460D4⋊C8C22×C11311yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C11311yescharacteristic
474C4⋊Q8C23×C11311yescharacteristic
475C4⋊Q8C23×C11311yescharacteristic
476C4⋊Q8C23×C11311yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C11311yescharacteristic
480#127C23×C11311yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C11311yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C11311yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C11311yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C11311yescharacteristic
514#121D4×C11311yescharacteristic
515#121D4×C11311yescharacteristic
516#121D4×C11312yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C11311yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C11312yes—
531C4×D4C23×C11311yescharacteristic
532C4×D4C23×C11311yescharacteristic
533C4×D4C23×C11311yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C11311yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C11311yescharacteristic
550C4⋊C8C23×C11311yescharacteristic
551C4⋊C8C23×C11311yescharacteristic
552C4⋊C8C23×C11311yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C11311yescharacteristic
565C4×C8C23×C11311yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C11311yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C11311yescharacteristic
598C2×D4C2×D4×C11311yescharacteristic
599C2×D4C2×D4×C11311yescharacteristic
600C2×D4C2×D4×C11312yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C11311yescharacteristic
608C22×C4C2×D4×C11311yescharacteristic
609C22×C4C2×D4×C11311yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C11311yescharacteristic
637C4⋊C4C2×D4×C11311yescharacteristic
638C4⋊C4C2×D4×C11311yescharacteristic
639C4⋊C4C2×D4×C11311yescharacteristic
640C4⋊C4C2×D4×C11312yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C11311yescharacteristic
662C42C2×D4×C11311yescharacteristic
663C42C2×D4×C11311yescharacteristic
664C42C24×C11311yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C11311yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C11311yescharacteristic
727C2×C4#120×C11311yescharacteristic
728C2×C4#120×C11311yescharacteristic
729C2×C4C22×D4×C11311yescharacteristic
730C2×C4C22×D4×C11311yescharacteristic
731C2×C4C22×D4×C11311yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C11311yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C11311yescharacteristic
768C4#576×C11311yescharacteristic
769C4#577×C11311yescharacteristic
770C4#577×C11311yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C113×#301211yescharacteristic
777C2C113×#301211yescharacteristic
778C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3546C2
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
2. C113×#3254C2semidirect
3. C113×#3248C2semidirect
4. C113×#3228C2semidirect
5. C113×#1654C2semidirect
6. C113×#1652C2semidirect
7. C113×#1650C2semidirect
8. C113×#1647C2semidirect
9. C113×#1642C2semidirect
10. C113×#1641C2semidirect
11. C113×#1639C2semidirect
12. C113×#1639C2semidirect
13. C113×#1547C2semidirect
14. C113×#1495C2semidirect
15. C113×#1480C2semidirect
30. #533×C113C22semidirect
34. #500×C113C22semidirect
35. #498×C113C22semidirect
42. #475×C113C22semidirect
45. #474×C113C22semidirect
51. #462×C113C22semidirect
54. #461×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
381. #18974C113direct (N × H)
391. #3254C2×C113semidirect
392. #3248C2×C113semidirect
393. #3228C2×C113semidirect
394. #1654C2×C113semidirect
395. #1652C2×C113semidirect
396. #1650C2×C113semidirect
397. #1647C2×C113semidirect
398. #1642C2×C113semidirect
399. #1641C2×C113semidirect
400. #1639C2×C113semidirect
401. #1639C2×C113semidirect
402. #1547C2×C113semidirect
403. #1495C2×C113semidirect
404. #1480C2×C113semidirect
405. C113#18974direct (N × H)
420. #533C22×C113semidirect
424. #500C22×C113semidirect
425. #498C22×C113semidirect
432. #475C22×C113semidirect
435. #474C22×C113semidirect
441. #462C22×C113semidirect
444. #461C22×C113semidirect
446. #431C22×C113semidirect
447. #423C22×C113semidirect
448. C2×C4⋊C8C22×C113semidirect
449. #332C22×C113semidirect
450. #332C22×C113semidirect
453. Q8⋊C8C22×C113semidirect
454. Q8⋊C8C22×C113semidirect
459. D4⋊C8C22×C113semidirect
460. 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×#32542
C113×#32482
C113×#32282
C113×#16542
C113×#16522
C113×#16502
C113×#16472
C113×#16422
C113×#16412
C113×#16392
C113×#15472
C113×#14952
C113×#14802
#18974113