Finite Group Databasebeta

← C113×#18931 #43286951

Subgroups — C113×#18931 #43286951

Order 28928.

986 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3543C211yesmaximal, characteristic
2C113×#3252C211yesmaximal, characteristic, complemented
3C113×#3233C211yesmaximal, characteristic, complemented
4C113×#3208C211yesmaximal, characteristic, complemented
5C113×#1642C211yesmaximal, characteristic, complemented
6C113×#1641C211yesmaximal, characteristic, complemented
7C113×#1640C211yesmaximal, characteristic, complemented
8C113×#1639C211yesmaximal, characteristic, complemented
9C113×#1631C211yesmaximal, characteristic, complemented
10C113×#1631C211yesmaximal, characteristic, complemented
11C113×#1630C211yesmaximal, characteristic, complemented
12C113×#1629C211yesmaximal, characteristic, complemented
13C113×#1545C211yesmaximal, characteristic, complemented
14C113×#1495C211yesmaximal, characteristic, complemented
15C113×#1482C211yesmaximal, characteristic, complemented
16#560×C113—22no—
17#559×C113C2211yescharacteristic
18#550×C113C2211yescharacteristic
19#550×C113C2211yescharacteristic
20#546×C113—21no—
21#546×C113—21no—
22D42×C113—21no—
23D42×C113—21no—
24D42×C113C2211yescharacteristic
25#540×C113—21no—
26#540×C113—21no—
27#535×C113—21no—
28#535×C113—21no—
29#534×C113—22no—
30#533×C113C2211yescharacteristic, complemented
31C2×#127×C113C2211yescharacteristic
32#529×C113C2211yescharacteristic
33#529×C113C2211yescharacteristic
34#499×C113—21no—
35#492×C113C2211yescharacteristic
36#492×C113C2211yescharacteristic, complemented
37#488×C113—21no—
38#486×C113C2211yescharacteristic
39#486×C113C2211yescharacteristic, complemented
40#485×C113—21no—
41#482×C113—21no—
42#479×C113—21no—
43#477×C113C2211yescharacteristic, complemented
44#477×C113C2211yescharacteristic, complemented
45#476×C113C2211yescharacteristic, complemented
46#476×C113C2211yescharacteristic, complemented
47#475×C113C2211yescharacteristic, complemented
48#474×C113C2211yescharacteristic, complemented
49#470×C113—21no—
50#468×C113—21no—
51#464×C113—21no—
52#462×C113C2211yescharacteristic, complemented
53#461×C113C2211yescharacteristic, complemented
54#460×C113—22no—
55#450×C113—22no—
56#431×C113C2211yescharacteristic, complemented
57#431×C113C2211yescharacteristic, complemented
58#423×C113C2211yescharacteristic, complemented
59#331×C113C2211yescharacteristic
60#331×C113C2211yescharacteristic
61#331×C113C2211yescharacteristic, complemented
62#331×C113C2211yescharacteristic, complemented
63Q8⋊C8×C113C2211yescharacteristic, complemented
64Q8⋊C8×C113C2211yescharacteristic, complemented
65Q8⋊C8×C113C2211yescharacteristic, complemented
66Q8⋊C8×C113C2211yescharacteristic, complemented
67D4⋊C8×C113C2211yescharacteristic, complemented
68D4⋊C8×C113C2211yescharacteristic, complemented
69D4⋊C8×C113C2211yescharacteristic, complemented
70D4⋊C8×C113C2211yescharacteristic, complemented
71C2×#41×C113—21no—
72C2×#41×C113—21no—
73C22×D4×C113—22no—
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113D412yes—
79C2×Q16×C113—21no—
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—21no—
83C2×M16×C113—21no—
84C4⋊Q8×C113C2311yescharacteristic
85C4⋊Q8×C113C2311yescharacteristic
86#127×C113—21no—
87#127×C113—21no—
88#127×C113—21no—
89#127×C113—21no—
90#127×C113D412yes—
91#127×C113C2311yescharacteristic
92#127×C113C2311yescharacteristic
93#126×C113—21no—
94#126×C113—21no—
95#125×C113—21no—
96#125×C113D411yescharacteristic
97#125×C113D411yescharacteristic
98#124×C113—21no—
99#124×C113—21no—
100#124×C113D411yescharacteristic
101#124×C113D411yescharacteristic
102#123×C113—22no—
103#123×C113—22no—
104#123×C113—22no—
105#123×C113—22no—
106#123×C113—21no—
107#123×C113—21no—
108C22⋊Q8×C113—21no—
109C22⋊Q8×C113—21no—
110C22⋊Q8×C113D411yescharacteristic
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—22no—
118#121×C113—22no—
119#121×C113—22no—
120#121×C113—21no—
121#121×C113—21no—
122#121×C113—21no—
123#121×C113—21no—
124#121×C113D411yescharacteristic
125#121×C113D411yescharacteristic
126#120×C113—22no—
127#120×C113—22no—
128#120×C113—22no—
129#120×C113—22no—
130#120×C113—22no—
131#120×C113—22no—
132C4×Q8×C113—21no—
133C4×Q8×C113—21no—
134C4×Q8×C113C2311yescharacteristic
135C4×Q8×C113C2311yescharacteristic
136C4×D4×C113—21no—
137C4×D4×C113—21no—
138C4×D4×C113—21no—
139C4×D4×C113—21no—
140C4×D4×C113—21no—
141C4×D4×C113—21no—
142C4×D4×C113C2311yescharacteristic
143C4×D4×C113C2311yescharacteristic
144#117×C113—21no—
145#117×C113—21no—
146#117×C113—21no—
147C2×C22⋊C4×C113—22no—
148C2×C42×C113C2311yescharacteristic
149#107×C113—21no—
150#107×C113—21no—
151#107×C113—21no—
152#106×C113—21no—
153#106×C113—21no—
154#106×C113—21no—
155C4⋊C8×C113—21no—
156C4⋊C8×C113—21no—
157C4⋊C8×C113C2311yescharacteristic
158C4⋊C8×C113C2311yescharacteristic
159C4⋊C8×C113C2311yescharacteristic
160C4⋊C8×C113C2311yescharacteristic
161#103×C113—21no—
162#103×C113—21no—
163#103×C113—21no—
164#103×C113—21no—
165#103×C113—21no—
166#102×C113—22no—
167#102×C113—22no—
168#102×C113—21no—
169#102×C113—21no—
170#102×C113—21no—
171C22⋊C8×C113—21no—
172C22⋊C8×C113—21no—
173C4×C8×C113—21no—
174C4×C8×C113C2311yescharacteristic
175C4×C8×C113C2311yescharacteristic
176C24×C113—22no—
177C24×C113—22no—
178#41×C113—81no—
179#41×C113—81no—
180#41×C113—81no—
181#41×C113—81no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113C2×D411yescharacteristic
185C2×Q8×C113C2×D411yescharacteristic
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—22no—
189C2×D4×C113—22no—
190C2×D4×C113—22no—
191C2×D4×C113—22no—
192C2×D4×C113—22no—
193C2×D4×C113—22no—
194C2×D4×C113—22no—
195C2×D4×C113—22no—
196C2×D4×C113—22no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—81no—
202C2×D4×C113—81no—
203C2×D4×C113—81no—
204C2×D4×C113—81no—
205C2×D4×C113—81no—
206C2×D4×C113—81no—
207C2×D4×C113—81no—
208C2×D4×C113—81no—
209C2×D4×C113—82no—
210C2×D4×C113—84no—
211C2×D4×C113C2×D411yescharacteristic
212C2×D4×C113C2×D411yescharacteristic
213C2×D4×C113C2×D412yes—
214C2×D4×C113C2×D412yes—
215C22×C4×C113—22no—
216C22×C4×C113—22no—
217C22×C4×C113—22no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113C2×D411yescharacteristic
221C22×C4×C113C2×D411yescharacteristic
222C22×C4×C113C2×D411yescharacteristic
223Q16×C113—81no—
224SD16×C113—81no—
225SD16×C113—82no—
226SD16×C113—82no—
227M16×C113—81no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
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—21no—
245C4⋊C4×C113—21no—
246C4⋊C4×C113—41no—
247C4⋊C4×C113—41no—
248C4⋊C4×C113C2×D411yescharacteristic
249C4⋊C4×C113C2×D411yescharacteristic
250C4⋊C4×C113C2×D411yescharacteristic
251C4⋊C4×C113C2×D411yescharacteristic
252C22⋊C4×C113—22no—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—22no—
255C22⋊C4×C113—22no—
256C22⋊C4×C113—22no—
257C22⋊C4×C113—22no—
258C22⋊C4×C113—21no—
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—21no—
266C22⋊C4×C113—21no—
267C22⋊C4×C113—21no—
268C22⋊C4×C113—41no—
269C42×C113—21no—
270C42×C113—21no—
271C42×C113—41no—
272C42×C113C2×D411yescharacteristic
273C42×C113C2×D411yescharacteristic
274C42×C113C2×D411yescharacteristic
275C42×C113C2411yescharacteristic
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—22no—
279C23×C113—22no—
280C23×C113—44no—
281C23×C113—82no—
282C23×C113—82no—
283C23×C113—82no—
284C23×C113—82no—
285C23×C113—82no—
286C23×C113#12011yescharacteristic
287Q8×C113—21no—
288Q8×C113—21no—
289Q8×C113—21no—
290Q8×C113—21no—
291Q8×C113—42no—
292Q8×C113—41no—
293Q8×C113—41no—
294D4×C113—21no—
295D4×C113—21no—
296D4×C113—21no—
297D4×C113—21no—
298D4×C113—42no—
299D4×C113—42no—
300D4×C113—42no—
301D4×C113—42no—
302D4×C113—41no—
303D4×C113—41no—
304D4×C113—41no—
305D4×C113—41no—
306D4×C113—41no—
307D4×C113—41no—
308D4×C113—41no—
309D4×C113—41no—
310D4×C113—82no—
311D4×C113—82no—
312D4×C113—82no—
313D4×C113—82no—
314D4×C113—82no—
315D4×C113—82no—
316D4×C113—82no—
317D4×C113—82no—
318D4×C113—82no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
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—21no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—82no—
337C2×C4×C113—82no—
338C2×C4×C113—82no—
339C2×C4×C113#12011yescharacteristic
340C2×C4×C113#12011yescharacteristic
341C2×C4×C113#12011yescharacteristic
342C2×C4×C113C22×D411yescharacteristic
343C2×C4×C113C22×D411yescharacteristic
344C2×C4×C113C22×D411yescharacteristic
345C8×C113—41no—
346C8×C113—41no—
347C8×C113—41no—
348C8×C113—41no—
349C8×C113—41no—
350C8×C113—41no—
351C22×C113—21no—
352C22×C113—21no—
353C22×C113—21no—
354C22×C113—41no—
355C22×C113—42no—
356C22×C113—41no—
357C22×C113—42no—
358C22×C113—41no—
359C22×C113—42no—
360C22×C113—41no—
361C22×C113—42no—
362C22×C113—42no—
363C22×C113—41no—
364C22×C113—41no—
365C22×C113—42no—
366C22×C113—164no—
367C22×C113—164no—
368C22×C113C2×#12011yescharacteristic
369C4×C113—21no—
370C4×C113—21no—
371C4×C113—21no—
372C4×C113—21no—
373C4×C113—41no—
374C4×C113—41no—
375C4×C113—41no—
376C4×C113—41no—
377C4×C113—41no—
378C4×C113—41no—
379C4×C113—81no—
380C4×C113—81no—
381C4×C113#57611yescharacteristic
382C4×C113#57711yescharacteristic
383C4×C113#57711yescharacteristic
384C4×C113#57711yescharacteristic
385#18931C11311yesmaximal, characteristic, direct product factor, Sylow
386C2×C113—41no—
387C2×C113—82no—
388C2×C113—81no—
389C2×C113—81no—
390C2×C113—82no—
391C2×C113#300911yescharacteristic
392C2×C113#301211yescharacteristic
393C2×C113#301911yescharacteristic
394#3543C2×C11311yescharacteristic
395#3252C2×C11311yescharacteristic, complemented
396#3233C2×C11311yescharacteristic, complemented
397#3208C2×C11311yescharacteristic, complemented
398#1642C2×C11311yescharacteristic, complemented
399#1641C2×C11311yescharacteristic, complemented
400#1640C2×C11311yescharacteristic, complemented
401#1639C2×C11311yescharacteristic, complemented
402#1631C2×C11311yescharacteristic, complemented
403#1631C2×C11311yescharacteristic, complemented
404#1630C2×C11311yescharacteristic, complemented
405#1629C2×C11311yescharacteristic, complemented
406#1545C2×C11311yescharacteristic, complemented
407#1495C2×C11311yescharacteristic, complemented
408#1482C2×C11311yescharacteristic, complemented
409C113#1893111yescharacteristic, direct product factor, Sylow
410#560—22no—
411#559C22×C11311yescharacteristic
412#550C22×C11311yescharacteristic
413#550C22×C11311yescharacteristic
414#546—21no—
415#546—21no—
416D42—21no—
417D42—21no—
418D42C22×C11311yescharacteristic
419#540—21no—
420#540—21no—
421#535—21no—
422#535—21no—
423#534—22no—
424#533C22×C11311yescharacteristic, complemented
425C2×#127C22×C11311yescharacteristic
426#529C22×C11311yescharacteristic
427#529C22×C11311yescharacteristic
428#499—21no—
429#492C22×C11311yescharacteristic
430#492C22×C11311yescharacteristic, complemented
431#488—21no—
432#486C22×C11311yescharacteristic
433#486C22×C11311yescharacteristic, complemented
434#485—21no—
435#482—21no—
436#479—21no—
437#477C22×C11311yescharacteristic, complemented
438#477C22×C11311yescharacteristic, complemented
439#476C22×C11311yescharacteristic, complemented
440#476C22×C11311yescharacteristic, complemented
441#475C22×C11311yescharacteristic, complemented
442#474C22×C11311yescharacteristic, complemented
443#470—21no—
444#468—21no—
445#464—21no—
446#462C22×C11311yescharacteristic, complemented
447#461C22×C11311yescharacteristic, complemented
448#460—22no—
449#450—22no—
450#431C22×C11311yescharacteristic, complemented
451#431C22×C11311yescharacteristic, complemented
452#423C22×C11311yescharacteristic, complemented
453#331C22×C11311yescharacteristic
454#331C22×C11311yescharacteristic
455#331C22×C11311yescharacteristic, complemented
456#331C22×C11311yescharacteristic, complemented
457Q8⋊C8C22×C11311yescharacteristic, complemented
458Q8⋊C8C22×C11311yescharacteristic, complemented
459Q8⋊C8C22×C11311yescharacteristic, complemented
460Q8⋊C8C22×C11311yescharacteristic, complemented
461D4⋊C8C22×C11311yescharacteristic, complemented
462D4⋊C8C22×C11311yescharacteristic, complemented
463D4⋊C8C22×C11311yescharacteristic, complemented
464D4⋊C8C22×C11311yescharacteristic, complemented
465C2×#41—21no—
466C2×#41—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C11312yes—
473C2×Q16—21no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—21no—
477C2×M16—21no—
478C4⋊Q8C23×C11311yescharacteristic
479C4⋊Q8C23×C11311yescharacteristic
480#127—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127D4×C11312yes—
485#127C23×C11311yescharacteristic
486#127C23×C11311yescharacteristic
487#126—21no—
488#126—21no—
489#125—21no—
490#125D4×C11311yescharacteristic
491#125D4×C11311yescharacteristic
492#124—21no—
493#124—21no—
494#124D4×C11311yescharacteristic
495#124D4×C11311yescharacteristic
496#123—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C11311yescharacteristic
505C22⋊Q8D4×C11311yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121D4×C11311yescharacteristic
519#121D4×C11311yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8C23×C11311yescharacteristic
529C4×Q8C23×C11311yescharacteristic
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4C23×C11311yescharacteristic
537C4×D4C23×C11311yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541C2×C22⋊C4—22no—
542C2×C42C23×C11311yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C11311yescharacteristic
552C4⋊C8C23×C11311yescharacteristic
553C4⋊C8C23×C11311yescharacteristic
554C4⋊C8C23×C11311yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C4×C8—21no—
568C4×C8C23×C11311yescharacteristic
569C4×C8C23×C11311yescharacteristic
570C24—22no—
571C24—22no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C11311yescharacteristic
579C2×Q8C2×D4×C11311yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—82no—
604C2×D4—84no—
605C2×D4C2×D4×C11311yescharacteristic
606C2×D4C2×D4×C11311yescharacteristic
607C2×D4C2×D4×C11312yes—
608C2×D4C2×D4×C11312yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4C2×D4×C11311yescharacteristic
615C22×C4C2×D4×C11311yescharacteristic
616C22×C4C2×D4×C11311yescharacteristic
617Q16—81no—
618SD16—81no—
619SD16—82no—
620SD16—82no—
621M16—81no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C11311yescharacteristic
643C4⋊C4C2×D4×C11311yescharacteristic
644C4⋊C4C2×D4×C11311yescharacteristic
645C4⋊C4C2×D4×C11311yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42C2×D4×C11311yescharacteristic
667C42C2×D4×C11311yescharacteristic
668C42C2×D4×C11311yescharacteristic
669C42C24×C11311yescharacteristic
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23#120×C11311yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709D4—82no—
710D4—82no—
711D4—82no—
712D4—82no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C11311yescharacteristic
734C2×C4#120×C11311yescharacteristic
735C2×C4#120×C11311yescharacteristic
736C2×C4C22×D4×C11311yescharacteristic
737C2×C4C22×D4×C11311yescharacteristic
738C2×C4C22×D4×C11311yescharacteristic
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—164no—
761C22—164no—
762C22C2×#120×C11311yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4#576×C11311yescharacteristic
776C4#577×C11311yescharacteristic
777C4#577×C11311yescharacteristic
778C4#577×C11311yescharacteristic
779C2—41no—
780C2—81no—
781C2—81no—
782C2—82no—
783C2—82no—
784C2C113×#300911yescharacteristic
785C2C113×#301211yescharacteristic
786C2C113×#301911yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3543C2
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×#3252C2semidirect
3. C113×#3233C2semidirect
4. C113×#3208C2semidirect
5. C113×#1642C2semidirect
6. C113×#1641C2semidirect
7. C113×#1640C2semidirect
8. C113×#1639C2semidirect
9. C113×#1631C2semidirect
10. C113×#1631C2semidirect
11. C113×#1630C2semidirect
12. C113×#1629C2semidirect
13. C113×#1545C2semidirect
14. C113×#1495C2semidirect
15. C113×#1482C2semidirect
30. #533×C113C22semidirect
36. #492×C113C22semidirect
39. #486×C113C22semidirect
43. #477×C113C22semidirect
44. #477×C113C22semidirect
45. #476×C113C22semidirect
46. #476×C113C22semidirect
47. #475×C113C22semidirect
48. #474×C113C22semidirect
52. #462×C113C22semidirect
53. #461×C113C22semidirect
56. #431×C113C22semidirect
57. #431×C113C22semidirect
58. #423×C113C22semidirect
61. #331×C113C22semidirect
62. #331×C113C22semidirect
63. Q8⋊C8×C113C22semidirect
64. Q8⋊C8×C113C22semidirect
65. Q8⋊C8×C113C22semidirect
66. Q8⋊C8×C113C22semidirect
67. D4⋊C8×C113C22semidirect
68. D4⋊C8×C113C22semidirect
69. D4⋊C8×C113C22semidirect
70. D4⋊C8×C113C22semidirect
385. #18931C113direct (N × H)
395. #3252C2×C113semidirect
396. #3233C2×C113semidirect
397. #3208C2×C113semidirect
398. #1642C2×C113semidirect
399. #1641C2×C113semidirect
400. #1640C2×C113semidirect
401. #1639C2×C113semidirect
402. #1631C2×C113semidirect
403. #1631C2×C113semidirect
404. #1630C2×C113semidirect
405. #1629C2×C113semidirect
406. #1545C2×C113semidirect
407. #1495C2×C113semidirect
408. #1482C2×C113semidirect
409. C113#18931direct (N × H)
424. #533C22×C113semidirect
430. #492C22×C113semidirect
433. #486C22×C113semidirect
437. #477C22×C113semidirect
438. #477C22×C113semidirect
439. #476C22×C113semidirect
440. #476C22×C113semidirect
441. #475C22×C113semidirect
442. #474C22×C113semidirect
446. #462C22×C113semidirect
447. #461C22×C113semidirect
450. #431C22×C113semidirect
451. #431C22×C113semidirect
452. #423C22×C113semidirect
455. #331C22×C113semidirect
456. #331C22×C113semidirect
457. Q8⋊C8C22×C113semidirect
458. Q8⋊C8C22×C113semidirect
459. Q8⋊C8C22×C113semidirect
460. Q8⋊C8C22×C113semidirect
461. D4⋊C8C22×C113semidirect
462. D4⋊C8C22×C113semidirect
463. D4⋊C8C22×C113semidirect
464. D4⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35432
C113×#32522
C113×#32332
C113×#32082
C113×#16422
C113×#16412
C113×#16402
C113×#16392
C113×#16312
C113×#16302
C113×#16292
C113×#15452
C113×#14952
C113×#14822
#18931113