Finite Group Databasebeta

← C113×#18965 #43286985

Subgroups — C113×#18965 #43286985

Order 28928.

900 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3547C211yesmaximal, characteristic, complemented
2C113×#3253C211yesmaximal, characteristic, complemented
3C113×#3247C211yesmaximal, characteristic, complemented
4C113×#3210C211yesmaximal, characteristic, complemented
5C113×#1637C211yesmaximal, characteristic, complemented
6C113×#1635C211yesmaximal, characteristic, complemented
7C113×#1634C211yesmaximal, characteristic, complemented
8C113×#1632C211yesmaximal, characteristic, complemented
9C113×#1627C211yesmaximal, characteristic, complemented
10C113×#1625C211yesmaximal, characteristic, complemented
11C113×#1624C211yesmaximal, characteristic, complemented
12C113×#1622C211yesmaximal, characteristic, complemented
13C113×#1550C211yesmaximal, characteristic, complemented
14C113×#1495C211yesmaximal, characteristic, complemented
15C113×#1480C211yesmaximal, characteristic, complemented
16#562×C113—22no—
17#555×C113—21no—
18#555×C113C2211yescharacteristic
19#554×C113C2211yescharacteristic
20#553×C113—21no—
21#552×C113—21no—
22D4×Q8×C113C2211yescharacteristic
23#548×C113—21no—
24#547×C113C2211yescharacteristic
25#544×C113—21no—
26#542×C113—22no—
27#540×C113—21no—
28#537×C113—21no—
29#536×C113—21no—
30#533×C113C2211yescharacteristic
31#532×C113C2211yescharacteristic
32#532×C113C2211yescharacteristic
33#529×C113C2211yescharacteristic
34#494×C113C2211yescharacteristic
35#492×C113C2211yescharacteristic
36#487×C113C2211yescharacteristic
37#486×C113C2211yescharacteristic
38#478×C113—21no—
39#477×C113C2211yescharacteristic
40#476×C113—21no—
41#476×C113C2211yescharacteristic
42#476×C113C2211yescharacteristic
43#476×C113C2211yescharacteristic
44#469×C113—21no—
45#469×C113—21no—
46#466×C113—21no—
47#465×C113—21no—
48#464×C113—22no—
49#463×C113—21no—
50#460×C113C2211yescharacteristic
51#459×C113—21no—
52#459×C113C2211yescharacteristic
53#459×C113C2211yescharacteristic
54#459×C113C2211yescharacteristic
55#452×C113—22no—
56#431×C113C2211yescharacteristic
57#423×C113C2211yescharacteristic
58C2×C4⋊C8×C113C2211yescharacteristic
59#333×C113C2211yescharacteristic
60#333×C113C2211yescharacteristic
61#332×C113C2211yescharacteristic
62#332×C113C2211yescharacteristic
63Q8⋊C8×C113C2211yescharacteristic
64Q8⋊C8×C113C2211yescharacteristic
65D4⋊C8×C113C2211yescharacteristic
66D4⋊C8×C113C2211yescharacteristic
67D4⋊C8×C113C2211yescharacteristic
68D4⋊C8×C113C2211yescharacteristic
69D4⋊C8×C113C2211yescharacteristic
70D4⋊C8×C113C2211yescharacteristic
71C2×#41×C113—21no—
72C2×#41×C113—21no—
73C2×#41×C113—21no—
74C22×Q8×C113—21no—
75C2×Q16×C113—22no—
76C2×SD16×C113—22no—
77C2×SD16×C113—21no—
78C2×D8×C113—21no—
79C2×D8×C113—21no—
80C2×D8×C113—21no—
81C2×M16×C113—21no—
82C22×C8×C113—21no—
83C4⋊Q8×C113—22no—
84C4⋊Q8×C113—21no—
85C4⋊Q8×C113D411yescharacteristic
86C4⋊Q8×C113C2311yescharacteristic
87C4⋊Q8×C113C2311yescharacteristic
88C4⋊Q8×C113C2311yescharacteristic
89#127×C113D411yescharacteristic
90#127×C113C2311yescharacteristic
91#126×C113—22no—
92#126×C113—21no—
93#125×C113—22no—
94#125×C113—21no—
95#125×C113—21no—
96#125×C113D411yescharacteristic
97#124×C113—22no—
98#124×C113—22no—
99#124×C113—22no—
100#124×C113—21no—
101#124×C113—21no—
102#124×C113D411yescharacteristic
103#123×C113—22no—
104#123×C113—22no—
105#123×C113—22no—
106#123×C113—21no—
107#123×C113—22no—
108C22⋊Q8×C113—22no—
109C22⋊Q8×C113—22no—
110C22⋊Q8×C113—21no—
111C22⋊Q8×C113—22no—
112C22⋊Q8×C113—21no—
113C22⋊Q8×C113—21no—
114C22⋊Q8×C113—21no—
115C22⋊Q8×C113—22no—
116C22⋊Q8×C113D411yescharacteristic
117C22⋊Q8×C113D412yes—
118#121×C113—22no—
119#121×C113—22no—
120#121×C113—22no—
121#121×C113—22no—
122#121×C113—21no—
123#121×C113—21no—
124#121×C113—21no—
125#121×C113—21no—
126#121×C113—21no—
127#121×C113—21no—
128#121×C113D411yescharacteristic
129#121×C113D411yescharacteristic
130#121×C113D411yescharacteristic
131C4×Q8×C113—21no—
132C4×Q8×C113D412yes—
133C4×Q8×C113C2311yescharacteristic
134C4×D4×C113—22no—
135C4×D4×C113—21no—
136C4×D4×C113—21no—
137C4×D4×C113—21no—
138C4×D4×C113—21no—
139C4×D4×C113—21no—
140C4×D4×C113—21no—
141C4×D4×C113C2311yescharacteristic
142C4×D4×C113C2311yescharacteristic
143C4×D4×C113C2311yescharacteristic
144#117×C113—22no—
145#117×C113—21no—
146#117×C113—21no—
147#117×C113—21no—
148#117×C113—21no—
149C2×C4⋊C4×C113—21no—
150C2×C4⋊C4×C113—21no—
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
176#41×C113—81no—
177#41×C113—81no—
178#41×C113—81no—
179#41×C113—81no—
180#41×C113—82no—
181C2×Q8×C113—22no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113—81no—
186C2×Q8×C113—81no—
187C2×Q8×C113C2×D411yescharacteristic
188C2×Q8×C113C2×D412yes—
189C2×D4×C113—22no—
190C2×D4×C113—22no—
191C2×D4×C113—21no—
192C2×D4×C113—21no—
193C2×D4×C113—21no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—41no—
200C2×D4×C113C2×D411yescharacteristic
201C2×D4×C113C2×D411yescharacteristic
202C2×D4×C113C2×D411yescharacteristic
203C22×C4×C113—22no—
204C22×C4×C113—22no—
205C22×C4×C113—22no—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—21no—
209C22×C4×C113—41no—
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D411yescharacteristic
213Q16×C113—82no—
214SD16×C113—81no—
215SD16×C113—82no—
216D8×C113—81no—
217D8×C113—81no—
218D8×C113—81no—
219M16×C113—81no—
220C2×C8×C113—21no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—81no—
227C4⋊C4×C113—22no—
228C4⋊C4×C113—22no—
229C4⋊C4×C113—22no—
230C4⋊C4×C113—22no—
231C4⋊C4×C113—21no—
232C4⋊C4×C113—21no—
233C4⋊C4×C113—21no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—22no—
236C4⋊C4×C113—22no—
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×C113C2×D412yes—
244C4⋊C4×C113C2×D411yescharacteristic
245C4⋊C4×C113C2×D411yescharacteristic
246C4⋊C4×C113C2×D411yescharacteristic
247C4⋊C4×C113C2×D411yescharacteristic
248C22⋊C4×C113—22no—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—22no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—21no—
255C22⋊C4×C113—21no—
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—21no—
263C22⋊C4×C113—41no—
264C22⋊C4×C113—41no—
265C42×C113—22no—
266C42×C113—22no—
267C42×C113—21no—
268C42×C113C2×D411yescharacteristic
269C42×C113C2×D411yescharacteristic
270C42×C113C2×D411yescharacteristic
271C42×C113C2411yescharacteristic
272C23×C113—21no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—41no—
276C23×C113#12011yescharacteristic
277Q8×C113—21no—
278Q8×C113—21no—
279Q8×C113—42no—
280Q8×C113—42no—
281Q8×C113—41no—
282Q8×C113—41no—
283Q8×C113—81no—
284Q8×C113—82no—
285D4×C113—21no—
286D4×C113—21no—
287D4×C113—21no—
288D4×C113—21no—
289D4×C113—21no—
290D4×C113—21no—
291D4×C113—42no—
292D4×C113—41no—
293D4×C113—41no—
294D4×C113—41no—
295D4×C113—41no—
296D4×C113—81no—
297D4×C113—81no—
298D4×C113—81no—
299D4×C113—81no—
300D4×C113—81no—
301D4×C113—82no—
302D4×C113—82no—
303D4×C113—82no—
304C2×C4×C113—21no—
305C2×C4×C113—21no—
306C2×C4×C113—21no—
307C2×C4×C113—21no—
308C2×C4×C113—21no—
309C2×C4×C113—22no—
310C2×C4×C113—21no—
311C2×C4×C113—21no—
312C2×C4×C113—21no—
313C2×C4×C113—22no—
314C2×C4×C113—21no—
315C2×C4×C113—41no—
316C2×C4×C113—41no—
317C2×C4×C113—41no—
318C2×C4×C113—41no—
319C2×C4×C113—41no—
320C2×C4×C113—41no—
321C2×C4×C113—41no—
322C2×C4×C113—41no—
323C2×C4×C113—82no—
324C2×C4×C113—82no—
325C2×C4×C113—82no—
326C2×C4×C113—82no—
327C2×C4×C113#12011yescharacteristic
328C2×C4×C113#12011yescharacteristic
329C2×C4×C113#12011yescharacteristic
330C2×C4×C113C22×D411yescharacteristic
331C2×C4×C113C22×D411yescharacteristic
332C2×C4×C113C22×D411yescharacteristic
333C8×C113—41no—
334C8×C113—41no—
335C8×C113—41no—
336C8×C113—41no—
337C8×C113—41no—
338C8×C113—41no—
339C22×C113—21no—
340C22×C113—21no—
341C22×C113—21no—
342C22×C113—41no—
343C22×C113—41no—
344C22×C113—41no—
345C22×C113—41no—
346C22×C113—41no—
347C22×C113—41no—
348C22×C113—41no—
349C22×C113—41no—
350C22×C113—41no—
351C22×C113—81no—
352C22×C113—81no—
353C22×C113—81no—
354C22×C113C2×#12011yescharacteristic
355C4×C113—21no—
356C4×C113—21no—
357C4×C113—21no—
358C4×C113—21no—
359C4×C113—41no—
360C4×C113—41no—
361C4×C113—42no—
362C4×C113—41no—
363C4×C113—41no—
364C4×C113—41no—
365C4×C113—42no—
366C4×C113—81no—
367C4×C113#57611yescharacteristic
368C4×C113#57711yescharacteristic
369C4×C113#57711yescharacteristic
370C4×C113#57811yescharacteristic
371#18965C11311yesmaximal, characteristic, direct product factor, Sylow
372C2×C113—41no—
373C2×C113—81no—
374C2×C113—81no—
375C2×C113—81no—
376C2×C113—161no—
377C2×C113#301211yescharacteristic
378C2×C113#301311yescharacteristic
379C2×C113#302111yescharacteristic
380#3547C2×C11311yescharacteristic, complemented
381#3253C2×C11311yescharacteristic, complemented
382#3247C2×C11311yescharacteristic, complemented
383#3210C2×C11311yescharacteristic, complemented
384#1637C2×C11311yescharacteristic, complemented
385#1635C2×C11311yescharacteristic, complemented
386#1634C2×C11311yescharacteristic, complemented
387#1632C2×C11311yescharacteristic, complemented
388#1627C2×C11311yescharacteristic, complemented
389#1625C2×C11311yescharacteristic, complemented
390#1624C2×C11311yescharacteristic, complemented
391#1622C2×C11311yescharacteristic, complemented
392#1550C2×C11311yescharacteristic, complemented
393#1495C2×C11311yescharacteristic, complemented
394#1480C2×C11311yescharacteristic, complemented
395C113#1896511yescharacteristic, direct product factor, Sylow
396#562—22no—
397#555—21no—
398#555C22×C11311yescharacteristic
399#554C22×C11311yescharacteristic
400#553—21no—
401#552—21no—
402D4×Q8C22×C11311yescharacteristic
403#548—21no—
404#547C22×C11311yescharacteristic
405#544—21no—
406#542—22no—
407#540—21no—
408#537—21no—
409#536—21no—
410#533C22×C11311yescharacteristic
411#532C22×C11311yescharacteristic
412#532C22×C11311yescharacteristic
413#529C22×C11311yescharacteristic
414#494C22×C11311yescharacteristic
415#492C22×C11311yescharacteristic
416#487C22×C11311yescharacteristic
417#486C22×C11311yescharacteristic
418#478—21no—
419#477C22×C11311yescharacteristic
420#476—21no—
421#476C22×C11311yescharacteristic
422#476C22×C11311yescharacteristic
423#476C22×C11311yescharacteristic
424#469—21no—
425#469—21no—
426#466—21no—
427#465—21no—
428#464—22no—
429#463—21no—
430#460C22×C11311yescharacteristic
431#459—21no—
432#459C22×C11311yescharacteristic
433#459C22×C11311yescharacteristic
434#459C22×C11311yescharacteristic
435#452—22no—
436#431C22×C11311yescharacteristic
437#423C22×C11311yescharacteristic
438C2×C4⋊C8C22×C11311yescharacteristic
439#333C22×C11311yescharacteristic
440#333C22×C11311yescharacteristic
441#332C22×C11311yescharacteristic
442#332C22×C11311yescharacteristic
443Q8⋊C8C22×C11311yescharacteristic
444Q8⋊C8C22×C11311yescharacteristic
445D4⋊C8C22×C11311yescharacteristic
446D4⋊C8C22×C11311yescharacteristic
447D4⋊C8C22×C11311yescharacteristic
448D4⋊C8C22×C11311yescharacteristic
449D4⋊C8C22×C11311yescharacteristic
450D4⋊C8C22×C11311yescharacteristic
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C22×Q8—21no—
455C2×Q16—22no—
456C2×SD16—22no—
457C2×SD16—21no—
458C2×D8—21no—
459C2×D8—21no—
460C2×D8—21no—
461C2×M16—21no—
462C22×C8—21no—
463C4⋊Q8—22no—
464C4⋊Q8—21no—
465C4⋊Q8D4×C11311yescharacteristic
466C4⋊Q8C23×C11311yescharacteristic
467C4⋊Q8C23×C11311yescharacteristic
468C4⋊Q8C23×C11311yescharacteristic
469#127D4×C11311yescharacteristic
470#127C23×C11311yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C11311yescharacteristic
477#124—22no—
478#124—22no—
479#124—22no—
480#124—21no—
481#124—21no—
482#124D4×C11311yescharacteristic
483#123—22no—
484#123—22no—
485#123—22no—
486#123—21no—
487#123—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—22no—
496C22⋊Q8D4×C11311yescharacteristic
497C22⋊Q8D4×C11312yes—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C11311yescharacteristic
509#121D4×C11311yescharacteristic
510#121D4×C11311yescharacteristic
511C4×Q8—21no—
512C4×Q8D4×C11312yes—
513C4×Q8C23×C11311yescharacteristic
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4C23×C11311yescharacteristic
522C4×D4C23×C11311yescharacteristic
523C4×D4C23×C11311yescharacteristic
524#117—22no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C42C23×C11311yescharacteristic
532#107—21no—
533#106—21no—
534#106—21no—
535#106—21no—
536C4⋊C8—21no—
537C4⋊C8—21no—
538C4⋊C8—21no—
539C4⋊C8C23×C11311yescharacteristic
540C4⋊C8C23×C11311yescharacteristic
541C4⋊C8C23×C11311yescharacteristic
542C4⋊C8C23×C11311yescharacteristic
543#103—21no—
544#103—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—22no—
549#102—21no—
550#102—21no—
551#102—21no—
552#102—21no—
553C22⋊C8—21no—
554C4×C8C23×C11311yescharacteristic
555C4×C8C23×C11311yescharacteristic
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560#41—82no—
561C2×Q8—22no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—81no—
566C2×Q8—81no—
567C2×Q8C2×D4×C11311yescharacteristic
568C2×Q8C2×D4×C11312yes—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—41no—
580C2×D4C2×D4×C11311yescharacteristic
581C2×D4C2×D4×C11311yescharacteristic
582C2×D4C2×D4×C11311yescharacteristic
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—41no—
590C22×C4C2×D4×C11311yescharacteristic
591C22×C4C2×D4×C11311yescharacteristic
592C22×C4C2×D4×C11311yescharacteristic
593Q16—82no—
594SD16—81no—
595SD16—82no—
596D8—81no—
597D8—81no—
598D8—81no—
599M16—81no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—81no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C11312yes—
624C4⋊C4C2×D4×C11311yescharacteristic
625C4⋊C4C2×D4×C11311yescharacteristic
626C4⋊C4C2×D4×C11311yescharacteristic
627C4⋊C4C2×D4×C11311yescharacteristic
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C42—22no—
646C42—22no—
647C42—21no—
648C42C2×D4×C11311yescharacteristic
649C42C2×D4×C11311yescharacteristic
650C42C2×D4×C11311yescharacteristic
651C42C24×C11311yescharacteristic
652C23—21no—
653C23—21no—
654C23—21no—
655C23—41no—
656C23#120×C11311yescharacteristic
657Q8—21no—
658Q8—21no—
659Q8—42no—
660Q8—42no—
661Q8—41no—
662Q8—41no—
663Q8—81no—
664Q8—82no—
665D4—21no—
666D4—21no—
667D4—21no—
668D4—21no—
669D4—21no—
670D4—21no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—81no—
677D4—81no—
678D4—81no—
679D4—81no—
680D4—81no—
681D4—82no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4#120×C11311yescharacteristic
708C2×C4#120×C11311yescharacteristic
709C2×C4#120×C11311yescharacteristic
710C2×C4C22×D4×C11311yescharacteristic
711C2×C4C22×D4×C11311yescharacteristic
712C2×C4C22×D4×C11311yescharacteristic
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—41no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22C2×#120×C11311yescharacteristic
735C4—21no—
736C4—21no—
737C4—21no—
738C4—21no—
739C4—41no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4#576×C11311yescharacteristic
748C4#577×C11311yescharacteristic
749C4#577×C11311yescharacteristic
750C4#578×C11311yescharacteristic
751C2—41no—
752C2—81no—
753C2—81no—
754C2—81no—
755C2—161no—
756C2C113×#301211yescharacteristic
757C2C113×#301311yescharacteristic
758C2C113×#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×#3547C2semidirect
2. C113×#3253C2semidirect
3. C113×#3247C2semidirect
4. C113×#3210C2semidirect
5. C113×#1637C2semidirect
6. C113×#1635C2semidirect
7. C113×#1634C2semidirect
8. C113×#1632C2semidirect
9. C113×#1627C2semidirect
10. C113×#1625C2semidirect
11. C113×#1624C2semidirect
12. C113×#1622C2semidirect
13. C113×#1550C2semidirect
14. C113×#1495C2semidirect
15. C113×#1480C2semidirect
371. #18965C113direct (N × H)
380. #3547C2×C113semidirect
381. #3253C2×C113semidirect
382. #3247C2×C113semidirect
383. #3210C2×C113semidirect
384. #1637C2×C113semidirect
385. #1635C2×C113semidirect
386. #1634C2×C113semidirect
387. #1632C2×C113semidirect
388. #1627C2×C113semidirect
389. #1625C2×C113semidirect
390. #1624C2×C113semidirect
391. #1622C2×C113semidirect
392. #1550C2×C113semidirect
393. #1495C2×C113semidirect
394. #1480C2×C113semidirect
395. C113#18965direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35472
C113×#32532
C113×#32472
C113×#32102
C113×#16372
C113×#16352
C113×#16342
C113×#16322
C113×#16272
C113×#16252
C113×#16242
C113×#16222
C113×#15502
C113×#14952
C113×#14802
#18965113