Finite Group Databasebeta

← C113×#18944 #43286964

Subgroups — C113×#18944 #43286964

Order 28928.

880 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3552C211yesmaximal, characteristic, complemented
2C113×#3251C211yesmaximal, characteristic, complemented
3C113×#3227C211yesmaximal, characteristic, complemented
4C113×#3212C211yesmaximal, characteristic, complemented
5C113×#1654C211yesmaximal, characteristic, complemented
6C113×#1653C211yesmaximal, characteristic, complemented
7C113×#1652C211yesmaximal, characteristic, complemented
8C113×#1651C211yesmaximal, characteristic, complemented
9C113×#1628C211yesmaximal, characteristic, complemented
10C113×#1627C211yesmaximal, characteristic, complemented
11C113×#1626C211yesmaximal, characteristic, complemented
12C113×#1625C211yesmaximal, characteristic, complemented
13C113×#1546C211yesmaximal, characteristic, complemented
14C113×#1495C211yesmaximal, characteristic, complemented
15C113×#1482C211yesmaximal, characteristic, complemented
16#563×C113—22no—
17#557×C113C2211yescharacteristic
18#556×C113C2211yescharacteristic
19#554×C113—21no—
20#553×C113—21no—
21D4×Q8×C113—21no—
22D4×Q8×C113C2211yescharacteristic
23#548×C113—21no—
24#547×C113C2211yescharacteristic
25#544×C113—21no—
26#542×C113—21no—
27#541×C113—21no—
28#539×C113—22no—
29#536×C113—21no—
30#532×C113C2211yescharacteristic
31C2×C4⋊Q8×C113C2211yescharacteristic
32#529×C113C2211yescharacteristic
33#529×C113C2211yescharacteristic
34#498×C113C2211yescharacteristic
35#498×C113C2211yescharacteristic
36#495×C113—21no—
37#488×C113—21no—
38#486×C113C2211yescharacteristic
39#486×C113C2211yescharacteristic
40#481×C113—22no—
41#478×C113—21no—
42#476×C113—22no—
43#475×C113C2211yescharacteristic
44#474×C113C2211yescharacteristic
45#469×C113—21no—
46#468×C113—21no—
47#463×C113—21no—
48#462×C113C2211yescharacteristic
49#461×C113C2211yescharacteristic
50#460×C113C2211yescharacteristic
51#460×C113C2211yescharacteristic
52#459×C113C2211yescharacteristic
53#459×C113C2211yescharacteristic
54#452×C113—21no—
55#449×C113—21no—
56#431×C113C2211yescharacteristic
57#431×C113C2211yescharacteristic
58#423×C113C2211yescharacteristic
59#332×C113C2211yescharacteristic
60#332×C113C2211yescharacteristic
61#332×C113C2211yescharacteristic
62#332×C113C2211yescharacteristic
63Q8⋊C8×C113C2211yescharacteristic
64Q8⋊C8×C113C2211yescharacteristic
65Q8⋊C8×C113C2211yescharacteristic
66Q8⋊C8×C113C2211yescharacteristic
67D4⋊C8×C113C2211yescharacteristic
68D4⋊C8×C113C2211yescharacteristic
69D4⋊C8×C113C2211yescharacteristic
70D4⋊C8×C113C2211yescharacteristic
71C2×#41×C113—21no—
72C2×#41×C113—21no—
73C22×Q8×C113—21no—
74C22×Q8×C113—21no—
75C2×Q16×C113—21no—
76C2×SD16×C113—21no—
77C2×SD16×C113—21no—
78C2×SD16×C113—21no—
79C2×D8×C113—21no—
80C2×D8×C113—21no—
81C2×M16×C113—21no—
82C4⋊Q8×C113—22no—
83C4⋊Q8×C113—21no—
84C4⋊Q8×C113—21no—
85C4⋊Q8×C113—21no—
86C4⋊Q8×C113—21no—
87C4⋊Q8×C113D412yes—
88C4⋊Q8×C113C2311yescharacteristic
89C4⋊Q8×C113C2311yescharacteristic
90C4⋊Q8×C113C2311yescharacteristic
91#127×C113C2311yescharacteristic
92#126×C113—22no—
93#126×C113—22no—
94#126×C113—22no—
95#126×C113—21no—
96#126×C113—21no—
97#125×C113—22no—
98#125×C113—22no—
99#125×C113—22no—
100#125×C113—21no—
101#125×C113D411yescharacteristic
102#125×C113D411yescharacteristic
103#124×C113—22no—
104#124×C113—21no—
105#124×C113—21no—
106#124×C113D411yescharacteristic
107#124×C113D411yescharacteristic
108#123×C113—22no—
109#123×C113—22no—
110#123×C113—21no—
111#123×C113—21no—
112#123×C113—22no—
113C22⋊Q8×C113—22no—
114C22⋊Q8×C113—22no—
115C22⋊Q8×C113—22no—
116C22⋊Q8×C113—22no—
117C22⋊Q8×C113—22no—
118C22⋊Q8×C113—21no—
119C22⋊Q8×C113—22no—
120C22⋊Q8×C113—21no—
121C22⋊Q8×C113—21no—
122C22⋊Q8×C113D411yescharacteristic
123C22⋊Q8×C113D411yescharacteristic
124#121×C113—22no—
125#121×C113—21no—
126#121×C113—21no—
127#121×C113—21no—
128#121×C113D411yescharacteristic
129#121×C113D411yescharacteristic
130C4×Q8×C113—21no—
131C4×Q8×C113—21no—
132C4×Q8×C113—21no—
133C4×Q8×C113C2311yescharacteristic
134C4×Q8×C113C2311yescharacteristic
135C4×D4×C113—22no—
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×C113C2311yescharacteristic
143C4×D4×C113C2311yescharacteristic
144#117×C113—21no—
145#117×C113—21no—
146#117×C113—21no—
147C2×C4⋊C4×C113—21no—
148C2×C4⋊C4×C113—21no—
149C2×C4⋊C4×C113D412yes—
150C2×C42×C113C2311yescharacteristic
151#107×C113—21no—
152#106×C113—21no—
153#106×C113—22no—
154#106×C113—22no—
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#102×C113—21no—
165#102×C113—21no—
166#102×C113—21no—
167#102×C113—21no—
168#102×C113—21no—
169#102×C113—22no—
170#102×C113—22no—
171C22⋊C8×C113—21no—
172C22⋊C8×C113—21no—
173C4×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—
180C2×Q8×C113—22no—
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×C113—81no—
188C2×Q8×C113—81no—
189C2×Q8×C113C2×D411yescharacteristic
190C2×Q8×C113C2×D411yescharacteristic
191C2×D4×C113—21no—
192C2×D4×C113—21no—
193C2×D4×C113—22no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—41no—
198C2×D4×C113C2×D411yescharacteristic
199C2×D4×C113C2×D411yescharacteristic
200C22×C4×C113—22no—
201C22×C4×C113—22no—
202C22×C4×C113—22no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—41no—
206C22×C4×C113C2×D411yescharacteristic
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D411yescharacteristic
209Q16×C113—81no—
210SD16×C113—81no—
211SD16×C113—81no—
212SD16×C113—81no—
213D8×C113—81no—
214D8×C113—81no—
215M16×C113—81no—
216C2×C8×C113—21no—
217C2×C8×C113—21no—
218C2×C8×C113—21no—
219C2×C8×C113—21no—
220C2×C8×C113—21no—
221C2×C8×C113—21no—
222C4⋊C4×C113—22no—
223C4⋊C4×C113—22no—
224C4⋊C4×C113—22no—
225C4⋊C4×C113—22no—
226C4⋊C4×C113—22no—
227C4⋊C4×C113—22no—
228C4⋊C4×C113—22no—
229C4⋊C4×C113—22no—
230C4⋊C4×C113—21no—
231C4⋊C4×C113—21no—
232C4⋊C4×C113—21no—
233C4⋊C4×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×C113C2×D411yescharacteristic
243C4⋊C4×C113C2×D411yescharacteristic
244C4⋊C4×C113C2×D412yes—
245C4⋊C4×C113C2×D412yes—
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—21no—
253C22⋊C4×C113—21no—
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—41no—
263C22⋊C4×C113—41no—
264C42×C113—22no—
265C42×C113—22no—
266C42×C113—21no—
267C42×C113—21no—
268C42×C113C2×D411yescharacteristic
269C42×C113C2×D411yescharacteristic
270C42×C113C2×D411yescharacteristic
271C42×C113C2411yescharacteristic
272C23×C113—21no—
273C23×C113—21no—
274C23×C113—41no—
275C23×C113#12011yescharacteristic
276Q8×C113—21no—
277Q8×C113—21no—
278Q8×C113—21no—
279Q8×C113—21no—
280Q8×C113—41no—
281Q8×C113—41no—
282Q8×C113—41no—
283Q8×C113—41no—
284Q8×C113—41no—
285Q8×C113—41no—
286Q8×C113—82no—
287Q8×C113—82no—
288D4×C113—21no—
289D4×C113—21no—
290D4×C113—21no—
291D4×C113—21no—
292D4×C113—42no—
293D4×C113—42no—
294D4×C113—42no—
295D4×C113—41no—
296D4×C113—41no—
297D4×C113—41no—
298D4×C113—41no—
299D4×C113—82no—
300D4×C113—82no—
301C2×C4×C113—21no—
302C2×C4×C113—21no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—21no—
306C2×C4×C113—21no—
307C2×C4×C113—21no—
308C2×C4×C113—21no—
309C2×C4×C113—21no—
310C2×C4×C113—22no—
311C2×C4×C113—22no—
312C2×C4×C113—21no—
313C2×C4×C113—41no—
314C2×C4×C113—41no—
315C2×C4×C113—41no—
316C2×C4×C113—41no—
317C2×C4×C113—41no—
318C2×C4×C113—41no—
319C2×C4×C113—82no—
320C2×C4×C113—82no—
321C2×C4×C113—82no—
322C2×C4×C113—82no—
323C2×C4×C113#12011yescharacteristic
324C2×C4×C113#12011yescharacteristic
325C2×C4×C113#12011yescharacteristic
326C2×C4×C113C22×D411yescharacteristic
327C2×C4×C113C22×D411yescharacteristic
328C2×C4×C113C22×D411yescharacteristic
329C8×C113—41no—
330C8×C113—41no—
331C8×C113—41no—
332C8×C113—41no—
333C8×C113—41no—
334C8×C113—41no—
335C22×C113—21no—
336C22×C113—21no—
337C22×C113—21no—
338C22×C113—41no—
339C22×C113—41no—
340C22×C113—41no—
341C22×C113—41no—
342C22×C113—41no—
343C22×C113—41no—
344C22×C113—81no—
345C22×C113—81no—
346C22×C113—81no—
347C22×C113C2×#12011yescharacteristic
348C4×C113—21no—
349C4×C113—21no—
350C4×C113—21no—
351C4×C113—21no—
352C4×C113—41no—
353C4×C113—41no—
354C4×C113—41no—
355C4×C113—42no—
356C4×C113—41no—
357C4×C113—42no—
358C4×C113—41no—
359C4×C113—41no—
360C4×C113—81no—
361C4×C113#57611yescharacteristic
362C4×C113#57711yescharacteristic
363C4×C113#57711yescharacteristic
364C4×C113#57711yescharacteristic
365#18944C11311yesmaximal, characteristic, direct product factor, Sylow
366C2×C113—41no—
367C2×C113—81no—
368C2×C113—81no—
369C2×C113—161no—
370C2×C113#301011yescharacteristic
371C2×C113#301211yescharacteristic
372C2×C113#302011yescharacteristic
373#3552C2×C11311yescharacteristic, complemented
374#3251C2×C11311yescharacteristic, complemented
375#3227C2×C11311yescharacteristic, complemented
376#3212C2×C11311yescharacteristic, complemented
377#1654C2×C11311yescharacteristic, complemented
378#1653C2×C11311yescharacteristic, complemented
379#1652C2×C11311yescharacteristic, complemented
380#1651C2×C11311yescharacteristic, complemented
381#1628C2×C11311yescharacteristic, complemented
382#1627C2×C11311yescharacteristic, complemented
383#1626C2×C11311yescharacteristic, complemented
384#1625C2×C11311yescharacteristic, complemented
385#1546C2×C11311yescharacteristic, complemented
386#1495C2×C11311yescharacteristic, complemented
387#1482C2×C11311yescharacteristic, complemented
388C113#1894411yescharacteristic, direct product factor, Sylow
389#563—22no—
390#557C22×C11311yescharacteristic
391#556C22×C11311yescharacteristic
392#554—21no—
393#553—21no—
394D4×Q8—21no—
395D4×Q8C22×C11311yescharacteristic
396#548—21no—
397#547C22×C11311yescharacteristic
398#544—21no—
399#542—21no—
400#541—21no—
401#539—22no—
402#536—21no—
403#532C22×C11311yescharacteristic
404C2×C4⋊Q8C22×C11311yescharacteristic
405#529C22×C11311yescharacteristic
406#529C22×C11311yescharacteristic
407#498C22×C11311yescharacteristic
408#498C22×C11311yescharacteristic
409#495—21no—
410#488—21no—
411#486C22×C11311yescharacteristic
412#486C22×C11311yescharacteristic
413#481—22no—
414#478—21no—
415#476—22no—
416#475C22×C11311yescharacteristic
417#474C22×C11311yescharacteristic
418#469—21no—
419#468—21no—
420#463—21no—
421#462C22×C11311yescharacteristic
422#461C22×C11311yescharacteristic
423#460C22×C11311yescharacteristic
424#460C22×C11311yescharacteristic
425#459C22×C11311yescharacteristic
426#459C22×C11311yescharacteristic
427#452—21no—
428#449—21no—
429#431C22×C11311yescharacteristic
430#431C22×C11311yescharacteristic
431#423C22×C11311yescharacteristic
432#332C22×C11311yescharacteristic
433#332C22×C11311yescharacteristic
434#332C22×C11311yescharacteristic
435#332C22×C11311yescharacteristic
436Q8⋊C8C22×C11311yescharacteristic
437Q8⋊C8C22×C11311yescharacteristic
438Q8⋊C8C22×C11311yescharacteristic
439Q8⋊C8C22×C11311yescharacteristic
440D4⋊C8C22×C11311yescharacteristic
441D4⋊C8C22×C11311yescharacteristic
442D4⋊C8C22×C11311yescharacteristic
443D4⋊C8C22×C11311yescharacteristic
444C2×#41—21no—
445C2×#41—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C2×Q16—21no—
449C2×SD16—21no—
450C2×SD16—21no—
451C2×SD16—21no—
452C2×D8—21no—
453C2×D8—21no—
454C2×M16—21no—
455C4⋊Q8—22no—
456C4⋊Q8—21no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—21no—
460C4⋊Q8D4×C11312yes—
461C4⋊Q8C23×C11311yescharacteristic
462C4⋊Q8C23×C11311yescharacteristic
463C4⋊Q8C23×C11311yescharacteristic
464#127C23×C11311yescharacteristic
465#126—22no—
466#126—22no—
467#126—22no—
468#126—21no—
469#126—21no—
470#125—22no—
471#125—22no—
472#125—22no—
473#125—21no—
474#125D4×C11311yescharacteristic
475#125D4×C11311yescharacteristic
476#124—22no—
477#124—21no—
478#124—21no—
479#124D4×C11311yescharacteristic
480#124D4×C11311yescharacteristic
481#123—22no—
482#123—22no—
483#123—21no—
484#123—21no—
485#123—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—21no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8D4×C11311yescharacteristic
496C22⋊Q8D4×C11311yescharacteristic
497#121—22no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121D4×C11311yescharacteristic
502#121D4×C11311yescharacteristic
503C4×Q8—21no—
504C4×Q8—21no—
505C4×Q8—21no—
506C4×Q8C23×C11311yescharacteristic
507C4×Q8C23×C11311yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4C23×C11311yescharacteristic
516C4×D4C23×C11311yescharacteristic
517#117—21no—
518#117—21no—
519#117—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4D4×C11312yes—
523C2×C42C23×C11311yescharacteristic
524#107—21no—
525#106—21no—
526#106—22no—
527#106—22no—
528C4⋊C8—21no—
529C4⋊C8—21no—
530C4⋊C8C23×C11311yescharacteristic
531C4⋊C8C23×C11311yescharacteristic
532C4⋊C8C23×C11311yescharacteristic
533C4⋊C8C23×C11311yescharacteristic
534#103—21no—
535#103—21no—
536#103—21no—
537#102—21no—
538#102—21no—
539#102—21no—
540#102—21no—
541#102—21no—
542#102—22no—
543#102—22no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C4×C8—21no—
547C4×C8C23×C11311yescharacteristic
548C4×C8C23×C11311yescharacteristic
549#41—81no—
550#41—81no—
551#41—81no—
552#41—81no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—81no—
559C2×Q8—81no—
560C2×Q8—81no—
561C2×Q8—81no—
562C2×Q8C2×D4×C11311yescharacteristic
563C2×Q8C2×D4×C11311yescharacteristic
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—41no—
571C2×D4C2×D4×C11311yescharacteristic
572C2×D4C2×D4×C11311yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—41no—
579C22×C4C2×D4×C11311yescharacteristic
580C22×C4C2×D4×C11311yescharacteristic
581C22×C4C2×D4×C11311yescharacteristic
582Q16—81no—
583SD16—81no—
584SD16—81no—
585SD16—81no—
586D8—81no—
587D8—81no—
588M16—81no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4C2×D4×C11311yescharacteristic
616C4⋊C4C2×D4×C11311yescharacteristic
617C4⋊C4C2×D4×C11312yes—
618C4⋊C4C2×D4×C11312yes—
619C4⋊C4C2×D4×C11311yescharacteristic
620C4⋊C4C2×D4×C11311yescharacteristic
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—41no—
636C22⋊C4—41no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42C2×D4×C11311yescharacteristic
642C42C2×D4×C11311yescharacteristic
643C42C2×D4×C11311yescharacteristic
644C42C24×C11311yescharacteristic
645C23—21no—
646C23—21no—
647C23—41no—
648C23#120×C11311yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—82no—
660Q8—82no—
661D4—21no—
662D4—21no—
663D4—21no—
664D4—21no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—82no—
673D4—82no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4#120×C11311yescharacteristic
697C2×C4#120×C11311yescharacteristic
698C2×C4#120×C11311yescharacteristic
699C2×C4C22×D4×C11311yescharacteristic
700C2×C4C22×D4×C11311yescharacteristic
701C2×C4C22×D4×C11311yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22C2×#120×C11311yescharacteristic
721C4—21no—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4#576×C11311yescharacteristic
735C4#577×C11311yescharacteristic
736C4#577×C11311yescharacteristic
737C4#577×C11311yescharacteristic
738C2—41no—
739C2—81no—
740C2—81no—
741C2—161no—
742C2C113×#301011yescharacteristic
743C2C113×#301211yescharacteristic
744C2C113×#302011yescharacteristic
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×#3552C2semidirect
2. C113×#3251C2semidirect
3. C113×#3227C2semidirect
4. C113×#3212C2semidirect
5. C113×#1654C2semidirect
6. C113×#1653C2semidirect
7. C113×#1652C2semidirect
8. C113×#1651C2semidirect
9. C113×#1628C2semidirect
10. C113×#1627C2semidirect
11. C113×#1626C2semidirect
12. C113×#1625C2semidirect
13. C113×#1546C2semidirect
14. C113×#1495C2semidirect
15. C113×#1482C2semidirect
365. #18944C113direct (N × H)
373. #3552C2×C113semidirect
374. #3251C2×C113semidirect
375. #3227C2×C113semidirect
376. #3212C2×C113semidirect
377. #1654C2×C113semidirect
378. #1653C2×C113semidirect
379. #1652C2×C113semidirect
380. #1651C2×C113semidirect
381. #1628C2×C113semidirect
382. #1627C2×C113semidirect
383. #1626C2×C113semidirect
384. #1625C2×C113semidirect
385. #1546C2×C113semidirect
386. #1495C2×C113semidirect
387. #1482C2×C113semidirect
388. C113#18944direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35522
C113×#32512
C113×#32272
C113×#32122
C113×#16542
C113×#16532
C113×#16522
C113×#16512
C113×#16282
C113×#16272
C113×#16262
C113×#16252
C113×#15462
C113×#14952
C113×#14822
#18944113