Finite Group Databasebeta

← C113×#18977 #43286997

Subgroups — C113×#18977 #43286997

Order 28928.

866 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3547C211yesmaximal, characteristic
2C113×#3254C211yesmaximal, characteristic, complemented
3C113×#3248C211yesmaximal, characteristic, complemented
4C113×#3231C211yesmaximal, characteristic, complemented
5C113×#1654C211yesmaximal, characteristic, complemented
6C113×#1651C211yesmaximal, characteristic, complemented
7C113×#1649C211yesmaximal, characteristic, complemented
8C113×#1647C211yesmaximal, characteristic, complemented
9C113×#1646C211yesmaximal, characteristic, complemented
10C113×#1646C211yesmaximal, characteristic, complemented
11C113×#1644C211yesmaximal, characteristic, complemented
12C113×#1643C211yesmaximal, 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#533×C113C2211yescharacteristic
32#532×C113C2211yescharacteristic
33#529×C113C2211yescharacteristic
34#500×C113C2211yescharacteristic
35#498×C113C2211yescharacteristic
36#487×C113C2211yescharacteristic
37#487×C113C2211yescharacteristic
38#485×C113—22no—
39#479×C113—21no—
40#479×C113—22no—
41#477×C113—21no—
42#475×C113C2211yescharacteristic
43#474×C113C2211yescharacteristic
44#474×C113C2211yescharacteristic
45#474×C113C2211yescharacteristic
46#468×C113—21no—
47#468×C113—21no—
48#467×C113—21no—
49#465×C113—21no—
50#464×C113—21no—
51#462×C113C2211yescharacteristic
52#461×C113C2211yescharacteristic
53#461×C113C2211yescharacteristic
54#461×C113C2211yescharacteristic
55#460×C113—21no—
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—
73C22×Q8×C113—21no—
74C2×Q16×C113—21no—
75C2×SD16×C113—21no—
76C2×SD16×C113—21no—
77C2×SD16×C113—21no—
78C2×M16×C113—21no—
79C22×C8×C113—21no—
80C4⋊Q8×C113—22no—
81C4⋊Q8×C113—21no—
82C4⋊Q8×C113D411yescharacteristic
83C4⋊Q8×C113C2311yescharacteristic
84C4⋊Q8×C113C2311yescharacteristic
85C4⋊Q8×C113C2311yescharacteristic
86C4⋊Q8×C113C2311yescharacteristic
87#127×C113D411yescharacteristic
88#126×C113—22no—
89#126×C113—21no—
90#125×C113—22no—
91#125×C113—21no—
92#125×C113—21no—
93#125×C113—21no—
94#125×C113D411yescharacteristic
95#124×C113—22no—
96#124×C113—22no—
97#124×C113—22no—
98#124×C113—21no—
99#124×C113D411yescharacteristic
100#123×C113—22no—
101#123×C113—22no—
102#123×C113—22no—
103#123×C113—21no—
104#123×C113—22no—
105C22⋊Q8×C113—22no—
106C22⋊Q8×C113—22no—
107C22⋊Q8×C113—21no—
108C22⋊Q8×C113—22no—
109C22⋊Q8×C113—21no—
110C22⋊Q8×C113—21no—
111C22⋊Q8×C113—21no—
112C22⋊Q8×C113—22no—
113C22⋊Q8×C113—21no—
114C22⋊Q8×C113—21no—
115C22⋊Q8×C113D411yescharacteristic
116C22⋊Q8×C113D412yes—
117#121×C113—22no—
118#121×C113—22no—
119#121×C113—22no—
120#121×C113—22no—
121#121×C113—21no—
122#121×C113—21no—
123#121×C113—21no—
124#121×C113—21no—
125#121×C113D411yescharacteristic
126#121×C113D411yescharacteristic
127#121×C113D411yescharacteristic
128C4×Q8×C113—21no—
129C4×Q8×C113—21no—
130C4×Q8×C113—21no—
131C4×Q8×C113D412yes—
132C4×Q8×C113C2311yescharacteristic
133C4×D4×C113—22no—
134C4×D4×C113—21no—
135C4×D4×C113—21no—
136C4×D4×C113—21no—
137C4×D4×C113—21no—
138C4×D4×C113C2311yescharacteristic
139C4×D4×C113C2311yescharacteristic
140C4×D4×C113C2311yescharacteristic
141#117×C113—22no—
142#117×C113—21no—
143#117×C113—21no—
144#117×C113—21no—
145#117×C113—21no—
146#117×C113—21no—
147C2×C4⋊C4×C113—21no—
148C2×C4⋊C4×C113—21no—
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—22no—
165#103×C113—22no—
166#103×C113—21no—
167#103×C113—21no—
168#103×C113—21no—
169#103×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—
180C2×Q8×C113—22no—
181C2×Q8×C113—21no—
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×C113C2×D411yescharacteristic
197C2×D4×C113C2×D411yescharacteristic
198C2×D4×C113C2×D411yescharacteristic
199C22×C4×C113—22no—
200C22×C4×C113—22no—
201C22×C4×C113—22no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113C2×D411yescharacteristic
206C22×C4×C113C2×D411yescharacteristic
207C22×C4×C113C2×D411yescharacteristic
208Q16×C113—81no—
209SD16×C113—81no—
210SD16×C113—81no—
211SD16×C113—81no—
212M16×C113—81no—
213C2×C8×C113—21no—
214C2×C8×C113—21no—
215C2×C8×C113—21no—
216C2×C8×C113—21no—
217C2×C8×C113—21no—
218C2×C8×C113—21no—
219C2×C8×C113—81no—
220C4⋊C4×C113—22no—
221C4⋊C4×C113—22no—
222C4⋊C4×C113—22no—
223C4⋊C4×C113—22no—
224C4⋊C4×C113—21no—
225C4⋊C4×C113—21no—
226C4⋊C4×C113—21no—
227C4⋊C4×C113—21no—
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—41no—
239C4⋊C4×C113—41no—
240C4⋊C4×C113C2×D411yescharacteristic
241C4⋊C4×C113C2×D411yescharacteristic
242C4⋊C4×C113C2×D411yescharacteristic
243C4⋊C4×C113C2×D411yescharacteristic
244C4⋊C4×C113C2×D412yes—
245C22⋊C4×C113—22no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—22no—
248C22⋊C4×C113—22no—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—21no—
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—41no—
261C42×C113—22no—
262C42×C113—22no—
263C42×C113—21no—
264C42×C113—41no—
265C42×C113C2×D411yescharacteristic
266C42×C113C2×D411yescharacteristic
267C42×C113C2×D411yescharacteristic
268C42×C113C2411yescharacteristic
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—21no—
272C23×C113#12011yescharacteristic
273Q8×C113—21no—
274Q8×C113—21no—
275Q8×C113—42no—
276Q8×C113—41no—
277Q8×C113—41no—
278Q8×C113—41no—
279Q8×C113—41no—
280Q8×C113—41no—
281Q8×C113—41no—
282Q8×C113—81no—
283Q8×C113—82no—
284D4×C113—21no—
285D4×C113—21no—
286D4×C113—21no—
287D4×C113—21no—
288D4×C113—21no—
289D4×C113—21no—
290D4×C113—81no—
291D4×C113—81no—
292D4×C113—81no—
293D4×C113—81no—
294D4×C113—81no—
295D4×C113—82no—
296D4×C113—82no—
297C2×C4×C113—21no—
298C2×C4×C113—21no—
299C2×C4×C113—21no—
300C2×C4×C113—21no—
301C2×C4×C113—21no—
302C2×C4×C113—22no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—21no—
306C2×C4×C113—22no—
307C2×C4×C113—21no—
308C2×C4×C113—41no—
309C2×C4×C113—41no—
310C2×C4×C113—41no—
311C2×C4×C113—41no—
312C2×C4×C113—41no—
313C2×C4×C113—41no—
314C2×C4×C113—41no—
315C2×C4×C113—41no—
316C2×C4×C113—41no—
317C2×C4×C113—82no—
318C2×C4×C113—82no—
319C2×C4×C113—82no—
320C2×C4×C113#12011yescharacteristic
321C2×C4×C113#12011yescharacteristic
322C2×C4×C113#12011yescharacteristic
323C2×C4×C113C22×D411yescharacteristic
324C2×C4×C113C22×D411yescharacteristic
325C2×C4×C113C22×D411yescharacteristic
326C8×C113—41no—
327C8×C113—41no—
328C8×C113—41no—
329C8×C113—41no—
330C8×C113—41no—
331C8×C113—41no—
332C22×C113—21no—
333C22×C113—21no—
334C22×C113—21no—
335C22×C113—41no—
336C22×C113—41no—
337C22×C113—41no—
338C22×C113—41no—
339C22×C113—41no—
340C22×C113—41no—
341C22×C113—41no—
342C22×C113—41no—
343C22×C113—41no—
344C22×C113C2×#12011yescharacteristic
345C4×C113—21no—
346C4×C113—21no—
347C4×C113—21no—
348C4×C113—21no—
349C4×C113—41no—
350C4×C113—41no—
351C4×C113—42no—
352C4×C113—41no—
353C4×C113—41no—
354C4×C113—41no—
355C4×C113—42no—
356C4×C113—81no—
357C4×C113—81no—
358C4×C113#57611yescharacteristic
359C4×C113#57711yescharacteristic
360C4×C113#57711yescharacteristic
361C4×C113#57811yescharacteristic
362#18977C11311yesmaximal, characteristic, direct product factor, Sylow
363C2×C113—41no—
364C2×C113—81no—
365C2×C113—81no—
366C2×C113—81no—
367C2×C113#301211yescharacteristic
368C2×C113#301311yescharacteristic
369C2×C113#302211yescharacteristic
370#3547C2×C11311yescharacteristic
371#3254C2×C11311yescharacteristic, complemented
372#3248C2×C11311yescharacteristic, complemented
373#3231C2×C11311yescharacteristic, complemented
374#1654C2×C11311yescharacteristic, complemented
375#1651C2×C11311yescharacteristic, complemented
376#1649C2×C11311yescharacteristic, complemented
377#1647C2×C11311yescharacteristic, complemented
378#1646C2×C11311yescharacteristic, complemented
379#1646C2×C11311yescharacteristic, complemented
380#1644C2×C11311yescharacteristic, complemented
381#1643C2×C11311yescharacteristic, complemented
382#1550C2×C11311yescharacteristic, complemented
383#1495C2×C11311yescharacteristic, complemented
384#1480C2×C11311yescharacteristic, complemented
385C113#1897711yescharacteristic, direct product factor, Sylow
386#562—22no—
387#555—21no—
388#555C22×C11311yescharacteristic
389#554C22×C11311yescharacteristic
390#553—21no—
391#552—21no—
392D4×Q8C22×C11311yescharacteristic
393#548—21no—
394#547C22×C11311yescharacteristic
395#544—21no—
396#542—22no—
397#540—21no—
398#537—21no—
399#536—21no—
400#533C22×C11311yescharacteristic
401#533C22×C11311yescharacteristic
402#532C22×C11311yescharacteristic
403#529C22×C11311yescharacteristic
404#500C22×C11311yescharacteristic
405#498C22×C11311yescharacteristic
406#487C22×C11311yescharacteristic
407#487C22×C11311yescharacteristic
408#485—22no—
409#479—21no—
410#479—22no—
411#477—21no—
412#475C22×C11311yescharacteristic
413#474C22×C11311yescharacteristic
414#474C22×C11311yescharacteristic
415#474C22×C11311yescharacteristic
416#468—21no—
417#468—21no—
418#467—21no—
419#465—21no—
420#464—21no—
421#462C22×C11311yescharacteristic
422#461C22×C11311yescharacteristic
423#461C22×C11311yescharacteristic
424#461C22×C11311yescharacteristic
425#460—21no—
426#431C22×C11311yescharacteristic
427#423C22×C11311yescharacteristic
428C2×C4⋊C8C22×C11311yescharacteristic
429#333C22×C11311yescharacteristic
430#333C22×C11311yescharacteristic
431#332C22×C11311yescharacteristic
432#332C22×C11311yescharacteristic
433Q8⋊C8C22×C11311yescharacteristic
434Q8⋊C8C22×C11311yescharacteristic
435D4⋊C8C22×C11311yescharacteristic
436D4⋊C8C22×C11311yescharacteristic
437D4⋊C8C22×C11311yescharacteristic
438D4⋊C8C22×C11311yescharacteristic
439D4⋊C8C22×C11311yescharacteristic
440D4⋊C8C22×C11311yescharacteristic
441C2×#41—21no—
442C2×#41—21no—
443C22×Q8—21no—
444C2×Q16—21no—
445C2×SD16—21no—
446C2×SD16—21no—
447C2×SD16—21no—
448C2×M16—21no—
449C22×C8—21no—
450C4⋊Q8—22no—
451C4⋊Q8—21no—
452C4⋊Q8D4×C11311yescharacteristic
453C4⋊Q8C23×C11311yescharacteristic
454C4⋊Q8C23×C11311yescharacteristic
455C4⋊Q8C23×C11311yescharacteristic
456C4⋊Q8C23×C11311yescharacteristic
457#127D4×C11311yescharacteristic
458#126—22no—
459#126—21no—
460#125—22no—
461#125—21no—
462#125—21no—
463#125—21no—
464#125D4×C11311yescharacteristic
465#124—22no—
466#124—22no—
467#124—22no—
468#124—21no—
469#124D4×C11311yescharacteristic
470#123—22no—
471#123—22no—
472#123—22no—
473#123—21no—
474#123—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8D4×C11311yescharacteristic
486C22⋊Q8D4×C11312yes—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121D4×C11311yescharacteristic
496#121D4×C11311yescharacteristic
497#121D4×C11311yescharacteristic
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8D4×C11312yes—
502C4×Q8C23×C11311yescharacteristic
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4C23×C11311yescharacteristic
509C4×D4C23×C11311yescharacteristic
510C4×D4C23×C11311yescharacteristic
511#117—22no—
512#117—21no—
513#117—21no—
514#117—21no—
515#117—21no—
516#117—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C42C23×C11311yescharacteristic
520#107—21no—
521#107—21no—
522#107—21no—
523#107—22no—
524#106—21no—
525#106—22no—
526C4⋊C8—21no—
527C4⋊C8—21no—
528C4⋊C8—21no—
529C4⋊C8C23×C11311yescharacteristic
530C4⋊C8C23×C11311yescharacteristic
531C4⋊C8C23×C11311yescharacteristic
532C4⋊C8C23×C11311yescharacteristic
533#103—21no—
534#103—22no—
535#103—22no—
536#103—21no—
537#103—21no—
538#103—21no—
539#103—21no—
540#102—21no—
541#102—21no—
542#102—21no—
543C22⋊C8—21no—
544C4×C8C23×C11311yescharacteristic
545C4×C8C23×C11311yescharacteristic
546#41—81no—
547#41—81no—
548#41—81no—
549#41—81no—
550C2×Q8—22no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—81no—
556C2×Q8—81no—
557C2×Q8C2×D4×C11311yescharacteristic
558C2×Q8C2×D4×C11312yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4C2×D4×C11311yescharacteristic
567C2×D4C2×D4×C11311yescharacteristic
568C2×D4C2×D4×C11311yescharacteristic
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4C2×D4×C11311yescharacteristic
576C22×C4C2×D4×C11311yescharacteristic
577C22×C4C2×D4×C11311yescharacteristic
578Q16—81no—
579SD16—81no—
580SD16—81no—
581SD16—81no—
582M16—81no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—81no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4C2×D4×C11311yescharacteristic
611C4⋊C4C2×D4×C11311yescharacteristic
612C4⋊C4C2×D4×C11311yescharacteristic
613C4⋊C4C2×D4×C11311yescharacteristic
614C4⋊C4C2×D4×C11312yes—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—41no—
631C42—22no—
632C42—22no—
633C42—21no—
634C42—41no—
635C42C2×D4×C11311yescharacteristic
636C42C2×D4×C11311yescharacteristic
637C42C2×D4×C11311yescharacteristic
638C42C24×C11311yescharacteristic
639C23—21no—
640C23—21no—
641C23—21no—
642C23#120×C11311yescharacteristic
643Q8—21no—
644Q8—21no—
645Q8—42no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—81no—
653Q8—82no—
654D4—21no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—81no—
661D4—81no—
662D4—81no—
663D4—81no—
664D4—81no—
665D4—82no—
666D4—82no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4#120×C11311yescharacteristic
691C2×C4#120×C11311yescharacteristic
692C2×C4#120×C11311yescharacteristic
693C2×C4C22×D4×C11311yescharacteristic
694C2×C4C22×D4×C11311yescharacteristic
695C2×C4C22×D4×C11311yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22C2×#120×C11311yescharacteristic
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4#576×C11311yescharacteristic
729C4#577×C11311yescharacteristic
730C4#577×C11311yescharacteristic
731C4#578×C11311yescharacteristic
732C2—41no—
733C2—81no—
734C2—81no—
735C2—81no—
736C2C113×#301211yescharacteristic
737C2C113×#301311yescharacteristic
738C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3547C2
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×#3231C2semidirect
5. C113×#1654C2semidirect
6. C113×#1651C2semidirect
7. C113×#1649C2semidirect
8. C113×#1647C2semidirect
9. C113×#1646C2semidirect
10. C113×#1646C2semidirect
11. C113×#1644C2semidirect
12. C113×#1643C2semidirect
13. C113×#1550C2semidirect
14. C113×#1495C2semidirect
15. C113×#1480C2semidirect
362. #18977C113direct (N × H)
371. #3254C2×C113semidirect
372. #3248C2×C113semidirect
373. #3231C2×C113semidirect
374. #1654C2×C113semidirect
375. #1651C2×C113semidirect
376. #1649C2×C113semidirect
377. #1647C2×C113semidirect
378. #1646C2×C113semidirect
379. #1646C2×C113semidirect
380. #1644C2×C113semidirect
381. #1643C2×C113semidirect
382. #1550C2×C113semidirect
383. #1495C2×C113semidirect
384. #1480C2×C113semidirect
385. C113#18977direct (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×#32542
C113×#32482
C113×#32312
C113×#16542
C113×#16512
C113×#16492
C113×#16472
C113×#16462
C113×#16442
C113×#16432
C113×#15502
C113×#14952
C113×#14802
#18977113