Finite Group Databasebeta

← C113×#18963 #43286983

Subgroups — C113×#18963 #43286983

Order 28928.

844 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3555C211yesmaximal, characteristic, complemented
2C113×#3254C211yesmaximal, characteristic, complemented
3C113×#3247C211yesmaximal, characteristic
4C113×#3210C211yesmaximal, characteristic, complemented
5C113×#1638C211yesmaximal, characteristic, complemented
6C113×#1636C211yesmaximal, characteristic, complemented
7C113×#1633C211yesmaximal, characteristic, complemented
8C113×#1632C211yesmaximal, characteristic, complemented
9C113×#1628C211yesmaximal, characteristic, complemented
10C113×#1626C211yesmaximal, characteristic, complemented
11C113×#1623C211yesmaximal, characteristic, complemented
12C113×#1622C211yesmaximal, characteristic, complemented
13C113×#1550C211yesmaximal, characteristic, complemented
14C113×#1495C211yesmaximal, characteristic, complemented
15C113×#1481C211yesmaximal, characteristic, complemented
16#563×C113—22no—
17Q82×C113C2211yescharacteristic
18#557×C113—21no—
19#557×C113C2211yescharacteristic
20#556×C113—21no—
21#556×C113—21no—
22#556×C113C2211yescharacteristic
23#554×C113C2211yescharacteristic
24#552×C113—21no—
25#544×C113—21no—
26#542×C113—21no—
27#541×C113—21no—
28#541×C113—21no—
29#541×C113—22no—
30#533×C113C2211yescharacteristic
31#533×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#477×C113C2211yescharacteristic
41#477×C113C2211yescharacteristic
42#476×C113C2211yescharacteristic
43#474×C113—21no—
44#468×C113—21no—
45#468×C113—21no—
46#466×C113—21no—
47#465×C113—21no—
48#464×C113—22no—
49#463×C113—21no—
50#461×C113—21no—
51#460×C113C2211yescharacteristic
52#460×C113C2211yescharacteristic
53#460×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
65Q8⋊C8×C113C2211yescharacteristic
66Q8⋊C8×C113C2211yescharacteristic
67Q8⋊C8×C113C2211yescharacteristic
68Q8⋊C8×C113C2211yescharacteristic
69D4⋊C8×C113C2211yescharacteristic
70D4⋊C8×C113C2211yescharacteristic
71C2×#41×C113—21no—
72C2×Q16×C113—22no—
73C2×SD16×C113—22no—
74C2×SD16×C113—21no—
75C2×SD16×C113—21no—
76C2×SD16×C113—21no—
77C2×D8×C113—21no—
78C2×M16×C113—21no—
79C22×C8×C113—21no—
80C4⋊Q8×C113—22no—
81C4⋊Q8×C113—21no—
82C4⋊Q8×C113—22no—
83C4⋊Q8×C113—21no—
84C4⋊Q8×C113—21no—
85C4⋊Q8×C113D411yescharacteristic
86C4⋊Q8×C113D411yescharacteristic
87C4⋊Q8×C113C2311yescharacteristic
88C4⋊Q8×C113C2311yescharacteristic
89C4⋊Q8×C113C2311yescharacteristic
90#127×C113C2311yescharacteristic
91#126×C113—22no—
92#126×C113—22no—
93#126×C113—22no—
94#126×C113—22no—
95#126×C113—22no—
96#126×C113—22no—
97#126×C113—21no—
98#125×C113—22no—
99#125×C113—22no—
100#125×C113—22no—
101#125×C113—22no—
102#125×C113—21no—
103#125×C113—22no—
104#125×C113—21no—
105#125×C113—21no—
106#125×C113—21no—
107#125×C113D411yescharacteristic
108#124×C113—22no—
109#124×C113—21no—
110#124×C113—21no—
111#124×C113D411yescharacteristic
112#123×C113—22no—
113#123×C113—21no—
114C22⋊Q8×C113—22no—
115C22⋊Q8×C113—22no—
116C22⋊Q8×C113—21no—
117C22⋊Q8×C113—21no—
118C22⋊Q8×C113—22no—
119C22⋊Q8×C113—21no—
120C22⋊Q8×C113—21no—
121C22⋊Q8×C113D411yescharacteristic
122C22⋊Q8×C113D411yescharacteristic
123C22⋊Q8×C113D411yescharacteristic
124C22⋊Q8×C113D412yes—
125#121×C113—21no—
126#121×C113—21no—
127#121×C113D411yescharacteristic
128C4×Q8×C113—22no—
129C4×Q8×C113—21no—
130C4×Q8×C113—21no—
131C4×Q8×C113—21no—
132C4×Q8×C113—21no—
133C4×Q8×C113—21no—
134C4×Q8×C113—21no—
135C4×Q8×C113—21no—
136C4×Q8×C113D412yes—
137C4×Q8×C113C2311yescharacteristic
138C4×Q8×C113C2311yescharacteristic
139C4×Q8×C113C2311yescharacteristic
140C4×D4×C113—21no—
141C4×D4×C113—21no—
142C4×D4×C113—21no—
143C4×D4×C113—21no—
144C4×D4×C113C2311yescharacteristic
145#117×C113—22no—
146#117×C113—21no—
147#117×C113—21no—
148#117×C113—21no—
149#117×C113—21no—
150C2×C4⋊C4×C113—21no—
151C2×C42×C113C2311yescharacteristic
152#107×C113—21no—
153#107×C113—21no—
154#107×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—21no—
165#103×C113—21no—
166#103×C113—22no—
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—82no—
177C2×Q8×C113—22no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113C2×D411yescharacteristic
182C2×Q8×C113C2×D411yescharacteristic
183C2×Q8×C113C2×D411yescharacteristic
184C2×Q8×C113C2×D412yes—
185C2×D4×C113—21no—
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—21no—
189C2×D4×C113—41no—
190C2×D4×C113C2×D411yescharacteristic
191C22×C4×C113—22no—
192C22×C4×C113—21no—
193C22×C4×C113—41no—
194C22×C4×C113C2×D411yescharacteristic
195C22×C4×C113C2×D411yescharacteristic
196C22×C4×C113C2×D411yescharacteristic
197Q16×C113—82no—
198SD16×C113—81no—
199SD16×C113—81no—
200SD16×C113—81no—
201SD16×C113—82no—
202D8×C113—81no—
203M16×C113—81no—
204C2×C8×C113—21no—
205C2×C8×C113—21no—
206C2×C8×C113—21no—
207C2×C8×C113—21no—
208C2×C8×C113—21no—
209C2×C8×C113—21no—
210C2×C8×C113—81no—
211C4⋊C4×C113—22no—
212C4⋊C4×C113—22no—
213C4⋊C4×C113—22no—
214C4⋊C4×C113—22no—
215C4⋊C4×C113—22no—
216C4⋊C4×C113—22no—
217C4⋊C4×C113—22no—
218C4⋊C4×C113—22no—
219C4⋊C4×C113—21no—
220C4⋊C4×C113—21no—
221C4⋊C4×C113—21no—
222C4⋊C4×C113—21no—
223C4⋊C4×C113—21no—
224C4⋊C4×C113—21no—
225C4⋊C4×C113—21no—
226C4⋊C4×C113—22no—
227C4⋊C4×C113—21no—
228C4⋊C4×C113—22no—
229C4⋊C4×C113—21no—
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×C113C2×D412yes—
238C4⋊C4×C113C2×D411yescharacteristic
239C4⋊C4×C113C2×D411yescharacteristic
240C4⋊C4×C113C2×D411yescharacteristic
241C4⋊C4×C113C2×D411yescharacteristic
242C22⋊C4×C113—22no—
243C22⋊C4×C113—22no—
244C22⋊C4×C113—22no—
245C22⋊C4×C113—21no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—21no—
248C22⋊C4×C113—21no—
249C22⋊C4×C113—21no—
250C22⋊C4×C113—21no—
251C22⋊C4×C113—21no—
252C22⋊C4×C113—21no—
253C22⋊C4×C113—41no—
254C22⋊C4×C113—41no—
255C42×C113—22no—
256C42×C113—22no—
257C42×C113—22no—
258C42×C113—22no—
259C42×C113—21no—
260C42×C113—21no—
261C42×C113—21no—
262C42×C113C2×D411yescharacteristic
263C42×C113C2×D411yescharacteristic
264C42×C113C2×D411yescharacteristic
265C42×C113C2411yescharacteristic
266C23×C113—21no—
267C23×C113—41no—
268C23×C113#12011yescharacteristic
269Q8×C113—21no—
270Q8×C113—21no—
271Q8×C113—21no—
272Q8×C113—21no—
273Q8×C113—21no—
274Q8×C113—21no—
275Q8×C113—42no—
276Q8×C113—42no—
277Q8×C113—41no—
278Q8×C113—41no—
279Q8×C113—81no—
280Q8×C113—82no—
281D4×C113—21no—
282D4×C113—21no—
283D4×C113—42no—
284D4×C113—41no—
285D4×C113—41no—
286D4×C113—41no—
287D4×C113—41no—
288D4×C113—81no—
289D4×C113—82no—
290C2×C4×C113—21no—
291C2×C4×C113—21no—
292C2×C4×C113—21no—
293C2×C4×C113—21no—
294C2×C4×C113—21no—
295C2×C4×C113—21no—
296C2×C4×C113—21no—
297C2×C4×C113—22no—
298C2×C4×C113—21no—
299C2×C4×C113—21no—
300C2×C4×C113—21no—
301C2×C4×C113—22no—
302C2×C4×C113—21no—
303C2×C4×C113—41no—
304C2×C4×C113—41no—
305C2×C4×C113—41no—
306C2×C4×C113—41no—
307C2×C4×C113—82no—
308C2×C4×C113—82no—
309C2×C4×C113#12011yescharacteristic
310C2×C4×C113#12011yescharacteristic
311C2×C4×C113#12011yescharacteristic
312C2×C4×C113C22×D411yescharacteristic
313C2×C4×C113C22×D411yescharacteristic
314C2×C4×C113C22×D411yescharacteristic
315C8×C113—41no—
316C8×C113—41no—
317C8×C113—41no—
318C8×C113—41no—
319C8×C113—41no—
320C8×C113—41no—
321C22×C113—21no—
322C22×C113—21no—
323C22×C113—21no—
324C22×C113—41no—
325C22×C113—41no—
326C22×C113—41no—
327C22×C113—81no—
328C22×C113—81no—
329C22×C113—81no—
330C22×C113C2×#12011yescharacteristic
331C4×C113—21no—
332C4×C113—21no—
333C4×C113—21no—
334C4×C113—21no—
335C4×C113—41no—
336C4×C113—41no—
337C4×C113—41no—
338C4×C113—41no—
339C4×C113—42no—
340C4×C113—41no—
341C4×C113—42no—
342C4×C113—41no—
343C4×C113—41no—
344C4×C113—81no—
345C4×C113#57711yescharacteristic
346C4×C113#57711yescharacteristic
347C4×C113#57811yescharacteristic
348C4×C113#57811yescharacteristic
349#18963C11311yesmaximal, characteristic, direct product factor, Sylow
350C2×C113—41no—
351C2×C113—81no—
352C2×C113—161no—
353C2×C113#301311yescharacteristic
354C2×C113#301311yescharacteristic
355C2×C113#302111yescharacteristic
356#3555C2×C11311yescharacteristic, complemented
357#3254C2×C11311yescharacteristic, complemented
358#3247C2×C11311yescharacteristic
359#3210C2×C11311yescharacteristic, complemented
360#1638C2×C11311yescharacteristic, complemented
361#1636C2×C11311yescharacteristic, complemented
362#1633C2×C11311yescharacteristic, complemented
363#1632C2×C11311yescharacteristic, complemented
364#1628C2×C11311yescharacteristic, complemented
365#1626C2×C11311yescharacteristic, complemented
366#1623C2×C11311yescharacteristic, complemented
367#1622C2×C11311yescharacteristic, complemented
368#1550C2×C11311yescharacteristic, complemented
369#1495C2×C11311yescharacteristic, complemented
370#1481C2×C11311yescharacteristic, complemented
371C113#1896311yescharacteristic, direct product factor, Sylow
372#563—22no—
373Q82C22×C11311yescharacteristic
374#557—21no—
375#557C22×C11311yescharacteristic
376#556—21no—
377#556—21no—
378#556C22×C11311yescharacteristic
379#554C22×C11311yescharacteristic
380#552—21no—
381#544—21no—
382#542—21no—
383#541—21no—
384#541—21no—
385#541—22no—
386#533C22×C11311yescharacteristic
387#533C22×C11311yescharacteristic
388#532C22×C11311yescharacteristic
389#529C22×C11311yescharacteristic
390#494C22×C11311yescharacteristic
391#492C22×C11311yescharacteristic
392#487C22×C11311yescharacteristic
393#486C22×C11311yescharacteristic
394#478—21no—
395#477C22×C11311yescharacteristic
396#477C22×C11311yescharacteristic
397#477C22×C11311yescharacteristic
398#476C22×C11311yescharacteristic
399#474—21no—
400#468—21no—
401#468—21no—
402#466—21no—
403#465—21no—
404#464—22no—
405#463—21no—
406#461—21no—
407#460C22×C11311yescharacteristic
408#460C22×C11311yescharacteristic
409#460C22×C11311yescharacteristic
410#459C22×C11311yescharacteristic
411#452—22no—
412#431C22×C11311yescharacteristic
413#423C22×C11311yescharacteristic
414C2×C4⋊C8C22×C11311yescharacteristic
415#333C22×C11311yescharacteristic
416#333C22×C11311yescharacteristic
417#332C22×C11311yescharacteristic
418#332C22×C11311yescharacteristic
419Q8⋊C8C22×C11311yescharacteristic
420Q8⋊C8C22×C11311yescharacteristic
421Q8⋊C8C22×C11311yescharacteristic
422Q8⋊C8C22×C11311yescharacteristic
423Q8⋊C8C22×C11311yescharacteristic
424Q8⋊C8C22×C11311yescharacteristic
425D4⋊C8C22×C11311yescharacteristic
426D4⋊C8C22×C11311yescharacteristic
427C2×#41—21no—
428C2×Q16—22no—
429C2×SD16—22no—
430C2×SD16—21no—
431C2×SD16—21no—
432C2×SD16—21no—
433C2×D8—21no—
434C2×M16—21no—
435C22×C8—21no—
436C4⋊Q8—22no—
437C4⋊Q8—21no—
438C4⋊Q8—22no—
439C4⋊Q8—21no—
440C4⋊Q8—21no—
441C4⋊Q8D4×C11311yescharacteristic
442C4⋊Q8D4×C11311yescharacteristic
443C4⋊Q8C23×C11311yescharacteristic
444C4⋊Q8C23×C11311yescharacteristic
445C4⋊Q8C23×C11311yescharacteristic
446#127C23×C11311yescharacteristic
447#126—22no—
448#126—22no—
449#126—22no—
450#126—22no—
451#126—22no—
452#126—22no—
453#126—21no—
454#125—22no—
455#125—22no—
456#125—22no—
457#125—22no—
458#125—21no—
459#125—22no—
460#125—21no—
461#125—21no—
462#125—21no—
463#125D4×C11311yescharacteristic
464#124—22no—
465#124—21no—
466#124—21no—
467#124D4×C11311yescharacteristic
468#123—22no—
469#123—21no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—22no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8D4×C11311yescharacteristic
478C22⋊Q8D4×C11311yescharacteristic
479C22⋊Q8D4×C11311yescharacteristic
480C22⋊Q8D4×C11312yes—
481#121—21no—
482#121—21no—
483#121D4×C11311yescharacteristic
484C4×Q8—22no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8D4×C11312yes—
493C4×Q8C23×C11311yescharacteristic
494C4×Q8C23×C11311yescharacteristic
495C4×Q8C23×C11311yescharacteristic
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4C23×C11311yescharacteristic
501#117—22no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506C2×C4⋊C4—21no—
507C2×C42C23×C11311yescharacteristic
508#107—21no—
509#107—21no—
510#107—21no—
511#106—21no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8C23×C11311yescharacteristic
516C4⋊C8C23×C11311yescharacteristic
517C4⋊C8C23×C11311yescharacteristic
518C4⋊C8C23×C11311yescharacteristic
519#103—21no—
520#103—21no—
521#103—21no—
522#103—22no—
523#102—21no—
524#102—22no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529C22⋊C8—21no—
530C4×C8C23×C11311yescharacteristic
531C4×C8C23×C11311yescharacteristic
532#41—82no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8C2×D4×C11311yescharacteristic
538C2×Q8C2×D4×C11311yescharacteristic
539C2×Q8C2×D4×C11311yescharacteristic
540C2×Q8C2×D4×C11312yes—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—41no—
546C2×D4C2×D4×C11311yescharacteristic
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—41no—
550C22×C4C2×D4×C11311yescharacteristic
551C22×C4C2×D4×C11311yescharacteristic
552C22×C4C2×D4×C11311yescharacteristic
553Q16—82no—
554SD16—81no—
555SD16—81no—
556SD16—81no—
557SD16—82no—
558D8—81no—
559M16—81no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—81no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4C2×D4×C11312yes—
594C4⋊C4C2×D4×C11311yescharacteristic
595C4⋊C4C2×D4×C11311yescharacteristic
596C4⋊C4C2×D4×C11311yescharacteristic
597C4⋊C4C2×D4×C11311yescharacteristic
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—22no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C2×D4×C11311yescharacteristic
619C42C2×D4×C11311yescharacteristic
620C42C2×D4×C11311yescharacteristic
621C42C24×C11311yescharacteristic
622C23—21no—
623C23—41no—
624C23#120×C11311yescharacteristic
625Q8—21no—
626Q8—21no—
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—42no—
632Q8—42no—
633Q8—41no—
634Q8—41no—
635Q8—81no—
636Q8—82no—
637D4—21no—
638D4—21no—
639D4—42no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—81no—
645D4—82no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4#120×C11311yescharacteristic
666C2×C4#120×C11311yescharacteristic
667C2×C4#120×C11311yescharacteristic
668C2×C4C22×D4×C11311yescharacteristic
669C2×C4C22×D4×C11311yescharacteristic
670C2×C4C22×D4×C11311yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22C2×#120×C11311yescharacteristic
687C4—21no—
688C4—21no—
689C4—21no—
690C4—21no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—81no—
701C4#577×C11311yescharacteristic
702C4#577×C11311yescharacteristic
703C4#578×C11311yescharacteristic
704C4#578×C11311yescharacteristic
705C2—41no—
706C2—81no—
707C2—161no—
708C2C113×#301311yescharacteristic
709C2C113×#301311yescharacteristic
710C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3247C2
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×#3555C2semidirect
2. C113×#3254C2semidirect
4. C113×#3210C2semidirect
5. C113×#1638C2semidirect
6. C113×#1636C2semidirect
7. C113×#1633C2semidirect
8. C113×#1632C2semidirect
9. C113×#1628C2semidirect
10. C113×#1626C2semidirect
11. C113×#1623C2semidirect
12. C113×#1622C2semidirect
13. C113×#1550C2semidirect
14. C113×#1495C2semidirect
15. C113×#1481C2semidirect
349. #18963C113direct (N × H)
356. #3555C2×C113semidirect
357. #3254C2×C113semidirect
359. #3210C2×C113semidirect
360. #1638C2×C113semidirect
361. #1636C2×C113semidirect
362. #1633C2×C113semidirect
363. #1632C2×C113semidirect
364. #1628C2×C113semidirect
365. #1626C2×C113semidirect
366. #1623C2×C113semidirect
367. #1622C2×C113semidirect
368. #1550C2×C113semidirect
369. #1495C2×C113semidirect
370. #1481C2×C113semidirect
371. C113#18963direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35552
C113×#32542
C113×#32472
C113×#32102
C113×#16382
C113×#16362
C113×#16332
C113×#16322
C113×#16282
C113×#16262
C113×#16232
C113×#16222
C113×#15502
C113×#14952
C113×#14812
#18963113