Finite Group Databasebeta

← C113×#18228 #43286248

Subgroups — C113×#18228 #43286248

Order 28928.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3537C211yesmaximal, characteristic, complemented
2C113×#3006C211yesmaximal, characteristic, complemented
3C113×#3002C211yesmaximal, characteristic, complemented
4C113×#2615C211yesmaximal, characteristic, complemented
5C113×#1606C212yesmaximal, complemented
6C113×#1601C212yesmaximal, complemented
7C113×#1600C212yesmaximal, complemented
8C113×#1595C212yesmaximal, complemented
9C113×#1519C211yesmaximal, characteristic, complemented
10C113×#1513C211yesmaximal, characteristic, complemented
11C113×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C113C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C113—21no—
14C2×#135×C113—21no—
15#560×C113—22no—
16#553×C113—21no—
17#553×C113—21no—
18D42×C113—22no—
19D42×C113—21no—
20D42×C113—21no—
21#540×C113—21no—
22#538×C113—21no—
23#538×C113C2212yes—
24#535×C113—21no—
25#534×C113—21no—
26#534×C113C2212yes—
27#525×C113C2211yescharacteristic
28C2×#121×C113—21no—
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31#452×C113—21no—
32#451×C113C2211yescharacteristic, complemented
33#450×C113C2211yescharacteristic, complemented
34#449×C113—21no—
35#449×C113—22no—
36#448×C113C2211yescharacteristic, complemented
37#448×C113C2212yescomplemented
38#447×C113C2211yescharacteristic, complemented
39#447×C113C2212yescomplemented
40#417×C113—21no—
41#416×C113—21no—
42#407×C113C2211yescharacteristic, complemented
43C2×C22⋊C8×C113C2211yescharacteristic, complemented
44#393×C113C2212yescomplemented
45#392×C113—22no—
46#392×C113C2212yescomplemented
47#380×C113—21no—
48#380×C113C2211yescharacteristic, complemented
49#328×C113C2212yescomplemented
50#327×C113C2212yescomplemented
51#327×C113C2212yescomplemented
52#327×C113C2212yescomplemented
53#323×C113C2212yescomplemented
54#323×C113C2212yescomplemented
55C2×#41×C113—21no—
56C2×#41×C113—21no—
57C2×#41×C113—21no—
58C2×#41×C113—21no—
59C2×#41×C113—44no—
60C2×#41×C113D411yescharacteristic, complemented
61C22×Q8×C113C2311yescharacteristic
62C22×D4×C113—22no—
63C22×D4×C113—21no—
64C22×D4×C113—21no—
65C22×D4×C113—22no—
66C22×D4×C113—21no—
67C22×D4×C113—22no—
68C22×D4×C113D411yescharacteristic
69C22×D4×C113D412yes—
70C22×D4×C113D411yescharacteristic, complemented
71C22×D4×C113C2311yescharacteristic
72C23×C4×C113—21no—
73C23×C4×C113C2311yescharacteristic
74AGL(1,ℤ/8)×C113—44no—
75#135×C113—44no—
76C2×Q16×C113—21no—
77C2×SD16×C113—21no—
78C2×SD16×C113—21no—
79C2×SD16×C113—22no—
80C2×D8×C113—21no—
81C2×D8×C113—22no—
82C2×M16×C113—21no—
83C22×C8×C113—21no—
84#127×C113—22no—
85#127×C113—21no—
86#126×C113—22no—
87#126×C113—22no—
88#125×C113—21no—
89#124×C113—22no—
90#123×C113—22no—
91#123×C113—21no—
92#123×C113—22no—
93#123×C113—22no—
94#123×C113—22no—
95C22⋊Q8×C113D411yescharacteristic, complemented
96C22⋊Q8×C113C2311yescharacteristic
97#121×C113—22no—
98#121×C113—21no—
99#121×C113—21no—
100#121×C113—22no—
101#121×C113—22no—
102#121×C113—22no—
103#121×C113—22no—
104#121×C113—21no—
105#121×C113—21no—
106#121×C113—21no—
107#121×C113—21no—
108#121×C113—21no—
109#121×C113—21no—
110#121×C113—22no—
111#121×C113—44no—
112#121×C113D412yescomplemented
113#121×C113D411yescharacteristic, complemented
114#121×C113C2312yes—
115#121×C113C2311yescharacteristic
116#120×C113—22no—
117#120×C113—22no—
118#120×C113—22no—
119#120×C113—21no—
120#120×C113—22no—
121#120×C113—22no—
122#120×C113—22no—
123C4×D4×C113—22no—
124C4×D4×C113—21no—
125C4×D4×C113—21no—
126C4×D4×C113—21no—
127C4×D4×C113—21no—
128C4×D4×C113—22no—
129#117×C113—21no—
130#117×C113D411yescharacteristic, complemented
131C2×C4⋊C4×C113—21no—
132C2×C4⋊C4×C113D411yescharacteristic
133C2×C4⋊C4×C113D411yescharacteristic, complemented
134C2×C22⋊C4×C113—21no—
135C2×C22⋊C4×C113—22no—
136C2×C22⋊C4×C113—21no—
137C2×C22⋊C4×C113—22no—
138C2×C22⋊C4×C113C2312yes—
139#103×C113—21no—
140#103×C113—21no—
141#103×C113—22no—
142#102×C113—21no—
143#102×C113—21no—
144#102×C113—22no—
145C22⋊C8×C113—21no—
146C22⋊C8×C113—21no—
147C22⋊C8×C113C2311yescharacteristic
148C22⋊C8×C113C2311yescharacteristic
149C22⋊C8×C113C2312yes—
150#95×C113—22no—
151#95×C113C2312yes—
152C24×C113—22no—
153C24×C113—21no—
154C24×C113—21no—
155C24×C113C2×D412yes—
156C24×C113C2×D411yescharacteristic
157#41×C113—24no—
158#41×C113—24no—
159#41×C113—42no—
160#41×C113—42no—
161#41×C113—42no—
162#41×C113—42no—
163#41×C113—42no—
164#41×C113—42no—
165#41×C113—42no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×Q8×C113—42no—
169C2×Q8×C113C2×D411yescharacteristic
170C2×D4×C113—22no—
171C2×D4×C113—21no—
172C2×D4×C113—21no—
173C2×D4×C113—22no—
174C2×D4×C113—22no—
175C2×D4×C113—22no—
176C2×D4×C113—22no—
177C2×D4×C113—22no—
178C2×D4×C113—22no—
179C2×D4×C113—21no—
180C2×D4×C113—22no—
181C2×D4×C113—22no—
182C2×D4×C113—21no—
183C2×D4×C113—21no—
184C2×D4×C113—21no—
185C2×D4×C113—21no—
186C2×D4×C113—21no—
187C2×D4×C113—42no—
188C2×D4×C113—42no—
189C2×D4×C113—42no—
190C2×D4×C113—42no—
191C2×D4×C113—42no—
192C2×D4×C113—41no—
193C2×D4×C113—41no—
194C2×D4×C113—44no—
195C2×D4×C113—82no—
196C2×D4×C113—82no—
197C2×D4×C113—82no—
198C2×D4×C113—82no—
199C2×D4×C113—81no—
200C2×D4×C113—81no—
201C2×D4×C113—82no—
202C2×D4×C113—82no—
203C2×D4×C113—84no—
204C2×D4×C113C2×D411yescharacteristic
205C2×D4×C113C2×D412yes—
206C22×C4×C113—24no—
207C22×C4×C113—21no—
208C22×C4×C113—22no—
209C22×C4×C113—22no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—22no—
213C22×C4×C113—42no—
214C22×C4×C113—42no—
215C22×C4×C113—41no—
216C22×C4×C113—41no—
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113C2×D411yescharacteristic
219C22×C4×C113C2×D411yescharacteristic
220C22×C4×C113C2×D412yes—
221C22×C4×C113C2×D411yescharacteristic
222C22×C4×C113C2×D411yescharacteristic
223C22×C4×C113C2411yescharacteristic
224Q16×C113—42no—
225SD16×C113—42no—
226SD16×C113—42no—
227SD16×C113—44no—
228D8×C113—42no—
229D8×C113—44no—
230M16×C113—42no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—22no—
234C2×C8×C113—42no—
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—42no—
243C4⋊C4×C113C2×D412yes—
244C4⋊C4×C113C2×D411yescharacteristic
245C4⋊C4×C113C2×D411yescharacteristic
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—22no—
255C22⋊C4×C113—21no—
256C22⋊C4×C113—22no—
257C22⋊C4×C113—22no—
258C22⋊C4×C113—22no—
259C22⋊C4×C113—21no—
260C22⋊C4×C113—44no—
261C22⋊C4×C113—81no—
262C22⋊C4×C113—82no—
263C42×C113—22no—
264C42×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—22no—
268C23×C113—22no—
269C23×C113—22no—
270C23×C113—21no—
271C23×C113—22no—
272C23×C113—22no—
273C23×C113—41no—
274C23×C113—41no—
275C23×C113—41no—
276C23×C113—41no—
277C23×C113—41no—
278C23×C113—42no—
279C23×C113—42no—
280C23×C113—42no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—81no—
285C23×C113—81no—
286C23×C113—82no—
287C23×C113—82no—
288C23×C113—82no—
289C23×C113#12011yescharacteristic
290C23×C113#12011yescharacteristic
291C23×C113C22×D411yescharacteristic
292Q8×C113—22no—
293Q8×C113—22no—
294Q8×C113—41no—
295Q8×C113—41no—
296Q8×C113—41no—
297D4×C113—22no—
298D4×C113—22no—
299D4×C113—42no—
300D4×C113—41no—
301D4×C113—41no—
302D4×C113—41no—
303D4×C113—44no—
304D4×C113—42no—
305D4×C113—44no—
306D4×C113—44no—
307D4×C113—42no—
308D4×C113—41no—
309D4×C113—42no—
310D4×C113—41no—
311D4×C113—42no—
312D4×C113—42no—
313D4×C113—81no—
314D4×C113—82no—
315D4×C113—82no—
316D4×C113—81no—
317D4×C113—82no—
318D4×C113—82no—
319D4×C113—82no—
320D4×C113—82no—
321D4×C113—82no—
322D4×C113—88no—
323C2×C4×C113—22no—
324C2×C4×C113—22no—
325C2×C4×C113—22no—
326C2×C4×C113—22no—
327C2×C4×C113—21no—
328C2×C4×C113—22no—
329C2×C4×C113—22no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—44no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—44no—
339C2×C4×C113—42no—
340C2×C4×C113—42no—
341C2×C4×C113—42no—
342C2×C4×C113—42no—
343C2×C4×C113—42no—
344C2×C4×C113—81no—
345C2×C4×C113—82no—
346C2×C4×C113—82no—
347C2×C4×C113#12011yescharacteristic
348C2×C4×C113#12011yescharacteristic
349C2×C4×C113C22×D411yescharacteristic
350C2×C4×C113C22×D411yescharacteristic
351C8×C113—41no—
352C8×C113—41no—
353C8×C113—42no—
354C22×C113—21no—
355C22×C113—21no—
356C22×C113—21no—
357C22×C113—21no—
358C22×C113—21no—
359C22×C113—21no—
360C22×C113—21no—
361C22×C113—21no—
362C22×C113—42no—
363C22×C113—42no—
364C22×C113—42no—
365C22×C113—42no—
366C22×C113—41no—
367C22×C113—42no—
368C22×C113—42no—
369C22×C113—41no—
370C22×C113—42no—
371C22×C113—41no—
372C22×C113—42no—
373C22×C113—42no—
374C22×C113—81no—
375C22×C113—81no—
376C22×C113—82no—
377C22×C113—82no—
378C22×C113—81no—
379C22×C113—81no—
380C22×C113—81no—
381C22×C113—81no—
382C22×C113—162no—
383C22×C113—164no—
384C22×C113C2×#12011yescharacteristic
385C22×C113#57611yescharacteristic
386C22×C113#57711yescharacteristic
387C4×C113—21no—
388C4×C113—21no—
389C4×C113—21no—
390C4×C113—42no—
391C4×C113—41no—
392C4×C113—42no—
393C4×C113—41no—
394C4×C113—42no—
395C4×C113—41no—
396C4×C113—82no—
397C4×C113B(4,𝔽2)12yes—
398#18228C11311yesmaximal, characteristic, direct product factor, Sylow
399C2×C113—21no—
400C2×C113—21no—
401C2×C113—41no—
402C2×C113—41no—
403C2×C113—82no—
404C2×C113—82no—
405C2×C113—82no—
406C2×C113—81no—
407C2×C113#301211yescharacteristic
408C2×C113#301911yescharacteristic
409C2×C113C2×B(4,𝔽2)11yescharacteristic
410#3537C2×C11311yescharacteristic, complemented
411#3006C2×C11311yescharacteristic, complemented
412#3002C2×C11311yescharacteristic, complemented
413#2615C2×C11311yescharacteristic, complemented
414#1606C2×C11312yescomplemented
415#1601C2×C11312yescomplemented
416#1600C2×C11312yescomplemented
417#1595C2×C11312yescomplemented
418#1519C2×C11311yescharacteristic, complemented
419#1513C2×C11311yescharacteristic, complemented
420#1471C2×C11311yescharacteristic, complemented
421C113#1822811yescharacteristic, direct product factor, Sylow
422C22×#41C22×C11311yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424C2×#135—21no—
425#560—22no—
426#553—21no—
427#553—21no—
428D42—22no—
429D42—21no—
430D42—21no—
431#540—21no—
432#538—21no—
433#538C22×C11312yes—
434#535—21no—
435#534—21no—
436#534C22×C11312yes—
437#525C22×C11311yescharacteristic
438C2×#121—21no—
439C2×#121C22×C11311yescharacteristic
440C2×#121C22×C11311yescharacteristic
441#452—21no—
442#451C22×C11311yescharacteristic, complemented
443#450C22×C11311yescharacteristic, complemented
444#449—21no—
445#449—22no—
446#448C22×C11311yescharacteristic, complemented
447#448C22×C11312yescomplemented
448#447C22×C11311yescharacteristic, complemented
449#447C22×C11312yescomplemented
450#417—21no—
451#416—21no—
452#407C22×C11311yescharacteristic, complemented
453C2×C22⋊C8C22×C11311yescharacteristic, complemented
454#393C22×C11312yescomplemented
455#392—22no—
456#392C22×C11312yescomplemented
457#380—21no—
458#380C22×C11311yescharacteristic, complemented
459#328C22×C11312yescomplemented
460#327C22×C11312yescomplemented
461#327C22×C11312yescomplemented
462#327C22×C11312yescomplemented
463#323C22×C11312yescomplemented
464#323C22×C11312yescomplemented
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C11311yescharacteristic, complemented
471C22×Q8C23×C11311yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C11311yescharacteristic
479C22×D4D4×C11312yes—
480C22×D4D4×C11311yescharacteristic, complemented
481C22×D4C23×C11311yescharacteristic
482C23×C4—21no—
483C23×C4C23×C11311yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C11311yescharacteristic, complemented
506C22⋊Q8C23×C11311yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
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#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C11312yescomplemented
523#121D4×C11311yescharacteristic, complemented
524#121C23×C11312yes—
525#121C23×C11311yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C11311yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C11311yescharacteristic
543C2×C4⋊C4D4×C11311yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C11312yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C11311yescharacteristic
558C22⋊C8C23×C11311yescharacteristic
559C22⋊C8C23×C11312yes—
560#95—22no—
561#95C23×C11312yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C11312yes—
566C24C2×D4×C11311yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C11311yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C11311yescharacteristic
615C2×D4C2×D4×C11312yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C11311yescharacteristic
628C22×C4C2×D4×C11311yescharacteristic
629C22×C4C2×D4×C11311yescharacteristic
630C22×C4C2×D4×C11312yes—
631C22×C4C2×D4×C11311yescharacteristic
632C22×C4C2×D4×C11311yescharacteristic
633C22×C4C24×C11311yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C11312yes—
654C4⋊C4C2×D4×C11311yescharacteristic
655C4⋊C4C2×D4×C11311yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C11311yescharacteristic
700C23#120×C11311yescharacteristic
701C23C22×D4×C11311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C11311yescharacteristic
758C2×C4#120×C11311yescharacteristic
759C2×C4C22×D4×C11311yescharacteristic
760C2×C4C22×D4×C11311yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C11311yescharacteristic
795C22#576×C11311yescharacteristic
796C22#577×C11311yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4B(4,𝔽2)×C11312yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C113×#301211yescharacteristic
817C2C113×#301911yescharacteristic
818C2C2×B(4,𝔽2)×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C113×#3537C2semidirect
2. C113×#3006C2semidirect
3. C113×#3002C2semidirect
4. C113×#2615C2semidirect
5. C113×#1606C2semidirect
6. C113×#1601C2semidirect
7. C113×#1600C2semidirect
8. C113×#1595C2semidirect
9. C113×#1519C2semidirect
10. C113×#1513C2semidirect
11. C113×#1471C2semidirect
12. C22×#41×C113C22semidirect
32. #451×C113C22semidirect
33. #450×C113C22semidirect
36. #448×C113C22semidirect
37. #448×C113C22semidirect
38. #447×C113C22semidirect
39. #447×C113C22semidirect
42. #407×C113C22semidirect
43. C2×C22⋊C8×C113C22semidirect
44. #393×C113C22semidirect
46. #392×C113C22semidirect
48. #380×C113C22semidirect
49. #328×C113C22semidirect
50. #327×C113C22semidirect
51. #327×C113C22semidirect
52. #327×C113C22semidirect
53. #323×C113C22semidirect
54. #323×C113C22semidirect
60. C2×#41×C113D4semidirect
70. C22×D4×C113D4semidirect
95. C22⋊Q8×C113D4semidirect
112. #121×C113D4semidirect
113. #121×C113D4semidirect
130. #117×C113D4semidirect
133. C2×C4⋊C4×C113D4semidirect
398. #18228C113direct (N × H)
410. #3537C2×C113semidirect
411. #3006C2×C113semidirect
412. #3002C2×C113semidirect
413. #2615C2×C113semidirect
414. #1606C2×C113semidirect
415. #1601C2×C113semidirect
416. #1600C2×C113semidirect
417. #1595C2×C113semidirect
418. #1519C2×C113semidirect
419. #1513C2×C113semidirect
420. #1471C2×C113semidirect
421. C113#18228direct (N × H)
422. C22×#41C22×C113semidirect
442. #451C22×C113semidirect
443. #450C22×C113semidirect
446. #448C22×C113semidirect
447. #448C22×C113semidirect
448. #447C22×C113semidirect
449. #447C22×C113semidirect
452. #407C22×C113semidirect
453. C2×C22⋊C8C22×C113semidirect
454. #393C22×C113semidirect
456. #392C22×C113semidirect
458. #380C22×C113semidirect
459. #328C22×C113semidirect
460. #327C22×C113semidirect
461. #327C22×C113semidirect
462. #327C22×C113semidirect
463. #323C22×C113semidirect
464. #323C22×C113semidirect
470. C2×#41D4×C113semidirect
480. C22×D4D4×C113semidirect
505. C22⋊Q8D4×C113semidirect
522. #121D4×C113semidirect
523. #121D4×C113semidirect
540. #117D4×C113semidirect
543. C2×C4⋊C4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35372
C113×#30062
C113×#30022
C113×#26152
C113×#16062
C113×#16012
C113×#16002
C113×#15952
C113×#15192
C113×#15132
C113×#14712
#18228113