Finite Group Databasebeta

← C113×#18229 #43286249

Subgroups — C113×#18229 #43286249

Order 28928.

1232 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3536C211yesmaximal, characteristic, complemented
2C113×#3007C211yesmaximal, characteristic, complemented
3C113×#3002C211yesmaximal, characteristic, complemented
4C113×#2615C211yesmaximal, characteristic, complemented
5C113×#1606C212yesmaximal, complemented
6C113×#1602C212yesmaximal, complemented
7C113×#1600C212yesmaximal, complemented
8C113×#1596C212yesmaximal, complemented
9C113×#1520C211yesmaximal, characteristic, complemented
10C113×#1513C211yesmaximal, characteristic, complemented
11C113×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C113C2211yescharacteristic
13C2×#137×C113—21no—
14C2×#135×C113—21no—
15#562×C113—22no—
16#554×C113—21no—
17#548×C113—21no—
18#547×C113—21no—
19#546×C113—22no—
20#546×C113—21no—
21#543×C113C2212yes—
22#542×C113—21no—
23#539×C113—21no—
24#538×C113C2212yes—
25#537×C113—21no—
26#537×C113—21no—
27#525×C113C2211yescharacteristic
28C2×C22⋊Q8×C113C2211yescharacteristic
29C2×#121×C113—21no—
30C2×#121×C113C2211yescharacteristic
31#452×C113—21no—
32#452×C113—22no—
33#451×C113C2211yescharacteristic
34#451×C113C2212yes—
35#450×C113C2211yescharacteristic
36#450×C113C2212yes—
37#449×C113—21no—
38#448×C113C2211yescharacteristic
39#447×C113C2211yescharacteristic
40#417×C113—21no—
41#416×C113—21no—
42#407×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44#393×C113C2212yes—
45#392×C113—22no—
46#392×C113C2212yes—
47#380×C113—21no—
48#380×C113C2211yescharacteristic
49#328×C113C2212yes—
50#328×C113C2212yes—
51#328×C113C2212yes—
52#327×C113C2212yes—
53#323×C113C2212yes—
54#323×C113C2212yes—
55C2×#41×C113—22no—
56C2×#41×C113—21no—
57C2×#41×C113—21no—
58C2×#41×C113—21no—
59C2×#41×C113—21no—
60C2×#41×C113—21no—
61C2×#41×C113—44no—
62C2×#41×C113D411yescharacteristic, complemented
63C22×Q8×C113D411yescharacteristic, complemented
64C22×Q8×C113C2311yescharacteristic
65C22×D4×C113—21no—
66C22×D4×C113—22no—
67C22×D4×C113D411yescharacteristic
68C22×D4×C113D412yes—
69C22×D4×C113C2311yescharacteristic
70C23×C4×C113—21no—
71C23×C4×C113C2311yescharacteristic
72#137×C113—44no—
73#135×C113—44no—
74C2×Q16×C113—21no—
75C2×Q16×C113—22no—
76C2×SD16×C113—21no—
77C2×SD16×C113—22no—
78C2×SD16×C113—21no—
79C2×D8×C113—21no—
80C2×M16×C113—21no—
81C22×C8×C113—21no—
82C4⋊Q8×C113—21no—
83#126×C113—22no—
84#125×C113—22no—
85#124×C113—21no—
86#124×C113—22no—
87#124×C113—22no—
88#123×C113—22no—
89#123×C113—22no—
90#123×C113—22no—
91#123×C113—21no—
92#123×C113—22no—
93C22⋊Q8×C113—21no—
94C22⋊Q8×C113—22no—
95C22⋊Q8×C113—22no—
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—21no—
98C22⋊Q8×C113—21no—
99C22⋊Q8×C113—22no—
100C22⋊Q8×C113—22no—
101C22⋊Q8×C113—22no—
102C22⋊Q8×C113D412yescomplemented
103C22⋊Q8×C113D411yescharacteristic, complemented
104C22⋊Q8×C113C2312yes—
105C22⋊Q8×C113C2311yescharacteristic
106#121×C113—21no—
107#121×C113—22no—
108#121×C113—22no—
109#121×C113—22no—
110#121×C113—22no—
111#121×C113—22no—
112#121×C113—21no—
113#121×C113—21no—
114#121×C113—21no—
115#121×C113—21no—
116#121×C113—44no—
117#121×C113D411yescharacteristic, complemented
118#121×C113C2311yescharacteristic
119#120×C113—21no—
120#120×C113—22no—
121C4×Q8×C113—21no—
122C4×D4×C113—22no—
123C4×D4×C113—21no—
124C4×D4×C113—21no—
125C4×D4×C113—21no—
126C4×D4×C113—22no—
127#117×C113D411yescharacteristic, complemented
128C2×C4⋊C4×C113—21no—
129C2×C4⋊C4×C113—21no—
130C2×C4⋊C4×C113—21no—
131C2×C4⋊C4×C113D411yescharacteristic
132C2×C4⋊C4×C113D411yescharacteristic, complemented
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—22no—
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×C113C2312yes—
148C22⋊C8×C113C2311yescharacteristic
149C22⋊C8×C113C2311yescharacteristic
150#95×C113—22no—
151#95×C113C2312yes—
152C24×C113—21no—
153C24×C113C2×D412yes—
154C24×C113C2×D411yescharacteristic
155#41×C113—24no—
156#41×C113—24no—
157#41×C113—42no—
158#41×C113—42no—
159#41×C113—42no—
160#41×C113—42no—
161#41×C113—42no—
162#41×C113—42no—
163#41×C113—42no—
164#41×C113—84no—
165#41×C113—82no—
166C2×Q8×C113—22no—
167C2×Q8×C113—21no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—42no—
171C2×Q8×C113—42no—
172C2×Q8×C113C2×D411yescharacteristic
173C2×Q8×C113C2×D412yes—
174C2×D4×C113—21no—
175C2×D4×C113—22no—
176C2×D4×C113—21no—
177C2×D4×C113—22no—
178C2×D4×C113—22no—
179C2×D4×C113—21no—
180C2×D4×C113—22no—
181C2×D4×C113—21no—
182C2×D4×C113—21no—
183C2×D4×C113—21no—
184C2×D4×C113—21no—
185C2×D4×C113—42no—
186C2×D4×C113—42no—
187C2×D4×C113—42no—
188C2×D4×C113—42no—
189C2×D4×C113—41no—
190C2×D4×C113—41no—
191C2×D4×C113—44no—
192C2×D4×C113—82no—
193C2×D4×C113—82no—
194C2×D4×C113—82no—
195C2×D4×C113C2×D411yescharacteristic
196C22×C4×C113—24no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—22no—
200C22×C4×C113—22no—
201C22×C4×C113—22no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—22no—
205C22×C4×C113—42no—
206C22×C4×C113—42no—
207C22×C4×C113—41no—
208C22×C4×C113—41no—
209C22×C4×C113C2×D411yescharacteristic
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D412yes—
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2411yescharacteristic
216Q16×C113—42no—
217Q16×C113—44no—
218SD16×C113—42no—
219SD16×C113—44no—
220SD16×C113—42no—
221D8×C113—42no—
222M16×C113—42no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—22no—
226C2×C8×C113—42no—
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—22no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—22no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—42no—
239C4⋊C4×C113C2×D412yes—
240C4⋊C4×C113C2×D411yescharacteristic
241C4⋊C4×C113C2×D411yescharacteristic
242C22⋊C4×C113—22no—
243C22⋊C4×C113—22no—
244C22⋊C4×C113—22no—
245C22⋊C4×C113—22no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—22no—
248C22⋊C4×C113—21no—
249C22⋊C4×C113—21no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—21no—
252C22⋊C4×C113—21no—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—22no—
255C22⋊C4×C113—21no—
256C22⋊C4×C113—44no—
257C22⋊C4×C113—81no—
258C22⋊C4×C113—82no—
259C42×C113—22no—
260C42×C113—21no—
261C23×C113—21no—
262C23×C113—21no—
263C23×C113—22no—
264C23×C113—22no—
265C23×C113—21no—
266C23×C113—22no—
267C23×C113—22no—
268C23×C113—41no—
269C23×C113—41no—
270C23×C113—41no—
271C23×C113—41no—
272C23×C113—41no—
273C23×C113—42no—
274C23×C113—42no—
275C23×C113—41no—
276C23×C113—41no—
277C23×C113—41no—
278C23×C113#12011yescharacteristic
279C23×C113#12011yescharacteristic
280C23×C113C22×D411yescharacteristic
281Q8×C113—22no—
282Q8×C113—22no—
283Q8×C113—42no—
284Q8×C113—41no—
285Q8×C113—41no—
286Q8×C113—41no—
287Q8×C113—42no—
288Q8×C113—82no—
289D4×C113—22no—
290D4×C113—22no—
291D4×C113—41no—
292D4×C113—41no—
293D4×C113—41no—
294D4×C113—44no—
295D4×C113—42no—
296D4×C113—44no—
297D4×C113—44no—
298D4×C113—41no—
299D4×C113—41no—
300D4×C113—42no—
301D4×C113—81no—
302D4×C113—82no—
303D4×C113—81no—
304D4×C113—82no—
305D4×C113—82no—
306D4×C113—88no—
307C2×C4×C113—22no—
308C2×C4×C113—22no—
309C2×C4×C113—22no—
310C2×C4×C113—22no—
311C2×C4×C113—21no—
312C2×C4×C113—22no—
313C2×C4×C113—21no—
314C2×C4×C113—22no—
315C2×C4×C113—21no—
316C2×C4×C113—22no—
317C2×C4×C113—41no—
318C2×C4×C113—41no—
319C2×C4×C113—41no—
320C2×C4×C113—44no—
321C2×C4×C113—41no—
322C2×C4×C113—42no—
323C2×C4×C113—41no—
324C2×C4×C113—44no—
325C2×C4×C113—42no—
326C2×C4×C113—42no—
327C2×C4×C113—42no—
328C2×C4×C113—42no—
329C2×C4×C113—42no—
330C2×C4×C113—81no—
331C2×C4×C113—82no—
332C2×C4×C113—82no—
333C2×C4×C113—82no—
334C2×C4×C113#12011yescharacteristic
335C2×C4×C113#12011yescharacteristic
336C2×C4×C113C22×D411yescharacteristic
337C2×C4×C113C22×D411yescharacteristic
338C8×C113—41no—
339C8×C113—41no—
340C8×C113—42no—
341C22×C113—21no—
342C22×C113—21no—
343C22×C113—21no—
344C22×C113—21no—
345C22×C113—21no—
346C22×C113—21no—
347C22×C113—21no—
348C22×C113—21no—
349C22×C113—42no—
350C22×C113—42no—
351C22×C113—41no—
352C22×C113—42no—
353C22×C113—41no—
354C22×C113—42no—
355C22×C113—42no—
356C22×C113—41no—
357C22×C113—42no—
358C22×C113—81no—
359C22×C113—81no—
360C22×C113—82no—
361C22×C113—82no—
362C22×C113—81no—
363C22×C113—81no—
364C22×C113—81no—
365C22×C113—81no—
366C22×C113C2×#12011yescharacteristic
367C22×C113#57711yescharacteristic
368C22×C113#57811yescharacteristic
369C4×C113—21no—
370C4×C113—21no—
371C4×C113—21no—
372C4×C113—41no—
373C4×C113—42no—
374C4×C113—42no—
375C4×C113—41no—
376C4×C113—42no—
377C4×C113—41no—
378C4×C113—42no—
379C4×C113—82no—
380C4×C113B(4,𝔽2)12yes—
381#18229C11311yesmaximal, characteristic, direct product factor, Sylow
382C2×C113—21no—
383C2×C113—21no—
384C2×C113—41no—
385C2×C113—41no—
386C2×C113—81no—
387C2×C113—82no—
388C2×C113—82no—
389C2×C113#301311yescharacteristic
390C2×C113#301911yescharacteristic
391C2×C113C2×B(4,𝔽2)11yescharacteristic
392#3536C2×C11311yescharacteristic, complemented
393#3007C2×C11311yescharacteristic, complemented
394#3002C2×C11311yescharacteristic, complemented
395#2615C2×C11311yescharacteristic, complemented
396#1606C2×C11312yescomplemented
397#1602C2×C11312yescomplemented
398#1600C2×C11312yescomplemented
399#1596C2×C11312yescomplemented
400#1520C2×C11311yescharacteristic, complemented
401#1513C2×C11311yescharacteristic, complemented
402#1471C2×C11311yescharacteristic, complemented
403C113#1822911yescharacteristic, direct product factor, Sylow
404C22×#41C22×C11311yescharacteristic
405C2×#137—21no—
406C2×#135—21no—
407#562—22no—
408#554—21no—
409#548—21no—
410#547—21no—
411#546—22no—
412#546—21no—
413#543C22×C11312yes—
414#542—21no—
415#539—21no—
416#538C22×C11312yes—
417#537—21no—
418#537—21no—
419#525C22×C11311yescharacteristic
420C2×C22⋊Q8C22×C11311yescharacteristic
421C2×#121—21no—
422C2×#121C22×C11311yescharacteristic
423#452—21no—
424#452—22no—
425#451C22×C11311yescharacteristic
426#451C22×C11312yes—
427#450C22×C11311yescharacteristic
428#450C22×C11312yes—
429#449—21no—
430#448C22×C11311yescharacteristic
431#447C22×C11311yescharacteristic
432#417—21no—
433#416—21no—
434#407C22×C11311yescharacteristic
435C2×C22⋊C8C22×C11311yescharacteristic
436#393C22×C11312yes—
437#392—22no—
438#392C22×C11312yes—
439#380—21no—
440#380C22×C11311yescharacteristic
441#328C22×C11312yes—
442#328C22×C11312yes—
443#328C22×C11312yes—
444#327C22×C11312yes—
445#323C22×C11312yes—
446#323C22×C11312yes—
447C2×#41—22no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—44no—
454C2×#41D4×C11311yescharacteristic, complemented
455C22×Q8D4×C11311yescharacteristic, complemented
456C22×Q8C23×C11311yescharacteristic
457C22×D4—21no—
458C22×D4—22no—
459C22×D4D4×C11311yescharacteristic
460C22×D4D4×C11312yes—
461C22×D4C23×C11311yescharacteristic
462C23×C4—21no—
463C23×C4C23×C11311yescharacteristic
464#137—44no—
465#135—44no—
466C2×Q16—21no—
467C2×Q16—22no—
468C2×SD16—21no—
469C2×SD16—22no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×M16—21no—
473C22×C8—21no—
474C4⋊Q8—21no—
475#126—22no—
476#125—22no—
477#124—21no—
478#124—22no—
479#124—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—21no—
484#123—22no—
485C22⋊Q8—21no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8D4×C11312yescomplemented
495C22⋊Q8D4×C11311yescharacteristic, complemented
496C22⋊Q8C23×C11312yes—
497C22⋊Q8C23×C11311yescharacteristic
498#121—21no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—44no—
509#121D4×C11311yescharacteristic, complemented
510#121C23×C11311yescharacteristic
511#120—21no—
512#120—22no—
513C4×Q8—21no—
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—22no—
519#117D4×C11311yescharacteristic, complemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C11311yescharacteristic
524C2×C4⋊C4D4×C11311yescharacteristic, complemented
525C2×C22⋊C4—21no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4C23×C11312yes—
531#103—21no—
532#103—21no—
533#103—22no—
534#102—21no—
535#102—21no—
536#102—22no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8C23×C11312yes—
540C22⋊C8C23×C11311yescharacteristic
541C22⋊C8C23×C11311yescharacteristic
542#95—22no—
543#95C23×C11312yes—
544C24—21no—
545C24C2×D4×C11312yes—
546C24C2×D4×C11311yescharacteristic
547#41—24no—
548#41—24no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—84no—
557#41—82no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8C2×D4×C11311yescharacteristic
565C2×Q8C2×D4×C11312yes—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—44no—
584C2×D4—82no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4C2×D4×C11311yescharacteristic
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4C2×D4×C11311yescharacteristic
602C22×C4C2×D4×C11311yescharacteristic
603C22×C4C2×D4×C11311yescharacteristic
604C22×C4C2×D4×C11312yes—
605C22×C4C2×D4×C11311yescharacteristic
606C22×C4C2×D4×C11311yescharacteristic
607C22×C4C24×C11311yescharacteristic
608Q16—42no—
609Q16—44no—
610SD16—42no—
611SD16—44no—
612SD16—42no—
613D8—42no—
614M16—42no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—22no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C11312yes—
632C4⋊C4C2×D4×C11311yescharacteristic
633C4⋊C4C2×D4×C11311yescharacteristic
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—44no—
649C22⋊C4—81no—
650C22⋊C4—82no—
651C42—22no—
652C42—21no—
653C23—21no—
654C23—21no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23#120×C11311yescharacteristic
671C23#120×C11311yescharacteristic
672C23C22×D4×C11311yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—42no—
680Q8—82no—
681D4—22no—
682D4—22no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—42no—
693D4—81no—
694D4—82no—
695D4—81no—
696D4—82no—
697D4—82no—
698D4—88no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C11311yescharacteristic
727C2×C4#120×C11311yescharacteristic
728C2×C4C22×D4×C11311yescharacteristic
729C2×C4C22×D4×C11311yescharacteristic
730C8—41no—
731C8—41no—
732C8—42no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—82no—
753C22—82no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22C2×#120×C11311yescharacteristic
759C22#577×C11311yescharacteristic
760C22#578×C11311yescharacteristic
761C4—21no—
762C4—21no—
763C4—21no—
764C4—41no—
765C4—42no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—42no—
771C4—82no—
772C4B(4,𝔽2)×C11312yes—
773C2—21no—
774C2—21no—
775C2—41no—
776C2—41no—
777C2—82no—
778C2—82no—
779C2—81no—
780C2C113×#301311yescharacteristic
781C2C113×#301911yescharacteristic
782C2C2×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×#3536C2semidirect
2. C113×#3007C2semidirect
3. C113×#3002C2semidirect
4. C113×#2615C2semidirect
5. C113×#1606C2semidirect
6. C113×#1602C2semidirect
7. C113×#1600C2semidirect
8. C113×#1596C2semidirect
9. C113×#1520C2semidirect
10. C113×#1513C2semidirect
11. C113×#1471C2semidirect
62. C2×#41×C113D4semidirect
63. C22×Q8×C113D4semidirect
102. C22⋊Q8×C113D4semidirect
103. C22⋊Q8×C113D4semidirect
117. #121×C113D4semidirect
127. #117×C113D4semidirect
132. C2×C4⋊C4×C113D4semidirect
381. #18229C113direct (N × H)
392. #3536C2×C113semidirect
393. #3007C2×C113semidirect
394. #3002C2×C113semidirect
395. #2615C2×C113semidirect
396. #1606C2×C113semidirect
397. #1602C2×C113semidirect
398. #1600C2×C113semidirect
399. #1596C2×C113semidirect
400. #1520C2×C113semidirect
401. #1513C2×C113semidirect
402. #1471C2×C113semidirect
403. C113#18229direct (N × H)
454. C2×#41D4×C113semidirect
455. C22×Q8D4×C113semidirect
494. C22⋊Q8D4×C113semidirect
495. C22⋊Q8D4×C113semidirect
509. #121D4×C113semidirect
519. #117D4×C113semidirect
524. 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×#35362
C113×#30072
C113×#30022
C113×#26152
C113×#16062
C113×#16022
C113×#16002
C113×#15962
C113×#15202
C113×#15132
C113×#14712
#18229113