Finite Group Databasebeta

← C113×#25587 #43293607

Subgroups — C113×#25587 #43293607

Order 28928.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3505C211yesmaximal, characteristic, complemented
2C113×#2561C211yesmaximal, characteristic, complemented
3C113×#2539C211yesmaximal, characteristic, complemented
4C113×#2534C211yesmaximal, characteristic, complemented
5C113×#2022C212yesmaximal, complemented
6C113×#2021C212yesmaximal, complemented
7C113×#1996C211yesmaximal, characteristic, complemented
8C113×#1964C211yesmaximal, characteristic, complemented
9C113×#1890C212yesmaximal, complemented
10C113×#1889C212yesmaximal, complemented
11C4×#99×C113C211yesmaximal, characteristic, complemented
12#553×C113—22no—
13#553×C113—21no—
14#552×C113—21no—
15#551×C113—22no—
16#548×C113—21no—
17#546×C113—21no—
18#539×C113—21no—
19#538×C113—21no—
20#534×C113C2212yes—
21#529×C113—21no—
22#525×C113—21no—
23C2×#123×C113C2212yes—
24C2×#123×C113C2211yescharacteristic
25C2×C22⋊Q8×C113C2211yescharacteristic
26C2×#121×C113C2211yescharacteristic
27C2×#120×C113C2212yes—
28C2×#120×C113C2211yescharacteristic
29#518×C113C2212yes—
30C2×C4×D4×C113C2211yescharacteristic
31C22×C22⋊C4×C113C2211yescharacteristic
32C2×#99×C113C2212yes—
33C2×#99×C113C2212yes—
34C2×#99×C113C2212yes—
35#399×C113—21no—
36#397×C113—21no—
37#396×C113—21no—
38#394×C113—21no—
39#393×C113—21no—
40#392×C113—21no—
41#390×C113—22no—
42#388×C113—22no—
43#388×C113—21no—
44#386×C113—21no—
45#381×C113C2212yes—
46#381×C113C2211yescharacteristic
47#380×C113C2211yescharacteristic
48#379×C113C2212yes—
49#379×C113C2211yescharacteristic
50C4×C22⋊C4×C113C2211yescharacteristic
51C4×C22⋊C4×C113C2211yescharacteristic
52#342×C113C2212yes—
53#342×C113C2212yes—
54#342×C113C2212yes—
55C25×C113C2311yescharacteristic
56C2×#41×C113—21no—
57C22×Q8×C113D411yescharacteristic, complemented
58C22×D4×C113—21no—
59C22×D4×C113—22no—
60C22×D4×C113D411yescharacteristic, complemented
61C22×D4×C113C2311yescharacteristic
62C22×D4×C113C2312yes—
63C23×C4×C113D411yescharacteristic, complemented
64C23×C4×C113C2311yescharacteristic
65C23×C4×C113C2311yescharacteristic
66#126×C113—22no—
67#126×C113—22no—
68#126×C113—22no—
69#125×C113—21no—
70#125×C113—22no—
71#124×C113—21no—
72#124×C113—22no—
73#123×C113—22no—
74#123×C113—22no—
75#123×C113—22no—
76#123×C113—22no—
77#123×C113—22no—
78#123×C113—24no—
79#123×C113—42no—
80#123×C113—42no—
81C22⋊Q8×C113—21no—
82C22⋊Q8×C113—22no—
83C22⋊Q8×C113—21no—
84C22⋊Q8×C113—21no—
85C22⋊Q8×C113—21no—
86C22⋊Q8×C113—21no—
87#121×C113—21no—
88#121×C113—22no—
89#121×C113—21no—
90#121×C113—21no—
91#121×C113—21no—
92#121×C113—21no—
93#121×C113—22no—
94#121×C113—22no—
95#120×C113—22no—
96#120×C113—22no—
97#120×C113—24no—
98#120×C113—42no—
99#120×C113—42no—
100C4×Q8×C113—21no—
101C4×D4×C113—22no—
102C4×D4×C113—21no—
103C4×D4×C113—21no—
104C4×D4×C113—21no—
105C4×D4×C113—21no—
106C4×D4×C113—21no—
107C4×D4×C113—22no—
108C4×D4×C113—22no—
109C4×D4×C113—22no—
110C4×D4×C113—22no—
111#117×C113—21no—
112#117×C113—22no—
113#117×C113—22no—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113—22no—
116C2×C4⋊C4×C113—21no—
117C2×C4⋊C4×C113D411yescharacteristic, complemented
118C2×C4⋊C4×C113D411yescharacteristic, complemented
119C2×C4⋊C4×C113D412yescomplemented
120C2×C4⋊C4×C113D411yescharacteristic, complemented
121C2×C22⋊C4×C113—22no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—22no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—22no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—22no—
134C2×C22⋊C4×C113—21no—
135C2×C22⋊C4×C113—22no—
136C2×C22⋊C4×C113D411yescharacteristic, complemented
137C2×C22⋊C4×C113D412yescomplemented
138C2×C22⋊C4×C113C2311yescharacteristic
139C2×C22⋊C4×C113C2311yescharacteristic
140C2×C22⋊C4×C113C2312yes—
141C2×C22⋊C4×C113C2311yescharacteristic
142C2×C22⋊C4×C113C2312yes—
143C2×C22⋊C4×C113C2312yes—
144C2×C42×C113—21no—
145C2×C42×C113—21no—
146C2×C42×C113D411yescharacteristic, complemented
147#99×C113—24no—
148#99×C113—42no—
149#99×C113—42no—
150#95×C113—21no—
151#95×C113—21no—
152#95×C113—21no—
153#95×C113—21no—
154#95×C113—22no—
155#95×C113—21no—
156#95×C113—22no—
157C24×C113—21no—
158C24×C113—21no—
159C24×C113—21no—
160C24×C113—22no—
161C24×C113—22no—
162C24×C113—42no—
163C24×C113—81no—
164C24×C113C2×D412yes—
165C24×C113C2×D411yescharacteristic
166C24×C113C2411yescharacteristic
167#41×C113—82no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—81no—
171C2×D4×C113—21no—
172C2×D4×C113—22no—
173C2×D4×C113—21no—
174C2×D4×C113—22no—
175C2×D4×C113—22no—
176C2×D4×C113—22no—
177C2×D4×C113—22no—
178C2×D4×C113—22no—
179C2×D4×C113—22no—
180C2×D4×C113—22no—
181C2×D4×C113—22no—
182C2×D4×C113—22no—
183C2×D4×C113—21no—
184C2×D4×C113—21no—
185C2×D4×C113—44no—
186C2×D4×C113—42no—
187C2×D4×C113—44no—
188C2×D4×C113—42no—
189C2×D4×C113—81no—
190C2×D4×C113—82no—
191C2×D4×C113—81no—
192C22×C4×C113—22no—
193C22×C4×C113—22no—
194C22×C4×C113—22no—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—22no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—22no—
204C22×C4×C113—22no—
205C22×C4×C113—81no—
206C22×C4×C113—81no—
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D412yes—
209C22×C4×C113C2×D411yescharacteristic
210C22×C4×C113C2×D412yes—
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D412yes—
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2×D411yescharacteristic
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113C2×D411yescharacteristic
219C4⋊C4×C113—22no—
220C4⋊C4×C113—22no—
221C4⋊C4×C113—22no—
222C4⋊C4×C113—22no—
223C4⋊C4×C113—21no—
224C4⋊C4×C113—22no—
225C4⋊C4×C113—21no—
226C4⋊C4×C113—21no—
227C4⋊C4×C113—21no—
228C4⋊C4×C113—21no—
229C4⋊C4×C113—22no—
230C4⋊C4×C113—21no—
231C4⋊C4×C113—44no—
232C4⋊C4×C113—42no—
233C4⋊C4×C113—81no—
234C22⋊C4×C113—22no—
235C22⋊C4×C113—22no—
236C22⋊C4×C113—22no—
237C22⋊C4×C113—22no—
238C22⋊C4×C113—22no—
239C22⋊C4×C113—22no—
240C22⋊C4×C113—21no—
241C22⋊C4×C113—22no—
242C22⋊C4×C113—21no—
243C22⋊C4×C113—22no—
244C22⋊C4×C113—22no—
245C22⋊C4×C113—22no—
246C22⋊C4×C113—21no—
247C22⋊C4×C113—21no—
248C22⋊C4×C113—22no—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—22no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—44no—
254C22⋊C4×C113—44no—
255C22⋊C4×C113—42no—
256C22⋊C4×C113—44no—
257C22⋊C4×C113—42no—
258C22⋊C4×C113—42no—
259C22⋊C4×C113—41no—
260C22⋊C4×C113—41no—
261C22⋊C4×C113—41no—
262C22⋊C4×C113—41no—
263C22⋊C4×C113—81no—
264C22⋊C4×C113—82no—
265C22⋊C4×C113#4114yescomplemented
266C42×C113—22no—
267C42×C113—22no—
268C42×C113—21no—
269C42×C113—21no—
270C42×C113—81no—
271C42×C113—81no—
272C23×C113—22no—
273C23×C113—22no—
274C23×C113—22no—
275C23×C113—22no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—22no—
280C23×C113—22no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—41no—
285C23×C113—42no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—42no—
289C23×C113—41no—
290C23×C113—41no—
291C23×C113—41no—
292C23×C113—42no—
293C23×C113—42no—
294C23×C113—41no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—42no—
298C23×C113—42no—
299C23×C113—84no—
300C23×C113—84no—
301C23×C113C22×D411yescharacteristic
302C23×C113C22×D411yescharacteristic
303C23×C113C22×D411yescharacteristic
304C23×C113C2×#4112yes—
305C23×C113H(5,𝔽2)12yes—
306Q8×C113—42no—
307Q8×C113—81no—
308D4×C113—42no—
309D4×C113—42no—
310D4×C113—42no—
311D4×C113—42no—
312D4×C113—42no—
313D4×C113—42no—
314D4×C113—42no—
315D4×C113—81no—
316D4×C113—82no—
317D4×C113—82no—
318D4×C113—88no—
319D4×C113—84no—
320C2×C4×C113—21no—
321C2×C4×C113—22no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—22no—
325C2×C4×C113—22no—
326C2×C4×C113—21no—
327C2×C4×C113—21no—
328C2×C4×C113—24no—
329C2×C4×C113—22no—
330C2×C4×C113—22no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—42no—
338C2×C4×C113—42no—
339C2×C4×C113—42no—
340C2×C4×C113—41no—
341C2×C4×C113—42no—
342C2×C4×C113—41no—
343C2×C4×C113—42no—
344C2×C4×C113—42no—
345C2×C4×C113—42no—
346C2×C4×C113—41no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113—41no—
354C2×C4×C113—41no—
355C2×C4×C113—42no—
356C2×C4×C113—42no—
357C2×C4×C113—42no—
358C2×C4×C113—81no—
359C2×C4×C113—82no—
360C2×C4×C113—82no—
361C2×C4×C113#12011yescharacteristic
362C2×C4×C113#12011yescharacteristic
363C2×C4×C113#12011yescharacteristic
364C2×C4×C113#12011yescharacteristic
365C22×C113—21no—
366C22×C113—21no—
367C22×C113—21no—
368C22×C113—21no—
369C22×C113—21no—
370C22×C113—21no—
371C22×C113—42no—
372C22×C113—42no—
373C22×C113—42no—
374C22×C113—44no—
375C22×C113—42no—
376C22×C113—44no—
377C22×C113—42no—
378C22×C113—41no—
379C22×C113—42no—
380C22×C113—42no—
381C22×C113—41no—
382C22×C113—42no—
383C22×C113—41no—
384C22×C113—42no—
385C22×C113—82no—
386C22×C113—82no—
387C22×C113—81no—
388C22×C113—82no—
389C22×C113—81no—
390C22×C113—82no—
391C22×C113—81no—
392C22×C113—81no—
393C22×C113—81no—
394C22×C113C2×#12011yescharacteristic
395C22×C113#53211yescharacteristic
396C22×C113#53511yescharacteristic
397C22×C113#54612yes—
398C22×C113#55012yes—
399C4×C113—21no—
400C4×C113—21no—
401C4×C113—21no—
402C4×C113—21no—
403C4×C113—44no—
404C4×C113—41no—
405C4×C113—42no—
406C4×C113—41no—
407C4×C113—42no—
408C4×C113—41no—
409C4×C113—42no—
410C4×C113—81no—
411C4×C113—82no—
412C4×C113—81no—
413C4×C113—81no—
414#25587C11311yesmaximal, characteristic, direct product factor, Sylow
415C2×C113—22no—
416C2×C113—21no—
417C2×C113—22no—
418C2×C113—21no—
419C2×C113—82no—
420C2×C113—81no—
421C2×C113—82no—
422C2×C113#243111yescharacteristic
423C2×C113#302511yescharacteristic
424C2×C113#302611yescharacteristic
425#3505C2×C11311yescharacteristic, complemented
426#2561C2×C11311yescharacteristic, complemented
427#2539C2×C11311yescharacteristic, complemented
428#2534C2×C11311yescharacteristic, complemented
429#2022C2×C11312yescomplemented
430#2021C2×C11312yescomplemented
431#1996C2×C11311yescharacteristic, complemented
432#1964C2×C11311yescharacteristic, complemented
433#1890C2×C11312yescomplemented
434#1889C2×C11312yescomplemented
435C4×#99C2×C11311yescharacteristic, complemented
436C113#2558711yescharacteristic, direct product factor, Sylow
437#553—22no—
438#553—21no—
439#552—21no—
440#551—22no—
441#548—21no—
442#546—21no—
443#539—21no—
444#538—21no—
445#534C22×C11312yes—
446#529—21no—
447#525—21no—
448C2×#123C22×C11312yes—
449C2×#123C22×C11311yescharacteristic
450C2×C22⋊Q8C22×C11311yescharacteristic
451C2×#121C22×C11311yescharacteristic
452C2×#120C22×C11312yes—
453C2×#120C22×C11311yescharacteristic
454#518C22×C11312yes—
455C2×C4×D4C22×C11311yescharacteristic
456C22×C22⋊C4C22×C11311yescharacteristic
457C2×#99C22×C11312yes—
458C2×#99C22×C11312yes—
459C2×#99C22×C11312yes—
460#399—21no—
461#397—21no—
462#396—21no—
463#394—21no—
464#393—21no—
465#392—21no—
466#390—22no—
467#388—22no—
468#388—21no—
469#386—21no—
470#381C22×C11312yes—
471#381C22×C11311yescharacteristic
472#380C22×C11311yescharacteristic
473#379C22×C11312yes—
474#379C22×C11311yescharacteristic
475C4×C22⋊C4C22×C11311yescharacteristic
476C4×C22⋊C4C22×C11311yescharacteristic
477#342C22×C11312yes—
478#342C22×C11312yes—
479#342C22×C11312yes—
480C25C23×C11311yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C11311yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C11311yescharacteristic, complemented
486C22×D4C23×C11311yescharacteristic
487C22×D4C23×C11312yes—
488C23×C4D4×C11311yescharacteristic, complemented
489C23×C4C23×C11311yescharacteristic
490C23×C4C23×C11311yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C11311yescharacteristic, complemented
543C2×C4⋊C4D4×C11311yescharacteristic, complemented
544C2×C4⋊C4D4×C11312yescomplemented
545C2×C4⋊C4D4×C11311yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C11311yescharacteristic, complemented
562C2×C22⋊C4D4×C11312yescomplemented
563C2×C22⋊C4C23×C11311yescharacteristic
564C2×C22⋊C4C23×C11311yescharacteristic
565C2×C22⋊C4C23×C11312yes—
566C2×C22⋊C4C23×C11311yescharacteristic
567C2×C22⋊C4C23×C11312yes—
568C2×C22⋊C4C23×C11312yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C11311yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C11312yes—
590C24C2×D4×C11311yescharacteristic
591C24C24×C11311yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C11311yescharacteristic
633C22×C4C2×D4×C11312yes—
634C22×C4C2×D4×C11311yescharacteristic
635C22×C4C2×D4×C11312yes—
636C22×C4C2×D4×C11311yescharacteristic
637C22×C4C2×D4×C11312yes—
638C22×C4C2×D4×C11311yescharacteristic
639C22×C4C2×D4×C11311yescharacteristic
640C22×C4C2×D4×C11311yescharacteristic
641C22×C4C2×D4×C11311yescharacteristic
642C22×C4C2×D4×C11311yescharacteristic
643C22×C4C2×D4×C11311yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C11314yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C11311yescharacteristic
727C23C22×D4×C11311yescharacteristic
728C23C22×D4×C11311yescharacteristic
729C23C2×#41×C11312yes—
730C23H(5,𝔽2)×C11312yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C11311yescharacteristic
787C2×C4#120×C11311yescharacteristic
788C2×C4#120×C11311yescharacteristic
789C2×C4#120×C11311yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C11311yescharacteristic
820C22#532×C11311yescharacteristic
821C22#535×C11311yescharacteristic
822C22#546×C11312yes—
823C22#550×C11312yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C113×#243111yescharacteristic
847C2C113×#302511yescharacteristic
848C2C113×#302611yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3505C2semidirect
2. C113×#2561C2semidirect
3. C113×#2539C2semidirect
4. C113×#2534C2semidirect
5. C113×#2022C2semidirect
6. C113×#2021C2semidirect
7. C113×#1996C2semidirect
8. C113×#1964C2semidirect
9. C113×#1890C2semidirect
10. C113×#1889C2semidirect
11. C4×#99×C113C2semidirect
57. C22×Q8×C113D4semidirect
60. C22×D4×C113D4semidirect
63. C23×C4×C113D4semidirect
117. C2×C4⋊C4×C113D4semidirect
118. C2×C4⋊C4×C113D4semidirect
119. C2×C4⋊C4×C113D4semidirect
120. C2×C4⋊C4×C113D4semidirect
136. C2×C22⋊C4×C113D4semidirect
137. C2×C22⋊C4×C113D4semidirect
146. C2×C42×C113D4semidirect
265. C22⋊C4×C113#41semidirect
414. #25587C113direct (N × H)
425. #3505C2×C113semidirect
426. #2561C2×C113semidirect
427. #2539C2×C113semidirect
428. #2534C2×C113semidirect
429. #2022C2×C113semidirect
430. #2021C2×C113semidirect
431. #1996C2×C113semidirect
432. #1964C2×C113semidirect
433. #1890C2×C113semidirect
434. #1889C2×C113semidirect
435. C4×#99C2×C113semidirect
436. C113#25587direct (N × H)
482. C22×Q8D4×C113semidirect
485. C22×D4D4×C113semidirect
488. C23×C4D4×C113semidirect
542. C2×C4⋊C4D4×C113semidirect
543. C2×C4⋊C4D4×C113semidirect
544. C2×C4⋊C4D4×C113semidirect
545. C2×C4⋊C4D4×C113semidirect
561. C2×C22⋊C4D4×C113semidirect
562. C2×C22⋊C4D4×C113semidirect
571. C2×C42D4×C113semidirect
690. C22⋊C4#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35052
C113×#25612
C113×#25392
C113×#25342
C113×#20222
C113×#20212
C113×#19962
C113×#19642
C113×#18902
C113×#18892
C4×#99×C1132
#25587113