Finite Group Databasebeta

← C113×#15215 #43283235

Subgroups — C113×#15215 #43283235

Order 28928.

2878 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C113C211yesmaximal, characteristic, complemented
2C22×C22⋊Q8×C113C211yesmaximal, characteristic, complemented
3C22×#121×C113C211yesmaximal, characteristic
4C2×#391×C113C211yesmaximal, characteristic, complemented
5C2×#390×C113C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
7C113×#1439C214yesmaximal, complemented
8C113×#1438C214yesmaximal, complemented
9C113×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×Q8×C113C2211yescharacteristic
11C23×D4×C113C2211yescharacteristic
12C23×D4×C113C2212yes—
13C24×C4×C113C2211yescharacteristic
14C2×#124×C113—24no—
15C2×#124×C113—24no—
16C2×#124×C113—24no—
17C2×C22⋊Q8×C113—24no—
18C2×C22⋊Q8×C113—24no—
19C2×C22⋊Q8×C113—24no—
20C2×#121×C113—24no—
21C2×#121×C113—24no—
22C2×#121×C113—24no—
23C22×C4⋊C4×C113C2212yes—
24C22×C4⋊C4×C113C2211yescharacteristic
25C22×C4⋊C4×C113C2211yescharacteristic
26C22×C22⋊C4×C113C2212yes—
27C22×C22⋊C4×C113C2212yes—
28C22×C22⋊C4×C113C2214yes—
29C22×C22⋊C4×C113C2212yes—
30C22×C22⋊C4×C113C2214yes—
31C22×C42×C113C2211yescharacteristic
32C22×C42×C113C2211yescharacteristic
33#391×C113—24no—
34#390×C113—24no—
35C4×C22⋊C4×C113—24no—
36C2×#95×C113C2214yes—
37C2×#95×C113C2212yes—
38C2×#95×C113C2214yes—
39C25×C113C2312yes—
40C25×C113C2311yescharacteristic
41C22×Q8×C113—22no—
42C22×Q8×C113—22no—
43C22×Q8×C113—22no—
44C22×Q8×C113—22no—
45C22×Q8×C113—22no—
46C22×Q8×C113—22no—
47C22×Q8×C113D414yescomplemented
48C22×D4×C113—24no—
49C22×D4×C113—24no—
50C22×D4×C113—28no—
51C22×D4×C113—24no—
52C22×D4×C113—22no—
53C22×D4×C113—22no—
54C22×D4×C113—22no—
55C22×D4×C113—22no—
56C22×D4×C113—22no—
57C22×D4×C113—22no—
58C22×D4×C113—44no—
59C22×D4×C113D414yes—
60C23×C4×C113—22no—
61C23×C4×C113—22no—
62C23×C4×C113—22no—
63C23×C4×C113—22no—
64C23×C4×C113—22no—
65C23×C4×C113—22no—
66C23×C4×C113D414yes—
67C23×C4×C113C2312yes—
68C23×C4×C113C2312yes—
69C23×C4×C113C2312yes—
70C23×C4×C113C2311yescharacteristic
71C23×C4×C113C2312yes—
72C23×C4×C113C2312yes—
73C23×C4×C113C2311yescharacteristic
74#124×C113—232no—
75C22⋊Q8×C113—232no—
76#121×C113—232no—
77C2×C4⋊C4×C113—22no—
78C2×C4⋊C4×C113—22no—
79C2×C4⋊C4×C113—24no—
80C2×C4⋊C4×C113—24no—
81C2×C4⋊C4×C113—24no—
82C2×C4⋊C4×C113—22no—
83C2×C4⋊C4×C113—22no—
84C2×C4⋊C4×C113D414yes—
85C2×C4⋊C4×C113D414yescomplemented
86C2×C22⋊C4×C113—24no—
87C2×C22⋊C4×C113—24no—
88C2×C22⋊C4×C113—28no—
89C2×C22⋊C4×C113—24no—
90C2×C22⋊C4×C113—24no—
91C2×C22⋊C4×C113—24no—
92C2×C22⋊C4×C113—24no—
93C2×C22⋊C4×C113—24no—
94C2×C22⋊C4×C113—28no—
95C2×C22⋊C4×C113—28no—
96C2×C22⋊C4×C113—24no—
97C2×C22⋊C4×C113—24no—
98C2×C22⋊C4×C113—28no—
99C2×C22⋊C4×C113—28no—
100C2×C22⋊C4×C113—44no—
101C2×C42×C113—22no—
102C2×C42×C113—22no—
103C2×C42×C113—22no—
104C2×C42×C113—22no—
105C2×C42×C113—22no—
106C2×C42×C113D414yescomplemented
107#95×C113—24no—
108#95×C113—28no—
109#95×C113—44no—
110C24×C113—21no—
111C24×C113—21no—
112C24×C113—21no—
113C24×C113—21no—
114C24×C113—21no—
115C24×C113—22no—
116C24×C113—21no—
117C24×C113—22no—
118C24×C113—22no—
119C24×C113—22no—
120C24×C113—22no—
121C24×C113—22no—
122C24×C113—22no—
123C24×C113—22no—
124C24×C113—24no—
125C24×C113—22no—
126C24×C113—24no—
127C24×C113—24no—
128C24×C113—24no—
129C24×C113C2×D414yes—
130C24×C113C2×D412yes—
131C24×C113#4114yes—
132C24×C113C2411yescharacteristic
133C2×Q8×C113—28no—
134C2×Q8×C113—28no—
135C2×Q8×C113—28no—
136C2×Q8×C113—44no—
137C2×Q8×C113—44no—
138C2×Q8×C113—44no—
139C2×Q8×C113—44no—
140C2×D4×C113—216no—
141C2×D4×C113—28no—
142C2×D4×C113—28no—
143C2×D4×C113—28no—
144C2×D4×C113—416no—
145C2×D4×C113—416no—
146C2×D4×C113—48no—
147C2×D4×C113—48no—
148C2×D4×C113—44no—
149C2×D4×C113—44no—
150C2×D4×C113—44no—
151C2×D4×C113—44no—
152C22×C4×C113—22no—
153C22×C4×C113—21no—
154C22×C4×C113—22no—
155C22×C4×C113—22no—
156C22×C4×C113—22no—
157C22×C4×C113—22no—
158C22×C4×C113—22no—
159C22×C4×C113—21no—
160C22×C4×C113—21no—
161C22×C4×C113—22no—
162C22×C4×C113—22no—
163C22×C4×C113—22no—
164C22×C4×C113—22no—
165C22×C4×C113—22no—
166C22×C4×C113—22no—
167C22×C4×C113—22no—
168C22×C4×C113—22no—
169C22×C4×C113—21no—
170C22×C4×C113—21no—
171C22×C4×C113—22no—
172C22×C4×C113—22no—
173C22×C4×C113—22no—
174C22×C4×C113—24no—
175C22×C4×C113—21no—
176C22×C4×C113—24no—
177C22×C4×C113—22no—
178C22×C4×C113—22no—
179C22×C4×C113—24no—
180C22×C4×C113—24no—
181C22×C4×C113—22no—
182C22×C4×C113—22no—
183C22×C4×C113—22no—
184C22×C4×C113—28no—
185C22×C4×C113—28no—
186C22×C4×C113—28no—
187C22×C4×C113—44no—
188C22×C4×C113—44no—
189C22×C4×C113—44no—
190C22×C4×C113—44no—
191C22×C4×C113C2×D414yes—
192C22×C4×C113C2×D414yes—
193C22×C4×C113C2×D414yes—
194C22×C4×C113C2×D414yes—
195C22×C4×C113C2×D412yes—
196C22×C4×C113C2×D412yes—
197C22×C4×C113C2×D412yes—
198C22×C4×C113C2×D412yes—
199C22×C4×C113C2×D412yes—
200C22×C4×C113C2×D412yes—
201C22×C4×C113C2×D412yes—
202C22×C4×C113#4114yes—
203C22×C4×C113#4112yes—
204C4⋊C4×C113—216no—
205C4⋊C4×C113—28no—
206C4⋊C4×C113—28no—
207C22⋊C4×C113—216no—
208C22⋊C4×C113—216no—
209C22⋊C4×C113—216no—
210C22⋊C4×C113—232no—
211C22⋊C4×C113—416no—
212C42×C113—28no—
213C42×C113—44no—
214C23×C113—22no—
215C23×C113—22no—
216C23×C113—22no—
217C23×C113—24no—
218C23×C113—24no—
219C23×C113—22no—
220C23×C113—22no—
221C23×C113—22no—
222C23×C113—24no—
223C23×C113—24no—
224C23×C113—24no—
225C23×C113—24no—
226C23×C113—24no—
227C23×C113—24no—
228C23×C113—24no—
229C23×C113—28no—
230C23×C113—28no—
231C23×C113—41no—
232C23×C113—41no—
233C23×C113—41no—
234C23×C113—41no—
235C23×C113—42no—
236C23×C113—42no—
237C23×C113—42no—
238C23×C113—42no—
239C23×C113—42no—
240C23×C113—42no—
241C23×C113—42no—
242C23×C113—42no—
243C23×C113—42no—
244C23×C113—44no—
245C23×C113—42no—
246C23×C113—44no—
247C23×C113—42no—
248C23×C113—42no—
249C23×C113—42no—
250C23×C113—42no—
251C23×C113—44no—
252C23×C113—44no—
253C23×C113—44no—
254C23×C113—44no—
255C23×C113—44no—
256C23×C113—44no—
257C23×C113—44no—
258C23×C113—44no—
259C23×C113#12414yescomplemented
260C23×C113C22×D411yescharacteristic
261C23×C113C22×D411yescharacteristic
262C23×C113C22×D411yescharacteristic
263C23×C113C22×D411yescharacteristic
264C23×C113C22×D411yescharacteristic
265C23×C113C22×D411yescharacteristic
266C23×C113C2×#4111yescharacteristic
267C23×C113C2×#4112yes—
268C23×C113C2×#4112yes—
269C23×C113H(5,𝔽2)12yes—
270C23×C1132−1+412yes—
271Q8×C113—416no—
272D4×C113—432no—
273D4×C113—416no—
274C2×C4×C113—24no—
275C2×C4×C113—22no—
276C2×C4×C113—24no—
277C2×C4×C113—24no—
278C2×C4×C113—24no—
279C2×C4×C113—24no—
280C2×C4×C113—22no—
281C2×C4×C113—22no—
282C2×C4×C113—24no—
283C2×C4×C113—24no—
284C2×C4×C113—24no—
285C2×C4×C113—24no—
286C2×C4×C113—24no—
287C2×C4×C113—28no—
288C2×C4×C113—28no—
289C2×C4×C113—24no—
290C2×C4×C113—41no—
291C2×C4×C113—42no—
292C2×C4×C113—41no—
293C2×C4×C113—41no—
294C2×C4×C113—42no—
295C2×C4×C113—42no—
296C2×C4×C113—42no—
297C2×C4×C113—42no—
298C2×C4×C113—41no—
299C2×C4×C113—42no—
300C2×C4×C113—42no—
301C2×C4×C113—42no—
302C2×C4×C113—42no—
303C2×C4×C113—42no—
304C2×C4×C113—42no—
305C2×C4×C113—42no—
306C2×C4×C113—44no—
307C2×C4×C113—42no—
308C2×C4×C113—42no—
309C2×C4×C113—42no—
310C2×C4×C113—42no—
311C2×C4×C113—44no—
312C2×C4×C113—416no—
313C2×C4×C113#12014yes—
314C2×C4×C113#12014yes—
315C2×C4×C113#12014yes—
316C2×C4×C113#12114yes—
317C2×C4×C113#12114yes—
318C2×C4×C113#12114yes—
319C2×C4×C113#12714yes—
320C22×C113—24no—
321C22×C113—24no—
322C22×C113—24no—
323C22×C113—42no—
324C22×C113—42no—
325C22×C113—44no—
326C22×C113—44no—
327C22×C113—44no—
328C22×C113—42no—
329C22×C113—42no—
330C22×C113—44no—
331C22×C113—44no—
332C22×C113—48no—
333C22×C113—48no—
334C22×C113—44no—
335C22×C113—44no—
336C22×C113—82no—
337C22×C113—82no—
338C22×C113—84no—
339C22×C113—82no—
340C22×C113—82no—
341C22×C113—84no—
342C22×C113C2×#12011yescharacteristic
343C22×C113C2×#12011yescharacteristic
344C22×C113C2×#12011yescharacteristic
345C22×C113C2×#12111yescharacteristic
346C22×C113C2×#12111yescharacteristic
347C22×C113C2×#12111yescharacteristic
348C22×C113#52512yes—
349C22×C113C2×#12411yescharacteristic
350C22×C113#52912yes—
351C22×C113C2×#12711yescharacteristic
352C22×C113#53211yescharacteristic
353C22×C113#53511yescharacteristic
354C22×C113#53611yescharacteristic
355C22×C113#53712yes—
356C22×C113#54212yes—
357C22×C113#54612yes—
358C22×C113#54612yes—
359C22×C113#54612yes—
360C22×C113#54712yes—
361C22×C113#54812yes—
362C22×C113#54812yes—
363C22×C113#54812yes—
364C22×C113#55012yes—
365C4×C113—42no—
366C4×C113—44no—
367C4×C113—44no—
368C4×C113—44no—
369C4×C113—44no—
370C4×C113—44no—
371C4×C113#39218yes—
372#15215C11311yesmaximal, characteristic, direct product factor, Sylow
373C2×C113—44no—
374C2×C113—84no—
375C2×C113C2×#39211yescharacteristic
376C2×C113#240712yes—
377C2×C113#242612yes—
378C2×C113#242712yes—
379C2×C113#243111yescharacteristic
380C2×C113#243211yescharacteristic
381C2×C113#243511yescharacteristic
382C2×C113#243611yescharacteristic
383C2×C113#254012yes—
384C2×C113#262011yescharacteristic
385C2×C113#285011yescharacteristic
386C22×#124C2×C11311yescharacteristic, complemented
387C22×C22⋊Q8C2×C11311yescharacteristic, complemented
388C22×#121C2×C11311yescharacteristic
389C2×#391C2×C11311yescharacteristic, complemented
390C2×#390C2×C11311yescharacteristic, complemented
391C2×C4×C22⋊C4C2×C11311yescharacteristic, complemented
392#1439C2×C11314yescomplemented
393#1438C2×C11314yescomplemented
394C4⋊#95C2×C11311yescharacteristic, complemented
395C113#1521511yescharacteristic, direct product factor, Sylow
396C23×Q8C22×C11311yescharacteristic
397C23×D4C22×C11311yescharacteristic
398C23×D4C22×C11312yes—
399C24×C4C22×C11311yescharacteristic
400C2×#124—24no—
401C2×#124—24no—
402C2×#124—24no—
403C2×C22⋊Q8—24no—
404C2×C22⋊Q8—24no—
405C2×C22⋊Q8—24no—
406C2×#121—24no—
407C2×#121—24no—
408C2×#121—24no—
409C22×C4⋊C4C22×C11312yes—
410C22×C4⋊C4C22×C11311yescharacteristic
411C22×C4⋊C4C22×C11311yescharacteristic
412C22×C22⋊C4C22×C11312yes—
413C22×C22⋊C4C22×C11312yes—
414C22×C22⋊C4C22×C11314yes—
415C22×C22⋊C4C22×C11312yes—
416C22×C22⋊C4C22×C11314yes—
417C22×C42C22×C11311yescharacteristic
418C22×C42C22×C11311yescharacteristic
419#391—24no—
420#390—24no—
421C4×C22⋊C4—24no—
422C2×#95C22×C11314yes—
423C2×#95C22×C11312yes—
424C2×#95C22×C11314yes—
425C25C23×C11312yes—
426C25C23×C11311yescharacteristic
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8D4×C11314yescomplemented
434C22×D4—24no—
435C22×D4—24no—
436C22×D4—28no—
437C22×D4—24no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—44no—
445C22×D4D4×C11314yes—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4D4×C11314yes—
453C23×C4C23×C11312yes—
454C23×C4C23×C11312yes—
455C23×C4C23×C11312yes—
456C23×C4C23×C11311yescharacteristic
457C23×C4C23×C11312yes—
458C23×C4C23×C11312yes—
459C23×C4C23×C11311yescharacteristic
460#124—232no—
461C22⋊Q8—232no—
462#121—232no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4D4×C11314yes—
471C2×C4⋊C4D4×C11314yescomplemented
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—28no—
481C2×C22⋊C4—28no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—44no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42D4×C11314yescomplemented
493#95—24no—
494#95—28no—
495#95—44no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—24no—
511C24—22no—
512C24—24no—
513C24—24no—
514C24—24no—
515C24C2×D4×C11314yes—
516C24C2×D4×C11312yes—
517C24#41×C11314yes—
518C24C24×C11311yescharacteristic
519C2×Q8—28no—
520C2×Q8—28no—
521C2×Q8—28no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×D4—216no—
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—416no—
531C2×D4—416no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4C2×D4×C11314yes—
578C22×C4C2×D4×C11314yes—
579C22×C4C2×D4×C11314yes—
580C22×C4C2×D4×C11314yes—
581C22×C4C2×D4×C11312yes—
582C22×C4C2×D4×C11312yes—
583C22×C4C2×D4×C11312yes—
584C22×C4C2×D4×C11312yes—
585C22×C4C2×D4×C11312yes—
586C22×C4C2×D4×C11312yes—
587C22×C4C2×D4×C11312yes—
588C22×C4#41×C11314yes—
589C22×C4#41×C11312yes—
590C4⋊C4—216no—
591C4⋊C4—28no—
592C4⋊C4—28no—
593C22⋊C4—216no—
594C22⋊C4—216no—
595C22⋊C4—232no—
596C22⋊C4—216no—
597C22⋊C4—416no—
598C42—28no—
599C42—44no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—28no—
616C23—28no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—44no—
631C23—42no—
632C23—44no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23#124×C11314yescomplemented
646C23C22×D4×C11311yescharacteristic
647C23C22×D4×C11311yescharacteristic
648C23C22×D4×C11311yescharacteristic
649C23C22×D4×C11311yescharacteristic
650C23C22×D4×C11311yescharacteristic
651C23C22×D4×C11311yescharacteristic
652C23C2×#41×C11311yescharacteristic
653C23C2×#41×C11312yes—
654C23C2×#41×C11312yes—
655C23H(5,𝔽2)×C11312yes—
656C232−1+4×C11312yes—
657Q8—416no—
658D4—432no—
659D4—416no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—416no—
699C2×C4#120×C11314yes—
700C2×C4#120×C11314yes—
701C2×C4#120×C11314yes—
702C2×C4#121×C11314yes—
703C2×C4#121×C11314yes—
704C2×C4#121×C11314yes—
705C2×C4#127×C11314yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—42no—
716C22—42no—
717C22—44no—
718C22—48no—
719C22—48no—
720C22—44no—
721C22—44no—
722C22—84no—
723C22—82no—
724C22—82no—
725C22—84no—
726C22—82no—
727C22—82no—
728C22C2×#120×C11311yescharacteristic
729C22C2×#120×C11311yescharacteristic
730C22C2×#120×C11311yescharacteristic
731C22C2×#121×C11311yescharacteristic
732C22C2×#121×C11311yescharacteristic
733C22C2×#121×C11311yescharacteristic
734C22#525×C11312yes—
735C22C2×#124×C11311yescharacteristic
736C22#529×C11312yes—
737C22C2×#127×C11311yescharacteristic
738C22#532×C11311yescharacteristic
739C22#535×C11311yescharacteristic
740C22#536×C11311yescharacteristic
741C22#537×C11312yes—
742C22#542×C11312yes—
743C22#546×C11312yes—
744C22#546×C11312yes—
745C22#546×C11312yes—
746C22#547×C11312yes—
747C22#548×C11312yes—
748C22#548×C11312yes—
749C22#548×C11312yes—
750C22#550×C11312yes—
751C4—44no—
752C4—42no—
753C4—44no—
754C4—44no—
755C4—44no—
756C4—44no—
757C4#392×C11318yes—
758C2—44no—
759C2—84no—
760C2C2×#392×C11311yescharacteristic
761C2C113×#240712yes—
762C2C113×#242612yes—
763C2C113×#242712yes—
764C2C113×#243111yescharacteristic
765C2C113×#243211yescharacteristic
766C2C113×#243511yescharacteristic
767C2C113×#243611yescharacteristic
768C2C113×#254012yes—
769C2C113×#262011yescharacteristic
770C2C113×#285011yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutator, Frattini, cosocleC24C24×C113
prime radicalC22×#121×C113C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#124×C113C2semidirect
2. C22×C22⋊Q8×C113C2semidirect
4. C2×#391×C113C2semidirect
5. C2×#390×C113C2semidirect
6. C2×C4×C22⋊C4×C113C2semidirect
7. C113×#1439C2semidirect
8. C113×#1438C2semidirect
9. C113×C4⋊#95C2semidirect
47. C22×Q8×C113D4semidirect
85. C2×C4⋊C4×C113D4semidirect
106. C2×C42×C113D4semidirect
259. C23×C113#124semidirect
372. #15215C113direct (N × H)
386. C22×#124C2×C113semidirect
387. C22×C22⋊Q8C2×C113semidirect
389. C2×#391C2×C113semidirect
390. C2×#390C2×C113semidirect
391. C2×C4×C22⋊C4C2×C113semidirect
392. #1439C2×C113semidirect
393. #1438C2×C113semidirect
394. C4⋊#95C2×C113semidirect
395. C113#15215direct (N × H)
433. C22×Q8D4×C113semidirect
471. C2×C4⋊C4D4×C113semidirect
492. C2×C42D4×C113semidirect
645. C23#124×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1132
C22×C22⋊Q8×C1132
C22×#121×C1132
C2×#391×C1132
C2×#390×C1132
C2×C4×C22⋊C4×C1132
C113×#14392
C113×#14382
C113×C4⋊#952
#15215113