Finite Group Databasebeta

← #14685188

Subgroups — #14685188

Order 2816.

2494 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3C2×#10622842C211yesmaximal, characteristic, complemented
4C2×#10622602C212yesmaximal
5#13066880C212yesmaximal, complemented
6#13066879C212yesmaximal, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066869C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C212yesmaximal
10(C2×D11)⋊#95C211yesmaximal, characteristic
11C2×C11×#395C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66999—24no—
19C2×#66999—28no—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C2×C4⋊C4×D11—24no—
29C2×C4⋊C4×D11—24no—
30C2×C4⋊C4×D11—24no—
31C11×#395—24no—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2212yes—
34#10622842—24no—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622602—28no—
43C24×D11C2311yescharacteristic
44C22×Q8×C11—24no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—42no—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—24no—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—24no—
72C22×C4×D11—42no—
73C22×C4×D11—42no—
74C22×C4×D11D414yes—
75C22×C4×D11Q814yescomplemented
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—42no—
81C2×C11×C4⋊C4D414yes—
82#66999—232no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4D418yes—
88C2×(C2×D11)⋊C4Q818yescomplemented
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—24no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4—42no—
105C2×Dic11⋊C4D414yes—
106C4⋊C4×D11—232no—
107C11×#95—22no—
108C11×#95—24no—
109C11⋊#95—22no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—42no—
116#14720—111nomaximal, Sylow
117C24×C11C2411yescharacteristic
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11C2×D414yes—
125C23×D11C2×D412yes—
126C23×D11C2×Q814yes—
127C23×D11C2×Q812yes—
128C23×D11#4112yes—
129C2×Q8×C11—28no—
130C2×Q8×C11—48no—
131C2×Q8×C11—48no—
132C2×Q8×C11—44no—
133C2×Q8×C11—44no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×Q814yes—
163C22×C4×C11C2×Q812yes—
164C22×C4×C11#4112yes—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11C2×D414yes—
190C22×Dic11C2×D412yes—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×Q814yes—
194C22×Dic11C2×Q812yes—
195C22×Dic11#4112yes—
196C2×C4×D11—28no—
197C2×C4×D11—28no—
198C2×C4×D11—28no—
199C2×C4×D11—28no—
200C2×C4×D11—28no—
201C2×C4×D11—28no—
202C2×C4×D11—28no—
203C2×C4×D11—28no—
204C2×C4×D11—28no—
205C2×C4×D11—28no—
206C2×C4×D11—44no—
207C2×C4×D11—48no—
208C2×C4×D11—48no—
209C2×C4×D11—48no—
210C2×C4×D11—48no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C11×C4⋊C4—28no—
214C11×C4⋊C4—48no—
215(C2×D11)⋊C4—216no—
216(C2×D11)⋊C4—216no—
217C4⋊Dic11—28no—
218C4⋊Dic11—28no—
219Dic11⋊C4—28no—
220Dic11⋊C4—216no—
221Dic11⋊C4—28no—
222Dic11⋊C4—48no—
223C22×C22⋊Q8—111no—
224C23×C4⋊C4—111no—
225C2×#395—111no—
226C2×#395D1111yescharacteristic, complemented
227C2×#385—112no—
228#1444—112no—
229#1444—112no—
230#1441—111no—
231#1441—111no—
232C22⋊#95—112no—
233C22⋊#95—111no—
234C23×C11C22×D411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C23×C11C22×D412yes—
237C23×C11C22×D411yescharacteristic
238C23×C11C22×Q811yescharacteristic
239C23×C11C22×Q812yes—
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4111yescharacteristic
242C23×C11C2×#4111yescharacteristic
243C23×C11H(5,𝔽2)12yes—
244C23×C112−1+412yes—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11#12014yes—
264C22×D11C22⋊Q818yes—
265C22×D11C22⋊Q814yes—
266C22×D11C4⋊Q814yes—
267C22×D11C4⋊Q818yes—
268Q8×C11—416no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—41no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11#12014yes—
299C2×C4×C11C22⋊Q814yescomplemented
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—41no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—41no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11C22⋊Q814yescomplemented
331C4×D11—232no—
332C4×D11—416no—
333C4×D11—416no—
334C23×Q8C2×D1111yescharacteristic
335C24×C4—111no—
336C24×C4—111no—
337C24×C4—111no—
338C2×C22⋊Q8—228no—
339C2×C22⋊Q8—224no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4—112no—
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—112no—
346C22×C4⋊C4—224no—
347C22×C4⋊C4—224no—
348C22×C4⋊C4—224no—
349C22×C4⋊C4C2×D1112yes—
350C22×C4⋊C4C2×D1111yescharacteristic
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353#395—24no—
354#395—224no—
355#385—228no—
356C2×#95—111no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95C2×D1111yescharacteristic
364C2×#95C2×D1112yes—
365C22×C11C2×#12011yescharacteristic
366C22×C11C2×#12011yescharacteristic
367C22×C11C2×C22⋊Q811yescharacteristic
368C22×C11C2×C22⋊Q811yescharacteristic
369C22×C11C2×C22⋊Q811yescharacteristic
370C22×C11C2×C22⋊Q812yes—
371C22×C11#52511yescharacteristic
372C22×C11#52511yescharacteristic
373C22×C11#52511yescharacteristic
374C22×C11C2×C4⋊Q811yescharacteristic
375C22×C11C2×C4⋊Q812yes—
376C22×C11#53411yescharacteristic
377C22×C11#53611yescharacteristic
378C22×C11#53912yes—
379C22×C11#54412yes—
380C22×C11D4212yes—
381C22×C11D4212yes—
382C22×C11#54712yes—
383C22×C11#54712yes—
384C22×C11D4×Q812yes—
385C22×C11D4×Q812yes—
386C22×C11#55412yes—
387C22×C11#55412yes—
388C2×D11—24no—
389C2×D11—24no—
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—24no—
393C2×D11—24no—
394C2×D11—28no—
395C2×D11—28no—
396C2×D11—28no—
397C2×D11—28no—
398C2×D11#39518yescomplemented
399C4×C11—24no—
400C4×C11—24no—
401C4×C11—44no—
402C4×C11—42no—
403C4×C11—44no—
404Dic11—24no—
405Dic11—42no—
406Dic11—42no—
407Dic11—44no—
408Dic11—44no—
409C25—111no—
410C22×Q8—24no—
411C22×Q8—22no—
412C22×Q8—22no—
413C22×Q8—22no—
414C22×Q8—42no—
415C23×C4—111no—
416C23×C4—112no—
417C23×C4—112no—
418C23×C4—111no—
419C23×C4—111no—
420C23×C4—114no—
421C23×C4—114no—
422C23×C4—222no—
423C23×C4—222no—
424C23×C4—222no—
425C23×C4—222no—
426C23×C4—222no—
427C23×C4—222no—
428C23×C4—224no—
429C23×C4—224no—
430C23×C4—222no—
431C23×C4—222no—
432C23×C4—222no—
433C23×C4—222no—
434C23×C4—222no—
435C23×C4—442no—
436C23×C4—442no—
437C23×C4C22×D1112yes—
438C23×C4C22×D1112yes—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C22⋊Q8—2232no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—2232no—
450C2×C4⋊C4—222no—
451C2×C4⋊C4—222no—
452C2×C4⋊C4—222no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—224no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—222no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4—224no—
465C2×C4⋊C4—442no—
466C2×C4⋊C4C22⋊D1114yes—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—118no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473#95—22no—
474#95—24no—
475#95—224no—
476#95—224no—
477#95—224no—
478#95—224no—
479#95—222no—
480#95—224no—
481#95—442no—
482C2×C11C2×#39511yescharacteristic
483C2×C11#240311yescharacteristic
484C2×C11#240611yescharacteristic
485C2×C11#243411yescharacteristic
486C2×C11#244012yes—
487C2×C11#244012yes—
488C2×C11#244912yes—
489C2×C11#244912yes—
490C2×C11#258311yescharacteristic
491C2×C11#262711yescharacteristic
492C2×C11#284811yescharacteristic
493D11—28no—
494C24—114no—
495C24—112no—
496C24—114no—
497C24—112no—
498C24—112no—
499C24—221no—
500C24—222no—
501C24—221no—
502C24—222no—
503C24—221no—
504C24—221no—
505C24C23×D1111yescharacteristic
506C2×Q8—28no—
507C2×Q8—48no—
508C2×Q8—48no—
509C2×Q8—44no—
510C2×Q8—44no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—114no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—114no—
540C22×C4—228no—
541C22×C4—228no—
542C22×C4—228no—
543C22×C4—228no—
544C22×C4—228no—
545C22×C4—228no—
546C22×C4—228no—
547C22×C4—228no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—228no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—228no—
574C22×C4—444no—
575C22×C4—448no—
576C22×C4—448no—
577C22×C4—448no—
578C22×C4—448no—
579C22×C4—444no—
580C22×C4—444no—
581C22×C4D4×D1114yes—
582C22×C4D4×D1112yes—
583C22×C4D4×D1112yes—
584C22×C4Q8×D1114yes—
585C22×C4Q8×D1112yes—
586C22×C4#434312yes—
587C22×C4C2×C22⋊D1112yes—
588C22×C4C2×C22⋊D1112yes—
589C22×C4C2×C22⋊D1112yes—
590C4⋊C4—28no—
591C4⋊C4—48no—
592C4⋊C4—228no—
593C4⋊C4—228no—
594C4⋊C4—2216no—
595C4⋊C4—228no—
596C4⋊C4—228no—
597C4⋊C4—448no—
598C22⋊C4—2216no—
599C22⋊C4—2216no—
600C11#1472011yescharacteristic, complemented, Sylow
601C23—114no—
602C23—118no—
603C23—114no—
604C23—118no—
605C23—114no—
606C23—222no—
607C23—224no—
608C23—224no—
609C23—224no—
610C23—224no—
611C23—222no—
612C23—224no—
613C23—222no—
614C23—224no—
615C23—222no—
616C23—222no—
617C23—224no—
618C23—222no—
619C23—222no—
620C23—222no—
621C23—224no—
622C23—224no—
623C23—224no—
624C23C2×D4×D1111yescharacteristic
625C23C2×D4×D1112yes—
626C23C2×D4×D1111yescharacteristic
627C23#6703712yes—
628C23C2×Q8×D1112yes—
629C23C2×Q8×D1111yescharacteristic
630C23C2×#434311yescharacteristic
631C23#6704012yes—
632C23#41×D1111yescharacteristic
633C23#41×D1111yescharacteristic
634C23C22×C22⋊D1111yescharacteristic
635Q8—416no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—114no—
666C2×C4—2232no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—224no—
674C2×C4—224no—
675C2×C4—224no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—224no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—224no—
682C2×C4—224no—
683C2×C4—224no—
684C2×C4—4416no—
685C2×C4—4416no—
686C2×C4—442no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4#6699014yes—
700C2×C4#6699914yescomplemented
701C22—118no—
702C22—228no—
703C22—228no—
704C22—224no—
705C22—224no—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—228no—
710C22—228no—
711C22—224no—
712C22D11×#12011yescharacteristic
713C22#1062312011yescharacteristic
714C22#1062312112yes—
715C22D11×C22⋊Q812yes—
716C22D11×C22⋊Q811yescharacteristic
717C22D11×C22⋊Q811yescharacteristic
718C22#1062315811yescharacteristic
719C22#1062315811yescharacteristic
720C22#1062316212yes—
721C22#1062316712yes—
722C22#1062316912yes—
723C22D11×C4⋊Q811yescharacteristic
724C22D11×C4⋊Q812yes—
725C22#1062325511yescharacteristic
726C22#1062325712yes—
727C22#1062325812yes—
728C22#1062326012yes—
729C22#1062326112yes—
730C22C2×#6699011yescharacteristic
731C22D4×C22⋊D1112yes—
732C22C2×#6699911yescharacteristic
733C22Q8×C22⋊D1112yes—
734C22#1062335911yescharacteristic
735C4—24no—
736C4—24no—
737C4—44no—
738C4—42no—
739C4—44no—
740C4—224no—
741C4—444no—
742C4—442no—
743C4—442no—
744C4—444no—
745C2—228no—
746C2D11×#39511yescharacteristic
747C2#1307192711yescharacteristic
748C2#1307195211yescharacteristic
749C2#1307225711yescharacteristic
750C2#1307231112yes—
751C2#1307231412yes—
752C2#1307241812yes—
753C2#1307242212yes—
754C2#1307399211yescharacteristic
755C2#1307442811yescharacteristic
756C2#1307690011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#395C2
prime radicalC24×D11C23
hypercenterC2×#395D11
hypocenterC11#14720
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. C2×#10622842C2semidirect
5. #13066880C2semidirect
6. #13066879C2semidirect
7. #13066870C2semidirect
8. #13066869C2semidirect
11. C2×C11×#395C2semidirect
75. C22×C4×D11Q8semidirect
88. C2×(C2×D11)⋊C4Q8semidirect
226. C2×#395D11semidirect
299. C2×C4×C11C22⋊Q8semidirect
330. C2×Dic11C22⋊Q8semidirect
398. C2×D11#395semidirect
600. C11#14720semidirect
700. C2×C4#66999semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
C22×C4⋊C4×D112
C2×#106228422
C2×#106226022
#130668802
#130668792
#130668702
#130668692
(C2×D11)⋊#952
C2×C11×#3952
#1472011