Finite Group Databasebeta

← #14685223

Subgroups — #14685223

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622842C211yesmaximal, characteristic, complemented
3C2×#10622844C211yesmaximal, characteristic, complemented
4C2×#10622602C212yesmaximal, complemented
5#13066866C211yesmaximal, characteristic, complemented
6#13066859C212yesmaximal, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal
9#13066848C212yesmaximal, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C2×C11×C22⋊Q8—24no—
17C2×C11×C22⋊Q8—28no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C2×C4×C22⋊D11—24no—
24C2×C4×C22⋊D11—24no—
25C2×C4×C22⋊D11—24no—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32#10622844—24no—
33#10622842—24no—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622602—28no—
43C25×C11C2311yescharacteristic
44C24×D11C2311yescharacteristic
45C22×Q8×C11—24no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—42no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—24no—
53C23×C4×C11—42no—
54C23×C4×C11D414yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11—22no—
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11Q814yescomplemented
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—24no—
75C22×C4×D11—42no—
76C11×C22⋊Q8—232no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4D418yescomplemented
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—24no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—42no—
91C4×C22⋊D11—232no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4D414yes—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4—42no—
106C2×Dic11⋊C4D414yes—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118#14723—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11C2×D412yes—
128C24×C11C2×Q812yes—
129C24×C11#4112yes—
130C24×C11C2411yescharacteristic
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—22no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11C2×D412yes—
140C23×D11C2×Q812yes—
141C23×D11#4112yes—
142C2×Q8×C11—28no—
143C2×Q8×C11—48no—
144C2×Q8×C11—48no—
145C2×Q8×C11—44no—
146C2×Q8×C11—44no—
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×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—28no—
165C22×C4×C11—28no—
166C22×C4×C11—44no—
167C22×C4×C11—48no—
168C22×C4×C11—48no—
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D414yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D414yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C2×C22⋊D11—28no—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—28no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11C2×D412yes—
209C22×Dic11C2×D412yes—
210C22×Dic11C2×D412yes—
211C22×Dic11C2×Q812yes—
212C22×Dic11#4114yes—
213C22×Dic11#4112yes—
214C2×C4×D11—28no—
215C2×C4×D11—48no—
216C2×C4×D11—48no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—216no—
221C11×C22⋊C4—216no—
222C22⋊Dic11—28no—
223C22⋊Dic11—48no—
224(C2×D11)⋊C4—216no—
225(C2×D11)⋊C4—28no—
226(C2×D11)⋊C4—48no—
227Dic11⋊C4—28no—
228Dic11⋊C4—48no—
229C4×Dic11—28no—
230C22×C22⋊Q8D1111yescharacteristic, complemented
231C22×C4×D4—111no—
232C2×#395—111no—
233C2×#393—111no—
234C2×#385—112no—
235#1441—111no—
236#1439—111no—
237#1439—112no—
238#1438—112no—
239#1436—112no—
240C22⋊#95—111no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11C22⋊Q814yes—
264C23×C11C22×D411yescharacteristic
265C23×C11C22×D411yescharacteristic
266C23×C11C22×D411yescharacteristic
267C23×C11C22×D412yes—
268C23×C11C22×Q811yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11C2×#4111yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4112yes—
273C23×C11H(5,𝔽2)12yes—
274C23×C112−1+412yes—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—24no—
283C22×D11—24no—
284C22×D11—24no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—42no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11C22⋊Q814yescomplemented
298Q8×C11—416no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—416no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11#12014yes—
323C2×C4×C11#12014yes—
324C22⋊D11—232no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—41no—
339C2×Dic11—42no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11C22⋊Q814yescomplemented
356C4×D11—416no—
357C23×Q8C2×D1111yescharacteristic
358C23×D4—111no—
359C24×C4—111no—
360C24×C4C2×D1111yescharacteristic
361C2×C22⋊Q8—24no—
362C2×C22⋊Q8—28no—
363C2×C4×D4—224no—
364C2×C4×D4—224no—
365C2×C4×D4—224no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—112no—
368C22×C4⋊C4C2×D1111yescharacteristic
369C22×C4⋊C4C2×D1112yes—
370C22×C22⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—112no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4—112no—
375C22×C22⋊C4C2×D1112yes—
376C22×C42—111no—
377#395—224no—
378#393—224no—
379#385—228no—
380C2×#95—111no—
381C2×#95—112no—
382C2×#95—111no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—112no—
388C22×C11—24no—
389C22×C11—24no—
390C22×C11—24no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—44no—
398C22×C11—44no—
399C22×C11C2×#12011yescharacteristic
400C22×C11C2×#12011yescharacteristic
401C22×C11C2×C22⋊Q811yescharacteristic
402C22×C11C2×C22⋊Q811yescharacteristic
403C22×C11C2×C22⋊Q811yescharacteristic
404C22×C11#52511yescharacteristic
405C22×C11#52512yes—
406C22×C11#52511yescharacteristic
407C22×C11#52511yescharacteristic
408C22×C11#53211yescharacteristic
409C22×C11#53212yes—
410C22×C11#53411yescharacteristic
411C22×C11#53611yescharacteristic
412C22×C11#53912yes—
413C22×C11#54212yes—
414C22×C11D4212yes—
415C22×C11D4212yes—
416C22×C11#54712yes—
417C22×C11#54812yes—
418C22×C11#54812yes—
419C22×C11D4×Q812yes—
420C22×C11#55112yes—
421C22×C11#55412yes—
422C2×D11—24no—
423C2×D11—28no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—44no—
431C2×D11—44no—
432C2×D11—44no—
433C4×C11—24no—
434C4×C11—24no—
435C4×C11—44no—
436C4×C11—44no—
437Dic11—24no—
438Dic11—42no—
439Dic11—42no—
440Dic11—44no—
441Dic11—82no—
442C25—111no—
443C25C22×D1111yescharacteristic
444C22×Q8—22no—
445C22×Q8—22no—
446C22×Q8—24no—
447C22×Q8—22no—
448C22×Q8—42no—
449C22×D4—114no—
450C22×D4—222no—
451C22×D4—222no—
452C22×D4—222no—
453C22×D4—222no—
454C22×D4—222no—
455C22×D4—222no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—24no—
459C23×C4—42no—
460C23×C4—111no—
461C23×C4—112no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—112no—
465C23×C4—222no—
466C23×C4—222no—
467C23×C4—222no—
468C23×C4—224no—
469C23×C4—442no—
470C23×C4C22⋊D1114yes—
471C23×C4C22×D1112yes—
472C23×C4C22×D1112yes—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C22⋊Q8—232no—
476C4×D4—2232no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—222no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—224no—
485C2×C4⋊C4—224no—
486C2×C4⋊C4—442no—
487C2×C4⋊C4C22⋊D1118yescomplemented
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—222no—
495C2×C22⋊C4—222no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—224no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4—442no—
506C2×C42—222no—
507C2×C42—222no—
508C2×C42—222no—
509#95—224no—
510#95—224no—
511#95—224no—
512#95—224no—
513#95—222no—
514#95—222no—
515#95—224no—
516#95—224no—
517C2×C11—44no—
518C2×C11#238811yescharacteristic
519C2×C11#240311yescharacteristic
520C2×C11#240911yescharacteristic
521C2×C11#243211yescharacteristic
522C2×C11#244912yes—
523C2×C11#245212yes—
524C2×C11#246112yes—
525C2×C11#246312yes—
526C2×C11#256411yescharacteristic
527C2×C11#263811yescharacteristic
528C2×C11#284811yescharacteristic
529D11—44no—
530C24—21no—
531C24—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—112no—
539C24—112no—
540C24—112no—
541C24—221no—
542C24—222no—
543C24—221no—
544C24—222no—
545C24—222no—
546C24—221no—
547C24—222no—
548C24—221no—
549C24Q8×D1112yes—
550C24#434312yes—
551C24C2×C22⋊D1112yes—
552C24C23×D1111yescharacteristic
553C2×Q8—28no—
554C2×Q8—48no—
555C2×Q8—48no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×D4—228no—
559C2×D4—228no—
560C2×D4—228no—
561C2×D4—228no—
562C2×D4—228no—
563C2×D4—228no—
564C2×D4—228no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—114no—
593C22×C4—228no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—222no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—448no—
620C22×C4—448no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4D4×D1112yes—
624C22×C4D4×D1112yes—
625C22×C4C2×C22⋊D1114yes—
626C22×C4C2×C22⋊D1114yes—
627C22×C4C2×C22⋊D1112yes—
628C22×C4C2×C22⋊D1114yes—
629C22×C4C2×C22⋊D1112yes—
630C4⋊C4—28no—
631C4⋊C4—216no—
632C4⋊C4—228no—
633C4⋊C4—448no—
634C22⋊C4—216no—
635C22⋊C4—2216no—
636C22⋊C4—228no—
637C22⋊C4—228no—
638C22⋊C4—448no—
639C22⋊C4—448no—
640C42—228no—
641C11#1472311yescharacteristic, complemented, Sylow
642C23—22no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—114no—
665C23—222no—
666C23—224no—
667C23—222no—
668C23—224no—
669C23—224no—
670C23—222no—
671C23—222no—
672C23—222no—
673C23—222no—
674C23—224no—
675C23—224no—
676C23—224no—
677C23—442no—
678C23—441no—
679C23—441no—
680C23—442no—
681C23—442no—
682C23—441no—
683C23—441no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23#6699914yes—
688C23C2×D4×D1111yescharacteristic
689C23C2×D4×D1111yescharacteristic
690C23#6703712yes—
691C23C2×Q8×D1111yescharacteristic
692C23C2×#434311yescharacteristic
693C23#6704012yes—
694C23#41×D1111yescharacteristic
695C23#41×D1111yescharacteristic
696C23#41×D1112yes—
697C23C22×C22⋊D1111yescharacteristic
698C23C22×C22⋊D1112yes—
699Q8—416no—
700D4—2232no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—416no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—114no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—4416no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—442no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4#6699014yes—
757C2×C4#6700614yes—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—228no—
770C22—224no—
771C22—442no—
772C22—444no—
773C22—442no—
774C22—442no—
775C22—442no—
776C22—442no—
777C22—444no—
778C22—442no—
779C22—444no—
780C22D11×C22⋊Q811yescharacteristic
781C22D11×C22⋊Q811yescharacteristic
782C22#1062315811yescharacteristic
783C22#1062315811yescharacteristic
784C22#1062316212yes—
785C22#1062316412yes—
786C22#1062316712yes—
787C22#1062316812yes—
788C22#1062316912yes—
789C22#1062317112yes—
790C22C2×#6699011yescharacteristic
791C22D4×C22⋊D1112yes—
792C22D4×C22⋊D1112yes—
793C22#1062333511yescharacteristic
794C22C2×#6699911yescharacteristic
795C22Q8×C22⋊D1112yes—
796C22#1062334711yescharacteristic
797C22#1062334812yes—
798C22#1062335912yes—
799C22#1062335911yescharacteristic
800C22#1062336312yes—
801C22#1062336311yescharacteristic
802C22C2×#6700611yescharacteristic
803C4—24no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—224no—
808C4—442no—
809C4—442no—
810C4—444no—
811C4—882no—
812C2—44no—
813C2—444no—
814C2#1307182911yescharacteristic
815C2#1307192611yescharacteristic
816C2#1307197511yescharacteristic
817C2#1307224511yescharacteristic
818C2#1307242212yes—
819C2#1307246512yes—
820C2#1307259012yes—
821C2#1307260912yes—
822C2#1307379811yescharacteristic
823C2#1307453411yescharacteristic
824C2#1307690011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC22×C11×C22⋊Q8C2
prime radicalC23×C22⋊D11C22
hypercenterC22×C22⋊Q8D11
hypocenterC11#14723
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622842C2semidirect
3. C2×#10622844C2semidirect
4. C2×#10622602C2semidirect
5. #13066866C2semidirect
6. #13066859C2semidirect
7. #13066858C2semidirect
9. #13066848C2semidirect
10. #13066839C2semidirect
11. C22×C11×C22⋊Q8C2semidirect
65. C22×C22⋊D11Q8semidirect
81. C2×C11×C4⋊C4D4semidirect
230. C22×C22⋊Q8D11semidirect
297. C22×D11C22⋊Q8semidirect
355. C2×Dic11C22⋊Q8semidirect
487. C2×C4⋊C4C22⋊D11semidirect
641. C11#14723semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228422
C2×#106228442
C2×#106226022
#130668662
#130668592
#130668582
#130668552
#130668482
#130668392
C22×C11×C22⋊Q82
#1472311