Finite Group Databasebeta

← #14685229

Subgroups — #14685229

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×#66977C211yesmaximal, characteristic, complemented
2C2×#10622592C211yesmaximal, characteristic, complemented
3C2×#10622560C211yesmaximal, characteristic, complemented
4C2×#10622823C212yesmaximal, complemented
5#13066869C211yesmaximal, characteristic, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066859C212yesmaximal, complemented
8#13066857C212yesmaximal
9#13066849C212yesmaximal, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C2×C4×D4×C11—24no—
17C2×C4×D4×C11—24no—
18C2×C4×D4×C11—24no—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977—24no—
29C2×#66977—28no—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32#10622823—28no—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622592—24no—
42#10622560—24no—
43C25×C11C2311yescharacteristic
44C25×C11C2311yescharacteristic
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11Q814yescomplemented
52C23×C4×C11—22no—
53C23×C4×C11—24no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—24no—
59C23×C4×C11—42no—
60C23×C4×C11—42no—
61C23×C4×C11D414yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C22×Dic22—22no—
72C22×Dic22—24no—
73C22×Dic22—22no—
74C22×Dic22—22no—
75C22×Dic22—42no—
76C4×D4×C11—232no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D414yes—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D414yes—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—24no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—42no—
100C2×C22⋊Dic11—42no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—24no—
103#66977—232no—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—42no—
109C2×Dic11⋊C4D418yescomplemented
110C11⋊#95—24no—
111C11⋊#95—22no—
112C11⋊#95—24no—
113C11⋊#95—22no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118#14723—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—21no—
128C24×C11—21no—
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11C2×D412yes—
136C24×C11C2×D412yes—
137C24×C11C2×Q812yes—
138C24×C11C2×Q812yes—
139C24×C11#4112yes—
140C24×C11#4112yes—
141C24×C11C2411yescharacteristic
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11—28no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—28no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—28no—
168C22×C4×C11—28no—
169C22×C4×C11—44no—
170C22×C4×C11—48no—
171C22×C4×C11—48no—
172C22×C4×C11—48no—
173C22×C4×C11—48no—
174C22×C4×C11—44no—
175C22×C4×C11—44no—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×Q812yes—
185C22×C4×C11#4112yes—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
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×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D414yes—
213C22×Dic11#4114yes—
214C2×Dic22—28no—
215C2×Dic22—48no—
216C2×Dic22—48no—
217C2×Dic22—44no—
218C2×Dic22—44no—
219C11×C4⋊C4—28no—
220C11×C22⋊C4—28no—
221C11×C22⋊C4—28no—
222C42×C11—28no—
223C22⋊Dic11—216no—
224C22⋊Dic11—216no—
225C22⋊Dic11—48no—
226C22⋊Dic11—48no—
227C4⋊Dic11—28no—
228Dic11⋊C4—216no—
229Dic11⋊C4—48no—
230C22×C22⋊Q8—111no—
231C22×C4×D4D1111yescharacteristic
232C2×#395—111no—
233C2×#393—111no—
234C2×#385—112no—
235#1441—111no—
236#1439—112no—
237#1439—111no—
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—24no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—24no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—41no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—42no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11C22⋊Q814yes—
286C23×C11C22⋊Q814yescomplemented
287C23×C11C22×D412yes—
288C23×C11C22×D411yescharacteristic
289C23×C11C22×D411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×Q811yescharacteristic
292C23×C11C2×#4111yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4112yes—
296C23×C11H(5,𝔽2)12yes—
297C23×C112−1+412yes—
298D4×C11—232no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—416no—
318C2×C4×C11—416no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11#12014yes—
326C2×C4×C11#12014yes—
327C2×C4×C11C22⋊Q814yescomplemented
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
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×Dic11—42no—
356Dic22—416no—
357C23×Q8—111no—
358C23×D4C2×D1111yescharacteristic
359C24×C4C2×D1111yescharacteristic
360C24×C4C2×D1111yescharacteristic
361C2×C22⋊Q8—228no—
362C2×C22⋊Q8—224no—
363C2×C4×D4—24no—
364C2×C4×D4—24no—
365C2×C4×D4—24no—
366C22×C4⋊C4—112no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4—112no—
369C22×C4⋊C4C2×D1111yescharacteristic
370C22×C22⋊C4—112no—
371C22×C22⋊C4—112no—
372C22×C22⋊C4—112no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1111yescharacteristic
376C22×C42C2×D1111yescharacteristic
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—24no—
392C22×C11—28no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—44no—
404C22×C11—44no—
405C22×C11—44no—
406C22×C11—44no—
407C22×C11—44no—
408C22×C11—44no—
409C22×C11—44no—
410C22×C11C2×#12011yescharacteristic
411C22×C11C2×#12011yescharacteristic
412C22×C11C2×C22⋊Q811yescharacteristic
413C22×C11C2×C22⋊Q811yescharacteristic
414C22×C11C2×C22⋊Q811yescharacteristic
415C22×C11#52511yescharacteristic
416C22×C11#52511yescharacteristic
417C22×C11#52511yescharacteristic
418C22×C11#52512yes—
419C22×C11#53212yes—
420C22×C11#53211yescharacteristic
421C22×C11#53411yescharacteristic
422C22×C11#53611yescharacteristic
423C22×C11#53912yes—
424C22×C11#54212yes—
425C22×C11D4212yes—
426C22×C11D4212yes—
427C22×C11#54712yes—
428C22×C11#54812yes—
429C22×C11#54812yes—
430C22×C11D4×Q812yes—
431C22×C11#55112yes—
432C22×C11#55412yes—
433C4×C11—24no—
434C4×C11—24no—
435C4×C11—24no—
436C4×C11—42no—
437C4×C11—42no—
438Dic11—44no—
439Dic11—44no—
440Dic11—44no—
441Dic11—82no—
442C25C22×D1111yescharacteristic
443C25C22×D1111yescharacteristic
444C22×Q8—224no—
445C22×Q8—222no—
446C22×Q8—222no—
447C22×Q8—222no—
448C22×Q8—442no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4Dic2214yescomplemented
456C23×C4—22no—
457C23×C4—24no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—24no—
463C23×C4—42no—
464C23×C4—42no—
465C23×C4—112no—
466C23×C4—112no—
467C23×C4—112no—
468C23×C4—112no—
469C23×C4C22⋊D1114yes—
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C22⋊Q8—2232no—
476C4×D4—232no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—118no—
480C2×C4⋊C4—224no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4—224no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—224no—
485C2×C4⋊C4—224no—
486C2×C4⋊C4—442no—
487C2×C4⋊C4C22⋊D1114yes—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—224no—
495C2×C22⋊C4—224no—
496C2×C22⋊C4—224no—
497C2×C22⋊C4—224no—
498C2×C22⋊C4—224no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—224no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—442no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4C22⋊D1114yes—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—22no—
509#95—224no—
510#95—224no—
511#95—224no—
512#95—224no—
513#95—224no—
514#95—222no—
515#95—222no—
516#95—224no—
517C2×C11—44no—
518C2×C11—44no—
519C2×C11#238811yescharacteristic
520C2×C11#240311yescharacteristic
521C2×C11#240911yescharacteristic
522C2×C11#243211yescharacteristic
523C2×C11#244912yes—
524C2×C11#245212yes—
525C2×C11#246112yes—
526C2×C11#246312yes—
527C2×C11#256411yescharacteristic
528C2×C11#263811yescharacteristic
529C2×C11#284811yescharacteristic
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24C2×Dic2212yes—
547C24C2×Dic2212yes—
548C24#433912yes—
549C24#433912yes—
550C24C2×C22⋊D1112yes—
551C24C2×C22⋊D1112yes—
552C24C23×D1111yescharacteristic
553C2×Q8—228no—
554C2×Q8—448no—
555C2×Q8—448no—
556C2×Q8—444no—
557C2×Q8—444no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—28no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—114no—
593C22×C4—114no—
594C22×C4—114no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
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—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4C2×Dic2212yes—
621C22×C4#433912yes—
622C22×C4D4×D1114yes—
623C22×C4C2×C22⋊D1112yes—
624C22×C4C2×C22⋊D1112yes—
625C22×C4C2×C22⋊D1112yes—
626C22×C4C2×C22⋊D1112yes—
627C22×C4C2×C22⋊D1112yes—
628C22×C4C2×C22⋊D1112yes—
629C22×C4C2×C22⋊D1112yes—
630C4⋊C4—28no—
631C4⋊C4—228no—
632C4⋊C4—2216no—
633C4⋊C4—448no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—2216no—
637C22⋊C4—2216no—
638C22⋊C4—448no—
639C22⋊C4—448no—
640C42—28no—
641C11#1472311yescharacteristic, complemented, Sylow
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23#6697714yes—
687C23#6697714yescomplemented
688C23C22×Dic2211yescharacteristic
689C23C2×#433911yescharacteristic
690C23C2×#433911yescharacteristic
691C23C2×#433911yescharacteristic
692C23C2×D4×D1112yes—
693C23#6703712yes—
694C23#41×D1112yes—
695C23#6704312yes—
696C23C22×C22⋊D1111yescharacteristic
697C23C22×C22⋊D1111yescharacteristic
698C23C22×C22⋊D1111yescharacteristic
699Q8—4416no—
700D4—232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
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#6697714yescomplemented
756C2×C4#6699014yes—
757C2×C4#6700614yes—
758C22—28no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—44no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22D4×Dic2212yes—
781C22#1062307012yes—
782C22#1062307812yes—
783C22#1062307912yes—
784C22#1062308312yes—
785C22#1062308712yes—
786C22#1062309212yes—
787C22#1062309512yes—
788C22C2×#6697711yescharacteristic
789C22C2×#6697711yescharacteristic
790C22C2×#6697711yescharacteristic
791C22#1062332211yescharacteristic
792C22#1062332211yescharacteristic
793C22#1062332211yescharacteristic
794C22C2×#6699011yescharacteristic
795C22D4×C22⋊D1112yes—
796C22D4×C22⋊D1112yes—
797C22#1062333511yescharacteristic
798C22#1062335512yes—
799C22#1062335611yescharacteristic
800C22#1062336212yes—
801C22#1062336311yescharacteristic
802C22C2×#6700611yescharacteristic
803C4—24no—
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—444no—
809C4—444no—
810C4—444no—
811C4—882no—
812C2—44no—
813C2—44no—
814C2#1307183111yescharacteristic
815C2#1307192611yescharacteristic
816C2#1307198111yescharacteristic
817C2#1307224011yescharacteristic
818C2#1307241912yes—
819C2#1307246012yes—
820C2#1307257712yes—
821C2#1307260712yes—
822C2#1307379211yescharacteristic
823C2#1307453311yescharacteristic
824C2#1307690311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC22×C4×D4×C11C2
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#14723
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66977C2semidirect
2. C2×#10622592C2semidirect
3. C2×#10622560C2semidirect
4. C2×#10622823C2semidirect
5. #13066869C2semidirect
6. #13066861C2semidirect
7. #13066859C2semidirect
9. #13066849C2semidirect
10. #13066839C2semidirect
51. C22×D4×C11Q8semidirect
109. C2×Dic11⋊C4D4semidirect
286. C23×C11C22⋊Q8semidirect
327. C2×C4×C11C22⋊Q8semidirect
455. C22×D4Dic22semidirect
641. C11#14723semidirect
687. C23#66977semidirect
755. C2×C4#66977semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106225922
C2×#106225602
C2×#106228232
#130668692
#130668612
#130668592
#130668572
#130668492
#130668392
C22×C4×D4×C112
#1472311