Finite Group Databasebeta

← #14676908

Subgroups — #14676908

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic, complemented
3C2×#10622586C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic
5C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#13066882C212yesmaximal, complemented
8#13066860C212yesmaximal
9#13066852C212yesmaximal
10Dic11⋊#95C212yesmaximal, complemented
11C2×C11×#391C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×#66999—24no—
17C2×#66999—24no—
18C2×#66999C418yescomplemented
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C11×#391—24no—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32#10622843—24no—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622600—24no—
41#10622586—24no—
42C4×(C2×D11)⋊C4—24no—
43C4×C4⋊Dic11—24no—
44C24×D11C2311yescharacteristic
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11C2×C414yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11C2×C414yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11D414yes—
75#66999—232no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4C2×C418yes—
87C2×(C2×D11)⋊C4Q814yescomplemented
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2×C414yes—
91C2×C4⋊Dic11D414yes—
92C2×C4⋊Dic11D414yes—
93C2×C4⋊Dic11D414yes—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—42no—
99C2×Dic11⋊C4C2×C418yes—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—24no—
104C2×C4×Dic11—24no—
105C2×C4×Dic11—42no—
106C11×#95—24no—
107C11×#95—24no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115#13997—111nomaximal, Sylow
116C24×C11C2411yescharacteristic
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11C22×C412yes—
130C23×D11C2×Q812yes—
131C23×D11#4112yes—
132C2×Q8×C11—28no—
133C2×Q8×C11—28no—
134C2×Q8×C11—28no—
135C2×Q8×C11—44no—
136C2×Q8×C11—44no—
137C2×Q8×C11—44no—
138C2×Q8×C11—44no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
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×C11C22×C414yes—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×Q812yes—
171C22×C4×C11#4112yes—
172C22×C4×C11#4112yes—
173C22×C4×C11#4112yes—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—21no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11C22×C412yes—
203C22×Dic11C22×C414yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D414yes—
206C22×Dic11C2×D414yes—
207C22×Dic11C2×Q812yes—
208C22×Dic11#4112yes—
209C2×C4×D11—28no—
210C2×C4×D11—28no—
211C2×C4×D11—28no—
212C2×C4×D11—44no—
213C2×C4×D11—44no—
214C2×C4×D11—44no—
215C2×C4×D11—44no—
216C11×C4⋊C4—44no—
217C42×C11—28no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—216no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4—48no—
222C4⋊Dic11—28no—
223C4⋊Dic11C22⋊C4116yescomplemented
224Dic11⋊C4—216no—
225Dic11⋊C4—48no—
226C4×Dic11—48no—
227C4×Dic11—44no—
228C22×C22⋊Q8—111no—
229C2×#391—111no—
230C2×#391D1111yescharacteristic, complemented
231C2×#389—111no—
232C2×#380—111no—
233C2×C4×C4⋊C4—111no—
234C2×C4×C22⋊C4—111no—
235#1445—112no—
236#1439—112no—
237#1437—112no—
238C4⋊#95—112no—
239C23×C11C23×C411yescharacteristic
240C23×C11C22×D411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C22×D411yescharacteristic
243C23×C11C22×D411yescharacteristic
244C23×C11C22×Q811yescharacteristic
245C23×C11C2×#4111yescharacteristic
246C23×C11C2×#4111yescharacteristic
247C23×C11C2×#4111yescharacteristic
248C23×C11C2×#4111yescharacteristic
249C23×C11C2×#4111yescharacteristic
250C23×C11H(5,𝔽2)11yescharacteristic
251C23×C112−1+411yescharacteristic
252C23×C112−1+411yescharacteristic
253C23×C112−1+411yescharacteristic
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11C4×Q814yes—
289Q8×C11—416no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11C2×C22⋊C414yes—
318C2×C4×C11C4×D414yes—
319C2×C4×C11C4×D414yes—
320C2×C4×C11#12114yes—
321C2×C4×C11#12114yes—
322C2×C4×C11C22⋊Q814yescomplemented
323C2×C4×C11#12414yes—
324C2×C4×C11#12714yes—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—42no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—42no—
358C2×Dic11—41no—
359C2×Dic11C2×C22⋊C418yes—
360C4×D11—416no—
361C23×Q8C2×D1111yescharacteristic
362C24×C4—111no—
363C2×C22⋊Q8—118no—
364C2×C22⋊Q8—224no—
365C2×C22⋊Q8—224no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—112no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—112no—
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4—112no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—112no—
375C22×C42—111no—
376C22×C42—112no—
377C22×C42C2×D1111yescharacteristic
378#391—24no—
379#391—224no—
380#389—224no—
381#380—224no—
382C4×C4⋊C4—224no—
383C4×C22⋊C4—224no—
384C2×#95—111no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—112no—
388C2×#95—112no—
389C2×#95—112no—
390C2×#95—111no—
391C2×#95C2×D1112yes—
392C2×#95C2×D1112yes—
393C22×C11C22×C22⋊C411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11C2×C4×D411yescharacteristic
396C22×C11C2×C4×Q811yescharacteristic
397C22×C11C4×#4111yescharacteristic
398C22×C11#51911yescharacteristic
399C22×C11#52011yescharacteristic
400C22×C11C2×#12111yescharacteristic
401C22×C11C2×#12111yescharacteristic
402C22×C11C2×C22⋊Q811yescharacteristic
403C22×C11#52511yescharacteristic
404C22×C11C2×#12411yescharacteristic
405C22×C11#52911yescharacteristic
406C22×C11C2×#12711yescharacteristic
407C22×C11#53311yescharacteristic
408C22×C11#53611yescharacteristic
409C22×C11#53711yescharacteristic
410C22×C11#54111yescharacteristic
411C22×C11#54211yescharacteristic
412C22×C11#54611yescharacteristic
413C22×C11#54611yescharacteristic
414C22×C11#54611yescharacteristic
415C22×C11#54711yescharacteristic
416C22×C11#54711yescharacteristic
417C22×C11#54711yescharacteristic
418C22×C11#54811yescharacteristic
419C22×C11#54811yescharacteristic
420C22×C11#54811yescharacteristic
421C22×C11D4×Q811yescharacteristic
422C22×C11D4×Q811yescharacteristic
423C22×C11D4×Q811yescharacteristic
424C22×C11#55211yescharacteristic
425C22×C11#55211yescharacteristic
426C22×C11#55411yescharacteristic
427C22×C11#55611yescharacteristic
428C2×D11—24no—
429C2×D11—24no—
430C2×D11—24no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C4×C11—24no—
444C4×C11—42no—
445C4×C11—44no—
446C4×C11—82no—
447C4×C11#39018yes—
448Dic11—28no—
449Dic11—44no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453C25—111no—
454C22×Q8—22no—
455C22×Q8—22no—
456C22×Q8—22no—
457C22×Q8—22no—
458C22×Q8—22no—
459C22×Q8—22no—
460C22×Q8C4×D1114yes—
461C23×C4—112no—
462C23×C4—111no—
463C23×C4—112no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—114no—
467C23×C4—222no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4C22×D1112yes—
474C23×C4C22×D1112yes—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C22⋊Q8—2232no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—118no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—224no—
489C2×C4⋊C4—222no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4—224no—
493C2×C4⋊C4—442no—
494C2×C22⋊C4—118no—
495C2×C22⋊C4—114no—
496C2×C22⋊C4—224no—
497C2×C22⋊C4—224no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—442no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—224no—
509C2×C42—222no—
510C2×C42—222no—
511C2×C42—224no—
512C2×C42—222no—
513C2×C42—442no—
514C2×C42C22⋊D1114yes—
515#95—24no—
516#95—24no—
517#95—224no—
518#95—224no—
519#95—224no—
520#95—224no—
521#95—224no—
522#95—222no—
523#95—222no—
524C2×C11C2×#39011yescharacteristic
525C2×C11C4×C22⋊Q811yescharacteristic
526C2×C11#232311yescharacteristic
527C2×C11#233911yescharacteristic
528C2×C11Q8×C22⋊C411yescharacteristic
529C2×C11#236011yescharacteristic
530C2×C11#236211yescharacteristic
531C2×C11#241511yescharacteristic
532C2×C11#241711yescharacteristic
533C2×C11#242711yescharacteristic
534C2×C11#242911yescharacteristic
535C2×C11#248911yescharacteristic
536C2×C11#249211yescharacteristic
537C2×C11#254011yescharacteristic
538C2×C11#254211yescharacteristic
539D11—44no—
540C24—112no—
541C24—112no—
542C24—112no—
543C24—221no—
544C24—221no—
545C24—221no—
546C24—221no—
547C24—221no—
548C24—221no—
549C24—221no—
550C24—221no—
551C24—221no—
552C24—221no—
553C24—221no—
554C24—221no—
555C24C23×D1111yescharacteristic
556C2×Q8—28no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—114no—
587C22×C4—114no—
588C22×C4—114no—
589C22×C4—112no—
590C22×C4—114no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—222no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—222no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—228no—
622C22×C4—228no—
623C22×C4—228no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4C2×C4×D1114yes—
629C22×C4C2×C4×D1112yes—
630C22×C4#433912yes—
631C22×C4D4×D1112yes—
632C22×C4D4×D1112yes—
633C22×C4D4×D1112yes—
634C22×C4#434112yes—
635C22×C4Q8×D1112yes—
636C22×C4#434312yes—
637C22×C4C2×C22⋊D1112yes—
638C22×C4C2×C22⋊D1112yes—
639C22×C4C2×C22⋊D1112yes—
640C4⋊C4—44no—
641C4⋊C4—1116no—
642C4⋊C4—2216no—
643C4⋊C4—228no—
644C4⋊C4—448no—
645C22⋊C4—2216no—
646C22⋊C4—228no—
647C22⋊C4—228no—
648C22⋊C4—448no—
649C42—28no—
650C42—448no—
651C42—444no—
652C11#1399711yescharacteristic, complemented, Sylow
653C23—114no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23C22×C4×D1111yescharacteristic
689C23C2×#433911yescharacteristic
690C23C2×D4×D1111yescharacteristic
691C23C2×D4×D1111yescharacteristic
692C23C2×D4×D1111yescharacteristic
693C23C2×#434111yescharacteristic
694C23C2×Q8×D1111yescharacteristic
695C23C2×#434311yescharacteristic
696C23#6704011yescharacteristic
697C23#6704011yescharacteristic
698C23#41×D1111yescharacteristic
699C23#41×D1111yescharacteristic
700C23#6704211yescharacteristic
701C23#6704311yescharacteristic
702C23C22×C22⋊D1111yescharacteristic
703Q8—416no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—118no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—224no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—224no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—4416no—
767C2×C4C22⋊C4×D1114yes—
768C2×C4(C22⋊D11)⋊C414yes—
769C2×C4#6693714yes—
770C2×C4#6693814yes—
771C2×C4C4×C22⋊D1114yes—
772C2×C4#6699214yes—
773C2×C4#6699314yes—
774C2×C4#6699914yescomplemented
775C22—224no—
776C22—224no—
777C22—224no—
778C22—442no—
779C22—442no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—442no—
790C22C2×C22⋊C4×D1111yescharacteristic
791C22C2×(C22⋊D11)⋊C411yescharacteristic
792C22C2×#6693711yescharacteristic
793C22C2×#6693811yescharacteristic
794C22C4×Q8×D1111yescharacteristic
795C22#1062310311yescharacteristic
796C22C4×#434311yescharacteristic
797C22#1062310511yescharacteristic
798C22#1062310911yescharacteristic
799C22#1062311111yescharacteristic
800C22#1062311311yescharacteristic
801C22#1062311411yescharacteristic
802C22#1062316111yescharacteristic
803C22#1062316211yescharacteristic
804C22#1062316311yescharacteristic
805C22#1062316411yescharacteristic
806C22#1062316611yescharacteristic
807C22#1062317011yescharacteristic
808C22#1062317211yescharacteristic
809C22#1062317311yescharacteristic
810C22#1062320711yescharacteristic
811C22#1062320711yescharacteristic
812C22#1062320811yescharacteristic
813C22#1062320811yescharacteristic
814C22#1062325711yescharacteristic
815C22#1062325711yescharacteristic
816C22#1062325811yescharacteristic
817C22#1062325811yescharacteristic
818C22C2×C4×C22⋊D1111yescharacteristic
819C22C2×#6699211yescharacteristic
820C22C2×#6699311yescharacteristic
821C22C2×#6699911yescharacteristic
822C22#1062334711yescharacteristic
823C22#1062335911yescharacteristic
824C22#1062336411yescharacteristic
825C4—24no—
826C4—42no—
827C4—44no—
828C4—82no—
829C4—228no—
830C4—444no—
831C4—442no—
832C4—442no—
833C4—442no—
834C4#1062257018yes—
835C2—444no—
836C2C2×#1062257011yescharacteristic
837C2C4×#6699911yescharacteristic
838C2#1307129211yescharacteristic
839C2#1307144511yescharacteristic
840C2#1307145011yescharacteristic
841C2#1307162611yescharacteristic
842C2#1307164811yescharacteristic
843C2#1307204611yescharacteristic
844C2#1307206811yescharacteristic
845C2#1307219411yescharacteristic
846C2#1307221611yescharacteristic
847C2#1307295811yescharacteristic
848C2#1307299111yescharacteristic
849C2#1307355611yescharacteristic
850C2#1307357011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#391D11
hypocenterC11#13997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#10622843C2semidirect
3. C2×#10622586C2semidirect
5. C2×C4×C4⋊Dic11C2semidirect
7. #13066882C2semidirect
10. Dic11⋊#95C2semidirect
11. C2×C11×#391C2semidirect
18. C2×#66999C4semidirect
87. C2×(C2×D11)⋊C4Q8semidirect
223. C4⋊Dic11C22⋊C4semidirect
230. C2×#391D11semidirect
322. C2×C4×C11C22⋊Q8semidirect
652. C11#13997semidirect
774. 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
C2×#106228432
C2×#106225862
C2×#106226002
C2×C4×C4⋊Dic112
C2×C4×(C2×D11)⋊C42
#130668822
#130668602
#130668522
Dic11⋊#952
C2×C11×#3912
#1399711