Finite Group Databasebeta

← #14676426

Subgroups — #14676426

Order 2816.

2006 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×#66945C211yesmaximal, characteristic
2C2×#10622541C211yesmaximal, characteristic, complemented
3C2×#10622586C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13066860C212yesmaximal
7#13066860C212yesmaximal
8#13066845C211yesmaximal, characteristic, complemented
9Dic11⋊#95C212yesmaximal, complemented
10#13066841C212yesmaximal, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C2×#66945—24no—
27C2×#66945—24no—
28C2×#66945C418yescomplemented
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622586—24no—
40C4×(C2×D11)⋊C4—24no—
41#10622541—24no—
42C24×D11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11C2×C414yes—
58C22×C4×D11D414yes—
59C22×C4×D11Q814yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4C2×C418yes—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11C2×C414yes—
85C2×C4⋊Dic11D414yes—
86C2×C4⋊Dic11D414yes—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—42no—
92C2×Dic11⋊C4—42no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11C2×C418yes—
99#66945—232no—
100C11×#95—24no—
101C11×#95—42no—
102C11⋊#95—24no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—42no—
109#13951—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11C22×C412yes—
124C23×D11C2×D412yes—
125C23×D11C2×Q812yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
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—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11C22×C414yes—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×Q812yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11C22×C414yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C2×D414yes—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×Q812yes—
194C22×Dic11#4112yes—
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×D11C4⋊C4116yescomplemented
203C11×C4⋊C4—28no—
204C11×C4⋊C4—44no—
205C42×C11—44no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—216no—
209(C2×D11)⋊C4—48no—
210C4⋊Dic11—44no—
211C4⋊Dic11C22⋊C4116yescomplemented
212Dic11⋊C4—48no—
213Dic11⋊C4—48no—
214C4×Dic11—216no—
215C4×Dic11—44no—
216C22×#117—111no—
217C2×#389—111no—
218C2×#389—111no—
219C2×#380—111no—
220C2×C4×C22⋊C4—111no—
221#1439—112no—
222#1439—112no—
223C4⋊#95—112no—
224C4⋊#95—111no—
225C4⋊#95D1111yescharacteristic, complemented
226#1434—112no—
227C23×C11C23×C411yescharacteristic
228C23×C11C22×D411yescharacteristic
229C23×C11C22×D411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C22×Q811yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11C2×#4111yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11H(5,𝔽2)11yescharacteristic
239C23×C11H(5,𝔽2)11yescharacteristic
240C23×C112−1+411yescharacteristic
241C23×C112−1+411yescharacteristic
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
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—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11C2×C4⋊C414yes—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11C2×C22⋊C414yes—
306C2×C4×C11C2×C4⋊C414yes—
307C2×C4×C11#11714yes—
308C2×C4×C11#12114yes—
309C2×C4×C11#12114yes—
310C2×C4×C11C22⋊Q814yes—
311C2×C4×C11C22⋊Q814yes—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11C2×C22⋊C418yes—
346C2×Dic11C2×C4⋊C414yes—
347C4×D11—232no—
348C24×C4—111no—
349C2×#117—118no—
350C2×#117—224no—
351C2×#117—224no—
352C22×C4⋊C4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—112no—
355C22×C4⋊C4—112no—
356C22×C4⋊C4C2×D1111yescharacteristic
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4—112no—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—112no—
362C22×C42—112no—
363C22×C42—111no—
364C22×C42C2×D1111yescharacteristic
365#389—224no—
366#389—224no—
367#380—224no—
368C4×C22⋊C4—224no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—111no—
375C2×#95—112no—
376C2×#95C2×D1112yes—
377C2×#95C2×D1112yes—
378C22×C11C22×C22⋊C411yescharacteristic
379C22×C11C22×C4⋊C411yescharacteristic
380C22×C11C2×#11711yescharacteristic
381C22×C11C4×#4111yescharacteristic
382C22×C11C4×#4111yescharacteristic
383C22×C11#52011yescharacteristic
384C22×C11#52011yescharacteristic
385C22×C11C2×#12111yescharacteristic
386C22×C11C2×#12111yescharacteristic
387C22×C11C2×C22⋊Q811yescharacteristic
388C22×C11C2×C22⋊Q811yescharacteristic
389C22×C11#52511yescharacteristic
390C22×C11#52511yescharacteristic
391C22×C11#53311yescharacteristic
392C22×C11#53311yescharacteristic
393C22×C11#53511yescharacteristic
394C22×C11#53611yescharacteristic
395C22×C11#54411yescharacteristic
396C22×C11#54411yescharacteristic
397C22×C11#54611yescharacteristic
398C22×C11#54611yescharacteristic
399C22×C11#54711yescharacteristic
400C22×C11#54711yescharacteristic
401C22×C11#54811yescharacteristic
402C22×C11#54811yescharacteristic
403C22×C11#55011yescharacteristic
404C22×C11#55011yescharacteristic
405C22×C11#55211yescharacteristic
406C22×C11#55211yescharacteristic
407C22×C11#55311yescharacteristic
408C22×C11#55311yescharacteristic
409C22×C11#55511yescharacteristic
410C22×C11#55511yescharacteristic
411C22×C11#55611yescharacteristic
412C22×C11#55611yescharacteristic
413C2×D11—24no—
414C2×D11—24no—
415C2×D11—24no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C4×C11—44no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—82no—
432C4×C11#38018yes—
433Dic11—28no—
434Dic11—24no—
435Dic11—42no—
436Dic11—42no—
437Dic11—82no—
438C25—111no—
439C23×C4—112no—
440C23×C4—111no—
441C23×C4—114no—
442C23×C4—114no—
443C23×C4—114no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—112no—
447C23×C4—222no—
448C23×C4—222no—
449C23×C4—222no—
450C23×C4—222no—
451C23×C4C22×D1112yes—
452C23×C4C22×D1112yes—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456#117—2232no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—114no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—224no—
466C2×C4⋊C4—224no—
467C2×C4⋊C4—224no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—442no—
473C2×C4⋊C4—442no—
474C2×C4⋊C4C4×D1114yes—
475C2×C22⋊C4—118no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—222no—
479C2×C22⋊C4—222no—
480C2×C22⋊C4—222no—
481C2×C22⋊C4—222no—
482C2×C22⋊C4—222no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—442no—
486C2×C22⋊C4—442no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—118no—
491C2×C42—224no—
492C2×C42—224no—
493C2×C42—222no—
494C2×C42—222no—
495C2×C42—222no—
496#95—24no—
497#95—42no—
498#95—224no—
499#95—222no—
500#95—222no—
501#95—224no—
502#95—224no—
503#95—224no—
504#95—442no—
505C2×C11C2×#38011yescharacteristic
506C2×C11#229611yescharacteristic
507C2×C11#231711yescharacteristic
508C2×C11#233911yescharacteristic
509C2×C11#234111yescharacteristic
510C2×C11#234611yescharacteristic
511C2×C11#234711yescharacteristic
512C2×C11#241411yescharacteristic
513C2×C11#241411yescharacteristic
514C2×C11#241511yescharacteristic
515C2×C11#241511yescharacteristic
516C2×C11#243911yescharacteristic
517C2×C11#243911yescharacteristic
518C2×C11#244111yescharacteristic
519C2×C11#244111yescharacteristic
520D11—44no—
521C24—112no—
522C24—112no—
523C24—112no—
524C24—221no—
525C24—221no—
526C24—221no—
527C24—221no—
528C24—221no—
529C24—221no—
530C24—221no—
531C24—221no—
532C24—221no—
533C24—221no—
534C24—221no—
535C24—221no—
536C24C23×D1111yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—112no—
563C22×C4—114no—
564C22×C4—112no—
565C22×C4—114no—
566C22×C4—114no—
567C22×C4—112no—
568C22×C4—1116no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—228no—
580C22×C4—228no—
581C22×C4—228no—
582C22×C4—228no—
583C22×C4—228no—
584C22×C4—228no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4C2×C4×D1114yes—
605C22×C4C2×C4×D1112yes—
606C22×C4#433912yes—
607C22×C4#433912yes—
608C22×C4D4×D1112yes—
609C22×C4D4×D1112yes—
610C22×C4D4×D1112yes—
611C22×C4#434112yes—
612C22×C4Q8×D1112yes—
613C22×C4#434312yes—
614C4⋊C4—28no—
615C4⋊C4—44no—
616C4⋊C4—1116no—
617C4⋊C4—448no—
618C4⋊C4—448no—
619C4⋊C4—444no—
620C22⋊C4—2216no—
621C22⋊C4—228no—
622C22⋊C4—228no—
623C22⋊C4—448no—
624C42—44no—
625C42—2216no—
626C42—444no—
627C11#1395111yescharacteristic, complemented, Sylow
628C23—114no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—222no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23C22×C4×D1111yescharacteristic
664C23C2×#433911yescharacteristic
665C23C2×#433911yescharacteristic
666C23C2×D4×D1111yescharacteristic
667C23C2×D4×D1111yescharacteristic
668C23C2×D4×D1111yescharacteristic
669C23C2×#434111yescharacteristic
670C23#6703711yescharacteristic
671C23C2×Q8×D1111yescharacteristic
672C23C2×#434311yescharacteristic
673C23#6704011yescharacteristic
674C23#41×D1111yescharacteristic
675C23#41×D1111yescharacteristic
676C23#6704211yescharacteristic
677C23#6704311yescharacteristic
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—118no—
707C2×C4—114no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—2232no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4#6692514yes—
743C2×C4C22⋊C4×D1114yes—
744C2×C4#6693714yes—
745C2×C4#6693714yes—
746C2×C4C4⋊C4×D1114yes—
747C2×C4#6694914yes—
748C2×C4#6694914yes—
749C22—224no—
750C22—224no—
751C22—224no—
752C22—442no—
753C22—442no—
754C22—442no—
755C22—442no—
756C22—442no—
757C22—442no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—442no—
762C22—442no—
763C22—442no—
764C22C2×#6692511yescharacteristic
765C22C2×C22⋊C4×D1111yescharacteristic
766C22C2×#6693711yescharacteristic
767C22C2×#6693711yescharacteristic
768C22C2×C4⋊C4×D1111yescharacteristic
769C22C2×#6694911yescharacteristic
770C22C2×#6694911yescharacteristic
771C22#1062304411yescharacteristic
772C22#1062304511yescharacteristic
773C22#1062306311yescharacteristic
774C22#1062306411yescharacteristic
775C22C4×#434111yescharacteristic
776C22#1062307711yescharacteristic
777C22#1062308911yescharacteristic
778C22#1062309411yescharacteristic
779C22C4×#434311yescharacteristic
780C22#1062310511yescharacteristic
781C22#1062311211yescharacteristic
782C22#1062311511yescharacteristic
783C22#1062312911yescharacteristic
784C22#1062313011yescharacteristic
785C22#1062313711yescharacteristic
786C22#1062313811yescharacteristic
787C22#1062315811yescharacteristic
788C22#1062315911yescharacteristic
789C22#1062316111yescharacteristic
790C22#1062316211yescharacteristic
791C22#1062320711yescharacteristic
792C22#1062320811yescharacteristic
793C22#1062321911yescharacteristic
794C22#1062322011yescharacteristic
795C22#1062324911yescharacteristic
796C22#1062325711yescharacteristic
797C22#1062325911yescharacteristic
798C22#1062326011yescharacteristic
799C4—44no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—228no—
804C4—224no—
805C4—442no—
806C4—442no—
807C4—882no—
808C4#1062228018yes—
809C2—444no—
810C2C2×#1062228011yescharacteristic
811C2#1307109711yescharacteristic
812C2#1307123811yescharacteristic
813C2#1307144511yescharacteristic
814C2#1307145511yescharacteristic
815C2#1307149711yescharacteristic
816C2#1307150511yescharacteristic
817C2#1307203611yescharacteristic
818C2#1307203711yescharacteristic
819C2#1307204711yescharacteristic
820C2#1307204811yescharacteristic
821C2#1307230911yescharacteristic
822C2#1307231011yescharacteristic
823C2#1307233111yescharacteristic
824C2#1307233211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13951
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622541C2semidirect
3. C2×#10622586C2semidirect
8. #13066845C2semidirect
9. Dic11⋊#95C2semidirect
10. #13066841C2semidirect
11. C11×C4⋊#95C2semidirect
28. C2×#66945C4semidirect
202. C2×C4×D11C4⋊C4semidirect
211. C4⋊Dic11C22⋊C4semidirect
225. C4⋊#95D11semidirect
627. C11#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106225412
C2×#106225862
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668602
#130668452
Dic11⋊#952
#130668412
C11×C4⋊#952
#1395111