Finite Group Databasebeta

← #14770281

Subgroups — #14770281

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C211yesmaximal, characteristic, complemented
2#13071081C211yesmaximal, characteristic, complemented
3#13069594C211yesmaximal, characteristic, complemented
4#13069561C211yesmaximal, characteristic, complemented
5#13069065C212yesmaximal, complemented
6#13068919C212yesmaximal, complemented
7#13068715C212yesmaximal, complemented
8#13068636C211yesmaximal, characteristic, complemented
9C4×#66901C211yesmaximal, characteristic, complemented
10#13068325C212yesmaximal, complemented
11C11×#3475C211yesmaximal, characteristic
12C11×#556C411yescharacteristic, complemented
13C11×#555C411yescharacteristic, complemented
14C11×#554C411yescharacteristic, complemented
15C11×#553C412yescomplemented
16C11×#552—21no—
17C11×#552C412yescomplemented
18C11×#551—22no—
19C11×#547C411yescharacteristic, complemented
20C11×#546—21no—
21C11×#533C2211yescharacteristic
22C11×#529—22no—
23C11×#529—21no—
24C11×#525C2212yes—
25C4×C11×#41—21no—
26C4×C11×#41C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2212yes—
29C2×#66979C2212yes—
30C22×#4318C2212yes—
31C2×#66901C2211yescharacteristic
32C2×#66901C2211yescharacteristic
33C2×#66901C2212yes—
34#10622834—21no—
35C4×C22⋊Dic11C2212yes—
36#10622820C2212yes—
37#10622625—21no—
38#10622624—22no—
39D4×C11⋊C8—21no—
40#10622598—21no—
41#10622564—22no—
42C4×C4⋊Dic11C2211yescharacteristic
43C42×Dic11C2211yescharacteristic
44#10622537C2211yescharacteristic
45C4×#4318C2211yescharacteristic
46#10622170C2212yes—
47#10622170C2212yes—
48#10622170C2212yes—
49#10622170C2211yescharacteristic
50#10622170C2212yes—
51#10622170C2212yes—
52#10622170C2211yescharacteristic
53C2×C11×#41—21no—
54C2×C11×#41C2311yescharacteristic
55C22×D4×C11D411yescharacteristic
56C23×C4×C11C2312yes—
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×C4⋊Q8C2×C411yescharacteristic
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#125—22no—
63C11×#125—21no—
64C11×#125C2×C412yes—
65C11×#124—21no—
66C11×#124—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2×C412yes—
76C11×C22⋊Q8C2×C412yes—
77C11×#121—22no—
78C11×#121—21no—
79C11×#121C2×C412yes—
80C11×#121C2×C412yes—
81C11×#120—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11C2×C411yescharacteristic
86C4×Q8×C11C2×C411yescharacteristic
87C4×D4×C11—21no—
88C4×D4×C11—22no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11C2×C411yescharacteristic
94C4×D4×C11C2×C411yescharacteristic
95C4×D4×C11C2×C411yescharacteristic
96C4×D4×C11C2×C412yes—
97C4×D4×C11C2×C411yescharacteristic
98C4×D4×C11D411yescharacteristic
99C4×D4×C11D411yescharacteristic
100C4×D4×C11D412yes—
101C11×#117—22no—
102C11×#117—22no—
103C11×#117—21no—
104C11×#117—22no—
105C11×#117—21no—
106C11×#117C2×C412yes—
107C11×#117C2×C412yes—
108C11×#117C2311yescharacteristic
109C11×#117C2312yes—
110C2×C11×C4⋊C4C2×C412yes—
111C2×C11×C4⋊C4C2×C412yes—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4D412yes—
115C2×C42×C11—22no—
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120#66979—24no—
121#66979—42no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—22no—
124C2×C4×Dic11—21no—
125C2×C4×Dic11—21no—
126C2×C4×Dic11C2311yescharacteristic
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×#4318—22no—
130C2×#4318—24no—
131C2×#4318—42no—
132C2×#4318C2311yescharacteristic
133C2×#4318C2312yes—
134C2×#4318C2311yescharacteristic
135C22×C11⋊C8—22no—
136#66901—22no—
137#66901—22no—
138#66901—42no—
139C11⋊#95—21no—
140C11⋊#95—22no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)—21no—
145#66867—21no—
146C4×C11⋊C8—21no—
147#22507—111nomaximal, Sylow
148C24×C11C2×D412yes—
149C11×#41—21no—
150C11×#41—21no—
151C11×#41—21no—
152C11×#41—21no—
153C11×#41—44no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11C22×C411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—42no—
161C2×D4×C11C22⋊C411yescharacteristic
162C2×D4×C11C22⋊C411yescharacteristic
163C2×D4×C11C22⋊C412yes—
164C2×D4×C11C22×C411yescharacteristic
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22×C412yes—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4C22⋊C411yescharacteristic
196C11×C4⋊C4C22⋊C411yescharacteristic
197C11×C4⋊C4C22⋊C412yes—
198C11×C4⋊C4C22×C411yescharacteristic
199C11×C4⋊C4C22×C411yescharacteristic
200C11×C4⋊C4C22×C412yes—
201C11×C4⋊C4C22×C412yes—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4C22⋊C412yes—
213C11×C22⋊C4C22⋊C412yes—
214C11×C22⋊C4C22⋊C412yes—
215C11×C22⋊C4C22⋊C412yes—
216C42×C11—22no—
217C42×C11—21no—
218C42×C11—22no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—22no—
222C42×C11C22×C411yescharacteristic
223C42×C11C22×C411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C22⋊Dic11—44no—
227C22⋊Dic11—44no—
228C4⋊Dic11—44no—
229C4⋊Dic11—42no—
230C4×Dic11—21no—
231C4×Dic11—22no—
232C4×Dic11—21no—
233C4×Dic11—22no—
234C4×Dic11—21no—
235C4×Dic11—42no—
236C4×Dic11—42no—
237C4×Dic11#4112yescomplemented
238#4318—21no—
239#4318—22no—
240#4318—21no—
241#4318—22no—
242#4318—21no—
243#4318—44no—
244#4318#4112yescomplemented
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—44no—
249#3475D1111yescharacteristic
250D4×M16—111no—
251#2293—111no—
252#1994—111no—
253#1986—111no—
254#1897—112no—
255#1871—112no—
256#1826—112no—
257#1806—111no—
258C4×#104—111no—
259#1733—112no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—21no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11C2×C22⋊C412yes—
266C23×C11C2×C22⋊C412yes—
267C23×C11C22×D411yescharacteristic
268Q8×C11—21no—
269Q8×C11—21no—
270Q8×C11—42no—
271Q8×C11—81no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—22no—
275D4×C11—22no—
276D4×C11—42no—
277D4×C11—44no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—82no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—41no—
298C2×C4×C11—44no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—42no—
302C2×C4×C11—81no—
303C2×C4×C11—82no—
304C2×C4×C11C2×C22⋊C412yes—
305C2×C4×C11C2×C22⋊C411yescharacteristic
306C2×C4×C11C2×C22⋊C411yescharacteristic
307C2×C4×C11C2×C22⋊C411yescharacteristic
308C2×C4×C11C2×C22⋊C412yes—
309C2×C4×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C23×C411yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C112−1+411yescharacteristic
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C11⋊C8—22no—
326C11⋊C8—42no—
327C11⋊C8—41no—
328C22×M16—112no—
329#556Dic1111yescharacteristic, complemented
330#555Dic1111yescharacteristic, complemented
331#554Dic1111yescharacteristic, complemented
332#553Dic1112yescomplemented
333#552—21no—
334#552Dic1112yescomplemented
335#551—22no—
336#547Dic1111yescharacteristic, complemented
337#546—21no—
338#533C2×D1111yescharacteristic
339#529—22no—
340#529—21no—
341#525C2×D1112yes—
342C4×#41—21no—
343C4×#41C2×D1111yescharacteristic
344C2×C4×D4C2×D1111yescharacteristic
345C2×#117—112no—
346C2×#117C2×D1112yes—
347#436—221no—
348#435—222no—
349C8×D4—221no—
350#423—111no—
351C2×#104—111no—
352C2×#104—111no—
353C2×#104—112no—
354#407—112no—
355C4×M16—111no—
356#390—221no—
357#389—221no—
358#388—222no—
359C4×C4⋊C4—111no—
360C4×C22⋊C4—112no—
361C43—111no—
362#339—112no—
363#339—111no—
364#339—112no—
365#339—112no—
366#339—112no—
367#339—112no—
368#339—111no—
369C22×C11—21no—
370C22×C11—21no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—82no—
381C22×C11—82no—
382C22×C11C22×C22⋊C411yescharacteristic
383C22×C11#54611yescharacteristic
384C22×C11#54711yescharacteristic
385C4×C11—22no—
386C4×C11—22no—
387C4×C11—21no—
388C4×C11—21no—
389C4×C11—21no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—42no—
395C4×C11#42112yes—
396C4×C11C4×#4111yescharacteristic
397C4×C11#52011yescharacteristic
398C4×C11#54611yescharacteristic
399C4×C11#54711yescharacteristic
400Dic11—42no—
401Dic11—42no—
402Dic11—82no—
403C2×#41—21no—
404C2×#41C22×D1111yescharacteristic
405C22×D4C22⋊D1111yescharacteristic
406C23×C4C22×D1112yes—
407C2×M16—111no—
408C2×M16—112no—
409C2×M16—111no—
410C2×M16—222no—
411C2×M16—224no—
412C2×M16—442no—
413C22×C8—222no—
414C4⋊Q8C2×Dic1111yescharacteristic
415C4⋊Q8C2×Dic1111yescharacteristic
416#126—22no—
417#126—22no—
418#126—22no—
419#125—22no—
420#125—21no—
421#125C2×Dic1112yes—
422#124—21no—
423#124—22no—
424#123—22no—
425#123—22no—
426#123—22no—
427#123—22no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—22no—
432C22⋊Q8C2×Dic1112yes—
433C22⋊Q8C2×Dic1112yes—
434#121—22no—
435#121—21no—
436#121C2×Dic1112yes—
437#121C2×Dic1112yes—
438#120—22no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8C2×Dic1111yescharacteristic
443C4×Q8C2×Dic1111yescharacteristic
444C4×D4—21no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4C2×Dic1111yescharacteristic
451C4×D4C2×Dic1111yescharacteristic
452C4×D4C2×Dic1111yescharacteristic
453C4×D4C2×Dic1112yes—
454C4×D4C2×Dic1111yescharacteristic
455C4×D4C22⋊D1111yescharacteristic
456C4×D4C22⋊D1111yescharacteristic
457C4×D4C22⋊D1112yes—
458#117—22no—
459#117—22no—
460#117—21no—
461#117—22no—
462#117—21no—
463#117—224no—
464#117—442no—
465#117C2×Dic1112yes—
466#117C2×Dic1112yes—
467#117C22×D1111yescharacteristic
468#117C22×D1112yes—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4C2×Dic1112yes—
472C2×C4⋊C4C2×Dic1112yes—
473C2×C4⋊C4C22⋊D1111yescharacteristic
474C2×C22⋊C4—22no—
475C2×C22⋊C4—222no—
476C2×C22⋊C4—222no—
477C2×C22⋊C4C22⋊D1112yes—
478C2×C42—22no—
479C2×C42—21no—
480C2×C42—111no—
481C2×C42—112no—
482C2×C42—111no—
483C2×C42—221no—
484C2×C42—221no—
485C2×C42C22×D1111yescharacteristic
486C4⋊C8—221no—
487C4⋊C8—221no—
488#104—222no—
489#104—222no—
490#104—442no—
491C22⋊C8—222no—
492C22⋊C8—222no—
493#97—221no—
494C4×C8—221no—
495#95—222no—
496#95—221no—
497C2×C11—21no—
498C2×C11—21no—
499C2×C11—42no—
500C2×C11—42no—
501C2×C11—81no—
502C2×C11#233911yescharacteristic
503C2×C11C2×#42111yescharacteristic
504C2×C11#290111yescharacteristic
505C24C2×C22⋊D1112yes—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510#41—44no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×Dic1111yescharacteristic
514C2×D4—22no—
515C2×D4—21no—
516C2×D4—22no—
517C2×D4—42no—
518C2×D4C22⋊Dic1111yescharacteristic
519C2×D4C22⋊Dic1111yescharacteristic
520C2×D4C22⋊Dic1112yes—
521C2×D4C22×Dic1111yescharacteristic
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—222no—
534C22×C4C22×Dic1112yes—
535C22×C4C22×Dic1112yes—
536C22×C4C2×C22⋊D1112yes—
537C22×C4C2×C22⋊D1111yescharacteristic
538C22×C4C2×C22⋊D1112yes—
539C22×C4C2×C22⋊D1112yes—
540C22×C4C2×C22⋊D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542M16—112no—
543M16—221no—
544M16—221no—
545M16—222no—
546M16—222no—
547M16—221no—
548M16—444no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—222no—
552C2×C8—444no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—444no—
564C4⋊C4—442no—
565C4⋊C4C22⋊Dic1111yescharacteristic
566C4⋊C4C22⋊Dic1111yescharacteristic
567C4⋊C4C22⋊Dic1112yes—
568C4⋊C4C22×Dic1111yescharacteristic
569C4⋊C4C22×Dic1111yescharacteristic
570C4⋊C4C22×Dic1112yes—
571C4⋊C4C22×Dic1112yes—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—21no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—22no—
582C22⋊C4—444no—
583C22⋊C4—444no—
584C22⋊C4C22⋊Dic1112yes—
585C22⋊C4C22⋊Dic1112yes—
586C22⋊C4C22⋊Dic1112yes—
587C22⋊C4C22⋊Dic1112yes—
588C42—22no—
589C42—21no—
590C42—22no—
591C42—21no—
592C42—21no—
593C42—22no—
594C42—112no—
595C42—221no—
596C42—221no—
597C42—222no—
598C42—222no—
599C42—221no—
600C42—442no—
601C42—442no—
602C42C22×Dic1111yescharacteristic
603C42C22×Dic1111yescharacteristic
604C42C2×C22⋊D1111yescharacteristic
605C42C2×C22⋊D1111yescharacteristic
606C11#2250711yescharacteristic, complemented, Sylow
607C23—22no—
608C23—22no—
609C23—21no—
610C23—42no—
611C23—42no—
612C23C2×C22⋊Dic1112yes—
613C23C2×C22⋊Dic1112yes—
614C23C22×C22⋊D1111yescharacteristic
615Q8—21no—
616Q8—21no—
617Q8—42no—
618Q8—81no—
619D4—21no—
620D4—21no—
621D4—22no—
622D4—22no—
623D4—42no—
624D4—44no—
625D4—41no—
626D4—41no—
627D4—82no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—41no—
645C2×C4—44no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—81no—
650C2×C4—82no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—442no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4C2×C22⋊Dic1112yes—
661C2×C4C2×C22⋊Dic1111yescharacteristic
662C2×C4C2×C22⋊Dic1111yescharacteristic
663C2×C4C2×C22⋊Dic1111yescharacteristic
664C2×C4C2×C22⋊Dic1112yes—
665C2×C4C2×C22⋊Dic1111yescharacteristic
666C2×C4#41×D1111yescharacteristic
667C2×C4#41×D1111yescharacteristic
668C2×C4#6704211yescharacteristic
669C2×C4#6704311yescharacteristic
670C2×C4C23×Dic1111yescharacteristic
671C2×C4C22×C22⋊D1111yescharacteristic
672C8—222no—
673C8—441no—
674C8—442no—
675C22—21no—
676C22—21no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—82no—
687C22—82no—
688C22#1062335511yescharacteristic
689C22#1062336011yescharacteristic
690C22C22×C22⋊Dic1111yescharacteristic
691C4—22no—
692C4—22no—
693C4—21no—
694C4—21no—
695C4—21no—
696C4—41no—
697C4—41no—
698C4—42no—
699C4—41no—
700C4—42no—
701C4—442no—
702C4—442no—
703C4—882no—
704C4#1062284912yes—
705C4#1062335511yescharacteristic
706C4#41×Dic1111yescharacteristic
707C4#1062335811yescharacteristic
708C4#1062336011yescharacteristic
709C2—21no—
710C2—21no—
711C2—42no—
712C2—42no—
713C2—81no—
714C2#1307144611yescharacteristic
715C2C2×#1062284911yescharacteristic
716C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3475D11
hypocenterC11#22507
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. D4×#4318C2semidirect
2. #13071081C2semidirect
3. #13069594C2semidirect
4. #13069561C2semidirect
5. #13069065C2semidirect
6. #13068919C2semidirect
7. #13068715C2semidirect
8. #13068636C2semidirect
9. C4×#66901C2semidirect
10. #13068325C2semidirect
12. C11×#556C4semidirect
13. C11×#555C4semidirect
14. C11×#554C4semidirect
15. C11×#553C4semidirect
17. C11×#552C4semidirect
19. C11×#547C4semidirect
237. C4×Dic11#41semidirect
244. #4318#41semidirect
329. #556Dic11semidirect
330. #555Dic11semidirect
331. #554Dic11semidirect
332. #553Dic11semidirect
334. #552Dic11semidirect
336. #547Dic11semidirect
606. C11#22507semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
#130710812
#130695942
#130695612
#130690652
#130689192
#130687152
#130686362
C4×#669012
#130683252
C11×#34752
#2250711