Finite Group Databasebeta

← #14770239

Subgroups — #14770239

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623172C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic
3#13071512C211yesmaximal, characteristic
4#13069575C211yesmaximal, characteristic, complemented
5#13069566C211yesmaximal, characteristic, complemented
6#13069046C211yesmaximal, characteristic, complemented
7#13068924C211yesmaximal, characteristic, complemented
8#13068920C211yesmaximal, characteristic, complemented
9#13068710C211yesmaximal, characteristic, complemented
10#13068708C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#103×Dic11C211yesmaximal, characteristic, complemented
13#13068336C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1894C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24#10623172—24no—
25#10623172C418yescomplemented
26C2×#66951—21no—
27C2×#66945C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×#66941C2211yescharacteristic
30C2×#66940—21no—
31C2×#66938—21no—
32C2×(C22⋊D11)⋊C4—21no—
33C2×#66932—21no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C11×#380C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622741—24no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622589C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47#10622559—21no—
48#10622281—21no—
49#10622260—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C23×Dic11—21no—
66C22×C4×D11—21no—
67C22×C4×D11C2311yescharacteristic
68C22×Dic22—21no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2×C414yescomplemented
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84#66999—22no—
85#66999C2×C414yescomplemented
86Q8×Dic11—22no—
87Q8×Dic11C2×C414yescomplemented
88C4×C22⋊D11C2×C414yes—
89C4×C22⋊D11D414yes—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4D411yescharacteristic
94#66979—22no—
95#66979C2×C414yescomplemented
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—41no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4D411yescharacteristic
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4313—22no—
118C2×#4313—22no—
119C2×#4313—41no—
120#66951—28no—
121#66945—22no—
122#66945C2×C414yescomplemented
123C4⋊C4×D11—22no—
124C4⋊C4×D11—41no—
125#66941—22no—
126#66941C2×C414yescomplemented
127#66940—28no—
128#66938—28no—
129(C22⋊D11)⋊C4—44no—
130#66932—28no—
131C11×#103—22no—
132C11×#103—41no—
133C11×#95—21no—
134#66899—22no—
135#66899—41no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C22⋊(C11⋊C8)—22no—
139(C2×D11)⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142#22504—111nomaximal, Sylow
143C24×C11C2×D411yescharacteristic
144C23×D11C2×D411yescharacteristic
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11C22⋊C414yes—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—81no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×C4×D11—81no—
183C2×C4×D11C22×C412yes—
184C2×C4×D11C2×D412yes—
185C2×Dic22—24no—
186C2×Dic22—42no—
187C2×Dic22—42no—
188C11×M16—44no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11#4112yes—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4C22×C412yes—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—42no—
204C22⋊Dic11—24no—
205C22⋊Dic11C22⋊C414yes—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4C22⋊C414yes—
210C4⋊Dic11—24no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—42no—
217C4⋊Dic11C22×C412yes—
218C4⋊Dic11C22×C412yes—
219C4⋊Dic11#4112yes—
220Dic11⋊C4—24no—
221Dic11⋊C4—24no—
222Dic11⋊C4—42no—
223Dic11⋊C4—42no—
224Dic11⋊C4—81no—
225Dic11⋊C4C22⋊C414yes—
226C4×Dic11—24no—
227C4×Dic11—24no—
228C4×Dic11—24no—
229C4×Dic11—42no—
230C4×Dic11C22×C412yes—
231C4×Dic11C2×D412yes—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238#4313—44no—
239C2×#556—111no—
240C2×#436—111no—
241D4×C4⋊C4—111no—
242#1990—111no—
243#1988—111no—
244#1894—111no—
245#1894D1111yescharacteristic, complemented
246#1872—111no—
247#1872—111no—
248#1825—111no—
249#1825—111no—
250#1803—111no—
251C4×#103—111no—
252#1736—111no—
253#1736—111no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11C2×C22⋊C412yes—
261C23×C11C22×D411yescharacteristic
262C22×D11—21no—
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11C2×C22⋊C412yes—
269Q8×C11—22no—
270Q8×C11—22no—
271Q8×C11—41no—
272Q8×C11—41no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11C2×C22⋊C412yes—
292C2×C4×C11C23×C411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C2×C4×C112−1+411yescharacteristic
298C22⋊D11—28no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—84no—
316C2×Dic11C2×C22⋊C412yes—
317C2×Dic11C2×C22⋊C412yes—
318C2×Dic11C2×C22⋊C412yes—
319C2×Dic11AGL(1,ℤ/8)12yes—
320C2×Dic11#13712yes—
321C4×D11—22no—
322C4×D11—22no—
323C4×D11—22no—
324C4×D11—22no—
325C4×D11—84no—
326Dic22—48no—
327C8×C11—22no—
328C8×C11—41no—
329C11⋊C8—41no—
330C11⋊C8—41no—
331C22×M16—111no—
332C22×M16C2×D1111yescharacteristic
333#556—118no—
334#556—224no—
335C2×C4⋊Q8—111no—
336C2×#126—221no—
337C2×#126—221no—
338C2×#124—221no—
339C2×C22⋊Q8—111no—
340C2×C22⋊Q8C2×D1111yescharacteristic
341C2×C4×Q8—111no—
342C2×C4×Q8—221no—
343C2×C4×D4—111no—
344C2×C4×D4—221no—
345C2×#117—111no—
346C2×#117—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—111no—
349#436—224no—
350C2×C4⋊C8—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103C2×D1111yescharacteristic
354C2×#103C2×D1111yescharacteristic
355C2×C22⋊C8—111no—
356C2×C22⋊C8—111no—
357C2×C4×C8—111no—
358#389—221no—
359#385—221no—
360#385—221no—
361#384—111no—
362#380—111no—
363#380C2×D1111yescharacteristic
364C4×C4⋊C4—111no—
365#340—111no—
366#340—111no—
367#340—111no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340C2×D1111yescharacteristic
376#340C2×D1111yescharacteristic
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11C22×C22⋊C411yescharacteristic
385C22×C11#54611yescharacteristic
386C22×C11#54711yescharacteristic
387C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C11C2×#13711yescharacteristic
389C22×C11#57711yescharacteristic
390C22×C11#57811yescharacteristic
391C2×D11—22no—
392C2×D11—22no—
393C2×D11—22no—
394C2×D11—41no—
395C2×D11—41no—
396C2×D11—41no—
397C2×D11—41no—
398C4×C11—22no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11C4×#4111yescharacteristic
404C4×C11#52011yescharacteristic
405C4×C11#54611yescharacteristic
406C4×C11#54711yescharacteristic
407Dic11—22no—
408Dic11—22no—
409Dic11—42no—
410Dic11—42no—
411Dic11—42no—
412Dic11—81no—
413Dic11#41714yes—
414C22×Q8—221no—
415C22×Q8C22×D1111yescharacteristic
416C22×D4—111no—
417C23×C4—111no—
418C23×C4—221no—
419C23×C4—221no—
420C23×C4C22×D1111yescharacteristic
421C2×M16—22no—
422C2×M16—22no—
423C2×M16—41no—
424C2×M16—222no—
425C2×M16—222no—
426C2×M16—441no—
427C22×C8—111no—
428C22×C8—111no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431C4⋊Q8—114no—
432C4⋊Q8—222no—
433#126—228no—
434#126—228no—
435#124—228no—
436C22⋊Q8—22no—
437C22⋊Q8—114no—
438C22⋊Q8—222no—
439C22⋊Q8C4×D1114yescomplemented
440C4×Q8—114no—
441C4×Q8—222no—
442C4×Q8—228no—
443C4×D4—114no—
444C4×D4—114no—
445C4×D4—444no—
446#117—114no—
447#117—114no—
448#117—222no—
449#117—222no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—221no—
459C2×C4⋊C4—221no—
460C2×C4⋊C4—221no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—441no—
466C2×C4⋊C4—441no—
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C42—111no—
479C2×C42—221no—
480C2×C42—221no—
481C2×C42—221no—
482C2×C42—221no—
483C4⋊C8—222no—
484#103—22no—
485#103—41no—
486#103—222no—
487#103—441no—
488C22⋊C8—222no—
489C22⋊C8—222no—
490C4×C8—222no—
491#95—21no—
492#95—221no—
493#95—221no—
494C2×C11—42no—
495C2×C11#233911yescharacteristic
496C2×C11C2×#41711yescharacteristic
497C2×C11#289811yescharacteristic
498C2×C11#332411yescharacteristic
499C2×C11#332811yescharacteristic
500C2×C11#335311yescharacteristic
501C2×C11#335611yescharacteristic
502D11—42no—
503C24—111no—
504C24D4×D1111yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—224no—
511C2×Q8—442no—
512C2×Q8—442no—
513C2×Q8C2×C4×D1112yes—
514C2×D4—114no—
515C2×D4—222no—
516C2×D4—222no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—111no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—442no—
539C22×C4—442no—
540C22×C4—442no—
541C22×C4—442no—
542C22×C4—881no—
543C22×C4—881no—
544C22×C4C2×C4×D1112yes—
545C22×C4D4×D1111yescharacteristic
546C22×C4D4×D1112yes—
547C22×C4C23×D1111yescharacteristic
548M16—44no—
549M16—444no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8#434112yes—
562C4⋊C4—24no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—114no—
569C4⋊C4—112no—
570C4⋊C4—112no—
571C4⋊C4—112no—
572C4⋊C4—224no—
573C4⋊C4—224no—
574C4⋊C4—224no—
575C4⋊C4—221no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—442no—
581C4⋊C4—442no—
582C4⋊C4—442no—
583C4⋊C4—881no—
584C4⋊C4C2×C4×D1112yes—
585C22⋊C4—24no—
586C22⋊C4—42no—
587C22⋊C4—114no—
588C22⋊C4—114no—
589C22⋊C4—224no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—442no—
593C42—112no—
594C42—112no—
595C42—224no—
596C42—224no—
597C42—224no—
598C42—442no—
599C11#2250411yescharacteristic, complemented, Sylow
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—112no—
607C23—221no—
608C23—221no—
609C23—221no—
610C23—221no—
611C23—221no—
612C23—221no—
613C23C22⋊C4×D1112yes—
614C23C2×D4×D1111yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—448no—
620D4—228no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—112no—
640C2×C4—112no—
641C2×C4—112no—
642C2×C4—112no—
643C2×C4—112no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4—884no—
665C2×C4—884no—
666C2×C4C22⋊C4×D1112yes—
667C2×C4C22×C4×D1111yescharacteristic
668C2×C4C2×D4×D1111yescharacteristic
669C2×C4C2×#434111yescharacteristic
670C2×C4#6703711yescharacteristic
671C2×C4#41×D1111yescharacteristic
672C2×C4#6704311yescharacteristic
673C8—22no—
674C8—41no—
675C8—441no—
676C8—441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—222no—
685C22—222no—
686C22—222no—
687C22—441no—
688C22—441no—
689C22—441no—
690C22—441no—
691C22C2×C22⋊C4×D1111yescharacteristic
692C22#1062314111yescharacteristic
693C22#1062314211yescharacteristic
694C22D11×AGL(1,ℤ/8)11yescharacteristic
695C22D11×#13711yescharacteristic
696C22#1062330911yescharacteristic
697C22#1062331011yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—114no—
704C4—222no—
705C4—222no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4—881no—
710C4C4×#434111yescharacteristic
711C4#1062307711yescharacteristic
712C4#1062312211yescharacteristic
713C4#1062318611yescharacteristic
714C2—42no—
715C2—442no—
716C2#1307144211yescharacteristic
717C2D11×#41711yescharacteristic
718C2#1307714811yescharacteristic
719C2#1308084211yescharacteristic
720C2#1308089411yescharacteristic
721C2#1308119511yescharacteristic
722C2#1308122611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11#22504
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #13069575C2semidirect
5. #13069566C2semidirect
6. #13069046C2semidirect
7. #13068924C2semidirect
8. #13068920C2semidirect
9. #13068710C2semidirect
10. #13068708C2semidirect
11. #13068619C2semidirect
12. #103×Dic11C2semidirect
13. #13068336C2semidirect
14. #13068334C2semidirect
15. C11×#1894C2semidirect
25. #10623172C4semidirect
75. C11×C22⋊Q8C2×C4semidirect
85. #66999C2×C4semidirect
87. Q8×Dic11C2×C4semidirect
95. #66979C2×C4semidirect
122. #66945C2×C4semidirect
126. #66941C2×C4semidirect
245. #1894D11semidirect
439. C22⋊Q8C4×D11semidirect
599. C11#22504semidirect

Maximal subgroups

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

subgroupindex
C2×#106231722
C2×#106227412
#130715122
#130695752
#130695662
#130690462
#130689242
#130689202
#130687102
#130687082
#130686192
#103×Dic112
#130683362
#130683342
C11×#18942
#2250411