Finite Group Databasebeta

← #14770064

Subgroups — #14770064

Order 2816.

1194 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×#10623170C211yesmaximal, characteristic
2C2×#10622341C211yesmaximal, characteristic
3C4⋊C4×C22⋊D11C211yesmaximal, characteristic
4#13069583C211yesmaximal, characteristic, complemented
5#13069570C211yesmaximal, characteristic, complemented
6#13069050C211yesmaximal, characteristic, complemented
7#13069036C211yesmaximal, characteristic, complemented
8#13068920C211yesmaximal, characteristic, complemented
9#13068712C211yesmaximal, characteristic, complemented
10#13068701C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#13068448C211yesmaximal, characteristic, complemented
13#13068335C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25#10623170—24no—
26#10623170C418yescomplemented
27C2×#66945—21no—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66943C2211yescharacteristic
31C2×#66942—21no—
32C2×#66936—21no—
33C2×#66932—21no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622825C2211yescharacteristic
40#10622823—21no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44#10622602—21no—
45#10622600C2211yescharacteristic
46#10622589C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48#10622585—21no—
49#10622341—24no—
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×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11D411yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8C2×C414yescomplemented
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84#66999—22no—
85#66999C2×C414yescomplemented
86Q8×Dic11—22no—
87Q8×Dic11C2×C414yescomplemented
88C4×C22⋊D11—44no—
89C4×C22⋊D11C2×C414yes—
90C4×C22⋊D11D414yes—
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—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4D411yescharacteristic
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11C2311yescharacteristic
113C2×#4318—22no—
114C2×#4318—22no—
115C2×#4318—41no—
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—41no—
121#66945—28no—
122C4⋊C4×D11—22no—
123C4⋊C4×D11—22no—
124C4⋊C4×D11—41no—
125C4⋊C4×D11C2×C414yescomplemented
126#66943—22no—
127#66943C2×C414yescomplemented
128#66942—28no—
129#66936—28no—
130#66932—28no—
131C11×#103—22no—
132C11×#103—41no—
133C11×C22⋊C8—22no—
134#66899—22no—
135#66899—41no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139(C2×D11)⋊C8—22no—
140#66879—22no—
141Dic11⋊C8—22no—
142#22491—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×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—81no—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—22no—
167C2×C22⋊D11—22no—
168C2×C22⋊D11C22⋊C414yes—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176C2×C4×D11—24no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×C4×D11—81no—
186C2×C4×D11C22×C412yes—
187C2×C4×D11C2×D412yes—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4C22×C412yes—
201C11×C4⋊C4#4112yes—
202C11×C22⋊C4—24no—
203C22⋊Dic11—24no—
204C22⋊Dic11—42no—
205C22⋊Dic11C22⋊C414yes—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—42no—
208(C2×D11)⋊C4C22⋊C414yes—
209C4⋊Dic11—24no—
210C4⋊Dic11—24no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11C22×C412yes—
218C4⋊Dic11C22×C412yes—
219Dic11⋊C4—24no—
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—42no—
229C4×Dic11C22×C412yes—
230C4×Dic11C2×D412yes—
231#4318—44no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8#4112yes—
238C8×D11—44no—
239C2×#552—111no—
240C2×#435—111no—
241D4×C4⋊C4—111no—
242#1992—111no—
243#1989—111no—
244#1894—111no—
245#1892—111no—
246#1872—111no—
247#1872D1111yescharacteristic, complemented
248#1825—111no—
249#1823—111no—
250#1803—111no—
251#1763—111no—
252#1736—111no—
253C2×#340—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×D11C2×C22⋊C412yes—
267C22×D11AGL(1,ℤ/8)12yes—
268C22×D11#13712yes—
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—22no—
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×C11—84no—
292C2×C4×C11C2×C22⋊C412yes—
293C2×C4×C11C23×C411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11H(5,𝔽2)11yescharacteristic
298C2×C4×C112−1+411yescharacteristic
299C22⋊D11—28no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11C2×C22⋊C412yes—
319C2×Dic11C2×C22⋊C412yes—
320C2×Dic11C2×C22⋊C412yes—
321C4×D11—22no—
322C4×D11—22no—
323C4×D11—22no—
324C4×D11—22no—
325C4×D11—48no—
326C4×D11—84no—
327C8×C11—41no—
328C8×C11—41no—
329C11⋊C8—22no—
330C11⋊C8—41no—
331C22×M16—111no—
332C23×C8—111no—
333#552—118no—
334#552—224no—
335C2×#126—221no—
336C2×#125—111no—
337C2×#125—221no—
338C2×#123—221no—
339C2×C22⋊Q8—111no—
340C2×C22⋊Q8C2×D1111yescharacteristic
341C2×C4×Q8—111no—
342C2×C4×D4—111no—
343C2×C4×D4—221no—
344C2×#117—111no—
345C2×#117—221no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4C2×D1111yescharacteristic
349#435—224no—
350C2×C4⋊C8—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103C2×D1111yescharacteristic
354C2×#103C2×D1111yescharacteristic
355C2×C22⋊C8—111no—
356C2×C22⋊C8C2×D1111yescharacteristic
357C2×#97—111no—
358#389—221no—
359#385—221no—
360#385—221no—
361#384—111no—
362#380—111no—
363#380—111no—
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—22no—
395C2×D11—22no—
396C2×D11—22no—
397C2×D11#41714yes—
398C4×C11—22no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—81no—
403C4×C11C4×#4111yescharacteristic
404C4×C11#52011yescharacteristic
405C4×C11#54611yescharacteristic
406C4×C11#54711yescharacteristic
407Dic11—22no—
408Dic11—22no—
409Dic11—22no—
410Dic11—42no—
411Dic11—42no—
412Dic11—81no—
413Dic11—81no—
414C22×Q8C22×D1111yescharacteristic
415C22×D4—111no—
416C23×C4—21no—
417C23×C4—111no—
418C23×C4—221no—
419C23×C4—221no—
420C23×C4C22×D1111yescharacteristic
421C2×M16—222no—
422C2×M16—222no—
423C2×M16—441no—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8—222no—
427C22×C8—222no—
428C22×C8—441no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431#126—228no—
432#125—114no—
433#125—222no—
434#125—228no—
435#123—228no—
436C22⋊Q8—22no—
437C22⋊Q8—114no—
438C22⋊Q8—222no—
439C22⋊Q8C4×D1114yescomplemented
440C4×Q8—114no—
441C4×Q8—222no—
442C4×D4—114no—
443C4×D4—114no—
444C4×D4—444no—
445#117—114no—
446#117—228no—
447#117—222no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—221no—
460C2×C4⋊C4—221no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—222no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—441no—
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C4⋊C4C22×D1111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C42—111no—
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—22no—
489C22⋊C8—222no—
490#97—222no—
491#95—221no—
492#95—221no—
493#95—221no—
494C2×C11—42no—
495C2×C11#233911yescharacteristic
496C2×C11C2×#41711yescharacteristic
497C2×C11#289811yescharacteristic
498C2×C11#331011yescharacteristic
499C2×C11#331211yescharacteristic
500C2×C11#334311yescharacteristic
501C2×C11#334411yescharacteristic
502D11—24no—
503C24—111no—
504C24D4×D1111yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C2×C4×D1112yes—
511C2×D4—114no—
512C2×D4—222no—
513C2×D4—222no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—111no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—224no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—442no—
540C22×C4—442no—
541C22×C4—442no—
542C22×C4—442no—
543C22×C4—881no—
544C22×C4C2×C4×D1112yes—
545C22×C4D4×D1111yescharacteristic
546C22×C4D4×D1112yes—
547C22×C4C23×D1111yescharacteristic
548M16—444no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—112no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—444no—
562C4⋊C4—24no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—114no—
569C4⋊C4—112no—
570C4⋊C4—112no—
571C4⋊C4—224no—
572C4⋊C4—224no—
573C4⋊C4—224no—
574C4⋊C4—224no—
575C4⋊C4—224no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—221no—
582C4⋊C4—442no—
583C4⋊C4—442no—
584C4⋊C4—881no—
585C4⋊C4C2×C4×D1112yes—
586C4⋊C4#434112yes—
587C22⋊C4—24no—
588C22⋊C4—114no—
589C22⋊C4—114no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—442no—
593C22⋊C4—442no—
594C42—112no—
595C42—112no—
596C42—224no—
597C42—224no—
598C42—442no—
599C11#2249111yescharacteristic, complemented, Sylow
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—112no—
607C23—112no—
608C23—112no—
609C23—221no—
610C23—221no—
611C23—221no—
612C23—221no—
613C23C22⋊C4×D1112yes—
614C23C2×D4×D1111yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—228no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
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—84no—
639C2×C4—112no—
640C2×C4—112no—
641C2×C4—112no—
642C2×C4—221no—
643C2×C4—221no—
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—448no—
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—441no—
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—41no—
674C8—41no—
675C8—222no—
676C8—441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—114no—
685C22—222no—
686C22—222no—
687C22—222no—
688C22—222no—
689C22—222no—
690C22—222no—
691C22C2×C22⋊C4×D1111yescharacteristic
692C22#1062312211yescharacteristic
693C22#1062318611yescharacteristic
694C22#1062329311yescharacteristic
695C22#1062329711yescharacteristic
696C22D11×AGL(1,ℤ/8)11yescharacteristic
697C22D11×#13711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—222no—
704C4—222no—
705C4—222no—
706C4—442no—
707C4—442no—
708C4—881no—
709C4—881no—
710C4C4×#434111yescharacteristic
711C4#1062307711yescharacteristic
712C4#1062314111yescharacteristic
713C4#1062314211yescharacteristic
714C2—42no—
715C2—224no—
716C2#1307144211yescharacteristic
717C2D11×#41711yescharacteristic
718C2#1307714411yescharacteristic
719C2#1308063011yescharacteristic
720C2#1308066011yescharacteristic
721C2#1308105911yescharacteristic
722C2#1308107411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11#22491
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #13069583C2semidirect
5. #13069570C2semidirect
6. #13069050C2semidirect
7. #13069036C2semidirect
8. #13068920C2semidirect
9. #13068712C2semidirect
10. #13068701C2semidirect
11. #13068619C2semidirect
12. #13068448C2semidirect
13. #13068335C2semidirect
14. D11×#340C2semidirect
15. C11×#1872C2semidirect
26. #10623170C4semidirect
72. C11×C22⋊Q8C2×C4semidirect
85. #66999C2×C4semidirect
87. Q8×Dic11C2×C4semidirect
95. #66979C2×C4semidirect
125. C4⋊C4×D11C2×C4semidirect
127. #66943C2×C4semidirect
247. #1872D11semidirect
439. C22⋊Q8C4×D11semidirect
599. C11#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#106231702
C2×#106223412
C4⋊C4×C22⋊D112
#130695832
#130695702
#130690502
#130690362
#130689202
#130687122
#130687012
#130686192
#130684482
#130683352
D11×#3402
C11×#18722
#2249111