Finite Group Databasebeta

← #14811295

Subgroups — #14811295

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic, complemented
2C2×#10622838C211yesmaximal, characteristic
3#13072329C211yesmaximal, characteristic
4#13070154C211yesmaximal, characteristic, complemented
5#13069997C211yesmaximal, characteristic, complemented
6#13069997C211yesmaximal, characteristic, complemented
7#13069767C211yesmaximal, characteristic, complemented
8#13068884C211yesmaximal, characteristic, complemented
9#13068870C211yesmaximal, characteristic, complemented
10#13068813C211yesmaximal, characteristic
11#13068801C211yesmaximal, characteristic
12#13068647C211yesmaximal, characteristic
13#13068621C211yesmaximal, characteristic, complemented
14#13068551C211yesmaximal, characteristic
15Q8×C11×C22⋊C4C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#391—21no—
23C11×#391—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#380—21no—
27C11×#380C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30#10622838—24no—
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622635—24no—
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622562—21no—
47#10622561—21no—
48#10622548C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622267—21no—
54#10622260—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—41no—
66C22×Q8×C11—41no—
67C22×Q8×C11Q814yes—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11—41no—
75C4×Q8×C11—41no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89#66979—22no—
90#66979—41no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×#4318—22no—
103C2×#4318—22no—
104C2×#4318—41no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66923—22no—
110#66923—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#66899—22no—
119#66899—22no—
120#66899—22no—
121#66899—22no—
122#66899—22no—
123#66899—41no—
124#66899—41no—
125#66899D414yes—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C22⋊(C11⋊C8)—22no—
130#66872—22no—
131#66872—41no—
132#66871—22no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—41no—
136#25981—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—28no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—42no—
149C2×Q8×C11—42no—
150C2×Q8×C11—44no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11C2×D412yes—
154C2×Q8×C11C2×Q812yes—
155C2×Q8×C11C2×Q812yes—
156C2×Q8×C11#4112yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×Q812yes—
174C22×C4×C11#4112yes—
175C22×C4×C11C2411yescharacteristic
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—42no—
194C42×C11—42no—
195C22⋊Dic11—42no—
196C22⋊Dic11—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—81no—
206C4⋊Dic11C2×D412yes—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211C4×Dic11—42no—
212#4318—44no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8C2×D412yes—
225C2×#479—111no—
226C2×#419—111no—
227#2441—111no—
228Q8×C22⋊C4D1111yescharacteristic
229#2095—111no—
230#2066—111no—
231#2066—111no—
232#2026—111no—
233#1865—111no—
234#1863—111no—
235#1854—111no—
236#1851—111no—
237#1809—111no—
238#1803—111no—
239#1787—111no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11C22⋊Q812yes—
247C23×C11C22×D411yescharacteristic
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—48no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11C22⋊Q814yes—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—48no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
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×C11C22⋊Q812yes—
288C2×C4×C11#13712yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×Q811yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×Dic11—22no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C23×Q8C2×D1111yescharacteristic
312C22×M16—111no—
313C2×#125—111no—
314C2×C4×Q8C2×D1111yescharacteristic
315C2×C4×Q8C2×D1111yescharacteristic
316C2×#117—111no—
317#479—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8—111no—
324#419—224no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×C22⋊C8—111no—
334#399—221no—
335#396—221no—
336#391—21no—
337#391—21no—
338#391C2×D1111yescharacteristic
339#391C2×D1111yescharacteristic
340#389—111no—
341#389—111no—
342#389—221no—
343#387—221no—
344#384—111no—
345#380—21no—
346#380—111no—
347#380C2×D1111yescharacteristic
348C4×C22⋊C4—21no—
349C4×C22⋊C4C2×D1111yescharacteristic
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#336—111no—
355#336—111no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11C2×C22⋊Q811yescharacteristic
364C22×C11D4211yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11C2×#13711yescharacteristic
367C22×C11#57511yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57811yescharacteristic
370C4×C11—22no—
371C4×C11—24no—
372C4×C11—22no—
373C4×C11—42no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11C2×C22⋊Q811yescharacteristic
380C4×C11#54311yescharacteristic
381C4×C11#54611yescharacteristic
382C4×C11#55111yescharacteristic
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387C22×Q8—22no—
388C22×Q8—21no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—41no—
392C22×Q8—41no—
393C22×Q8Dic2214yes—
394C22×Q8C22×D1111yescharacteristic
395C22×Q8C22×D1111yescharacteristic
396C23×C4—21no—
397C23×C4C22×D1111yescharacteristic
398C2×M16—222no—
399C2×M16—222no—
400C2×M16—441no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—111no—
405#125—222no—
406#125—441no—
407C4×Q8—22no—
408C4×Q8—22no—
409C4×Q8—41no—
410C4×Q8—41no—
411#117—222no—
412#117—441no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4C22⋊D1111yescharacteristic
431C2×C22⋊C4C22⋊D1111yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—221no—
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437#107—222no—
438#107—441no—
439#106—222no—
440#106—441no—
441C4⋊C8—222no—
442C4⋊C8—441no—
443#103—114no—
444#103—222no—
445#103—222no—
446#103—222no—
447#103—222no—
448#103—222no—
449#103—441no—
450#103—441no—
451C22⋊C8—222no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95C22⋊D1111yescharacteristic
461#95C22⋊D1111yescharacteristic
462C2×C11—42no—
463C2×C11#243711yescharacteristic
464C2×C11#307811yescharacteristic
465C2×C11#308211yescharacteristic
466C2×C11#327111yescharacteristic
467C2×C11#327611yescharacteristic
468C2×C11#332011yescharacteristic
469C2×C11#332711yescharacteristic
470C24C2×C22⋊D1111yescharacteristic
471C2×Q8—24no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—28no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8C2×Dic2212yes—
487C2×Q8C2×Dic2212yes—
488C2×Q8D4×D1112yes—
489C2×Q8#434112yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4C2×Dic2212yes—
506C22×C4#433912yes—
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513M16—444no—
514C2×C8—112no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—112no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—881no—
545C4⋊C4—881no—
546C22⋊C4—22no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—42no—
557C42—442no—
558C11#2598111yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#6697712yes—
566C23C22×C22⋊D1111yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—48no—
573Q8—41no—
574Q8—41no—
575Q8#6693114yes—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—48no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—222no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4#6697712yes—
619C2×C4#6699512yes—
620C2×C4C22×Dic2211yescharacteristic
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#6703711yescharacteristic
626C8—222no—
627C8—441no—
628C8—441no—
629C8—441no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22C2×#6697711yescharacteristic
638C22D4×C22⋊D1111yescharacteristic
639C22#1062333711yescharacteristic
640C22C2×#6699511yescharacteristic
641C22#1062335311yescharacteristic
642C22#1062336811yescharacteristic
643C22#1062336911yescharacteristic
644C4—22no—
645C4—24no—
646C4—22no—
647C4—41no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—81no—
652C4—81no—
653C4—442no—
654C4—881no—
655C4—881no—
656C4—881no—
657C4C2×#6693111yescharacteristic
658C4#1062301411yescharacteristic
659C4#1062302111yescharacteristic
660C4#1062302611yescharacteristic
661C2—42no—
662C2#1307227711yescharacteristic
663C2#1307842111yescharacteristic
664C2#1307845811yescharacteristic
665C2#1308020211yescharacteristic
666C2#1308026211yescharacteristic
667C2#1308078711yescharacteristic
668C2#1308088411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterQ8×C22⋊C4D11
hypocenterC11#25981
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
4. #13070154C2semidirect
5. #13069997C2semidirect
6. #13069997C2semidirect
7. #13069767C2semidirect
8. #13068884C2semidirect
9. #13068870C2semidirect
13. #13068621C2semidirect
558. C11#25981semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C2×#106228382
#130723292
#130701542
#130699972
#130697672
#130688842
#130688702
#130688132
#130688012
#130686472
#130686212
#130685512
Q8×C11×C22⋊C42
#2598111