Finite Group Databasebeta

← #14789977

Subgroups — #14789977

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C211yesmaximal, characteristic, complemented
2C2×#10622704C211yesmaximal, characteristic, complemented
3#13071298C211yesmaximal, characteristic
4#13069951C211yesmaximal, characteristic, complemented
5#13069941C211yesmaximal, characteristic, complemented
6#13069764C211yesmaximal, characteristic, complemented
7#13069754C211yesmaximal, characteristic, complemented
8#13069574C211yesmaximal, characteristic, complemented
9#13069569C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic
11#13068923C211yesmaximal, characteristic
12#13068815C211yesmaximal, characteristic
13#13068804C211yesmaximal, characteristic
14#13068600C211yesmaximal, characteristic
15C2×C11×#544C211yesmaximal, characteristic
16C11×#544—24no—
17C11×#544—24no—
18C2×C11×C4⋊Q8—21no—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×#125C2211yescharacteristic
23C2×C11×#125C2211yescharacteristic
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×#117C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622704—24no—
35#10622676—24no—
36#10622591—21no—
37#10622585—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622558—21no—
47#10622557—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×Dic22C2311yescharacteristic
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8D414yes—
73C11×#125—28no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#125—22no—
77C11×#125D414yes—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—28no—
80C11×#117—22no—
81C11×#117—22no—
82C11×#117—22no—
83C11×#117—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110#66977—22no—
111#66977Q814yescomplemented
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C4×Dic22—22no—
122C4×Dic22—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130#66874—22no—
131#66874—22no—
132#66874—22no—
133#66874—22no—
134#66872—22no—
135#66871—22no—
136#66871—22no—
137#66871—22no—
138C4⋊(C11⋊C8)—22no—
139C4⋊(C11⋊C8)—22no—
140#24311—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—81no—
145C2×Q8×C11—81no—
146C2×Q8×C11—81no—
147C2×Q8×C11—81no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—81no—
158C22×C4×C11—81no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×Q812yes—
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22C2×Q812yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C2×D412yes—
191C11×C4⋊C4C2×D412yes—
192C11×C4⋊C4C2×D412yes—
193C11×C4⋊C4C2×D412yes—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C42×C11—24no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11C2×D412yes—
201C42×C11C2×D412yes—
202C22⋊Dic11—24no—
203C22⋊Dic11—81no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11C2×Q812yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—42no—
212Dic11⋊C4—81no—
213C4×Dic11—42no—
214C4×Dic11—81no—
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⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×#544D1111yescharacteristic
228C2×#479—111no—
229C2×#477—111no—
230#2323—111no—
231#2059—111no—
232#2057—111no—
233#2026—111no—
234#2024—111no—
235#1989—111no—
236#1988—111no—
237#1873—111no—
238#1872—111no—
239#1854—111no—
240#1852—111no—
241#1798—111no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11C22⋊Q812yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—84no—
251Q8×C11—84no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—84no—
281C2×C4×C11#12012yes—
282C2×C4×C11#12012yes—
283C2×C4×C11C22⋊Q812yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×Q811yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302Dic22—22no—
303Dic22—22no—
304Dic22—41no—
305Dic22—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310#544—24no—
311#544—24no—
312C2×C4⋊Q8—21no—
313C2×C4⋊Q8C2×D1111yescharacteristic
314C2×C4⋊Q8C2×D1111yescharacteristic
315C2×#125—21no—
316C2×#125C2×D1111yescharacteristic
317C2×#125C2×D1111yescharacteristic
318C2×C22⋊Q8—21no—
319C2×C22⋊Q8—21no—
320C2×C22⋊Q8—111no—
321C2×C4×Q8—111no—
322C2×#117C2×D1111yescharacteristic
323C2×#117C2×D1111yescharacteristic
324C22×C4⋊C4C2×D1111yescharacteristic
325#479—224no—
326#477—224no—
327C2×#107—111no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#106—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×C22⋊C8—111no—
338C2×C22⋊C8—111no—
339#391—111no—
340#389—111no—
341#389—221no—
342#388—221no—
343#388—221no—
344#387—221no—
345#380—111no—
346C4×C4⋊C4—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12011yescharacteristic
365C22×C11C2×C22⋊Q811yescharacteristic
366C22×C11#53611yescharacteristic
367C22×C11#57611yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57811yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—41no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11#54811yescharacteristic
381C4×C11#54811yescharacteristic
382C4×C11D4×Q811yescharacteristic
383C4×C11D4×Q811yescharacteristic
384Dic11—42no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—111no—
391C23×C4—21no—
392C23×C4C22×D1111yescharacteristic
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C4⋊Q8—28no—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8—22no—
401C4⋊Q8C22⋊D1114yes—
402#125—28no—
403#125—22no—
404#125—22no—
405#125—22no—
406#125C22⋊D1114yes—
407C22⋊Q8—28no—
408C22⋊Q8—28no—
409C22⋊Q8—114no—
410C22⋊Q8—222no—
411C4×Q8—222no—
412C4×Q8—222no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4C22⋊D1111yescharacteristic
433C2×C4⋊C4C22⋊D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4C22⋊D1111yescharacteristic
442C2×C22⋊C4C22⋊D1111yescharacteristic
443C2×C42—21no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448#107—222no—
449#107—222no—
450#107—222no—
451#106—222no—
452C4⋊C8—222no—
453C4⋊C8—222no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—222no—
458C22⋊C8—222no—
459C22⋊C8—222no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465C2×C11—42no—
466C2×C11#240911yescharacteristic
467C2×C11#301111yescharacteristic
468C2×C11#301211yescharacteristic
469C2×C11#308211yescharacteristic
470C2×C11#308311yescharacteristic
471C2×C11#324211yescharacteristic
472C2×C11#324311yescharacteristic
473C24C2×C22⋊D1111yescharacteristic
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—81no—
477C2×Q8—81no—
478C2×Q8—81no—
479C2×Q8—81no—
480C2×Q8—112no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4Q8×D1112yes—
502C22×C4#434312yes—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—112no—
535C4⋊C4—224no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—442no—
542C4⋊C4—881no—
543C4⋊C4C2×C22⋊D1112yes—
544C4⋊C4C2×C22⋊D1112yes—
545C4⋊C4C2×C22⋊D1112yes—
546C4⋊C4C2×C22⋊D1112yes—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—224no—
551C22⋊C4—881no—
552C42—24no—
553C42—21no—
554C42—21no—
555C42—442no—
556C42—881no—
557C42C2×C22⋊D1112yes—
558C42C2×C22⋊D1112yes—
559C11#2431111yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#6699912yes—
567C23C22×C22⋊D1111yescharacteristic
568Q8—84no—
569Q8—84no—
570Q8—222no—
571Q8—222no—
572Q8—441no—
573Q8—441no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—441no—
606C2×C4—441no—
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#6699912yes—
616C2×C4#6700612yes—
617C2×C4#6700612yes—
618C2×C4C2×Q8×D1111yescharacteristic
619C2×C4C2×#434311yescharacteristic
620C2×C4#6704011yescharacteristic
621C2×C4#6704011yescharacteristic
622C2×C4C22×C22⋊D1111yescharacteristic
623C2×C4C22×C22⋊D1111yescharacteristic
624C8—441no—
625C8—441no—
626C8—441no—
627C8—441no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#6699911yescharacteristic
636C22#1062334711yescharacteristic
637C22#1062336611yescharacteristic
638C22#1062336711yescharacteristic
639C22#1062336911yescharacteristic
640C22#1062336911yescharacteristic
641C22C2×#6700611yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—442no—
652C4—442no—
653C4—881no—
654C4—881no—
655C4Q8×C22⋊D1111yescharacteristic
656C4Q8×C22⋊D1111yescharacteristic
657C4#1062334811yescharacteristic
658C4#1062334811yescharacteristic
659C2—42no—
660C2#1307197511yescharacteristic
661C2#1307791111yescharacteristic
662C2#1307792011yescharacteristic
663C2#1307845211yescharacteristic
664C2#1307846311yescharacteristic
665C2#1307988411yescharacteristic
666C2#1307989911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11#24311
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
2. C2×#10622704C2semidirect
4. #13069951C2semidirect
5. #13069941C2semidirect
6. #13069764C2semidirect
7. #13069754C2semidirect
8. #13069574C2semidirect
9. #13069569C2semidirect
111. #66977Q8semidirect
559. C11#24311semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×#106227042
#130712982
#130699512
#130699412
#130697642
#130697542
#130695742
#130695692
#130689282
#130689232
#130688152
#130688042
#130686002
C2×C11×#5442
#2431111