Finite Group Databasebeta

← #14813612

Subgroups — #14813612

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622474C211yesmaximal, characteristic, complemented
2#13072063C211yesmaximal, characteristic
3#13071541C211yesmaximal, characteristic
4#13070162C211yesmaximal, characteristic, complemented
5#13070101C211yesmaximal, characteristic, complemented
6#13070044C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069253C211yesmaximal, characteristic, complemented
9#13069196C211yesmaximal, characteristic, complemented
10#13069046C211yesmaximal, characteristic, complemented
11#13068925C211yesmaximal, characteristic, complemented
12#13068910C211yesmaximal, characteristic
13#13068809C211yesmaximal, characteristic, complemented
14#13068807C211yesmaximal, characteristic, complemented
15C2×C11×#483C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C11×#483—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622826—21no—
33#10622825C2211yescharacteristic
34#10622825C2211yescharacteristic
35C4×C22⋊Dic11—21no—
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39#10622603—21no—
40#10622600—21no—
41#10622600C2211yescharacteristic
42#10622598C2211yescharacteristic
43#10622593—21no—
44#10622591—21no—
45#10622590C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622569—21no—
51#10622561—21no—
52#10622474—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—41no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82#66999—22no—
83#66999—22no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×#4313—22no—
104C2×#4313—22no—
105C2×#4313—22no—
106#66945—22no—
107#66945—41no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—41no—
110C11×#106—22no—
111C11×#106D414yescomplemented
112C11×#103—22no—
113C11×#103—22no—
114C11×C22⋊C8—22no—
115#66899—22no—
116#66899—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127(C2×D11)⋊C8—22no—
128#66882—22no—
129#66872—22no—
130#66872—41no—
131#66871—22no—
132#26149—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—81no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—41no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11#4112yes—
174C2×C4×D11#4112yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—42no—
190C22⋊Dic11—22no—
191C22⋊Dic11—42no—
192C22⋊Dic11—81no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—81no—
206Dic11⋊C4—22no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—81no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8#4112yes—
219#4313—28no—
220C2×#483D1111yescharacteristic, complemented
221C2×#428—111no—
222#2417—111no—
223#2352—111no—
224#2097—111no—
225#2085—111no—
226#2076—111no—
227#2036—111no—
228#1927—111no—
229#1919—111no—
230#1894—111no—
231#1873—111no—
232#1870—111no—
233#1853—111no—
234#1853—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11#13712yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11#12312yes—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—84no—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—44no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
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#12312yes—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—84no—
307C8×C11—22no—
308C8×C11—41no—
309C11⋊C8—22no—
310C11⋊C8—41no—
311C22×M16—111no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×C4×D4—111no—
315C2×#117—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4C2×D1111yescharacteristic
318#483—24no—
319#428—224no—
320C2×#107—111no—
321C2×#107—111no—
322C2×#106—111no—
323C2×#106—111no—
324C2×#106C2×D1111yescharacteristic
325C2×#106C2×D1111yescharacteristic
326C2×#103—111no—
327C2×#103—111no—
328C2×#103C2×D1111yescharacteristic
329C2×#103C2×D1111yescharacteristic
330C2×C22⋊C8—111no—
331C2×C22⋊C8—111no—
332C2×C22⋊C8C2×D1111yescharacteristic
333#398—221no—
334#396—221no—
335#391—111no—
336#389—111no—
337#388—221no—
338#387—221no—
339#386—221no—
340#386—221no—
341#382—111no—
342#380—111no—
343#380—111no—
344#380—111no—
345#380—221no—
346C4×C4⋊C4—111no—
347C4×C22⋊C4—221no—
348#340—111no—
349#340—111no—
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×#12311yescharacteristic
364C22×C11D4211yescharacteristic
365C22×C11#54711yescharacteristic
366C22×C11C2×#13711yescharacteristic
367C22×C11#57511yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57711yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11#52511yescharacteristic
383C4×C11#53911yescharacteristic
384C4×C11#54811yescharacteristic
385C4×C11#55311yescharacteristic
386Dic11—22no—
387Dic11—41no—
388Dic11—41no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—111no—
395C23×C4—21no—
396C23×C4—111no—
397C23×C4—221no—
398C23×C4C22×D1111yescharacteristic
399C2×M16—222no—
400C2×M16—222no—
401C2×M16—222no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C22⋊Q8—22no—
407C22⋊Q8—41no—
408C22⋊Q8—222no—
409C22⋊Q8—222no—
410C4×D4—222no—
411C4×D4—222no—
412#117—222no—
413#117—441no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—222no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—441no—
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C42—111no—
440C2×C42—221no—
441C2×C42—221no—
442#107—222no—
443#107—222no—
444#106—22no—
445#106—222no—
446#106—441no—
447#106C22⋊D1114yescomplemented
448#103—22no—
449#103—22no—
450#103—222no—
451#103—441no—
452C22⋊C8—22no—
453C22⋊C8—222no—
454C22⋊C8—222no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464C2×C11—42no—
465C2×C11#244311yescharacteristic
466C2×C11#309511yescharacteristic
467C2×C11#309911yescharacteristic
468C2×C11#326611yescharacteristic
469C2×C11#327511yescharacteristic
470C2×C11#334411yescharacteristic
471C2×C11#335111yescharacteristic
472D11—42no—
473C24—111no—
474C24D4×D1111yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×D4—222no—
482C2×D4—222no—
483C2×D4—441no—
484C22×C4—21no—
485C22×C4—21no—
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—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—111no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—881no—
513C22×C4D4×D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515M16—228no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—112no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8C2×C22⋊D1112yes—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—222no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—881no—
546C4⋊C4C2×C22⋊D1112yes—
547C4⋊C4C2×C22⋊D1112yes—
548C22⋊C4—42no—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—881no—
555C22⋊C4—881no—
556C42—221no—
557C42—221no—
558C42—442no—
559C42—881no—
560C11#2614911yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—112no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23#6696812yes—
575C23C2×D4×D1111yescharacteristic
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580D4—444no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—112no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—884no—
627C2×C4#6703711yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#6704311yescharacteristic
632C2×C4C22×C22⋊D1111yescharacteristic
633C8—22no—
634C8—41no—
635C8—222no—
636C8—441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—441no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22D11×#12311yescharacteristic
652C22#1062318611yescharacteristic
653C22C2×#6696811yescharacteristic
654C22#1062329311yescharacteristic
655C22#1062330811yescharacteristic
656C22#1062330911yescharacteristic
657C22D4×C22⋊D1111yescharacteristic
658C4—42no—
659C4—42no—
660C4—41no—
661C4—81no—
662C4—81no—
663C4—222no—
664C4—441no—
665C4—441no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062319111yescharacteristic
671C4#1062319211yescharacteristic
672C4#1062335911yescharacteristic
673C4#1062336211yescharacteristic
674C2—42no—
675C2—442no—
676C2#1307234811yescharacteristic
677C2#1307855911yescharacteristic
678C2#1307860011yescharacteristic
679C2#1308012611yescharacteristic
680C2#1308024111yescharacteristic
681C2#1308107511yescharacteristic
682C2#1308117911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#483C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#483D11
hypocenterC11#26149
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#10622474C2semidirect
4. #13070162C2semidirect
5. #13070101C2semidirect
6. #13070044C2semidirect
7. #13069816C2semidirect
8. #13069253C2semidirect
9. #13069196C2semidirect
10. #13069046C2semidirect
11. #13068925C2semidirect
13. #13068809C2semidirect
14. #13068807C2semidirect
15. C2×C11×#483C2semidirect
111. C11×#106D4semidirect
220. C2×#483D11semidirect
447. #106C22⋊D11semidirect
560. C11#26149semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
#130720632
#130715412
#130701622
#130701012
#130700442
#130698162
#130692532
#130691962
#130690462
#130689252
#130689102
#130688092
#130688072
C2×C11×#4832
#2614911