Finite Group Databasebeta

← #14811831

Subgroups — #14811831

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072327C211yesmaximal, characteristic
2#13071489C211yesmaximal, characteristic
3#13070180C211yesmaximal, characteristic, complemented
4#13070117C211yesmaximal, characteristic, complemented
5#13070108C211yesmaximal, characteristic, complemented
6#13069956C211yesmaximal, characteristic, complemented
7#13069570C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13069204C211yesmaximal, characteristic, complemented
10#13068814C211yesmaximal, characteristic
11#13068800C211yesmaximal, characteristic
12#13068701C211yesmaximal, characteristic
13#13068648C211yesmaximal, characteristic
14#13068334C211yesmaximal, characteristic
15C11×#1919C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×#66945C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×Dic11⋊C8C2211yescharacteristic
25#10622607—21no—
26#10622600C2211yescharacteristic
27#10622600C2211yescharacteristic
28#10622598—21no—
29#10622598C2211yescharacteristic
30C4⋊C4×Dic11C2211yescharacteristic
31#10622586C2211yescharacteristic
32C2×#66872C2211yescharacteristic
33C2×#66871C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35C4×(C2×D11)⋊C4—21no—
36C4×(C2×D11)⋊C4C2211yescharacteristic
37#10622548C2211yescharacteristic
38#10622546—21no—
39#10622541C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622290—21no—
42#10622280—21no—
43#10622266—21no—
44#10622265—21no—
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4D411yescharacteristic
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×#4313—22no—
93C2×#4313—22no—
94C2×#4313—41no—
95#66945—22no—
96#66945—41no—
97C4⋊C4×D11—22no—
98C4⋊C4×D11Q814yes—
99#66943—22no—
100#66943—41no—
101C11×#106—22no—
102C11×#95—21no—
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112(C2×D11)⋊C8—22no—
113Dic11⋊C8—41no—
114#66872—22no—
115#66871—41no—
116#66871—41no—
117C4⋊(C11⋊C8)—22no—
118#26018—111nomaximal, Sylow
119C23×D11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×C4×D11—24no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—81no—
140C2×C4×D11—81no—
141C2×C4×D11C2×Q812yes—
142C2×C4×D11#4112yes—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4C2×Q812yes—
157C11×C4⋊C4#4112yes—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—81no—
161(C2×D11)⋊C4—22no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—81no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—42no—
174C4⋊Dic11—42no—
175C4⋊Dic11—81no—
176C4⋊Dic11—81no—
177C4⋊Dic11C2×Q812yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—42no—
185C4×Dic11—81no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8#4112yes—
192#4313—44no—
193#2441—111no—
194#2345—111no—
195#2100—111no—
196#2088—111no—
197#2086—111no—
198#2059—111no—
199#1989—111no—
200#1947—111no—
201#1920—111no—
202#1919D1111yescharacteristic, complemented
203#1854—111no—
204#1851—111no—
205#1823—111no—
206#1809—111no—
207#1736—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11C22⋊Q812yes—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11#13712yes—
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11C22⋊Q812yes—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—84no—
266C8×C11—41no—
267C8×C11—41no—
268C11⋊C8—22no—
269C11⋊C8—41no—
270C22×M16—111no—
271C2×#125—111no—
272C2×#117—111no—
273C22×C4⋊C4—111no—
274C2×#107—111no—
275C2×#107—111no—
276C2×#106—111no—
277C2×#106C2×D1111yescharacteristic
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×C22⋊C8—111no—
281#399—221no—
282#396—221no—
283#389—111no—
284#389—111no—
285#389—111no—
286#389—221no—
287#389C2×D1111yescharacteristic
288#387—221no—
289#387—221no—
290#387—221no—
291#384—111no—
292#380—111no—
293#380—111no—
294#380—221no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4C2×D1111yescharacteristic
297C4×C22⋊C4—111no—
298C4×C22⋊C4—221no—
299#340—111no—
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340C2×D1111yescharacteristic
309#340C2×D1111yescharacteristic
310#340C2×D1111yescharacteristic
311#336—111no—
312#336C2×D1111yescharacteristic
313C22×C11C2×C22⋊Q811yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11#54711yescharacteristic
316C22×C11C2×#13711yescharacteristic
317C22×C11#57511yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—22no—
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C4×C11—22no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—41no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11#53311yescharacteristic
334C4×C11#54411yescharacteristic
335C4×C11#55111yescharacteristic
336C4×C11#55211yescharacteristic
337Dic11—22no—
338Dic11—41no—
339Dic11—42no—
340Dic11—41no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344C23×C4—111no—
345C23×C4—221no—
346C2×M16—222no—
347C2×M16—222no—
348C2×M16—441no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353#125—222no—
354#125—441no—
355#117—222no—
356#117—441no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—111no—
377C2×C22⋊C4—111no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—21no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—441no—
387#107—441no—
388#106—22no—
389#106—222no—
390C4⋊C8—222no—
391C4⋊C8—441no—
392C22⋊C8—222no—
393#95—21no—
394#95—21no—
395#95—111no—
396#95—111no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11#243811yescharacteristic
404C2×C11#307811yescharacteristic
405C2×C11#308111yescharacteristic
406C2×C11#330911yescharacteristic
407C2×C11#333111yescharacteristic
408C2×C11#334611yescharacteristic
409C2×C11#335111yescharacteristic
410D11—42no—
411C24—111no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—111no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—224no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—881no—
431C22×C4—881no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435M16—444no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—112no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—112no—
456C4⋊C4—224no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C4⋊C4—881no—
468C4⋊C4—881no—
469C4⋊C4—881no—
470C4⋊C4—881no—
471C4⋊C4#433912yes—
472C4⋊C4Q8×D1112yes—
473C22⋊C4—222no—
474C22⋊C4—441no—
475C22⋊C4—442no—
476C22⋊C4—442no—
477C22⋊C4—881no—
478C42—21no—
479C42—21no—
480C42—81no—
481C42—221no—
482C42—221no—
483C42—442no—
484C42—881no—
485C11#2601811yescharacteristic, complemented, Sylow
486C23—112no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23—221no—
492C23—221no—
493C23C2×D4×D1111yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—112no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—222no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—884no—
537C2×C4#6696812yes—
538C2×C4C2×#433911yescharacteristic
539C2×C4C2×Q8×D1111yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#41×D1111yescharacteristic
542C2×C4#6704211yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—41no—
545C8—41no—
546C8—222no—
547C8—441no—
548C22—222no—
549C22—222no—
550C22—222no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22—441no—
555C22#1062308111yescharacteristic
556C22D11×C22⋊Q811yescharacteristic
557C22#1062318611yescharacteristic
558C22C2×#6696811yescharacteristic
559C22#1062330111yescharacteristic
560C22#1062330511yescharacteristic
561C22#1062330811yescharacteristic
562C4—22no—
563C4—41no—
564C4—42no—
565C4—42no—
566C4—81no—
567C4—81no—
568C4—222no—
569C4—441no—
570C4—441no—
571C4—442no—
572C4—881no—
573C4—881no—
574C4—881no—
575C4#1062306011yescharacteristic
576C4#1062310911yescharacteristic
577C4#1062322011yescharacteristic
578C4#1062323611yescharacteristic
579C2—442no—
580C2#1307229711yescharacteristic
581C2#1307841611yescharacteristic
582C2#1307844611yescharacteristic
583C2#1308062711yescharacteristic
584C2#1308093411yescharacteristic
585C2#1308109911yescharacteristic
586C2#1308117411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1919C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1919D11
hypocenterC11#26018
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
3. #13070180C2semidirect
4. #13070117C2semidirect
5. #13070108C2semidirect
6. #13069956C2semidirect
7. #13069570C2semidirect
8. #13069374C2semidirect
9. #13069204C2semidirect
15. C11×#1919C2semidirect
202. #1919D11semidirect
485. C11#26018semidirect

Maximal subgroups

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

subgroupindex
#130723272
#130714892
#130701802
#130701172
#130701082
#130699562
#130695702
#130693742
#130692042
#130688142
#130688002
#130687012
#130686482
#130683342
C11×#19192
#2601811