Finite Group Databasebeta

← #14909569

Subgroups — #14909569

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078198C211yesmaximal, characteristic, complemented
2D11×#466C211yesmaximal, characteristic, complemented
3#13070815C211yesmaximal, characteristic, complemented
4#13070807C211yesmaximal, characteristic, complemented
5#13070798C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070720C211yesmaximal, characteristic, complemented
9#13070718C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070541C211yesmaximal, characteristic, complemented
12#13070537C211yesmaximal, characteristic, complemented
13#13070529C211yesmaximal, characteristic, complemented
14#13070225C211yesmaximal, characteristic, complemented
15C11×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C2×#66957C2211yescharacteristic, complemented
18C22×C8×D11C2211yescharacteristic
19D11×#121—21no—
20#10623055—21no—
21C11×#466C2211yescharacteristic
22C11×#427C2211yescharacteristic, complemented
23#10622770C2211yescharacteristic
24C2×#66891C2211yescharacteristic, complemented
25C2×#66890C2211yescharacteristic, complemented
26#10622728C2211yescharacteristic
27#10622651—21no—
28#10622615—21no—
29C2×#66864C2211yescharacteristic, complemented
30C2×D176C2211yescharacteristic, complemented
31C2×#66862C2211yescharacteristic, complemented
32C2×#66862C2211yescharacteristic, complemented
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic, complemented
35#10622496C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622496C2211yescharacteristic, complemented
38D11×#107C2211yescharacteristic
39#10622477—21no—
40#10622477—21no—
41#10622388—21no—
42D11×#102—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#366C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic, complemented
46C11×#357C2211yescharacteristic, complemented
47C11×C22⋊C16C2211yescharacteristic, complemented
48C22⋊(C11⋊C16)C2211yescharacteristic, complemented
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622141C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×D4×D11—41no—
61C2×#4339—21no—
62C22×C4×D11D411yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#121—21no—
66C11×#117—21no—
67#66992—41no—
68#66991—21no—
69C2×#4323—21no—
70#66983—21no—
71C22×C11⋊C8D411yescharacteristic
72D8×D11—41no—
73D8×D11—41no—
74C2×Dic44C2311yescharacteristic
75#66957—41no—
76#66957—41no—
77C2×D88C2311yescharacteristic
78C2×D88C2311yescharacteristic
79C2×#4314—21no—
80C2×C8×D11—41no—
81C2×C8×D11—41no—
82C2×C8×D11D411yescharacteristic
83C2×C8×D11D411yescharacteristic
84C2×C8×D11C2311yescharacteristic
85C2×C8×D11C2311yescharacteristic
86#66950—21no—
87#66950—21no—
88#66948—21no—
89#66948—21no—
90#66948—21no—
91C4⋊C4×D11—21no—
92#66939—41no—
93#66937—41no—
94#66935—41no—
95C22⋊C4×D11—41no—
96C4×D44—41no—
97C4×D44—41no—
98C2×C11×C16C2311yescharacteristic
99C2×C11×C16C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#106—21no—
104C11×#102—21no—
105#66896—21no—
106#66891—41no—
107#66890—41no—
108#66885—21no—
109#66882C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66874—21no—
113#66874—21no—
114#66873—21no—
115#66873—21no—
116#66873—21no—
117#66871—21no—
118#66864—41no—
119D176—41no—
120#66862—41no—
121#66862—41no—
122#33760—111nomaximal, Sylow
123C23×D11—41no—
124C23×D11D811yescharacteristic
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132C22×Dic11D811yescharacteristic
133D4×D11—42no—
134D4×D11—42no—
135D4×D11—84no—
136#4339—42no—
137#4339—42no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—41no—
141C2×D44—41no—
142C2×D44—41no—
143C2×C4×D11—41no—
144C2×C4×D11—41no—
145C2×C4×D11—41no—
146C2×C4×D11—41no—
147C2×C4×D11D811yescharacteristic
148C2×C4×D11D811yescharacteristic
149C2×C4×D11C2×D411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×Dic22—21no—
152C11×D8—21no—
153C11×D8—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2411yescharacteristic
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—41no—
164C22⋊Dic11—41no—
165#4323—42no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174C4⋊Dic11—41no—
175Dic11⋊C4—41no—
176C2×C11⋊C8—41no—
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179Dic44—21no—
180Dic44—21no—
181D88—21no—
182D88—21no—
183D88—21no—
184D88—21no—
185#4314—42no—
186C8×D11—21no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—41no—
191C8×D11—41no—
192C11×C16—21no—
193C11×C16—21no—
194C11⋊C16—21no—
195C11⋊C16—21no—
196#3050—111no—
197C2×#466—111no—
198#2235—111no—
199#2234—111no—
200#2234D1111yescharacteristic, complemented
201#2232—111no—
202#2220—111no—
203#2220—111no—
204#2218—111no—
205#2218—111no—
206#2187—111no—
207#2186—111no—
208#2186—111no—
209#2184—111no—
210#2112—111no—
211C23×C11—41no—
212C23×C11C2×D811yescharacteristic
213C22×D11—22no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—82no—
219C22×D11—82no—
220C22×D11—82no—
221C22×D11C2×D811yescharacteristic
222C22×D11C2×D811yescharacteristic
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—82no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11C2×D811yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C22⋊D11—82no—
234C22⋊D11—82no—
235C22⋊D11—82no—
236C22⋊D11—82no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11C2×D811yescharacteristic
241C2×Dic11C2×D811yescharacteristic
242D44—41no—
243D44—41no—
244D44—41no—
245D44—41no—
246D44—82no—
247D44—82no—
248D44—82no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—82no—
256C4×D11—82no—
257Dic22—41no—
258Dic22—41no—
259C8×C11—21no—
260C8×C11H(5,𝔽2)11yescharacteristic
261C8×C11H(5,𝔽2)11yescharacteristic
262C11⋊C8—21no—
263C11⋊C8—21no—
264C2×#135—111no—
265C22×D8—111no—
266C23×C8—111no—
267#525—221no—
268C2×#121—221no—
269C2×SD32—111no—
270C2×SD32—111no—
271C2×D16—111no—
272C2×D16—111no—
273C2×M32—111no—
274C2×M32—111no—
275#467—111no—
276#467—111no—
277#466—111no—
278#466—111no—
279#466—111no—
280#466—111no—
281#466—111no—
282#466—221no—
283#466—221no—
284#466C2×D1111yescharacteristic
285#465—221no—
286#465—221no—
287#427C2×D1111yescharacteristic, complemented
288C2×#107—111no—
289#416—221no—
290C2×#102—221no—
291#367—111no—
292#367C2×D1111yescharacteristic, complemented
293#366—111no—
294#366C2×D1111yescharacteristic, complemented
295#358—111no—
296#358—111no—
297#357—111no—
298#357—111no—
299#357—111no—
300#357—111no—
301#357C2×D1111yescharacteristic, complemented
302#357C2×D1111yescharacteristic, complemented
303C22⋊C16—111no—
304C22⋊C16—111no—
305C22⋊C16—111no—
306C22⋊C16C2×D1111yescharacteristic, complemented
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11C22×D811yescharacteristic
314C2×D11—21no—
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—44no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—164no—
327C2×D11#50912yes—
328C4×C11—21no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11#53411yescharacteristic
333C4×C11#57511yescharacteristic
334Dic11—21no—
335Dic11—21no—
336Dic11—81no—
337Dic11—81no—
338C2×#41—221no—
339C22×D4—221no—
340C22×D4—441no—
341C23×C4—111no—
342#135—441no—
343#135—441no—
344C2×Q16—111no—
345C2×SD16—221no—
346C2×D8—111no—
347C2×D8—111no—
348C2×D8—221no—
349C2×D8—441no—
350C2×D8—441no—
351C2×D8C22×D1111yescharacteristic
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—441no—
358C22×C8—441no—
359C22×C8C22×D1111yescharacteristic
360#123—441no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363#121—21no—
364#121—221no—
365#121—221no—
366#121—221no—
367#121—221no—
368#121—221no—
369#121—441no—
370#121—441no—
371#120—441no—
372C4×D4—441no—
373C4×D4—441no—
374#117—21no—
375C2×C4⋊C4—221no—
376C2×C22⋊C4—441no—
377SD32—441no—
378SD32—441no—
379D16—441no—
380D16—441no—
381M32—441no—
382M32—441no—
383C2×C16—111no—
384C2×C16—111no—
385C2×C16C22×D1111yescharacteristic
386C2×C16C22×D1111yescharacteristic
387#107—111no—
388#107—221no—
389#107C22×D1111yescharacteristic
390#107C22×D1111yescharacteristic
391#107C22×D1111yescharacteristic
392#106—21no—
393#103—221no—
394#103—221no—
395#102—21no—
396#102—221no—
397#102—221no—
398#102—221no—
399#102—221no—
400#102—221no—
401C2×C11—41no—
402C2×C11—161no—
403C2×C11#318611yescharacteristic
404C2×C11C2×#50911yescharacteristic
405C2×C11#341411yescharacteristic
406D11—22no—
407D11—41no—
408D11—161no—
409D11—161no—
410C24—111no—
411C24—441no—
412#41—442no—
413#41—442no—
414C2×Q8—221no—
415C2×D4—21no—
416C2×D4—41no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—441no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—441no—
423C2×D4—442no—
424C2×D4—442no—
425C2×D4—441no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—884no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—441no—
435C22×C4—441no—
436C22×C4—441no—
437C22×C4—441no—
438C22×C4D4×D1111yescharacteristic
439Q16—221no—
440Q16—221no—
441SD16—442no—
442D8—21no—
443D8—21no—
444D8—221no—
445D8—221no—
446D8—221no—
447D8—221no—
448D8—442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—441no—
458C2×C8—441no—
459C2×C8—441no—
460C2×C8D4×D1111yescharacteristic
461C2×C8C23×D1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—221no—
466C4⋊C4—441no—
467C4⋊C4—441no—
468C4⋊C4—441no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C42—41no—
479C16—21no—
480C16—21no—
481C16—221no—
482C16—221no—
483C11#3376011yescharacteristic, complemented, Sylow
484C23—41no—
485C23—111no—
486C23—111no—
487C23—222no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—882no—
493C23—882no—
494C23—882no—
495C23D8×D1111yescharacteristic
496Q8—441no—
497Q8—441no—
498D4—41no—
499D4—41no—
500D4—82no—
501D4—441no—
502D4—441no—
503D4—441no—
504D4—441no—
505D4—882no—
506D4—882no—
507D4—882no—
508D4—882no—
509D4—882no—
510D4—882no—
511D4—882no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—111no—
518C2×C4—111no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—882no—
529C2×C4—882no—
530C2×C4D8×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C8—21no—
533C8—221no—
534C8—221no—
535C8#6704211yescharacteristic
536C8#6704211yescharacteristic
537C22—21no—
538C22—21no—
539C22—21no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—112no—
544C22—221no—
545C22—221no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22—444no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—1764no—
557C22C2×D8×D1111yescharacteristic
558C4—21no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—221no—
563C4—221no—
564C4—881no—
565C4—881no—
566C4#1062318411yescharacteristic
567C4#1062330811yescharacteristic
568C2—41no—
569C2—161no—
570C2—222no—
571C2—441no—
572C2—1761no—
573C2—1761no—
574C2#1307936611yescharacteristic
575C2D11×#50911yescharacteristic
576C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2234C2
socleC22×C11C22×D8
hypercenter#2234D11
hypocenterC11#33760
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
1. #13078198C2semidirect
2. D11×#466C2semidirect
3. #13070815C2semidirect
4. #13070807C2semidirect
5. #13070798C2semidirect
6. #13070730C2semidirect
7. #13070728C2semidirect
8. #13070720C2semidirect
9. #13070718C2semidirect
10. #13070546C2semidirect
11. #13070541C2semidirect
12. #13070537C2semidirect
13. #13070529C2semidirect
14. #13070225C2semidirect
15. C11×#2234C2semidirect
17. C2×#66957C22semidirect
22. C11×#427C22semidirect
24. C2×#66891C22semidirect
25. C2×#66890C22semidirect
29. C2×#66864C22semidirect
30. C2×D176C22semidirect
31. C2×#66862C22semidirect
32. C2×#66862C22semidirect
34. #10622500C22semidirect
37. #10622496C22semidirect
43. C11×#367C22semidirect
44. C11×#366C22semidirect
45. C11×#357C22semidirect
46. C11×#357C22semidirect
47. C11×C22⋊C16C22semidirect
48. C22⋊(C11⋊C16)C22semidirect
49. #10622147C22semidirect
52. #10622141C22semidirect
53. #10622130C22semidirect
54. #10622129C22semidirect
55. #10622129C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
200. #2234D11semidirect
287. #427C2×D11semidirect
292. #367C2×D11semidirect
294. #366C2×D11semidirect
301. #357C2×D11semidirect
302. #357C2×D11semidirect
306. C22⋊C16C2×D11semidirect
483. C11#33760semidirect

Maximal subgroups

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

subgroupindex
#130781982
D11×#4662
#130708152
#130708072
#130707982
#130707302
#130707282
#130707202
#130707182
#130705462
#130705412
#130705372
#130705292
#130702252
C11×#22342
#3376011