Finite Group Databasebeta

← #14910801

Subgroups — #14910801

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080983C211yesmaximal, characteristic, complemented
2D8×D44C211yesmaximal, characteristic
3#13070859C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070798C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070713C211yesmaximal, characteristic, complemented
8#13070657C211yesmaximal, characteristic, complemented
9#13070546C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070440C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18#10623225—21no—
19D4×D44—21no—
20C11×#499C2211yescharacteristic, complemented
21C4×C11×D8C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23#10622676—21no—
24#10622628—21no—
25C2×#66864C2211yescharacteristic, complemented
26C2×#66864C2211yescharacteristic, complemented
27C2×#66862C2211yescharacteristic, complemented
28C2×C16×D11C2211yescharacteristic, complemented
29#10622500C2211yescharacteristic, complemented
30#10622500C2211yescharacteristic, complemented
31#10622496C2211yescharacteristic
32#10622496C2211yescharacteristic
33#10622493C2211yescharacteristic, complemented
34D11×#107C2211yescharacteristic, complemented
35#10622480—21no—
36#10622475—21no—
37#10622386—21no—
38#10622386—21no—
39C4×Dic44C2211yescharacteristic, complemented
40#10622308C2211yescharacteristic
41C8×D44C2211yescharacteristic
42C11×#367C2211yescharacteristic, complemented
43C11×#366C2211yescharacteristic, complemented
44C11×C4⋊C16C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic, complemented
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51(C2×D11)⋊C16C2211yescharacteristic, complemented
52#10622130C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×D4×D11—21no—
61C22×D44—41no—
62C2×C11×D8C2311yescharacteristic
63C11×#125—21no—
64C4×D4×C11—21no—
65C2×#4323—21no—
66C2×#4323—21no—
67#66983—41no—
68D8×D11—22no—
69D8×D11—22no—
70D8×D11—41no—
71D8×D11—41no—
72C2×Dic44C2311yescharacteristic
73C2×D88—21no—
74C2×D88C2311yescharacteristic
75C2×D88C2311yescharacteristic
76C2×C8×D11C2311yescharacteristic
77C2×C8×D11C2311yescharacteristic
78#66951—41no—
79#66950—21no—
80#66950—21no—
81#66948—21no—
82#66948—21no—
83#66947—41no—
84#66945—21no—
85#66945—41no—
86C4⋊C4×D11—21no—
87#66943—41no—
88#66935—41no—
89#66935—41no—
90#66927—21no—
91C4×D44D411yescharacteristic
92C4×Dic22—21no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66891—22no—
102(C2×D11)⋊C8D411yescharacteristic
103(C2×D11)⋊C8D411yescharacteristic
104#66882C2311yescharacteristic
105#66880—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66874—21no—
110#66873—21no—
111#66873—21no—
112#66872—21no—
113#66871—21no—
114C4⋊(C11⋊C8)D411yescharacteristic
115#66864—41no—
116#66864—41no—
117#66862—41no—
118C16×D11—41no—
119#33877—111nomaximal, Sylow
120C23×D11—41no—
121C23×D11—41no—
122C2×D4×C11—21no—
123C22×C4×C11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126D4×D11—42no—
127D4×D11—42no—
128D4×D11—81no—
129D4×D11—81no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—41no—
133C2×D44—41no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—84no—
137C2×D44D811yescharacteristic
138C2×C4×D11—41no—
139C2×C4×D11C2×D411yescharacteristic
140C2×C4×D11C2×D411yescharacteristic
141C2×Dic22—21no—
142C11×D8—21no—
143C11×D8#4112yes—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C22⋊C4—41no—
152C42×C11C2×D411yescharacteristic
153#4323—42no—
154#4323—42no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4D811yescharacteristic
161(C2×D11)⋊C4D811yescharacteristic
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C4⋊Dic11D811yescharacteristic
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C2×C11⋊C8C2×D411yescharacteristic
171C2×C11⋊C8C2×D411yescharacteristic
172Dic44—21no—
173Dic44—21no—
174D88—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—81no—
179C8×D11—21no—
180C8×D11—21no—
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3336—111no—
188D4×D8—111no—
189#2244—111no—
190#2234—111no—
191#2232—111no—
192#2228D1111yescharacteristic, complemented
193#2220—111no—
194#2217—111no—
195#2207—111no—
196#2187—111no—
197#2187—111no—
198#2175—111no—
199#2168—111no—
200#2140—111no—
201C2×#357—111no—
202C23×C11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11—82no—
209C22×D11—161no—
210C22×D11—161no—
211C22×D11C2×D811yescharacteristic
212C22×D11C2×D811yescharacteristic
213D4×C11—22no—
214D4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—82no—
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C2×D811yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C22⋊D11—82no—
223C22⋊D11—82no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228D44—22no—
229D44—41no—
230D44—41no—
231D44—41no—
232D44—41no—
233D44—82no—
234D44—82no—
235D44—82no—
236D44—161no—
237C4×D11—21no—
238C4×D11—21no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—82no—
242Dic22—41no—
243Dic22—41no—
244C8×C11—21no—
245C8×C11C2×#4111yescharacteristic
246C8×C11H(5,𝔽2)11yescharacteristic
247C11⋊C8—21no—
248C11⋊C8—21no—
249C22×D8—111no—
250C22×D8—111no—
251#552—221no—
252D42—221no—
253C2×SD32—111no—
254C2×SD32—111no—
255C2×SD32—111no—
256C2×M32—111no—
257C22×C16—111no—
258#499C2×D1111yescharacteristic, complemented
259#493—111no—
260#485—221no—
261#483—221no—
262#479—221no—
263#467—111no—
264#467—111no—
265#466—111no—
266#466—111no—
267#459—221no—
268#447—221no—
269#447—221no—
270C4×Q16—111no—
271C4×D8C2×D1111yescharacteristic
272C8×D4—111no—
273#427—111no—
274C2×#107—111no—
275#367C2×D1111yescharacteristic, complemented
276#366—111no—
277#366C2×D1111yescharacteristic, complemented
278C4⋊C16C2×D1111yescharacteristic, complemented
279#358—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286#357—111no—
287#357C2×D1111yescharacteristic
288#357C2×D1111yescharacteristic
289C22⋊C16—111no—
290C22⋊C16—111no—
291#346—111no—
292C22×C11—42no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11C22×D811yescharacteristic
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—164no—
308C2×D11—164no—
309C2×D11#50912yes—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11#54611yescharacteristic
316C4×C11#57711yescharacteristic
317Dic11—21no—
318Dic11—21no—
319Dic11—81no—
320Dic11—81no—
321C22×D4—221no—
322C22×D4—221no—
323C22×D4—441no—
324C2×Q16—111no—
325C2×D8—111no—
326C2×D8—111no—
327C2×D8—221no—
328C2×D8—221no—
329C2×D8—222no—
330C2×D8—222no—
331C2×D8—221no—
332C2×D8—441no—
333C2×D8—441no—
334C2×D8C22×D1111yescharacteristic
335C22×C8—111no—
336C22×C8—111no—
337#127—221no—
338#126—441no—
339#125—21no—
340#125—441no—
341#123—441no—
342C22⋊Q8—221no—
343C22⋊Q8—221no—
344#121—221no—
345#121—221no—
346#121—441no—
347#120—441no—
348#120—441no—
349C4×Q8—221no—
350C4×D4—21no—
351C4×D4—111no—
352#117—221no—
353#117—441no—
354C2×C4⋊C4—221no—
355SD32—222no—
356SD32—441no—
357SD32—441no—
358M32—441no—
359C2×C16—111no—
360C2×C16—111no—
361C2×C16—441no—
362C2×C16C22×D1111yescharacteristic
363C2×C16C22×D1111yescharacteristic
364#107—111no—
365#107—221no—
366#107C22×D1111yescharacteristic
367#107C22×D1111yescharacteristic
368#107C22×D1111yescharacteristic
369#106—21no—
370#106—221no—
371C4⋊C8—111no—
372#103—221no—
373#103—221no—
374#103—221no—
375#102—21no—
376#102—221no—
377#102—221no—
378C22⋊C8—111no—
379C22⋊C8—111no—
380C4×C8C22×D1111yescharacteristic
381C2×C11—82no—
382C2×C11#329411yescharacteristic
383C2×C11C2×#50911yescharacteristic
384C2×C11#341611yescharacteristic
385D11—22no—
386D11—41no—
387D11—161no—
388D11—161no—
389C24—441no—
390C24—441no—
391C2×Q8—221no—
392C2×D4—21no—
393C2×D4—111no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4—441no—
400C2×D4—442no—
401C2×D4—442no—
402C2×D4—441no—
403C2×D4—441no—
404C2×D4—884no—
405C2×D4—881no—
406C2×D4—881no—
407C22×C4—41no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—441no—
411Q16—221no—
412Q16—221no—
413D8—21no—
414D8—221no—
415D8—221no—
416D8—221no—
417D8—221no—
418D8—442no—
419D8—442no—
420D8—881no—
421D8#434312yes—
422C2×C8—111no—
423C2×C8—111no—
424C2×C8—221no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8D4×D1111yescharacteristic
429C2×C8C23×D1111yescharacteristic
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—111no—
436C4⋊C4—221no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C4⋊C4—441no—
441C22⋊C4—41no—
442C22⋊C4—111no—
443C22⋊C4—111no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4—441no—
449C42—441no—
450C42—441no—
451C42D4×D1111yescharacteristic
452C16—21no—
453C16—21no—
454C16—221no—
455C16—221no—
456C11#3387711yescharacteristic, complemented, Sylow
457C23—41no—
458C23—111no—
459C23—111no—
460C23—441no—
461C23—441no—
462C23—882no—
463C23—882no—
464C23—882no—
465C23—882no—
466C23—1761no—
467C23—1761no—
468Q8—441no—
469Q8—441no—
470D4—22no—
471D4—41no—
472D4—222no—
473D4—441no—
474D4—441no—
475D4—441no—
476D4—441no—
477D4—882no—
478D4—882no—
479D4—882no—
480D4—882no—
481D4—882no—
482D4—1761no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—111no—
488C2×C4—111no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—882no—
496C2×C4D8×D1111yescharacteristic
497C2×C4D8×D1111yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C8—21no—
500C8—221no—
501C8—221no—
502C8C2×#434311yescharacteristic
503C8#6704211yescharacteristic
504C22—42no—
505C22—81no—
506C22—81no—
507C22—112no—
508C22—221no—
509C22—221no—
510C22—221no—
511C22—221no—
512C22—221no—
513C22—881no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22—881no—
518C22—881no—
519C22—1764no—
520C22—1764no—
521C22C2×D8×D1111yescharacteristic
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—221no—
528C4—221no—
529C4—881no—
530C4—881no—
531C4#1062316111yescharacteristic
532C4#1062330911yescharacteristic
533C2—82no—
534C2—222no—
535C2—441no—
536C2—1761no—
537C2—1761no—
538C2#1308042611yescharacteristic
539C2D11×#50911yescharacteristic
540C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radicalD8×D44C2
hypercenter#2228D11
hypocenterC11#33877
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13080983C2semidirect
3. #13070859C2semidirect
4. #13070809C2semidirect
5. #13070798C2semidirect
6. #13070730C2semidirect
7. #13070713C2semidirect
8. #13070657C2semidirect
9. #13070546C2semidirect
10. #13070546C2semidirect
11. #13070480C2semidirect
12. #13070440C2semidirect
13. #13070330C2semidirect
14. D11×#357C2semidirect
15. C11×#2228C2semidirect
20. C11×#499C22semidirect
25. C2×#66864C22semidirect
26. C2×#66864C22semidirect
27. C2×#66862C22semidirect
28. C2×C16×D11C22semidirect
29. #10622500C22semidirect
30. #10622500C22semidirect
33. #10622493C22semidirect
34. D11×#107C22semidirect
39. C4×Dic44C22semidirect
42. C11×#367C22semidirect
43. C11×#366C22semidirect
44. C11×C4⋊C16C22semidirect
48. #10622147C22semidirect
49. #10622147C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. (C2×D11)⋊C16C22semidirect
52. #10622130C22semidirect
53. #10622129C22semidirect
54. #10622129C22semidirect
55. #10622129C22semidirect
56. #10622129C22semidirect
57. #10622127C22semidirect
58. #10622099C22semidirect
192. #2228D11semidirect
258. #499C2×D11semidirect
275. #367C2×D11semidirect
277. #366C2×D11semidirect
278. C4⋊C16C2×D11semidirect
456. C11#33877semidirect

Maximal subgroups

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

subgroupindex
#130809832
D8×D442
#130708592
#130708092
#130707982
#130707302
#130707132
#130706572
#130705462
#130704802
#130704402
#130703302
D11×#3572
C11×#22282
#3387711