Finite Group Databasebeta

← #14910615

Subgroups — #14910615

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080983C211yesmaximal, characteristic, complemented
2#13080302C211yesmaximal, characteristic
3#13070850C211yesmaximal, characteristic, complemented
4#13070815C211yesmaximal, characteristic, complemented
5#13070810C211yesmaximal, characteristic, complemented
6#13070713C211yesmaximal, characteristic, complemented
7#13070708C211yesmaximal, characteristic, complemented
8#13070679C211yesmaximal, characteristic, complemented
9#13070557C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11C4×#66891C211yesmaximal, characteristic, complemented
12#13070435C211yesmaximal, characteristic, complemented
13#13070320C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18#10623225—21no—
19#10623085—21no—
20C11×#499C2211yescharacteristic, complemented
21C4×C11×D8C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23#10622676—21no—
24#10622629—21no—
25C2×Dic88C2211yescharacteristic, complemented
26C2×#66864C2211yescharacteristic
27C2×C16×D11C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic, complemented
29#10622500C2211yescharacteristic
30#10622500C2211yescharacteristic
31#10622500C2211yescharacteristic, complemented
32#10622496C2211yescharacteristic
33#10622493C2211yescharacteristic, complemented
34D11×#107C2211yescharacteristic
35#10622480—21no—
36#10622475—21no—
37#10622394—21no—
38#10622389—21no—
39C4×Dic44C2211yescharacteristic, complemented
40#10622309C2211yescharacteristic
41C8×D44C2211yescharacteristic
42C11×#367C2211yescharacteristic, complemented
43C11×#366C2211yescharacteristic, complemented
44C11×C4⋊C16C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51#10622141C2211yescharacteristic, complemented
52#10622130C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic, complemented
58C4×C11⋊C16C2211yescharacteristic, complemented
59C2×#4341—21no—
60C2×D4×D11—21no—
61C2×C11×D8C2311yescharacteristic
62C11×#125—21no—
63C4×D4×C11—21no—
64C2×#4324—21no—
65C2×#4323—21no—
66#66983—41no—
67C2×(C2×D11)⋊C4—41no—
68#66965—22no—
69#66965—41no—
70D8×D11—22no—
71D8×D11—41no—
72C2×Dic44C2311yescharacteristic
73C2×Dic44C2311yescharacteristic
74C2×D88C2311yescharacteristic
75C2×#4314—21no—
76C2×C8×D11C2311yescharacteristic
77C2×C8×D11C2311yescharacteristic
78#66951—41no—
79#66950—21no—
80#66950—21no—
81#66950—21no—
82#66948—21no—
83#66947—41no—
84#66945—21no—
85#66945—41no—
86C4⋊C4×D11—21no—
87#66943—41no—
88#66939—41no—
89#66935—41no—
90#66928—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#66874—21no—
111#66873—21no—
112#66872—21no—
113#66871—21no—
114C4⋊(C11⋊C8)D411yescharacteristic
115Dic88—41no—
116#66864—41no—
117C16×D11—41no—
118C16×D11—41no—
119#33863—111nomaximal, Sylow
120C23×D11—41no—
121C2×D4×C11—21no—
122C22×C4×C11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C22×Dic11—41no—
126#4341—42no—
127#4341—81no—
128D4×D11—42no—
129D4×D11—81no—
130C2×D44—21no—
131C2×D44—41no—
132C2×D44D811yescharacteristic
133C2×C4×D11—41no—
134C2×C4×D11C2×D411yescharacteristic
135C2×C4×D11C2×D411yescharacteristic
136C2×Dic22—21no—
137C2×Dic22—21no—
138C11×D8—21no—
139C11×D8#4112yes—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11C2×D411yescharacteristic
149#4324—42no—
150#4323—42no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4D811yescharacteristic
159(C2×D11)⋊C4D811yescharacteristic
160C4⋊Dic11—21no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164C4⋊Dic11D811yescharacteristic
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167C4×Dic11—41no—
168C4×Dic11—41no—
169C2×C11⋊C8C2×D411yescharacteristic
170C2×C11⋊C8C2×D411yescharacteristic
171Dic44—21no—
172Dic44—21no—
173Dic44—21no—
174Dic44—21no—
175D88—21no—
176D88—21no—
177#4314—81no—
178C8×D11—21no—
179C8×D11—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3336—111no—
187#3280—111no—
188#2242—111no—
189#2235—111no—
190#2234—111no—
191#2228D1111yescharacteristic, complemented
192#2217—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#357—111no—
201C23×C11—41no—
202C22×D11—41no—
203C22×D11—82no—
204C22×D11—82no—
205C22×D11—161no—
206C22×D11C2×D811yescharacteristic
207C22×D11C2×D811yescharacteristic
208D4×C11—22no—
209D4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—161no—
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11—82no—
218C22⋊D11—82no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—82no—
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225D44—22no—
226D44—41no—
227D44—41no—
228D44—161no—
229C4×D11—21no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—21no—
233C4×D11—82no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C22×D8—111no—
245#552—221no—
246#546—221no—
247C2×Q32—111no—
248C2×SD32—111no—
249C2×SD32—111no—
250C22×C16—111no—
251C22×C16—111no—
252#499C2×D1111yescharacteristic, complemented
253#495—111no—
254#485—221no—
255#483—221no—
256#479—221no—
257#467—111no—
258#467—111no—
259#467—111no—
260#466—111no—
261#463—221no—
262#450—221no—
263#449—221no—
264C4×Q16—111no—
265C4×D8C2×D1111yescharacteristic
266C8×D4—111no—
267#427—111no—
268C2×#107—111no—
269#367—111no—
270#367C2×D1111yescharacteristic, complemented
271#366C2×D1111yescharacteristic, complemented
272C4⋊C16C2×D1111yescharacteristic, complemented
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357C2×D1111yescharacteristic
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C22×C11—42no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11C22×D811yescharacteristic
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—164no—
299C2×D11#50812yes—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—81no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11#54611yescharacteristic
306C4×C11#57711yescharacteristic
307Dic11—21no—
308Dic11—21no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—221no—
313C22×D4—221no—
314#135—222no—
315#135—441no—
316C2×Q16—111no—
317C2×Q16—111no—
318C2×SD16—221no—
319C2×SD16—221no—
320C2×D8—111no—
321C2×D8—221no—
322C2×D8—222no—
323C2×D8—441no—
324C2×D8C22×D1111yescharacteristic
325C22×C8—111no—
326C22×C8—111no—
327#126—441no—
328#125—21no—
329#125—441no—
330#124—221no—
331#123—441no—
332#123—441no—
333C22⋊Q8—221no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—221no—
337#121—441no—
338#120—441no—
339C4×Q8—221no—
340C4×D4—21no—
341C4×D4—111no—
342#117—221no—
343#117—441no—
344C2×C4⋊C4—221no—
345C2×C22⋊C4—441no—
346Q32—441no—
347SD32—222no—
348SD32—441no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—441no—
352C2×C16—441no—
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355#107—111no—
356#107—221no—
357#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#107C22×D1111yescharacteristic
360#106—21no—
361#106—221no—
362C4⋊C8—111no—
363#103—221no—
364#103—221no—
365#103—221no—
366#103—221no—
367#102—21no—
368#102—221no—
369C22⋊C8—111no—
370C22⋊C8—111no—
371C4×C8C22×D1111yescharacteristic
372C2×C11—82no—
373C2×C11#329411yescharacteristic
374C2×C11C2×#50811yescharacteristic
375C2×C11#341611yescharacteristic
376D11—22no—
377D11—41no—
378D11—161no—
379C24—441no—
380#41—442no—
381#41—881no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×D4—21no—
385C2×D4—111no—
386C2×D4—221no—
387C2×D4—441no—
388C2×D4—441no—
389C2×D4—442no—
390C2×D4—441no—
391C2×D4—881no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—441no—
396C22×C4—441no—
397Q16—221no—
398Q16—221no—
399Q16—221no—
400Q16—221no—
401SD16—442no—
402SD16—881no—
403D8—21no—
404D8—221no—
405D8—221no—
406D8—442no—
407D8#434312yes—
408C2×C8—111no—
409C2×C8—111no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8D4×D1111yescharacteristic
415C2×C8C23×D1111yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—111no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—41no—
429C22⋊C4—111no—
430C22⋊C4—111no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—441no—
439C42—441no—
440C42D4×D1111yescharacteristic
441C16—21no—
442C16—21no—
443C16—221no—
444C16—221no—
445C11#3386311yescharacteristic, complemented, Sylow
446C23—41no—
447C23—111no—
448C23—111no—
449C23—441no—
450C23—882no—
451C23—882no—
452C23—1761no—
453Q8—441no—
454Q8—441no—
455Q8—441no—
456Q8—441no—
457D4—22no—
458D4—41no—
459D4—222no—
460D4—441no—
461D4—441no—
462D4—882no—
463D4—882no—
464D4—1761no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—111no—
469C2×C4—111no—
470C2×C4—161no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—882no—
479C2×C4—882no—
480C2×C4D8×D1111yescharacteristic
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8C2×#434311yescharacteristic
487C8#6704211yescharacteristic
488C22—42no—
489C22—81no—
490C22—81no—
491C22—112no—
492C22—221no—
493C22—221no—
494C22—221no—
495C22—221no—
496C22—221no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—1764no—
501C22C2×D8×D1111yescharacteristic
502C4—21no—
503C4—21no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—221no—
508C4—221no—
509C4—881no—
510C4—881no—
511C4—881no—
512C4#1062316111yescharacteristic
513C4#1062330911yescharacteristic
514C2—82no—
515C2—222no—
516C2—441no—
517C2—1761no—
518C2#1308042611yescharacteristic
519C2D11×#50811yescharacteristic
520C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radical#13080302C2
hypercenter#2228D11
hypocenterC11#33863
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. #13070850C2semidirect
4. #13070815C2semidirect
5. #13070810C2semidirect
6. #13070713C2semidirect
7. #13070708C2semidirect
8. #13070679C2semidirect
9. #13070557C2semidirect
10. #13070546C2semidirect
11. C4×#66891C2semidirect
12. #13070435C2semidirect
13. #13070320C2semidirect
14. D11×#357C2semidirect
15. C11×#2228C2semidirect
20. C11×#499C22semidirect
25. C2×Dic88C22semidirect
28. C2×C16×D11C22semidirect
31. #10622500C22semidirect
33. #10622493C22semidirect
39. C4×Dic44C22semidirect
42. C11×#367C22semidirect
43. C11×#366C22semidirect
44. C11×C4⋊C16C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. #10622141C22semidirect
52. #10622130C22semidirect
53. #10622130C22semidirect
54. #10622130C22semidirect
57. #10622128C22semidirect
58. C4×C11⋊C16C22semidirect
191. #2228D11semidirect
252. #499C2×D11semidirect
270. #367C2×D11semidirect
271. #366C2×D11semidirect
272. C4⋊C16C2×D11semidirect
445. C11#33863semidirect

Maximal subgroups

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

subgroupindex
#130809832
#130803022
#130708502
#130708152
#130708102
#130707132
#130707082
#130706792
#130705572
#130705462
C4×#668912
#130704352
#130703202
D11×#3572
C11×#22282
#3386311