Finite Group Databasebeta

← #14909818

Subgroups — #14909818

Order 2816.

594 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079272C211yesmaximal, characteristic, complemented
2#13079098C211yesmaximal, characteristic
3#13070873C211yesmaximal, characteristic, complemented
4#13070858C211yesmaximal, characteristic, complemented
5#13070847C211yesmaximal, characteristic, complemented
6#13070680C212yesmaximal, complemented
7#13070654C212yesmaximal, complemented
8#13070555C212yesmaximal, complemented
9#13070543C212yesmaximal, complemented
10#13070424C211yesmaximal, characteristic, complemented
11C11×#2251C211yesmaximal, characteristic, complemented
12C2×#66972C2211yescharacteristic
13C2×#66967—21no—
14C2×D8×D11C2211yescharacteristic
15#10623262—21no—
16#10623205—21no—
17C2×C11×Q32C2212yescomplemented
18C2×C11×SD32C2212yes—
19C11×#495C2211yescharacteristic
20C11×#494C2211yescharacteristic, complemented
21#10622804C2211yescharacteristic
22#10622802—21no—
23#10622801C2212yes—
24#10622797—21no—
25Q16×Dic11C2212yescomplemented
26C2×#66892C2212yes—
27C2×#66892C2212yescomplemented
28#10622789—21no—
29#10622764C2211yescharacteristic
30#10622695—21no—
31#10622671—21no—
32#10622308C2211yescharacteristic
33#10622302C2211yescharacteristic
34#10622296C2211yescharacteristic, complemented
35C11×#346C2211yescharacteristic, complemented
36#10622202C2212yescomplemented
37#10622200C2212yes—
38#10622147C2212yes—
39#10622147C2212yescomplemented
40(C2×D11)⋊C16C2212yes—
41Dic11⋊C16C2212yescomplemented
42C4×C11⋊C16C2211yescharacteristic, complemented
43C2×#4343—21no—
44C2×D4×D11—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16C2312yes—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×D8C2311yescharacteristic
50C11×C4⋊Q8—21no—
51C11×#124—21no—
52#67000—21no—
53#66999—22no—
54Q8×Dic11—22no—
55C2×#4325—21no—
56C2×#4325—21no—
57#66993—21no—
58C2×#4323—21no—
59C2×#4323—21no—
60#66972—42no—
61#66967—44no—
62D8×D11—42no—
63C2×D88—21no—
64C2×D88C2311yescharacteristic
65C2×D88C2311yescharacteristic
66C2×#4313D411yescharacteristic
67C2×C8×D11C2311yescharacteristic
68#66951—42no—
69#66942—42no—
70#66937—42no—
71#66935—42no—
72#66927—21no—
73#66925D411yescharacteristic
74#66923—21no—
75C11×Q32—42no—
76C11×SD32—42no—
77C2×C11×C16C2312yes—
78C4×C8×C11C2311yescharacteristic
79#66899—22no—
80#66899—22no—
81#66892—42no—
82#66892—42no—
83#66882C2312yes—
84#66881—21no—
85#66879D411yescharacteristic
86C8×Dic11C2311yescharacteristic
87C2×C11⋊C16C2312yes—
88#66867D411yescharacteristic
89#33788—111nomaximal, Sylow
90C23×D11—41no—
91C2×Q8×C11—22no—
92C2×Q8×C11—21no—
93C2×D4×C11—21no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—42no—
96#4343—42no—
97#4343—42no—
98D4×D11—42no—
99D4×D11—42no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—41no—
103C2×D44—42no—
104C2×C4×D11—41no—
105C2×C4×D11C2×D411yescharacteristic
106C11×Q16—22no—
107C11×Q16—22no—
108C11×Q16—22no—
109C11×Q16—42no—
110C11×SD16—42no—
111C11×D8—22no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—42no—
115C11×C22⋊C4—42no—
116C42×C11C2×D411yescharacteristic
117#4325—42no—
118#4325—42no—
119#4323—42no—
120#4323—42no—
121(C2×D11)⋊C4—42no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4D812yes—
124C4⋊Dic11—22no—
125C4⋊Dic11—42no—
126Dic11⋊C4—42no—
127Dic11⋊C4—42no—
128Dic11⋊C4D812yes—
129C4×Dic11—42no—
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133D88—22no—
134D88—22no—
135D88—42no—
136#4313—22no—
137C8×D11—22no—
138C11×C16—22no—
139C11⋊C16—22no—
140#3177—111no—
141#3155—111no—
142#2251D1111yescharacteristic, complemented
143#2248—111no—
144#2244—111no—
145#2242—111no—
146#2211—112no—
147#2207—112no—
148#2189—112no—
149#2187—112no—
150#2164—111no—
151C23×C11—41no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—82no—
155C22×D11—162no—
156C22×D11C2×D811yescharacteristic
157Q8×C11—41no—
158Q8×C11—42no—
159Q8×C11—41no—
160Q8×C11—42no—
161D4×C11—41no—
162D4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11C2×D812yes—
166C2×C4×C11C22×D411yescharacteristic
167C22⋊D11—82no—
168C22⋊D11—162no—
169C2×Dic11—42no—
170C2×Dic11C2×D812yes—
171C2×Dic11C2×D811yescharacteristic
172D44—41no—
173D44—41no—
174D44—41no—
175D44—41no—
176D44—82no—
177D44—162no—
178C4×D11—21no—
179C4×D11—21no—
180C4×D11—82no—
181C8×C11AGL(1,ℤ/8)12yes—
182C8×C11H(5,𝔽2)12yes—
183C11⋊C8—21no—
184C11⋊C8—21no—
185C2×AGL(1,ℤ/8)—221no—
186C2×#135—111no—
187C22×D8—111no—
188#541—221no—
189#535—221no—
190C2×Q32C2×D1112yescomplemented
191C2×SD32—112no—
192C2×SD32—112no—
193C2×SD32C2×D1112yes—
194#499—111no—
195#496—221no—
196#496—221no—
197#495—111no—
198#495C2×D1111yescharacteristic
199#494C2×D1111yescharacteristic, complemented
200#493—111no—
201#493—111no—
202#491—221no—
203#470—221no—
204#467—112no—
205#441—221no—
206C4×Q16—112no—
207#405—111no—
208C4⋊C16—112no—
209#358—112no—
210#357—112no—
211#357—112no—
212#357—112no—
213C22⋊C16—112no—
214#346C2×D1111yescharacteristic, complemented
215C4×C16—111no—
216C22×C11—82no—
217C22×C11—81no—
218C22×C11C22×D811yescharacteristic
219C2×D11—22no—
220C2×D11—21no—
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—164no—
226C4×C11—22no—
227C4×C11—82no—
228C4×C11—81no—
229C4×C11#53511yescharacteristic
230C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
231Dic11—22no—
232Dic11—21no—
233Dic11—82no—
234C2×#41—221no—
235C22×D4—221no—
236AGL(1,ℤ/8)—444no—
237#135—442no—
238C2×Q16—21no—
239C2×Q16C22×D1111yescharacteristic
240C2×Q16C22×D1112yes—
241C2×SD16—21no—
242C2×SD16—221no—
243C2×SD16—221no—
244C2×D8—111no—
245C2×D8—111no—
246C2×D8—221no—
247C2×D8—221no—
248C2×D8—221no—
249C2×D8—442no—
250C2×D8C22×D1111yescharacteristic
251C2×M16—111no—
252C22×C8—111no—
253C4⋊Q8—21no—
254#127—221no—
255#127—221no—
256#126—442no—
257#125—221no—
258#125—442no—
259#124—21no—
260#124—221no—
261C22⋊Q8—222no—
262#121—442no—
263#120—442no—
264C4×Q8—222no—
265#117—111no—
266Q32—42no—
267SD32—42no—
268SD32—442no—
269SD32—442no—
270C2×C16—112no—
271C2×C16C22×D1112yes—
272#107—112no—
273#106—221no—
274#103—222no—
275#103—222no—
276#97—111no—
277#97—111no—
278C4×C8—111no—
279C4×C8C22×D1111yescharacteristic
280C2×C11—161no—
281C2×C11#320511yescharacteristic
282C2×C11#341612yes—
283D11—41no—
284D11—161no—
285D11—161no—
286C24—441no—
287#41—442no—
288#41—442no—
289C2×Q8—22no—
290C2×Q8—21no—
291C2×D4—21no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—442no—
300C22×C4—111no—
301C22×C4—441no—
302Q16—22no—
303Q16—22no—
304Q16—22no—
305Q16—42no—
306SD16—42no—
307SD16—442no—
308SD16—442no—
309D8—22no—
310D8—222no—
311D8—222no—
312D8—442no—
313D8—442no—
314D8—442no—
315M16—222no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—222no—
319C2×C8D4×D1111yescharacteristic
320C2×C8C23×D1111yescharacteristic
321C4⋊C4—42no—
322C4⋊C4—112no—
323C4⋊C4—222no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C4⋊C4—442no—
327C22⋊C4—42no—
328C22⋊C4—112no—
329C22⋊C4—442no—
330C22⋊C4—442no—
331C42—111no—
332C42—442no—
333C42D4×D1111yescharacteristic
334C16—22no—
335C16—222no—
336C11#3378811yescharacteristic, complemented, Sylow
337C23—41no—
338C23—111no—
339C23—441no—
340C23—441no—
341C23—882no—
342C23—1762no—
343Q8—41no—
344Q8—42no—
345Q8—41no—
346Q8—42no—
347D4—41no—
348D4—41no—
349D4—441no—
350D4—441no—
351D4—441no—
352D4—441no—
353D4—882no—
354D4—882no—
355D4—1762no—
356D4—1762no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—112no—
360C2×C4—111no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—442no—
364C2×C4—882no—
365C2×C4D8×D1112yes—
366C2×C4C2×D4×D1111yescharacteristic
367C8—221no—
368C8—221no—
369C8#6696412yes—
370C8#6703712yes—
371C22—82no—
372C22—81no—
373C22—222no—
374C22—221no—
375C22—882no—
376C22—882no—
377C22—881no—
378C22—881no—
379C22—1764no—
380C22C2×D8×D1111yescharacteristic
381C4—22no—
382C4—81no—
383C4—82no—
384C4—222no—
385C4—221no—
386C4—882no—
387C4#1062324611yescharacteristic
388C4C2×#6696411yescharacteristic
389C2—161no—
390C2—441no—
391C2—1761no—
392C2—1761no—
393C2#1307953011yescharacteristic
394C2#1308176112yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2251C2
socleC22×C11C22×D8
prime radical#13079098C2
hypercenter#2251D11
hypocenterC11#33788
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2251

Complements

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

NH ≅ G/Ntype
1. #13079272C2semidirect
3. #13070873C2semidirect
4. #13070858C2semidirect
5. #13070847C2semidirect
6. #13070680C2semidirect
7. #13070654C2semidirect
8. #13070555C2semidirect
9. #13070543C2semidirect
10. #13070424C2semidirect
11. C11×#2251C2semidirect
17. C2×C11×Q32C22semidirect
20. C11×#494C22semidirect
25. Q16×Dic11C22semidirect
27. C2×#66892C22semidirect
34. #10622296C22semidirect
35. C11×#346C22semidirect
36. #10622202C22semidirect
39. #10622147C22semidirect
41. Dic11⋊C16C22semidirect
42. C4×C11⋊C16C22semidirect
142. #2251D11semidirect
190. C2×Q32C2×D11semidirect
199. #494C2×D11semidirect
214. #346C2×D11semidirect
336. C11#33788semidirect

Maximal subgroups

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

subgroupindex
#130792722
#130790982
#130708732
#130708582
#130708472
#130706802
#130706542
#130705552
#130705432
#130704242
C11×#22512
#3378811