Finite Group Databasebeta

← #14909710

Subgroups — #14909710

Order 2816.

592 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 139 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#13079203C211yesmaximal, characteristic, complemented
2#13079045C211yesmaximal, characteristic
3#13070872C211yesmaximal, characteristic, complemented
4#13070868C211yesmaximal, characteristic, complemented
5#13070841C211yesmaximal, characteristic, complemented
6#13070681C214yesmaximal, complemented
7#13070559C214yesmaximal, complemented
8#13070413C211yesmaximal, characteristic, complemented
9C11×#2241C211yesmaximal, characteristic, complemented
10C2×#66972—21no—
11C2×#66972C2212yes—
12#10623259—21no—
13#10623256—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16#10622804—21no—
17#10622804C2212yes—
18C2×#66893C2214yes—
19#10622706—21no—
20#10622698—21no—
21C2×#66864C2214yes—
22#10622500—21no—
23#10622500C2212yes—
24#10622486—21no—
25#10622486C2212yes—
26#10622312C2211yescharacteristic
27#10622308C2211yescharacteristic
28C4×C8×D11C2211yescharacteristic
29C11×#358C2214yes—
30C4×C11×C16C2211yescharacteristic
31(C2×D11)⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622129C2214yes—
34C4×C11⋊C16C2211yescharacteristic
35C2×#4343—22no—
36C2×C11×Q16—21no—
37C2×C11×Q16C2312yes—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40#67000—22no—
41#66999—41no—
42Q8×Dic11—41no—
43C2×#4325—22no—
44C2×#4325—22no—
45#66972—44no—
46#66972—44no—
47C2×Dic44—21no—
48C2×Dic44C2312yes—
49C2×D88—21no—
50C2×D88C2312yes—
51C2×C8×D11D411yescharacteristic
52C2×C8×D11C2311yescharacteristic
53#66950—22no—
54#66948—41no—
55#66948—41no—
56#66946—41no—
57#66946—41no—
58#66945—41no—
59#66943—41no—
60#66940—22no—
61#66927—21no—
62C42×D11D411yescharacteristic
63#66922—21no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2312yes—
67C4×C8×C11C2311yescharacteristic
68#66893—44no—
69C8×Dic11D411yescharacteristic
70C8×Dic11C2311yescharacteristic
71C2×C11⋊C16C2312yes—
72#66874—22no—
73#66874—22no—
74C4×C11⋊C8D411yescharacteristic
75#66864—44no—
76#33776—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79#4343—44no—
80#4343—44no—
81C2×D44—22no—
82C2×D44—42no—
83C2×D44—41no—
84C2×D44—41no—
85C2×C4×D11—42no—
86C2×C4×D11D811yescharacteristic
87C2×C4×D11D811yescharacteristic
88C2×C4×D11C2×D411yescharacteristic
89C2×Dic22—22no—
90C11×Q16—24no—
91C11×Q16—42no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99#4325—44no—
100#4325—44no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—42no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—42no—
108C4×Dic11—42no—
109C4×Dic11D811yescharacteristic
110C4×Dic11D811yescharacteristic
111C4×Dic11C2×D411yescharacteristic
112C2×C11⋊C8C2×D411yescharacteristic
113C2×C11⋊C8C2×D411yescharacteristic
114Dic44—24no—
115Dic44—42no—
116D88—24no—
117D88—42no—
118C8×D11—22no—
119C8×D11—22no—
120C11×C16—22no—
121C11⋊C16—22no—
122#3170—111no—
123#3147—111no—
124#2248—111no—
125#2247—111no—
126#2241D1111yescharacteristic, complemented
127#2240—111no—
128#2211—114no—
129#2189—114no—
130#2162—111no—
131C22×D11—42no—
132C22×D11C2×D811yescharacteristic
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—82no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—42no—
142C2×Dic11C2×D811yescharacteristic
143C2×Dic11C2×D811yescharacteristic
144C2×Dic11C2×D811yescharacteristic
145D44—42no—
146D44—42no—
147D44—84no—
148D44—82no—
149D44—82no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—84no—
155Dic22—42no—
156Dic22—42no—
157C8×C11AGL(1,ℤ/8)12yes—
158C8×C11H(5,𝔽2)12yes—
159C11⋊C8—21no—
160C11⋊C8—21no—
161C2×#135—112no—
162C2×#135—221no—
163#533—221no—
164#532—221no—
165C2×Q32—114no—
166C2×SD32—114no—
167#500C2×D1111yescharacteristic
168#495—112no—
169#495—221no—
170#494—111no—
171#494C2×D1111yescharacteristic
172#493—111no—
173#492—221no—
174#487—221no—
175#467—112no—
176#467—221no—
177C4×Q16—112no—
178C4×Q16—221no—
179C2×C4×C8—111no—
180C4⋊C16—112no—
181#358C2×D1114yes—
182#357—114no—
183C22⋊C16—112no—
184C4×C16—111no—
185C4×C16C2×D1111yescharacteristic
186C22×C11C22×D811yescharacteristic
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C4×C11—82no—
194C4×C11—82no—
195C4×C11#50812yes—
196C4×C11#51012yes—
197C4×C11#53511yescharacteristic
198C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
199Dic11—21no—
200Dic11—21no—
201Dic11—21no—
202Dic11—82no—
203C2×#41—222no—
204#135—444no—
205#135—444no—
206C2×Q16—21no—
207C2×Q16—112no—
208C2×Q16—221no—
209C2×Q16C22×D1112yes—
210C2×SD16—222no—
211C2×SD16—222no—
212C2×D8—112no—
213C2×D8—221no—
214C22×C8—111no—
215C22×C8—111no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—221no—
219#127—221no—
220#125—441no—
221#124—222no—
222C22⋊Q8—222no—
223C22⋊Q8—441no—
224#121—441no—
225#121—441no—
226C4×Q8—222no—
227C4×Q8—441no—
228C4×D4—441no—
229C4×D4—441no—
230#117—441no—
231C2×C42—111no—
232Q32—444no—
233SD32—444no—
234C2×C16—112no—
235C2×C16C22×D1112yes—
236#107—21no—
237#107C22×D1112yes—
238#103—222no—
239#103—222no—
240C4×C8—111no—
241C4×C8—111no—
242C4×C8—111no—
243C4×C8C22×D1111yescharacteristic
244C2×C11#320511yescharacteristic
245C2×C11C2×#50811yescharacteristic
246C2×C11C2×#51011yescharacteristic
247D11—41no—
248D11—162no—
249#41—444no—
250#41—444no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—222no—
254C2×D4—222no—
255C2×D4—442no—
256C2×D4—441no—
257C2×D4—441no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—442no—
262Q16—24no—
263Q16—42no—
264Q16—224no—
265Q16—442no—
266SD16—444no—
267SD16—444no—
268D8—224no—
269D8—442no—
270C2×C8—111no—
271C2×C8—111no—
272C2×C8—222no—
273C2×C8—222no—
274C2×C8D4×D1111yescharacteristic
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C42—111no—
288C42—111no—
289C42—111no—
290C42—442no—
291C42D4×D1111yescharacteristic
292C16—22no—
293C16—222no—
294C11#3377611yescharacteristic, complemented, Sylow
295C23—111no—
296C23—442no—
297Q8—42no—
298Q8—42no—
299Q8—82no—
300Q8—442no—
301Q8—442no—
302D4—442no—
303D4—442no—
304D4—884no—
305D4—882no—
306D4—882no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—221no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—221no—
316C2×C4—442no—
317C2×C4—884no—
318C2×C4D8×D1111yescharacteristic
319C2×C4D8×D1111yescharacteristic
320C2×C4C2×D4×D1111yescharacteristic
321C8—221no—
322C8—221no—
323C8#6696712yes—
324C8#6704212yes—
325C22—221no—
326C22—221no—
327C22—221no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22C2×D8×D1111yescharacteristic
332C4—82no—
333C4—82no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—882no—
338C4#1062252912yes—
339C4#1062253112yes—
340C4#1062320511yescharacteristic
341C4C2×#6696711yescharacteristic
342C2—441no—
343C2—1762no—
344C2#1307953511yescharacteristic
345C2C2×#1062252911yescharacteristic
346C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radical#13079045C2
hypercenter#2241D11
hypocenterC11#33776
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
1. #13079203C2semidirect
3. #13070872C2semidirect
4. #13070868C2semidirect
5. #13070841C2semidirect
6. #13070681C2semidirect
7. #13070559C2semidirect
8. #13070413C2semidirect
9. C11×#2241C2semidirect
126. #2241D11semidirect
294. C11#33776semidirect

Maximal subgroups

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

subgroupindex
#130792032
#130790452
#130708722
#130708682
#130708412
#130706812
#130705592
#130704132
C11×#22412
#3377611