Finite Group Databasebeta

← #14667427

Subgroups — #14667427

Order 2816.

302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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#13081192C211yesmaximal, characteristic, complemented
2#13070857C211yesmaximal, characteristic, complemented
3#13068092C211yesmaximal, characteristic
4#13066667C211yesmaximal, characteristic, complemented
5#13066586C211yesmaximal, characteristic, complemented
6#13066573C211yesmaximal, characteristic, complemented
7C11×#2207C211yesmaximal, characteristic, complemented
8#10623112—21no—
9C2×C11×SD32—21no—
10C11×#493C2211yescharacteristic
11C4×C11×Q16C2211yescharacteristic
12#10622802—21no—
13#10622685—21no—
14#10622635—21no—
15#10622494—21no—
16#10622427—21no—
17#10622422—21no—
18#10622301C2211yescharacteristic
19#10622296C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#357—21no—
22#10622200—21no—
23#10622200—21no—
24#10622182—21no—
25#10622099C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×Q16D411yescharacteristic
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C11×#127—21no—
31C4×Q8×C11—21no—
32#66999—21no—
33#66999—21no—
34C2×#4323—41no—
35C2×#4313—21no—
36#66947—41no—
37#66945—21no—
38C4⋊C4×D11—21no—
39#66942—41no—
40#66929—41no—
41C4×D44D411yescharacteristic
42#66925—41no—
43#66923—21no—
44C11×SD32—42no—
45C2×C11×C16—21no—
46C11×#107D411yescharacteristic
47C11×#103—21no—
48C4×C8×C11C2311yescharacteristic
49#66899—21no—
50#66899—21no—
51#66896—41no—
52(C2×D11)⋊C8—21no—
53#66882D411yescharacteristic
54#66882D411yescharacteristic
55#66881—21no—
56C2×C11⋊C16—21no—
57#66872—21no—
58#66871—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D411yescharacteristic
61#12349—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D44D811yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11—41no—
69C11×Q16—21no—
70C11×Q16—21no—
71C11×D8—42no—
72C11×D8—41no—
73C11×D8—41no—
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—41no—
78C42×C11—41no—
79C42×C11C2×D411yescharacteristic
80#4323—82no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—41no—
83(C2×D11)⋊C4—41no—
84(C2×D11)⋊C4—41no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11D811yescharacteristic
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—41no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—41no—
96#4313—41no—
97#4313—41no—
98C11×C16—41no—
99C11⋊C16—41no—
100#3352—111no—
101#2244—111no—
102#2207D1111yescharacteristic, complemented
103#1687—111no—
104#1363—111no—
105#1334—111no—
106#1330—111no—
107C23×C11—81no—
108C22×D11—21no—
109Q8×C11—41no—
110Q8×C11—41no—
111D4×C11—81no—
112D4×C11—81no—
113D4×C11—81no—
114D4×C11—81no—
115D4×C11—161no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C2×Dic11—21no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124D44—41no—
125C4×D11—41no—
126C4×D11—41no—
127C4×D11—82no—
128C8×C11—21no—
129C8×C11#13511yescharacteristic
130C8×C11AGL(1,ℤ/8)11yescharacteristic
131C11⋊C8—41no—
132C11⋊C8—81no—
133#552—221no—
134C2×SD32—21no—
135#499—111no—
136#493C2×D1111yescharacteristic
137#485—221no—
138#484—221no—
139#479—221no—
140#470—221no—
141#459—221no—
142C4×Q16C2×D1111yescharacteristic
143#436—111no—
144#428—221no—
145C4⋊C16C2×D1111yescharacteristic
146#357—21no—
147#357—221no—
148#357—221no—
149#346—111no—
150#334—111no—
151#331—221no—
152C22×C11—161no—
153C22×C11—161no—
154C22×C11—161no—
155C22×C11#44711yescharacteristic
156C2×D11—41no—
157C2×D11—41no—
158C2×D11—41no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—81no—
162C4×C11—81no—
163C4×C11#44911yescharacteristic
164C4×C11#45411yescharacteristic
165Dic11—41no—
166Dic11—81no—
167Dic11—81no—
168C2×Q16C22⋊D1111yescharacteristic
169C2×D8—21no—
170C2×D8—21no—
171C2×D8—441no—
172C2×M16—221no—
173#127—21no—
174#126—441no—
175#125—221no—
176#125—441no—
177#123—441no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—21no—
181C4×D4—111no—
182#117—221no—
183#117—441no—
184C2×C4⋊C4—221no—
185SD32—42no—
186C2×C16—21no—
187C2×C16—221no—
188#107—111no—
189#107—111no—
190#107—221no—
191#107C22⋊D1111yescharacteristic
192#106—221no—
193#106—221no—
194C4⋊C8—111no—
195C4⋊C8—221no—
196#103—21no—
197#103—221no—
198#103—221no—
199#102—441no—
200C22⋊C8—221no—
201C4×C8C22×D1111yescharacteristic
202C2×C11—321no—
203C2×C11#162511yescharacteristic
204C2×C11#219011yescharacteristic
205C2×C11#219311yescharacteristic
206D11—81no—
207C2×Q8—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—111no—
212C22×C4—221no—
213C22×C4—441no—
214Q16—21no—
215Q16—21no—
216D8—42no—
217D8—41no—
218D8—41no—
219D8—882no—
220M16—441no—
221M16—441no—
222C2×C8—221no—
223C2×C8—441no—
224C2×C8D4×D1111yescharacteristic
225C2×C8C2×C22⋊D1111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—111no—
229C4⋊C4—221no—
230C4⋊C4—221no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C22⋊C4—221no—
237C22⋊C4—441no—
238C22⋊C4—441no—
239C22⋊C4—441no—
240C42—41no—
241C42—441no—
242C42D4×D1111yescharacteristic
243C16—41no—
244C16—441no—
245C11#1234911yescharacteristic, complemented, Sylow
246C23—81no—
247C23—221no—
248Q8—41no—
249Q8—41no—
250D4—81no—
251D4—81no—
252D4—81no—
253D4—81no—
254D4—161no—
255D4—441no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—221no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—882no—
264C2×C4D8×D1111yescharacteristic
265C2×C4#6696411yescharacteristic
266C2×C4#6699011yescharacteristic
267C8—21no—
268C8—441no—
269C8—881no—
270C8#6698511yescharacteristic
271C8#6700311yescharacteristic
272C22—161no—
273C22—161no—
274C22—161no—
275C22—441no—
276C22—441no—
277C22—441no—
278C22#1062276911yescharacteristic
279C4—21no—
280C4—21no—
281C4—81no—
282C4—81no—
283C4—441no—
284C4—881no—
285C4—881no—
286C4#1062265011yescharacteristic
287C4#1062281411yescharacteristic
288C2—321no—
289C2—881no—
290C2#1306770411yescharacteristic
291C2#1307056011yescharacteristic
292C2#1307057911yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2207C2
socleC22×C11#447
prime radical#13068092C2
hypercenter#2207D11
hypocenterC11#12349
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13081192C2semidirect
2. #13070857C2semidirect
4. #13066667C2semidirect
5. #13066586C2semidirect
6. #13066573C2semidirect
7. C11×#2207C2semidirect
102. #2207D11semidirect
245. C11#12349semidirect

Maximal subgroups

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

subgroupindex
#130811922
#130708572
#130680922
#130666672
#130665862
#130665732
C11×#22072
#1234911