Finite Group Databasebeta

← #14667056

Subgroups — #14667056

Order 2816.

310 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 63 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#13079957C211yesmaximal, characteristic
2#13070818C211yesmaximal, characteristic
3#13070110C211yesmaximal, characteristic
4#13066629C211yesmaximal, characteristic
5#13066628C211yesmaximal, characteristic
6#13066555C211yesmaximal, characteristic
7C11×#2236C211yesmaximal, characteristic
8#10623153—21no—
9C11×#467C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11#10622795—21no—
12#10622729C2211yescharacteristic
13C2×Dic11⋊C8C2211yescharacteristic
14#10622664—21no—
15#10622586—21no—
16#10622488—21no—
17#10622407—21no—
18#10622406—21no—
19C11×#366—21no—
20C11×#358—21no—
21C11×C22⋊C16C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25#10622130—21no—
26#10622127—21no—
27C2×C11×Q16D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×C22⋊Q8—21no—
30C2×C11×C4⋊C4—21no—
31Q8×Dic11—21no—
32#66997—21no—
33C2×#4326—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36C2×Dic11⋊C4—41no—
37C2×C4×Dic11D411yescharacteristic
38C22×C11⋊C8D411yescharacteristic
39C2×Dic44D411yescharacteristic
40#66942—41no—
41#66941—21no—
42#66940—21no—
43#66940—41no—
44#66931—41no—
45#66930—41no—
46C2×C11×C16—21no—
47C11×#107—21no—
48C11×#107—21no—
49C11×#107D411yescharacteristic
50C11×#103—21no—
51#66899—21no—
52C11⋊#95—41no—
53#66882D411yescharacteristic
54#66880—21no—
55Dic11⋊C8—21no—
56Dic11⋊C8—21no—
57C2×C11⋊C16—21no—
58#66874—21no—
59#66871—21no—
60#12292—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—41no—
65C22×Dic11D811yescharacteristic
66C22×Dic11D811yescharacteristic
67C2×Dic22—21no—
68C2×Dic22—41no—
69C11×Q16—41no—
70C2×C8×C11—41no—
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—41no—
79#4326—81no—
80C4⋊Dic11—22no—
81C4⋊Dic11—21no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—82no—
90C4×Dic11—21no—
91C4×Dic11—21no—
92C4×Dic11—41no—
93C4×Dic11—41no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—41no—
96Dic44—41no—
97C11×C16—41no—
98C11⋊C16—41no—
99#3249—111no—
100#2236—111no—
101#2236D1111yescharacteristic
102#2087—111no—
103#1348—111no—
104#1348—111no—
105#1322—111no—
106C23×C11C2×D811yescharacteristic
107Q8×C11—41no—
108Q8×C11—41no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—81no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—41no—
122C2×Dic11—42no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—81no—
126C2×Dic11—81no—
127C2×Dic11Q3212yes—
128Dic22—41no—
129Dic22—41no—
130Dic22—82no—
131C8×C11—21no—
132C8×C11—21no—
133C11⋊C8—41no—
134#533—221no—
135#477—221no—
136#477—221no—
137#467—111no—
138#467—221no—
139#467C2×D1111yescharacteristic
140#462—221no—
141#462—221no—
142C2×#107C2×D1111yescharacteristic
143C2×C4⋊C8—111no—
144#389—221no—
145#366—21no—
146#366—221no—
147#358—21no—
148#358—221no—
149C22⋊C16—111no—
150C22⋊C16C2×D1111yescharacteristic
151#340—111no—
152#340—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11#44711yescharacteristic
156C22×C11C2×Q3211yescharacteristic
157C22×C11#51011yescharacteristic
158C4×C11—21no—
159C4×C11—81no—
160C4×C11—81no—
161C4×C11—161no—
162C4×C11#45611yescharacteristic
163C4×C11#45811yescharacteristic
164Dic11—22no—
165Dic11—41no—
166Dic11—82no—
167Dic11—81no—
168Dic11—81no—
169C2×Q16—111no—
170C2×Q16—221no—
171C2×Q16C22⋊D1111yescharacteristic
172C22×C8—111no—
173C22×C8C22×D1111yescharacteristic
174C4⋊Q8—221no—
175C4⋊Q8—221no—
176#125—441no—
177C22⋊Q8—21no—
178C22⋊Q8—221no—
179C22⋊Q8—441no—
180C4×Q8—221no—
181C4×Q8—221no—
182C4×Q8—441no—
183#117—441no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—441no—
187C2×C42—111no—
188C2×C16—21no—
189C2×C16—221no—
190#107—21no—
191#107—21no—
192#107—111no—
193#107—221no—
194#107C22⋊D1111yescharacteristic
195C4⋊C8—221no—
196C4⋊C8—221no—
197#103—21no—
198#103—221no—
199#103—221no—
200#103—221no—
201#95—441no—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11#161011yescharacteristic
205C2×C11#218811yescharacteristic
206C2×C11#219011yescharacteristic
207C2×Q8—21no—
208C2×Q8—221no—
209C2×Q8—441no—
210C22×C4—41no—
211C22×C4—111no—
212C22×C4—111no—
213C22×C4—441no—
214C22×C4D4×D1111yescharacteristic
215Q16—41no—
216Q16—441no—
217Q16—881no—
218C2×C8—41no—
219C2×C8—221no—
220C2×C8—441no—
221C2×C8D4×D1111yescharacteristic
222C2×C8C2×C22⋊D1111yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—222no—
228C4⋊C4—221no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—882no—
237C22⋊C4—41no—
238C22⋊C4—441no—
239C42—221no—
240C42—221no—
241C42—441no—
242C42—441no—
243C16—41no—
244C16—441no—
245C11#1229211yescharacteristic, complemented, Sylow
246C23D8×D1111yescharacteristic
247Q8—41no—
248Q8—41no—
249Q8—441no—
250Q8—441no—
251Q8—882no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—112no—
260C2×C4—221no—
261C2×C4—221no—
262C2×C4—221no—
263C2×C4—441no—
264C2×C4—442no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—881no—
268C2×C4—881no—
269C2×C4#6696411yescharacteristic
270C2×C4#6699011yescharacteristic
271C8—21no—
272C8—21no—
273C8—441no—
274C22—21no—
275C22—21no—
276C22D11×Q3211yescharacteristic
277C22#1062253111yescharacteristic
278C22#1062276911yescharacteristic
279C4—21no—
280C4—81no—
281C4—81no—
282C4—161no—
283C4—222no—
284C4—441no—
285C4—882no—
286C4—881no—
287C4—881no—
288C4#1062266611yescharacteristic
289C4#1062281811yescharacteristic
290C2—21no—
291C2—21no—
292C2#1306761711yescharacteristic
293C2#1307054811yescharacteristic
294C2#1307056011yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2236C2
socleC22×C11#447
prime radicalC23×C11C2×D8
hypercenter#2236D11
hypocenterC11#12292
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
245. C11#12292semidirect

Maximal subgroups

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

subgroupindex
#130799572
#130708182
#130701102
#130666292
#130666282
#130665552
C11×#22362
#1229211