Finite Group Databasebeta

← #14658123

Subgroups — #14658123

Order 2816.

448 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 81 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#13069085C212yesmaximal
2#13068798C211yesmaximal, characteristic
3#13067136C212yesmaximal
4#13066493C211yesmaximal, characteristic
5C11×#3189C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2212yes—
7C22×#4318C2211yescharacteristic
8C11×#484—22no—
9C11×#467—21no—
10C11×#467—21no—
11C11×#451—22no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×#66900—22no—
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2212yes—
16C2×Dic11⋊C8—21no—
17#10622188—21no—
18#10622176—22no—
19#10622176—22no—
20#10622168—22no—
21C22×Q8×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—22no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C22⋊C4—22no—
34C2×C22⋊Dic11—21no—
35C2×C4×Dic11—21no—
36C2×#4318—22no—
37C2×#4318—22no—
38C2×#4318—42no—
39C22×C11⋊C8—21no—
40C11×#107—21no—
41C11×#107—21no—
42C11×#103—22no—
43C11×#103—22no—
44C11×C22⋊C8—22no—
45#66900—44no—
46C11⋊#95D411yescharacteristic
47C11⋊#95D411yescharacteristic
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50Dic11⋊C8—42no—
51#10559—111nomaximal, Sylow
52C24×C11#4111yescharacteristic
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×Q8×C11—42no—
56C2×Q8×C11—42no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4112yes—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C11×Q16—81no—
68C11×Q16—81no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C22⋊Dic11—42no—
80C4×Dic11—41no—
81C4×Dic11—41no—
82#4318—24no—
83#4318—42no—
84#4318—42no—
85#4318—42no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—42no—
90#3189D1111yescharacteristic
91#1901—112no—
92#1851—111no—
93#1508—112no—
94#1293—111no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11#12111yescharacteristic
100C23×C11#12312yes—
101Q8×C11—42no—
102Q8×C11—42no—
103Q8×C11—82no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—44no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—82no—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11#12112yes—
116C2×C4×C11#12411yescharacteristic
117C2×Dic11—22no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C8×C11—41no—
124C8×C11—41no—
125C11⋊C8—42no—
126C11⋊C8—82no—
127C22×M16—111no—
128C2×C22⋊Q8C2×D1112yes—
129#484—22no—
130#467—21no—
131#467—21no—
132#451—22no—
133C2×C4⋊C8—221no—
134C2×#101—222no—
135#407—112no—
136C2×C22⋊C8C2×D1111yescharacteristic
137C4×C22⋊C4—111no—
138#343—222no—
139#336—221no—
140#328—222no—
141#328—222no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—81no—
148C22×C11—81no—
149C22×C11#39411yescharacteristic
150C22×C11#47311yescharacteristic
151C22×C11#47311yescharacteristic
152C4×C11—22no—
153C4×C11—21no—
154C4×C11—82no—
155C4×C11—82no—
156C4×C11B(4,𝔽2)11yescharacteristic
157C4×C11#45811yescharacteristic
158Dic11—42no—
159Dic11—81no—
160C22×Q8C22⋊D1112yes—
161C23×C4C22×D1111yescharacteristic
162C2×Q16—21no—
163C2×Q16—21no—
164C2×M16—222no—
165C2×M16—222no—
166C2×M16—442no—
167C22×C8—221no—
168C22×C8C22⋊D1111yescharacteristic
169C22×C8C22⋊D1111yescharacteristic
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4C22⋊D1112yes—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—221no—
178C2×C42—221no—
179#107—21no—
180#107—21no—
181C4⋊C8—442no—
182#103—22no—
183#103—22no—
184#101—444no—
185C22⋊C8—22no—
186C22⋊C8—222no—
187C22⋊C8—222no—
188#95—111no—
189#95—111no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11—42no—
193C2×C11#204411yescharacteristic
194C2×C11#204711yescharacteristic
195C2×C11#205011yescharacteristic
196C24#434111yescharacteristic
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—42no—
200C2×Q8—42no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—221no—
206C22×C4—221no—
207C22×C4D4×D1111yescharacteristic
208C22×C4#434112yes—
209C22×C4C2×C22⋊D1111yescharacteristic
210C22×C4C2×C22⋊D1112yes—
211Q16—81no—
212Q16—81no—
213M16—224no—
214M16—442no—
215M16—442no—
216M16—442no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—222no—
222C2×C8—441no—
223C2×C8—441no—
224C2×C8—442no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—442no—
232C42—441no—
233C42—441no—
234C11#1055911yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#6698812yes—
240C23#6699111yescharacteristic
241Q8—42no—
242Q8—42no—
243Q8—82no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—44no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—82no—
254C2×C4—222no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4#6698911yescharacteristic
261C2×C4#6699212yes—
262C2×C4#6700611yescharacteristic
263C8—41no—
264C8—41no—
265C8—442no—
266C8—882no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22#1062280511yescharacteristic
275C22#1062280511yescharacteristic
276C22#1062283511yescharacteristic
277C4—22no—
278C4—21no—
279C4—82no—
280C4—82no—
281C4—442no—
282C4—881no—
283C4#1062285611yescharacteristic
284C4#1062285711yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2#1306986411yescharacteristic
289C2#1306988111yescharacteristic
290C2#1306990011yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3189C2
socleC22×C11#394
prime radicalC24×C11#41
hypercenter#3189D11
hypocenterC11#10559
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
234. C11#10559semidirect

Maximal subgroups

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

subgroupindex
#130690852
#130687982
#130671362
#130664932
C11×#31892
#1055911