Finite Group Databasebeta

← #14666582

Subgroups — #14666582

Order 2816.

456 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076880C211yesmaximal, characteristic
2#13069780C211yesmaximal, characteristic
3#13067643C212yesmaximal, complemented
4#13066641C212yesmaximal, complemented
5C11×#1316C211yesmaximal, characteristic
6#10623014C2211yescharacteristic
7C11×#379C2211yescharacteristic
8#10622860—21no—
9#10622860—21no—
10#10622562—21no—
11#10622562C2212yes—
12#10622561—22no—
13#10622561—22no—
14#10622335—22no—
15C11×#323C2212yes—
16#10622165—21no—
17#10622164C2211yescharacteristic
18#10622105—22no—
19C25×C11D411yescharacteristic
20C2×C11×C22⋊C4—22no—
21C2×C11×C22⋊C4D411yescharacteristic
22C2×C11×C22⋊C4C2311yescharacteristic
23C2×C22⋊Dic11—21no—
24C2×C22⋊Dic11—21no—
25C2×C22⋊Dic11—21no—
26C2×C22⋊Dic11—22no—
27C2×C22⋊Dic11—21no—
28C2×C22⋊Dic11—22no—
29C2×C22⋊Dic11—42no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11D412yes—
32#66977—22no—
33C2×Dic11⋊C4—22no—
34C2×Dic11⋊C4—22no—
35#66931—42no—
36C11×C22⋊C8—22no—
37C11⋊#95—21no—
38C11⋊#95D412yes—
39#66882—42no—
40#66880—42no—
41#12218—111nomaximal, Sylow
42C24×C11—21no—
43C24×C11—21no—
44C24×C11—41no—
45C24×C11—41no—
46C24×C11—82no—
47C24×C11Q1612yes—
48C24×C11C2×D411yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11C2×D412yes—
51C22×Dic11—22no—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C22×Dic11—41no—
55C2×Dic22—22no—
56C2×C8×C11—42no—
57C11×C22⋊C4—41no—
58C11×C22⋊C4—41no—
59C11×C22⋊C4—82no—
60C22⋊Dic11—41no—
61C22⋊Dic11—41no—
62C22⋊Dic11—41no—
63C22⋊Dic11—41no—
64C22⋊Dic11—82no—
65C22⋊Dic11—82no—
66C22⋊Dic11—81no—
67C22⋊Dic11—81no—
68C22⋊Dic11—84no—
69C4⋊Dic11—22no—
70C4⋊Dic11—42no—
71C4⋊Dic11—81no—
72Dic11⋊C4—42no—
73Dic11⋊C4—82no—
74Dic11⋊C4—82no—
75#2842—111no—
76#2029—111no—
77#1614—112no—
78#1352—112no—
79#1316D1111yescharacteristic
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—22no—
83C23×C11—42no—
84C23×C11—42no—
85C23×C11—42no—
86C23×C11—42no—
87C23×C11—44no—
88C23×C11—41no—
89C23×C11—41no—
90C23×C11—81no—
91C23×C11—82no—
92C23×C11—82no—
93C23×C11—82no—
94C23×C11—84no—
95C23×C11#12011yescharacteristic
96C23×C11C2×Q1611yescharacteristic
97C23×C11#13711yescharacteristic
98C2×C4×C11—22no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—41no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—82no—
110C2×Dic11—81no—
111C2×Dic11—82no—
112Dic22—82no—
113C8×C11—82no—
114#543—111no—
115#484—222no—
116#399—112no—
117#399—221no—
118#396—222no—
119#396—222no—
120#379—221no—
121#379—221no—
122#379C2×D1111yescharacteristic
123#342—111no—
124#342—221no—
125#328—222no—
126#323C2×D1112yes—
127C22×C11—22no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—44no—
136C22×C11—42no—
137C22×C11—81no—
138C22×C11—82no—
139C22×C11—82no—
140C22×C11—84no—
141C22×C11—82no—
142C22×C11#45111yescharacteristic
143C22×C11#45511yescharacteristic
144C22×C11B(4,𝔽2)11yescharacteristic
145C4×C11—42no—
146C4×C11—81no—
147Dic11—82no—
148Dic11—82no—
149Dic11—82no—
150Dic11—161no—
151C25D4411yescharacteristic
152C22⋊Q8—222no—
153C22⋊Q8—442no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—222no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4—222no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—221no—
160C2×C22⋊C4—221no—
161C2×C22⋊C4—221no—
162C2×C22⋊C4—222no—
163C2×C22⋊C4—221no—
164C2×C22⋊C4—222no—
165C2×C22⋊C4—442no—
166C2×C22⋊C4D4411yescharacteristic
167C2×C22⋊C4C22×D1111yescharacteristic
168#107—442no—
169#103—442no—
170C22⋊C8—22no—
171#95—112no—
172#95—221no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11—41no—
176C2×C11—41no—
177C2×C11—82no—
178C2×C11#160211yescharacteristic
179C2×C11#220012yes—
180C24—21no—
181C24—21no—
182C24—41no—
183C24—41no—
184C24—82no—
185C24Dic4412yes—
186C24C2×D4411yescharacteristic
187C2×Q8—222no—
188C22×C4—21no—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4—222no—
192C22×C4—441no—
193C22×C4D4×D1112yes—
194C2×C8—42no—
195C4⋊C4—222no—
196C4⋊C4—442no—
197C4⋊C4—442no—
198C4⋊C4—882no—
199C4⋊C4—882no—
200C4⋊C4—881no—
201C22⋊C4—41no—
202C22⋊C4—41no—
203C22⋊C4—82no—
204C22⋊C4—441no—
205C22⋊C4—441no—
206C22⋊C4—441no—
207C22⋊C4—441no—
208C22⋊C4—882no—
209C22⋊C4—882no—
210C22⋊C4—881no—
211C22⋊C4—881no—
212C22⋊C4—884no—
213C11#1221811yescharacteristic, complemented, Sylow
214C23—21no—
215C23—21no—
216C23—22no—
217C23—42no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—44no—
222C23—41no—
223C23—41no—
224C23—81no—
225C23—82no—
226C23—82no—
227C23—82no—
228C23—84no—
229C23#6693511yescharacteristic
230C23C2×Dic4411yescharacteristic
231C23#6696211yescharacteristic
232Q8—882no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—882no—
245C2×C4—881no—
246C2×C4—882no—
247C8—82no—
248C22—22no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—44no—
257C22—42no—
258C22—81no—
259C22—82no—
260C22—82no—
261C22—84no—
262C22—82no—
263C22#1062235211yescharacteristic
264C22#1062235411yescharacteristic
265C22#1062235911yescharacteristic
266C4—42no—
267C4—81no—
268C4—882no—
269C4—882no—
270C4—882no—
271C4—1761no—
272C2—21no—
273C2—21no—
274C2—41no—
275C2—41no—
276C2—82no—
277C2#1306757511yescharacteristic
278C2#1307062512yes—
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1316C2
socleC22×C11B(4,𝔽2)
prime radicalC25×C11D4
hypercenter#1316D11
hypocenterC11#12218
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
3. #13067643C2semidirect
4. #13066641C2semidirect
213. C11#12218semidirect

Maximal subgroups

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

subgroupindex
#130768802
#130697802
#130676432
#130666412
C11×#13162
#1221811