Finite Group Databasebeta

← #14673459

Subgroups — #14673459

Order 2816.

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

normal subgroups only

This group has 416 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#13076609C211yesmaximal, characteristic
2#13068833C212yesmaximal
3#13068830C211yesmaximal, characteristic
4#13066742C212yesmaximal
5C11×#1394C211yesmaximal, characteristic
6#10623343C2211yescharacteristic
7C2×C11×#101C2212yes—
8C11×#391C2211yescharacteristic
9#10622843C2212yes—
10C2×#66900C2211yescharacteristic
11#10622734—22no—
12#10622592—21no—
13#10622577—21no—
14#10622542—21no—
15#10622269—22no—
16#10622259—22no—
17#10622193—22no—
18#10622161—21no—
19C22×Q8×C11C2311yescharacteristic
20C22×Dic22—21no—
21C22×Dic22—21no—
22C2×C11×M16—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C42×C11D411yescharacteristic
25Q8×Dic11—41no—
26Q8×Dic11—41no—
27#66979—22no—
28#66979—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31C2×Dic11⋊C4—22no—
32C2×C4×Dic11D412yes—
33C2×#4318—21no—
34C11×#101—22no—
35C11×#101Q814yescomplemented
36C11×#95—22no—
37#66900—21no—
38#66900Q812yescomplemented
39C11⋊#95—21no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43#66882—42no—
44#66881—42no—
45#66872—41no—
46#66871—41no—
47#13464—111nomaximal, Sylow
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11C2×Q812yes—
51C2×Q8×C11C2×Q811yescharacteristic
52C2×Q8×C11#4111yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D412yes—
57C22×Dic11—22no—
58C22×Dic11—22no—
59C2×Dic22—24no—
60C2×Dic22—81no—
61C2×Dic22—81no—
62C2×Dic22—82no—
63C2×Dic22—81no—
64C11×M16—24no—
65C11×M16—42no—
66C2×C8×C11—42no—
67C11×C4⋊C4—41no—
68C42×C11—41no—
69C22⋊Dic11—41no—
70C4⋊Dic11—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11—42no—
75C4⋊Dic11—81no—
76Dic11⋊C4—82no—
77C4×Dic11—42no—
78C4×Dic11—41no—
79C4×Dic11—42no—
80#4318—22no—
81#4318—41no—
82C2×C11⋊C8—41no—
83#2811—111no—
84#1857—112no—
85#1857—111no—
86#1394—112no—
87#1394D1111yescharacteristic
88C23×C11#12011yescharacteristic
89Q8×C11—42no—
90Q8×C11—41no—
91Q8×C11—41no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11C22⋊Q812yes—
102C2×C4×C11C22⋊Q811yescharacteristic
103C2×C4×C11C4⋊Q811yescharacteristic
104C2×C4×C11C4⋊Q812yes—
105C2×Dic11—24no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—42no—
113Dic22—84no—
114Dic22—84no—
115C8×C11—44no—
116C11⋊C8—42no—
117#519—111no—
118#428—222no—
119#428—221no—
120C2×#101—111no—
121C2×#101C2×D1112yes—
122#395—222no—
123#395—221no—
124#391—112no—
125#391—222no—
126#391—221no—
127#391C2×D1111yescharacteristic
128#339—222no—
129#339—221no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11#39511yescharacteristic
133C22×C11B(4,𝔽2)11yescharacteristic
134C22×C11#45811yescharacteristic
135C4×C11—21no—
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11—81no—
141Dic11—44no—
142Dic11—82no—
143Dic11—81no—
144Dic11—81no—
145C22×Q8—221no—
146C22×Q8—221no—
147C22×Q8C22×D1111yescharacteristic
148C2×M16—22no—
149C2×M16—221no—
150C4×Q8—441no—
151C4×Q8—441no—
152#117—221no—
153#117—222no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—222no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4D4411yescharacteristic
158C2×C42—112no—
159C2×C42D4411yescharacteristic
160#107—441no—
161#107—442no—
162#106—441no—
163#106—442no—
164#101—22no—
165#101—112no—
166#101—221no—
167#101Dic2214yescomplemented
168#95—22no—
169#95—222no—
170#95—221no—
171#95—222no—
172#95—222no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11#206211yescharacteristic
176C2×C11#220211yescharacteristic
177C2×C11#220511yescharacteristic
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—224no—
181C2×Q8—881no—
182C2×Q8—881no—
183C2×Q8—882no—
184C2×Q8—881no—
185C2×Q8C2×Dic2212yes—
186C2×Q8#434111yescharacteristic
187C2×Q8Q8×D1111yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—222no—
191C22×C4—222no—
192C22×C4C2×D4411yescharacteristic
193C22×C4D4×D1112yes—
194M16—24no—
195M16—42no—
196M16—222no—
197M16—441no—
198C2×C8—42no—
199C2×C8—441no—
200C4⋊C4—41no—
201C4⋊C4—221no—
202C4⋊C4—222no—
203C4⋊C4—221no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C4⋊C4—882no—
207C4⋊C4—881no—
208C22⋊C4—441no—
209C42—41no—
210C42—442no—
211C42—441no—
212C42—442no—
213C11#1346411yescharacteristic, complemented, Sylow
214C23#6693511yescharacteristic
215Q8—42no—
216Q8—41no—
217Q8—41no—
218Q8—884no—
219Q8—884no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—224no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4—442no—
234C2×C4—441no—
235C2×C4—441no—
236C2×C4—442no—
237C2×C4#6692211yescharacteristic
238C2×C4#6693112yes—
239C2×C4#6694112yes—
240C2×C4#6695011yescharacteristic
241C8—44no—
242C8—442no—
243C22—21no—
244C22—21no—
245C22#1062226911yescharacteristic
246C22#1062235411yescharacteristic
247C22#1062235511yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—42no—
253C4—81no—
254C4—444no—
255C4—882no—
256C4—881no—
257C4—881no—
258C2—21no—
259C2—21no—
260C2#1306997011yescharacteristic
261C2#1307063411yescharacteristic
262C2#1307064711yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#1394C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1394D11
hypocenterC11#13464
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
35. C11×#101Q8semidirect
38. #66900Q8semidirect
167. #101Dic22semidirect
213. C11#13464semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130688332
#130688302
#130667422
C11×#13942
#1346411