Finite Group Databasebeta

← #14658270

Subgroups — #14658270

Order 2816.

406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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#13076888C211yesmaximal, characteristic
2#13068782C212yesmaximal
3#13066498C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#1847C211yesmaximal, characteristic
6C2×C11×#107—21no—
7C2×C11×#106—21no—
8C2×C11×#97C2211yescharacteristic
9C11×#384C2211yescharacteristic
10C11×#382C2211yescharacteristic
11#10622599—21no—
12#10622592—21no—
13C2×#66872—22no—
14C2×#66871—22no—
15#10622549C2212yes—
16C2×#66867C2212yes—
17#10622273—22no—
18#10622269—22no—
19C22×Dic22—21no—
20C22×C8×C11—21no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11D412yes—
28C2×C4⋊Dic11D412yes—
29C2×Dic11⋊C4—22no—
30C22×C11⋊C8—22no—
31C11×#107—42no—
32C11×#106—42no—
33C11×#97—21no—
34C11×#97Q812yescomplemented
35C11×#95—22no—
36C11⋊#95—22no—
37C11⋊#95—21no—
38C11⋊#95—21no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41#66872—44no—
42#66871—44no—
43#66867—22no—
44#66867Q814yescomplemented
45#10583—111nomaximal, Sylow
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11—41no—
49C22×C4×C11C2×D412yes—
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—22no—
52C22×Dic11—22no—
53C2×Dic22—82no—
54C2×Dic22—81no—
55C2×C8×C11—22no—
56C2×C8×C11—22no—
57C2×C8×C11—22no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C42×C11C2×Q811yescharacteristic
65C42×C11C2×Q812yes—
66C42×C11#4111yescharacteristic
67C4⋊Dic11—42no—
68C4⋊Dic11—42no—
69C4⋊Dic11—81no—
70Dic11⋊C4—82no—
71C2×C11⋊C8—24no—
72C2×C11⋊C8—24no—
73C2×C11⋊C8—24no—
74#2844—111no—
75#1847—112no—
76#1847D1111yescharacteristic
77#1295—112no—
78#1295—111no—
79C23×C11#12011yescharacteristic
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—42no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—42no—
88C2×C4×C11—82no—
89C2×C4×C11—81no—
90C2×C4×C11C22⋊Q812yes—
91C2×C4×C11C22⋊Q811yescharacteristic
92C2×C4×C11C4⋊Q812yes—
93C2×C4×C11C4⋊Q811yescharacteristic
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100Dic22—84no—
101C8×C11—24no—
102C11⋊C8—28no—
103C2×#107—21no—
104C2×#107—222no—
105C2×#106—21no—
106C2×#106—222no—
107C2×#97—112no—
108C2×#97C2×D1111yescharacteristic
109#400—222no—
110#400—221no—
111#395—222no—
112#395—221no—
113#384C2×D1111yescharacteristic
114#382—112no—
115#382C2×D1111yescharacteristic
116C22×C11#39511yescharacteristic
117C22×C11#45312yes—
118C22×C11#45311yescharacteristic
119C22×C11#45612yes—
120C22×C11#45611yescharacteristic
121C4×C11—22no—
122C4×C11—21no—
123C4×C11—22no—
124C4×C11—21no—
125C4×C11—81no—
126C4×C11—81no—
127C4×C11—161no—
128Dic11—82no—
129Dic11—82no—
130C22×Q8—221no—
131C22×C8—21no—
132C22×C8—222no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4—222no—
138C2×C4⋊C4—221no—
139C2×C4⋊C4C22⋊D1111yescharacteristic
140C2×C4⋊C4C22⋊D1111yescharacteristic
141C2×C42C22×D1111yescharacteristic
142#107—42no—
143#107—444no—
144#106—42no—
145#106—444no—
146#97—21no—
147#97—114no—
148#97—222no—
149#97Dic2212yescomplemented
150#95—22no—
151#95—222no—
152#95—221no—
153#95—221no—
154#95—222no—
155#95—222no—
156C2×C11#165511yescharacteristic
157C2×C11#166011yescharacteristic
158C2×C11#166012yes—
159C2×C11#206012yes—
160C2×C11#206011yescharacteristic
161C2×Q8—882no—
162C2×Q8—881no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—41no—
166C22×C4—222no—
167C22×C4—222no—
168C22×C4D4×D1112yes—
169C22×C4C2×C22⋊D1111yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—224no—
174C2×C8—224no—
175C2×C8—224no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C4⋊C4—442no—
183C4⋊C4—442no—
184C4⋊C4—882no—
185C4⋊C4—881no—
186C42C2×Dic2211yescharacteristic
187C42#433911yescharacteristic
188C42Q8×D1112yes—
189C11#1058311yescharacteristic, complemented, Sylow
190C23#6699011yescharacteristic
191Q8—884no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—82no—
201C2×C4—81no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4—442no—
207C2×C4—442no—
208C2×C4#6694112yes—
209C2×C4#6694912yes—
210C2×C4#6697711yescharacteristic
211C2×C4#6699711yescharacteristic
212C8—24no—
213C8—228no—
214C22#1062259211yescharacteristic
215C22#1062269011yescharacteristic
216C22#1062270811yescharacteristic
217C22#1062281112yes—
218C22#1062281812yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—161no—
226C4—882no—
227C4—882no—
228C2#1306790411yescharacteristic
229C2#1306792511yescharacteristic
230C2#1306792612yes—
231C2#1306995912yes—
232C2#1306996111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1847C2
socle, prime radicalC23×C11#120
hypercenter#1847D11
hypocenterC11#10583
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
34. C11×#97Q8semidirect
44. #66867Q8semidirect
149. #97Dic22semidirect
189. C11#10583semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130687822
#130664982
#130664972
C11×#18472
#1058311