Finite Group Databasebeta

← #14655111

Subgroups — #14655111

Order 2816.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#10622315C212yesmaximal
2#13076684C211yesmaximal, characteristic
3#13069435C211yesmaximal, characteristic
4C2×#10622103C212yesmaximal
5C11×#1295C211yesmaximal, characteristic
6C2×#66923C2212yes—
7C2×#66922C2211yescharacteristic
8C2×C11×#97C2212yes—
9C11×#382C2211yescharacteristic
10C2×#66882—22no—
11C2×#66881—22no—
12#10622596—22no—
13C2×#66874—22no—
14C2×#66867C2211yescharacteristic
15#10622315—24no—
16#10622315—24no—
17#10622274—22no—
18#10622272—22no—
19#10622103—24no—
20C22×Dic22—21no—
21C22×C8×C11—22no—
22C2×C11×C4⋊C4D412yes—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11D412yes—
27C2×C4⋊Dic11D412yes—
28C2×Dic11⋊C4—22no—
29C2×Dic11⋊C4—22no—
30C22×C11⋊C8—21no—
31#66923—22no—
32#66923—22no—
33#66923—22no—
34#66923—22no—
35#66922—22no—
36#66922—21no—
37#66922D412yes—
38C11×#97—22no—
39C11×#97D414yes—
40C11×#95—22no—
41C11⋊#95—22no—
42C11⋊#95—24no—
43#66882—28no—
44#66881—28no—
45#66874—44no—
46#66867—22no—
47#10087—111nomaximal, Sylow
48C22×C4×C11—22no—
49C22×C4×C11C2×D412yes—
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—22no—
52C22×Dic11—22no—
53C22×Dic11—41no—
54C2×Dic22—22no—
55C2×Dic22—42no—
56C2×Dic22—42no—
57C2×Dic22—41no—
58C2×C8×C11—28no—
59C2×C8×C11—24no—
60C11×C4⋊C4—42no—
61C42×C11C2×D411yescharacteristic
62C42×C11C2×D412yes—
63C42×C11#4111yescharacteristic
64C4⋊Dic11—22no—
65C4⋊Dic11—24no—
66C4⋊Dic11—22no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70C4⋊Dic11—82no—
71Dic11⋊C4—42no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—41no—
78C2×#501—112no—
79#2822—111no—
80#1960—111no—
81C2×#330—112no—
82#1295D1111yescharacteristic
83C23×C11#12011yescharacteristic
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—24no—
87C2×C4×C11—42no—
88C2×C4×C11—44no—
89C2×C4×C11#12012yes—
90C2×C4×C11#12111yescharacteristic
91C2×C4×C11#12112yes—
92C2×C4×C11#12711yescharacteristic
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—44no—
99C2×Dic11—81no—
100C2×Dic11—81no—
101Dic22—44no—
102Dic22—82no—
103C8×C11—28no—
104C11⋊C8—42no—
105C2×C4⋊Q8—111no—
106C2×#125—112no—
107#501—224no—
108#501—224no—
109C2×#107—222no—
110C2×#106—222no—
111C2×#103—222no—
112C2×#97—111no—
113C2×#97C2×D1112yes—
114#400—222no—
115#398—222no—
116#398—222no—
117#382C2×D1111yescharacteristic
118#330—224no—
119C22×C11#39211yescharacteristic
120C22×C11#45311yescharacteristic
121C22×C11#45411yescharacteristic
122C22×C11#45614yes—
123C4×C11—22no—
124C4×C11—22no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—82no—
128Dic11—82no—
129Dic11—82no—
130Dic11—82no—
131C22×Q8—221no—
132C22×C8—22no—
133C22×C8—221no—
134C4⋊Q8—112no—
135C4⋊Q8—222no—
136C4⋊Q8—221no—
137#125—222no—
138#125—222no—
139#125—222no—
140#125—222no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—222no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4D4412yes—
148C2×C42C22×D1111yescharacteristic
149#107—228no—
150#106—228no—
151#103—444no—
152#97—22no—
153#97—222no—
154#97D4414yes—
155#95—22no—
156#95—224no—
157#95—222no—
158C2×C11#166012yes—
159C2×C11#166312yes—
160C2×C11#200512yes—
161C2×C11#200611yescharacteristic
162C2×Q8—222no—
163C2×Q8—442no—
164C2×Q8—442no—
165C2×Q8—441no—
166C22×C4—22no—
167C22×C4—222no—
168C22×C4—222no—
169C22×C4—441no—
170C22×C4C2×D4411yescharacteristic
171C22×C4D4×D1112yes—
172C2×C8—28no—
173C2×C8—24no—
174C2×C8—222no—
175C2×C8—441no—
176C2×C8—441no—
177C4⋊C4—42no—
178C4⋊C4—222no—
179C4⋊C4—224no—
180C4⋊C4—222no—
181C4⋊C4—222no—
182C4⋊C4—222no—
183C4⋊C4—442no—
184C4⋊C4—442no—
185C4⋊C4—442no—
186C4⋊C4—442no—
187C4⋊C4—442no—
188C4⋊C4—882no—
189C42C2×D4412yes—
190C42D4×D1111yescharacteristic
191C42#434311yescharacteristic
192C11#1008711yescharacteristic, complemented, Sylow
193C23#6693511yescharacteristic
194Q8—444no—
195Q8—882no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4—444no—
207C2×C4—881no—
208C2×C4—881no—
209C2×C4#6692711yescharacteristic
210C2×C4#6693512yes—
211C2×C4#6694812yes—
212C2×C4#6694811yescharacteristic
213C8—28no—
214C8—442no—
215C22#1062228411yescharacteristic
216C22#1062236011yescharacteristic
217C22#1062236611yescharacteristic
218C22#1062243914yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—882no—
225C4—882no—
226C4—882no—
227C2#1306792812yes—
228C2#1306794512yes—
229C2#1306965512yes—
230C2#1306966011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10087
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
192. C11#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#106223152
#130766842
#130694352
C2×#106221032
C11×#12952
#1008711