Finite Group Databasebeta

← #14658280

Subgroups — #14658280

Order 2816.

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

normal subgroups only

This group has 382 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#13076891C211yesmaximal, characteristic
2#13068782C212yesmaximal
3#13066498C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#1836C211yesmaximal, characteristic
6C2×C11×#97C2211yescharacteristic
7C11×#384C2211yescharacteristic
8C11×#382C2211yescharacteristic
9#10622597—22no—
10C2×#66872—22no—
11C2×#66871—22no—
12#10622549C2212yes—
13C2×#66867C2212yes—
14#10622274—22no—
15#10622270—22no—
16C11×#340—22no—
17C22×C8×C11—21no—
18C2×C11×C4⋊C4—21no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4D412yes—
21C2×C42×C11C2311yescharacteristic
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11D412yes—
24C2×C4⋊Dic11D412yes—
25C2×Dic11⋊C4—22no—
26C2×Dic11⋊C4—22no—
27C22×C11⋊C8—22no—
28C11×#97—21no—
29C11×#97Q812yes—
30C11×#95—22no—
31C11⋊#95—22no—
32C11⋊#95—22no—
33C11⋊#95—22no—
34#66872—44no—
35#66871—44no—
36#66867—22no—
37#66867Q814yes—
38#10585—111nomaximal, Sylow
39C22×C4×C11—22no—
40C22×C4×C11—41no—
41C22×C4×C11C2×D412yes—
42C22×C4×C11C2×D411yescharacteristic
43C22×Dic11—22no—
44C22×Dic11—22no—
45C2×C8×C11—22no—
46C2×C8×C11—41no—
47C2×C8×C11—41no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—42no—
50C11×C4⋊C4—42no—
51C11×C4⋊C4—42no—
52C42×C11C2×Q811yescharacteristic
53C42×C11C2×Q812yes—
54C42×C11#4111yescharacteristic
55C4⋊Dic11—42no—
56C4⋊Dic11—42no—
57C4⋊Dic11—82no—
58Dic11⋊C4—82no—
59Dic11⋊C4—82no—
60C2×C11⋊C8—24no—
61C2×C11⋊C8—24no—
62C2×C11⋊C8—24no—
63#2845—111no—
64#1847—112no—
65#1836D1111yescharacteristic
66#1295—112no—
67#1295—111no—
68C23×C11#12011yescharacteristic
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—42no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—82no—
77C2×C4×C11—81no—
78C2×C4×C11C22⋊Q812yes—
79C2×C4×C11C22⋊Q811yescharacteristic
80C2×C4×C11C4⋊Q812yes—
81C2×C4×C11C4⋊Q811yescharacteristic
82C2×Dic11—42no—
83C2×Dic11—42no—
84C2×Dic11—42no—
85C2×Dic11—42no—
86C2×Dic11—42no—
87C2×Dic11—42no—
88C8×C11—42no—
89C11⋊C8—28no—
90C2×#107—222no—
91C2×#106—222no—
92C2×#97—112no—
93C2×#97C2×D1111yescharacteristic
94#398—222no—
95#398—222no—
96#398—222no—
97#384C2×D1111yescharacteristic
98#382—112no—
99#382C2×D1111yescharacteristic
100#340—22no—
101C22×C11#39511yescharacteristic
102C22×C11#45312yes—
103C22×C11#45411yescharacteristic
104C22×C11#45511yescharacteristic
105C22×C11#45612yes—
106C4×C11—22no—
107C4×C11—22no—
108C4×C11—21no—
109C4×C11—21no—
110C4×C11—82no—
111C4×C11—161no—
112Dic11—82no—
113Dic11—82no—
114C22×C8—21no—
115C22×C8—222no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—222no—
121C2×C4⋊C4—222no—
122C2×C4⋊C4—222no—
123C2×C4⋊C4C22⋊D1112yes—
124C2×C42C22×D1111yescharacteristic
125#107—444no—
126#106—444no—
127#97—21no—
128#97—114no—
129#97—222no—
130#97Dic2212yes—
131#95—22no—
132#95—222no—
133#95—222no—
134#95—222no—
135C2×C11#165611yescharacteristic
136C2×C11#166112yes—
137C2×C11#166311yescharacteristic
138C2×C11#206012yes—
139C2×C11#206111yescharacteristic
140C22×C4—22no—
141C22×C4—41no—
142C22×C4—222no—
143C22×C4—222no—
144C22×C4D4×D1112yes—
145C22×C4C2×C22⋊D1111yescharacteristic
146C2×C8—22no—
147C2×C8—41no—
148C2×C8—41no—
149C2×C8—224no—
150C2×C8—224no—
151C2×C8—224no—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—442no—
157C4⋊C4—442no—
158C4⋊C4—882no—
159C4⋊C4—882no—
160C4⋊C4—882no—
161C42C2×Dic2211yescharacteristic
162C42#433911yescharacteristic
163C42Q8×D1112yes—
164C11#1058511yescharacteristic, complemented, Sylow
165C23#6699011yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—82no—
174C2×C4—81no—
175C2×C4—442no—
176C2×C4—442no—
177C2×C4—442no—
178C2×C4—442no—
179C2×C4—442no—
180C2×C4—442no—
181C2×C4#6694112yes—
182C2×C4#6694912yes—
183C2×C4#6697711yescharacteristic
184C2×C4#6699711yescharacteristic
185C8—42no—
186C8—228no—
187C22#1062259211yescharacteristic
188C22#1062267411yescharacteristic
189C22#1062267511yescharacteristic
190C22#1062281112yes—
191C22#1062281812yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—161no—
198C4—882no—
199C4—882no—
200C2#1306790811yescharacteristic
201C2#1306793212yes—
202C2#1306794211yescharacteristic
203C2#1306995912yes—
204C2#1306996611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1836C2
socle, prime radicalC23×C11#120
hypercenter#1836D11
hypocenterC11#10585
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
164. C11#10585semidirect

Maximal subgroups

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

subgroupindex
#130768912
#130687822
#130664982
#130664972
C11×#18362
#1058511