Finite Group Databasebeta

← #14658209

Subgroups — #14658209

Order 2816.

494 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 137 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#13073645C211yesmaximal, characteristic
2#13069375C212yesmaximal
3#13068775C211yesmaximal, characteristic
4#13066455C212yesmaximal
5C11×#1296C211yesmaximal, characteristic
6C2×#66941—22no—
7C2×C11×C4⋊C8C2212yes—
8C11×#384C2211yescharacteristic
9C2×#66882—22no—
10#10622592—22no—
11#10622586—22no—
12C2×#66871—22no—
13#10622548C2211yescharacteristic
14C4×C4⋊Dic11C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622189—22no—
17C22×Dic22—22no—
18C22×C8×C11—22no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4D412yes—
21C2×C42×C11C2311yescharacteristic
22C2×C4⋊Dic11—21no—
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×Dic11⋊C4—24no—
27C2×C4×Dic11—22no—
28C22×C11⋊C8—21no—
29#66941—44no—
30#66941—44no—
31C11×C4⋊C8—22no—
32C11×C4⋊C8Q814yescomplemented
33C11⋊#95—22no—
34C11⋊#95—22no—
35#66882—44no—
36#66871—44no—
37C4×C11⋊C8—21no—
38C4×C11⋊C8Q812yescomplemented
39#10573—111nomaximal, Sylow
40C22×C4×C11—22no—
41C22×C4×C11C2×D411yescharacteristic
42C22×C4×C11C2×D412yes—
43C22×Dic11—22no—
44C22×Dic11—22no—
45C22×Dic11—41no—
46C2×Dic22—48no—
47C2×Dic22—82no—
48C2×C8×C11—24no—
49C2×C8×C11—42no—
50C2×C8×C11—42no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—42no—
54C42×C11C2×Q812yes—
55C42×C11C2×Q811yescharacteristic
56C42×C11#4111yescharacteristic
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59C4⋊Dic11—42no—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62C4⋊Dic11D814yes—
63C4⋊Dic11Q1614yes—
64Dic11⋊C4—48no—
65C4×Dic11—42no—
66C4×Dic11—42no—
67C2×C11⋊C8—22no—
68C2×C11⋊C8—22no—
69C2×C11⋊C8—22no—
70#2551—111no—
71#1947—112no—
72#1845—111no—
73#1296D1111yescharacteristic
74#1279—112no—
75C23×C11#12011yescharacteristic
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—44no—
79C2×C4×C11—42no—
80C2×C4×C11C22⋊Q812yes—
81C2×C4×C11C22⋊Q811yescharacteristic
82C2×C4×C11C4⋊Q811yescharacteristic
83C2×C4×C11C4⋊Q812yes—
84C2×C4×C11C2×D812yes—
85C2×C4×C11C2×Q1612yes—
86C2×C4×C11AGL(1,ℤ/8)12yes—
87C2×C4×C11#13712yes—
88C2×Dic11—24no—
89C2×Dic11—24no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—82no—
95C2×Dic11—81no—
96Dic22—88no—
97C8×C11—44no—
98C11⋊C8—24no—
99C2×C4⋊Q8—222no—
100C2×#107—222no—
101C2×#107—222no—
102C2×C4⋊C8C2×D1112yes—
103C2×C4×C8—111no—
104#395—222no—
105#389—222no—
106#384—111no—
107#384C2×D1111yescharacteristic
108C4×C4⋊C4—112no—
109#340—222no—
110C22×C11#39511yescharacteristic
111C22×C11#44712yes—
112C22×C11#45112yes—
113C22×C11#45311yescharacteristic
114C22×C11#45611yescharacteristic
115C4×C11—21no—
116C4×C11—21no—
117C4×C11—82no—
118C4×C11#47412yes—
119C4×C11#47712yes—
120C4×C11#50012yes—
121C4×C11#50112yes—
122Dic11—44no—
123Dic11—44no—
124Dic11—161no—
125C22×Q8—222no—
126C22×C8—22no—
127C22×C8—221no—
128C4⋊Q8—444no—
129C4⋊Q8—444no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4—224no—
134C2×C4⋊C4—221no—
135C2×C4⋊C4—222no—
136C2×C4⋊C4D4412yes—
137C2×C42—222no—
138C2×C42C22×D1111yescharacteristic
139#107—444no—
140#107—444no—
141C4⋊C8—22no—
142C4⋊C8Dic2214yescomplemented
143C4×C8—112no—
144C4×C8—221no—
145#95—222no—
146#95—222no—
147C2×C11#161911yescharacteristic
148C2×C11#163311yescharacteristic
149C2×C11#164912yes—
150C2×C11#205712yes—
151C2×C11#206011yescharacteristic
152C2×Q8—448no—
153C2×Q8—882no—
154C22×C4—22no—
155C22×C4—222no—
156C22×C4—222no—
157C22×C4—441no—
158C22×C4C2×D4411yescharacteristic
159C22×C4D4×D1112yes—
160C2×C8—24no—
161C2×C8—42no—
162C2×C8—42no—
163C2×C8—222no—
164C2×C8—222no—
165C2×C8—222no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—114no—
170C4⋊C4—114no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4—442no—
174C4⋊C4—448no—
175C4⋊C4—442no—
176C4⋊C4—442no—
177C42—442no—
178C42—442no—
179C42C2×Dic2212yes—
180C42#434111yescharacteristic
181C42Q8×D1111yescharacteristic
182C11#1057311yescharacteristic, complemented, Sylow
183C23#6693511yescharacteristic
184Q8—888no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4—224no—
190C2×C4—224no—
191C2×C4—442no—
192C2×C4—442no—
193C2×C4—442no—
194C2×C4—442no—
195C2×C4—881no—
196C2×C4—882no—
197C2×C4#6692211yescharacteristic
198C2×C4#6693112yes—
199C2×C4#6694112yes—
200C2×C4#6695011yescharacteristic
201C2×C4D8×D1112yes—
202C2×C4#6696712yes—
203C2×C4#6696812yes—
204C2×C4Q16×D1112yes—
205C8—44no—
206C8—224no—
207C22#1062226911yescharacteristic
208C22#1062236011yescharacteristic
209C22#1062236511yescharacteristic
210C22#1062238612yes—
211C22#1062242112yes—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—444no—
216C4—444no—
217C4—1761no—
218C4#1062237212yes—
219C4#1062240712yes—
220C4#1062246912yes—
221C4#1062248712yes—
222C2#1306767111yescharacteristic
223C2#1306775711yescharacteristic
224C2#1306786612yes—
225C2#1306994312yes—
226C2#1306996211yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#120
hypercenter#1296D11
hypocenterC11#10573
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
32. C11×C4⋊C8Q8semidirect
38. C4×C11⋊C8Q8semidirect
142. C4⋊C8Dic22semidirect
182. C11#10573semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130693752
#130687752
#130664552
C11×#12962
#1057311