Finite Group Databasebeta

← #13073070

Subgroups — #13073070

Order 1408.

484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic
3#10622843C211yesmaximal, characteristic, complemented
4#10622843C211yesmaximal, characteristic, complemented
5C4×C22⋊Dic11C211yesmaximal, characteristic
6#10622591C214yesmaximal, complemented
7#10622590C211yesmaximal, characteristic, complemented
8#10622589C211yesmaximal, characteristic, complemented
9#10622565C214yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C11×C22⋊Q8—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18#66979—24no—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2214yes—
22C2×C4×Dic11C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24C2×C4×Dic11C2211yescharacteristic
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C24×C11C2311yescharacteristic
30C2×Q8×C11—22no—
31C2×Q8×C11—22no—
32C2×Q8×C11—22no—
33C22×C4×C11—22no—
34C22×C4×C11—22no—
35C22×C4×C11D414yes—
36C22×C4×C11C2312yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C11×C4⋊C4—22no—
45C11×C4⋊C4—24no—
46C11×C22⋊C4—24no—
47C22⋊Dic11—24no—
48C22⋊Dic11—24no—
49C4⋊Dic11—22no—
50C4⋊Dic11—22no—
51Dic11⋊C4—28no—
52C4×Dic11—24no—
53C4×Dic11—22no—
54C4×Dic11—22no—
55#2499—111nomaximal, Sylow
56C23×C11—22no—
57C23×C11—21no—
58C23×C11—21no—
59C23×C11—22no—
60C23×C11C2×D412yes—
61C23×C11C2411yescharacteristic
62Q8×C11—44no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—28no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—24no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×D412yes—
73C2×C4×C11#4112yes—
74C2×C4×C11#4112yes—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—24no—
81C2×Dic11—22no—
82C2×Dic11—24no—
83C2×Dic11—22no—
84C2×Dic11#4114yes—
85C2×C22⋊Q8D1111yescharacteristic
86C2×#117—111no—
87#397—114no—
88#391—111no—
89#391—111no—
90#387—114no—
91#384—111no—
92#382—111no—
93C4×C22⋊C4—111no—
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—22no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11C22×D411yescharacteristic
100C22×C11C2×#4111yescharacteristic
101C22×C11C2×#4111yescharacteristic
102C22×C11C2×#4112yes—
103C22×C112−1+412yes—
104C4×C11—22no—
105C4×C11—42no—
106C4×C11—42no—
107C4×C11#12314yes—
108Dic11—24no—
109Dic11—42no—
110Dic11—42no—
111Dic11—42no—
112C22×Q8C2×D1111yescharacteristic
113C23×C4C2×D1111yescharacteristic
114C22⋊Q8—24no—
115#117—224no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—114no—
119C2×C4⋊C4C2×D1111yescharacteristic
120C2×C4⋊C4C2×D1112yes—
121C2×C22⋊C4—112no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4C2×D1112yes—
124C2×C42—112no—
125C2×C42—111no—
126C2×C42—111no—
127#95—112no—
128#95—114no—
129#95—114no—
130#95—114no—
131C2×C11—42no—
132C2×C11C2×#12311yescharacteristic
133C2×C11#53211yescharacteristic
134C2×C11#53611yescharacteristic
135C2×C11#55212yes—
136C2×C11#55612yes—
137C24C22×D1111yescharacteristic
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—112no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4C22⋊D1114yes—
148C22×C4C22×D1112yes—
149C22×C4C22×D1112yes—
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—24no—
154C4⋊C4—228no—
155C4⋊C4—222no—
156C4⋊C4—222no—
157C22⋊C4—24no—
158C22⋊C4—224no—
159C22⋊C4—224no—
160C42—222no—
161C42—222no—
162C42—224no—
163C11#249911yescharacteristic, complemented, Sylow
164C23—21no—
165C23—21no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D1112yes—
169C23C23×D1111yescharacteristic
170Q8—44no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—28no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—114no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—224no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—224no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4#434112yes—
190C2×C4#434112yes—
191C2×C4C2×C22⋊D1112yes—
192C2×C4C2×C22⋊D1112yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C2×#434111yescharacteristic
199C22C2×#434111yescharacteristic
200C22#6704012yes—
201C22#41×D1112yes—
202C22C22×C22⋊D1111yescharacteristic
203C4—22no—
204C4—42no—
205C4—42no—
206C4—224no—
207C4—442no—
208C4—442no—
209C4—442no—
210C4#6698814yes—
211C2—42no—
212C2#1062317012yes—
213C2#1062317212yes—
214C2C2×#6698811yescharacteristic
215C2#1062334711yescharacteristic
216C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2499
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10622843C2semidirect
4. #10622843C2semidirect
6. #10622591C2semidirect
7. #10622590C2semidirect
8. #10622589C2semidirect
163. C11#2499semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669792
#106228432
C4×C22⋊Dic112
#106225912
#106225902
#106225892
#106225652
#249911