Finite Group Databasebeta

← #13073599

Subgroups — #13073599

Order 1408.

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

normal subgroups only

This group has 576 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×#67000C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic, complemented
3C2×#66940C211yesmaximal, characteristic, complemented
4C2×#66928C211yesmaximal, characteristic
5C11×#391C211yesmaximal, characteristic, complemented
6#10622601C211yesmaximal, characteristic
7C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
8#10622289C214yesmaximal, complemented
9#10622282C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15#67000—24no—
16#66997—24no—
17C2×(C2×D11)⋊C4C2214yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2214yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27#66940—24no—
28#66928—24no—
29C11×#95C2214yes—
30C11⋊#95C2212yes—
31C23×D11C2312yes—
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C22×C4×C11C2312yes—
36C22×C4×C11C2312yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2311yescharacteristic
40C22×Dic11C2311yescharacteristic
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×D44—22no—
44C2×D44—22no—
45C2×D44—22no—
46C2×Dic22—22no—
47C2×Dic22—22no—
48C2×Dic22D414yes—
49C11×C4⋊C4—22no—
50C42×C11—22no—
51(C2×D11)⋊C4—28no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—28no—
55Dic11⋊C4—24no—
56Dic11⋊C4—28no—
57Dic11⋊C4—24no—
58C4×Dic11—24no—
59C4×Dic11—22no—
60C4×Dic11D414yes—
61#2545—111nomaximal, Sylow
62C23×C11C2411yescharacteristic
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—24no—
66C22×D11—22no—
67C22×D11—24no—
68Q8×C11—44no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—24no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11#4112yes—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11C2×D412yes—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D414yes—
89C2×Dic11#4114yes—
90D44—44no—
91Dic22—28no—
92C2×C4⋊Q8—111no—
93C2×#124—111no—
94C2×#124—111no—
95C2×C4×Q8—111no—
96#396—114no—
97#391D1111yescharacteristic, complemented
98#390—111no—
99#388—114no—
100C4×C4⋊C4—111no—
101C22×C11C22×D411yescharacteristic
102C22×C11C22×D411yescharacteristic
103C22×C11C2×#4111yescharacteristic
104C22×C11C2×#4112yes—
105C22×C112−1+412yes—
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—44no—
110C2×D11—44no—
111C4×C11—42no—
112C4×C11—42no—
113C4×C11—42no—
114C4×C11#12114yes—
115Dic11—24no—
116Dic11—22no—
117Dic11—22no—
118Dic11—24no—
119C22×Q8—111no—
120C22×Q8C2×D1111yescharacteristic
121C22×D4—111no—
122C4⋊Q8—224no—
123#124—224no—
124#124—224no—
125C4×Q8—224no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—114no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4C2×D1111yescharacteristic
130C2×C22⋊C4—112no—
131C2×C22⋊C4—114no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—114no—
134C2×C42—111no—
135C2×C42—112no—
136C2×C42—111no—
137C2×C42C2×D1111yescharacteristic
138#95—112no—
139#95C2×D1114yes—
140C2×C11C2×#12111yescharacteristic
141C2×C11#53211yescharacteristic
142C2×C11#53611yescharacteristic
143C2×C11#54812yes—
144C2×C11#55612yes—
145D11—82no—
146C24—112no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—114no—
151C2×Q8—222no—
152C2×Q8—222no—
153C2×D4—222no—
154C2×D4—222no—
155C2×D4—222no—
156C22×C4—111no—
157C22×C4—112no—
158C22×C4—111no—
159C22×C4—112no—
160C22×C4C22×D1112yes—
161C22×C4C22×D1112yes—
162C22×C4C22×D1112yes—
163C22×C4C22×D1111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—224no—
166C4⋊C4—228no—
167C4⋊C4—224no—
168C22⋊C4—228no—
169C22⋊C4—224no—
170C22⋊C4—224no—
171C22⋊C4—228no—
172C42—22no—
173C42—114no—
174C42—224no—
175C42—222no—
176C11#254511yescharacteristic, complemented, Sylow
177C23—222no—
178C23—222no—
179C23—222no—
180C23—224no—
181C23—224no—
182C23C23×D1111yescharacteristic
183Q8—44no—
184Q8—228no—
185D4—444no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—112no—
195C2×C4—112no—
196C2×C4—114no—
197C2×C4—114no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4#433912yes—
205C2×C4D4×D1112yes—
206C2×C4D4×D1112yes—
207C22—442no—
208C22—442no—
209C22—444no—
210C22—444no—
211C22—442no—
212C22C2×#433911yescharacteristic
213C22C2×D4×D1111yescharacteristic
214C22C2×D4×D1111yescharacteristic
215C22#6704012yes—
216C22#41×D1112yes—
217C4—42no—
218C4—42no—
219C4—42no—
220C4—222no—
221C4—224no—
222C4—224no—
223C4—222no—
224C4#6693714yes—
225C2—882no—
226C2C2×#6693711yescharacteristic
227C2#1062309912yes—
228C2#1062316412yes—
229C2#1062319911yescharacteristic
230C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2545
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#66997C2semidirect
3. C2×#66940C2semidirect
5. C11×#391C2semidirect
7. C4×Dic11⋊C4C2semidirect
8. #10622289C2semidirect
9. #10622282C2semidirect
97. #391D11semidirect
176. C11#2545semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669972
C2×#669402
C2×#669282
C11×#3912
#106226012
C4×Dic11⋊C42
#106222892
#106222822
#254511