Finite Group Databasebeta

← #13074560

Subgroups — #13074560

Order 1408.

584 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66993C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3C11×#390C211yesmaximal, characteristic, complemented
4#10622834C211yesmaximal, characteristic, complemented
5#10622601C211yesmaximal, characteristic, complemented
6#10622574C214yesmaximal, complemented
7#10622572C214yesmaximal, complemented
8#10622552C211yesmaximal, characteristic, complemented
9#10622545C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C22⋊D11C2212yes—
13C22×D44C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2214yes—
16C2×C42×C11C2211yescharacteristic
17C2×C22⋊Dic11C2214yes—
18#66993—24no—
19C2×(C2×D11)⋊C4C2214yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25C2×C4×Dic11C2211yescharacteristic
26#66943—24no—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C24×C11C2312yes—
30C23×D11C2312yes—
31C2×D4×C11—22no—
32C2×D4×C11—22no—
33C2×D4×C11—22no—
34C22×C4×C11C2312yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—24no—
38C2×C22⋊D11—24no—
39C2×C22⋊D11—44no—
40C2×C22⋊D11—44no—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C2×D44—22no—
46C2×D44—22no—
47C2×D44—22no—
48C11×C4⋊C4—22no—
49C11×C22⋊C4—44no—
50C42×C11—22no—
51C22⋊Dic11—44no—
52(C2×D11)⋊C4—44no—
53(C2×D11)⋊C4—44no—
54C4⋊Dic11—24no—
55C4⋊Dic11—22no—
56Dic11⋊C4—24no—
57C4×Dic11—22no—
58C4×Dic11D414yes—
59#2641—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—24no—
64C23×C11—24no—
65C23×C11C2411yescharacteristic
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—24no—
70C22×D11—24no—
71D4×C11—44no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—24no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11#4112yes—
79C2×C4×C11#4112yes—
80C22⋊D11—48no—
81C22⋊D11—48no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—24no—
88C2×Dic11—22no—
89C2×Dic11C2×D412yes—
90C2×Dic11C2×D412yes—
91D44—44no—
92C2×#127—111no—
93C2×#125—111no—
94#394—114no—
95#394—114no—
96#390—111no—
97#390—111no—
98#390—111no—
99#390D1111yescharacteristic, complemented
100#376—111no—
101C22×C11—42no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11—44no—
105C22×C11—44no—
106C22×C11C22×D411yescharacteristic
107C22×C11C2×#4111yescharacteristic
108C22×C11C2×#4111yescharacteristic
109C22×C11H(5,𝔽2)12yes—
110C22×C11H(5,𝔽2)12yes—
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—42no—
114C2×D11—44no—
115C2×D11—44no—
116C4×C11—42no—
117C4×C11—42no—
118C4×C11#12414yes—
119Dic11—22no—
120Dic11—22no—
121Dic11—42no—
122Dic11—42no—
123C22×D4—112no—
124C22×D4—112no—
125C22×D4—111no—
126C22×D4C2×D1111yescharacteristic
127#127—224no—
128#125—224no—
129C2×C4⋊C4—111no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4C2×D1111yescharacteristic
133C2×C22⋊C4—114no—
134C2×C22⋊C4—114no—
135C2×C22⋊C4—114no—
136C2×C22⋊C4C2×D1114yes—
137C2×C42—111no—
138C2×C42—111no—
139C2×C42C2×D1111yescharacteristic
140#95—112no—
141#95—112no—
142C2×C11—82no—
143C2×C11C2×#12411yescharacteristic
144C2×C11#53511yescharacteristic
145C2×C11#53511yescharacteristic
146C2×C11#54012yes—
147C2×C11#54012yes—
148D11—82no—
149C24—112no—
150C24C22×D1112yes—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—224no—
155C2×D4—224no—
156C2×D4—222no—
157C2×D4—222no—
158C2×D4—222no—
159C2×D4—444no—
160C2×D4—444no—
161C22×C4—111no—
162C22×C4—111no—
163C22×C4—112no—
164C22×C4—112no—
165C22×C4C22×D1112yes—
166C22×C4C22×D1112yes—
167C22×C4C22×D1111yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—224no—
170C4⋊C4—224no—
171C4⋊C4—222no—
172C22⋊C4—44no—
173C22⋊C4—444no—
174C22⋊C4—444no—
175C22⋊C4—444no—
176C42—22no—
177C42—114no—
178C42—222no—
179C11#264111yescharacteristic, complemented, Sylow
180C23—22no—
181C23—22no—
182C23—22no—
183C23—24no—
184C23—24no—
185C23—222no—
186C23—222no—
187C23—222no—
188C23—224no—
189C23—224no—
190C23C23×D1111yescharacteristic
191D4—44no—
192D4—448no—
193D4—448no—
194D4—444no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—112no—
201C2×C4—112no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—224no—
209C2×C4#433912yes—
210C2×C4D4×D1112yes—
211C2×C4#434112yes—
212C22—42no—
213C22—42no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—442no—
218C22—442no—
219C22—444no—
220C22—444no—
221C22—442no—
222C22C2×#433911yescharacteristic
223C22C2×D4×D1111yescharacteristic
224C22C2×#434111yescharacteristic
225C22#6703712yes—
226C22#6704212yes—
227C4—42no—
228C4—42no—
229C4—222no—
230C4—222no—
231C4—442no—
232C4—442no—
233C4#6693814yes—
234C2—82no—
235C2—882no—
236C2C2×#6693811yescharacteristic
237C2#1062309312yes—
238C2#1062315012yes—
239C2#1062320511yescharacteristic
240C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC2×#66993C2
hypercenter#390D11
hypocenterC11#2641
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
3. C11×#390C2semidirect
4. #10622834C2semidirect
5. #10622601C2semidirect
6. #10622574C2semidirect
7. #10622572C2semidirect
8. #10622552C2semidirect
9. #10622545C2semidirect
99. #390D11semidirect
179. C11#2641semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669432
C11×#3902
#106228342
#106226012
#106225742
#106225722
#106225522
#106225452
#264111