Finite Group Databasebeta

← #13069868

Subgroups — #13069868

Order 1408.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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#10623024C211yesmaximal, characteristic
2#10622571C212yesmaximal, complemented
3C2×#66870C212yesmaximal, complemented
4#10622559C211yesmaximal, characteristic, complemented
5C11×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D11C2212yes—
7C23×Dic11C2211yescharacteristic
8C2×C11×C22⋊C4C2212yes—
9C2×C11×C22⋊C4C2211yescharacteristic
10C2×C22⋊Dic11C2211yescharacteristic
11#66983—21no—
12#66983—21no—
13C2×(C2×D11)⋊C4—22no—
14C2×Dic11⋊C4—21no—
15#66939—22no—
16#66935—22no—
17C11⋊#95—21no—
18C11⋊#95—22no—
19#66870—24no—
20C24×C11C2311yescharacteristic
21C23×D11D412yes—
22C22×C4×C11—22no—
23C22×C4×C11D411yescharacteristic
24C22×C4×C11D411yescharacteristic
25C2×C22⋊D11—22no—
26C2×C22⋊D11—22no—
27C2×C22⋊D11—22no—
28C2×C22⋊D11—22no—
29C2×C22⋊D11—22no—
30C2×C22⋊D11—22no—
31C22×Dic11—21no—
32C22×Dic11—21no—
33C22×Dic11—22no—
34C22×Dic11—42no—
35C22×Dic11D412yes—
36C2×D44—21no—
37C2×D44—21no—
38C11×C22⋊C4—22no—
39C11×C22⋊C4—22no—
40C11×C22⋊C4—22no—
41C22⋊Dic11—21no—
42C22⋊Dic11D412yescomplemented
43(C2×D11)⋊C4—22no—
44(C2×D11)⋊C4—22no—
45(C2×D11)⋊C4—44no—
46C4⋊Dic11—21no—
47C4⋊Dic11—21no—
48Dic11⋊C4—42no—
49#2044—111nomaximal, Sylow
50C23×C11—41no—
51C23×C11—41no—
52C23×C11C2×D411yescharacteristic
53C23×C11C2×D412yes—
54C23×C11C2×D411yescharacteristic
55C23×C11#4112yes—
56C23×C11#4111yescharacteristic
57C22×D11—22no—
58C22×D11—22no—
59C22×D11—22no—
60C22×D11—42no—
61C22×D11—42no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—42no—
67C2×C4×C11—42no—
68C2×C4×C11—42no—
69C22⋊D11—42no—
70C22⋊D11—42no—
71C22⋊D11—42no—
72C22⋊D11—42no—
73C2×Dic11—22no—
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—42no—
82C2×Dic11—41no—
83C2×Dic11—41no—
84D44—81no—
85D44—81no—
86#534—111no—
87C2×#99—112no—
88#386—112no—
89#385—111no—
90#342D1111yescharacteristic, complemented
91C22×C11—22no—
92C22×C11—21no—
93C22×C11—22no—
94C22×C11—21no—
95C22×C11—41no—
96C22×C11—42no—
97C22×C11—41no—
98C22×C11#12011yescharacteristic
99C22×C11#12112yes—
100C22×C11#12111yescharacteristic
101C22×C11#12312yes—
102C22×C11#12411yescharacteristic
103C2×D11—44no—
104C2×D11—42no—
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—82no—
108C4×C11—41no—
109C4×C11—41no—
110C4×C11—82no—
111Dic11—42no—
112Dic11—42no—
113Dic11—42no—
114C22×D4—112no—
115C23×C4—111no—
116#123—222no—
117#121—221no—
118#121—221no—
119#120—222no—
120C2×C4⋊C4—221no—
121C2×C22⋊C4—111no—
122C2×C22⋊C4—222no—
123C2×C22⋊C4C2×D1112yes—
124C2×C22⋊C4C2×D1111yescharacteristic
125#99—224no—
126#95—222no—
127#95—221no—
128C2×C11—21no—
129C2×C11—22no—
130C2×C11—22no—
131C2×C11—21no—
132C2×C11#39411yescharacteristic
133C2×C11B(4,𝔽2)11yescharacteristic
134C2×C11#45811yescharacteristic
135D11—82no—
136C24—112no—
137C24C22×D1111yescharacteristic
138C2×D4—221no—
139C2×D4—221no—
140C2×D4—222no—
141C2×D4—222no—
142C2×D4—222no—
143C2×D4—222no—
144C2×D4—222no—
145C2×D4—222no—
146C22×C4—22no—
147C22×C4—112no—
148C22×C4—221no—
149C22×C4—221no—
150C22×C4—222no—
151C22×C4—442no—
152C22×C4D4411yescharacteristic
153C22×C4D4411yescharacteristic
154C4⋊C4—221no—
155C4⋊C4—221no—
156C4⋊C4—442no—
157C22⋊C4—22no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—112no—
161C22⋊C4—222no—
162C22⋊C4—222no—
163C22⋊C4—221no—
164C22⋊C4—444no—
165C11#204411yescharacteristic, complemented, Sylow
166C23—41no—
167C23—41no—
168C23—222no—
169C23—222no—
170C23—222no—
171C23—442no—
172C23—442no—
173C23C2×D4411yescharacteristic
174C23#433912yes—
175C23D4×D1112yes—
176C23D4×D1111yescharacteristic
177C23#434311yescharacteristic
178D4—442no—
179D4—442no—
180D4—442no—
181D4—442no—
182D4—881no—
183D4—881no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—224no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—441no—
198C2×C4—441no—
199C2×C4—442no—
200C2×C4—441no—
201C2×C4—441no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—42no—
207C22—41no—
208C22—41no—
209C22—444no—
210C22—442no—
211C22—442no—
212C22—442no—
213C22—882no—
214C22#6692811yescharacteristic
215C22#6693511yescharacteristic
216C22#6693712yes—
217C22#6694712yes—
218C22#6694811yescharacteristic
219C4—41no—
220C4—41no—
221C4—82no—
222C4—442no—
223C4—442no—
224C4—442no—
225C2—22no—
226C2—21no—
227C2—22no—
228C2—21no—
229C2—882no—
230C2#1062228511yescharacteristic
231C2#1062235411yescharacteristic
232C2#1062235511yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC24×C11C23
FrattiniC24C22×D11
FittingC11×#342C2
socleC22×C11#120
prime radical#10623024C2
hypercenter#342D11
hypocenterC11#2044
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #10622571C2semidirect
3. C2×#66870C2semidirect
4. #10622559C2semidirect
5. C11×#342C2semidirect
42. C22⋊Dic11D4semidirect
90. #342D11semidirect
165. C11#2044semidirect

Maximal subgroups

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

subgroupindex
#106230242
#106225712
C2×#668702
#106225592
C11×#3422
#204411