Finite Group Databasebeta

← #13068554

Subgroups — #13068554

Order 1408.

612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C22×#4339C211yesmaximal, characteristic
2C11×#380C211yesmaximal, characteristic, complemented
3C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
4C2×#66874C212yesmaximal, complemented
5C2×#66873C212yesmaximal, complemented
6C23×C4×C11C2211yescharacteristic
7C22×C22⋊D11—21no—
8C2×#4339—22no—
9C2×#4339—24no—
10C2×#4339—24no—
11C2×#4339C414yescomplemented
12C22×D44C2211yescharacteristic
13C22×C4×D11—21no—
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16C2×C11×C22⋊C4—21no—
17C22×C11⋊C8C2212yes—
18C11×#95—21no—
19C22⋊(C11⋊C8)—22no—
20#66874—24no—
21#66873—24no—
22C24×C11D411yescharacteristic
23C23×D11—21no—
24C22×C4×C11—22no—
25C22×C4×C11—22no—
26C22×C4×C11—22no—
27C22×C4×C11C2×C412yes—
28C22×C4×C11D411yescharacteristic
29C22×C4×C11D412yes—
30C22×C4×C11C2311yescharacteristic
31C2×C22⋊D11—28no—
32C2×C22⋊D11—24no—
33C22×Dic11—21no—
34#4339—216no—
35#4339—28no—
36#4339—28no—
37C2×D44—21no—
38C2×D44—22no—
39C2×D44C2×C412yes—
40C2×D44D414yes—
41C2×C4×D11—28no—
42C2×C4×D11—24no—
43C2×Dic22—21no—
44C2×Dic22—22no—
45C2×Dic22C2×C412yes—
46C2×Dic22D414yes—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—22no—
49C11×C22⋊C4—42no—
50C2×C11⋊C8—22no—
51C2×C11⋊C8—22no—
52C2×C11⋊C8—22no—
53#1788—111nomaximal, Sylow
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—21no—
57C23×C11—21no—
58C23×C11C22⋊C412yes—
59C23×C11C2×D411yescharacteristic
60C22×D11—22no—
61C22×D11—24no—
62C22×D11—42no—
63C22×D11—41no—
64C22×D11—41no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—24no—
69C2×C4×C11—42no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11C22⋊C412yes—
73C2×C4×C11C22×C411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D412yes—
77C22⋊D11—216no—
78C2×Dic11—22no—
79C2×Dic11—24no—
80D44—22no—
81D44—24no—
82D44C22⋊C414yescomplemented
83C4×D11—216no—
84Dic22—22no—
85Dic22—24no—
86Dic22C22⋊C414yescomplemented
87C11⋊C8—42no—
88C22×#41—111no—
89C2×#103—112no—
90C2×#102—112no—
91C2×C22⋊C8—111no—
92#380D1111yescharacteristic, complemented
93C22×C11—22no—
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—42no—
97C22×C11—42no—
98C22×C11C2×C22⋊C411yescharacteristic
99C22×C11#12012yes—
100C22×C11#13512yes—
101C22×C11AGL(1,ℤ/8)11yescharacteristic
102C22×C11#13711yescharacteristic
103C2×D11—24no—
104C2×D11—42no—
105C2×D11—42no—
106C2×D11—44no—
107C2×D11—44no—
108C4×C11—22no—
109C4×C11—82no—
110C4×C11C2×C22⋊C411yescharacteristic
111C4×C11C2×C22⋊C411yescharacteristic
112C4×C11#12012yes—
113Dic11—24no—
114C2×#41—114no—
115C2×#41—224no—
116C2×#41—224no—
117C2×#41—222no—
118C22×Q8—111no—
119C22×D4—111no—
120C22×D4—221no—
121C23×C4—221no—
122C23×C4C2×D1111yescharacteristic
123C22×C8—112no—
124C2×C4⋊C4C2×D1112yes—
125C2×C22⋊C4—21no—
126#103—224no—
127#102—224no—
128C22⋊C8—222no—
129#95—21no—
130C2×C11—42no—
131C2×C11#37911yescharacteristic
132C2×C11#41611yescharacteristic
133C2×C11#41711yescharacteristic
134C2×C11#44912yes—
135C2×C11#45212yes—
136D11—44no—
137C24—221no—
138C24C22⋊D1111yescharacteristic
139#41—228no—
140#41—228no—
141#41—2216no—
142C2×Q8—112no—
143C2×Q8—114no—
144C2×Q8—221no—
145C2×Q8—222no—
146C2×D4—112no—
147C2×D4—114no—
148C2×D4—228no—
149C2×D4—224no—
150C2×D4—221no—
151C2×D4—222no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—228no—
156C22×C4—221no—
157C22×C4—224no—
158C22×C4C4×D1112yes—
159C22×C4D4412yes—
160C22×C4C22⋊D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C2×C8—222no—
163C2×C8—222no—
164C2×C8—222no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C22⋊C4—42no—
168C11#178811yescharacteristic, complemented, Sylow
169C23—21no—
170C23—22no—
171C23—21no—
172C23—22no—
173C23—222no—
174C23—224no—
175C23—441no—
176C23—441no—
177C23—442no—
178C23(C2×D11)⋊C412yes—
179C23C2×C22⋊D1111yescharacteristic
180Q8—114no—
181Q8—222no—
182Q8—224no—
183D4—114no—
184D4—2216no—
185D4—222no—
186D4—224no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—2216no—
195C2×C4—222no—
196C2×C4—224no—
197C2×C4(C2×D11)⋊C412yes—
198C2×C4C2×C4×D1111yescharacteristic
199C2×C4C2×D4411yescharacteristic
200C2×C4D4×D1112yes—
201C2×C4D4×D1112yes—
202C8—442no—
203C22—22no—
204C22—22no—
205C22—22no—
206C22—42no—
207C22—42no—
208C22—224no—
209C22—442no—
210C22—442no—
211C22—444no—
212C22—444no—
213C22C2×(C2×D11)⋊C411yescharacteristic
214C22#6698511yescharacteristic
215C22#6699012yes—
216C22#6699511yescharacteristic
217C22#6700312yes—
218C4—22no—
219C4—82no—
220C4—224no—
221C4C22⋊C4×D1111yescharacteristic
222C4C22⋊C4×D1111yescharacteristic
223C4#6693512yes—
224C2—42no—
225C2—444no—
226C2#1062256811yescharacteristic
227C2#1062257911yescharacteristic
228C2#1062261511yescharacteristic
229C2#1062265012yes—
230C2#1062266012yes—
subgroupG/H
centerC23C2×C22⋊D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#380C2
socleC23×C11C2×D4
prime radicalC22×#4339C2
cosocleC22×C4×C11C23
hypercenter#380D11
hypocenterC11#1788
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C11×#380C2semidirect
3. C2×C22⋊(C11⋊C8)C2semidirect
4. C2×#66874C2semidirect
5. C2×#66873C2semidirect
11. C2×#4339C4semidirect
82. D44C22⋊C4semidirect
86. Dic22C22⋊C4semidirect
92. #380D11semidirect
168. C11#1788semidirect

Maximal subgroups

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

subgroupindex
C22×#43392
C11×#3802
C2×C22⋊(C11⋊C8)2
C2×#668742
C2×#668732
#178811