Finite Group Databasebeta

← #13069933

Subgroups — #13069933

Order 1408.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#4324C211yesmaximal, characteristic
2C11×#390C211yesmaximal, characteristic
3C2×#66896C211yesmaximal, characteristic
4C2×#66874C211yesmaximal, characteristic, complemented
5#10622542C211yesmaximal, characteristic, complemented
6C2×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C22⋊C4—21no—
12C2×C11×C22⋊C4—21no—
13C2×C42×C11C2211yescharacteristic
14C2×#4324—22no—
15C2×#4324—22no—
16C2×#4324—22no—
17C2×C4⋊Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20#66896—22no—
21C11⋊#95—21no—
22C11⋊#95—21no—
23#66874—22no—
24C4⋊(C11⋊C8)—22no—
25C24×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11D412yes—
32C22×C4×C11—21no—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D411yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—21no—
37C22×Dic11—21no—
38C2×Dic22—21no—
39C2×Dic22—21no—
40C2×Dic22—21no—
41C2×Dic22—21no—
42C2×Dic22—21no—
43C2×Dic22D412yes—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C22⋊C4—42no—
47C11×C22⋊C4—42no—
48C42×C11—21no—
49C42×C11—21no—
50#4324—28no—
51C4⋊Dic11—21no—
52C4⋊Dic11—21no—
53C2×C11⋊C8—21no—
54C2×C11⋊C8—21no—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8D412yes—
59#2055—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—41no—
62C23×C11—41no—
63C23×C11—41no—
64C23×C11—41no—
65C23×C11—41no—
66C23×C11—41no—
67C23×C11C2×D411yescharacteristic
68D4×C11—22no—
69D4×C11—22no—
70D4×C11—41no—
71D4×C11—41no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11SD1612yescomplemented
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11#4111yescharacteristic
85C2×C4×C11#4111yescharacteristic
86C2×C4×C11#4111yescharacteristic
87C2×Dic11—22no—
88C2×Dic11—41no—
89C2×Dic11—41no—
90C2×Dic11—41no—
91C2×Dic11—41no—
92C2×Dic11—41no—
93Dic22—22no—
94Dic22—22no—
95Dic22—41no—
96Dic22—41no—
97C11⋊C8—22no—
98C11⋊C8—41no—
99C22×SD16—111no—
100C2×C4⋊C8—111no—
101C2×#103—111no—
102C2×#102—111no—
103#391—111no—
104#390D1111yescharacteristic
105#340—111no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11—42no—
109C22×C11—81no—
110C22×C11—81no—
111C22×C11—81no—
112C22×C11—81no—
113C22×C11#12111yescharacteristic
114C22×C11#12111yescharacteristic
115C22×C11#12111yescharacteristic
116C22×C11C2×SD1611yescharacteristic
117C22×C11#13511yescharacteristic
118C22×C11AGL(1,ℤ/8)11yescharacteristic
119C22×C11#13711yescharacteristic
120C4×C11—22no—
121C4×C11—41no—
122C4×C11—81no—
123C4×C11#12011yescharacteristic
124C4×C11#12311yescharacteristic
125C4×C11#12311yescharacteristic
126C4×C11#12411yescharacteristic
127Dic11—42no—
128Dic11—81no—
129C22×Q8—111no—
130C22×D4C2×D1111yescharacteristic
131C2×SD16—222no—
132C2×SD16—222no—
133C2×SD16—222no—
134C22×C8—111no—
135C22×C8—111no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4C2×D1111yescharacteristic
138C2×C22⋊C4—21no—
139C2×C22⋊C4—21no—
140C2×C42C2×D1111yescharacteristic
141C4⋊C8—222no—
142#103—222no—
143#102—222no—
144#95—221no—
145#95—221no—
146C2×C11—82no—
147C2×C11#39411yescharacteristic
148C2×C11#46011yescharacteristic
149C2×C11#46111yescharacteristic
150C2×C11#46311yescharacteristic
151C2×C11#46411yescharacteristic
152C2×C11#46511yescharacteristic
153C2×C11#46811yescharacteristic
154C24—21no—
155C2×Q8—112no—
156C2×Q8—221no—
157C2×Q8—221no—
158C2×Q8—221no—
159C2×Q8—221no—
160C2×Q8—221no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4D4412yes—
167C22×C4—21no—
168C22×C4—221no—
169C22×C4—221no—
170C22×C4C22⋊D1111yescharacteristic
171C22×C4C22⋊D1111yescharacteristic
172C22×C4C22×D1111yescharacteristic
173SD16—228no—
174C2×C8—112no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8—221no—
179C2×C8—221no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—221no—
183C4⋊C4—221no—
184C22⋊C4—42no—
185C22⋊C4—42no—
186C42—21no—
187C42—21no—
188C11#205511yescharacteristic, complemented, Sylow
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23C2×C22⋊D1111yescharacteristic
197Q8—222no—
198Q8—222no—
199Q8—441no—
200Q8—441no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—222no—
214C2×C4—441no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4#432412yescomplemented
220C2×C4C2×D4411yescharacteristic
221C2×C4#433911yescharacteristic
222C2×C4D4×D1111yescharacteristic
223C2×C4D4×D1111yescharacteristic
224C2×C4#434111yescharacteristic
225C2×C4#434111yescharacteristic
226C8—222no—
227C8—441no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#6698311yescharacteristic
236C22#6698511yescharacteristic
237C22C2×#432411yescharacteristic
238C22#6699111yescharacteristic
239C22#6699211yescharacteristic
240C22#6700311yescharacteristic
241C22#6700411yescharacteristic
242C4—22no—
243C4—41no—
244C4—81no—
245C4—442no—
246C4—881no—
247C4#6693511yescharacteristic
248C4#6693611yescharacteristic
249C4#6693811yescharacteristic
250C4#6693911yescharacteristic
251C2—82no—
252C2#1062257411yescharacteristic
253C2#1062262911yescharacteristic
254C2#1062263211yescharacteristic
255C2#1062265411yescharacteristic
256C2#1062265511yescharacteristic
257C2#1062266711yescharacteristic
258C2#1062268811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#390C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2055
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
4. C2×#66874C2semidirect
5. #10622542C2semidirect
6. C2×C4⋊(C11⋊C8)C2semidirect
7. #10622167C2semidirect
80. C2×C4×C11SD16semidirect
188. C11#2055semidirect
219. C2×C4#4324semidirect

Maximal subgroups

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

subgroupindex
C22×#43242
C11×#3902
C2×#668962
C2×#668742
#106225422
C2×C4⋊(C11⋊C8)2
#106221672
#205511