Finite Group Databasebeta

← #13069809

Subgroups — #13069809

Order 1408.

316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 91 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×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×#66899C211yesmaximal, characteristic, complemented
3C2×#66899C211yesmaximal, characteristic, complemented
4#10622825C211yesmaximal, characteristic
5C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic
6C2×#66872C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C23×C4×C11C2211yescharacteristic
10C11×C22⋊Q8—22no—
11C11×C22⋊Q8—22no—
12C2×C11×C4⋊C4—21no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4—21no—
15C2×C22⋊Dic11—21no—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20#66899—22no—
21#66899—22no—
22C11⋊#95—21no—
23C22⋊(C11⋊C8)—22no—
24#66872—22no—
25C24×C11D411yescharacteristic
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11—21no—
30C2×Q8×C11—21no—
31C2×Q8×C11D412yes—
32C22×C4×C11—21no—
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11—21no—
36C22×C4×C11—21no—
37C22×C4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11D411yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11—21no—
43C22×Dic11—21no—
44C11×C4⋊C4—24no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4D412yes—
47C11×C22⋊C4—24no—
48C22⋊Dic11—42no—
49C4⋊Dic11—21no—
50C4⋊Dic11—21no—
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#2035—111nomaximal, Sylow
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—21no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11SD1612yes—
67C23×C11C2×D411yescharacteristic
68Q8×C11—22no—
69Q8×C11—22no—
70Q8×C11—41no—
71Q8×C11—41no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
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×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11#4111yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C2×C4×C11#4111yescharacteristic
91C2×Dic11—41no—
92C2×Dic11—41no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95C2×Dic11—41no—
96C2×Dic11—41no—
97C11⋊C8—22no—
98C11⋊C8—41no—
99C2×C22⋊Q8D1111yescharacteristic
100C2×#106—111no—
101C2×#103—111no—
102C2×#103—111no—
103C2×C22⋊C8—111no—
104#380—111no—
105#340—111no—
106C22×C11—22no—
107C22×C11—22no—
108C22×C11—22no—
109C22×C11—41no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11#12011yescharacteristic
114C22×C11#12111yescharacteristic
115C22×C11#12311yescharacteristic
116C22×C11C2×SD1611yescharacteristic
117C22×C11#13511yescharacteristic
118C22×C11#13711yescharacteristic
119C22×C11#13711yescharacteristic
120C4×C11—41no—
121C4×C11—42no—
122C4×C11—42no—
123C4×C11#12111yescharacteristic
124C4×C11#12111yescharacteristic
125C4×C11#12311yescharacteristic
126C4×C11#12411yescharacteristic
127Dic11—81no—
128Dic11—81no—
129C22×Q8C2×D1111yescharacteristic
130C23×C4C2×D1111yescharacteristic
131C22×C8—111no—
132C22×C8—111no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4C2×D1111yescharacteristic
139C2×C22⋊C4—21no—
140C2×C22⋊C4—221no—
141#106—222no—
142#103—222no—
143#103—222no—
144C22⋊C8—222no—
145#95—221no—
146C2×C11—42no—
147C2×C11#39411yescharacteristic
148C2×C11#44811yescharacteristic
149C2×C11#45211yescharacteristic
150C2×C11#46511yescharacteristic
151C2×C11#47011yescharacteristic
152C2×C11#48311yescharacteristic
153C2×C11#48511yescharacteristic
154C24C22⋊D1111yescharacteristic
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8C22⋊D1112yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—221no—
170C22×C4—221no—
171C22×C4C22⋊D1111yescharacteristic
172C22×C4C22×D1111yescharacteristic
173C2×C8—112no—
174C2×C8—221no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8—221no—
179C4⋊C4—24no—
180C4⋊C4—21no—
181C4⋊C4—221no—
182C4⋊C4—221no—
183C4⋊C4—221no—
184C4⋊C4—221no—
185C4⋊C4C22⋊D1112yes—
186C22⋊C4—24no—
187C22⋊C4—442no—
188C11#203511yescharacteristic, complemented, Sylow
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23#432512yes—
196C23C2×C22⋊D1111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—441no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4D4×D1111yescharacteristic
221C2×C4#434111yescharacteristic
222C2×C4#434111yescharacteristic
223C2×C4#434111yescharacteristic
224C2×C4C2×C22⋊D1111yescharacteristic
225C2×C4C2×C22⋊D1111yescharacteristic
226C8—222no—
227C8—441no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#6698811yescharacteristic
236C22#6699211yescharacteristic
237C22C2×#432511yescharacteristic
238C22#6699511yescharacteristic
239C22#6700311yescharacteristic
240C22#6700411yescharacteristic
241C22#6700611yescharacteristic
242C4—41no—
243C4—42no—
244C4—42no—
245C4—881no—
246C4—881no—
247C4#6698811yescharacteristic
248C4#6698911yescharacteristic
249C4#6699111yescharacteristic
250C4#6699211yescharacteristic
251C2—42no—
252C2#1062265611yescharacteristic
253C2#1062265811yescharacteristic
254C2#1062266111yescharacteristic
255C2#1062266511yescharacteristic
256C2#1062283511yescharacteristic
257C2#1062284011yescharacteristic
258C2#1062285211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×C22⋊Q8C2
socleC23×C11C2×D4
prime radicalC24×C11D4
hypercenterC2×C22⋊Q8D11
hypocenterC11#2035
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#66899C2semidirect
3. C2×#66899C2semidirect
6. C2×#66872C2semidirect
7. #10622167C2semidirect
188. C11#2035semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#668992
#106228252
C2×C22⋊(C11⋊C8)2
C2×#668722
#106221672
#203511