Finite Group Databasebeta

← #13069818

Subgroups — #13069818

Order 1408.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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×#66999C211yesmaximal, characteristic
2C2×C11×#103C211yesmaximal, characteristic, complemented
3C2×#66899C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C8C211yesmaximal, characteristic
5C2×#66882C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic
7#10622167C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×C4×D11C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12#66999—22no—
13#66999—22no—
14C2×(C2×D11)⋊C4—21no—
15C2×(C2×D11)⋊C4—21no—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4—21no—
19C22×C11⋊C8C2211yescharacteristic
20C11×#103—22no—
21#66899—22no—
22C11⋊#95—21no—
23(C2×D11)⋊C8—22no—
24#66882—22no—
25C23×D11D411yescharacteristic
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×C11C2311yescharacteristic
35C22×Dic11—21no—
36C22×Dic11—21no—
37C22×Dic11D411yescharacteristic
38C2×C4×D11—21no—
39C2×C4×D11—21no—
40C2×C4×D11—21no—
41C2×C4×D11—21no—
42C2×C4×D11—21no—
43C2×C4×D11—21no—
44C2×C8×C11—21no—
45C2×C8×C11—21no—
46C2×C8×C11D412yes—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49(C2×D11)⋊C4—24no—
50(C2×D11)⋊C4—42no—
51C4⋊Dic11—21no—
52C4⋊Dic11—21no—
53C4⋊Dic11—21no—
54C4⋊Dic11D412yes—
55Dic11⋊C4—24no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8—21no—
59#2036—111nomaximal, Sylow
60C23×C11C2×D411yescharacteristic
61C22×D11—21no—
62C22×D11—21no—
63C22×D11—21no—
64C22×D11—21no—
65C22×D11—21no—
66C22×D11—21no—
67C22×D11Q1612yes—
68Q8×C11—22no—
69Q8×C11—22no—
70Q8×C11—41no—
71Q8×C11—41no—
72C2×C4×C11—22no—
73C2×C4×C11—41no—
74C2×C4×C11—41no—
75C2×C4×C11—41no—
76C2×C4×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11#4111yescharacteristic
82C2×C4×C11#4111yescharacteristic
83C2×C4×C11#4111yescharacteristic
84C2×Dic11—21no—
85C2×Dic11—22no—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—41no—
89C2×Dic11—41no—
90C2×Dic11—41no—
91C2×Dic11—41no—
92C2×Dic11—41no—
93C4×D11—41no—
94C4×D11—41no—
95C4×D11—41no—
96C4×D11—41no—
97C8×C11—22no—
98C11⋊C8—41no—
99C2×C22⋊Q8—111no—
100C2×#107—111no—
101C2×#103—111no—
102C2×#103D1111yescharacteristic, complemented
103C2×C22⋊C8—111no—
104#380—111no—
105#340—111no—
106C22×C11#12011yescharacteristic
107C22×C11#12111yescharacteristic
108C22×C11#12311yescharacteristic
109C22×C11C2×Q1611yescharacteristic
110C22×C11#13511yescharacteristic
111C22×C11AGL(1,ℤ/8)11yescharacteristic
112C22×C11#13711yescharacteristic
113C2×D11—22no—
114C2×D11—22no—
115C2×D11—22no—
116C2×D11—41no—
117C2×D11—41no—
118C2×D11—41no—
119C2×D11—41no—
120C4×C11—42no—
121C4×C11—81no—
122C4×C11#12111yescharacteristic
123C4×C11#12111yescharacteristic
124C4×C11#12311yescharacteristic
125C4×C11#12411yescharacteristic
126Dic11—41no—
127Dic11—42no—
128Dic11—81no—
129C22×Q8C2×D1111yescharacteristic
130C23×C4—111no—
131C22×C8—111no—
132C22×C8C2×D1111yescharacteristic
133C22⋊Q8—222no—
134C22⋊Q8—222no—
135C2×C4⋊C4—111no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—221no—
138C2×C4⋊C4C2×D1111yescharacteristic
139C2×C22⋊C4—221no—
140C2×C22⋊C4—221no—
141#107—222no—
142#103—22no—
143#103—222no—
144C22⋊C8—222no—
145#95—221no—
146C2×C11#39411yescharacteristic
147C2×C11#44911yescharacteristic
148C2×C11#45111yescharacteristic
149C2×C11#46711yescharacteristic
150C2×C11#46811yescharacteristic
151C2×C11#48411yescharacteristic
152C2×C11#48511yescharacteristic
153D11—42no—
154C24—111no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8D4412yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—111no—
164C22×C4—221no—
165C22×C4—221no—
166C22×C4—221no—
167C22×C4—221no—
168C22×C4—221no—
169C22×C4—221no—
170C22×C4—221no—
171C22×C4—221no—
172C22×C4C22×D1111yescharacteristic
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8C22⋊D1112yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—112no—
182C4⋊C4—224no—
183C4⋊C4—221no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C22⋊C4—224no—
187C22⋊C4—442no—
188C11#203611yescharacteristic, complemented, Sylow
189C23—112no—
190C23—221no—
191C23—221no—
192C23—221no—
193C23—221no—
194C23—221no—
195C23—221no—
196C23D4×D1111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—222no—
208C2×C4—221no—
209C2×C4—221no—
210C2×C4—221no—
211C2×C4—441no—
212C2×C4—441no—
213C2×C4—441no—
214C2×C4—441no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4C2×D4411yescharacteristic
221C2×C4#433911yescharacteristic
222C2×C4D4×D1111yescharacteristic
223C2×C4#434111yescharacteristic
224C2×C4#434111yescharacteristic
225C2×C4C2×C22⋊D1111yescharacteristic
226C8—22no—
227C8—441no—
228C22—222no—
229C22—222no—
230C22—222no—
231C22—441no—
232C22—441no—
233C22—441no—
234C22—441no—
235C22#6693511yescharacteristic
236C22#6693611yescharacteristic
237C22#6696711yescharacteristic
238C22#6696811yescharacteristic
239C22Q16×D1111yescharacteristic
240C22#6697211yescharacteristic
241C22#6699111yescharacteristic
242C4—42no—
243C4—81no—
244C4—441no—
245C4—442no—
246C4—881no—
247C4#6693811yescharacteristic
248C4#6693911yescharacteristic
249C4#6698311yescharacteristic
250C4#6699211yescharacteristic
251C2—442no—
252C2#1062242111yescharacteristic
253C2#1062242211yescharacteristic
254C2#1062242411yescharacteristic
255C2#1062242711yescharacteristic
256C2#1062257411yescharacteristic
257C2#1062278711yescharacteristic
258C2#1062280111yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#103C2
socleC23×C11C2×D4
prime radicalC23×D11D4
hypercenterC2×#103D11
hypocenterC11#2036
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C11×#103C2semidirect
3. C2×#66899C2semidirect
5. C2×#66882C2semidirect
7. #10622167C2semidirect
102. C2×#103D11semidirect
188. C11#2036semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C11×#1032
C2×#668992
C2×(C2×D11)⋊C82
C2×#668822
#106226002
#106221672
#203611