Finite Group Databasebeta

← #13069644

Subgroups — #13069644

Order 1408.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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#10623361C211yesmaximal, characteristic
2C2×#67004C211yesmaximal, characteristic, complemented
3C2×#66928C211yesmaximal, characteristic, complemented
4C2×C11×#104C211yesmaximal, characteristic, complemented
5C2×#66887C211yesmaximal, characteristic, complemented
6#10622733C211yesmaximal, characteristic, complemented
7#10622161C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13#67004—22no—
14#67004—22no—
15#67000—21no—
16C2×#4326—21no—
17#66993—21no—
18#66990—22no—
19C2×#4324—21no—
20#66983—22no—
21C2×(C2×D11)⋊C4—22no—
22#66979C2211yescharacteristic
23C2×#4318C2211yescharacteristic
24#66928—22no—
25#66928—22no—
26C11×#104—22no—
27#66887—22no—
28#66880—22no—
29C23×D11D412yes—
30C11×#41—21no—
31C11×#41—21no—
32C11×#41—21no—
33C11×#41—21no—
34C2×Q8×C11D411yescharacteristic
35C2×D4×C11—21no—
36C2×D4×C11D411yescharacteristic
37C22×C4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—24no—
41C22×Dic11—21no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44—21no—
45C2×D44—21no—
46C2×D44—21no—
47C2×D44—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22—21no—
51C2×Dic22—21no—
52C2×Dic22—21no—
53C2×Dic22D412yescomplemented
54C11×M16—21no—
55C11×M16—21no—
56C2×C8×C11—21no—
57C42×C11—21no—
58C42×C11D412yescomplemented
59C22⋊Dic11—21no—
60#4326—24no—
61#4324—24no—
62(C2×D11)⋊C4—28no—
63(C2×D11)⋊C4—24no—
64C4⋊Dic11D412yes—
65C4×Dic11—21no—
66#4318—21no—
67#4318D412yescomplemented
68C2×C11⋊C8—21no—
69#2004—111nomaximal, Sylow
70C23×C11—21no—
71C23×C11C2×D411yescharacteristic
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—44no—
76Q8×C11—21no—
77Q8×C11—21no—
78D4×C11—21no—
79D4×C11—21no—
80D4×C11—41no—
81D4×C11—41no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—42no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11#4111yescharacteristic
93C22⋊D11—84no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—41no—
97C2×Dic11—41no—
98D44—41no—
99D44—41no—
100D44—41no—
101D44—41no—
102Dic22—22no—
103Dic22—22no—
104Dic22—41no—
105Dic22—41no—
106C8×C11—41no—
107C11⋊C8—22no—
108C2×#137—111no—
109#535—111no—
110C2×#124—111no—
111C2×#104D1111yescharacteristic, complemented
112#419—111no—
113C2×#100—111no—
114#339—111no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—42no—
118C22×C11#12011yescharacteristic
119C22×C11#12011yescharacteristic
120C22×C11#12111yescharacteristic
121C2×D11—44no—
122C2×D11—42no—
123C2×D11—44no—
124C2×D11—82no—
125C4×C11—42no—
126C4×C11—41no—
127C4×C11#12011yescharacteristic
128C4×C11#12111yescharacteristic
129C4×C11#12111yescharacteristic
130C4×C11#12711yescharacteristic
131Dic11—42no—
132Dic11—42no—
133C2×#41C2×D1111yescharacteristic
134C22×Q8—111no—
135C22×D4—111no—
136#137—222no—
137#137—222no—
138C2×Q16—221no—
139C2×SD16—221no—
140C2×M16—111no—
141C2×M16C2×D1111yescharacteristic
142#127—221no—
143#124—222no—
144#124—221no—
145#124—222no—
146#121—222no—
147#120—222no—
148#117—111no—
149C2×C22⋊C4—222no—
150C2×C42C2×D1111yescharacteristic
151#104—22no—
152#103—222no—
153#100—222no—
154C2×C11—21no—
155C2×C11—21no—
156C2×C11—81no—
157C2×C11#39211yescharacteristic
158C2×C11#45512yes—
159D11—82no—
160C24—112no—
161#41—21no—
162#41—21no—
163#41—21no—
164#41—21no—
165C2×Q8—112no—
166C2×Q8—221no—
167C2×Q8—221no—
168C2×Q8—221no—
169C2×Q8—221no—
170C2×Q8—221no—
171C2×Q8D4411yescharacteristic
172C2×D4—21no—
173C2×D4—224no—
174C2×D4—221no—
175C2×D4—221no—
176C2×D4—221no—
177C2×D4—221no—
178C2×D4—221no—
179C2×D4—221no—
180C2×D4D4411yescharacteristic
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—221no—
184C22×C4C22×D1111yescharacteristic
185Q16—224no—
186SD16—224no—
187M16—21no—
188M16—21no—
189M16—112no—
190M16—221no—
191C2×C8—21no—
192C2×C8—221no—
193C4⋊C4—112no—
194C22⋊C4—228no—
195C22⋊C4—224no—
196C22⋊C4—221no—
197C42—21no—
198C42—221no—
199C42C22⋊D1112yescomplemented
200C11#200411yescharacteristic, complemented, Sylow
201C23—21no—
202C23—222no—
203C23—222no—
204C23—222no—
205C23—444no—
206C23D4×D1111yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—222no—
210Q8—222no—
211Q8—441no—
212Q8—441no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—441no—
218D4—441no—
219D4—441no—
220D4—441no—
221D4—884no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—441no—
230C2×C4—441no—
231C2×C4C2×D4411yescharacteristic
232C2×C4#433911yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4D4×D1111yescharacteristic
235C2×C4D4×D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C8—41no—
238C8—222no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—444no—
243C22—442no—
244C22—444no—
245C22—882no—
246C22#6693511yescharacteristic
247C22#6693711yescharacteristic
248C22#6699011yescharacteristic
249C4—42no—
250C4—41no—
251C4—442no—
252C4—442no—
253C4#6693511yescharacteristic
254C4#6693711yescharacteristic
255C4#6698311yescharacteristic
256C4#6699311yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—882no—
261C2#1062243812yes—
262C2#1062257311yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#104C2
socleC22×C11#120
prime radical#10623361C2
hypercenterC2×#104D11
hypocenterC11#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#67004C2semidirect
3. C2×#66928C2semidirect
4. C2×C11×#104C2semidirect
5. C2×#66887C2semidirect
6. #10622733C2semidirect
7. #10622161C2semidirect
53. C2×Dic22D4semidirect
58. C42×C11D4semidirect
67. #4318D4semidirect
111. C2×#104D11semidirect
199. C42C22⋊D11semidirect
200. C11#2004semidirect

Maximal subgroups

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

subgroupindex
#106233612
C2×#670042
C2×#669282
C2×C11×#1042
C2×#668872
#106227332
#106221612
#200411