Finite Group Databasebeta

← #13069643

Subgroups — #13069643

Order 1408.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C11×#535C211yesmaximal, characteristic
2C2×#67004C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic, complemented
4C2×#66901C211yesmaximal, characteristic, complemented
5C2×#66897C211yesmaximal, characteristic, complemented
6#10622617C211yesmaximal, characteristic, complemented
7#10622170C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C11×#127—21no—
12C11×#124—21no—
13C11×#121—22no—
14C11×#120—22no—
15C11×#117C2211yescharacteristic
16C2×C22⋊Dic11—22no—
17#67004—22no—
18#67004—22no—
19C2×#4326—21no—
20#66989—22no—
21#66989—22no—
22C2×#4324—21no—
23C2×C4×Dic11C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C2×#4318C2211yescharacteristic
26#66901—22no—
27#66897—22no—
28#66874—22no—
29C24×C11D412yes—
30C11×#41—21no—
31C11×#41—21no—
32C11×#41—21no—
33C11×#41—21no—
34C2×Q8×C11D411yescharacteristic
35C2×D4×C11—21no—
36C2×D4×C11—24no—
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11—21no—
41C2×D4×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11D411yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C22×Dic11—21no—
47C22×Dic11—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22—21no—
51C2×Dic22—21no—
52C2×Dic22—21no—
53C2×Dic22D412yescomplemented
54C11×C4⋊C4D412yes—
55C11×C22⋊C4—24no—
56C11×C22⋊C4—21no—
57C42×C11—21no—
58C22⋊Dic11—28no—
59#4326—24no—
60#4324—24no—
61C4×Dic11—21no—
62C4×Dic11D412yescomplemented
63#4318—21no—
64#4318—21no—
65#4318—21no—
66#4318D412yescomplemented
67C2×C11⋊C8—21no—
68C2×C11⋊C8—21no—
69#2004—111nomaximal, Sylow
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—44no—
75C23×C11C2×D411yescharacteristic
76Q8×C11—21no—
77Q8×C11—21no—
78D4×C11—21no—
79D4×C11—21no—
80D4×C11—41no—
81D4×C11—41no—
82D4×C11—41no—
83D4×C11—41no—
84D4×C11—41no—
85D4×C11—41no—
86D4×C11—84no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11#4111yescharacteristic
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—42no—
100C2×Dic11—41no—
101C2×Dic11—41no—
102Dic22—22no—
103Dic22—22no—
104Dic22—41no—
105Dic22—41no—
106C11⋊C8—22no—
107C11⋊C8—41no—
108C2×#137—111no—
109#535D1111yescharacteristic
110C2×#124—111no—
111C2×#104—111no—
112#419—111no—
113C2×#100—111no—
114#339—111no—
115C22×C11—22no—
116C22×C11—44no—
117C22×C11—41no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11—44no—
121C22×C11—82no—
122C22×C11#12011yescharacteristic
123C22×C11#12011yescharacteristic
124C22×C11#12111yescharacteristic
125C4×C11—41no—
126C4×C11—42no—
127C4×C11#12011yescharacteristic
128C4×C11#12111yescharacteristic
129C4×C11#12111yescharacteristic
130C4×C11#12711yescharacteristic
131Dic11—42no—
132Dic11—42no—
133C2×#41C2×D1111yescharacteristic
134C22×Q8—111no—
135C22×D4C2×D1111yescharacteristic
136#137—222no—
137#137—222no—
138C2×Q16—221no—
139C2×SD16—221no—
140C2×M16—111no—
141C2×M16—111no—
142#127—21no—
143#124—21no—
144#124—222no—
145#124—222no—
146#121—22no—
147#120—22no—
148#117C2×D1111yescharacteristic
149C2×C22⋊C4—222no—
150C2×C42—111no—
151#104—222no—
152#103—222no—
153#100—222no—
154C2×C11—21no—
155C2×C11—21no—
156C2×C11—81no—
157C2×C11—82no—
158C2×C11#39211yescharacteristic
159C2×C11#45512yes—
160C24C22⋊D1112yes—
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×Q8C22⋊D1111yescharacteristic
172C2×D4—21no—
173C2×D4—24no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4C22⋊D1111yescharacteristic
181C22×C4—21no—
182C22×C4—221no—
183C22×C4—221no—
184C22×C4C22×D1111yescharacteristic
185Q16—224no—
186SD16—224no—
187M16—112no—
188M16—221no—
189M16—221no—
190M16—221no—
191C2×C8—221no—
192C2×C8—221no—
193C4⋊C4C22⋊D1112yes—
194C22⋊C4—24no—
195C22⋊C4—21no—
196C22⋊C4—228no—
197C42—21no—
198C42—112no—
199C42—221no—
200C11#200411yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23—21no—
204C23—22no—
205C23—44no—
206C23C2×C22⋊D1111yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—222no—
210Q8—222no—
211Q8—441no—
212Q8—441no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221D4—84no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—442no—
229C2×C4—441no—
230C2×C4—441no—
231C2×C4D4×D1111yescharacteristic
232C2×C4D4×D1111yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4#434111yescharacteristic
235C2×C4C2×C22⋊D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C8—222no—
238C8—441no—
239C22—22no—
240C22—44no—
241C22—41no—
242C22—42no—
243C22—42no—
244C22—44no—
245C22—82no—
246C22#6699011yescharacteristic
247C22#6699211yescharacteristic
248C22#6700611yescharacteristic
249C4—41no—
250C4—42no—
251C4—442no—
252C4—442no—
253C4#6699011yescharacteristic
254C4#6699111yescharacteristic
255C4#6699211yescharacteristic
256C4#6699311yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—81no—
261C2#1062283611yescharacteristic
262C2#1062285512yes—
subgroupG/H
centerC22#67006
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC11×#535C2
socleC22×C11#120
hypercenter#535D11
hypocenterC11#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
2. C2×#67004C2semidirect
3. C2×#66989C2semidirect
4. C2×#66901C2semidirect
5. C2×#66897C2semidirect
6. #10622617C2semidirect
7. #10622170C2semidirect
53. C2×Dic22D4semidirect
62. C4×Dic11D4semidirect
66. #4318D4semidirect
200. C11#2004semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
C2×#670042
C2×#669892
C2×#669012
C2×#668972
#106226172
#106221702
#200411