Finite Group Databasebeta

← #13081233

Subgroups — #13081233

Order 1408.

342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623115C211yesmaximal, characteristic
2#10623110C211yesmaximal, characteristic
3C4×C11×Q16C211yesmaximal, characteristic, complemented
4#10622802C212yesmaximal, complemented
5#10622634C211yesmaximal, characteristic, complemented
6#10622633C211yesmaximal, characteristic, complemented
7#10622494C212yesmaximal, complemented
8#10622428C212yesmaximal, complemented
9#10622418C212yesmaximal, complemented
10#10622301C211yesmaximal, characteristic
11#10622293C211yesmaximal, characteristic, complemented
12C2×C11×Q16C2211yescharacteristic
13C4×Q8×C11C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#66999C2212yes—
16#66999C2212yes—
17C2×#4313C2212yes—
18#66951—22no—
19#66949—22no—
20#66945C2212yes—
21C4⋊C4×D11C2212yes—
22#66928—21no—
23C4×D44—21no—
24C4×D44C2211yescharacteristic
25#66923—21no—
26#66922C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22—21no—
29C11×#107C2211yescharacteristic
30C11×#103C2211yescharacteristic
31C11×#103C2211yescharacteristic
32C4×C8×C11C2211yescharacteristic
33#66899C2212yes—
34#66899C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66881C2212yes—
37#66881C2212yes—
38#66872C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11C2311yescharacteristic
42C2×Q8×C11C2311yescharacteristic
43C2×D44D411yescharacteristic
44C2×C4×D11—22no—
45C2×C4×D11C2312yes—
46C2×Dic22—21no—
47C2×Dic22—21no—
48C11×Q16—22no—
49C2×C8×C11C2311yescharacteristic
50C2×C8×C11C2311yescharacteristic
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4C2311yescharacteristic
54C11×C4⋊C4C2311yescharacteristic
55C42×C11—21no—
56C42×C11—21no—
57C42×C11C2311yescharacteristic
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4D412yes—
62C4⋊Dic11—21no—
63C4⋊Dic11—21no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2312yes—
66C4⋊Dic11C2312yes—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—22no—
71C2×C11⋊C8C2312yes—
72#4313—24no—
73#3356—111nomaximal, Sylow
74C22×D11C2×D412yes—
75Q8×C11—21no—
76Q8×C11—21no—
77Q8×C11—21no—
78Q8×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11C2×D412yes—
89D44—22no—
90C4×D11—22no—
91C4×D11—22no—
92C4×D11—82no—
93Dic22—42no—
94Dic22—81no—
95C8×C11—21no—
96C8×C11#4112yes—
97C11⋊C8—22no—
98#556—111no—
99#554—111no—
100#498—111no—
101#485—112no—
102#483—112no—
103#477—111no—
104#475—111no—
105#470—112no—
106C4×Q16D1111yescharacteristic, complemented
107#436—111no—
108#428—112no—
109C22×C11C22×D411yescharacteristic
110C2×D11—22no—
111C2×D11—22no—
112C2×D11—22no—
113C4×C11—21no—
114C4×C11—41no—
115C4×C11—41no—
116C4×C11—41no—
117C4×C11—41no—
118C4×C11#13712yes—
119C4×C11C2×#4111yescharacteristic
120C4×C112−1+411yescharacteristic
121Dic11—22no—
122Dic11—42no—
123Dic11—42no—
124C2×Q16C2×D1111yescharacteristic
125C2×M16—112no—
126C4⋊Q8—111no—
127C4⋊Q8—111no—
128#126—222no—
129#125—221no—
130#124—221no—
131C22⋊Q8—112no—
132C22⋊Q8—112no—
133C22⋊Q8—222no—
134C4×Q8—221no—
135C4×Q8C2×D1111yescharacteristic
136C4×Q8C2×D1111yescharacteristic
137C4×D4—111no—
138C4×D4—221no—
139#117—112no—
140C2×C4⋊C4—112no—
141#107—112no—
142#107C2×D1111yescharacteristic
143#106—112no—
144#106—112no—
145#106—112no—
146C4⋊C8—111no—
147#103—112no—
148#103—112no—
149#103C2×D1111yescharacteristic
150#103C2×D1111yescharacteristic
151C22⋊C8—112no—
152C4×C8C2×D1111yescharacteristic
153C2×C11#54711yescharacteristic
154C2×C11C2×#13711yescharacteristic
155C2×C11#57711yescharacteristic
156D11—42no—
157C2×Q8—221no—
158C2×Q8—221no—
159C2×Q8C22×D1111yescharacteristic
160C2×Q8C22×D1111yescharacteristic
161C2×D4—111no—
162C22×C4—112no—
163C22×C4—222no—
164Q16—22no—
165M16—224no—
166C2×C8—112no—
167C2×C8C22×D1111yescharacteristic
168C2×C8C22×D1111yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—111no—
172C4⋊C4—112no—
173C4⋊C4—112no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—221no—
178C4⋊C4—221no—
179C4⋊C4C22×D1111yescharacteristic
180C4⋊C4C22×D1111yescharacteristic
181C22⋊C4—112no—
182C22⋊C4—222no—
183C22⋊C4—222no—
184C22⋊C4—222no—
185C42—21no—
186C42—21no—
187C42—222no—
188C42C22×D1111yescharacteristic
189C11#335611yescharacteristic, complemented, Sylow
190C23—112no—
191Q8—21no—
192Q8—21no—
193Q8—21no—
194Q8—21no—
195Q8—442no—
196Q8—881no—
197D4—222no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—112no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—882no—
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—21no—
212C8—222no—
213C8#433912yes—
214C22—222no—
215C22—222no—
216C22—222no—
217C22C2×D4×D1111yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—41no—
223C4—222no—
224C4—442no—
225C4—442no—
226C4#6697112yes—
227C4C2×#433911yescharacteristic
228C4#6704311yescharacteristic
229C2—442no—
230C2#1062308211yescharacteristic
231C2C2×#6697111yescharacteristic
232C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×Q16C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenterC4×Q16D11
hypocenterC11#3356
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×C11×Q16C2semidirect
4. #10622802C2semidirect
5. #10622634C2semidirect
6. #10622633C2semidirect
7. #10622494C2semidirect
8. #10622428C2semidirect
9. #10622418C2semidirect
11. #10622293C2semidirect
106. C4×Q16D11semidirect
189. C11#3356semidirect

Maximal subgroups

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

subgroupindex
#106231152
#106231102
C4×C11×Q162
#106228022
#106226342
#106226332
#106224942
#106224282
#106224182
#106223012
#106222932
#335611