Finite Group Databasebeta

← #13078699

Subgroups — #13078699

Order 1408.

390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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#10623155C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic, complemented
3C11×#483C211yesmaximal, characteristic, complemented
4#10622663C211yesmaximal, characteristic, complemented
5#10622580C211yesmaximal, characteristic
6#10622470C212yesmaximal, complemented
7#10622465C212yesmaximal, complemented
8#10622411C212yesmaximal, complemented
9#10622403C212yesmaximal, complemented
10#10622351C211yesmaximal, characteristic
11#10622331C211yesmaximal, characteristic, complemented
12C22×Dic22C2211yescharacteristic
13C11×C22⋊Q8C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15#67000C2211yescharacteristic
16Q8×Dic11C2211yescharacteristic
17C2×#4326C2212yes—
18#66983C2211yescharacteristic
19C2×Dic11⋊C4—21no—
20C2×C4×Dic11—21no—
21C2×C4×Dic11C2211yescharacteristic
22C2×#4314C2212yes—
23#66951—21no—
24#66946C2211yescharacteristic
25#66945—21no—
26#66943C2211yescharacteristic
27#66940—21no—
28#66940—21no—
29#66940C2212yes—
30#66940C2212yes—
31#66939—21no—
32(C22⋊D11)⋊C4—21no—
33C11×#106C2212yes—
34C11×#103C2212yes—
35C11×C22⋊C8C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66880C2212yes—
38Dic11⋊C8C2212yes—
39C8×Dic11C2212yes—
40#66874C2212yes—
41#66873C2212yes—
42#66871C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C22×Dic11—21no—
48C22×Dic11D411yescharacteristic
49C22×Dic11D411yescharacteristic
50C2×D44C2311yescharacteristic
51C2×C4×D11—21no—
52C2×Dic22—24no—
53C2×Dic22—21no—
54C2×Dic22C2312yes—
55C2×C8×C11C2312yes—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2312yes—
59C11×C4⋊C4C2311yescharacteristic
60C11×C22⋊C4—21no—
61#4326—24no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—21no—
64(C2×D11)⋊C4—21no—
65(C2×D11)⋊C4—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—21no—
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72C4×Dic11—21no—
73C4×Dic11—22no—
74C4×Dic11—22no—
75C4×Dic11D411yescharacteristic
76C4×Dic11D411yescharacteristic
77C4×Dic11C2311yescharacteristic
78C4×Dic11C2311yescharacteristic
79C2×C11⋊C8C2312yes—
80#4314—24no—
81#3108—111nomaximal, Sylow
82C23×C11C2×D411yescharacteristic
83C22×D11—21no—
84Q8×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—42no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2411yescharacteristic
92C22⋊D11—42no—
93C2×Dic11—24no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11C2×D411yescharacteristic
99C2×Dic11C2×D411yescharacteristic
100C2×Dic11C2×D411yescharacteristic
101C2×Dic11C2×D411yescharacteristic
102D44—22no—
103C4×D11—42no—
104Dic22—24no—
105Dic22—22no—
106Dic22#4114yes—
107C8×C11—22no—
108C11⋊C8—22no—
109#529—111no—
110C2×C4×Q8—111no—
111#483D1111yescharacteristic, complemented
112#480—111no—
113#479—112no—
114#464—112no—
115#451—111no—
116#448—111no—
117C4×Q16—112no—
118C4×SD16—112no—
119#431—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#13512yes—
123C22×C11C22×D411yescharacteristic
124C2×D11—41no—
125C2×D11—41no—
126C2×D11—41no—
127C4×C11—21no—
128C4×C11—41no—
129C4×C11—42no—
130C4×C11—41no—
131C4×C11C2×#4112yes—
132Dic11—24no—
133Dic11—21no—
134Dic11—21no—
135Dic11—21no—
136Dic11—41no—
137Dic11#13712yes—
138C22×Q8—111no—
139C2×Q16—112no—
140C2×SD16—112no—
141#126—221no—
142#125—111no—
143#124—111no—
144#123—221no—
145C22⋊Q8C2×D1111yescharacteristic
146#121—111no—
147C4×Q8—111no—
148C4×Q8—112no—
149C4×Q8—112no—
150C4×Q8—221no—
151C4×Q8—221no—
152C4×D4—111no—
153C4×D4—221no—
154#117—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4C2×D1111yescharacteristic
157C2×C42—111no—
158C2×C42—221no—
159#107—112no—
160#106C2×D1112yes—
161C4⋊C8—112no—
162#103—112no—
163#103—112no—
164#103C2×D1112yes—
165#102—112no—
166C22⋊C8—111no—
167C22⋊C8C2×D1111yescharacteristic
168C4×C8—112no—
169C2×C11—22no—
170C2×C11#52511yescharacteristic
171C2×C11C2×#13511yescharacteristic
172C2×C11C2×#13711yescharacteristic
173D11—81no—
174C2×Q8—112no—
175C2×Q8—224no—
176C2×Q8—221no—
177C2×Q8C22×D1111yescharacteristic
178C2×D4—111no—
179C2×D4—221no—
180C22×C4—21no—
181C22×C4—111no—
182C22×C4—111no—
183C22×C4—221no—
184C22×C4—221no—
185C22×C4C22×D1111yescharacteristic
186Q16—224no—
187SD16—224no—
188C2×C8—112no—
189C2×C8C22×D1112yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—111no—
193C4⋊C4—222no—
194C4⋊C4—222no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4C22×D1112yes—
199C4⋊C4C22×D1111yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—221no—
202C22⋊C4—221no—
203C22⋊C4—221no—
204C22⋊C4—221no—
205C42—111no—
206C42—111no—
207C42—111no—
208C42—111no—
209C42—222no—
210C42—222no—
211C42—221no—
212C11#310811yescharacteristic, complemented, Sylow
213C23—221no—
214C23D4×D1111yescharacteristic
215Q8—22no—
216Q8—114no—
217Q8—224no—
218Q8—222no—
219D4—222no—
220D4—442no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—111no—
227C2×C4—111no—
228C2×C4—111no—
229C2×C4—111no—
230C2×C4—222no—
231C2×C4—224no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—442no—
236C2×C4D4×D1111yescharacteristic
237C2×C4C23×D1111yescharacteristic
238C8—22no—
239C8—222no—
240C22—21no—
241C22—21no—
242C22—441no—
243C22—441no—
244C22—441no—
245C22#6696912yes—
246C22C2×D4×D1111yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—112no—
252C4—221no—
253C4—221no—
254C4—221no—
255C4—224no—
256C4—441no—
257C4#41×D1112yes—
258C2—22no—
259C2—881no—
260C2#1062318711yescharacteristic
261C2C2×#6696911yescharacteristic
262C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#483C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#483D11
hypocenterC11#3108
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×#66940C2semidirect
3. C11×#483C2semidirect
4. #10622663C2semidirect
6. #10622470C2semidirect
7. #10622465C2semidirect
8. #10622411C2semidirect
9. #10622403C2semidirect
11. #10622331C2semidirect
111. #483D11semidirect
212. C11#3108semidirect

Maximal subgroups

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

subgroupindex
#106231552
C2×#669402
C11×#4832
#106226632
#106225802
#106224702
#106224652
#106224112
#106224032
#106223512
#106223312
#310811