Finite Group Databasebeta

← #13078787

Subgroups — #13078787

Order 1408.

386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×Q8×C11C211yesmaximal, characteristic, complemented
2#10623010C211yesmaximal, characteristic
3#10622841C211yesmaximal, characteristic, complemented
4#10622840C211yesmaximal, characteristic
5#10622643C212yesmaximal, complemented
6#10622641C212yesmaximal, complemented
7#10622639C212yesmaximal, complemented
8#10622635C212yesmaximal, complemented
9#10622583C211yesmaximal, characteristic, complemented
10#10622581C211yesmaximal, characteristic
11#10622539C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C4×Q8×C11—21no—
14C4×Q8×C11—21no—
15C4×Q8×C11C2212yes—
16C4×Q8×C11C2212yes—
17C2×C11×C4⋊C4—21no—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C42×C11—21no—
20C2×C42×C11C2211yescharacteristic
21C2×#4326C2212yes—
22C2×#4325C2212yes—
23#66983C2211yescharacteristic
24#66982—21no—
25C4×C22⋊D11—21no—
26#66977C2211yescharacteristic
27#66929—21no—
28#66928C2211yescharacteristic
29C4×D44C2211yescharacteristic
30#66925—21no—
31#66923C2211yescharacteristic
32C4×Dic22C2211yescharacteristic
33#66899C2212yes—
34#66899C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66874C2212yes—
38#66873C2212yes—
39#66872C2212yes—
40#66871C2212yes—
41C4⋊(C11⋊C8)C2212yes—
42#66867C2212yes—
43C2×Q8×C11—24no—
44C2×Q8×C11—21no—
45C2×Q8×C11C2312yes—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11D411yescharacteristic
49C22×C4×C11D411yescharacteristic
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—21no—
52C2×D44C2311yescharacteristic
53C2×C4×D11—21no—
54C2×Dic22C2311yescharacteristic
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2312yes—
59C42×C11—22no—
60C42×C11—22no—
61C42×C11D411yescharacteristic
62C42×C11D411yescharacteristic
63C42×C11C2311yescharacteristic
64C42×C11C2311yescharacteristic
65C22⋊Dic11—21no—
66#4326—24no—
67#4325—24no—
68(C2×D11)⋊C4—21no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—21no—
72C4⋊Dic11C2311yescharacteristic
73C4⋊Dic11C2311yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77Dic11⋊C4—21no—
78C4×Dic11—21no—
79C2×C11⋊C8C2312yes—
80C2×C11⋊C8C2312yes—
81#3117—111nomaximal, Sylow
82C23×C11C2×D411yescharacteristic
83C22×D11—21no—
84Q8×C11—24no—
85Q8×C11—22no—
86Q8×C11#4114yes—
87C2×C4×C11—24no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C22⋊D11—42no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104D44—22no—
105C4×D11—42no—
106Dic22—22no—
107C11⋊C8—22no—
108C11⋊C8—22no—
109#529—111no—
110C2×C4×Q8D1111yescharacteristic, complemented
111#484—111no—
112#481—111no—
113#479—112no—
114#464—112no—
115#451—111no—
116#448—111no—
117#441—112no—
118#440—112no—
119#432—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#13712yes—
123C22×C11C22×D411yescharacteristic
124C2×D11—41no—
125C2×D11—41no—
126C2×D11—41no—
127C4×C11—24no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11—42no—
134C4×C11C2×#4112yes—
135Dic11—41no—
136Dic11—41no—
137Dic11—41no—
138C22×Q8C2×D1111yescharacteristic
139C2×Q16—112no—
140C2×SD16—112no—
141#126—221no—
142#125—111no—
143#124—111no—
144#123—221no—
145C22⋊Q8—111no—
146#121—111no—
147C4×Q8—21no—
148C4×Q8—21no—
149C4×Q8—111no—
150C4×Q8C2×D1112yes—
151C4×Q8C2×D1112yes—
152C4×D4—111no—
153C4×D4—221no—
154#117—221no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×D1111yescharacteristic
157C2×C42—21no—
158C2×C42C2×D1111yescharacteristic
159#107—112no—
160#106—112no—
161C4⋊C8—112no—
162#103—112no—
163#103—112no—
164#103—112no—
165#102—112no—
166C22⋊C8—111no—
167C22⋊C8—111no—
168#97—112no—
169C2×C11—22no—
170C2×C11#52511yescharacteristic
171C2×C11C2×#13711yescharacteristic
172C2×C11#57511yescharacteristic
173D11—81no—
174C2×Q8—24no—
175C2×Q8—21no—
176C2×Q8—111no—
177C2×Q8C22×D1112yes—
178C2×D4—111no—
179C2×D4—221no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—221no—
183C22×C4C22⋊D1111yescharacteristic
184C22×C4C22⋊D1111yescharacteristic
185C22×C4C22×D1111yescharacteristic
186Q16—224no—
187SD16—224no—
188C2×C8—112no—
189C2×C8—112no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C4⋊C4—111no—
194C4⋊C4—111no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C4⋊C4C22×D1112yes—
200C22⋊C4—221no—
201C22⋊C4—221no—
202C22⋊C4—221no—
203C22⋊C4—221no—
204C22⋊C4—221no—
205C42—22no—
206C42—22no—
207C42—221no—
208C42C22⋊D1111yescharacteristic
209C42C22⋊D1111yescharacteristic
210C42C22×D1111yescharacteristic
211C42C22×D1111yescharacteristic
212C11#311711yescharacteristic, complemented, Sylow
213C23—221no—
214C23C2×C22⋊D1111yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—222no—
218Q8#433914yes—
219D4—222no—
220D4—442no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—442no—
232C2×C4C2×C22⋊D1111yescharacteristic
233C2×C4C2×C22⋊D1111yescharacteristic
234C2×C4C2×C22⋊D1111yescharacteristic
235C2×C4C2×C22⋊D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C2×C4C23×D1111yescharacteristic
238C8—222no—
239C8—222no—
240C22—21no—
241C22—21no—
242C22—441no—
243C22—441no—
244C22—441no—
245C22#6699512yes—
246C22C22×C22⋊D1111yescharacteristic
247C4—24no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—42no—
254C4—441no—
255C4—441no—
256C4—441no—
257C4C2×#433912yes—
258C2—22no—
259C2—881no—
260C2#1062332211yescharacteristic
261C2C2×#6699511yescharacteristic
262C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C4×Q8×C11C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenterC2×C4×Q8D11
hypocenterC11#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C11C2semidirect
3. #10622841C2semidirect
5. #10622643C2semidirect
6. #10622641C2semidirect
7. #10622639C2semidirect
8. #10622635C2semidirect
9. #10622583C2semidirect
11. #10622539C2semidirect
110. C2×C4×Q8D11semidirect
212. C11#3117semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C112
#106230102
#106228412
#106228402
#106226432
#106226412
#106226392
#106226352
#106225832
#106225812
#106225392
#311711