Finite Group Databasebeta

← #13078650

Subgroups — #13078650

Order 1408.

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

normal subgroups only

This group has 384 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×Q8×Dic11C211yesmaximal, characteristic
2#10623153C211yesmaximal, characteristic
3C11×#451C211yesmaximal, characteristic
4#10622841C211yesmaximal, characteristic
5Q16×Dic11C212yesmaximal, complemented
6#10622795C212yesmaximal, complemented
7#10622657C211yesmaximal, characteristic
8#10622407C212yesmaximal, complemented
9#10622403C212yesmaximal, complemented
10#10622335C211yesmaximal, characteristic
11#10622331C211yesmaximal, characteristic
12C22×Q8×C11C2211yescharacteristic
13C2×C11×Q16C2212yes—
14C11×C22⋊Q8C2211yescharacteristic
15Q8×Dic11—21no—
16Q8×Dic11—21no—
17Q8×Dic11C2212yes—
18Q8×Dic11C2211yescharacteristic
19Q8×Dic11C2212yes—
20#66997C2211yescharacteristic
21C2×#4326C2212yes—
22C2×C4⋊Dic11—21no—
23C2×C4⋊Dic11C2211yescharacteristic
24#66977C2211yescharacteristic
25C2×C4×Dic11—21no—
26C2×C4×Dic11C2211yescharacteristic
27#66942—21no—
28#66941C2211yescharacteristic
29#66940—21no—
30#66940C2211yescharacteristic
31#66931—21no—
32#66930—21no—
33C11×#103C2212yes—
34C11×C22⋊C8C2211yescharacteristic
35#66899C2212yes—
36#66899C2212yes—
37C22⋊(C11⋊C8)C2211yescharacteristic
38#66882C2212yes—
39#66880C2212yes—
40Dic11⋊C8C2212yes—
41C8×Dic11C2212yes—
42#66871C2212yes—
43C2×Q8×C11—24no—
44C2×Q8×C11—21no—
45C2×Q8×C11C2311yescharacteristic
46C2×Q8×C11C2312yes—
47C22×C4×C11—21no—
48C22×C4×C11C2311yescharacteristic
49C22×Dic11—21no—
50C22×Dic11D411yescharacteristic
51C22×Dic11D411yescharacteristic
52C2×Dic22—21no—
53C2×Dic22C2311yescharacteristic
54C11×Q16—24no—
55C2×C8×C11C2312yes—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2311yescharacteristic
58C11×C22⋊C4—21no—
59C22⋊Dic11—21no—
60#4326—24no—
61C4⋊Dic11—21no—
62C4⋊Dic11—22no—
63C4⋊Dic11—22no—
64C4⋊Dic11—21no—
65C4⋊Dic11C2312yes—
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—21no—
68Dic11⋊C4—21no—
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—21no—
72C4×Dic11—21no—
73C4×Dic11—21no—
74C4×Dic11—22no—
75C4×Dic11—22no—
76C4×Dic11D411yescharacteristic
77C4×Dic11D411yescharacteristic
78C4×Dic11C2311yescharacteristic
79C4×Dic11C2311yescharacteristic
80C2×C11⋊C8C2312yes—
81#3104—111nomaximal, Sylow
82C23×C11C2×D411yescharacteristic
83Q8×C11—24no—
84Q8×C11—22no—
85Q8×C11—22no—
86Q8×C11#4114yes—
87C2×C4×C11—24no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2411yescharacteristic
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—41no—
98C2×Dic11—42no—
99C2×Dic11Q1614yescomplemented
100C2×Dic11C2×D411yescharacteristic
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104Dic22—22no—
105Dic22—42no—
106C8×C11—22no—
107C11⋊C8—22no—
108#533—111no—
109C2×C4×Q8—111no—
110#484—111no—
111#484—111no—
112#477—112no—
113#462—112no—
114#451—111no—
115#451D1111yescharacteristic
116C4×Q16—112no—
117C4×Q16—112no—
118#431—111no—
119C22×C11—21no—
120C22×C11—21no—
121C22×C11C2×Q1612yes—
122C22×C11C22×D411yescharacteristic
123C4×C11—24no—
124C4×C11—21no—
125C4×C11—41no—
126C4×C11—41no—
127C4×C11C2×#4112yes—
128Dic11—21no—
129Dic11—21no—
130Dic11—41no—
131Dic11—41no—
132Dic11—42no—
133Dic11C2×Q1612yes—
134Dic11C2×Q1612yes—
135C22×Q8C2×D1111yescharacteristic
136C2×Q16—112no—
137C2×Q16C2×D1112yes—
138C4⋊Q8—111no—
139C4⋊Q8—111no—
140#125—221no—
141C22⋊Q8—111no—
142C22⋊Q8—221no—
143C22⋊Q8C2×D1111yescharacteristic
144C4×Q8—112no—
145C4×Q8—112no—
146C4×Q8—111no—
147C4×Q8—111no—
148C4×Q8—221no—
149C4×Q8—221no—
150C4×Q8—221no—
151#117—221no—
152C2×C4⋊C4—111no—
153C2×C4⋊C4—221no—
154C2×C42—111no—
155C2×C42—221no—
156#107—112no—
157#107—112no—
158C4⋊C8—112no—
159#103—112no—
160#103—112no—
161#103—112no—
162#103C2×D1112yes—
163C22⋊C8—111no—
164C22⋊C8C2×D1111yescharacteristic
165C4×C8—112no—
166C2×C11—22no—
167C2×C11#52511yescharacteristic
168C2×C11C22×Q1611yescharacteristic
169C2×C11#57511yescharacteristic
170C2×Q8—24no—
171C2×Q8—21no—
172C2×Q8—111no—
173C2×Q8—221no—
174C2×Q8C22×D1111yescharacteristic
175C2×Q8C22×D1112yes—
176C22×C4—21no—
177C22×C4—111no—
178C22×C4—111no—
179C22×C4—221no—
180C22×C4C22×D1111yescharacteristic
181Q16—24no—
182Q16—224no—
183C2×C8—112no—
184C2×C8C22×D1112yes—
185C4⋊C4—21no—
186C4⋊C4—112no—
187C4⋊C4—111no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4C22×D1111yescharacteristic
198C22⋊C4—21no—
199C22⋊C4—221no—
200C42—111no—
201C42—111no—
202C42—111no—
203C42—111no—
204C42—222no—
205C42—222no—
206C42—221no—
207C42—221no—
208C11#310411yescharacteristic, complemented, Sylow
209C23D4×D1111yescharacteristic
210Q8—24no—
211Q8—22no—
212Q8—22no—
213Q8—222no—
214Q8—442no—
215Q8#434114yes—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—114no—
222C2×C4—111no—
223C2×C4—111no—
224C2×C4—111no—
225C2×C4—111no—
226C2×C4—222no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—441no—
230C2×C4—442no—
231C2×C4D4×D1111yescharacteristic
232C2×C4C23×D1111yescharacteristic
233C8—22no—
234C8—222no—
235C22—21no—
236C22—21no—
237C22Q16×D1112yes—
238C22C2×D4×D1111yescharacteristic
239C4—24no—
240C4—21no—
241C4—41no—
242C4—41no—
243C4—112no—
244C4—112no—
245C4—221no—
246C4—221no—
247C4—442no—
248C4—441no—
249C4—441no—
250C4C2×#434112yes—
251C2—22no—
252C2#1062311711yescharacteristic
253C2C2×Q16×D1111yescharacteristic
254C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#451D11
hypocenterC11#3104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. Q16×Dic11C2semidirect
6. #10622795C2semidirect
8. #10622407C2semidirect
9. #10622403C2semidirect
99. C2×Dic11Q16semidirect
208. C11#3104semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
#106231532
C11×#4512
#106228412
Q16×Dic112
#106227952
#106226572
#106224072
#106224032
#106223352
#106223312
#310411