Finite Group Databasebeta

← #13079562

Subgroups — #13079562

Order 1408.

384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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×#66997C211yesmaximal, characteristic
2#10623153C211yesmaximal, characteristic
3C11×#451C211yesmaximal, characteristic
4#10622841C211yesmaximal, characteristic
5#10622795C212yesmaximal, complemented
6#10622794C212yesmaximal, complemented
7#10622663C211yesmaximal, characteristic
8#10622406C212yesmaximal, complemented
9#10622405C212yesmaximal, complemented
10#10622352C211yesmaximal, characteristic
11#10622331C211yesmaximal, characteristic
12C22×Q8×C11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×Q16C2212yes—
15C11×C22⋊Q8C2211yescharacteristic
16Q8×Dic11C2211yescharacteristic
17#66997—21no—
18#66997—21no—
19#66997C2211yescharacteristic
20#66997C2212yes—
21#66997C2212yes—
22C2×#4326C2212yes—
23C2×#4326C2212yes—
24#66977C2211yescharacteristic
25C2×Dic11⋊C4—21no—
26C2×Dic11⋊C4—21no—
27C2×C4×Dic11C2211yescharacteristic
28C2×Dic44C2212yes—
29#66942—21no—
30#66941C2211yescharacteristic
31#66940—21no—
32#66940C2211yescharacteristic
33#66931—21no—
34#66930—21no—
35C11×#103C2212yes—
36C11×C22⋊C8C2211yescharacteristic
37#66899C2212yes—
38C22⋊(C11⋊C8)C2211yescharacteristic
39#66880C2212yes—
40Dic11⋊C8C2212yes—
41C8×Dic11C2212yes—
42#66874C2212yes—
43C2×Q8×C11—21no—
44C2×Q8×C11—42no—
45C2×Q8×C11C2312yes—
46C2×Q8×C11C2311yescharacteristic
47C22×C4×C11—21no—
48C22×C4×C11C2311yescharacteristic
49C22×Dic11—21no—
50C22×Dic11D411yescharacteristic
51C22×Dic11D411yescharacteristic
52C2×Dic22—21no—
53C2×Dic22—21no—
54C2×Dic22—42no—
55C2×Dic22C2312yes—
56C2×Dic22C2311yescharacteristic
57C11×Q16—42no—
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2311yescharacteristic
61C11×C22⋊C4—21no—
62C22⋊Dic11—21no—
63#4326—42no—
64#4326—42no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—21no—
68Dic11⋊C4—21no—
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73Dic11⋊C4—22no—
74Dic11⋊C4—22no—
75Dic11⋊C4—21no—
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11D411yescharacteristic
79C4×Dic11D411yescharacteristic
80C4×Dic11C2311yescharacteristic
81C4×Dic11C2311yescharacteristic
82C2×C11⋊C8C2312yes—
83Dic44—42no—
84#3209—111nomaximal, Sylow
85C23×C11C2×D411yescharacteristic
86Q8×C11—22no—
87Q8×C11—22no—
88Q8×C11—22no—
89Q8×C11—42no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—42no—
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2411yescharacteristic
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—42no—
102C2×Dic11Q1614yescomplemented
103C2×Dic11C2×D411yescharacteristic
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106C2×Dic11C2×D411yescharacteristic
107Dic22—22no—
108Dic22—22no—
109Dic22—22no—
110Dic22—42no—
111Dic22—42no—
112C8×C11—22no—
113C11⋊C8—22no—
114#533—111no—
115C2×C4⋊Q8—111no—
116#494—112no—
117#487—112no—
118#462—112no—
119#462—112no—
120#451—111no—
121#451—111no—
122#451—111no—
123#451D1111yescharacteristic
124#431—111no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11C2×Q1612yes—
128C22×C11C22×D411yescharacteristic
129C4×C11—21no—
130C4×C11—42no—
131C4×C11—41no—
132C4×C11—41no—
133C4×C11H(5,𝔽2)12yes—
134Dic11—21no—
135Dic11—42no—
136Dic11—41no—
137Dic11—41no—
138Dic11C2×Q1612yes—
139Dic11C2×Q1612yes—
140Dic11#13712yes—
141C22×Q8—111no—
142C22×Q8C2×D1111yescharacteristic
143C2×Q16—112no—
144C2×Q16—112no—
145C2×Q16—112no—
146C2×Q16C2×D1112yes—
147C4⋊Q8—111no—
148C4⋊Q8—112no—
149C4⋊Q8—112no—
150C4⋊Q8—111no—
151C4⋊Q8—221no—
152C4⋊Q8—221no—
153#125—221no—
154C22⋊Q8—111no—
155C22⋊Q8—221no—
156C22⋊Q8C2×D1111yescharacteristic
157C4×Q8—111no—
158C4×Q8—111no—
159C4×Q8—221no—
160#117—221no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4—221no—
163C2×C42—111no—
164C4⋊C8—112no—
165#103—112no—
166#103—112no—
167#103—112no—
168#103C2×D1112yes—
169C22⋊C8—111no—
170C22⋊C8C2×D1111yescharacteristic
171C4×C8—112no—
172C2×C11—22no—
173C2×C11#53511yescharacteristic
174C2×C11C22×Q1611yescharacteristic
175C2×C11C2×#13711yescharacteristic
176C2×Q8—21no—
177C2×Q8—42no—
178C2×Q8—112no—
179C2×Q8—111no—
180C2×Q8—221no—
181C2×Q8—221no—
182C2×Q8—442no—
183C2×Q8C22×D1112yes—
184C2×Q8C22×D1111yescharacteristic
185C22×C4—21no—
186C22×C4—111no—
187C22×C4—111no—
188C22×C4—221no—
189C22×C4C22×D1111yescharacteristic
190Q16—42no—
191Q16—442no—
192Q16—442no—
193Q16—442no—
194C2×C8—112no—
195C2×C8C22×D1112yes—
196C4⋊C4—21no—
197C4⋊C4—111no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4—221no—
203C4⋊C4—221no—
204C4⋊C4—221no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4C22×D1111yescharacteristic
209C22⋊C4—21no—
210C22⋊C4—221no—
211C42—111no—
212C42—111no—
213C42—111no—
214C42—111no—
215C42—221no—
216C42—221no—
217C11#320911yescharacteristic, complemented, Sylow
218C23D4×D1111yescharacteristic
219Q8—22no—
220Q8—22no—
221Q8—22no—
222Q8—42no—
223Q8—222no—
224Q8—222no—
225Q8—222no—
226Q8—442no—
227Q8—442no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—114no—
234C2×C4—111no—
235C2×C4—111no—
236C2×C4—111no—
237C2×C4—111no—
238C2×C4—222no—
239C2×C4—221no—
240C2×C4—221no—
241C2×C4—222no—
242C2×C4—442no—
243C2×C4D4×D1111yescharacteristic
244C2×C4C23×D1111yescharacteristic
245C8—22no—
246C8—222no—
247C22—21no—
248C22—21no—
249C22Q16×D1112yes—
250C22C2×D4×D1111yescharacteristic
251C4—21no—
252C4—41no—
253C4—42no—
254C4—41no—
255C4—112no—
256C4—112no—
257C4—112no—
258C4—221no—
259C4—441no—
260C4—442no—
261C4—441no—
262C4#6703712yes—
263C2—22no—
264C2#1062312311yescharacteristic
265C2C2×Q16×D1111yescharacteristic
266C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#451D11
hypocenterC11#3209
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. #10622795C2semidirect
6. #10622794C2semidirect
8. #10622406C2semidirect
9. #10622405C2semidirect
102. C2×Dic11Q16semidirect
217. C11#3209semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
#106231532
C11×#4512
#106228412
#106227952
#106227942
#106226632
#106224062
#106224052
#106223522
#106223312
#320911