Finite Group Databasebeta

← #13079780

Subgroups — #13079780

Order 1408.

334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C11×#529C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3#10622677C212yesmaximal, complemented
4#10622669C212yesmaximal, complemented
5#10622657C211yesmaximal, characteristic, complemented
6#10622656C211yesmaximal, characteristic, complemented
7#10622647C211yesmaximal, characteristic
8#10622646C211yesmaximal, characteristic
9#10622635C212yesmaximal, complemented
10#10622622C212yesmaximal, complemented
11#10622538C211yesmaximal, characteristic, complemented
12C11×#126—21no—
13C11×#125C2211yescharacteristic
14C11×#124C2211yescharacteristic
15C11×#123—21no—
16C11×C22⋊Q8C2211yescharacteristic
17C11×#121C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11—21no—
20C4×D4×C11C2211yescharacteristic
21C11×#117—21no—
22C2×C42×C11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×Dic11⋊C4—21no—
26C2×Dic11⋊C4—21no—
27#66923—21no—
28#66923—21no—
29#66923C2212yes—
30#66923C2212yes—
31#66899C2212yes—
32#66899C2212yes—
33#66896C2212yes—
34#66896C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66872C2212yes—
38#66872C2212yes—
39#66871C2212yes—
40#66871C2212yes—
41C4⋊(C11⋊C8)C2212yes—
42C4×C11⋊C8C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11D411yescharacteristic
48C22×C4×C11D411yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C22×Dic11—21no—
51C22×Dic11—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2311yescharacteristic
57C11×C4⋊C4C2311yescharacteristic
58C11×C22⋊C4—21no—
59C11×C22⋊C4—21no—
60C11×C22⋊C4—21no—
61C11×C22⋊C4—21no—
62C11×C22⋊C4—21no—
63C42×C11—21no—
64C42×C11D411yescharacteristic
65C42×C11D411yescharacteristic
66C42×C11C2311yescharacteristic
67C42×C11C2311yescharacteristic
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11C2312yes—
71C4⋊Dic11C2312yes—
72Dic11⋊C4—22no—
73Dic11⋊C4—22no—
74Dic11⋊C4—22no—
75Dic11⋊C4—22no—
76C2×C11⋊C8C2312yes—
77C2×C11⋊C8C2312yes—
78#3232—111nomaximal, Sylow
79C23×C11—21no—
80C23×C11C2×D411yescharacteristic
81Q8×C11—22no—
82D4×C11—22no—
83D4×C11—42no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—41no—
90C2×C4×C11—42no—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2411yescharacteristic
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C11⋊C8—22no—
102C11⋊C8—22no—
103#529D1111yescharacteristic
104C2×#125—111no—
105#499—112no—
106#488—112no—
107#484—111no—
108#483—111no—
109#481—111no—
110#480—111no—
111#479—112no—
112#478—112no—
113#431—111no—
114C22×C11—21no—
115C22×C11—21no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11#13512yes—
120C22×C11C22×D411yescharacteristic
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—41no—
127C4×C11—41no—
128C4×C11—41no—
129C4×C112−1+412yes—
130Dic11—42no—
131Dic11—42no—
132#126—21no—
133#125—112no—
134#125—112no—
135#125—221no—
136#125—221no—
137#125C2×D1111yescharacteristic
138#124C2×D1111yescharacteristic
139#123—21no—
140C22⋊Q8C2×D1111yescharacteristic
141#121C2×D1111yescharacteristic
142C4×Q8C2×D1111yescharacteristic
143C4×D4—21no—
144C4×D4C2×D1111yescharacteristic
145#117—21no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—221no—
150C2×C42C2×D1111yescharacteristic
151#107—112no—
152#107—112no—
153#106—112no—
154#106—112no—
155C4⋊C8—112no—
156#103—112no—
157#103—112no—
158#102—112no—
159#102—112no—
160C22⋊C8—111no—
161C22⋊C8—111no—
162C4×C8—112no—
163C2×C11—22no—
164C2×C11—81no—
165C2×C11#53611yescharacteristic
166C2×C11C2×#13511yescharacteristic
167C2×C11#57511yescharacteristic
168C2×Q8C22×D1111yescharacteristic
169C2×D4—21no—
170C2×D4C22×D1111yescharacteristic
171C22×C4—21no—
172C22×C4—221no—
173C22×C4—221no—
174C22×C4C22⋊D1111yescharacteristic
175C22×C4C22⋊D1111yescharacteristic
176C22×C4C22×D1111yescharacteristic
177C2×C8—112no—
178C2×C8—112no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—112no—
184C4⋊C4—112no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4C22×D1111yescharacteristic
192C4⋊C4C22×D1111yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—21no—
198C42—21no—
199C42C22⋊D1111yescharacteristic
200C42C22⋊D1111yescharacteristic
201C42C22×D1111yescharacteristic
202C42C22×D1111yescharacteristic
203C11#323211yescharacteristic, complemented, Sylow
204C23—21no—
205C23C2×C22⋊D1111yescharacteristic
206Q8—22no—
207D4—22no—
208D4—42no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4C2×C22⋊D1111yescharacteristic
221C2×C4C2×C22⋊D1111yescharacteristic
222C2×C4C2×C22⋊D1111yescharacteristic
223C2×C4C2×C22⋊D1111yescharacteristic
224C2×C4C2×C22⋊D1111yescharacteristic
225C2×C4C23×D1111yescharacteristic
226C8—222no—
227C8—222no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22#6700312yes—
234C22C22×C22⋊D1111yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—41no—
243C4—442no—
244C4—442no—
245C4#6704312yes—
246C2—22no—
247C2—81no—
248C2C2×#6700311yescharacteristic
249C2#1062335311yescharacteristic
250C2#1062335611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#529C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#529D11
hypocenterC11#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
3. #10622677C2semidirect
4. #10622669C2semidirect
5. #10622657C2semidirect
6. #10622656C2semidirect
9. #10622635C2semidirect
10. #10622622C2semidirect
11. #10622538C2semidirect
203. C11#3232semidirect

Maximal subgroups

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

subgroupindex
C11×#5292
C2×#669232
#106226772
#106226692
#106226572
#106226562
#106226472
#106226462
#106226352
#106226222
#106225382
#323211