Finite Group Databasebeta

← #13079623

Subgroups — #13079623

Order 1408.

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

normal subgroups only

This group has 390 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×#533C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic
3#10622702C212yesmaximal, complemented
4#10622699C212yesmaximal, complemented
5#10622660C214yesmaximal, complemented
6#10622644C212yesmaximal, complemented
7#10622640C212yesmaximal, complemented
8#10622539C211yesmaximal, characteristic, complemented
9C2×#4339C2212yes—
10C11×C4⋊Q8C2211yescharacteristic
11C11×C4⋊Q8C2211yescharacteristic
12C11×#125—21no—
13C11×C22⋊Q8—21no—
14C11×C22⋊Q8C2212yes—
15C4×Q8×C11—21no—
16C4×Q8×C11C2212yes—
17C11×#117—21no—
18C2×C42×C11C2211yescharacteristic
19C2×#4326C2214yes—
20C2×#4325C2214yes—
21#66983—21no—
22#66983—21no—
23#66928C2212yes—
24#66927C2211yescharacteristic
25C4×D44—21no—
26C4×D44—21no—
27#66922C2211yescharacteristic
28C22⋊(C11⋊C8)C2212yes—
29#66874C2214yes—
30#66873C2214yes—
31C4⋊(C11⋊C8)C2212yes—
32#66867C2212yes—
33C2×Q8×C11—21no—
34C2×Q8×C11C2312yes—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39#4339—44no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C2×Dic22C2312yes—
45C11×C4⋊C4—21no—
46C11×C4⋊C4—21no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4C2312yes—
51C11×C22⋊C4—22no—
52C42×C11—22no—
53C42×C11D411yescharacteristic
54C42×C11D411yescharacteristic
55C42×C11C2311yescharacteristic
56C42×C11C2311yescharacteristic
57#4326—44no—
58#4325—44no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11—21no—
62C4⋊Dic11—21no—
63C2×C11⋊C8C2314yes—
64#3216—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67Q8×C11—22no—
68Q8×C11—22no—
69Q8×C11—42no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—41no—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C22⋊D11—44no—
82C2×Dic11—22no—
83D44—24no—
84D44—42no—
85D44—42no—
86C4×D11—44no—
87Dic22—24no—
88C11⋊C8—24no—
89#533D1111yescharacteristic, complemented
90#532—111no—
91#497—112no—
92#489—112no—
93#462—112no—
94#460—112no—
95#452—114no—
96#432—111no—
97C22×C11—21no—
98C22×C11—21no—
99C22×C11—21no—
100C22×C11C22×D411yescharacteristic
101C2×D11—42no—
102C2×D11—42no—
103C2×D11—42no—
104C4×C11—21no—
105C4×C11—21no—
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—42no—
109C4×C11—42no—
110C4×C11#13712yes—
111C4×C11H(5,𝔽2)12yes—
112Dic11—42no—
113C2×#41—112no—
114C2×Q16—114no—
115C2×SD16—114no—
116C4⋊Q8—111no—
117C4⋊Q8C2×D1111yescharacteristic
118C4⋊Q8C2×D1111yescharacteristic
119#127—111no—
120#125—21no—
121#124—112no—
122C22⋊Q8—21no—
123C22⋊Q8C2×D1112yes—
124#121—221no—
125#121—221no—
126C4×Q8—21no—
127C4×Q8C2×D1112yes—
128C4×D4—221no—
129C4×D4—221no—
130#117—21no—
131C2×C42C2×D1111yescharacteristic
132C4⋊C8—112no—
133#103—114no—
134#102—114no—
135C22⋊C8—112no—
136#97—112no—
137C2×C11—41no—
138C2×C11#53511yescharacteristic
139C2×C11C2×#13711yescharacteristic
140C2×C11#57511yescharacteristic
141D11—82no—
142#41—444no—
143C2×Q8—21no—
144C2×Q8—112no—
145C2×Q8C22×D1112yes—
146C2×D4—112no—
147C2×D4—222no—
148C2×D4—221no—
149C2×D4—221no—
150C22×C4—222no—
151C22×C4C22⋊D1111yescharacteristic
152C22×C4C22⋊D1111yescharacteristic
153C22×C4C22×D1111yescharacteristic
154Q16—444no—
155SD16—444no—
156C2×C8—114no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—221no—
163C4⋊C4—221no—
164C4⋊C4C22×D1112yes—
165C22⋊C4—22no—
166C22⋊C4—222no—
167C22⋊C4—222no—
168C42—22no—
169C42C22⋊D1111yescharacteristic
170C42C22⋊D1111yescharacteristic
171C42C22×D1111yescharacteristic
172C42C22×D1111yescharacteristic
173C11#321611yescharacteristic, complemented, Sylow
174C23—222no—
175C23C2×C22⋊D1111yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—42no—
179Q8—224no—
180D4—224no—
181D4—442no—
182D4—444no—
183D4—442no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—222no—
190C2×C4—444no—
191C2×C4C2×C22⋊D1111yescharacteristic
192C2×C4C2×C22⋊D1111yescharacteristic
193C2×C4C2×C22⋊D1111yescharacteristic
194C2×C4C2×C22⋊D1111yescharacteristic
195C2×C4C2×C22⋊D1111yescharacteristic
196C2×C4C23×D1111yescharacteristic
197C8—224no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—442no—
202C22—442no—
203C22—442no—
204C22C22×C22⋊D1111yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—42no—
210C4—42no—
211C4—442no—
212C4#6699512yes—
213C4#6704212yes—
214C2—41no—
215C2—882no—
216C2C2×#6699511yescharacteristic
217C2#1062335311yescharacteristic
218C2#1062336111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radical#10623008C2
hypercenter#533D11
hypocenterC11#3216
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C11×#533C2semidirect
3. #10622702C2semidirect
4. #10622699C2semidirect
5. #10622660C2semidirect
6. #10622644C2semidirect
7. #10622640C2semidirect
8. #10622539C2semidirect
89. #533D11semidirect
173. C11#3216semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230082
#106227022
#106226992
#106226602
#106226442
#106226402
#106225392
#321611