Finite Group Databasebeta

← #13079607

Subgroups — #13079607

Order 1408.

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

normal subgroups only

This group has 434 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×#532C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic, complemented
3#10622702C212yesmaximal, complemented
4#10622687C212yesmaximal, complemented
5#10622650C214yesmaximal, complemented
6#10622632C212yesmaximal, complemented
7#10622628C212yesmaximal, complemented
8#10622539C211yesmaximal, characteristic, complemented
9C2×C11×#41—21no—
10C2×#4339C2212yes—
11C11×C4⋊Q8C2211yescharacteristic
12C11×#127C2211yescharacteristic
13C11×#124—21no—
14C11×#121—21no—
15C11×#121C2212yes—
16C4×D4×C11—21no—
17C4×D4×C11C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×#4324C2214yes—
20C2×#4323C2214yes—
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—
33C11×#41—44no—
34C2×Q8×C11—21no—
35C2×D4×C11—22no—
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11C2312yes—
39C22×C4×C11—22no—
40C22×C4×C11D411yescharacteristic
41C22×C4×C11D411yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C2×C22⋊D11—22no—
44#4339—44no—
45C2×D44—21no—
46C2×D44—21no—
47C2×D44C2312yes—
48C2×C4×D11—22no—
49C2×Dic22C2312yes—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2312yes—
52C11×C22⋊C4—22no—
53C11×C22⋊C4—22no—
54C42×C11D411yescharacteristic
55C42×C11D411yescharacteristic
56C42×C11C2311yescharacteristic
57C42×C11C2311yescharacteristic
58#4324—44no—
59#4323—44no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11—21no—
64C2×C11⋊C8C2314yes—
65#3214—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11C2×D411yescharacteristic
68C22×D11—22no—
69Q8×C11—42no—
70D4×C11—22no—
71D4×C11—22no—
72D4×C11—42no—
73D4×C11—42no—
74D4×C11—44no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—41no—
79C2×C4×C11—44no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C22⋊D11—44no—
87C2×Dic11—22no—
88D44—24no—
89D44—42no—
90D44—42no—
91C4×D11—44no—
92Dic22—24no—
93C11⋊C8—24no—
94#532—111no—
95#532D1111yescharacteristic, complemented
96#496—112no—
97#489—112no—
98#461—112no—
99#459—112no—
100#449—114no—
101#432—111no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11C22×D411yescharacteristic
109C2×D11—42no—
110C2×D11—42no—
111C2×D11—42no—
112C4×C11—21no—
113C4×C11—21no—
114C4×C11—21no—
115C4×C11—21no—
116C4×C11—42no—
117C4×C11AGL(1,ℤ/8)12yes—
118C4×C11H(5,𝔽2)12yes—
119Dic11—42no—
120C2×#41—21no—
121C2×#41—112no—
122C2×SD16—114no—
123C2×D8—114no—
124C4⋊Q8—111no—
125C4⋊Q8C2×D1111yescharacteristic
126#127—111no—
127#127C2×D1111yescharacteristic
128#124—21no—
129#124—112no—
130#121—21no—
131#121—221no—
132#121—221no—
133#121C2×D1112yes—
134C4×D4—21no—
135C4×D4—221no—
136C4×D4—221no—
137C4×D4C2×D1112yes—
138C2×C42C2×D1111yescharacteristic
139C4⋊C8—112no—
140#103—114no—
141#102—114no—
142C22⋊C8—112no—
143#97—112no—
144C2×C11—41no—
145C2×C11—82no—
146C2×C11#53511yescharacteristic
147C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C11#57511yescharacteristic
149D11—82no—
150#41—44no—
151#41—444no—
152C2×Q8—21no—
153C2×Q8—112no—
154C2×D4—22no—
155C2×D4—21no—
156C2×D4—21no—
157C2×D4—112no—
158C2×D4—222no—
159C2×D4—221no—
160C2×D4—221no—
161C2×D4C22×D1112yes—
162C22×C4—22no—
163C22×C4—222no—
164C22×C4C22⋊D1111yescharacteristic
165C22×C4C22⋊D1111yescharacteristic
166C22×C4C22×D1111yescharacteristic
167SD16—444no—
168D8—444no—
169C2×C8—114no—
170C4⋊C4—21no—
171C4⋊C4—221no—
172C4⋊C4—221no—
173C4⋊C4C22×D1112yes—
174C22⋊C4—22no—
175C22⋊C4—22no—
176C22⋊C4—222no—
177C22⋊C4—222no—
178C42C22⋊D1111yescharacteristic
179C42C22⋊D1111yescharacteristic
180C42C22×D1111yescharacteristic
181C42C22×D1111yescharacteristic
182C11#321411yescharacteristic, complemented, Sylow
183C23—22no—
184C23—222no—
185C23C2×C22⋊D1111yescharacteristic
186Q8—42no—
187Q8—224no—
188D4—22no—
189D4—22no—
190D4—42no—
191D4—42no—
192D4—44no—
193D4—224no—
194D4—442no—
195D4—444no—
196D4—442no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—44no—
202C2×C4—222no—
203C2×C4—444no—
204C2×C4C2×C22⋊D1111yescharacteristic
205C2×C4C2×C22⋊D1111yescharacteristic
206C2×C4C2×C22⋊D1111yescharacteristic
207C2×C4C2×C22⋊D1111yescharacteristic
208C2×C4C2×C22⋊D1111yescharacteristic
209C2×C4C23×D1111yescharacteristic
210C8—224no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—442no—
218C22—442no—
219C22—442no—
220C22C22×C22⋊D1111yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—42no—
226C4—442no—
227C4#6698512yes—
228C4#6704212yes—
229C2—41no—
230C2—82no—
231C2—882no—
232C2C2×#6698511yescharacteristic
233C2#1062335311yescharacteristic
234C2#1062336111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#532C2
socleC22×C11C22×D4
hypercenter#532D11
hypocenterC11#3214
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C11×#532C2semidirect
2. #10623008C2semidirect
3. #10622702C2semidirect
4. #10622687C2semidirect
5. #10622650C2semidirect
6. #10622632C2semidirect
7. #10622628C2semidirect
8. #10622539C2semidirect
95. #532D11semidirect
182. C11#3214semidirect

Maximal subgroups

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

subgroupindex
C11×#5322
#106230082
#106227022
#106226872
#106226502
#106226322
#106226282
#106225392
#321411