Finite Group Databasebeta

← #13070627

Subgroups — #13070627

Order 1408.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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
1#10623182C211yesmaximal, characteristic, complemented
2C11×#458C211yesmaximal, characteristic
3#10622856C211yesmaximal, characteristic
4#10622855C211yesmaximal, characteristic
5#10622177C211yesmaximal, characteristic, complemented
6#10622111C211yesmaximal, characteristic, complemented
7#10622110C211yesmaximal, characteristic, complemented
8C11×H(5,𝔽2)C2211yescharacteristic
9C11×#123—21no—
10C11×#123C2211yescharacteristic
11#67004—21no—
12#66989C2211yescharacteristic
13#66988—21no—
14#66988C2211yescharacteristic
15#66977—21no—
16#66942—21no—
17#66941—21no—
18#66932—21no—
19#66932—21no—
20#66931—21no—
21C11×#99—21no—
22C11×#99C2211yescharacteristic
23#66901—21no—
24#66898—21no—
25#66898C2211yescharacteristic
26#66897C2211yescharacteristic
27C11×#41—21no—
28C11×#41—41no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—41no—
32C2×D4×C11C2311yescharacteristic
33C22×C4×C11D411yescharacteristic
34C22×Dic11D411yescharacteristic
35C2×Dic22—21no—
36C2×Dic22D411yescharacteristic
37C11×C4⋊C4—21no—
38C11×C4⋊C4—41no—
39C11×C22⋊C4—21no—
40C11×C22⋊C4—21no—
41C11×C22⋊C4—41no—
42C11×C22⋊C4D411yescharacteristic
43C22⋊Dic11—21no—
44C22⋊Dic11—21no—
45C22⋊Dic11—21no—
46C22⋊Dic11—21no—
47C22⋊Dic11—41no—
48C22⋊Dic11D411yescharacteristic
49#4326—41no—
50#4324—41no—
51C4⋊Dic11—21no—
52C4⋊Dic11—21no—
53Dic11⋊C4—21no—
54Dic11⋊C4—21no—
55Dic11⋊C4—21no—
56Dic11⋊C4—21no—
57Dic11⋊C4—21no—
58Dic11⋊C4—41no—
59C4×Dic11—21no—
60C4×Dic11D411yescharacteristic
61#4318—21no—
62#2201—111nomaximal, Sylow
63C23×C11—21no—
64C23×C11—21no—
65C23×C11C2×D411yescharacteristic
66C23×C11C2×D411yescharacteristic
67Q8×C11—21no—
68D4×C11—21no—
69D4×C11—41no—
70D4×C11—41no—
71D4×C11—41no—
72D4×C11—41no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11C2×D411yescharacteristic
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—21no—
84C2×Dic11—21no—
85C2×Dic11—41no—
86C2×Dic11—41no—
87Dic22—41no—
88Dic22—81no—
89C11⋊C8—41no—
90#563—111no—
91#458—111no—
92#458D1111yescharacteristic
93#455—111no—
94#354—111no—
95#352—111no—
96#352—111no—
97C22×C11—21no—
98C22×C11—21no—
99C22×C11—41no—
100C22×C11—41no—
101C22×C11—41no—
102C22×C11—81no—
103C22×C11—81no—
104C22×C11#12011yescharacteristic
105C4×C11—21no—
106C4×C11—41no—
107C4×C11—41no—
108C4×C11—41no—
109C4×C11—81no—
110Dic11—41no—
111Dic11—41no—
112Dic11—41no—
113Dic11—41no—
114Dic11—81no—
115H(5,𝔽2)C2×D1111yescharacteristic
116#137—221no—
117C4⋊Q8—221no—
118#126—221no—
119#126—221no—
120#125—221no—
121#124—111no—
122#123—21no—
123#123—111no—
124#123—221no—
125#123C2×D1111yescharacteristic
126C22⋊Q8—221no—
127C22⋊Q8—221no—
128#104—221no—
129#100—111no—
130#99—21no—
131#99—111no—
132#99—221no—
133#99C2×D1111yescharacteristic
134C2×C11—21no—
135C2×C11—41no—
136C2×C11—41no—
137C2×C11—81no—
138C2×C11B(4,𝔽2)11yescharacteristic
139#41—21no—
140#41—41no—
141C2×Q8—111no—
142C2×Q8—221no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—41no—
146C2×D4C22×D1111yescharacteristic
147C22×C4—111no—
148C22×C4C22⋊D1111yescharacteristic
149Q16—441no—
150SD16—441no—
151M16—221no—
152C4⋊C4—21no—
153C4⋊C4—41no—
154C4⋊C4—221no—
155C4⋊C4—221no—
156C4⋊C4—221no—
157C4⋊C4—221no—
158C4⋊C4—221no—
159C4⋊C4—221no—
160C4⋊C4—221no—
161C4⋊C4—441no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—41no—
165C22⋊C4—111no—
166C22⋊C4—221no—
167C22⋊C4—221no—
168C22⋊C4—221no—
169C22⋊C4—221no—
170C22⋊C4—441no—
171C22⋊C4C22⋊D1111yescharacteristic
172C42—111no—
173C42—221no—
174C11#220111yescharacteristic, complemented, Sylow
175C23—21no—
176C23—21no—
177C23D4×D1111yescharacteristic
178C23C2×C22⋊D1111yescharacteristic
179Q8—21no—
180Q8—441no—
181Q8—881no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—221no—
195C2×C4—221no—
196C2×C4—221no—
197C2×C4—221no—
198C2×C4—441no—
199C2×C4—441no—
200C2×C4D4×D1111yescharacteristic
201C8—441no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#6699011yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—441no—
216C4—441no—
217C4—441no—
218C4—441no—
219C4—881no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#1062264511yescharacteristic
subgroupG/H
centerC2#10622645
commutator, cosocleC2×D4×C11C23
FrattiniC2×D4C22×D11
FittingC11×#458C2
socleC2×C11B(4,𝔽2)
prime radicalC11×H(5,𝔽2)C22
hypercenter#458D11
hypocenterC11#2201
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #10623182C2semidirect
5. #10622177C2semidirect
6. #10622111C2semidirect
7. #10622110C2semidirect
174. C11#2201semidirect

Maximal subgroups

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

subgroupindex
#106231822
C11×#4582
#106228562
#106228552
#106221772
#106221112
#106221102
#220111