Finite Group Databasebeta

← #13079694

Subgroups — #13079694

Order 1408.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623262C211yesmaximal, characteristic, complemented
2#10623206C211yesmaximal, characteristic
3C11×#497C211yesmaximal, characteristic, complemented
4#10622799C212yesmaximal, complemented
5#10622795C212yesmaximal, complemented
6#10622786C212yesmaximal
7#10622779C212yesmaximal, complemented
8#10622705C211yesmaximal, characteristic, complemented
9#10622669C211yesmaximal, characteristic, complemented
10#10622322C211yesmaximal, characteristic, complemented
11#10622316C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic
13C2×#4341C2211yescharacteristic
14C2×C11×Q16C2212yes—
15C2×C11×SD16C2212yes—
16C11×C4⋊Q8C2211yescharacteristic
17C11×#124C2211yescharacteristic
18#66999C2212yes—
19Q8×Dic11C2212yes—
20#66997C2211yescharacteristic
21C2×#4326C2212yes—
22C2×#4326C2212yes—
23#66989C2211yescharacteristic
24#66951—22no—
25#66942—22no—
26#66936—22no—
27#66931—22no—
28#66925C2211yescharacteristic
29#66923C2211yescharacteristic
30#66922C2211yescharacteristic
31C11×#97C2211yescharacteristic
32#66899C2212yes—
33#66896C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66880C2212yes—
36#66880C2212yes—
37Dic11⋊C8C2212yes—
38C4×C11⋊C8C2211yescharacteristic
39C2×Q8×C11C2311yescharacteristic
40C2×Q8×C11C2312yes—
41C2×D4×C11C2311yescharacteristic
42C2×C22⋊D11—21no—
43C22×Dic11—21no—
44Q8×D11—42no—
45#4341—42no—
46C2×C4×D11—21no—
47C2×C4×D11C2311yescharacteristic
48C2×Dic22—21no—
49C2×Dic22C2311yescharacteristic
50C2×Dic22C2311yescharacteristic
51C11×Q16—42no—
52C11×SD16—42no—
53C2×C8×C11C2312yes—
54C11×C4⋊C4—22no—
55C11×C22⋊C4—22no—
56C42×C11C2311yescharacteristic
57C22⋊Dic11—22no—
58#4326—42no—
59#4326—42no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4D412yes—
62C4⋊Dic11—22no—
63C4⋊Dic11—22no—
64C4⋊Dic11C2312yes—
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4D412yes—
69C4×Dic11—22no—
70C4×Dic11C2311yescharacteristic
71C2×C11⋊C8C2312yes—
72#3223—111nomaximal, Sylow
73C23×C11—21no—
74C22×D11C2×D411yescharacteristic
75Q8×C11—22no—
76Q8×C11—22no—
77Q8×C11—22no—
78D4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11C2×D412yes—
82C2×C4×C11C2411yescharacteristic
83C22⋊D11—42no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—42no—
88C2×Dic11C2×D412yes—
89C2×Dic11C2×D411yescharacteristic
90C4×D11—22no—
91C4×D11—42no—
92Dic22—22no—
93Dic22—22no—
94Dic22—42no—
95C8×C11—22no—
96C11⋊C8—22no—
97#541—111no—
98#536—111no—
99#497D1111yescharacteristic, complemented
100#494—111no—
101#491—111no—
102#488—111no—
103#464—112no—
104#462—112no—
105#452—112no—
106#451—112no—
107#433—111no—
108C22×C11—41no—
109C22×C11—42no—
110C22×C11C22×D411yescharacteristic
111C2×D11—21no—
112C2×D11—22no—
113C4×C11—22no—
114C4×C11—42no—
115C4×C11—41no—
116C4×C11H(5,𝔽2)12yes—
117Dic11—21no—
118Dic11—22no—
119Dic11—41no—
120Dic11—41no—
121Dic11—42no—
122C2×#41—111no—
123C22×Q8—111no—
124C2×Q16—112no—
125C2×Q16—112no—
126C2×Q16C2×D1112yes—
127C2×SD16C2×D1112yes—
128C4⋊Q8—111no—
129C4⋊Q8—111no—
130C4⋊Q8C2×D1111yescharacteristic
131#126—222no—
132#125—111no—
133#125—222no—
134#124—111no—
135#124C2×D1111yescharacteristic
136#123—222no—
137C22⋊Q8—112no—
138C22⋊Q8—222no—
139C4×Q8—112no—
140#117—111no—
141C4⋊C8—112no—
142#103—112no—
143#103—112no—
144#103—112no—
145#102—112no—
146C22⋊C8—112no—
147#97C2×D1111yescharacteristic
148C4×C8—111no—
149C2×C11—81no—
150C2×C11#53511yescharacteristic
151C2×C11#57812yes—
152D11—41no—
153#41—442no—
154C2×Q8—111no—
155C2×Q8—111no—
156C2×Q8—221no—
157C2×Q8—442no—
158C2×Q8C22×D1111yescharacteristic
159C2×Q8C22×D1112yes—
160C2×D4—221no—
161C2×D4C22×D1111yescharacteristic
162C22×C4—111no—
163C22×C4—221no—
164C22×C4—221no—
165Q16—42no—
166Q16—442no—
167Q16—442no—
168SD16—42no—
169C2×C8—112no—
170C2×C8C22×D1112yes—
171C4⋊C4—22no—
172C4⋊C4—112no—
173C4⋊C4—112no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C22⋊C4—22no—
180C22⋊C4—112no—
181C22⋊C4—222no—
182C22⋊C4—222no—
183C42—111no—
184C42—222no—
185C42C22×D1111yescharacteristic
186C11#322311yescharacteristic, complemented, Sylow
187C23—21no—
188C23—111no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—222no—
193Q8—222no—
194Q8—442no—
195D4—22no—
196D4—442no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—112no—
200C2×C4—111no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—221no—
204C2×C4—221no—
205C2×C4—442no—
206C2×C4—442no—
207C2×C4D4×D1112yes—
208C2×C4C23×D1111yescharacteristic
209C8—22no—
210C8—222no—
211C22—41no—
212C22—42no—
213C22—221no—
214C22—222no—
215C22C2×D4×D1111yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—221no—
220C4—222no—
221C4—441no—
222C4—441no—
223C4—442no—
224C4#6703712yes—
225C2—81no—
226C2—441no—
227C2#1062324611yescharacteristic
228C2#1062331012yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#497C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenter#497D11
hypocenterC11#3223
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #10623262C2semidirect
3. C11×#497C2semidirect
4. #10622799C2semidirect
5. #10622795C2semidirect
7. #10622779C2semidirect
8. #10622705C2semidirect
9. #10622669C2semidirect
10. #10622322C2semidirect
11. #10622316C2semidirect
99. #497D11semidirect
186. C11#3223semidirect

Maximal subgroups

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

subgroupindex
#106232622
#106232062
C11×#4972
#106227992
#106227952
#106227862
#106227792
#106227052
#106226692
#106223222
#106223162
#322311