Finite Group Databasebeta

← #13081356

Subgroups — #13081356

Order 1408.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q82×C11C211yesmaximal, characteristic, complemented
2#10623115C211yesmaximal, characteristic
3#10622707C212yesmaximal, complemented
4#10622706C211yesmaximal, characteristic, complemented
5#10622702C212yesmaximal
6#10622697C211yesmaximal, characteristic
7#10622644C211yesmaximal, characteristic, complemented
8#10622643C212yesmaximal, complemented
9#10622641C212yesmaximal
10C4×#4325C211yesmaximal, characteristic
11#10622637C211yesmaximal, characteristic, complemented
12C11×C4⋊Q8—21no—
13C11×C4⋊Q8—22no—
14C11×C4⋊Q8C2211yescharacteristic
15C11×C4⋊Q8C2212yes—
16C4×Q8×C11—21no—
17C4×Q8×C11C2211yescharacteristic
18C4×Q8×C11C2212yes—
19C4×Q8×C11C2211yescharacteristic
20#66999—21no—
21C2×#4326C2212yes—
22C2×#4325C2211yescharacteristic
23#66951—22no—
24#66945—21no—
25#66928C2212yes—
26C4×D44C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22C2212yes—
29#66899C2211yescharacteristic
30#66874C2212yes—
31#66874C2212yes—
32#66874C2212yes—
33#66873C2211yescharacteristic
34#66873C2212yes—
35#66872C2211yescharacteristic
36#66872C2212yes—
37C4⋊(C11⋊C8)C2212yes—
38C4⋊(C11⋊C8)C2211yescharacteristic
39#66867C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—21no—
43C2×Q8×C11D411yescharacteristic
44C2×Q8×C11C2311yescharacteristic
45C2×D44C2311yescharacteristic
46C2×C4×D11—21no—
47C2×Dic22C2312yes—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4D411yescharacteristic
53C11×C4⋊C4D412yes—
54C11×C4⋊C4C2311yescharacteristic
55C11×C4⋊C4C2312yes—
56C42×C11—22no—
57C42×C11—21no—
58C42×C11C2311yescharacteristic
59C42×C11C2312yes—
60#4326—24no—
61#4325—22no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—22no—
69C4×Dic11—22no—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2312yes—
73#3369—111nomaximal, Sylow
74C22×D11—21no—
75Q8×C11—22no—
76Q8×C11—21no—
77Q8×C11—82no—
78Q8×C11—81no—
79Q8×C11#4112yes—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11C2×D412yes—
84C2×C4×C11C2×D412yes—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C2×Dic11—21no—
89C2×Dic11—22no—
90D44—21no—
91D44—21no—
92C4×D11—42no—
93Dic22—22no—
94Dic22—22no—
95C11⋊C8—21no—
96C11⋊C8—22no—
97C11⋊C8—21no—
98Q82D1111yescharacteristic, complemented
99#556—111no—
100#489—112no—
101#487—111no—
102#476—111no—
103#475—112no—
104#464—112no—
105#462—111no—
106#446—111no—
107#441—112no—
108C4×SD16—111no—
109C22×C11C22×D411yescharacteristic
110C2×D11—41no—
111C2×D11—41no—
112C2×D11—41no—
113C4×C11—22no—
114C4×C11—22no—
115C4×C11—22no—
116C4×C11—21no—
117C4×C11—42no—
118C4×C11—41no—
119C4×C11#13712yes—
120C4×C11C2×#4111yescharacteristic
121C4×C112−1+411yescharacteristic
122Dic11—42no—
123Dic11—41no—
124C2×Q16—112no—
125C2×SD16—111no—
126C4⋊Q8—21no—
127C4⋊Q8—22no—
128C4⋊Q8—111no—
129C4⋊Q8C2×D1112yes—
130C4⋊Q8C2×D1111yescharacteristic
131#126—222no—
132#124—112no—
133C22⋊Q8—221no—
134C4×Q8—21no—
135C4×Q8—112no—
136C4×Q8C2×D1111yescharacteristic
137C4×Q8C2×D1112yes—
138C4×Q8C2×D1111yescharacteristic
139C4×D4—111no—
140#117—221no—
141#106—111no—
142#106—112no—
143C4⋊C8—111no—
144C4⋊C8—112no—
145#103—111no—
146#103—112no—
147#103—112no—
148#103—112no—
149#102—111no—
150#102—112no—
151#97—112no—
152C4×C8—111no—
153C2×C11#54811yescharacteristic
154C2×C11C2×#13711yescharacteristic
155C2×C11#57711yescharacteristic
156D11—81no—
157C2×Q8—22no—
158C2×Q8—21no—
159C2×Q8—112no—
160C2×Q8C22⋊D1111yescharacteristic
161C2×Q8C22×D1111yescharacteristic
162C2×D4—111no—
163C22×C4—221no—
164Q16—224no—
165SD16—222no—
166C2×C8—111no—
167C2×C8—111no—
168C2×C8—112no—
169C4⋊C4—22no—
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—21no—
173C4⋊C4—111no—
174C4⋊C4—221no—
175C4⋊C4—222no—
176C4⋊C4—221no—
177C4⋊C4C22⋊D1111yescharacteristic
178C4⋊C4C22⋊D1112yes—
179C4⋊C4C22×D1111yescharacteristic
180C4⋊C4C22×D1112yes—
181C22⋊C4—222no—
182C22⋊C4—221no—
183C22⋊C4—222no—
184C42—22no—
185C42—21no—
186C42—222no—
187C42C22×D1111yescharacteristic
188C42C22×D1112yes—
189C11#336911yescharacteristic, complemented, Sylow
190C23—221no—
191Q8—22no—
192Q8—21no—
193Q8—82no—
194Q8—81no—
195Q8—222no—
196Q8—222no—
197Q8#434312yes—
198D4—221no—
199D4—221no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—221no—
204C2×C4—222no—
205C2×C4—442no—
206C2×C4C2×C22⋊D1112yes—
207C2×C4C2×C22⋊D1112yes—
208C2×C4C2×C22⋊D1111yescharacteristic
209C2×C4C2×C22⋊D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—221no—
212C8—222no—
213C8—221no—
214C22—441no—
215C22—441no—
216C22—441no—
217C22C22×C22⋊D1111yescharacteristic
218C4—22no—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—42no—
223C4—41no—
224C4—441no—
225C4—442no—
226C4#6699512yes—
227C4C2×#434311yescharacteristic
228C4#6704011yescharacteristic
229C2—881no—
230C2C2×#6699511yescharacteristic
231C2#1062334811yescharacteristic
232C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingQ82×C11C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenterQ82D11
hypocenterC11#3369
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
1. Q82×C11C2semidirect
3. #10622707C2semidirect
4. #10622706C2semidirect
7. #10622644C2semidirect
8. #10622643C2semidirect
11. #10622637C2semidirect
98. Q82D11semidirect
189. C11#3369semidirect

Maximal subgroups

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

subgroupindex
Q82×C112
#106231152
#106227072
#106227062
#106227022
#106226972
#106226442
#106226432
#106226412
C4×#43252
#106226372
#336911