Finite Group Databasebeta

← #14674125

Subgroups — #14674125

Order 2816.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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#13079015C211yesmaximal, characteristic
2#13070278C212yesmaximal
3#13066787C211yesmaximal, characteristic, complemented
4#13066786C212yesmaximal, complemented
5C11×#1412C211yesmaximal, characteristic, complemented
6#10623247C2211yescharacteristic
7D11×#125C411yescharacteristic, complemented
8C11×#490C2211yescharacteristic
9#10622684C2211yescharacteristic
10#10622682C411yescharacteristic, complemented
11#10622384—22no—
12#10622381—22no—
13#10622353—22no—
14#10622320C411yescharacteristic, complemented
15#10622316C411yescharacteristic, complemented
16C11×#353C2212yes—
17#10622183C2212yes—
18#10622111—22no—
19C2×#4341D412yes—
20C11×#127C2311yescharacteristic
21C11×#125C2×C411yescharacteristic
22#66991—41no—
23#66989D412yes—
24D4×Dic11—41no—
25C2×#4313—21no—
26C4⋊C4×D11—21no—
27C4⋊C4×D11—41no—
28#66943—21no—
29#66942—41no—
30#66930—42no—
31C42×D11C2×C411yescharacteristic
32#66923C2×C411yescharacteristic
33#66922C2×C411yescharacteristic
34C11×#102—22no—
35C11×#99—22no—
36C11×#97C2×C411yescharacteristic
37#66898—22no—
38#66896—22no—
39#66880—22no—
40C8×Dic11—21no—
41#66874—22no—
42#66870—42no—
43#66867C2×C411yescharacteristic
44#13596—111nomaximal, Sylow
45C2×D4×C11—41no—
46C2×D4×C11C2×D412yes—
47C2×C22⋊D11—22no—
48C22×Dic11—22no—
49#4341—42no—
50#4341—42no—
51C2×C4×D11—21no—
52C2×C4×D11—41no—
53C2×C4×D11C22⋊C411yescharacteristic
54C2×Dic22C22⋊C412yes—
55C2×C8×C11—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—41no—
58C11×C22⋊C4—42no—
59C42×C11C22×C411yescharacteristic
60C22⋊Dic11—42no—
61C22⋊Dic11—42no—
62C4⋊Dic11—21no—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65Dic11⋊C4—41no—
66Dic11⋊C4—41no—
67Dic11⋊C4—41no—
68Dic11⋊C4—82no—
69C4×Dic11—21no—
70C4×Dic11—82no—
71C4×Dic11C22⋊C411yescharacteristic
72C2×C11⋊C8—21no—
73#4313—42no—
74#3142—111no—
75#2126—112no—
76#1412—111no—
77#1412—112no—
78#1412D1111yescharacteristic, complemented
79C23×C11—22no—
80C22×D11#9911yescharacteristic
81D4×C11—42no—
82D4×C11—82no—
83C2×C4×C11—21no—
84C2×C4×C11—41no—
85C2×C4×C11—82no—
86C2×C4×C11C2×C22⋊C411yescharacteristic
87C22⋊D11—82no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—41no—
93C2×Dic11—82no—
94C2×Dic11#9911yescharacteristic
95C4×D11—22no—
96C4×D11—81no—
97C4×D11—82no—
98Dic22—42no—
99C8×C11—41no—
100C11⋊C8—41no—
101#532—111no—
102C2×#125—111no—
103#491—111no—
104#491—111no—
105#490—111no—
106#490C2×D1111yescharacteristic
107#488—222no—
108#417—222no—
109#410—222no—
110C4×M16—111no—
111#354—222no—
112#353—112no—
113#353C2×D1112yes—
114C22×C11—42no—
115C22×C11—82no—
116C22×C11C2×#9911yescharacteristic
117C2×D11—21no—
118C2×D11—41no—
119C4×C11—21no—
120C4×C11—41no—
121C4×C11—81no—
122C4×C11—162no—
123Dic11—41no—
124Dic11—42no—
125Dic11—81no—
126Dic11—162no—
127Dic11#35412yes—
128C2×#41—112no—
129C2×M16—221no—
130C4⋊Q8—111no—
131#127C22×D1111yescharacteristic
132#125—111no—
133#125—221no—
134#125—441no—
135#125C4×D1111yescharacteristic
136#124—112no—
137#121—441no—
138C4×D4—441no—
139#117—442no—
140C2×C4⋊C4—221no—
141C2×C4⋊C4—441no—
142C2×C42—111no—
143#103—222no—
144#103—222no—
145#102—22no—
146#102—222no—
147#99—22no—
148#99—222no—
149#99—442no—
150#97—111no—
151#97C4×D1111yescharacteristic
152C4×C8—221no—
153C2×C11—21no—
154C2×C11—82no—
155C2×C11C2×#35411yescharacteristic
156D11—41no—
157#41—442no—
158#41—442no—
159C2×Q8—112no—
160C2×D4—41no—
161C2×D4—222no—
162C2×D4D4×D1112yes—
163C22×C4—111no—
164C22×C4—221no—
165C22×C4—222no—
166C22×C4—441no—
167M16—442no—
168C2×C8—21no—
169C2×C8—221no—
170C4⋊C4—21no—
171C4⋊C4—41no—
172C4⋊C4—221no—
173C4⋊C4—441no—
174C4⋊C4—441no—
175C4⋊C4—441no—
176C4⋊C4—441no—
177C4⋊C4—441no—
178C4⋊C4—882no—
179C22⋊C4—42no—
180C22⋊C4—442no—
181C22⋊C4—442no—
182C42—111no—
183C42—221no—
184C42—882no—
185C42C2×C4×D1111yescharacteristic
186C11#1359611yescharacteristic, complemented, Sylow
187C23—22no—
188C23—111no—
189Q8—442no—
190D4—42no—
191D4—82no—
192D4—882no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—82no—
196C2×C4—111no—
197C2×C4—222no—
198C2×C4—221no—
199C2×C4—222no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4—441no—
203C2×C4—881no—
204C2×C4—882no—
205C2×C4—882no—
206C2×C4C22⋊C4×D1111yescharacteristic
207C8—41no—
208C8—441no—
209C22—42no—
210C22—82no—
211C22—221no—
212C22—441no—
213C22D11×#9911yescharacteristic
214C4—21no—
215C4—41no—
216C4—81no—
217C4—112no—
218C4—162no—
219C4—441no—
220C4—442no—
221C4—881no—
222C4—1762no—
223C2—21no—
224C2—82no—
225C2—441no—
226C2D11×#35411yescharacteristic
subgroupG/H
centerC2D11×#354
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC11×#1412C2
socleC2×C11C2×#354
prime radical#10623247C22
cosocleC11×#127C23
hypercenter#1412D11
hypocenterC11#13596
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #13066787C2semidirect
4. #13066786C2semidirect
5. C11×#1412C2semidirect
7. D11×#125C4semidirect
10. #10622682C4semidirect
14. #10622320C4semidirect
15. #10622316C4semidirect
78. #1412D11semidirect
186. C11#13596semidirect

Maximal subgroups

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

subgroupindex
#130790152
#130702782
#130667872
#130667862
C11×#14122
#1359611