Finite Group Databasebeta

← #14674137

Subgroups — #14674137

Order 2816.

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

normal subgroups only

This group has 318 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#13079018C211yesmaximal, characteristic
2#13070300C212yesmaximal
3#13066789C211yesmaximal, characteristic, complemented
4#13066788C212yesmaximal, complemented
5C11×#1413C211yesmaximal, characteristic, complemented
6#10623256C2211yescharacteristic
7D11×#125C411yescharacteristic
8C11×#491C2211yescharacteristic
9#10622695C2211yescharacteristic
10#10622680C411yescharacteristic
11#10622416—22no—
12#10622413—22no—
13#10622364—22no—
14#10622326C411yescharacteristic
15#10622320C411yescharacteristic
16C11×#356C2212yes—
17#10622186C2212yes—
18#10622115—22no—
19C2×#4343D412yes—
20C11×C4⋊Q8C2311yescharacteristic
21C11×#125C2×C411yescharacteristic
22#67000D412yes—
23M16×D11—42no—
24C2×#4313—21no—
25#66948—41no—
26#66946—41no—
27C4⋊C4×D11—21no—
28C4⋊C4×D11—41no—
29#66943—21no—
30#66942—41no—
31#66927C2×C411yescharacteristic
32C42×D11C2×C411yescharacteristic
33#66923C2×C411yescharacteristic
34C11×#103—22no—
35C11×#101—22no—
36C11×#97C2×C411yescharacteristic
37#66900—22no—
38#66899—22no—
39#66887—42no—
40#66885—22no—
41C8×Dic11—21no—
42#66873—22no—
43#66867C2×C411yescharacteristic
44#13600—111nomaximal, Sylow
45C2×Q8×C11C2×D412yes—
46#4343—42no—
47#4343—42no—
48C2×D44—22no—
49C2×D44—41no—
50C2×D44C22⋊C412yes—
51C2×C4×D11—22no—
52C2×C4×D11—21no—
53C2×C4×D11—41no—
54C2×C4×D11C22⋊C411yescharacteristic
55C11×M16—42no—
56C2×C8×C11—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C42×C11C22×C411yescharacteristic
61(C2×D11)⋊C4—42no—
62C4⋊Dic11—21no—
63C4⋊Dic11—41no—
64Dic11⋊C4—41no—
65Dic11⋊C4—41no—
66Dic11⋊C4—41no—
67C4×Dic11—21no—
68C4×Dic11C22⋊C411yescharacteristic
69#4318—42no—
70C2×C11⋊C8—21no—
71#4313—42no—
72#4313—82no—
73C8×D11—82no—
74#3142—111no—
75#2132—112no—
76#1413—111no—
77#1413—112no—
78#1413D1111yescharacteristic, complemented
79C22×D11—22no—
80C22×D11#9911yescharacteristic
81Q8×C11—42no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—41no—
85C2×C4×C11C2×C22⋊C411yescharacteristic
86C2×Dic11—21no—
87C2×Dic11—41no—
88C2×Dic11#9911yescharacteristic
89D44—42no—
90D44—82no—
91D44—82no—
92C4×D11—22no—
93C4×D11—42no—
94C4×D11—42no—
95C4×D11—81no—
96C4×D11—82no—
97C8×C11—41no—
98C8×C11—82no—
99C11⋊C8—41no—
100C11⋊C8—82no—
101#532—111no—
102C2×#125—111no—
103#491—111no—
104#491C2×D1111yescharacteristic
105#490—111no—
106#490—111no—
107#488—222no—
108#417—222no—
109#413—222no—
110C4×M16—111no—
111#356—112no—
112#356C2×D1112yes—
113#355—222no—
114C22×C11C2×#9911yescharacteristic
115C2×D11—21no—
116C2×D11—41no—
117C2×D11—42no—
118C2×D11—82no—
119C4×C11—21no—
120C4×C11—41no—
121C4×C11—42no—
122C4×C11—81no—
123Dic11—41no—
124Dic11—81no—
125Dic11#35412yes—
126C2×#41—112no—
127C2×M16—221no—
128C2×M16—442no—
129C4⋊Q8C22×D1111yescharacteristic
130#127—111no—
131#125—111no—
132#125—221no—
133#125—441no—
134#125C4×D1111yescharacteristic
135#124—112no—
136#121—441no—
137C4×D4—441no—
138C2×C4⋊C4—221no—
139C2×C4⋊C4—441no—
140C2×C42—111no—
141#103—22no—
142#103—222no—
143#102—222no—
144#102—222no—
145#101—22no—
146#101—222no—
147#100—442no—
148#97—111no—
149#97C4×D1111yescharacteristic
150C4×C8—221no—
151C2×C11—21no—
152C2×C11C2×#35411yescharacteristic
153D11—41no—
154D11—82no—
155#41—442no—
156#41—442no—
157C2×Q8D4×D1112yes—
158C2×D4—112no—
159C2×D4—222no—
160C2×D4—441no—
161C22×C4—111no—
162C22×C4—222no—
163C22×C4—221no—
164C22×C4—441no—
165M16—42no—
166M16—442no—
167M16—442no—
168M16—882no—
169C2×C8—21no—
170C2×C8—221no—
171C2×C8—882no—
172C4⋊C4—21no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—221no—
176C4⋊C4—441no—
177C4⋊C4—441no—
178C4⋊C4—441no—
179C4⋊C4—441no—
180C22⋊C4—442no—
181C42—111no—
182C42—221no—
183C42C2×C4×D1111yescharacteristic
184C11#1360011yescharacteristic, complemented, Sylow
185C23—111no—
186C23—222no—
187Q8—42no—
188D4—442no—
189D4—882no—
190D4—882no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—111no—
195C2×C4—222no—
196C2×C4—221no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4—441no—
200C2×C4—881no—
201C2×C4—882no—
202C2×C4C22⋊C4×D1111yescharacteristic
203C8—41no—
204C8—82no—
205C8—441no—
206C8—882no—
207C22—221no—
208C22—441no—
209C22—442no—
210C22—882no—
211C22D11×#9911yescharacteristic
212C4—21no—
213C4—41no—
214C4—42no—
215C4—81no—
216C4—112no—
217C4—441no—
218C4—881no—
219C2—21no—
220C2—441no—
221C2—882no—
222C2D11×#35411yescharacteristic
subgroupG/H
centerC2D11×#354
commutatorC42×C11C22×C4
FrattiniC4⋊Q8C22×D11
FittingC11×#1413C2
socleC2×C11C2×#354
prime radical#10623256C22
cosocleC11×C4⋊Q8C23
hypercenter#1413D11
hypocenterC11#13600
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1413

Complements

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

NH ≅ G/Ntype
3. #13066789C2semidirect
4. #13066788C2semidirect
5. C11×#1413C2semidirect
78. #1413D11semidirect
184. C11#13600semidirect

Maximal subgroups

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

subgroupindex
#130790182
#130703002
#130667892
#130667882
C11×#14132
#1360011