Finite Group Databasebeta

← #14674139

Subgroups — #14674139

Order 2816.

318 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070301C212yesmaximal
2#13066789C214yesmaximal, complemented
3C11×#3142C211yesmaximal, characteristic
4C11×#532C2211yescharacteristic
5C2×C11×#125C411yescharacteristic
6C11×#491C2212yes—
7C11×#490C412yes—
8C11×#488—22no—
9C11×#417—22no—
10C4×C11×M16C411yescharacteristic
11#10622850—22no—
12#10622186C2214yes—
13#10622180—22no—
14C2×C11×#41D412yes—
15C2×C11×M16—21no—
16C11×C4⋊Q8C2311yescharacteristic
17C11×#127C2×C411yescharacteristic
18C11×#125—21no—
19C11×#125—41no—
20C11×#125C2×C412yes—
21C11×#124D412yes—
22C11×#121—41no—
23C4×D4×C11—41no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—41no—
26C2×C42×C11C2×C411yescharacteristic
27C2×#4318—42no—
28C11×#103—24no—
29C11×#102—24no—
30C11×#97C2×C412yes—
31C4×C8×C11—21no—
32#66900—24no—
33#66897—42no—
34#13600—111nomaximal, Sylow
35C11×#41—42no—
36C11×#41—42no—
37C2×Q8×C11C2×D412yes—
38C2×D4×C11—22no—
39C2×D4×C11—41no—
40C2×D4×C11C22⋊C412yes—
41C22×C4×C11—21no—
42C22×C4×C11—22no—
43C22×C4×C11—41no—
44C22×C4×C11C22⋊C411yescharacteristic
45C11×M16—42no—
46C2×C8×C11—22no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—41no—
49C11×C4⋊C4—42no—
50C11×C4⋊C4—42no—
51C11×C4⋊C4—41no—
52C11×C22⋊C4—42no—
53C42×C11—21no—
54C42×C11C22⋊C411yescharacteristic
55C42×C11C22×C411yescharacteristic
56#4318—44no—
57#4318—82no—
58C2×C11⋊C8—82no—
59#3142D1111yescharacteristic
60#2132—112no—
61#1413—114no—
62C23×C11—22no—
63C23×C11#9911yescharacteristic
64Q8×C11—42no—
65D4×C11—42no—
66D4×C11—82no—
67D4×C11—82no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—42no—
73C2×C4×C11—42no—
74C2×C4×C11—42no—
75C2×C4×C11—81no—
76C2×C4×C11—82no—
77C2×C4×C11#9911yescharacteristic
78C2×C4×C11C2×C22⋊C411yescharacteristic
79C8×C11—42no—
80C11⋊C8—84no—
81#532C2×D1111yescharacteristic
82C2×#125Dic1111yescharacteristic
83#491C2×D1112yes—
84#490Dic1112yes—
85#488—22no—
86#417—22no—
87#413—222no—
88C4×M16Dic1111yescharacteristic
89#356—114no—
90#355—222no—
91C22×C11—21no—
92C22×C11—41no—
93C22×C11—42no—
94C22×C11—82no—
95C22×C11C2×#9911yescharacteristic
96C4×C11—21no—
97C4×C11—41no—
98C4×C11—41no—
99C4×C11—42no—
100C4×C11—82no—
101C4×C11#35412yes—
102C2×#41C22⋊D1112yes—
103C2×M16—21no—
104C2×M16—442no—
105C4⋊Q8C22×D1111yescharacteristic
106#127C2×Dic1111yescharacteristic
107#125—21no—
108#125—41no—
109#125C2×Dic1112yes—
110#124C22⋊D1112yes—
111#121—41no—
112C4×D4—41no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—41no—
115C2×C42C2×Dic1111yescharacteristic
116#103—24no—
117#102—24no—
118#101—224no—
119#100—442no—
120#97C2×Dic1112yes—
121C4×C8—21no—
122C2×C11—21no—
123C2×C11—41no—
124C2×C11—82no—
125C2×C11C2×#35411yescharacteristic
126#41—42no—
127#41—42no—
128C2×Q8C2×C22⋊D1112yes—
129C2×D4—22no—
130C2×D4—41no—
131C2×D4C22⋊Dic1112yes—
132C22×C4—21no—
133C22×C4—22no—
134C22×C4—41no—
135C22×C4C22⋊Dic1111yescharacteristic
136M16—42no—
137M16—444no—
138M16—882no—
139C2×C8—22no—
140C2×C8—882no—
141C4⋊C4—22no—
142C4⋊C4—41no—
143C4⋊C4—42no—
144C4⋊C4—42no—
145C4⋊C4—41no—
146C22⋊C4—42no—
147C42—21no—
148C42C22⋊Dic1111yescharacteristic
149C42C22×Dic1111yescharacteristic
150C11#1360011yescharacteristic, complemented, Sylow
151C23—22no—
152C23#6689811yescharacteristic
153Q8—42no—
154D4—42no—
155D4—82no—
156D4—82no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—82no—
166C2×C4#6689811yescharacteristic
167C2×C4C2×C22⋊Dic1111yescharacteristic
168C8—42no—
169C8—884no—
170C22—21no—
171C22—41no—
172C22—42no—
173C22—82no—
174C22C2×#6689811yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—42no—
179C4—82no—
180C4#1062217912yes—
181C2—21no—
182C2—41no—
183C2—82no—
184C2C2×#1062217911yescharacteristic
subgroupG/H
centerC2C2×#10622179
commutatorC42×C11C22×C4
FrattiniC4⋊Q8C22×D11
FittingC11×#3142C2
socleC2×C11C2×#354
prime radicalC11×#532C22
cosocleC11×C4⋊Q8C23
hypercenter#3142D11
hypocenterC11#13600
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3142

Complements

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

NH ≅ G/Ntype
2. #13066789C2semidirect
150. C11#13600semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130667892
C11×#31422
#1360011