Finite Group Databasebeta

← #26018929

Subgroups — #26018929

Order 11392.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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#19151622C211yesmaximal, characteristic, complemented
2C2×C4⋊#10623494C211yesmaximal, characteristic, complemented
3#19151344C212yesmaximal, complemented
4#19151342C212yesmaximal, complemented
5#532×C89C211yesmaximal, characteristic
6C2×#13083558—21no—
7C22×#10623494—21no—
8C4⋊#10623494—21no—
9C4⋊#10623494—21no—
10C4⋊#10623494C2212yes—
11C4⋊#10623494C2212yes—
12C2×#41×C89—21no—
13C4⋊Q8×C89C2211yescharacteristic
14#127×C89C2211yescharacteristic
15#124×C89—21no—
16#121×C89—21no—
17#121×C89C412yes—
18C4×D4×C89—21no—
19C4×D4×C89C412yes—
20C2×C42×C89C2211yescharacteristic
21#13083558—42no—
22C2×#10623494—22no—
23C2×#10623494—22no—
24C2×#10623494—42no—
25#41×C89—42no—
26#41×C89—42no—
27C2×Q8×C89—21no—
28C2×D4×C89—22no—
29C2×D4×C89—21no—
30C2×D4×C89—21no—
31C2×D4×C89C2×C412yes—
32C22×C4×C89—22no—
33C22×C4×C89C2×C411yescharacteristic
34C22×C4×C89D411yescharacteristic
35C22×C4×C89D411yescharacteristic
36C4⋊C4×C89—21no—
37C4⋊C4×C89C2×C412yes—
38C22⋊C4×C89—22no—
39C22⋊C4×C89—22no—
40C42×C89C2×C411yescharacteristic
41C42×C89D411yescharacteristic
42C42×C89D411yescharacteristic
43C42×C89C2311yescharacteristic
44C23×C89—22no—
45C23×C89C22⋊C411yescharacteristic
46Q8×C89—41no—
47Q8×C89—41no—
48D4×C89—42no—
49D4×C89—44no—
50D4×C89—41no—
51D4×C89—41no—
52D4×C89—41no—
53D4×C89—41no—
54C2×C4×C89—21no—
55C2×C4×C89—21no—
56C2×C4×C89—22no—
57C2×C4×C89—41no—
58C2×C4×C89—44no—
59C2×C4×C89C22⋊C411yescharacteristic
60C2×C4×C89C22⋊C411yescharacteristic
61C2×C4×C89C22⋊C411yescharacteristic
62C2×C4×C89D812yes—
63C2×C4×C89SD1612yes—
64C2×C4×C89C22×C411yescharacteristic
65C2×C4×C89C2×D411yescharacteristic
66C2×C4×C89C2×D411yescharacteristic
67#10623494—42no—
68#10623494—42no—
69C22×C89—21no—
70C22×C89—21no—
71C22×C89—42no—
72C22×C89—42no—
73C22×C89—42no—
74C22×C89#10212yes—
75C22×C89C2×C22⋊C411yescharacteristic
76C4×C89—21no—
77C4×C89—21no—
78C4×C89—21no—
79C4×C89—42no—
80C4×C89#10212yes—
81C4×C89C2×D811yescharacteristic
82C4×C89C2×SD1611yescharacteristic
83C4×C89AGL(1,ℤ/8)11yescharacteristic
84C4×C89#13711yescharacteristic
85C2×C89—22no—
86C2×C89—82no—
87C2×C89#41311yescharacteristic
88C2×C89C2×#10211yescharacteristic
89C2×C89#41711yescharacteristic
90#1547—891nomaximal, Sylow
91C89#154711yescharacteristic, complemented, Sylow
92#532D8911yescharacteristic
93#423—891no—
94C2×C4⋊C8—891no—
95#332—892no—
96#331—892no—
97C2×#41—21no—
98C2×M16—1781no—
99C22×C8—1781no—
100C4⋊Q8C2×D8911yescharacteristic
101#127C2×D8911yescharacteristic
102#124—21no—
103#121—21no—
104#121Dic8912yes—
105C4×D4—21no—
106C4×D4Dic8912yes—
107C2×C42C2×D8911yescharacteristic
108C4⋊C8—892no—
109C4⋊C8—892no—
110C4⋊C8—1781no—
111C4⋊C8—1781no—
112#41—42no—
113#41—42no—
114C2×Q8—21no—
115C2×D4—22no—
116C2×D4—21no—
117C2×D4—21no—
118C2×D4C2×Dic8912yes—
119C22×C4—22no—
120C22×C4C2×Dic8911yescharacteristic
121C22×C4C22⋊D8911yescharacteristic
122C22×C4C22⋊D8911yescharacteristic
123M16—3562no—
124C2×C8—3562no—
125C2×C8—1782no—
126C2×C8—1782no—
127C4⋊C4—21no—
128C4⋊C4C2×Dic8912yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C42C2×Dic8911yescharacteristic
132C42C22⋊D8911yescharacteristic
133C42C22⋊D8911yescharacteristic
134C42C22×D8911yescharacteristic
135C23—22no—
136C23C22⋊Dic8911yescharacteristic
137Q8—41no—
138Q8—41no—
139D4—42no—
140D4—44no—
141D4—41no—
142D4—41no—
143D4—41no—
144D4—41no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—44no—
150C2×C4C22⋊Dic8911yescharacteristic
151C2×C4C22⋊Dic8911yescharacteristic
152C2×C4C22⋊Dic8911yescharacteristic
153C2×C4#1308355912yes—
154C2×C4#1308356212yes—
155C2×C4C22×Dic8911yescharacteristic
156C2×C4C2×C22⋊D8911yescharacteristic
157C2×C4C2×C22⋊D8911yescharacteristic
158C8—3562no—
159C8—3562no—
160C22—21no—
161C22—21no—
162C22—42no—
163C22—42no—
164C22—42no—
165C22#1566793312yes—
166C22C2×C22⋊Dic8911yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—42no—
171C4#1566793312yes—
172C4C2×#1308355911yescharacteristic
173C4C2×#1308356211yescharacteristic
174C4#1566803711yescharacteristic
175C4#1566804211yescharacteristic
176C2—22no—
177C2—82no—
178C2#1915158211yescharacteristic
179C2C2×#1566793311yescharacteristic
180C2#1915159911yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic89
commutatorC2×C4×C89C22×C4
FrattiniC42C22×D89
Fitting, prime radical#532×C89C2
socleC22×C89C2×C22⋊C4
cosocleC42×C89C23
hypercenter#532D89
hypocenterC89#1547
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #19151622C2semidirect
2. C2×C4⋊#10623494C2semidirect
3. #19151344C2semidirect
4. #19151342C2semidirect
91. C89#1547semidirect

Maximal subgroups

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

subgroupindex
#191516222
C2×C4⋊#106234942
#191513442
#191513422
#532×C892
#154789