Finite Group Databasebeta

← #20245082

Subgroups — #20245082

Order 6016.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689694C211yesmaximal, characteristic
2#15689107C211yesmaximal, characteristic
3#15688921C214yesmaximal, complemented
4C47×#413C211yesmaximal, characteristic
5C22×Dic94C411yescharacteristic
6C2×#10625329—21no—
7#13094022C2212yes—
8#13094011C412yes—
9#13094005—21no—
10#13094005—21no—
11#13094003—21no—
12#13094003—21no—
13#13093983C411yescharacteristic
14#13093943C2212yes—
15#13093941—21no—
16C2×#41×C47C2211yescharacteristic
17C2×M16×C47—21no—
18#101×C47C2212yes—
19#100×C47—21no—
20#41×C47—41no—
21#41×C47—41no—
22C2×Q8×C47C2311yescharacteristic
23C2×D4×C47C2×C411yescharacteristic
24C2×D4×C47D411yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×Dic47—21no—
30C2×Dic94—21no—
31C2×Dic94—41no—
32C2×Dic94—41no—
33C2×Dic94C2×C412yes—
34M16×C47—22no—
35M16×C47—41no—
36C2×C8×C47—41no—
37C22⋊Dic47—21no—
38C22⋊Dic47—22no—
39C22⋊Dic47—22no—
40C4⋊Dic47—21no—
41Dic47⋊C4—22no—
42Dic47⋊C4—22no—
43C4×Dic47C2×C412yes—
44#10625329—22no—
45#10625329—41no—
46C2×C47⋊C8—41no—
47C23×C47C22⋊C411yescharacteristic
48C23×C47C22⋊C411yescharacteristic
49C23×C47C22⋊C411yescharacteristic
50Q8×C47—41no—
51D4×C47—41no—
52D4×C47—41no—
53D4×C47—41no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—42no—
67Dic94—41no—
68Dic94—41no—
69Dic94—42no—
70C8×C47—42no—
71C47⋊C8—42no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47C2×C22⋊C411yescharacteristic
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47#9911yescharacteristic
83C4×C47#9911yescharacteristic
84Dic47—42no—
85Dic47—42no—
86#2135—471nomaximal, Sylow
87C2×C47—21no—
88C2×C47—41no—
89C2×C47—41no—
90C2×C47—41no—
91C2×C47C2×#9911yescharacteristic
92#536—471no—
93#413—471no—
94#413D4711yescharacteristic
95#356—474no—
96C47#213511yescharacteristic, complemented, Sylow
97C2×#41C2×D4711yescharacteristic
98C22×Q8—471no—
99C2×M16—21no—
100C2×M16—941no—
101C4⋊Q8—472no—
102#124—472no—
103#123—941no—
104#123—941no—
105C22⋊Q8—941no—
106C22⋊Q8—941no—
107#117—471no—
108#101—472no—
109#101C2×D4712yes—
110#100—21no—
111#100—941no—
112#41—41no—
113#41—41no—
114C2×Q8—472no—
115C2×Q8—941no—
116C2×Q8—1881no—
117C2×Q8—1881no—
118C2×Q8C22×D4711yescharacteristic
119C2×D4C4×D4711yescharacteristic
120C2×D4D18811yescharacteristic
121C2×D4C22⋊D4711yescharacteristic
122C22×C4—941no—
123C22×C4C4×D4711yescharacteristic
124C22×C4D18811yescharacteristic
125C22×C4C22⋊D4711yescharacteristic
126M16—22no—
127M16—41no—
128M16—942no—
129M16—1881no—
130C2×C8—41no—
131C2×C8—1881no—
132C4⋊C4—941no—
133C4⋊C4—942no—
134C4⋊C4—942no—
135C22⋊C4—941no—
136C22⋊C4—942no—
137C22⋊C4—942no—
138C42—472no—
139C23(C2×D47)⋊C411yescharacteristic
140C23(C2×D47)⋊C411yescharacteristic
141C23(C2×D47)⋊C411yescharacteristic
142Q8—41no—
143Q8—1882no—
144Q8—1881no—
145Q8—1881no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—942no—
156C2×C4—942no—
157C2×C4—1882no—
158C2×C4(C2×D47)⋊C411yescharacteristic
159C2×C4C2×C4×D4711yescharacteristic
160C2×C4C2×D18811yescharacteristic
161C2×C4C2×C22⋊D4711yescharacteristic
162C8—42no—
163C8—1882no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D47)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—1882no—
175C4—1882no—
176C4#1309393811yescharacteristic
177C4#1309393811yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1309393811yescharacteristic
subgroupG/H
centerC2C2×#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#413C2
socleC2×C47C2×#99
hypercenter#413D47
hypocenterC47#2135
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #15688921C2semidirect
96. C47#2135semidirect