Finite Group Databasebeta

← #20245059

Subgroups — #20245059

Order 6016.

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

normal subgroups only

This group has 270 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#15689687C211yesmaximal, characteristic
2#15689097C211yesmaximal, characteristic, complemented
3#15688915C214yesmaximal, complemented
4C47×#410C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic, complemented
6#13094020C2212yes—
7#13094013C412yescomplemented
8#13093998—21no—
9#13093998—21no—
10#13093992—21no—
11#13093992—21no—
12#13093983—21no—
13#13093983C411yescharacteristic, complemented
14#13093939—21no—
15#13093939C2212yescomplemented
16C2×#41×C47C2211yescharacteristic
17#117×C47—21no—
18#99×C47—21no—
19#99×C47C2212yescomplemented
20C23×D47—21no—
21#41×C47—41no—
22#41×C47—41no—
23C2×Q8×C47C2×C411yescharacteristic
24C2×D4×C47D411yescharacteristic
25C2×D4×C47D411yescharacteristic
26C2×D4×C47C2311yescharacteristic
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C2×C22⋊D47—22no—
31C2×C22⋊D47—22no—
32C2×D188—21no—
33C2×D188—41no—
34C2×D188—41no—
35C2×D188C2×C412yes—
36C4⋊C4×C47—41no—
37C22⋊C4×C47—22no—
38C42×C47—41no—
39C22⋊Dic47—21no—
40C22⋊Dic47—22no—
41(C2×D47)⋊C4—22no—
42(C2×D47)⋊C4—22no—
43C4⋊Dic47—21no—
44C4⋊Dic47—41no—
45C4×Dic47—41no—
46C4×Dic47C2×C412yes—
47C23×C47C22⋊C411yescharacteristic
48C23×C47C2×D411yescharacteristic
49C23×C47C2×D411yescharacteristic
50C22×D47—22no—
51C22×D47—42no—
52C22×D47—82no—
53Q8×C47—41no—
54D4×C47—41no—
55D4×C47—41no—
56D4×C47—41no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—42no—
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22⋊C411yescharacteristic
66C2×C4×C47C22⋊C411yescharacteristic
67C2×C4×C47C22×C411yescharacteristic
68C22⋊D47—82no—
69C22⋊D47—82no—
70C2×Dic47—22no—
71C2×Dic47—42no—
72D188—42no—
73D188—41no—
74D188—41no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47—41no—
81C22×C47C2×C22⋊C411yescharacteristic
82C2×D47—42no—
83C2×D47—42no—
84C2×D47—42no—
85C2×D47—84no—
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—82no—
90C4×C47#9911yescharacteristic
91C4×C47#9911yescharacteristic
92Dic47—42no—
93Dic47—82no—
94#2128—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—41no—
97C2×C47—41no—
98C2×C47—41no—
99C2×C47C2×#9911yescharacteristic
100D47—82no—
101#535—471no—
102#410—471no—
103#410D4711yescharacteristic, complemented
104#353—474no—
105C47#212811yescharacteristic, complemented, Sylow
106C2×#41C2×D4711yescharacteristic
107C22×D4—471no—
108#127—472no—
109#124—472no—
110#121—941no—
111#121—941no—
112#120—941no—
113#120—941no—
114#117—21no—
115#117—471no—
116#117—941no—
117#99—21no—
118#99—472no—
119#99—941no—
120#99C2×D4712yescomplemented
121C24—941no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D4711yescharacteristic
125C2×D4—472no—
126C2×D4—942no—
127C2×D4—942no—
128C2×D4—941no—
129C2×D4—1881no—
130C2×D4—1881no—
131C2×D4D18811yescharacteristic
132C2×D4C22⋊D4711yescharacteristic
133C2×D4C22×D4711yescharacteristic
134C22×C4C4×D4711yescharacteristic
135C22×C4D18811yescharacteristic
136C22×C4C22⋊D4711yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—941no—
139C4⋊C4—1881no—
140C22⋊C4—22no—
141C22⋊C4—941no—
142C22⋊C4—942no—
143C22⋊C4—942no—
144C22⋊C4—942no—
145C42—41no—
146C42—472no—
147C42—1881no—
148C23—942no—
149C23—3762no—
150C23—1882no—
151C23(C2×D47)⋊C411yescharacteristic
152C23C2×D18811yescharacteristic
153C23C2×C22⋊D4711yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—3762no—
159D4—3762no—
160D4—1882no—
161D4—1881no—
162D4—1881no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—942no—
171C2×C4—1882no—
172C2×C4(C2×D47)⋊C411yescharacteristic
173C2×C4(C2×D47)⋊C411yescharacteristic
174C2×C4(C2×D47)⋊C411yescharacteristic
175C2×C4C2×C4×D4711yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—3764no—
183C22—1882no—
184C22—1882no—
185C22—1882no—
186C22C2×(C2×D47)⋊C411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—3762no—
192C4—1882no—
193C4#1309393811yescharacteristic
194C4#1309393811yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—3762no—
200C2C2×#1309393811yescharacteristic
subgroupG/H
centerC2C2×#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#410C2
socleC2×C47C2×#99
hypercenter#410D47
hypocenterC47#2128
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #15689097C2semidirect
3. #15688915C2semidirect
4. C47×#410C2semidirect
5. C22×D188C4semidirect
7. #13094013C4semidirect
13. #13093983C4semidirect
15. #13093939C22semidirect
19. #99×C47C22semidirect
103. #410D47semidirect
105. C47#2128semidirect
120. #99C2×D47semidirect