Finite Group Databasebeta

← #20256344

Subgroups — #20256344

Order 6016.

348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689832C212yesmaximal, complemented
2#15689531C212yesmaximal, complemented
3#15689525C211yesmaximal, characteristic, complemented
4#15689423C212yesmaximal, complemented
5#15689421C212yesmaximal, complemented
6#15689401C212yesmaximal, complemented
7#15689253C211yesmaximal, characteristic, complemented
8#15689235C212yesmaximal
9C4×D8×C47C211yesmaximal, characteristic
10#13094023C2212yes—
11#13094016C2212yes—
12#13094015C2212yes—
13#13094003—22no—
14#13094001—22no—
15#13094001—22no—
16C4×Dic94C2211yescharacteristic
17D4×Dic47C2212yes—
18D4×Dic47C2212yes—
19C2×Dic47⋊C4—22no—
20#13093958C2211yescharacteristic
21#13093958C2211yescharacteristic
22#13093957C2212yes—
23#13093956C2212yes—
24#13093955C2212yes—
25C4⋊(C47⋊C8)C2211yescharacteristic
26Dic47⋊C8C2212yes—
27#13093945C2212yes—
28#13093945C2212yes—
29#13093934C2212yes—
30C2×D8×C47C2211yescharacteristic
31C4×D4×C47C2212yes—
32#107×C47C2211yescharacteristic
33#102×C47C2212yes—
34C4×C8×C47C2211yescharacteristic
35C2×D4×C47C2312yes—
36C22×C4×C47—22no—
37C22×Dic47—22no—
38C22×Dic47—22no—
39C2×Dic94—22no—
40C2×Dic94D411yescharacteristic
41D8×C47Q814yescomplemented
42C2×C8×C47C2311yescharacteristic
43C2×C8×C47C2311yescharacteristic
44C4⋊C4×C47C2312yes—
45C22⋊C4×C47—22no—
46C42×C47C2311yescharacteristic
47C22⋊Dic47—22no—
48C22⋊Dic47—22no—
49C4⋊Dic47—22no—
50C4⋊Dic47D411yescharacteristic
51C4⋊Dic47C2312yes—
52C4⋊Dic47C2312yes—
53Dic47⋊C4—22no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57Dic47⋊C4D412yes—
58C4×Dic47C2312yes—
59C2×C47⋊C8C2312yes—
60C23×C47—22no—
61D4×C47—22no—
62D4×C47C2×Q814yes—
63C2×C4×C47—22no—
64C2×C4×C47—82no—
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2411yescharacteristic
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—44no—
71C2×Dic47—82no—
72C2×Dic47C2×D412yes—
73C2×Dic47C2×D412yes—
74Dic94—41no—
75Dic94—82no—
76C8×C47—21no—
77C8×C47C2×Q812yes—
78C47⋊C8—22no—
79C22×C47—24no—
80C22×C47—42no—
81C22×C47—42no—
82C22×C47C22×D411yescharacteristic
83C4×C47—21no—
84C4×C47—21no—
85C4×C47—42no—
86C4×C47C22×Q811yescharacteristic
87C4×C472−1+411yescharacteristic
88Dic47—22no—
89Dic47—22no—
90Dic47—42no—
91Dic47—42no—
92#3389—471nomaximal, Sylow
93C2×C47—44no—
94C2×C47D4×Q811yescharacteristic
95C2×C47#57511yescharacteristic
96C2×C47#57611yescharacteristic
97#554—472no—
98#501—472no—
99#499—471no—
100#478—472no—
101#478—472no—
102#474—472no—
103#446—471no—
104#442—472no—
105C4×D8D4711yescharacteristic
106C47#338911yescharacteristic, complemented, Sylow
107C2×D8C2×D4711yescharacteristic
108C4⋊Q8—472no—
109#125—472no—
110#125—472no—
111C22⋊Q8—942no—
112C22⋊Q8—942no—
113C22⋊Q8—942no—
114C4×Q8—471no—
115C4×D4—472no—
116C4×D4—472no—
117C4×D4C2×D4712yes—
118C2×C4⋊C4—942no—
119#107—471no—
120#107—471no—
121#107—472no—
122#107C2×D4711yescharacteristic
123#106—472no—
124#106—472no—
125C4⋊C8—472no—
126C4⋊C8—471no—
127#102—472no—
128#102—472no—
129#102C2×D4712yes—
130#97—472no—
131C4×C8C2×D4711yescharacteristic
132C2×Q8—471no—
133C2×Q8—942no—
134C2×D4C22×D4712yes—
135C22×C4—22no—
136C22×C4—942no—
137C22×C4—942no—
138D8Dic9414yescomplemented
139C2×C8—472no—
140C2×C8C22×D4711yescharacteristic
141C2×C8C22×D4711yescharacteristic
142C4⋊C4—472no—
143C4⋊C4—471no—
144C4⋊C4—472no—
145C4⋊C4—472no—
146C4⋊C4—942no—
147C4⋊C4—942no—
148C4⋊C4—942no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4C22×D4712yes—
152C22⋊C4—22no—
153C22⋊C4—942no—
154C22⋊C4—942no—
155C42—472no—
156C42C22×D4711yescharacteristic
157C23—22no—
158Q8—3762no—
159Q8—1881no—
160D4—22no—
161D4C2×Dic9414yes—
162C2×C4—22no—
163C2×C4—82no—
164C2×C4—472no—
165C2×C4—472no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—3762no—
169C2×C4—1884no—
170C2×C4D4×D4711yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4C23×D4711yescharacteristic
173C8—21no—
174C8—942no—
175C8C2×Dic9412yes—
176C22—24no—
177C22—42no—
178C22—42no—
179C22C2×D4×D4711yescharacteristic
180C4—21no—
181C4—21no—
182C4—42no—
183C4—942no—
184C4—942no—
185C4—1882no—
186C4—1882no—
187C4C22×Dic9411yescharacteristic
188C4#1309407111yescharacteristic
189C2—44no—
190C2D4×Dic9411yescharacteristic
191C2#1568992011yescharacteristic
192C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×D8×C47C2
socleC22×C47C22×D4
hypercenterC4×D8D47
hypocenterC47#3389
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #15689832C2semidirect
2. #15689531C2semidirect
3. #15689525C2semidirect
4. #15689423C2semidirect
5. #15689421C2semidirect
6. #15689401C2semidirect
7. #15689253C2semidirect
41. D8×C47Q8semidirect
106. C47#3389semidirect
138. D8Dic94semidirect