Finite Group Databasebeta

← #20243381

Subgroups — #20243381

Order 6016.

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

normal subgroups only

This group has 272 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
1C2×C4×Dic94C211yesmaximal, characteristic
2#15689147C211yesmaximal, characteristic
3C2×#13093942C212yesmaximal
4#15688891C212yesmaximal
5C47×#423C211yesmaximal, characteristic
6C22×Dic94C2211yescharacteristic
7C2×#10625329C2212yes—
8C4×Dic94—21no—
9C4×Dic94—21no—
10C4×Dic94—21no—
11C4×Dic94—21no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C412yes—
14C2×C4×Dic47C412yes—
15C4⋊(C47⋊C8)—21no—
16C4⋊(C47⋊C8)—21no—
17#13093942—24no—
18C2×M16×C47C2212yes—
19C2×C42×C47C2211yescharacteristic
20C4⋊C8×C47—21no—
21C4⋊C8×C47—21no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47C2311yescharacteristic
25C22×Dic47C2×C412yes—
26C22×Dic47C2×C412yes—
27C2×Dic94—21no—
28C2×Dic94—21no—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C2×Dic94D412yes—
32C2×Dic94Q812yes—
33M16×C47—22no—
34M16×C47—22no—
35C2×C8×C47—22no—
36C42×C47D411yescharacteristic
37C42×C47D411yescharacteristic
38C42×C47D411yescharacteristic
39C42×C47D411yescharacteristic
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42Dic47⋊C4—22no—
43Dic47⋊C4—22no—
44C4×Dic47—22no—
45C4×Dic47—22no—
46#10625329—22no—
47#10625329—22no—
48C2×C47⋊C8—22no—
49C23×C47C22×C411yescharacteristic
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C22⋊C411yescharacteristic
54C2×C4×C47C22⋊C411yescharacteristic
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×Dic47—22no—
63C2×Dic47—22no—
64C2×Dic47—22no—
65C2×Dic47—42no—
66C2×Dic47C4⋊C414yes—
67Dic94—22no—
68Dic94—22no—
69Dic94—22no—
70Dic94—22no—
71C8×C47—42no—
72C47⋊C8—42no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47C2×C22⋊C411yescharacteristic
76C22×C47C2×C4⋊C411yescharacteristic
77C22×C47#11711yescharacteristic
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47#10112yescomplemented
82C4×C47#12111yescharacteristic
83C4×C47#12111yescharacteristic
84C4×C47C22⋊Q811yescharacteristic
85C4×C47C22⋊Q811yescharacteristic
86Dic47—24no—
87Dic47—42no—
88#1801—471nomaximal, Sylow
89C2×C47—21no—
90C2×C47—21no—
91C2×C47#38011yescharacteristic
92C2×C47C2×#10111yescharacteristic
93C2×C47#41311yescharacteristic
94C2×C4×Q8—471no—
95#423—471no—
96#423D4711yescharacteristic
97C2×#101—472no—
98#343—472no—
99C47#180111yescharacteristic, complemented, Sylow
100C22×Q8—471no—
101C2×M16—472no—
102C2×M16C2×D4712yes—
103C4×Q8—941no—
104C4×Q8—941no—
105C4×Q8—941no—
106C4×Q8—941no—
107C2×C4⋊C4—472no—
108C2×C4⋊C4—471no—
109C2×C42—472no—
110C2×C42C2×D4711yescharacteristic
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8—941no—
114C4⋊C8—941no—
115#101—944no—
116C2×Q8—472no—
117C2×Q8—472no—
118C2×Q8—941no—
119C2×Q8—941no—
120C2×Q8—941no—
121C2×Q8—941no—
122C22×C4—472no—
123C22×C4—472no—
124C22×C4C4×D4711yescharacteristic
125C22×C4C4×D4711yescharacteristic
126C22×C4C22×D4711yescharacteristic
127M16—22no—
128M16—22no—
129M16—942no—
130M16—942no—
131C2×C8—22no—
132C2×C8—942no—
133C4⋊C4—942no—
134C4⋊C4—942no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C42—942no—
138C42—942no—
139C42D18811yescharacteristic
140C42D18811yescharacteristic
141C42C22⋊D4711yescharacteristic
142C42C22⋊D4711yescharacteristic
143C23C2×C4×D4711yescharacteristic
144Q8—942no—
145Q8—942no—
146Q8—942no—
147Q8—942no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—474no—
151C2×C4—942no—
152C2×C4—942no—
153C2×C4—942no—
154C2×C4—1882no—
155C2×C4(C2×D47)⋊C411yescharacteristic
156C2×C4(C2×D47)⋊C411yescharacteristic
157C2×C4(C2×D47)⋊C411yescharacteristic
158C2×C4(C2×D47)⋊C411yescharacteristic
159C2×C4C2×D18811yescharacteristic
160C2×C4D4×D4711yescharacteristic
161C2×C4#1062535211yescharacteristic
162C2×C4Q8×D4711yescharacteristic
163C2×C4#1062535411yescharacteristic
164C2×C4C2×C22⋊D4711yescharacteristic
165C8—42no—
166C8—1882no—
167C22—21no—
168C22—21no—
169C22C2×(C2×D47)⋊C411yescharacteristic
170C22C4⋊C4×D4711yescharacteristic
171C22#1309398211yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—944no—
176C4—1882no—
177C4#1309394212yescomplemented
178C4#1309399511yescharacteristic
179C4#1309399911yescharacteristic
180C4#1309400011yescharacteristic
181C4#1309400411yescharacteristic
182C2—21no—
183C2—21no—
184C2#1568898011yescharacteristic
185C2C2×#1309394211yescharacteristic
186C2#1568910511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#423C2
socleC22×C47C2×C22⋊C4
hypercenter#423D47
hypocenterC47#1801
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
81. C4×C47#101semidirect
99. C47#1801semidirect
177. C4#13093942semidirect