Finite Group Databasebeta

← #20244041

Subgroups — #20244041

Order 6016.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689163C211yesmaximal, characteristic
2#15689133C211yesmaximal, characteristic
3C2×#13093947C211yesmaximal, characteristic
4C2×#13093942C211yesmaximal, characteristic
5#15689081C211yesmaximal, characteristic
6#15688887C211yesmaximal, characteristic
7C47×#343C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13093983C2211yescharacteristic
12#13093957—21no—
13#13093955—21no—
14#13093949—21no—
15#13093949—21no—
16#13093947—21no—
17#13093947—21no—
18#13093942C414yescomplemented
19#13093934—21no—
20C8×Dic47—21no—
21C2×M16×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24C22×C4×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—21no—
27C2×Dic94—21no—
28C2×Dic94—21no—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94C2×C412yes—
33M16×C47—21no—
34M16×C47—21no—
35M16×C47—21no—
36M16×C47C2×C412yes—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C22⋊Dic47—21no—
42C4⋊Dic47D411yescharacteristic
43C4⋊Dic47D411yescharacteristic
44C4×Dic47—21no—
45#10625329—21no—
46#10625329C2×C412yes—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8D411yescharacteristic
51C2×C47⋊C8D411yescharacteristic
52C23×C47#4111yescharacteristic
53C2×C4×C47—41no—
54C2×C4×C47—81no—
55C2×C4×C47C22×C411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×Dic47—22no—
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66Dic94—22no—
67Dic94—22no—
68Dic94—41no—
69Dic94—41no—
70C8×C47—22no—
71C8×C47—41no—
72C47⋊C8—22no—
73C47⋊C8—21no—
74C47⋊C8—21no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47#11711yescharacteristic
78C22×C47#12111yescharacteristic
79C22×C47#12611yescharacteristic
80C4×C47—81no—
81C4×C47C4×D411yescharacteristic
82C4×C47C4×D411yescharacteristic
83C4×C47#12311yescharacteristic
84C4×C47#12411yescharacteristic
85Dic47—42no—
86Dic47—41no—
87Dic47—41no—
88#1930—471nomaximal, Sylow
89C2×C47—21no—
90C2×C47—21no—
91C2×C47#38811yescharacteristic
92C2×C47#47111yescharacteristic
93C2×C47#47311yescharacteristic
94#428—471no—
95#419—471no—
96C2×#103—471no—
97C2×#101—471no—
98#405—471no—
99#343D4711yescharacteristic
100#341—471no—
101C47#193011yescharacteristic, complemented, Sylow
102C22×Q8—471no—
103C2×M16—471no—
104C2×M16C2×D4711yescharacteristic
105C2×M16C2×D4711yescharacteristic
106C22×C8—471no—
107#117—471no—
108C2×C4⋊C4C2×D4711yescharacteristic
109#107—941no—
110#106—941no—
111#103—941no—
112#103—941no—
113#103—941no—
114#103—941no—
115#101—474no—
116#97—941no—
117C4×C8—941no—
118C2×Q8—472no—
119C2×Q8—941no—
120C2×Q8—941no—
121C2×Q8—941no—
122C2×Q8—941no—
123C2×Q8—941no—
124C22×C4—21no—
125C22×C4—941no—
126C22×C4C22×D4711yescharacteristic
127M16—21no—
128M16—21no—
129M16—21no—
130M16—472no—
131M16—941no—
132M16C4×D4712yes—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—471no—
136C2×C8—471no—
137C2×C8—941no—
138C2×C8—941no—
139C2×C8—941no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—471no—
143C4⋊C4—471no—
144C22⋊C4—941no—
145C42—941no—
146C23#1062535011yescharacteristic
147Q8—942no—
148Q8—942no—
149Q8—1881no—
150Q8—1881no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—942no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—1881no—
157C2×C4—1881no—
158C2×C4C2×C4×D4711yescharacteristic
159C2×C4#1062535011yescharacteristic
160C2×C4D4×D4711yescharacteristic
161C2×C4D4×D4711yescharacteristic
162C2×C4#1062535211yescharacteristic
163C2×C4#1062535411yescharacteristic
164C8—22no—
165C8—41no—
166C8—942no—
167C8—941no—
168C8—941no—
169C22—21no—
170C22—21no—
171C22#1309398111yescharacteristic
172C22#1309399711yescharacteristic
173C22#1309401911yescharacteristic
174C4—81no—
175C4—1882no—
176C4—1881no—
177C4—1881no—
178C4(C22⋊D47)⋊C411yescharacteristic
179C4#1309398611yescharacteristic
180C4#1309400911yescharacteristic
181C4#1309401011yescharacteristic
182C2—21no—
183C2—21no—
184C2#1568901211yescharacteristic
185C2#1568938511yescharacteristic
186C2#1568939711yescharacteristic
subgroupG/H
centerC22#13093997
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#343C2
socleC22×C47#121
hypercenter#343D47
hypocenterC47#1930
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
18. #13093942C4semidirect
101. C47#1930semidirect