Finite Group Databasebeta

← #18010879

Subgroups — #18010879

Order 4736.

238 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 52 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#14558514C212yesmaximal
2#14558440C212yesmaximal, complemented
3#14558439C212yesmaximal, complemented
4#14558108C211yesmaximal, characteristic
5#11924615—22no—
6#11924595—22no—
7#11924595C2214yes—
8C2×#10596966C2211yescharacteristic
9C2×Q8×D37C411yescharacteristic, complemented
10#11924534C411yescharacteristic, complemented
11#11924525C2211yescharacteristic
12#11924524C2211yescharacteristic
13#11924521—22no—
14#11924514—22no—
15#11924493C411yescharacteristic, complemented
16C4⋊Q8×C37C411yescharacteristic, complemented
17C2×Q8×C37C2×C411yescharacteristic
18C2×Q8×C37C2×C411yescharacteristic
19#10596966—42no—
20Q8×D37—42no—
21C2×D148D412yes—
22C2×D148C2311yescharacteristic
23C2×C4×D37—21no—
24C2×C4×D37C2×C411yescharacteristic
25C2×C4×D37D412yes—
26C2×Dic74—21no—
27C2×Dic74C2×C411yescharacteristic
28C22⋊#3866—24no—
29C4⋊#3866—42no—
30C4×#3866—42no—
31C4⋊C4×C37—22no—
32C42×C37C2×C411yescharacteristic
33#10596938—21no—
34#10596938—22no—
35#10596938—22no—
36#10596936—22no—
37#10596936—21no—
38C4×Dic37C2×C411yescharacteristic
39C22×D37C22⋊C411yescharacteristic
40C22×D37C2×D412yes—
41C2×#3866—44no—
42Q8×C37—41no—
43Q8×C37—41no—
44C2×C4×C37—21no—
45C2×C4×C37—21no—
46C2×C4×C37C22⋊C412yes—
47C2×C4×C37C22×C411yescharacteristic
48C2×Dic37—21no—
49C2×Dic37—21no—
50C2×Dic37C22⋊C411yescharacteristic
51D148—42no—
52D148—41no—
53C4×D37—22no—
54C4×D37—22no—
55C4×D37—22no—
56C4×D37—42no—
57Dic74—42no—
58Dic74—41no—
59C22×C37C2×C22⋊C411yescharacteristic
60C2×D37—21no—
61C2×D37—22no—
62C2×D37—41no—
63C2×D37—42no—
64#3866—84no—
65C4×C37—21no—
66C4×C37—22no—
67C4×C37—41no—
68C4×C37—41no—
69Dic37—41no—
70Dic37—41no—
71Dic37#9912yes—
72#2129—371nomaximal, Sylow
73C2×C37—21no—
74C2×C37C2×#9911yescharacteristic
75D37—42no—
76D37—41no—
77#536—371no—
78#410—372no—
79#354—372no—
80#354—372no—
81C37#212911yescharacteristic, complemented, Sylow
82C2×#41—371no—
83C22×Q8—371no—
84C4⋊Q8—371no—
85C4⋊Q8#386611yescharacteristic, complemented
86#124—371no—
87#124—371no—
88#123—742no—
89C22⋊Q8—742no—
90#117—371no—
91#117—742no—
92#99—374no—
93#99—742no—
94#41—1482no—
95C2×Q8—371no—
96C2×Q8—741no—
97C2×Q8—1482no—
98C2×Q8C2×#386611yescharacteristic
99C2×Q8C2×#386611yescharacteristic
100C2×D4—372no—
101C2×D4—371no—
102C22×C4—372no—
103C22×C4—371no—
104C22×C4—741no—
105C4⋊C4—22no—
106C4⋊C4—741no—
107C4⋊C4—742no—
108C4⋊C4—1482no—
109C22⋊C4—741no—
110C22⋊C4—742no—
111C22⋊C4—742no—
112C22⋊C4—744no—
113C42—371no—
114C42—1482no—
115C42C2×#386611yescharacteristic
116C23—372no—
117C23—371no—
118Q8—41no—
119Q8—41no—
120Q8—1481no—
121Q8—1482no—
122D4—1482no—
123D4—1481no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—371no—
127C2×C4—742no—
128C2×C4—742no—
129C2×C4—742no—
130C2×C4—741no—
131C2×C4—741no—
132C2×C4—1482no—
133C2×C4—1484no—
134C2×C4C22⋊#386612yes—
135C2×C4C22×#386611yescharacteristic
136C22—742no—
137C22—741no—
138C22—1482no—
139C22—1481no—
140C22C2×C22⋊#386611yescharacteristic
141C4—22no—
142C4—21no—
143C4—41no—
144C4—41no—
145C4—372no—
146C4—2964no—
147C4—1481no—
148C4—1481no—
149C2—21no—
150C2—1482no—
151C2—1481no—
152C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC2×C37C2×#99
prime radicalC2×#10596966C22
cosocleC2×D148C23
hypercenterC4⋊Q8#3866
hypocenterC37#2129
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14558440C2semidirect
3. #14558439C2semidirect
9. C2×Q8×D37C4semidirect
10. #11924534C4semidirect
15. #11924493C4semidirect
16. C4⋊Q8×C37C4semidirect
81. C37#2129semidirect
85. C4⋊Q8#3866semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145585142
#145584402
#145584392
#145581082
#212937