Finite Group Databasebeta

← #18009682

Subgroups — #18009682

Order 4736.

234 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D37⋊#99C211yesmaximal, characteristic
2#14558481C211yesmaximal, characteristic
3#100×D37C211yesmaximal, characteristic
4C23×#3866C411yescharacteristic, complemented
5C2×C22⋊#3866—21no—
6C2×C22⋊#3866—21no—
7C2×C22⋊#3866C411yescharacteristic, complemented
8#11924595—21no—
9#11924594C412yescomplemented
10(C2×#3866)⋊C4—21no—
11C2×D4×D37C2211yescharacteristic
12M16×D37—21no—
13#11924453C411yescharacteristic, complemented
14#11924452—21no—
15#100×C37C411yescharacteristic, complemented
16C23×D37C2×C411yescharacteristic
17C23×D37D411yescharacteristic
18C22×#3866—21no—
19C22×#3866—21no—
20C22×#3866—42no—
21C22×#3866—41no—
22C22×#3866—41no—
23C2×D4×C37C2×C411yescharacteristic
24C2×C22⋊D37C2×C411yescharacteristic
25C2×C22⋊D37Q811yescharacteristic
26D4×D37—41no—
27D4×D37—41no—
28C2×D148D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C22⋊#3866—22no—
31C22⋊#3866—42no—
32C22⋊#3866—41no—
33C22⋊#3866—41no—
34M16×C37—21no—
35#10596934—21no—
36#10596929—41no—
37C8×D37—41no—
38C23×C37C4211yescharacteristic
39C23×C37C4⋊C411yescharacteristic
40C22×D37—21no—
41C22×D37—21no—
42C22×D37—21no—
43C22×D37—21no—
44C22×D37—41no—
45C22×D37—41no—
46C22×D37—41no—
47C22×D37—41no—
48C22×D37C22⋊C411yescharacteristic
49C22×D37C22⋊C411yescharacteristic
50C22×D37C4⋊C411yescharacteristic
51C2×#3866—22no—
52C2×#3866—41no—
53C2×#3866—42no—
54C2×#3866—41no—
55C2×#3866—42no—
56C2×#3866—42no—
57C2×#3866—41no—
58C2×#3866—41no—
59C2×#3866—41no—
60C2×#3866—81no—
61C2×#3866—81no—
62D4×C37—41no—
63C2×C4×C37C22⋊C411yescharacteristic
64C22⋊D37—41no—
65C22⋊D37—41no—
66C2×Dic37C4⋊C411yescharacteristic
67D148—41no—
68C4×D37—21no—
69C4×D37—21no—
70C8×C37—41no—
71#64436—41no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37#9511yescharacteristic
77C2×D37—21no—
78C2×D37—21no—
79C2×D37—21no—
80C2×D37—21no—
81C2×D37—42no—
82C2×D37—41no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—81no—
89C2×D37#9911yescharacteristic
90C2×D37#9911yescharacteristic
91#3866—42no—
92#3866—81no—
93#3866—82no—
94C4×C37—21no—
95Dic37—21no—
96#1390—371nomaximal, Sylow
97C2×C37—21no—
98C2×C37—41no—
99C2×C37—41no—
100C2×C37#34211yescharacteristic
101D37—21no—
102D37—41no—
103D37—41no—
104D37AΣL(1,𝔽16)11yescharacteristic
105D37#35211yescharacteristic
106C2×#100—371no—
107C2×#99—371no—
108#386—371no—
109C37#139011yescharacteristic, complemented, Sylow
110C22×D4—371no—
111C23×C4—371no—
112C2×M16—741no—
113C2×C22⋊C4—371no—
114C2×C22⋊C4—741no—
115C2×C22⋊C4—741no—
116#100—371no—
117#100—741no—
118#100#386611yescharacteristic, complemented
119#99—372no—
120#99—741no—
121#95—741no—
122C24—371no—
123C24—371no—
124C2×D4—371no—
125C2×D4—371no—
126C2×D4—371no—
127C2×D4—1481no—
128C2×D4—1481no—
129C2×D4C2×#386611yescharacteristic
130C22×C4—371no—
131C22×C4—741no—
132C22×C4—741no—
133C22×C4—1481no—
134C22×C4—1482no—
135C22×C4—1481no—
136M16—21no—
137M16—741no—
138M16—1481no—
139C2×C8—1481no—
140C22⋊C4—742no—
141C22⋊C4—1482no—
142C22⋊C4—1481no—
143C22⋊C4—1481no—
144C23—371no—
145C23—371no—
146C23—371no—
147C23—741no—
148C23—741no—
149C23—741no—
150C23—741no—
151C23—1481no—
152C23—1481no—
153C23—1481no—
154C23—1481no—
155C23C4×#386611yescharacteristic
156C23C4⋊#386611yescharacteristic
157D4—41no—
158D4—1481no—
159D4—1481no—
160D4—1481no—
161C2×C4—371no—
162C2×C4—2961no—
163C2×C4—2961no—
164C2×C4—741no—
165C2×C4—741no—
166C2×C4—742no—
167C2×C4—1481no—
168C2×C4—1482no—
169C2×C4—1481no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4—1481no—
173C2×C4—1482no—
174C2×C4—1482no—
175C2×C4C22⋊#386611yescharacteristic
176C8—41no—
177C8—1481no—
178C22—21no—
179C22—21no—
180C22—41no—
181C22—41no—
182C22—371no—
183C22—371no—
184C22—2961no—
185C22—741no—
186C22—741no—
187C22—741no—
188C22—741no—
189C22—1481no—
190C22—1481no—
191C22—1481no—
192C22—1481no—
193C22—1481no—
194C22—1481no—
195C22—1482no—
196C22(C2×#3866)⋊C411yescharacteristic
197C4—21no—
198C4—2961no—
199C4—2962no—
200C4—741no—
201C4—1482no—
202C2—21no—
203C2—41no—
204C2—41no—
205C2—371no—
206C2—371no—
207C2—741no—
208C2—1481no—
209C2—1481no—
210C2#1455841011yescharacteristic
subgroupG/H
centerC2#14558410
commutatorC23×C37C42
FrattiniC2×D4C2×#3866
Fitting#100×C37C4
socleC2×C37#342
prime radical, cosocleC2×D4×D37C22
hypercenter#100#3866
hypocenterC37#1390
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
4. C23×#3866C4semidirect
7. C2×C22⋊#3866C4semidirect
9. #11924594C4semidirect
13. #11924453C4semidirect
15. #100×C37C4semidirect
109. C37#1390semidirect
118. #100#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#992
#145584812
#100×D372
#139037