Finite Group Databasebeta

← #18010632

Subgroups — #18010632

Order 4736.

310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558601C211yesmaximal, characteristic, complemented
2#14558531C211yesmaximal, characteristic
3#14558526C211yesmaximal, characteristic, complemented
4#14558513C211yesmaximal, characteristic
5#14558415C211yesmaximal, characteristic, complemented
6#14558401C211yesmaximal, characteristic, complemented
7C2×#11924565C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9Q8×#3866—22no—
10Q8×#3866—22no—
11#11924615—22no—
12#11924615C2211yescharacteristic
13#11924615C2211yescharacteristic
14#11924615C2211yescharacteristic
15#11924600—22no—
16#11924599—22no—
17#11924594—22no—
18C2×#10596964C2211yescharacteristic
19C2×Q8×D37C2211yescharacteristic
20#11924565—22no—
21#11924565—22no—
22C2×Dic148C411yescharacteristic, complemented
23C2×#10596942C411yescharacteristic, complemented
24C2×#10596940C411yescharacteristic, complemented
25C2×#10596929C2211yescharacteristic
26C2×SD16×C37C411yescharacteristic, complemented
27C2×Q8×C37C2×C411yescharacteristic
28C2×D4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C22×Dic37—21no—
31Q8×D37—21no—
32Q8×D37—21no—
33Q8×D37D412yes—
34Q8×D37D412yes—
35#10596964—21no—
36#10596964—21no—
37#10596964—21no—
38#10596964—21no—
39C2×C4×D37—21no—
40C2×C4×D37C2311yescharacteristic
41C2×Dic74—21no—
42C2×Dic74C2×C411yescharacteristic
43C2×Dic74C2×C411yescharacteristic
44C22⋊#3866—21no—
45C22⋊#3866—21no—
46C22⋊#3866D412yes—
47#10596957—21no—
48C4⋊#3866—24no—
49C4⋊#3866—21no—
50C4⋊#3866—21no—
51C4⋊#3866—21no—
52C4×#3866—24no—
53C4×#3866—21no—
54C4×#3866—21no—
55C4×#3866D412yes—
56#10596953—21no—
57D37⋊C8—21no—
58SD16×C37—22no—
59C2×C8×C37C2×C411yescharacteristic
60#10596942—22no—
61#10596940—22no—
62C2×#64436C2×C411yescharacteristic
63Dic148—22no—
64#10596929—21no—
65#10596929—21no—
66C23×C37—21no—
67C22×D37C2×D411yescharacteristic
68C2×#3866—22no—
69C2×#3866—22no—
70C2×#3866—41no—
71Q8×C37—21no—
72Q8×C37C22⋊C412yes—
73D4×C37—21no—
74D4×C37—21no—
75C2×C4×C37—21no—
76C2×C4×C37C22×C411yescharacteristic
77C22⋊D37—41no—
78C22⋊D37—41no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—41no—
82C2×Dic37—41no—
83C2×Dic37#4111yescharacteristic
84C4×D37—22no—
85C4×D37—22no—
86C4×D37C2×D411yescharacteristic
87C4×D37C2×D411yescharacteristic
88C4×D37C2×D411yescharacteristic
89C4×D37#4111yescharacteristic
90Dic74—21no—
91Dic74—22no—
92Dic74—22no—
93Dic74—21no—
94Dic74—21no—
95Dic74C22⋊C412yes—
96#64438—41no—
97C8×C37—21no—
98#64436—21no—
99C22×C37—41no—
100C22×C37—81no—
101C22×C37C4×D411yescharacteristic
102C2×D37—41no—
103C2×D37#12011yescharacteristic
104C2×D37#12111yescharacteristic
105#3866—42no—
106#3866—42no—
107#3866—81no—
108C4×C37—22no—
109C4×C37C2×C22⋊C411yescharacteristic
110C4×C37C4×D411yescharacteristic
111Dic37—22no—
112Dic37—41no—
113Dic37#12111yescharacteristic
114Dic37#12311yescharacteristic
115#1905—371nomaximal, Sylow
116C2×C37—21no—
117C2×C37—81no—
118C2×C37#38611yescharacteristic
119D37—21no—
120D37—21no—
121C2×#137—371no—
122#519—371no—
123#421—371no—
124#419—371no—
125#410—371no—
126#344—371no—
127H(3,ℤ/4)—371no—
128C37#190511yescharacteristic, complemented, Sylow
129C2×#41—371no—
130C22×Q8—371no—
131#137—742no—
132#137—742no—
133C2×Q16—371no—
134C2×Q16—371no—
135C2×SD16—371no—
136C2×SD16#386611yescharacteristic, complemented
137C2×M16—371no—
138C2×M16—371no—
139C4×Q8—742no—
140C4×Q8—742no—
141#117—371no—
142#117—371no—
143#117—371no—
144#117—742no—
145#104—742no—
146#103—742no—
147#99—742no—
148#41—741no—
149#41—741no—
150#41—741no—
151#41—741no—
152C2×Q8—372no—
153C2×Q8—372no—
154C2×Q8—371no—
155C2×Q8—371no—
156C2×Q8—741no—
157C2×Q8—741no—
158C2×Q8—741no—
159C2×Q8C2×#386611yescharacteristic
160C2×D4—741no—
161C2×D4C2×#386611yescharacteristic
162C22×C4—371no—
163C22×C4—741no—
164C22×C4—741no—
165Q16—742no—
166Q16—742no—
167SD16—22no—
168SD16—742no—
169M16—741no—
170M16—741no—
171M16—741no—
172M16—741no—
173C2×C8—371no—
174C2×C8—741no—
175C2×C8C2×#386611yescharacteristic
176C4⋊C4—741no—
177C4⋊C4—741no—
178C4⋊C4—741no—
179C4⋊C4—744no—
180C22⋊C4—372no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C42—372no—
184C42—741no—
185C42—741no—
186C42—744no—
187C23—21no—
188C23—371no—
189Q8—21no—
190Q8—372no—
191Q8—742no—
192Q8—742no—
193Q8—741no—
194Q8—741no—
195Q8—741no—
196Q8C22⋊#386612yes—
197D4—21no—
198D4—21no—
199D4—1481no—
200D4—1481no—
201C2×C4—21no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—371no—
205C2×C4—371no—
206C2×C4—371no—
207C2×C4—742no—
208C2×C4—742no—
209C2×C4—741no—
210C2×C4—742no—
211C2×C4—742no—
212C2×C4—741no—
213C2×C4—1481no—
214C2×C4—1481no—
215C2×C4—1481no—
216C2×C4C22×#386611yescharacteristic
217C8—21no—
218C8—741no—
219C8—1481no—
220C22—41no—
221C22—81no—
222C22—371no—
223C22—371no—
224C22—1481no—
225C22D4×#386611yescharacteristic
226C4—22no—
227C4—371no—
228C4—371no—
229C4—2961no—
230C4—742no—
231C4—1482no—
232C4—1482no—
233C4—1481no—
234C4C2×C22⋊#386611yescharacteristic
235C4D4×#386611yescharacteristic
236C2—21no—
237C2—81no—
238C2—741no—
239C2—741no—
240C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×SD16×C37C4
socleC2×C37#386
prime radicalC2×#10596964C22
cosocleC2×C4×D37C23
hypercenterC2×SD16#3866
hypocenterC37#1905
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #14558601C2semidirect
3. #14558526C2semidirect
5. #14558415C2semidirect
6. #14558401C2semidirect
22. C2×Dic148C4semidirect
23. C2×#10596942C4semidirect
24. C2×#10596940C4semidirect
26. C2×SD16×C37C4semidirect
128. C37#1905semidirect
136. C2×SD16#3866semidirect

Maximal subgroups

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

subgroupindex
#145586012
#145585312
#145585262
#145585132
#145584152
#145584012
C2×#119245652
#190537