Finite Group Databasebeta

← #18009975

Subgroups — #18009975

Order 4736.

284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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#14558551C211yesmaximal, characteristic, complemented
2C4×C4⋊#3866C211yesmaximal, characteristic, complemented
3#14558385C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#14558080C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C2×C4×#3866—21no—
8#11924603—21no—
9#11924593C2212yes—
10C4×#64438—21no—
11(C2×#3866)⋊C4C2212yes—
12C2×#10596962—21no—
13#11924535C411yescharacteristic, complemented
14#11924532C411yescharacteristic, complemented
15#11924522—21no—
16#11924511C2211yescharacteristic
17#11924509—21no—
18#11924507C2211yescharacteristic
19C4×D148C411yescharacteristic, complemented
20C4×C22⋊D37—21no—
21C42×D37C2211yescharacteristic
22C4×D4×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37—21no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29#10596962—42no—
30#10596962—42no—
31C2×D148—21no—
32C2×D148C2×C411yescharacteristic
33C2×C4×D37—21no—
34C2×C4×D37D411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37C2311yescharacteristic
37C2×Dic74—21no—
38C2×#64438—22no—
39C4⋊#3866—24no—
40C4×#3866—42no—
41C4⋊C4×C37C2×C411yescharacteristic
42C22⋊C4×C37—21no—
43C42×C37C2×C411yescharacteristic
44C22⋊Dic37—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37C2×C411yescharacteristic
48#10596936—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C23×C37—21no—
53C22×D37—21no—
54C22×D37C2×D411yescharacteristic
55C2×#3866—24no—
56C2×#3866—42no—
57C2×#3866—42no—
58D4×C37—41no—
59C2×C4×C37—21no—
60C2×C4×C37—42no—
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22×C411yescharacteristic
64C22⋊D37—41no—
65C22⋊D37—41no—
66C22⋊D37—42no—
67C22⋊D37—42no—
68C2×Dic37—21no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C2×D411yescharacteristic
72D148—41no—
73D148—41no—
74D148—41no—
75C4×D37—22no—
76C4×D37—41no—
77C4×D37—42no—
78C4×D37D812yes—
79C4×D37SD1612yes—
80Dic74—42no—
81#64438—42no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—21no—
87C2×D37—21no—
88C2×D37—41no—
89C2×D37—41no—
90C2×D37—41no—
91C2×D37C2×D811yescharacteristic
92C2×D37C2×SD1611yescharacteristic
93#3866—44no—
94C4×C37—21no—
95C4×C37—21no—
96C4×C37—41no—
97C4×C37#10212yes—
98Dic37—21no—
99Dic37—41no—
100Dic37#10212yes—
101Dic37#10412yes—
102#1502—371nomaximal, Sylow
103C2×C37—81no—
104C2×C37#41011yescharacteristic
105C2×C37C2×#10211yescharacteristic
106C2×C37C2×#10411yescharacteristic
107D37—21no—
108D37—21no—
109D37—81no—
110#532—371no—
111#431—371no—
112C4×C4⋊C4—371no—
113#327—372no—
114#327—372no—
115C37#150211yescharacteristic, complemented, Sylow
116C2×#41—741no—
117C4⋊Q8—371no—
118#127—371no—
119#124—741no—
120#121—371no—
121#121—371no—
122#121—741no—
123C4×D4—371no—
124C4×D4—741no—
125C4×D4#386611yescharacteristic, complemented
126C2×C4⋊C4—741no—
127C2×C42—371no—
128C2×C42—741no—
129C4⋊C8—741no—
130C22⋊C8—372no—
131C4×C8—741no—
132#95—372no—
133#41—1482no—
134#41—1482no—
135C2×Q8—741no—
136C2×D4—371no—
137C2×D4—741no—
138C2×D4—741no—
139C2×D4—741no—
140C2×D4—741no—
141C2×D4C2×#386611yescharacteristic
142C22×C4—21no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—371no—
146C22×C4—742no—
147C22×C4—741no—
148C2×C8—742no—
149C4⋊C4—371no—
150C4⋊C4—741no—
151C4⋊C4—744no—
152C4⋊C4C2×#386611yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C42—371no—
158C42—371no—
159C42—371no—
160C42—1482no—
161C42C2×#386611yescharacteristic
162C23—21no—
163C23—371no—
164C23—741no—
165Q8—1482no—
166D4—41no—
167D4—1481no—
168D4—1481no—
169D4—1481no—
170D4—1482no—
171D4—1482no—
172D4—1481no—
173D4—1481no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—371no—
177C2×C4—371no—
178C2×C4—372no—
179C2×C4—372no—
180C2×C4—371no—
181C2×C4—742no—
182C2×C4—744no—
183C2×C4—741no—
184C2×C4—1481no—
185C2×C4—1482no—
186C2×C4—1482no—
187C2×C4—1482no—
188C2×C4C22⋊#386611yescharacteristic
189C2×C4C22⋊#386611yescharacteristic
190C2×C4C22×#386611yescharacteristic
191C8—1482no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—371no—
196C22—371no—
197C22—741no—
198C22—741no—
199C22—1481no—
200C22—1481no—
201C22—1481no—
202C22C2×C22⋊#386611yescharacteristic
203C4—21no—
204C4—21no—
205C4—41no—
206C4—372no—
207C4—372no—
208C4—741no—
209C4—1484no—
210C4—1481no—
211C4#1192459812yes—
212C2—81no—
213C2—2961no—
214C2—741no—
215C2—741no—
216C2#1455851211yescharacteristic
217C2C2×#1192459811yescharacteristic
218C2D37⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558080C2
cosocleC2×C4×D37C23
hypercenterC4×D4#3866
hypocenterC37#1502
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14558551C2semidirect
2. C4×C4⋊#3866C2semidirect
3. #14558385C2semidirect
4. #14558384C2semidirect
13. #11924535C4semidirect
14. #11924532C4semidirect
19. C4×D148C4semidirect
22. C4×D4×C37C4semidirect
115. C37#1502semidirect
125. C4×D4#3866semidirect

Maximal subgroups

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

subgroupindex
#145585512
C4×C4⋊#38662
#145583852
#145583842
#145580802
#150237