Finite Group Databasebeta

← #18010026

Subgroups — #18010026

Order 4736.

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

normal subgroups only

This group has 264 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#14558552C211yesmaximal, characteristic, complemented
2#14558477C211yesmaximal, characteristic, complemented
3#14558385C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#14558080C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C4⋊#64438—21no—
8#11924593C2212yes—
9C4×#64438—21no—
10(C2×#3866)⋊C4—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—42no—
40C4⋊C4×C37C2×C411yescharacteristic
41C22⋊C4×C37—21no—
42C42×C37C2×C411yescharacteristic
43C22⋊Dic37—21no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48C4×Dic37C2×C411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37D411yescharacteristic
51C23×C37—21no—
52C22×D37—21no—
53C22×D37C2×D411yescharacteristic
54C2×#3866—42no—
55C2×#3866—42no—
56C2×#3866—42no—
57D4×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37—42no—
60C2×C4×C37C22⋊C411yescharacteristic
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22×C411yescharacteristic
63C22⋊D37—42no—
64C22⋊D37—41no—
65C22⋊D37—41no—
66C22⋊D37—42no—
67C2×Dic37—21no—
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C2×D411yescharacteristic
71D148—41no—
72D148—41no—
73D148—41no—
74C4×D37—41no—
75C4×D37—41no—
76C4×D37—42no—
77C4×D37D812yes—
78C4×D37SD1612yes—
79Dic74—42no—
80#64438—42no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37C2×C22⋊C411yescharacteristic
85C2×D37—21no—
86C2×D37—21no—
87C2×D37—41no—
88C2×D37—41no—
89C2×D37—41no—
90C2×D37C2×D811yescharacteristic
91C2×D37C2×SD1611yescharacteristic
92#3866—82no—
93C4×C37—21no—
94C4×C37—21no—
95C4×C37—41no—
96C4×C37#10212yes—
97Dic37—21no—
98Dic37—21no—
99Dic37—41no—
100Dic37#10212yes—
101#1517—371nomaximal, Sylow
102C2×C37—81no—
103C2×C37#41011yescharacteristic
104C2×C37C2×#10211yescharacteristic
105C2×C37#42111yescharacteristic
106D37—21no—
107D37—21no—
108D37—81no—
109#532—371no—
110#431—371no—
111#382—371no—
112#327—372no—
113#327—372no—
114C37#151711yescharacteristic, complemented, Sylow
115C2×#41—741no—
116C4⋊Q8—371no—
117#127—371no—
118#124—741no—
119#121—371no—
120#121—371no—
121#121—741no—
122C4×D4—371no—
123C4×D4—741no—
124C4×D4#386611yescharacteristic, complemented
125C2×C4⋊C4—741no—
126C2×C42—371no—
127C4⋊C8—741no—
128C22⋊C8—372no—
129C4×C8—741no—
130#95—372no—
131#95—741no—
132#41—1482no—
133#41—1482no—
134C2×Q8—741no—
135C2×D4—371no—
136C2×D4—741no—
137C2×D4—741no—
138C2×D4—741no—
139C2×D4—741no—
140C2×D4C2×#386611yescharacteristic
141C22×C4—21no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—741no—
146C22×C4—742no—
147C2×C8—742no—
148C4⋊C4—371no—
149C4⋊C4—741no—
150C4⋊C4—1482no—
151C4⋊C4C2×#386611yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—741no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C42—371no—
157C42—371no—
158C42—371no—
159C42C2×#386611yescharacteristic
160C23—21no—
161C23—371no—
162C23—741no—
163Q8—1482no—
164D4—41no—
165D4—1481no—
166D4—1481no—
167D4—1481no—
168D4—1482no—
169D4—1482no—
170D4—1481no—
171D4—1481no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—371no—
175C2×C4—372no—
176C2×C4—372no—
177C2×C4—371no—
178C2×C4—371no—
179C2×C4—741no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4—1482no—
183C2×C4—1482no—
184C2×C4—1482no—
185C2×C4—1482no—
186C2×C4C22⋊#386611yescharacteristic
187C2×C4C22⋊#386611yescharacteristic
188C2×C4C22×#386611yescharacteristic
189C8—1482no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—371no—
194C22—371no—
195C22—741no—
196C22—741no—
197C22—1481no—
198C22—1481no—
199C22—1481no—
200C22C2×C22⋊#386611yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—372no—
205C4—2962no—
206C4—741no—
207C4—741no—
208C4—1481no—
209C4#1192459812yes—
210C2—81no—
211C2—2961no—
212C2—741no—
213C2—741no—
214C2#1455851211yescharacteristic
215C2C2×#1192459811yescharacteristic
216C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#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#1517
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14558552C2semidirect
2. #14558477C2semidirect
3. #14558385C2semidirect
4. #14558384C2semidirect
13. #11924535C4semidirect
14. #11924532C4semidirect
19. C4×D148C4semidirect
22. C4×D4×C37C4semidirect
114. C37#1517semidirect
124. C4×D4#3866semidirect

Maximal subgroups

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

subgroupindex
#145585522
#145584772
#145583852
#145583842
#145580802
#151737