Finite Group Databasebeta

← #18010368

Subgroups — #18010368

Order 4736.

324 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×#11924599C212yesmaximal
2#14558492C211yesmaximal, characteristic
3C4×C4⋊#3866C211yesmaximal, characteristic
4#14558406C212yesmaximal
5C4×Q8×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7C2×C4⋊#3866C2212yes—
8C2×C4×#3866—21no—
9#11924599C418yescomplemented
10#11924591—21no—
11#11924591—21no—
12(C2×#3866)⋊C4—21no—
13C2×Q8×D37C2211yescharacteristic
14Q8×Dic37C411yescharacteristic, complemented
15C4×Dic74—21no—
16C4×Dic74C411yescharacteristic, complemented
17#11924501—21no—
18#11924501C411yescharacteristic, complemented
19C4⋊C4×D37—21no—
20C4⋊C4×D37C2211yescharacteristic
21C42×D37—21no—
22C42×D37C2211yescharacteristic
23C4×Q8×C37C411yescharacteristic, complemented
24C22×#3866—22no—
25C2×Q8×C37C2×C411yescharacteristic
26Q8×D37—22no—
27Q8×D37C2×C414yes—
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37D411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37C2311yescharacteristic
33C2×Dic74—21no—
34C2×Dic74C2×C411yescharacteristic
35C2×#64438—22no—
36C4⋊#3866—22no—
37C4⋊#3866C2×C414yes—
38C4×#3866—42no—
39D37⋊C8—22no—
40D37⋊C8C2×C414yes—
41C4⋊C4×C37—21no—
42C4⋊C4×C37C2×C411yescharacteristic
43C42×C37—21no—
44C42×C37C2×C411yescharacteristic
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50C4×Dic37—21no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C4×Dic37C2×C411yescharacteristic
54C4×Dic37D411yescharacteristic
55C4×Dic37D411yescharacteristic
56C22×D37C2×D411yescharacteristic
57C2×#3866—24no—
58C2×#3866—42no—
59C2×#3866—42no—
60Q8×C37—21no—
61Q8×C37C4212yescomplemented
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22×C411yescharacteristic
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C2×D411yescharacteristic
72C4×D37—24no—
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—22no—
76C4×D37—41no—
77C4×D37—41no—
78C4×D37C22×C412yes—
79C4×D37#4112yes—
80Dic74—21no—
81Dic74—24no—
82Dic74C4212yescomplemented
83#64438—24no—
84C22×C37C2×C22⋊C411yescharacteristic
85C2×D37C4×D412yes—
86C2×D37AGL(1,ℤ/8)11yescharacteristic
87C2×D37#13712yes—
88C2×D37#13711yescharacteristic
89#3866—44no—
90C4×C37—22no—
91C4×C37—21no—
92C4×C37—21no—
93C4×C37—41no—
94C4×C37C2×C4211yescharacteristic
95C4×C37#11711yescharacteristic
96Dic37—22no—
97Dic37—21no—
98Dic37—21no—
99Dic37—41no—
100Dic37C4×D412yes—
101#1763—371nomaximal, Sylow
102C2×C37C4×C22⋊C411yescharacteristic
103C2×C37#41711yescharacteristic
104C2×C37#41911yescharacteristic
105D37#44012yes—
106D37#44112yes—
107C2×C4×Q8—371no—
108C2×#103—372no—
109C2×#97—371no—
110C4×C4⋊C4—371no—
111#340—372no—
112C37#176311yescharacteristic, complemented, Sylow
113C22×Q8—371no—
114C22×C8—372no—
115C4×Q8—371no—
116C4×Q8—371no—
117C4×Q8—371no—
118C4×Q8—741no—
119C4×Q8—741no—
120C4×Q8#386611yescharacteristic, complemented
121C2×C4⋊C4—372no—
122C2×C4⋊C4—371no—
123C2×C4⋊C4—741no—
124C2×C42—371no—
125C2×C42—741no—
126C2×C42—741no—
127#103—378no—
128#97—741no—
129#97—741no—
130#95—741no—
131C2×Q8—374no—
132C2×Q8—371no—
133C2×Q8—741no—
134C2×Q8—742no—
135C2×Q8C2×#386611yescharacteristic
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—741no—
140C22×C4—741no—
141C22×C4—742no—
142C2×C8—374no—
143C2×C8—742no—
144C2×C8—742no—
145C4⋊C4—21no—
146C4⋊C4—374no—
147C4⋊C4—371no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—742no—
152C4⋊C4—741no—
153C4⋊C4C2×#386611yescharacteristic
154C42—21no—
155C42—371no—
156C42—371no—
157C42—371no—
158C42—741no—
159C42—741no—
160C42—741no—
161C42—1482no—
162C42C2×#386611yescharacteristic
163C23—371no—
164Q8—21no—
165Q8—372no—
166Q8—744no—
167Q8—741no—
168Q8C4×#386612yescomplemented
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—371no—
172C2×C4—372no—
173C2×C4—372no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—742no—
179C2×C4—744no—
180C2×C4—741no—
181C2×C4—744no—
182C2×C4—741no—
183C2×C4—1481no—
184C2×C4—1481no—
185C2×C4—1482no—
186C2×C4—1482no—
187C2×C4C22⋊#386611yescharacteristic
188C2×C4C22⋊#386611yescharacteristic
189C2×C4C22×#386611yescharacteristic
190C8—744no—
191C22—372no—
192C22—371no—
193C22—371no—
194C22—372no—
195C22C2×C22⋊#386611yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—372no—
201C4—742no—
202C4—741no—
203C4—741no—
204C4—1484no—
205C4—1481no—
206C4C2×C4×#386611yescharacteristic
207C4#1192461511yescharacteristic
208C2—372no—
209C2—372no—
210C2C4×C22⋊#386611yescharacteristic
211C2#1455852411yescharacteristic
212C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenterC4×Q8#3866
hypocenterC37#1763
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
9. #11924599C4semidirect
14. Q8×Dic37C4semidirect
16. C4×Dic74C4semidirect
18. #11924501C4semidirect
23. C4×Q8×C37C4semidirect
61. Q8×C37C42semidirect
82. Dic74C42semidirect
112. C37#1763semidirect
120. C4×Q8#3866semidirect
168. Q8C4×#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245992
#145584922
C4×C4⋊#38662
#145584062
C4×Q8×D372
#176337