Finite Group Databasebeta

← #17995040

Subgroups — #17995040

Order 4736.

442 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×C4×Dic37C211yesmaximal, characteristic, complemented
2C2×#11924463C212yesmaximal, complemented
3#14557497C211yesmaximal, characteristic, complemented
4#14557292C212yesmaximal, complemented
5C37×#525C211yesmaximal, characteristic
6C23×Dic37—21no—
7C2×#10596934C2212yes—
8C2×C4×Dic37—21no—
9C2×C4×Dic37—24no—
10C2×C4×Dic37C2212yes—
11#11924463—24no—
12C22⋊#64436—22no—
13C2×#41×C37C2211yescharacteristic
14C23×C4×C37C2211yescharacteristic
15#123×C37—21no—
16C22⋊Q8×C37C412yescomplemented
17#121×C37C412yescomplemented
18#120×C37—21no—
19C4×D4×C37—22no—
20#117×C37C2211yescharacteristic
21C24×C37D411yescharacteristic
22#41×C37—22no—
23#41×C37—22no—
24C2×Q8×C37C2×C411yescharacteristic, complemented
25C2×D4×C37—22no—
26C2×D4×C37—21no—
27C2×D4×C37C2×C411yescharacteristic, complemented
28C22×C4×C37—22no—
29C22×C4×C37—22no—
30C22×C4×C37—21no—
31C22×C4×C37C2×C412yes—
32C22×C4×C37D411yescharacteristic
33C22×C4×C37D412yes—
34C22×C4×C37C2311yescharacteristic
35C22×Dic37—24no—
36C22×Dic37—28no—
37C22×Dic37—22no—
38C4⋊C4×C37—22no—
39C4⋊C4×C37C2×C412yescomplemented
40C22⋊C4×C37—22no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—22no—
43C42×C37—21no—
44C4×Dic37—24no—
45C4×Dic37—22no—
46C4×Dic37D414yescomplemented
47#10596934—22no—
48#10596934—22no—
49C2×#64436—22no—
50C23×C37—24no—
51C23×C37—21no—
52C23×C37—21no—
53C23×C37—21no—
54C23×C37C22⋊C412yes—
55C23×C37C2×D411yescharacteristic
56Q8×C37—22no—
57D4×C37—22no—
58D4×C37—44no—
59D4×C37—41no—
60D4×C37—41no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—24no—
64C2×C4×C37—24no—
65C2×C4×C37—22no—
66C2×C4×C37—21no—
67C2×C4×C37—42no—
68C2×C4×C37C22⋊C412yes—
69C2×C4×C37C22×C411yescharacteristic
70C2×C4×C37C2×D412yes—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37#4112yes—
73C2×Dic37—216no—
74C2×Dic37—28no—
75C2×Dic37—24no—
76#64436—42no—
77C22×C37—24no—
78C22×C37—24no—
79C22×C37—22no—
80C22×C37—22no—
81C22×C37—22no—
82C22×C37—41no—
83C22×C37—42no—
84C22×C37#10414yescomplemented
85C22×C37C2×C22⋊C411yescharacteristic
86C22×C37#12011yescharacteristic
87C22×C37#12311yescharacteristic
88C4×C37—22no—
89C4×C37—41no—
90C4×C37—42no—
91C4×C37C4×D412yes—
92C4×C37#12112yes—
93Dic37—28no—
94#1896—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—24no—
97C2×C37—21no—
98C2×C37—81no—
99C2×C37#38611yescharacteristic
100C2×C37C2×#10412yes—
101#525D3711yescharacteristic
102C22×C42—371no—
103C2×#104—372no—
104#407—371no—
105#339—372no—
106C37#189611yescharacteristic, complemented, Sylow
107C2×#41C2×D3711yescharacteristic
108C23×C4—741no—
109C23×C4C2×D3711yescharacteristic
110C2×M16—372no—
111#123—21no—
112C22⋊Q8Dic3712yescomplemented
113#121Dic3712yescomplemented
114#120—21no—
115C4×D4—22no—
116#117C2×D3711yescharacteristic
117C2×C42—372no—
118C2×C42—744no—
119C2×C42—741no—
120#104—744no—
121C22⋊C8—742no—
122C24C22⋊D3711yescharacteristic
123#41—22no—
124#41—22no—
125C2×Q8C2×Dic3711yescharacteristic, complemented
126C2×D4—22no—
127C2×D4—21no—
128C2×D4C2×Dic3711yescharacteristic, complemented
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—744no—
133C22×C4—748no—
134C22×C4—742no—
135C22×C4C2×Dic3712yes—
136C22×C4C22⋊D3711yescharacteristic
137C22×C4C22⋊D3712yes—
138C22×C4C22×D3711yescharacteristic
139M16—742no—
140M16—742no—
141C2×C8—742no—
142C4⋊C4—22no—
143C4⋊C4C2×Dic3712yescomplemented
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C42—21no—
148C42—374no—
149C42—744no—
150C42—742no—
151C23—21no—
152C23—21no—
153C23—24no—
154C23—21no—
155C23C22⋊Dic3712yes—
156C23C2×C22⋊D3711yescharacteristic
157Q8—22no—
158D4—22no—
159D4—41no—
160D4—41no—
161D4—44no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—7416no—
170C2×C4—748no—
171C2×C4—744no—
172C2×C4C22⋊Dic3712yes—
173C2×C4D4×D3712yes—
174C2×C4#1059696412yes—
175C2×C4C22×Dic3711yescharacteristic
176C2×C4C2×C22⋊D3711yescharacteristic
177C8—1482no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—42no—
184C22—41no—
185C22#1192446314yescomplemented
186C22C2×C22⋊Dic3711yescharacteristic
187C22#1192450411yescharacteristic
188C22#1192451711yescharacteristic
189C4—22no—
190C4—42no—
191C4—41no—
192C4—748no—
193C4D4×Dic3712yes—
194C4#1192450812yes—
195C2—21no—
196C2—21no—
197C2—24no—
198C2—81no—
199C2#1455741311yescharacteristic
200C2C2×#1192446312yes—
subgroupG/H
centerC2×C4C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#525C2
socleC22×C37C2×C22⋊C4
cosocleC22×C4×C37C23
hypercenter#525D37
hypocenterC37#1896
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic37C2semidirect
2. C2×#11924463C2semidirect
3. #14557497C2semidirect
4. #14557292C2semidirect
16. C22⋊Q8×C37C4semidirect
17. #121×C37C4semidirect
24. C2×Q8×C37C2×C4semidirect
27. C2×D4×C37C2×C4semidirect
39. C4⋊C4×C37C2×C4semidirect
46. C4×Dic37D4semidirect
84. C22×C37#104semidirect
106. C37#1896semidirect
112. C22⋊Q8Dic37semidirect
113. #121Dic37semidirect
125. C2×Q8C2×Dic37semidirect
128. C2×D4C2×Dic37semidirect
143. C4⋊C4C2×Dic37semidirect
185. C22#11924463semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic372
C2×#119244632
#145574972
#145572922
C37×#5252
#189637