Finite Group Databasebeta

← #18010599

Subgroups — #18010599

Order 4736.

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

normal subgroups only

This group has 332 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#14558611C211yesmaximal, characteristic, complemented
2#14558531C212yesmaximal, complemented
3#14558513C211yesmaximal, characteristic, complemented
4#14558404C212yesmaximal, complemented
5#14558081C211yesmaximal, characteristic
6#11924623—24no—
7D37⋊M16C2212yes—
8C2×#10596957—22no—
9#11924615C2212yes—
10#11924600—24no—
11#11924594—22no—
12C2×#10596964C2211yescharacteristic
13C2×#10596964C2211yescharacteristic
14#11924536C411yescharacteristic, complemented
15#11924523C411yescharacteristic, complemented
16#11924523C411yescharacteristic, complemented
17#11924507—22no—
18D4×Dic37—22no—
19C42×D37C2211yescharacteristic
20#127×C37C411yescharacteristic, complemented
21C2×D4×C37—22no—
22C2×D4×C37C2×C411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C2×C22⋊D37—21no—
25C2×C22⋊D37D412yes—
26C22×Dic37—21no—
27C22×Dic37D412yes—
28#10596964—22no—
29#10596964—22no—
30#10596964—22no—
31#10596964—22no—
32C2×C4×D37—21no—
33C2×C4×D37C2311yescharacteristic
34C2×Dic74C2×C411yescharacteristic
35C2×Dic74C2×C411yescharacteristic
36C22⋊#3866—22no—
37#10596957—24no—
38#10596957—22no—
39C2×#64438—24no—
40C4⋊#3866—22no—
41C4×#3866—22no—
42#10596953D414yescomplemented
43D37⋊C8—22no—
44C42×C37C2×C411yescharacteristic
45C22⋊Dic37—22no—
46C22⋊Dic37—22no—
47C4⋊Dic37—22no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C23×C37—21no—
51C23×C37C22⋊C412yes—
52C22×D37C2×D411yescharacteristic
53C2×#3866—42no—
54D4×C37—22no—
55D4×C37—22no—
56D4×C37—44no—
57C2×C4×C37—21no—
58C2×C4×C37C22×C411yescharacteristic
59C22⋊D37—24no—
60C22⋊D37—42no—
61C2×Dic37—22no—
62C2×Dic37—22no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65C2×Dic37—41no—
66C2×Dic37—41no—
67C2×Dic37C22⋊C412yes—
68C2×Dic37C2×D411yescharacteristic
69C4×D37—42no—
70C4×D37C2×D412yes—
71C4×D37#4112yes—
72Dic74—22no—
73Dic74—22no—
74#64438—24no—
75C22×C37—22no—
76C22×C37—42no—
77C22×C37—42no—
78C22×C37—41no—
79C22×C37C2×C22⋊C411yescharacteristic
80C2×D37—41no—
81C2×D37#12112yes—
82#3866—82no—
83C4×C37—22no—
84C4×C37C4×D412yes—
85Dic37—22no—
86Dic37—41no—
87Dic37—41no—
88Dic37#12011yescharacteristic
89Dic37#12311yescharacteristic
90#1884—371nomaximal, Sylow
91C2×C37—21no—
92C2×C37—42no—
93C2×C37—81no—
94C2×C37#38611yescharacteristic
95D37—22no—
96#568—371no—
97#532—371no—
98#421—372no—
99#410—371no—
100#339—372no—
101C37#188411yescharacteristic, complemented, Sylow
102C2×#41—371no—
103C2×#41—371no—
104#131—744no—
105C2×M16—372no—
106C2×M16—742no—
107C4⋊Q8—371no—
108#127#386611yescharacteristic, complemented
109#124—371no—
110#124—371no—
111#121—742no—
112C4×D4—742no—
113#117—372no—
114C2×C42—371no—
115#104—744no—
116#99—742no—
117#41—742no—
118#41—742no—
119#41—742no—
120#41—742no—
121C2×Q8—371no—
122C2×Q8—371no—
123C2×D4—22no—
124C2×D4—372no—
125C2×D4—741no—
126C2×D4C2×#386611yescharacteristic
127C2×D4C2×#386611yescharacteristic
128C22×C4—371no—
129C22×C4—372no—
130C22×C4—741no—
131C22×C4—741no—
132M16—374no—
133M16—742no—
134M16—744no—
135C2×C8—742no—
136C2×C8—744no—
137C4⋊C4—742no—
138C4⋊C4—742no—
139C22⋊C4—742no—
140C22⋊C4—742no—
141C22⋊C4—742no—
142C42—371no—
143C42—741no—
144C42—742no—
145C42C2×#386611yescharacteristic
146C23—21no—
147C23—371no—
148C23C22⋊#386612yes—
149Q8—742no—
150Q8—742no—
151D4—22no—
152D4—22no—
153D4—44no—
154D4—744no—
155D4—1482no—
156C2×C4—21no—
157C2×C4—371no—
158C2×C4—372no—
159C2×C4—372no—
160C2×C4—372no—
161C2×C4—742no—
162C2×C4—742no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—1482no—
166C2×C4—1481no—
167C2×C4—1481no—
168C2×C4—1482no—
169C2×C4C22×#386611yescharacteristic
170C8—744no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—41no—
175C22—372no—
176C22—1481no—
177C22C2×C22⋊#386611yescharacteristic
178C4—22no—
179C4—371no—
180C4—371no—
181C4—2962no—
182C4—742no—
183C4—1481no—
184C4—1481no—
185C4D4×#386612yes—
186C2—21no—
187C2—42no—
188C2—81no—
189C2—742no—
190C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC2×C37#386
prime radical#14558081C2
cosocleC2×C4×D37C23
hypercenter#127#3866
hypocenterC37#1884
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14558611C2semidirect
2. #14558531C2semidirect
3. #14558513C2semidirect
4. #14558404C2semidirect
14. #11924536C4semidirect
15. #11924523C4semidirect
16. #11924523C4semidirect
20. #127×C37C4semidirect
42. #10596953D4semidirect
101. C37#1884semidirect
108. #127#3866semidirect

Maximal subgroups

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

subgroupindex
#145586112
#145585312
#145585132
#145584042
#145580812
#188437