Finite Group Databasebeta

← #17995643

Subgroups — #17995643

Order 4736.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11924566C212yesmaximal, complemented
2C2×#11924463C212yesmaximal, complemented
3#14557438C211yesmaximal, characteristic, complemented
4#14557302C211yesmaximal, characteristic, complemented
5C37×#537C211yesmaximal, characteristic
6C22×Dic74C2211yescharacteristic
7#11924566—24no—
8#11924566—24no—
9C2×#10596942—22no—
10C2×#10596940—22no—
11C2×#10596934C2212yes—
12C2×C4×Dic37C2211yescharacteristic
13#11924463—24no—
14#11924443—22no—
15C2×#41×C37C2212yes—
16C22⋊Q8×C37—22no—
17#121×C37—22no—
18#121×C37—22no—
19C2×C4⋊C4×C37C2211yescharacteristic
20#41×C37—22no—
21#41×C37—22no—
22#41×C37—22no—
23#41×C37—22no—
24C2×Q8×C37D412yes—
25C2×D4×C37—22no—
26C2×D4×C37—22no—
27C2×D4×C37D412yes—
28C22×C4×C37—22no—
29C22×C4×C37D412yes—
30C22×C4×C37C2311yescharacteristic
31C22×Dic37—21no—
32C22×Dic37—21no—
33C2×Dic74—22no—
34C2×Dic74—22no—
35C2×Dic74—21no—
36C2×Dic74D412yescomplemented
37C4⋊C4×C37—22no—
38C4⋊C4×C37—22no—
39C22⋊C4×C37—24no—
40#10596942—28no—
41#10596940—28no—
42C4×Dic37—22no—
43#10596934—22no—
44#10596934D414yescomplemented
45C2×#64436—22no—
46C23×C37—22no—
47C23×C37C2×D411yescharacteristic
48Q8×C37—22no—
49Q8×C37—22no—
50D4×C37—22no—
51D4×C37—22no—
52D4×C37—42no—
53D4×C37—42no—
54D4×C37—82no—
55C2×C4×C37—22no—
56C2×C4×C37—22no—
57C2×C4×C37—42no—
58C2×C4×C37—42no—
59C2×C4×C37—42no—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D412yes—
62C2×C4×C37C2×D412yes—
63C2×C4×C37#4111yescharacteristic
64C2×Dic37—22no—
65C2×Dic37—22no—
66C2×Dic37—41no—
67C2×Dic37—41no—
68C2×Dic37—41no—
69C2×Dic37—41no—
70Dic74—24no—
71Dic74—42no—
72#64436—24no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37—42no—
78C22×C37#12011yescharacteristic
79C22×C37#12111yescharacteristic
80C22×C37#12711yescharacteristic
81C4×C37—42no—
82C4×C37—42no—
83C4×C37#12012yes—
84C4×C37#12112yes—
85Dic37—42no—
86Dic37—42no—
87#2007—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—21no—
90C2×C37—82no—
91C2×C37#39211yescharacteristic
92C2×C37#45511yescharacteristic
93C2×C37#45611yescharacteristic
94C2×#137—372no—
95#537D3711yescharacteristic
96C2×#104—372no—
97#391—371no—
98#343—371no—
99C37#200711yescharacteristic, complemented, Sylow
100C2×#41C2×D3712yes—
101C22×Q8—371no—
102#137—744no—
103#137—744no—
104C2×Q16—742no—
105C2×SD16—742no—
106C2×M16—372no—
107C22⋊Q8—22no—
108#121—22no—
109#121—22no—
110C2×C4⋊C4C2×D3711yescharacteristic
111C2×C42—371no—
112#104—744no—
113#95—742no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—372no—
119C2×Q8—741no—
120C2×Q8—742no—
121C2×Q8—742no—
122C2×Q8C22⋊D3712yes—
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C22⋊D3712yes—
126C22×C4—22no—
127C22×C4—741no—
128C22×C4—741no—
129C22×C4C22⋊D3712yes—
130C22×C4C22×D3711yescharacteristic
131Q16—748no—
132SD16—748no—
133M16—374no—
134M16—742no—
135C2×C8—742no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—742no—
140C23—22no—
141C23C2×C22⋊D3711yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—744no—
145Q8—1482no—
146D4—22no—
147D4—22no—
148D4—42no—
149D4—42no—
150D4—82no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—742no—
157C2×C4—742no—
158C2×C4—1481no—
159C2×C4—1481no—
160C2×C4—1481no—
161C2×C4—1481no—
162C2×C4D4×D3711yescharacteristic
163C2×C4D4×D3712yes—
164C2×C4#1059696411yescharacteristic
165C2×C4C2×C22⋊D3712yes—
166C8—744no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#1192450511yescharacteristic
173C22#1192450711yescharacteristic
174C22#1192453211yescharacteristic
175C4—42no—
176C4—42no—
177C4—1482no—
178C4—1482no—
179C4#1192450412yes—
180C4#1192450812yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#1455744111yescharacteristic
185C2#1455771111yescharacteristic
186C2#1455771611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#537C2
socleC22×C37#120
hypercenter#537D37
hypocenterC37#2007
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#11924566C2semidirect
2. C2×#11924463C2semidirect
3. #14557438C2semidirect
4. #14557302C2semidirect
36. C2×Dic74D4semidirect
44. #10596934D4semidirect
99. C37#2007semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
C2×#119244632
#145574382
#145573022
C37×#5372
#200737