Finite Group Databasebeta

← #17995817

Subgroups — #17995817

Order 4736.

306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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×#11924463C212yesmaximal, complemented
2#14557534C212yesmaximal, complemented
3#14557402C211yesmaximal, characteristic, complemented
4#14557302C211yesmaximal, characteristic, complemented
5C37×#537C211yesmaximal, characteristic
6C2×#10596934C2212yes—
7C2×C4⋊Dic37C2211yescharacteristic
8C2×#10596936—22no—
9C2×C4×Dic37C2211yescharacteristic
10#11924463—24no—
11#11924460—22no—
12#11924457—22no—
13C2×#41×C37C2212yes—
14C22⋊Q8×C37—22no—
15#121×C37—22no—
16#121×C37—22no—
17C2×C4⋊C4×C37C2211yescharacteristic
18#41×C37—22no—
19#41×C37—22no—
20#41×C37—22no—
21#41×C37—22no—
22C2×Q8×C37D412yes—
23C2×D4×C37—22no—
24C2×D4×C37—22no—
25C2×D4×C37D412yes—
26C22×C4×C37—22no—
27C22×C4×C37D412yes—
28C22×C4×C37C2311yescharacteristic
29C22×Dic37—21no—
30C22×Dic37—21no—
31C4⋊C4×C37—22no—
32C4⋊C4×C37—22no—
33C22⋊C4×C37—24no—
34C4⋊Dic37—22no—
35#10596936—44no—
36C4×Dic37—21no—
37C4×Dic37D412yescomplemented
38#10596934—22no—
39#10596934—22no—
40C2×#64436—22no—
41C23×C37—22no—
42C23×C37C2×D411yescharacteristic
43Q8×C37—22no—
44Q8×C37—22no—
45D4×C37—22no—
46D4×C37—22no—
47D4×C37—42no—
48D4×C37—42no—
49D4×C37—82no—
50C2×C4×C37—22no—
51C2×C4×C37—22no—
52C2×C4×C37—42no—
53C2×C4×C37—42no—
54C2×C4×C37—42no—
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D412yes—
57C2×C4×C37#4112yes—
58C2×C4×C37#4111yescharacteristic
59C2×Dic37—22no—
60C2×Dic37—22no—
61C2×Dic37—22no—
62C2×Dic37—42no—
63C2×Dic37—41no—
64#64436—42no—
65C22×C37—21no—
66C22×C37—21no—
67C22×C37—42no—
68C22×C37—42no—
69C22×C37—42no—
70C22×C37#12011yescharacteristic
71C22×C37#12111yescharacteristic
72C22×C37#12411yescharacteristic
73C4×C37—42no—
74C4×C37—42no—
75C4×C37#12112yes—
76C4×C37#12312yes—
77Dic37—24no—
78Dic37—81no—
79#2039—371nomaximal, Sylow
80C2×C37—21no—
81C2×C37—21no—
82C2×C37—82no—
83C2×C37#39411yescharacteristic
84C2×C37#45311yescharacteristic
85C2×C37#45611yescharacteristic
86#537D3711yescharacteristic
87C2×#104—372no—
88#417—372no—
89#384—371no—
90#343—371no—
91C37#203911yescharacteristic, complemented, Sylow
92C2×#41C2×D3712yes—
93C2×M16—372no—
94C22⋊Q8—22no—
95#121—22no—
96#121—22no—
97C2×C4⋊C4—371no—
98C2×C4⋊C4—742no—
99C2×C4⋊C4C2×D3711yescharacteristic
100C2×C42—371no—
101#104—744no—
102#103—742no—
103#102—742no—
104#41—22no—
105#41—22no—
106#41—22no—
107#41—22no—
108C2×Q8C22⋊D3712yes—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4C22⋊D3712yes—
112C22×C4—22no—
113C22×C4—741no—
114C22×C4—741no—
115C22×C4C22⋊D3712yes—
116C22×C4C22×D3711yescharacteristic
117M16—742no—
118M16—742no—
119C2×C8—742no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—742no—
123C4⋊C4—1484no—
124C22⋊C4—24no—
125C42—372no—
126C42—741no—
127C23—22no—
128C23C2×C22⋊D3711yescharacteristic
129Q8—22no—
130Q8—22no—
131D4—22no—
132D4—22no—
133D4—42no—
134D4—42no—
135D4—82no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—742no—
142C2×C4—742no—
143C2×C4—742no—
144C2×C4—1482no—
145C2×C4—1481no—
146C2×C4D4×D3711yescharacteristic
147C2×C4#1059696412yes—
148C2×C4#1059696411yescharacteristic
149C2×C4C2×C22⋊D3712yes—
150C8—1482no—
151C22—21no—
152C22—21no—
153C22—42no—
154C22—42no—
155C22—42no—
156C22#1192450511yescharacteristic
157C22#1192450711yescharacteristic
158C22#1192452311yescharacteristic
159C4—42no—
160C4—42no—
161C4—2961no—
162C4—744no—
163C4#1192450812yes—
164C4#1192451712yes—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#1455744711yescharacteristic
169C2#1455770111yescharacteristic
170C2#1455771611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#537C2
socleC22×C37#120
hypercenter#537D37
hypocenterC37#2039
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×#11924463C2semidirect
2. #14557534C2semidirect
3. #14557402C2semidirect
4. #14557302C2semidirect
37. C4×Dic37D4semidirect
91. C37#2039semidirect

Maximal subgroups

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

subgroupindex
C2×#119244632
#145575342
#145574022
#145573022
C37×#5372
#203937