Finite Group Databasebeta

← #17993880

Subgroups — #17993880

Order 4736.

240 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 61 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#14557929C211yesmaximal, characteristic, complemented
2#14557813C211yesmaximal, characteristic, complemented
3#14557738C211yesmaximal, characteristic, complemented
4#14557279C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#547C211yesmaximal, characteristic
8C2×#10596940—21no—
9#11924536C2211yescharacteristic
10#11924469—21no—
11#11924467—22no—
12C4⋊#64436C2211yescharacteristic
13C4⋊#64436C2211yescharacteristic
14#11924459—21no—
15#11924457—21no—
16C4×#64436C2211yescharacteristic
17C2×#41×C37—21no—
18C4⋊Q8×C37C2211yescharacteristic
19#123×C37—22no—
20C22⋊Q8×C37—21no—
21#121×C37—21no—
22C4×D4×C37C2211yescharacteristic
23C4×D4×C37C2211yescharacteristic
24C2×C4⋊C4×C37—21no—
25#41×C37—42no—
26#41×C37—42no—
27C2×Q8×C37—21no—
28C2×D4×C37—22no—
29C2×D4×C37D411yescharacteristic
30C2×D4×C37D411yescharacteristic
31C22×C4×C37—22no—
32C22×C4×C37—21no—
33C22×C4×C37—21no—
34C2×Dic74—21no—
35C4⋊C4×C37—22no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C4⋊C4×C37D411yescharacteristic
39C4⋊C4×C37D412yes—
40C22⋊C4×C37—22no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—21no—
43C42×C37C2311yescharacteristic
44#10596940—42no—
45C4⋊Dic37—21no—
46C4⋊Dic37—21no—
47C2×#64436—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—21no—
51C23×C37—21no—
52Q8×C37—41no—
53Q8×C37—41no—
54D4×C37—21no—
55D4×C37—21no—
56D4×C37—21no—
57D4×C37—44no—
58D4×C37SD1612yescomplemented
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—22no—
62C2×C4×C37—44no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×Dic37—41no—
71Dic74—41no—
72Dic74—41no—
73#64436—22no—
74#64436—41no—
75#64436—41no—
76C22×C37—22no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37—41no—
82C22×C37#12011yescharacteristic
83C4×C37—21no—
84C4×C37—41no—
85C4×C37—41no—
86C4×C37—42no—
87C4×C37C2×SD1611yescharacteristic
88C4×C37#13511yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90C4×C37AGL(1,ℤ/8)11yescharacteristic
91Dic37—81no—
92#1654—371nomaximal, Sylow
93C2×C37—42no—
94C2×C37—81no—
95C2×C37#44911yescharacteristic
96C2×C37#45011yescharacteristic
97C2×C37#45611yescharacteristic
98#547D3711yescharacteristic
99#498—371no—
100#474—371no—
101#461—371no—
102#332—371no—
103D4⋊C8—371no—
104D4⋊C8—371no—
105C37#165411yescharacteristic, complemented, Sylow
106C2×#41—21no—
107C2×SD16—741no—
108C4⋊Q8—371no—
109C4⋊Q8C2×D3711yescharacteristic
110#123—22no—
111C22⋊Q8—21no—
112#121—21no—
113C4×D4C2×D3711yescharacteristic
114C4×D4C2×D3711yescharacteristic
115C2×C4⋊C4—21no—
116#107—741no—
117#106—742no—
118C4⋊C8—371no—
119C4⋊C8—371no—
120#103—741no—
121#102—741no—
122C4×C8—371no—
123#41—42no—
124#41—42no—
125C2×Q8—21no—
126C2×Q8—741no—
127C2×D4—22no—
128C2×D4C22⋊D3711yescharacteristic
129C2×D4C22⋊D3711yescharacteristic
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133SD16—1482no—
134C2×C8—741no—
135C2×C8—741no—
136C2×C8—741no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—741no—
140C4⋊C4—741no—
141C4⋊C4C22⋊D3711yescharacteristic
142C4⋊C4C22⋊D3712yes—
143C4⋊C4C22⋊D3711yescharacteristic
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—21no—
147C42C22×D3711yescharacteristic
148C23—21no—
149C23—21no—
150Q8—41no—
151Q8—41no—
152Q8—1481no—
153Q8—1481no—
154D4—21no—
155D4—21no—
156D4—21no—
157D4—44no—
158D4#1059694012yescomplemented
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—1481no—
168C2×C4C2×C22⋊D3711yescharacteristic
169C2×C4C2×C22⋊D3711yescharacteristic
170C2×C4C2×C22⋊D3711yescharacteristic
171C8—742no—
172C8—1481no—
173C8—1481no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22#1192450511yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—2961no—
186C4C2×#1059694011yescharacteristic
187C4#1192455611yescharacteristic
188C4#1192456111yescharacteristic
189C4#1192456211yescharacteristic
190C2—42no—
191C2—81no—
192C2#1455767811yescharacteristic
193C2#1455768411yescharacteristic
194C2#1455771611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×#547C2
socleC22×C37#120
hypercenter#547D37
hypocenterC37#1654
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14557929C2semidirect
2. #14557813C2semidirect
3. #14557738C2semidirect
4. #14557279C2semidirect
5. D4⋊#64436C2semidirect
6. D4⋊#64436C2semidirect
58. D4×C37SD16semidirect
105. C37#1654semidirect
158. D4#10596940semidirect

Maximal subgroups

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

subgroupindex
#145579292
#145578132
#145577382
#145572792
D4⋊#644362
C37×#5472
#165437