Finite Group Databasebeta

← #17993747

Subgroups — #17993747

Order 4736.

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

normal subgroups only

This group has 234 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#14557885C211yesmaximal, characteristic, complemented
2#14557823C211yesmaximal, characteristic, complemented
3#14557823C211yesmaximal, characteristic, complemented
4#14557279C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#547C211yesmaximal, characteristic
8#11924536C2211yescharacteristic
9#11924467—21no—
10#11924467—21no—
11C4⋊#64436C2211yescharacteristic
12C4⋊#64436C2211yescharacteristic
13#11924459—22no—
14#11924457—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
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C2×#64436—21no—
49C23×C37—21no—
50C23×C37—21no—
51Q8×C37—41no—
52Q8×C37—41no—
53D4×C37—21no—
54D4×C37—21no—
55D4×C37—21no—
56D4×C37—44no—
57D4×C37SD1612yes—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—22no—
61C2×C4×C37—44no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C2×Dic37—41no—
70Dic74—42no—
71#64436—41no—
72#64436—41no—
73#64436—41no—
74C22×C37—22no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37#12011yescharacteristic
81C4×C37—21no—
82C4×C37—41no—
83C4×C37—42no—
84C4×C37—41no—
85C4×C37C2×SD1611yescharacteristic
86C4×C37#13511yescharacteristic
87C4×C37AGL(1,ℤ/8)11yescharacteristic
88C4×C37#13711yescharacteristic
89Dic37—81no—
90#1635—371nomaximal, Sylow
91C2×C37—42no—
92C2×C37—81no—
93C2×C37#45011yescharacteristic
94C2×C37#45211yescharacteristic
95C2×C37#45411yescharacteristic
96#547D3711yescharacteristic
97#487—371no—
98#476—371no—
99#476—371no—
100#332—371no—
101D4⋊C8—371no—
102D4⋊C8—371no—
103C37#163511yescharacteristic, complemented, Sylow
104C2×#41—21no—
105C4⋊Q8—371no—
106C4⋊Q8C2×D3711yescharacteristic
107#123—22no—
108C22⋊Q8—21no—
109#121—21no—
110C4×D4C2×D3711yescharacteristic
111C4×D4C2×D3711yescharacteristic
112C2×C4⋊C4—21no—
113#106—741no—
114#106—741no—
115C4⋊C8—371no—
116C4⋊C8—371no—
117#103—742no—
118#102—741no—
119#102—741no—
120C4×C8—371no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×Q8—741no—
125C2×D4—22no—
126C2×D4C22⋊D3711yescharacteristic
127C2×D4C22⋊D3711yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C2×C8—741no—
132C2×C8—741no—
133C2×C8—741no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—741no—
137C4⋊C4—741no—
138C4⋊C4C22⋊D3712yes—
139C4⋊C4C22⋊D3711yescharacteristic
140C4⋊C4C22⋊D3711yescharacteristic
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C42C22×D3711yescharacteristic
145C23—21no—
146C23—21no—
147Q8—41no—
148Q8—41no—
149Q8—1482no—
150D4—21no—
151D4—21no—
152D4—21no—
153D4—44no—
154D4#1059694012yes—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1481no—
164C2×C4C2×C22⋊D3711yescharacteristic
165C2×C4C2×C22⋊D3711yescharacteristic
166C2×C4C2×C22⋊D3711yescharacteristic
167C8—1481no—
168C8—1481no—
169C8—1481no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#1192450511yescharacteristic
177C4—21no—
178C4—41no—
179C4—42no—
180C4—41no—
181C4—2961no—
182C4C2×#1059694011yescharacteristic
183C4#1192455611yescharacteristic
184C4#1192456211yescharacteristic
185C4#1192456611yescharacteristic
186C2—42no—
187C2—81no—
188C2#1455768411yescharacteristic
189C2#1455769511yescharacteristic
190C2#1455770611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×#547C2
socleC22×C37#120
hypercenter#547D37
hypocenterC37#1635
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. #14557885C2semidirect
2. #14557823C2semidirect
3. #14557823C2semidirect
4. #14557279C2semidirect
5. D4⋊#64436C2semidirect
6. D4⋊#64436C2semidirect
103. C37#1635semidirect

Maximal subgroups

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

subgroupindex
#145578852
#145578232
#145572792
D4⋊#644362
C37×#5472
#163537