Finite Group Databasebeta

← #17993842

Subgroups — #17993842

Order 4736.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558198C211yesmaximal, characteristic
2#14557810C211yesmaximal, characteristic
3#14557740C211yesmaximal, characteristic, complemented
4#14557279C211yesmaximal, characteristic, complemented
5#14557265C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic
7C37×#500C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9C2×#10596942—21no—
10#11924535—21no—
11#11924514—22no—
12#11924512—21no—
13C4×Dic74C2211yescharacteristic
14C4×D148C2211yescharacteristic
15#11924498—21no—
16#11924469—21no—
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924460—21no—
20#11924456—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23#107×C37—22no—
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27Q8×D37—42no—
28Q8×D37—42no—
29C2×D148D411yescharacteristic
30C2×C4×D37—22no—
31C2×C4×D37—21no—
32C2×Dic74—22no—
33C2×Dic74D411yescharacteristic
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37D412yes—
39C42×C37C2311yescharacteristic
40#10596942—42no—
41#10596938—22no—
42#10596938—21no—
43C4⋊Dic37D411yescharacteristic
44C4⋊Dic37D411yescharacteristic
45#10596936—22no—
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C22×D37—21no—
51Q8×C37—41no—
52Q8×C37—41no—
53Q8×C37—41no—
54Q8×C37—41no—
55C2×C4×C37—22no—
56C2×C4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63D148—21no—
64D148Q1612yescomplemented
65C4×D37—44no—
66C4×D37—41no—
67C4×D37—41no—
68Dic74—21no—
69Dic74—44no—
70Dic74D812yes—
71C8×C37—22no—
72#64436—41no—
73#64436—41no—
74C22×C37#12011yescharacteristic
75C2×D37—22no—
76C2×D37—41no—
77C2×D37—41no—
78C4×C37—21no—
79C4×C37—42no—
80C4×C37—81no—
81C4×C37C2×D811yescharacteristic
82C4×C37C2×Q1611yescharacteristic
83C4×C37AGL(1,ℤ/8)11yescharacteristic
84C4×C37#13711yescharacteristic
85Dic37—22no—
86Dic37—41no—
87Dic37—41no—
88#1649—371nomaximal, Sylow
89C2×C37#44711yescharacteristic
90C2×C37#45111yescharacteristic
91C2×C37#45611yescharacteristic
92D37—42no—
93D4×Q8—371no—
94#500D3711yescharacteristic, complemented
95#474—371no—
96#462—371no—
97#332—371no—
98Q8⋊C8—371no—
99D4⋊C8—371no—
100C37#164911yescharacteristic, complemented, Sylow
101C22×Q8—741no—
102C2×Q16—741no—
103C4⋊Q8—741no—
104C4⋊Q8C2×D3711yescharacteristic
105C4⋊Q8C2×D3711yescharacteristic
106C22⋊Q8—741no—
107C22⋊Q8—742no—
108C4×Q8—371no—
109C4×D4—371no—
110C4×D4—741no—
111#107—22no—
112#107—741no—
113C4⋊C8—371no—
114C4⋊C8—371no—
115#103—741no—
116#102—741no—
117C4×C8C2×D3711yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—371no—
121C2×Q8—742no—
122C2×Q8—1482no—
123C2×Q8—1482no—
124C2×D4—371no—
125C22×C4—742no—
126C22×C4—741no—
127Q16—1482no—
128C2×C8—21no—
129C2×C8—741no—
130C2×C8—741no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—371no—
135C4⋊C4—371no—
136C4⋊C4—742no—
137C4⋊C4—741no—
138C4⋊C4C22⋊D3712yes—
139C22⋊C4—742no—
140C22⋊C4—741no—
141C42—741no—
142C42C22×D3711yescharacteristic
143C23—741no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—372no—
149Q8—741no—
150Q8—1484no—
151D4—372no—
152D4—741no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—741no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4—1484no—
159C2×C4—1481no—
160C2×C4—1481no—
161C2×C4D4×D3711yescharacteristic
162C2×C4D4×D3711yescharacteristic
163C2×C4C2×C22⋊D3711yescharacteristic
164C8—22no—
165C8—1481no—
166C8—1481no—
167C22—742no—
168C22—1481no—
169C22—1481no—
170C22#1192450411yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—742no—
175C4—1481no—
176C4—1481no—
177C4D8×D3711yescharacteristic
178C4Q16×D3711yescharacteristic
179C4#1192456011yescharacteristic
180C4#1192456811yescharacteristic
181C2—1482no—
182C2#1455766511yescharacteristic
183C2#1455768711yescharacteristic
184C2#1455771511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#500C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#500D37
hypocenterC37#1649
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #14557740C2semidirect
4. #14557279C2semidirect
5. #14557265C2semidirect
7. C37×#500C2semidirect
64. D148Q16semidirect
94. #500D37semidirect
100. C37#1649semidirect

Maximal subgroups

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

subgroupindex
#145581982
#145578102
#145577402
#145572792
#145572652
#145572622
C37×#5002
#164937