Finite Group Databasebeta

← #17993858

Subgroups — #17993858

Order 4736.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D148C211yesmaximal, characteristic
2#14557929C211yesmaximal, characteristic, complemented
3#14557735C211yesmaximal, characteristic
4#14557280C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic
7C37×#475C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9C2×#10596941—21no—
10#11924536—21no—
11#11924536C2211yescharacteristic
12#11924516—21no—
13#11924516—22no—
14C4×D148—21no—
15C4×D148C2211yescharacteristic
16#11924467—22no—
17C4⋊#64436C2211yescharacteristic
18#11924460—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4×Q8×C37C2211yescharacteristic
22#106×C37—21no—
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37D411yescharacteristic
27Q8×D37—42no—
28Q8×D37—42no—
29C2×D148D411yescharacteristic
30C2×C4×D37—22no—
31C2×C4×D37—21no—
32C2×Dic74—22no—
33C2×Dic74—21no—
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37D411yescharacteristic
39C42×C37—21no—
40C42×C37C2311yescharacteristic
41#10596941—42no—
42#10596938—22no—
43#10596938—21no—
44C4⋊Dic37—22no—
45C4⋊Dic37—21no—
46C4⋊Dic37D411yescharacteristic
47C4⋊Dic37D412yes—
48C2×#64436—21no—
49C2×#64436—21no—
50C22×D37—21no—
51Q8×C37—21no—
52Q8×C37—41no—
53Q8×C37—41no—
54Q8×C37SD1612yescomplemented
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×Dic37—21no—
62C2×Dic37—22no—
63D148—21no—
64D148SD1612yes—
65C4×D37—44no—
66C4×D37—41no—
67C4×D37—41no—
68Dic74—44no—
69Dic74—41no—
70Dic74—41no—
71C8×C37—41no—
72#64436—22no—
73#64436—41no—
74C22×C37#12011yescharacteristic
75C2×D37—22no—
76C2×D37—41no—
77C2×D37—41no—
78C4×C37—22no—
79C4×C37—21no—
80C4×C37—41no—
81C4×C37—81no—
82C4×C37C2×SD1611yescharacteristic
83C4×C37C2×SD1611yescharacteristic
84C4×C37AGL(1,ℤ/8)11yescharacteristic
85C4×C37#13711yescharacteristic
86Dic37—41no—
87Dic37—42no—
88#1651—371nomaximal, Sylow
89C2×C37#44811yescharacteristic
90C2×C37#45011yescharacteristic
91C2×C37#45611yescharacteristic
92D37—42no—
93D4×Q8—371no—
94#498—371no—
95#475D3711yescharacteristic, complemented
96#461—371no—
97#332—371no—
98Q8⋊C8—371no—
99D4⋊C8—371no—
100C37#165111yescharacteristic, complemented, Sylow
101C22×Q8—741no—
102C2×SD16—741no—
103C4⋊Q8—371no—
104C4⋊Q8—741no—
105C4⋊Q8C2×D3711yescharacteristic
106C22⋊Q8—742no—
107C22⋊Q8—741no—
108C4×Q8C2×D3711yescharacteristic
109C4×D4—371no—
110C4×D4—741no—
111#106—21no—
112#106—742no—
113C4⋊C8—371no—
114C4⋊C8C2×D3711yescharacteristic
115#103—21no—
116#103—741no—
117C4×C8—371no—
118C2×Q8—21no—
119C2×Q8—742no—
120C2×Q8—741no—
121C2×Q8—1482no—
122C2×Q8—1482no—
123C2×Q8C22⋊D3711yescharacteristic
124C2×D4—371no—
125C22×C4—742no—
126C22×C4—741no—
127SD16—1482no—
128C2×C8—21no—
129C2×C8—741no—
130C2×C8—741no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—371no—
135C4⋊C4—372no—
136C4⋊C4—742no—
137C4⋊C4—741no—
138C4⋊C4C22⋊D3711yescharacteristic
139C22⋊C4—742no—
140C22⋊C4—741no—
141C42—21no—
142C42C22×D3711yescharacteristic
143C23—741no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—1484no—
148Q8—1481no—
149Q8—1481no—
150Q8#1059694112yescomplemented
151D4—372no—
152D4—741no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—742no—
157C2×C4—741no—
158C2×C4—1484no—
159C2×C4—1481no—
160C2×C4—1481no—
161C2×C4D4×D3711yescharacteristic
162C2×C4D4×D3711yescharacteristic
163C2×C4C2×C22⋊D3711yescharacteristic
164C8—41no—
165C8—742no—
166C8—1481no—
167C22—742no—
168C22—1481no—
169C22—1481no—
170C22#1192450411yescharacteristic
171C4—21no—
172C4—22no—
173C4—41no—
174C4—81no—
175C4—1482no—
176C4—1481no—
177C4SD16×D3711yescharacteristic
178C4C2×#1059694111yescharacteristic
179C4#1192456111yescharacteristic
180C4#1192456511yescharacteristic
181C2—1482no—
182C2#1455767011yescharacteristic
183C2#1455768311yescharacteristic
184C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#475C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#475D37
hypocenterC37#1651
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #14557929C2semidirect
4. #14557280C2semidirect
5. Q8⋊#64436C2semidirect
7. C37×#475C2semidirect
54. Q8×C37SD16semidirect
95. #475D37semidirect
100. C37#1651semidirect
150. Q8#10596941semidirect

Maximal subgroups

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

subgroupindex
Q8×D1482
#145579292
#145577352
#145572802
Q8⋊#644362
#145572602
C37×#4752
#165137