Finite Group Databasebeta

← #17996522

Subgroups — #17996522

Order 4736.

230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#11924559C211yesmaximal, characteristic, complemented
2C2×#11924479C211yesmaximal, characteristic, complemented
3C2×D592C211yesmaximal, characteristic, complemented
4#14557770C211yesmaximal, characteristic, complemented
5#14557333C211yesmaximal, characteristic, complemented
6#14557312C211yesmaximal, characteristic, complemented
7C37×#358C211yesmaximal, characteristic, complemented
8C2×#10596966—21no—
9#11924559—22no—
10#11924559—22no—
11C2×#10596941—21no—
12C2×D296C2211yescharacteristic
13C2×D296C2211yescharacteristic
14C2×C8×D37C2211yescharacteristic
15#11924511—21no—
16#11924479—22no—
17D592—22no—
18C2×#10596925C2211yescharacteristic
19#11924456—21no—
20C2×Q16×C37C2211yescharacteristic
21C2×C16×C37C2211yescharacteristic
22#107×C37C2211yescharacteristic
23C2×Q8×C37—21no—
24#10596966—24no—
25#10596966—42no—
26C2×D148—21no—
27C2×D148—21no—
28C2×D148—41no—
29C2×D148—41no—
30C2×C4×D37—41no—
31C2×C4×D37D411yescharacteristic
32Q16×C37—21no—
33Q16×C37D412yescomplemented
34C2×C8×C37C2311yescharacteristic
35C4⋊C4×C37—21no—
36#10596941—24no—
37#10596938—41no—
38C2×#64436D411yescharacteristic
39D296—21no—
40D296—21no—
41D296—21no—
42D296D412yescomplemented
43C8×D37—21no—
44C8×D37—21no—
45C16×C37—21no—
46#10596925—21no—
47C22×D37—41no—
48C22×D37—41no—
49C22×D37D811yescharacteristic
50Q8×C37—22no—
51Q8×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37C2×D411yescharacteristic
55C2×Dic37D811yescharacteristic
56D148—22no—
57D148—44no—
58D148—41no—
59D148—41no—
60D148—41no—
61D148—82no—
62C4×D37—21no—
63C4×D37—21no—
64C4×D37—44no—
65C8×C37C2×D411yescharacteristic
66C8×C37C2×D411yescharacteristic
67#64436—21no—
68C22×C37C2×D811yescharacteristic
69C2×D37—21no—
70C2×D37—21no—
71C2×D37—21no—
72C2×D37—42no—
73C2×D37—81no—
74C2×D37—81no—
75C2×D37—81no—
76C2×D37—81no—
77C2×D37—81no—
78C4×C37—42no—
79C4×C37—81no—
80C4×C37#12011yescharacteristic
81C4×C37AGL(1,ℤ/8)11yescharacteristic
82Dic37—21no—
83#2186—371nomaximal, Sylow
84C2×C37#44711yescharacteristic
85C2×C37#50811yescharacteristic
86C2×C37#50911yescharacteristic
87D37—41no—
88D37—82no—
89D37—161no—
90C2×#135—371no—
91C2×SD32—371no—
92C2×D16—371no—
93#466—371no—
94#358D3711yescharacteristic, complemented
95#357—371no—
96C22⋊C16—371no—
97C37#218611yescharacteristic, complemented, Sylow
98C2×#41—741no—
99#135—742no—
100#135—742no—
101C2×Q16C2×D3711yescharacteristic
102C2×SD16—741no—
103C2×D8—371no—
104C2×D8—371no—
105C22×C8—371no—
106#121—741no—
107SD32—742no—
108D16—742no—
109C2×C16—371no—
110C2×C16C2×D3711yescharacteristic
111#107C2×D3711yescharacteristic
112#102—741no—
113#41—744no—
114#41—1482no—
115C2×Q8—21no—
116C2×D4—741no—
117C2×D4—741no—
118C2×D4—1481no—
119C2×D4—1481no—
120C22×C4—371no—
121C22×C4—1481no—
122Q16—21no—
123Q16D14812yescomplemented
124SD16—744no—
125D8—372no—
126D8—741no—
127D8—741no—
128D8—741no—
129C2×C8—371no—
130C2×C8—741no—
131C2×C8—741no—
132C2×C8C22×D3711yescharacteristic
133C4⋊C4—21no—
134C22⋊C4—1481no—
135C16—21no—
136C16—741no—
137C23—371no—
138C23—1481no—
139C23—1481no—
140Q8—22no—
141Q8—41no—
142D4—2962no—
143D4—742no—
144D4—1484no—
145D4—1481no—
146D4—1481no—
147D4—1481no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—371no—
151C2×C4—741no—
152C2×C4—741no—
153C2×C4—1484no—
154C2×C4D4×D3711yescharacteristic
155C8—741no—
156C8C2×D14811yescharacteristic
157C8D4×D3711yescharacteristic
158C22—2961no—
159C22—2961no—
160C22—2961no—
161C22—2961no—
162C22—2961no—
163C22—741no—
164C22—741no—
165C22—741no—
166C22—1482no—
167C22D8×D3711yescharacteristic
168C4—42no—
169C4—81no—
170C4—741no—
171C4#1192450611yescharacteristic
172C4#1192456311yescharacteristic
173C2—2962no—
174C2—5921no—
175C2—1481no—
176C2#1455766811yescharacteristic
177C2#1455796611yescharacteristic
178C2#1455797011yescharacteristic
subgroupG/H
centerC22D8×D37
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#358C2
socleC22×C37C2×D8
hypercenter#358D37
hypocenterC37#2186
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×#11924559C2semidirect
2. C2×#11924479C2semidirect
3. C2×D592C2semidirect
4. #14557770C2semidirect
5. #14557333C2semidirect
6. #14557312C2semidirect
7. C37×#358C2semidirect
33. Q16×C37D4semidirect
42. D296D4semidirect
94. #358D37semidirect
97. C37#2186semidirect
123. Q16D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245592
C2×#119244792
C2×D5922
#145577702
#145573332
#145573122
C37×#3582
#218637