Finite Group Databasebeta

← #17996520

Subgroups — #17996520

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×#11924555C211yesmaximal, characteristic, complemented
2C2×#11924481C211yesmaximal, characteristic, complemented
3C2×#11924477C211yesmaximal, characteristic, complemented
4#14557770C211yesmaximal, characteristic, complemented
5#14557336C211yesmaximal, characteristic, complemented
6#14557312C211yesmaximal, characteristic, complemented
7C37×#357C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9#11924555—22no—
10#11924555—22no—
11C2×Dic148C2211yescharacteristic
12C2×#10596940—21no—
13C2×D296C2211yescharacteristic
14C2×C8×D37C2211yescharacteristic
15#11924511—21no—
16#11924481—22no—
17#11924477—22no—
18C2×#10596925C2211yescharacteristic
19#11924456—21no—
20C2×D8×C37C2211yescharacteristic
21C2×C16×C37C2211yescharacteristic
22#107×C37C2211yescharacteristic
23C2×D4×C37—21no—
24C2×C22⋊D37—41no—
25C22×Dic37—41no—
26#10596964—24no—
27#10596964—42no—
28C2×D148—21no—
29C2×D148—41no—
30C2×C4×D37D411yescharacteristic
31C2×Dic74—21no—
32D8×C37—21no—
33D8×C37D412yescomplemented
34C2×C8×C37C2311yescharacteristic
35C4⋊C4×C37—21no—
36#10596940—24no—
37#10596938—41no—
38C2×#64436D411yescharacteristic
39Dic148—21no—
40Dic148D412yescomplemented
41D296—21no—
42D296—21no—
43C8×D37—21no—
44C8×D37—21no—
45C16×C37—21no—
46#10596925—21no—
47C23×C37—41no—
48C22×D37—41no—
49C22×D37D811yescharacteristic
50D4×C37—22no—
51D4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37C2×D411yescharacteristic
54C22⋊D37—44no—
55C2×Dic37—44no—
56C2×Dic37—41no—
57C2×Dic37D811yescharacteristic
58D148—41no—
59D148—41no—
60D148—82no—
61C4×D37—21no—
62C4×D37—21no—
63Dic74—22no—
64Dic74—41no—
65C8×C37C2×D411yescharacteristic
66C8×C37C2×D411yescharacteristic
67#64436—21no—
68C22×C37—42no—
69C22×C37—81no—
70C22×C37—81no—
71C22×C37C2×D811yescharacteristic
72C2×D37—21no—
73C2×D37—21no—
74C2×D37—21no—
75C2×D37—81no—
76C2×D37—81no—
77C2×D37—81no—
78C4×C37—81no—
79C4×C37#12011yescharacteristic
80C4×C37AGL(1,ℤ/8)11yescharacteristic
81Dic37—21no—
82Dic37—42no—
83#2186—371nomaximal, Sylow
84C2×C37—82no—
85C2×C37#44711yescharacteristic
86C2×C37#50811yescharacteristic
87C2×C37#50911yescharacteristic
88D37—41no—
89D37—161no—
90C2×#135—371no—
91C2×SD32—371no—
92C2×D16—371no—
93#466—371no—
94#358—371no—
95#357D3711yescharacteristic, complemented
96C22⋊C16—371no—
97C37#218611yescharacteristic, complemented, Sylow
98C2×#41—741no—
99#135—742no—
100#135—742no—
101C2×Q16—371no—
102C2×SD16—741no—
103C2×D8—371no—
104C2×D8C2×D3711yescharacteristic
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—741no—
116C2×D4—21no—
117C2×D4—741no—
118C2×D4—1481no—
119C2×D4—1481no—
120C22×C4—371no—
121C22×C4—1481no—
122Q16—372no—
123Q16—741no—
124SD16—744no—
125D8—21no—
126D8—741no—
127D8—741no—
128D8D14812yescomplemented
129C2×C8—371no—
130C2×C8—741no—
131C2×C8—741no—
132C2×C8C22×D3711yescharacteristic
133C4⋊C4—21no—
134C22⋊C4—1481no—
135C16—21no—
136C16—741no—
137C23—41no—
138C23—371no—
139C23—1481no—
140Q8—742no—
141Q8—1481no—
142D4—22no—
143D4—41no—
144D4—2962no—
145D4—1484no—
146D4—1481no—
147D4—1481no—
148C2×C4—41no—
149C2×C4—371no—
150C2×C4—741no—
151C2×C4—741no—
152C2×C4—1484no—
153C2×C4—1481no—
154C2×C4D4×D3711yescharacteristic
155C8—741no—
156C8C2×D14811yescharacteristic
157C8D4×D3711yescharacteristic
158C22—42no—
159C22—81no—
160C22—81no—
161C22—2961no—
162C22—2961no—
163C22—2961no—
164C22—741no—
165C22—741no—
166C22—741no—
167C22D8×D3711yescharacteristic
168C4—81no—
169C4—741no—
170C4—1482no—
171C4#1192450611yescharacteristic
172C4#1192456311yescharacteristic
173C2—82no—
174C2—5921no—
175C2—1481no—
176C2#1455766811yescharacteristic
177C2#1455796411yescharacteristic
178C2#1455796711yescharacteristic
subgroupG/H
centerC22D8×D37
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#357C2
socleC22×C37C2×D8
hypercenter#357D37
hypocenterC37#2186
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. C2×#11924555C2semidirect
2. C2×#11924481C2semidirect
3. C2×#11924477C2semidirect
4. #14557770C2semidirect
5. #14557336C2semidirect
6. #14557312C2semidirect
7. C37×#357C2semidirect
33. D8×C37D4semidirect
40. Dic148D4semidirect
95. #357D37semidirect
97. C37#2186semidirect
128. D8D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245552
C2×#119244812
C2×#119244772
#145577702
#145573362
#145573122
C37×#3572
#218637