Finite Group Databasebeta

← #18010639

Subgroups — #18010639

Order 4736.

344 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558611C211yesmaximal, characteristic, complemented
2#14558525C212yesmaximal, complemented
3#14558513C211yesmaximal, characteristic, complemented
4#14558400C212yesmaximal, complemented
5#14558096C211yesmaximal, characteristic
6#11924623—24no—
7D37⋊M16C2212yes—
8C2×#10596957—22no—
9#11924615C2212yes—
10#11924598—24no—
11#11924594—22no—
12C2×#10596964C2211yescharacteristic
13C2×D4×D37C2211yescharacteristic
14#11924532C411yescharacteristic, complemented
15#11924524C411yescharacteristic, complemented
16#11924523C411yescharacteristic, complemented
17#11924508—22no—
18#11924504—22no—
19#11924493C2211yescharacteristic
20#127×C37C411yescharacteristic, complemented
21C23×D37—21no—
22C2×D4×C37—22no—
23C2×D4×C37C2×C411yescharacteristic
24C2×D4×C37C2×C411yescharacteristic
25C2×C22⋊D37—22no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37D412yes—
28C22×Dic37D412yes—
29#10596964—22no—
30#10596964—22no—
31D4×D37—22no—
32D4×D37—22no—
33C2×D148C2×C411yescharacteristic
34C2×C4×D37C2311yescharacteristic
35C2×Dic74C2×C411yescharacteristic
36C22⋊#3866—22no—
37#10596957—24no—
38#10596957—22no—
39C2×#64438—24no—
40C4⋊#3866—22no—
41C4×#3866—22no—
42#10596953—22no—
43D37⋊C8D414yescomplemented
44C42×C37C2×C411yescharacteristic
45C22⋊Dic37—22no—
46#10596938—21no—
47#10596938—22no—
48#10596936—21no—
49C4×Dic37C2×C411yescharacteristic
50C23×C37—21no—
51C23×C37C22⋊C412yes—
52C22×D37—21no—
53C22×D37—42no—
54C22×D37—82no—
55C22×D37C2×D411yescharacteristic
56C2×#3866—42no—
57D4×C37—22no—
58D4×C37—22no—
59D4×C37—82no—
60C2×C4×C37—21no—
61C2×C4×C37C22×C411yescharacteristic
62C22⋊D37—24no—
63C22⋊D37—41no—
64C22⋊D37—41no—
65C22⋊D37—82no—
66C2×Dic37—22no—
67C2×Dic37—22no—
68C2×Dic37—21no—
69C2×Dic37C22⋊C412yes—
70C2×Dic37C2×D411yescharacteristic
71D148—22no—
72C4×D37C2×D412yes—
73C4×D37#4112yes—
74Dic74—22no—
75#64438—24no—
76C22×C37—22no—
77C22×C37—42no—
78C22×C37—42no—
79C22×C37—41no—
80C22×C37C2×C22⋊C411yescharacteristic
81C2×D37—41no—
82C2×D37—42no—
83C2×D37—41no—
84C2×D37—84no—
85C2×D37#12112yes—
86#3866—82no—
87C4×C37—41no—
88C4×C37C4×D412yes—
89Dic37—22no—
90Dic37—41no—
91Dic37#12011yescharacteristic
92Dic37#12311yescharacteristic
93#1910—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—42no—
96C2×C37—81no—
97C2×C37#38611yescharacteristic
98D37—22no—
99D37—81no—
100#568—371no—
101#535—371no—
102#418—372no—
103#410—371no—
104H(3,ℤ/4)—372no—
105C37#191011yescharacteristic, complemented, Sylow
106C2×#41—371no—
107C22×D4—371no—
108#131—744no—
109C2×M16—372no—
110C2×M16—742no—
111#127—371no—
112#127#386611yescharacteristic, complemented
113#124—371no—
114#124—371no—
115#121—742no—
116#120—742no—
117#117—371no—
118#117—372no—
119#102—744no—
120#99—742no—
121C24—741no—
122#41—742no—
123#41—742no—
124C2×Q8—371no—
125C2×D4—22no—
126C2×D4—372no—
127C2×D4—371no—
128C2×D4—742no—
129C2×D4—742no—
130C2×D4—741no—
131C2×D4—742no—
132C2×D4C2×#386611yescharacteristic
133C2×D4C2×#386611yescharacteristic
134C22×C4—371no—
135C22×C4—372no—
136M16—742no—
137M16—742no—
138M16—744no—
139C2×C8—374no—
140C2×C8—744no—
141C4⋊C4—741no—
142C4⋊C4—742no—
143C22⋊C4—742no—
144C22⋊C4—741no—
145C22⋊C4—742no—
146C22⋊C4—742no—
147C42—371no—
148C42—742no—
149C42C2×#386611yescharacteristic
150C23—21no—
151C23—371no—
152C23—2962no—
153C23—741no—
154C23—1482no—
155C23C22⋊#386612yes—
156Q8—742no—
157D4—22no—
158D4—22no—
159D4—82no—
160D4—2962no—
161D4—744no—
162D4—742no—
163D4—1481no—
164D4—1481no—
165C2×C4—21no—
166C2×C4—371no—
167C2×C4—372no—
168C2×C4—372no—
169C2×C4—372no—
170C2×C4—742no—
171C2×C4—742no—
172C2×C4—741no—
173C2×C4—1482no—
174C2×C4C22×#386611yescharacteristic
175C8—744no—
176C22—22no—
177C22—42no—
178C22—42no—
179C22—41no—
180C22—372no—
181C22—2964no—
182C22—1482no—
183C22—1481no—
184C22—1481no—
185C22C2×C22⋊#386611yescharacteristic
186C4—41no—
187C4—371no—
188C4—371no—
189C4—2962no—
190C4—742no—
191C4—1481no—
192C4D4×#386612yes—
193C2—21no—
194C2—42no—
195C2—81no—
196C2—2961no—
197C2—742no—
198C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC2×C37#386
prime radical#14558096C2
cosocleC2×C4×D37C23
hypercenter#127#3866
hypocenterC37#1910
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14558611C2semidirect
2. #14558525C2semidirect
3. #14558513C2semidirect
4. #14558400C2semidirect
14. #11924532C4semidirect
15. #11924524C4semidirect
16. #11924523C4semidirect
20. #127×C37C4semidirect
43. D37⋊C8D4semidirect
105. C37#1910semidirect
112. #127#3866semidirect

Maximal subgroups

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

subgroupindex
#145586112
#145585252
#145585132
#145584002
#145580962
#191037