Finite Group Databasebeta

← #18010640

Subgroups — #18010640

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#14558613C211yesmaximal, characteristic, complemented
2#14558525C212yesmaximal, complemented
3#14558514C211yesmaximal, characteristic, complemented
4#14558400C212yesmaximal, complemented
5#14558101C211yesmaximal, characteristic
6#11924624—24no—
7D37⋊M16—22no—
8D37⋊M16C2212yes—
9#11924615C2212yes—
10#11924598—24no—
11#11924595—22no—
12C2×#10596966C2211yescharacteristic
13C2×D4×D37C2211yescharacteristic
14#11924533C411yescharacteristic, complemented
15#11924532C411yescharacteristic, complemented
16#11924525C411yescharacteristic, complemented
17#11924509—22no—
18#11924506—22no—
19#11924493C2211yescharacteristic
20#124×C37C411yescharacteristic, complemented
21C23×D37—21no—
22C2×Q8×C37C2×C411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C2×C22⋊D37—22no—
25C2×C22⋊D37—21no—
26#10596966—22no—
27#10596966—22no—
28D4×D37—22no—
29D4×D37—22no—
30C2×D148—22no—
31C2×D148C2×C411yescharacteristic
32C2×D148C2×C411yescharacteristic
33C2×D148D412yes—
34C2×C4×D37D412yes—
35C2×C4×D37C2311yescharacteristic
36C22⋊#3866—22no—
37#10596957—22no—
38C4⋊#3866—22no—
39C4×#3866—22no—
40#10596953—24no—
41#10596953—22no—
42D37⋊C8—24no—
43D37⋊C8D414yescomplemented
44C22⋊C4×C37—22no—
45C42×C37C2×C411yescharacteristic
46#10596938—21no—
47#10596938—22no—
48#10596936—21no—
49C4×Dic37C2×C411yescharacteristic
50C23×C37—21no—
51C22×D37—21no—
52C22×D37—42no—
53C22×D37—82no—
54C22×D37C22⋊C412yes—
55C22×D37C2×D411yescharacteristic
56C2×#3866—42no—
57Q8×C37—22no—
58D4×C37—22no—
59C2×C4×C37—21no—
60C2×C4×C37C22⋊C412yes—
61C2×C4×C37C22×C411yescharacteristic
62C22⋊D37—41no—
63C22⋊D37—41no—
64C22⋊D37—82no—
65C2×Dic37—21no—
66C2×Dic37C2×D411yescharacteristic
67D148—24no—
68D148—22no—
69D148—22no—
70D148—82no—
71C4×D37—22no—
72C4×D37—22no—
73C4×D37C2×D412yes—
74C4×D37#4112yes—
75#64438—24no—
76C22×C37—42no—
77C22×C37—41no—
78C22×C37C2×C22⋊C411yescharacteristic
79C2×D37—22no—
80C2×D37—41no—
81C2×D37—42no—
82C2×D37—42no—
83C2×D37—41no—
84C2×D37—84no—
85C2×D37#12112yes—
86#3866—82no—
87C4×C37—22no—
88C4×C37—41no—
89C4×C37C4×D412yes—
90Dic37—41no—
91Dic37#12011yescharacteristic
92Dic37#12311yescharacteristic
93#1910—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—81no—
96C2×C37#38611yescharacteristic
97D37—22no—
98D37—42no—
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—371no—
113#124—371no—
114#124#386611yescharacteristic, complemented
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×Q8C2×#386611yescharacteristic
125C2×D4—372no—
126C2×D4—371no—
127C2×D4—371no—
128C2×D4—742no—
129C2×D4—742no—
130C2×D4—742no—
131C2×D4—741no—
132C2×D4—742no—
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—22no—
144C22⋊C4—741no—
145C22⋊C4—742no—
146C22⋊C4—742no—
147C42—371no—
148C42—742no—
149C42C2×#386611yescharacteristic
150C23—21no—
151C23—371no—
152C23—372no—
153C23—2962no—
154C23—741no—
155C23—1482no—
156Q8—22no—
157D4—22no—
158D4—2962no—
159D4—2962no—
160D4—744no—
161D4—742no—
162D4—742no—
163D4—1481no—
164D4—1481no—
165C2×C4—21no—
166C2×C4—371no—
167C2×C4—372no—
168C2×C4—372no—
169C2×C4—742no—
170C2×C4—742no—
171C2×C4—741no—
172C2×C4—1482no—
173C2×C4C22⋊#386612yes—
174C2×C4C22×#386611yescharacteristic
175C8—744no—
176C22—42no—
177C22—41no—
178C22—372no—
179C22—2964no—
180C22—742no—
181C22—1482no—
182C22—1481no—
183C22—1482no—
184C22—1481no—
185C22C2×C22⋊#386611yescharacteristic
186C4—22no—
187C4—41no—
188C4—371no—
189C4—371no—
190C4—2962no—
191C4—1481no—
192C4D4×#386612yes—
193C2—21no—
194C2—81no—
195C2—2961no—
196C2—742no—
197C2—1482no—
198C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37#386
prime radical#14558101C2
cosocleC2×C4×D37C23
hypercenter#124#3866
hypocenterC37#1910
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14558613C2semidirect
2. #14558525C2semidirect
3. #14558514C2semidirect
4. #14558400C2semidirect
14. #11924533C4semidirect
15. #11924532C4semidirect
16. #11924525C4semidirect
20. #124×C37C4semidirect
43. D37⋊C8D4semidirect
105. C37#1910semidirect
114. #124#3866semidirect

Maximal subgroups

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

subgroupindex
#145586132
#145585252
#145585142
#145584002
#145581012
#191037