Finite Group Databasebeta

← #18010600

Subgroups — #18010600

Order 4736.

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

normal subgroups only

This group has 332 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#14558531C212yesmaximal, complemented
3#14558514C211yesmaximal, characteristic, complemented
4#14558404C212yesmaximal, complemented
5#14558082C211yesmaximal, characteristic
6#11924624—24no—
7D37⋊M16—22no—
8D37⋊M16C2212yes—
9#11924615C2212yes—
10#11924600—24no—
11#11924595—22no—
12C2×#10596966C2211yescharacteristic
13C2×#10596964C2211yescharacteristic
14#11924534C411yescharacteristic, complemented
15#11924532C411yescharacteristic, complemented
16#11924524C411yescharacteristic, complemented
17#11924509—22no—
18#11924496—22no—
19C42×D37C2211yescharacteristic
20#124×C37C411yescharacteristic, complemented
21C2×Q8×C37C2×C411yescharacteristic
22C2×D4×C37C2×C411yescharacteristic
23C2×C22⋊D37—22no—
24C2×C22⋊D37—21no—
25C22×Dic37—21no—
26#10596966—22no—
27#10596966—22no—
28#10596964—22no—
29#10596964—22no—
30C2×D148C2×C411yescharacteristic
31C2×D148D412yes—
32C2×C4×D37—21no—
33C2×C4×D37D412yes—
34C2×C4×D37C2311yescharacteristic
35C2×Dic74C2×C411yescharacteristic
36C22⋊#3866—22no—
37#10596957—22no—
38C4⋊#3866—22no—
39C4×#3866—22no—
40#10596953—24no—
41#10596953D414yescomplemented
42D37⋊C8—24no—
43D37⋊C8—22no—
44C22⋊C4×C37—22no—
45C42×C37C2×C411yescharacteristic
46#10596938—22no—
47#10596936—22no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C23×C37—21no—
51C22×D37C22⋊C412yes—
52C22×D37C2×D411yescharacteristic
53C2×#3866—42no—
54Q8×C37—22no—
55D4×C37—22no—
56C2×C4×C37—21no—
57C2×C4×C37C22⋊C412yes—
58C2×C4×C37C22×C411yescharacteristic
59C22⋊D37—44no—
60C22⋊D37—42no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—41no—
64C2×Dic37—41no—
65C2×Dic37C2×D411yescharacteristic
66D148—24no—
67D148—22no—
68C4×D37—22no—
69C4×D37—22no—
70C4×D37—42no—
71C4×D37C2×D412yes—
72C4×D37#4112yes—
73Dic74—22no—
74#64438—24no—
75C22×C37—42no—
76C22×C37—41no—
77C22×C37C2×C22⋊C411yescharacteristic
78C2×D37—22no—
79C2×D37—41no—
80C2×D37—42no—
81C2×D37#12112yes—
82#3866—82no—
83C4×C37—22no—
84C4×C37—41no—
85C4×C37C4×D412yes—
86Dic37—22no—
87Dic37—41no—
88Dic37#12011yescharacteristic
89Dic37#12311yescharacteristic
90#1884—371nomaximal, Sylow
91C2×C37—21no—
92C2×C37—81no—
93C2×C37#38611yescharacteristic
94D37—22no—
95D37—42no—
96#568—371no—
97#532—371no—
98#421—372no—
99#410—371no—
100#339—372no—
101C37#188411yescharacteristic, complemented, Sylow
102C2×#41—371no—
103C2×#41—371no—
104#131—744no—
105C2×M16—372no—
106C2×M16—742no—
107C4⋊Q8—371no—
108#127—371no—
109#124—371no—
110#124#386611yescharacteristic, complemented
111#121—742no—
112C4×D4—742no—
113#117—372no—
114C2×C42—371no—
115#104—744no—
116#99—742no—
117#41—742no—
118#41—742no—
119#41—742no—
120#41—742no—
121C2×Q8—371no—
122C2×Q8C2×#386611yescharacteristic
123C2×D4—372no—
124C2×D4—371no—
125C2×D4—742no—
126C2×D4—741no—
127C2×D4C2×#386611yescharacteristic
128C22×C4—371no—
129C22×C4—372no—
130C22×C4—741no—
131C22×C4—741no—
132M16—374no—
133M16—742no—
134M16—744no—
135C2×C8—742no—
136C2×C8—744no—
137C4⋊C4—742no—
138C4⋊C4—742no—
139C22⋊C4—22no—
140C22⋊C4—742no—
141C22⋊C4—742no—
142C42—371no—
143C42—741no—
144C42—742no—
145C42C2×#386611yescharacteristic
146C23—21no—
147C23—371no—
148C23—372no—
149Q8—22no—
150Q8—742no—
151D4—22no—
152D4—744no—
153D4—742no—
154D4—1484no—
155D4—1482no—
156C2×C4—21no—
157C2×C4—371no—
158C2×C4—372no—
159C2×C4—372no—
160C2×C4—742no—
161C2×C4—742no—
162C2×C4—741no—
163C2×C4—741no—
164C2×C4—1482no—
165C2×C4—1481no—
166C2×C4—1481no—
167C2×C4—1482no—
168C2×C4C22⋊#386612yes—
169C2×C4C22×#386611yescharacteristic
170C8—744no—
171C22—42no—
172C22—41no—
173C22—372no—
174C22—742no—
175C22—1481no—
176C22—1482no—
177C22C2×C22⋊#386611yescharacteristic
178C4—22no—
179C4—41no—
180C4—371no—
181C4—371no—
182C4—2962no—
183C4—742no—
184C4—1481no—
185C4D4×#386612yes—
186C2—21no—
187C2—81no—
188C2—742no—
189C2—1482no—
190C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37#386
prime radical#14558082C2
cosocleC2×C4×D37C23
hypercenter#124#3866
hypocenterC37#1884
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. #14558531C2semidirect
3. #14558514C2semidirect
4. #14558404C2semidirect
14. #11924534C4semidirect
15. #11924532C4semidirect
16. #11924524C4semidirect
20. #124×C37C4semidirect
41. #10596953D4semidirect
101. C37#1884semidirect
110. #124#3866semidirect

Maximal subgroups

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

subgroupindex
#145586132
#145585312
#145585142
#145584042
#145580822
#188437