Finite Group Databasebeta

← #18010598

Subgroups — #18010598

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#14558532C212yesmaximal, complemented
3#14558514C211yesmaximal, characteristic, complemented
4#14558404C212yesmaximal, complemented
5#14558084C211yesmaximal, characteristic
6#11924624—24no—
7D37⋊M16—22no—
8D37⋊M16C2212yes—
9#11924615C2212yes—
10#11924601—24no—
11#11924595—22no—
12C2×#10596966C2211yescharacteristic
13C2×#10596966C2211yescharacteristic
14#11924533C411yescharacteristic, complemented
15#11924525C411yescharacteristic, complemented
16#11924525C411yescharacteristic, complemented
17#11924511—22no—
18#11924498—22no—
19C42×D37C2211yescharacteristic
20C4⋊Q8×C37C411yescharacteristic, complemented
21C2×Q8×C37C2×C411yescharacteristic
22C2×Q8×C37C2×C411yescharacteristic
23#10596966—22no—
24#10596966—22no—
25#10596966—22no—
26#10596966—22no—
27C2×D148—22no—
28C2×D148—21no—
29C2×D148C2×C411yescharacteristic
30C2×D148C2×C411yescharacteristic
31C2×D148D412yes—
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37D412yes—
35C2×C4×D37C2311yescharacteristic
36C22⋊#3866—22no—
37#10596957—22no—
38C4⋊#3866—22no—
39C4×#3866—22no—
40#10596953—24no—
41#10596953D414yescomplemented
42D37⋊C8—24no—
43D37⋊C8—22no—
44C4⋊C4×C37—22no—
45C42×C37C2×C411yescharacteristic
46#10596938—22no—
47#10596938—22no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C22×D37—21no—
51C22×D37C22⋊C412yes—
52C22×D37C2×D411yescharacteristic
53C2×#3866—42no—
54Q8×C37—22no—
55Q8×C37—22no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37C22⋊C412yes—
59C2×C4×C37C22×C411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37C2×D411yescharacteristic
62D148—24no—
63D148—22no—
64D148—22no—
65D148—44no—
66D148—42no—
67C4×D37—22no—
68C4×D37—22no—
69C4×D37—42no—
70C4×D37—41no—
71C4×D37—41no—
72C4×D37C2×D412yes—
73C4×D37#4112yes—
74#64438—24no—
75C22×C37C2×C22⋊C411yescharacteristic
76C2×D37—22no—
77C2×D37—41no—
78C2×D37—42no—
79C2×D37—42no—
80C2×D37—41no—
81C2×D37#12112yes—
82#3866—82no—
83C4×C37—22no—
84C4×C37—22no—
85C4×C37—41no—
86C4×C37C4×D412yes—
87Dic37—41no—
88Dic37#12011yescharacteristic
89Dic37#12311yescharacteristic
90#1884—371nomaximal, Sylow
91C2×C37—21no—
92C2×C37#38611yescharacteristic
93D37—22no—
94D37—42no—
95D37—81no—
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#386611yescharacteristic, complemented
108#127—371no—
109#124—371no—
110#124—371no—
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×Q8C2×#386611yescharacteristic
122C2×Q8C2×#386611yescharacteristic
123C2×D4—372no—
124C2×D4—371no—
125C2×D4—371no—
126C2×D4—742no—
127C2×D4—741no—
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—22no—
138C4⋊C4—742no—
139C22⋊C4—742no—
140C22⋊C4—742no—
141C22⋊C4—742no—
142C42—371no—
143C42—741no—
144C42—742no—
145C42C2×#386611yescharacteristic
146C23—371no—
147C23—372no—
148C23—741no—
149Q8—22no—
150Q8—22no—
151D4—744no—
152D4—742no—
153D4—742no—
154D4—1484no—
155D4—1482no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—371no—
159C2×C4—372no—
160C2×C4—372no—
161C2×C4—742no—
162C2×C4—742no—
163C2×C4—741no—
164C2×C4—1482no—
165C2×C4—1481no—
166C2×C4—1481no—
167C2×C4—1482no—
168C2×C4C22⋊#386612yes—
169C2×C4C22×#386611yescharacteristic
170C8—744no—
171C22—372no—
172C22—742no—
173C22—1482no—
174C22—1481no—
175C22—1482no—
176C22—1481no—
177C22C2×C22⋊#386611yescharacteristic
178C4—22no—
179C4—22no—
180C4—41no—
181C4—371no—
182C4—371no—
183C4—2962no—
184C4—1481no—
185C4D4×#386612yes—
186C2—21no—
187C2—2961no—
188C2—742no—
189C2—1482no—
190C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC2×C37#386
prime radical#14558084C2
cosocleC2×C4×D37C23
hypercenterC4⋊Q8#3866
hypocenterC37#1884
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14558613C2semidirect
2. #14558532C2semidirect
3. #14558514C2semidirect
4. #14558404C2semidirect
14. #11924533C4semidirect
15. #11924525C4semidirect
16. #11924525C4semidirect
20. C4⋊Q8×C37C4semidirect
41. #10596953D4semidirect
101. C37#1884semidirect
107. C4⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145586132
#145585322
#145585142
#145584042
#145580842
#188437