Finite Group Databasebeta

← #18010857

Subgroups — #18010857

Order 4736.

266 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 54 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#14558519C211yesmaximal, characteristic, complemented
2#14558512C211yesmaximal, characteristic, complemented
3#14558434C214yesmaximal, complemented
4#14558102C211yesmaximal, characteristic
5D37⋊M16—21no—
6#11924615—21no—
7#11924597—21no—
8#11924596C2212yes—
9#11924595—21no—
10#11924594C2212yes—
11C2×#10596962C2211yescharacteristic
12C22×D148C411yescharacteristic, complemented
13#11924533—21no—
14#11924524—21no—
15#11924511—21no—
16#11924511—21no—
17#11924506C412yescomplemented
18#11924506C2212yes—
19#117×C37C411yescharacteristic, complemented
20C23×D37C2×C412yes—
21C22×C4×C37C2×C411yescharacteristic
22C2×C22⋊D37C2×C411yescharacteristic
23C2×C22⋊D37C2311yescharacteristic
24#10596962—41no—
25#10596962—41no—
26C2×D148—21no—
27C2×D148—21no—
28C2×D148—22no—
29C2×D148—22no—
30C2×D148—41no—
31C2×D148—41no—
32C2×D148D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×Dic74D411yescharacteristic
36C22⋊#3866—22no—
37#10596957—22no—
38C4⋊#3866—41no—
39C4×#3866—41no—
40#10596953—41no—
41D37⋊C8—41no—
42C4⋊C4×C37—21no—
43C22⋊C4×C37C2×C412yes—
44C42×C37—21no—
45#10596938—22no—
46#10596938—22no—
47C23×C37C22×C411yescharacteristic
48C22×D37—22no—
49C22×D37—42no—
50C22×D37—82no—
51C22×D37C22⋊C411yescharacteristic
52C22×D37C2×D411yescharacteristic
53C2×#3866—42no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—22no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C22⋊D37—41no—
60C22⋊D37—41no—
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63D148—41no—
64D148—42no—
65D148—41no—
66D148—41no—
67D148—82no—
68D148—82no—
69C4×D37—21no—
70C4×D37—21no—
71C4×D37—21no—
72C4×D37—21no—
73Dic74—41no—
74#64438—42no—
75C22×C37—21no—
76C22×C37—41no—
77C22×C37C2×C22⋊C411yescharacteristic
78C2×D37—21no—
79C2×D37—21no—
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—42no—
83C2×D37—42no—
84C2×D37—42no—
85C2×D37—84no—
86#3866—82no—
87C4×C37—21no—
88C4×C37—42no—
89C4×C37#9911yescharacteristic
90C4×C37#9911yescharacteristic
91Dic37—21no—
92Dic37—21no—
93#2122—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—41no—
96C2×C37C2×#9911yescharacteristic
97D37—41no—
98D37—41no—
99D37—82no—
100#535—371no—
101#413—371no—
102#410—371no—
103AΣL(1,𝔽16)—374no—
104C37#212211yescharacteristic, complemented, Sylow
105C2×#41—371no—
106C22×D4—371no—
107C2×M16—741no—
108#127—741no—
109#124—741no—
110#121—741no—
111#121—741no—
112#120—372no—
113#120—372no—
114#117—741no—
115#117#386611yescharacteristic, complemented
116#101—741no—
117#100—372no—
118#99—372no—
119#99—741no—
120C24—372no—
121#41—1481no—
122#41—1481no—
123C2×Q8—371no—
124C2×D4—371no—
125C2×D4—371no—
126C2×D4—371no—
127C2×D4—742no—
128C2×D4—742no—
129C2×D4—741no—
130C2×D4—741no—
131C2×D4—1481no—
132C2×D4—1481no—
133C22×C4—371no—
134C22×C4—371no—
135C22×C4C2×#386611yescharacteristic
136M16—742no—
137M16—1481no—
138C2×C8—1481no—
139C4⋊C4—21no—
140C4⋊C4—1481no—
141C22⋊C4—742no—
142C22⋊C4—742no—
143C22⋊C4—742no—
144C22⋊C4C2×#386612yes—
145C42—21no—
146C42—1481no—
147C23—371no—
148C23—371no—
149C23—2962no—
150C23—742no—
151C23—1482no—
152C23C22×#386611yescharacteristic
153Q8—1481no—
154D4—2962no—
155D4—2962no—
156D4—1481no—
157D4—1482no—
158D4—1481no—
159D4—1481no—
160D4—1481no—
161D4—1481no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—371no—
166C2×C4—371no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—741no—
171C2×C4—1482no—
172C2×C4C22⋊#386611yescharacteristic
173C2×C4C22⋊#386611yescharacteristic
174C8—1482no—
175C22—21no—
176C22—41no—
177C22—2964no—
178C22—741no—
179C22—741no—
180C22—1482no—
181C22—1482no—
182C22—1481no—
183C22—1481no—
184C22—1482no—
185C22C2×C22⋊#386611yescharacteristic
186C4—21no—
187C4—42no—
188C4—2962no—
189C4—741no—
190C4—741no—
191C4#1192459511yescharacteristic
192C4#1192459511yescharacteristic
193C2—21no—
194C2—41no—
195C2—2962no—
196C2—1481no—
197C2—1481no—
198C2C2×#1192459511yescharacteristic
subgroupG/H
centerC2C2×#11924595
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#117×C37C4
socleC2×C37C2×#99
prime radical#14558102C2
cosocleC2×C22⋊D37C23
hypercenter#117#3866
hypocenterC37#2122
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #14558519C2semidirect
2. #14558512C2semidirect
3. #14558434C2semidirect
12. C22×D148C4semidirect
17. #11924506C4semidirect
19. #117×C37C4semidirect
104. C37#2122semidirect
115. #117#3866semidirect

Maximal subgroups

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

subgroupindex
#145585192
#145585122
#145584342
#145581022
#212237