Finite Group Databasebeta

← #18010477

Subgroups — #18010477

Order 4736.

272 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C2×#11924607C211yesmaximal, characteristic, complemented
2C2×#11924606C211yesmaximal, characteristic, complemented
3#14558504C212yesmaximal
4#14558409C212yesmaximal, complemented
5C2×M16×D37C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7C2×#10596953C2212yes—
8#11924607—22no—
9#11924606—22no—
10#11924593—22no—
11C22⋊#64438—22no—
12C22×C4×D37C2211yescharacteristic
13C2×#10596934C411yescharacteristic
14C2×#10596929C411yescharacteristic
15C2×#10596929C411yescharacteristic
16M16×D37—22no—
17M16×D37—22no—
18C2×C8×D37C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20C2×M16×C37C411yescharacteristic
21C23×D37Q811yescharacteristic
22C22×C4×C37C2×C411yescharacteristic
23C22×Dic37D411yescharacteristic
24C2×C4×D37—21no—
25C2×C4×D37—21no—
26C2×C4×D37—21no—
27C2×C4×D37—21no—
28C2×C4×D37C2×C411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37Q811yescharacteristic
31C2×C4×D37C2311yescharacteristic
32C2×#64438—22no—
33C2×#64438—22no—
34#10596953—22no—
35#10596953—22no—
36#10596953—22no—
37#10596953—22no—
38M16×C37—22no—
39C2×C8×C37C2×C411yescharacteristic
40C2×C8×C37C2×C411yescharacteristic
41#10596934—22no—
42C2×#64436C2×C411yescharacteristic
43C2×#64436C2×C411yescharacteristic
44#10596929—22no—
45#10596929—22no—
46C8×D37—21no—
47C8×D37—21no—
48C8×D37D412yes—
49C8×D37D412yes—
50C23×C37C4⋊C411yescharacteristic
51C22×D37—21no—
52C22×D37—21no—
53C22×D37—42no—
54C22×D37C4⋊C411yescharacteristic
55C22×D37C2×Q811yescharacteristic
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37C4⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37C4⋊C411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64C4×D37—21no—
65C4×D37—21no—
66C4×D37—21no—
67C4×D37—21no—
68C4×D37—21no—
69C4×D37—21no—
70C4×D37C2×D411yescharacteristic
71C4×D37C2×D411yescharacteristic
72C4×D37#4111yescharacteristic
73C4×D37#4111yescharacteristic
74#64438—42no—
75#64438—42no—
76C8×C37—21no—
77C8×C37C22⋊C412yes—
78#64436—21no—
79#64436C22⋊C412yes—
80C22×C37—21no—
81C22×C37—22no—
82C22×C37C2×C4⋊C411yescharacteristic
83C2×D37—22no—
84C2×D37—21no—
85C2×D37—22no—
86C2×D37—42no—
87C2×D37—42no—
88C2×D37C22⋊Q811yescharacteristic
89C2×D37C22⋊Q811yescharacteristic
90C4×C37—21no—
91C4×C37C2×C22⋊C411yescharacteristic
92C4×C37#11711yescharacteristic
93Dic37—21no—
94Dic37#12111yescharacteristic
95Dic37#12111yescharacteristic
96#1811—371nomaximal, Sylow
97C2×C37—41no—
98C2×C37#38011yescharacteristic
99C2×C37#43012yes—
100D37—21no—
101D37—21no—
102D37—41no—
103C22×M16—371no—
104C2×#108—371no—
105C2×#108—371no—
106#407—372no—
107#341—372no—
108C37#181111yescharacteristic, complemented, Sylow
109C23×C4—371no—
110C2×M16—371no—
111C2×M16—371no—
112C2×M16—371no—
113C2×M16—372no—
114C2×M16—372no—
115C2×M16—742no—
116C2×M16—742no—
117C2×M16#386611yescharacteristic
118C22×C8—371no—
119C22×C8—371no—
120#108—742no—
121#108—742no—
122C22⋊C8—742no—
123C22⋊C8—742no—
124C24—371no—
125C22×C4—371no—
126C22×C4—371no—
127C22×C4—371no—
128C22×C4—371no—
129C22×C4—371no—
130C22×C4—741no—
131C22×C4—741no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4C2×#386611yescharacteristic
135M16—22no—
136M16—742no—
137M16—742no—
138M16—742no—
139M16—742no—
140M16—742no—
141M16—742no—
142M16—742no—
143C2×C8—371no—
144C2×C8—372no—
145C2×C8—372no—
146C2×C8—371no—
147C2×C8—741no—
148C2×C8—741no—
149C2×C8—742no—
150C2×C8—742no—
151C2×C8C2×#386611yescharacteristic
152C2×C8C2×#386611yescharacteristic
153C23—371no—
154C23—371no—
155C23—741no—
156C23—741no—
157C23—1482no—
158C23C4⋊#386611yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—371no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—371no—
165C2×C4—371no—
166C2×C4—371no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—741no—
171C2×C4—741no—
172C2×C4—741no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4C4⋊#386611yescharacteristic
176C2×C4C22×#386611yescharacteristic
177C8—21no—
178C8—372no—
179C8—741no—
180C8—1482no—
181C8—1482no—
182C8C22⋊#386612yes—
183C22—21no—
184C22—22no—
185C22—371no—
186C22—371no—
187C22—742no—
188C22—741no—
189C22—742no—
190C22—1482no—
191C22—1482no—
192C22C2×C4⋊#386611yescharacteristic
193C4—21no—
194C4—371no—
195C4—371no—
196C4—741no—
197C4C2×C22⋊#386611yescharacteristic
198C4#1192461511yescharacteristic
199C2—41no—
200C2—741no—
201C2—741no—
202C2—1481no—
203C2#1455847511yescharacteristic
204C2#1455854812yes—
subgroupG/H
centerC22C2×C4⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×M16×C37C4
socleC22×C37C2×C4⋊C4
prime radicalC23×D37Q8
cosocleC2×C4×D37C23
hypercenterC2×M16#3866
hypocenterC37#1811
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#11924607C2semidirect
2. C2×#11924606C2semidirect
4. #14558409C2semidirect
108. C37#1811semidirect

Maximal subgroups

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

subgroupindex
C2×#119246072
C2×#119246062
#145585042
#145584092
C2×M16×D372
#181137