Finite Group Databasebeta

← #17994996

Subgroups — #17994996

Order 4736.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11924523C211yesmaximal, characteristic
2#14558010C211yesmaximal, characteristic, complemented
3#14557538C211yesmaximal, characteristic
4C2×#11924454C211yesmaximal, characteristic, complemented
5#14557294C211yesmaximal, characteristic, complemented
6#14557292C211yesmaximal, characteristic, complemented
7C37×#418C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924523—22no—
11#11924523C414yescomplemented
12C4×Dic74—22no—
13#11924501—22no—
14#11924495C2211yescharacteristic
15#11924492—22no—
16C2×C22⋊Dic37—22no—
17C2×C4×Dic37C2211yescharacteristic
18#11924457—22no—
19#11924454—22no—
20C22×D4×C37C2211yescharacteristic
21C2×M16×C37C2211yescharacteristic
22#117×C37C2211yescharacteristic
23#102×C37—22no—
24C24×C37—21no—
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D4×C37—21no—
30C2×D4×C37C2×C412yes—
31C22×C4×C37C2311yescharacteristic
32C22×Dic37—21no—
33C22×Dic37D412yes—
34C2×Dic74—21no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74C2×C412yes—
39C2×Dic74D412yes—
40M16×C37—21no—
41M16×C37—21no—
42C2×C8×C37—21no—
43C4⋊C4×C37D412yes—
44C22⋊C4×C37—21no—
45C42×C37—21no—
46C22⋊Dic37—21no—
47C22⋊Dic37—28no—
48C4⋊Dic37D412yes—
49#10596936—24no—
50C4×Dic37—24no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C4×Dic37C2×C412yes—
54#10596934—21no—
55#10596934—21no—
56C2×#64436—21no—
57C23×C37—22no—
58C23×C37—44no—
59C23×C37—41no—
60C23×C37—41no—
61C23×C37C2×D411yescharacteristic
62D4×C37—22no—
63D4×C37—22no—
64D4×C37—41no—
65D4×C37—41no—
66C2×C4×C37—22no—
67C2×C4×C37C22×C411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37#4111yescharacteristic
72C2×C4×C37#4111yescharacteristic
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37—42no—
78C2×Dic37C22⋊C414yes—
79Dic74—22no—
80Dic74—22no—
81Dic74—22no—
82Dic74—22no—
83C8×C37—41no—
84#64436—41no—
85C22×C37—22no—
86C22×C37—44no—
87C22×C37—42no—
88C22×C37—82no—
89C22×C37—82no—
90C22×C37C2×C22⋊C411yescharacteristic
91C22×C37#12011yescharacteristic
92C22×C37#12311yescharacteristic
93C4×C37—42no—
94C4×C37C4×D411yescharacteristic
95C4×C37C4×D411yescharacteristic
96C4×C37#12111yescharacteristic
97C4×C37#12111yescharacteristic
98Dic37—24no—
99Dic37—42no—
100Dic37—42no—
101#1888—371nomaximal, Sylow
102C2×C37—21no—
103C2×C37—21no—
104C2×C37—82no—
105C2×C37#38611yescharacteristic
106C2×C37#45412yes—
107C2×#124—371no—
108#519—371no—
109#418—371no—
110#418D3711yescharacteristic
111C2×#101—371no—
112#339—371no—
113#339—371no—
114C37#188811yescharacteristic, complemented, Sylow
115C22×Q8—371no—
116C22×D4C2×D3711yescharacteristic
117C2×M16—371no—
118C2×M16C2×D3711yescharacteristic
119#124—374no—
120#124—742no—
121C4×Q8—742no—
122C4×Q8—742no—
123#117—371no—
124#117—742no—
125#117C2×D3711yescharacteristic
126C2×C22⋊C4—742no—
127C2×C42—371no—
128#102—22no—
129#102—742no—
130#101—742no—
131C24—21no—
132C2×Q8—372no—
133C2×Q8—372no—
134C2×Q8—741no—
135C2×Q8—741no—
136C2×Q8—741no—
137C2×Q8—741no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4C4×D3712yes—
144C22×C4—372no—
145C22×C4—741no—
146C22×C4C22×D3711yescharacteristic
147M16—21no—
148M16—21no—
149M16—741no—
150M16—741no—
151C2×C8—21no—
152C2×C8—741no—
153C4⋊C4—372no—
154C4⋊C4—744no—
155C4⋊C4C22⋊D3712yes—
156C22⋊C4—21no—
157C22⋊C4—748no—
158C22⋊C4—741no—
159C42—21no—
160C42—372no—
161C42—744no—
162C42—741no—
163C42—741no—
164C23—22no—
165C23—44no—
166C23—41no—
167C23—41no—
168C23D4×D3711yescharacteristic
169Q8—742no—
170Q8—742no—
171Q8—742no—
172Q8—742no—
173D4—22no—
174D4—22no—
175D4—41no—
176D4—41no—
177C2×C4—22no—
178C2×C4—374no—
179C2×C4—742no—
180C2×C4—742no—
181C2×C4—742no—
182C2×C4—742no—
183C2×C4—1482no—
184C2×C4C2×C4×D3711yescharacteristic
185C2×C4#1059696211yescharacteristic
186C2×C4D4×D3711yescharacteristic
187C2×C4D4×D3711yescharacteristic
188C2×C4#1059696411yescharacteristic
189C2×C4C2×C22⋊D3711yescharacteristic
190C8—41no—
191C8—1481no—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—82no—
196C22—82no—
197C22C22⋊C4×D3711yescharacteristic
198C22#1192450411yescharacteristic
199C22#1192451811yescharacteristic
200C4—42no—
201C4—744no—
202C4—1482no—
203C4—1482no—
204C4#1192449611yescharacteristic
205C4C4×C22⋊D3711yescharacteristic
206C4#1192450711yescharacteristic
207C4#1192450911yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1455740911yescharacteristic
212C2#1455770412yes—
subgroupG/H
centerC22#11924504
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#418C2
socleC22×C37#120
prime radicalC22×D4×C37C22
cosocleC22×C4×C37C23
hypercenter#418D37
hypocenterC37#1888
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #14558010C2semidirect
4. C2×#11924454C2semidirect
5. #14557294C2semidirect
6. #14557292C2semidirect
11. #11924523C4semidirect
114. C37#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#119245232
#145580102
#145575382
C2×#119244542
#145572942
#145572922
C37×#4182
#188837