Finite Group Databasebeta

← #18009911

Subgroups — #18009911

Order 4736.

234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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×C4⋊#64438C211yesmaximal, characteristic, complemented
2C4×#10596957C211yesmaximal, characteristic, complemented
3#14558383C212yesmaximal, complemented
4D4⋊#64438C212yesmaximal, complemented
5#14558064C211yesmaximal, characteristic
6C2×#10596957—21no—
7C22×#64438—21no—
8C4⋊#64438—21no—
9C4⋊#64438C2212yes—
10#11924591—21no—
11C4×#64438C2212yes—
12#11924529—21no—
13#11924527C411yescharacteristic
14#11924523C411yescharacteristic
15#11924517—21no—
16#11924515C411yescharacteristic
17#11924501C2211yescharacteristic
18D4×Dic37—21no—
19D4×Dic37C2211yescharacteristic
20#11924492—21no—
21C2×C4×Dic37C2211yescharacteristic
22#121×C37C411yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37—21no—
27C22×Dic37D411yescharacteristic
28C22×Dic37D411yescharacteristic
29C2×Dic74C2×C411yescharacteristic
30#10596957—24no—
31C2×#64438—22no—
32C2×#64438—22no—
33C2×#64438—42no—
34C4⋊C4×C37C2×C411yescharacteristic
35C22⋊C4×C37—21no—
36C22⋊Dic37—21no—
37C22⋊Dic37—21no—
38C22⋊Dic37—21no—
39C22⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37C2×C411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45C4×Dic37—21no—
46C4×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37C2311yescharacteristic
50C23×C37—21no—
51C23×C37C22⋊C411yescharacteristic
52D4×C37—22no—
53D4×C37—42no—
54C2×C4×C37—22no—
55C2×C4×C37—21no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C2×Dic37—22no—
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—41no—
64C2×Dic37—41no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68C2×Dic37C2×D411yescharacteristic
69Dic74—22no—
70#64438—24no—
71#64438—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37#10412yes—
78C22×C37C2×C22⋊C411yescharacteristic
79C4×C37—21no—
80C4×C37—41no—
81C4×C37#13112yes—
82Dic37—21no—
83Dic37—21no—
84Dic37—21no—
85Dic37—41no—
86Dic37—41no—
87Dic37AGL(1,ℤ/8)11yescharacteristic
88Dic37#13711yescharacteristic
89#1483—371nomaximal, Sylow
90C2×C37—22no—
91C2×C37—81no—
92C2×C37#40811yescharacteristic
93C2×C37#41711yescharacteristic
94C2×C37C2×#10411yescharacteristic
95#529—371no—
96C2×C4⋊C8—371no—
97C4×M16—371no—
98Q8⋊C8—372no—
99D4⋊C8—372no—
100C37#148311yescharacteristic, complemented, Sylow
101C2×M16—741no—
102C22×C8—741no—
103#126—741no—
104#125—371no—
105#124—371no—
106#123—741no—
107C22⋊Q8—371no—
108#121#386611yescharacteristic
109C4×Q8—371no—
110C4×D4—371no—
111C4×D4—741no—
112#117—741no—
113C2×C42—371no—
114C4⋊C8—372no—
115C4⋊C8—741no—
116#97—741no—
117C4×C8—372no—
118C2×Q8—371no—
119C2×D4—21no—
120C2×D4C2×#386611yescharacteristic
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—741no—
124C22×C4C2×#386611yescharacteristic
125M16—744no—
126C2×C8—742no—
127C2×C8—742no—
128C2×C8—1482no—
129C4⋊C4—371no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4C2×#386611yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—741no—
137C22⋊C4—741no—
138C22⋊C4—741no—
139C22⋊C4—741no—
140C42—371no—
141C42—371no—
142C42—371no—
143C42—371no—
144C42—741no—
145C23—21no—
146C23C22⋊#386611yescharacteristic
147Q8—742no—
148D4—22no—
149D4—42no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—371no—
153C2×C4—371no—
154C2×C4—371no—
155C2×C4—371no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4—742no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—1481no—
162C2×C4—1481no—
163C2×C4C22⋊#386611yescharacteristic
164C2×C4C22×#386611yescharacteristic
165C8—744no—
166C8—1482no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1192460012yes—
173C22C2×C22⋊#386611yescharacteristic
174C4—21no—
175C4—41no—
176C4—371no—
177C4—371no—
178C4—741no—
179C4—741no—
180C4—741no—
181C4—1481no—
182C4—1481no—
183C4#1192462312yes—
184C2—22no—
185C2—81no—
186C2#1455850611yescharacteristic
187C2#1455852411yescharacteristic
188C2C2×#1192460011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting, prime radical#121×C37C4
socleC22×C37C2×C22⋊C4
cosocleC4×Dic37C23
hypercenter#121#3866
hypocenterC37#1483
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#64438C2semidirect
2. C4×#10596957C2semidirect
3. #14558383C2semidirect
4. D4⋊#64438C2semidirect
100. C37#1483semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#644382
C4×#105969572
#145583832
D4⋊#644382
#145580642
#148337