Finite Group Databasebeta

← #18009912

Subgroups — #18009912

Order 4736.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D37⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×#10596953C211yesmaximal, characteristic, complemented
3Q8⋊#64438C212yesmaximal, complemented
4D4⋊#64438C212yesmaximal, complemented
5#14558062C211yesmaximal, characteristic
6C2×#10596953—21no—
7C2×D37⋊C8—21no—
8#11924603—21no—
9C4⋊#64438C2212yes—
10#11924591—21no—
11C4×#64438C2212yes—
12#11924529—21no—
13#11924528C411yescharacteristic
14#11924518—21no—
15#11924512C411yescharacteristic
16#11924507C411yescharacteristic
17Q8×Dic37C2211yescharacteristic
18D4×Dic37C2211yescharacteristic
19#11924496—21no—
20#11924492—21no—
21C42×D37C2211yescharacteristic
22#124×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C2×D4×C37C2×C411yescharacteristic
25C2×C22⋊D37—21no—
26C22×Dic37—21no—
27C2×C4×D37C2×C411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×#64438—22no—
31C2×#64438—22no—
32#10596953—24no—
33D37⋊C8—42no—
34C22⋊C4×C37—21no—
35C22⋊C4×C37—21no—
36C42×C37C2×C411yescharacteristic
37C22⋊Dic37—21no—
38C22⋊Dic37—21no—
39#10596938—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37C2×C411yescharacteristic
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46C4×Dic37—21no—
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37C2311yescharacteristic
50C23×C37—21no—
51C22×D37C22⋊C411yescharacteristic
52Q8×C37—22no—
53D4×C37—22no—
54C2×C4×C37—21no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C22⋊D37—42no—
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37—41no—
62C2×Dic37—41no—
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65C2×Dic37C2×D411yescharacteristic
66C4×D37—22no—
67C4×D37—22no—
68C4×D37—21no—
69C4×D37—21no—
70#64438—24no—
71#64438—42no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37C2×C22⋊C411yescharacteristic
76C2×D37—21no—
77C2×D37—21no—
78C2×D37#10412yes—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—41no—
82C4×C37#13112yes—
83Dic37—21no—
84Dic37—21no—
85Dic37—41no—
86Dic37—41no—
87Dic37AGL(1,ℤ/8)11yescharacteristic
88Dic37#13711yescharacteristic
89#1483—371nomaximal, Sylow
90C2×C37—81no—
91C2×C37#40811yescharacteristic
92C2×C37#41711yescharacteristic
93C2×C37C2×#10411yescharacteristic
94D37—22no—
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#386611yescharacteristic
106#123—741no—
107C22⋊Q8—371no—
108#121—371no—
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×Q8C2×#386611yescharacteristic
119C2×D4—741no—
120C2×D4C2×#386611yescharacteristic
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—741no—
125M16—744no—
126C2×C8—742no—
127C2×C8—742no—
128C2×C8—1482no—
129C4⋊C4—371no—
130C4⋊C4—371no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—741no—
138C22⋊C4—741no—
139C22⋊C4—741no—
140C42—371no—
141C42—371no—
142C42—371no—
143C42—741no—
144C42C2×#386611yescharacteristic
145C23—21no—
146C23—371no—
147Q8—22no—
148D4—22no—
149D4—1482no—
150C2×C4—21no—
151C2×C4—371no—
152C2×C4—371no—
153C2×C4—371no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—742no—
157C2×C4—742no—
158C2×C4—741no—
159C2×C4—741no—
160C2×C4—1481no—
161C2×C4—1481no—
162C2×C4C22⋊#386611yescharacteristic
163C2×C4C22⋊#386611yescharacteristic
164C2×C4C22×#386611yescharacteristic
165C8—744no—
166C8—1482no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—372no—
171C22—741no—
172C22—741no—
173C22C2×C22⋊#386611yescharacteristic
174C4—21no—
175C4—21no—
176C4—41no—
177C4—371no—
178C4—371no—
179C4—741no—
180C4—741no—
181C4—1481no—
182C4—1481no—
183C4#1192462312yes—
184C2—81no—
185C2—742no—
186C2#1455850711yescharacteristic
187C2#1455852411yescharacteristic
188C2D37⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC22×C37C2×C22⋊C4
prime radical#11924507C4
cosocleC4×Dic37C23
hypercenter#124#3866
hypocenterC37#1483
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D37⋊(C4⋊C8)C2semidirect
2. C4×#10596953C2semidirect
3. Q8⋊#64438C2semidirect
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
D37⋊(C4⋊C8)2
C4×#105969532
Q8⋊#644382
D4⋊#644382
#145580622
#148337