Finite Group Databasebeta

← #17993008

Subgroups — #17993008

Order 4736.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#14558070C211yesmaximal, characteristic
2C4⋊C8×D37C211yesmaximal, characteristic, complemented
3C4×#10596929C211yesmaximal, characteristic, complemented
4Q8⋊#64436C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596929—21no—
9C2×C8×D37—21no—
10#11924531—21no—
11#11924527C411yescharacteristic
12#11924525C411yescharacteristic
13#11924521—21no—
14#11924512C411yescharacteristic
15#11924511C411yescharacteristic
16C4×D148—21no—
17C4×D148C2211yescharacteristic
18#11924493—21no—
19C42×D37C2211yescharacteristic
20C4⋊#64436C2211yescharacteristic
21#11924465—21no—
22#11924446—21no—
23C4×#64436C2211yescharacteristic
24C4×Q8×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C2×D148—21no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37C2×C411yescharacteristic
38C42×C37—21no—
39C42×C37C2311yescharacteristic
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54#10596929—24no—
55C8×D37—42no—
56C22×D37—21no—
57C22×D37C22⋊C411yescharacteristic
58Q8×C37—21no—
59Q8×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37C22×C411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×Dic37—21no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C22⋊C411yescharacteristic
69D148—21no—
70D148—21no—
71D148—42no—
72C4×D37—22no—
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—21no—
76C4×D37—21no—
77C4×D37—41no—
78C4×D37—41no—
79C8×C37—22no—
80C8×C37—41no—
81#64436—22no—
82#64436—41no—
83C22×C37C2×C22⋊C411yescharacteristic
84C2×D37—21no—
85C2×D37—21no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—41no—
89C2×D37#10412yes—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37—41no—
93C4×C37#13111yescharacteristic
94C4×C37#13111yescharacteristic
95C4×C37AGL(1,ℤ/8)11yescharacteristic
96C4×C37#13711yescharacteristic
97Dic37—21no—
98Dic37—21no—
99Dic37—21no—
100Dic37—41no—
101#1483—371nomaximal, Sylow
102C2×C37#40811yescharacteristic
103C2×C37#41711yescharacteristic
104C2×C37C2×#10411yescharacteristic
105D37—22no—
106D37—81no—
107#529—371no—
108C2×C4⋊C8—371no—
109C4×M16—371no—
110Q8⋊C8—371no—
111Q8⋊C8D3711yescharacteristic, complemented
112D4⋊C8—371no—
113D4⋊C8—371no—
114C37#148311yescharacteristic, complemented, Sylow
115C2×M16—741no—
116C22×C8—741no—
117#126—741no—
118#125—371no—
119#124—371no—
120#123—741no—
121C22⋊Q8—371no—
122#121—371no—
123C4×Q8C2×D3711yescharacteristic
124C4×D4—371no—
125C4×D4—741no—
126#117—741no—
127C2×C42—371no—
128C4⋊C8—371no—
129C4⋊C8—741no—
130C4⋊C8C2×D3711yescharacteristic
131#97—741no—
132C4×C8—371no—
133C4×C8C2×D3711yescharacteristic
134C2×Q8C4×D3711yescharacteristic
135C2×D4—371no—
136C2×D4—741no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—371no—
140C22×C4—741no—
141M16—744no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—741no—
145C2×C8—741no—
146C2×C8—1482no—
147C4⋊C4—21no—
148C4⋊C4—371no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4C4×D3711yescharacteristic
153C22⋊C4—741no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C42—21no—
159C42—371no—
160C42—371no—
161C42—371no—
162C42C22×D3711yescharacteristic
163C23—371no—
164C23—741no—
165Q8—21no—
166Q8—21no—
167D4—741no—
168D4—741no—
169D4—1482no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—742no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4C2×C4×D3711yescharacteristic
184C2×C4D4×D3711yescharacteristic
185C2×C4D4×D3711yescharacteristic
186C8—22no—
187C8—41no—
188C8—742no—
189C8—1481no—
190C22—372no—
191C22—741no—
192C22—741no—
193C22—1481no—
194C22—1481no—
195C22—1481no—
196C22C22⋊C4×D3711yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—741no—
201C4—741no—
202C4—741no—
203C4—1481no—
204C4#1192454211yescharacteristic
205C4#1192454411yescharacteristic
206C4#1192456311yescharacteristic
207C4#1192456811yescharacteristic
208C2—2961no—
209C2—742no—
210C2#1455749811yescharacteristic
211C2#1455753311yescharacteristic
212C2#104×D3711yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37C2×C22⋊C4
prime radical#11924511C4
cosocleC42×C37C23
hypercenterQ8⋊C8D37
hypocenterC37#1483
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D37C2semidirect
3. C4×#10596929C2semidirect
4. Q8⋊#64436C2semidirect
5. #14557262C2semidirect
6. #14557260C2semidirect
7. C37×Q8⋊C8C2semidirect
111. Q8⋊C8D37semidirect
114. C37#1483semidirect

Maximal subgroups

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

subgroupindex
#145580702
C4⋊C8×D372
C4×#105969292
Q8⋊#644362
#145572622
#145572602
C37×Q8⋊C82
#148337