Finite Group Databasebeta

← #17993029

Subgroups — #17993029

Order 4736.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C4×#10596966C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic, complemented
3#14557584C211yesmaximal, characteristic, complemented
4Q8⋊#64436C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596966C411yescharacteristic
9Q8×Dic37C411yescharacteristic
10C4×D148—21no—
11C4×D148C2211yescharacteristic
12#11924498—21no—
13#11924498C411yescharacteristic
14#11924494—21no—
15#11924494C411yescharacteristic
16C42×D37—21no—
17C42×D37C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924448—21no—
22#11924446—21no—
23C4×#64436C2211yescharacteristic
24C4×Q8×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28#10596966—22no—
29#10596966—22no—
30C2×D148—21no—
31C2×D148C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37C2×C411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C8×C37—21no—
39C2×C8×C37—21no—
40C4⋊C4×C37—21no—
41C4⋊C4×C37C2×C411yescharacteristic
42C42×C37—21no—
43C42×C37C2311yescharacteristic
44#10596938—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37C2×C411yescharacteristic
49C4×Dic37—21no—
50C4×Dic37—21no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C2×#64436—21no—
56C22×D37—21no—
57C22×D37C22⋊C411yescharacteristic
58Q8×C37—21no—
59Q8×C37M1612yes—
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—24no—
70D148—21no—
71D148M1612yes—
72C4×D37—24no—
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—21no—
76C4×D37—21no—
77C4×D37—41no—
78C4×D37—42no—
79C4×D37—41no—
80C4×D37—41no—
81C8×C37—41no—
82C8×C37—41no—
83#64436—41no—
84#64436—41no—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—21no—
87C2×D37—22no—
88C2×D37—21no—
89C2×D37—21no—
90C2×D37—41no—
91C2×D37—41no—
92C4×C37—22no—
93C4×C37—21no—
94C4×C37—41no—
95C4×C37C2×M1611yescharacteristic
96C4×C37C2×M1611yescharacteristic
97C4×C37#13511yescharacteristic
98C4×C37#13511yescharacteristic
99Dic37—21no—
100Dic37—21no—
101Dic37—21no—
102Dic37—41no—
103#1488—371nomaximal, Sylow
104C2×C37#40711yescharacteristic
105C2×C37#41611yescharacteristic
106C2×C37#42111yescharacteristic
107D37—41no—
108D37—42no—
109C4×#41—371no—
110#432—371no—
111#431—371no—
112Q8⋊C8—371no—
113Q8⋊C8D3711yescharacteristic, complemented
114D4⋊C8—371no—
115D4⋊C8—371no—
116C37#148811yescharacteristic, complemented, Sylow
117C2×#41—371no—
118C4×Q8—371no—
119C4×Q8C2×D3711yescharacteristic
120C4×D4—371no—
121C4×D4—371no—
122C4×D4—741no—
123C4×D4—741no—
124#117—371no—
125#117—741no—
126C2×C42—371no—
127C2×C42—741no—
128C4⋊C8—371no—
129C4⋊C8—741no—
130C4⋊C8C2×D3711yescharacteristic
131C22⋊C8—741no—
132C22⋊C8—741no—
133#97—741no—
134C4×C8—371no—
135C4×C8C2×D3711yescharacteristic
136#41—742no—
137#41—742no—
138C2×Q8C4×D3711yescharacteristic
139C2×D4—371no—
140C2×D4—741no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—741no—
145C22×C4—741no—
146C22×C4—741no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—741no—
150C2×C8—741no—
151C4⋊C4—21no—
152C4⋊C4—371no—
153C4⋊C4—741no—
154C4⋊C4C4×D3711yescharacteristic
155C22⋊C4—741no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C42—21no—
159C42—371no—
160C42—371no—
161C42—371no—
162C42—741no—
163C42—741no—
164C42C22×D3711yescharacteristic
165C23—371no—
166C23—741no—
167Q8—21no—
168Q8#1059692912yes—
169D4—372no—
170D4—744no—
171D4—741no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—744no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4—741no—
183C2×C4—1481no—
184C2×C4—1482no—
185C2×C4—1481no—
186C2×C4—1481no—
187C2×C4C2×C4×D3711yescharacteristic
188C2×C4D4×D3711yescharacteristic
189C2×C4D4×D3711yescharacteristic
190C8—41no—
191C8—41no—
192C8—1481no—
193C8—1481no—
194C22—742no—
195C22—741no—
196C22—741no—
197C22—741no—
198C22—1481no—
199C22—1481no—
200C22C22⋊C4×D3711yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—741no—
205C4—741no—
206C4—741no—
207C4—1481no—
208C4M16×D3711yescharacteristic
209C4C2×#1059692911yescharacteristic
210C4#1192455711yescharacteristic
211C4#1192455911yescharacteristic
212C2—1481no—
213C2—1482no—
214C2#1455749511yescharacteristic
215C2#1455752811yescharacteristic
216C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37C2×C22⋊C4
prime radicalC2×#10596966C4
cosocleC42×C37C23
hypercenterQ8⋊C8D37
hypocenterC37#1488
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. #14557589C2semidirect
3. #14557584C2semidirect
4. Q8⋊#64436C2semidirect
5. #14557262C2semidirect
6. #14557260C2semidirect
7. C37×Q8⋊C8C2semidirect
113. Q8⋊C8D37semidirect
116. C37#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#105969662
#145575892
#145575842
Q8⋊#644362
#145572622
#145572602
C37×Q8⋊C82
#148837