Finite Group Databasebeta

← #17993205

Subgroups — #17993205

Order 4736.

256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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#14558082C211yesmaximal, characteristic
2#14557588C211yesmaximal, characteristic, complemented
3#97×D37C211yesmaximal, characteristic, complemented
4#14557273C211yesmaximal, characteristic, complemented
5#14557272C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#329C211yesmaximal, characteristic, complemented
8C2×#10596966C411yescharacteristic
9C2×#10596964C411yescharacteristic
10C2×C8×D37—21no—
11#11924534C411yescharacteristic
12#11924532C411yescharacteristic
13#11924524C2211yescharacteristic
14#11924509—21no—
15#11924509—21no—
16#11924496—21no—
17#11924496—21no—
18C42×D37C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924447C2211yescharacteristic
22#11924447C2211yescharacteristic
23#11924446—21no—
24#124×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C2×D4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C22×Dic37—21no—
33#10596966—42no—
34#10596964—42no—
35C2×D148—21no—
36C2×D148C2×C411yescharacteristic
37C2×C4×D37—21no—
38C2×C4×D37C2×C411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×Dic74C2×C411yescharacteristic
42C2×C8×C37—21no—
43C2×C8×C37—21no—
44C22⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C42×C37C2311yescharacteristic
47#10596938—21no—
48#10596938—21no—
49#10596936—21no—
50#10596936—21no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C2×#64436—21no—
56C8×D37—24no—
57C23×C37—21no—
58C22×D37—21no—
59C22×D37C22⋊C411yescharacteristic
60Q8×C37—41no—
61D4×C37—41no—
62C2×C4×C37—21no—
63C2×C4×C37C22×C411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C22⋊D37—42no—
67C22⋊D37—42no—
68C22⋊D37—42no—
69C2×Dic37—21no—
70C2×Dic37—42no—
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74D148—41no—
75D148—42no—
76C4×D37—22no—
77C4×D37—22no—
78C4×D37—41no—
79C4×D37—42no—
80Dic74—41no—
81C8×C37—22no—
82C8×C37—41no—
83#64436—22no—
84#64436—41no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37—41no—
88C22×C37C2×C22⋊C411yescharacteristic
89C2×D37—21no—
90C2×D37—21no—
91C2×D37—41no—
92C2×D37—41no—
93C2×D37—41no—
94C2×D37#10012yes—
95C4×C37—21no—
96C4×C37—21no—
97C4×C37—21no—
98C4×C37—41no—
99Dic37—21no—
100Dic37—21no—
101Dic37—41no—
102Dic37#10412yes—
103#1530—371nomaximal, Sylow
104C2×C37—81no—
105C2×C37C2×#10011yescharacteristic
106C2×C37C2×#10411yescharacteristic
107C2×C37#42111yescharacteristic
108D37—22no—
109D37—81no—
110#532—371no—
111#432—371no—
112C2×#97—371no—
113#329—371no—
114#329—371no—
115#329—371no—
116#329D3711yescharacteristic, complemented
117C37#153011yescharacteristic, complemented, Sylow
118C2×#41—371no—
119C2×#41—371no—
120C22×C8—741no—
121C4⋊Q8—371no—
122#127—371no—
123#124—371no—
124#124C2×D3711yescharacteristic
125#121—741no—
126#121—741no—
127C4×D4—741no—
128C4×D4—741no—
129C2×C42—371no—
130C4⋊C8—741no—
131C22⋊C8—741no—
132#97—371no—
133#97—371no—
134#97—741no—
135#97C2×D3711yescharacteristic
136#97C2×D3711yescharacteristic
137#41—1482no—
138#41—1482no—
139C2×Q8—371no—
140C2×Q8C4×D3711yescharacteristic
141C2×D4—371no—
142C2×D4—741no—
143C2×D4—741no—
144C2×D4—741no—
145C2×D4—741no—
146C2×D4C4×D3711yescharacteristic
147C22×C4—371no—
148C22×C4—371no—
149C22×C4—371no—
150C22×C4—741no—
151C22×C4—741no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—744no—
155C2×C8—741no—
156C2×C8—741no—
157C4⋊C4—741no—
158C4⋊C4—741no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—741no—
162C22⋊C4—741no—
163C42—371no—
164C42—371no—
165C42—371no—
166C42C22×D3711yescharacteristic
167C23—21no—
168C23—371no—
169C23—741no—
170Q8—41no—
171Q8—1481no—
172D4—41no—
173D4—1481no—
174D4—1482no—
175D4—1482no—
176D4—1482no—
177D4—1482no—
178C2×C4—21no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4—741no—
185C2×C4—1481no—
186C2×C4—1482no—
187C2×C4—1482no—
188C2×C4C2×C4×D3711yescharacteristic
189C2×C4D4×D3711yescharacteristic
190C2×C4D4×D3711yescharacteristic
191C8—22no—
192C8—41no—
193C8—742no—
194C8—1481no—
195C22—41no—
196C22—41no—
197C22—41no—
198C22—372no—
199C22—741no—
200C22—741no—
201C22—1481no—
202C22—1481no—
203C22—1481no—
204C22C22⋊C4×D3711yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—41no—
209C4—372no—
210C4—741no—
211C4—741no—
212C4—1481no—
213C2—81no—
214C2—2961no—
215C2—742no—
216C2#100×D3711yescharacteristic
217C2#104×D3711yescharacteristic
218C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37C2×C22⋊C4
prime radical#14558082C2
cosocleC42×C37C23
hypercenter#329D37
hypocenterC37#1530
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14557588C2semidirect
3. #97×D37C2semidirect
4. #14557273C2semidirect
5. #14557272C2semidirect
6. #14557272C2semidirect
7. C37×#329C2semidirect
116. #329D37semidirect
117. C37#1530semidirect

Maximal subgroups

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

subgroupindex
#145580822
#145575882
#97×D372
#145572732
#145572722
C37×#3292
#153037