Finite Group Databasebeta

← #17993192

Subgroups — #17993192

Order 4736.

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

normal subgroups only

This group has 264 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#124×D37C211yesmaximal, characteristic
2#14557588C211yesmaximal, characteristic, complemented
3#14557485C211yesmaximal, characteristic, complemented
4#14557273C211yesmaximal, characteristic, complemented
5#14557272C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#329C211yesmaximal, characteristic, complemented
8C2×Q8×D37C411yescharacteristic
9C2×D4×D37C411yescharacteristic
10C2×#10596929—21no—
11#11924525C411yescharacteristic
12#11924524C2211yescharacteristic
13#11924523C411yescharacteristic
14#11924522—21no—
15#11924522—21no—
16C22⋊C4×D37—21no—
17C22⋊C4×D37—21no—
18C42×D37C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924447C2211yescharacteristic, complemented
22#11924447C2211yescharacteristic, complemented
23C8×Dic37—21no—
24#124×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic, complemented
26#97×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C2×Q8×C37C2×C411yescharacteristic
29C2×D4×C37C2×C411yescharacteristic
30C2×C22⋊D37—21no—
31Q8×D37—42no—
32D4×D37—42no—
33C2×D148C2×C411yescharacteristic
34C2×C4×D37—21no—
35C2×C4×D37C2×C411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×Dic74—21no—
39C2×Dic74C2×C411yescharacteristic
40C2×C8×C37—21no—
41C2×C8×C37—21no—
42C22⋊C4×C37—21no—
43C22⋊C4×C37—21no—
44C42×C37C2311yescharacteristic
45C22⋊Dic37—21no—
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C2×#64436—21no—
56#10596929—24no—
57C23×C37—21no—
58C22×D37—21no—
59C22×D37—42no—
60C22×D37—42no—
61C22×D37—42no—
62C22×D37C22⋊C411yescharacteristic
63Q8×C37—41no—
64D4×C37—41no—
65C2×C4×C37—21no—
66C2×C4×C37C22×C411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C22⋊D37—42no—
70C2×Dic37—21no—
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74D148—41no—
75C4×D37—22no—
76C4×D37—22no—
77C4×D37—41no—
78C4×D37—42no—
79Dic74—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—84no—
95C2×D37#10412yes—
96C4×C37—21no—
97C4×C37—21no—
98C4×C37—21no—
99C4×C37—41no—
100Dic37—21no—
101Dic37—21no—
102Dic37—41no—
103Dic37#10012yes—
104#1527—371nomaximal, Sylow
105C2×C37—81no—
106C2×C37C2×#10011yescharacteristic
107C2×C37C2×#10411yescharacteristic
108C2×C37#42111yescharacteristic
109D37—22no—
110D37—81no—
111C2×#124—371no—
112#432—371no—
113C4×M16—371no—
114#329—371no—
115#329—371no—
116#329—371no—
117#329D3711yescharacteristic, complemented
118C37#152711yescharacteristic, complemented, Sylow
119C22×Q8—371no—
120C22×D4—371no—
121C2×M16—741no—
122#124—371no—
123#124—371no—
124#124—371no—
125#124—741no—
126#124—741no—
127#124C2×D3711yescharacteristic
128C2×C22⋊C4—741no—
129C2×C22⋊C4—741no—
130C2×C42—371no—
131C4⋊C8—741no—
132C22⋊C8—741no—
133#97—371no—
134#97—371no—
135#97C2×D3711yescharacteristic, complemented
136#97C2×D3711yescharacteristic, complemented
137C4×C8—741no—
138C24—741no—
139C2×Q8—371no—
140C2×Q8—741no—
141C2×Q8—1482no—
142C2×Q8C4×D3711yescharacteristic
143C2×D4—371no—
144C2×D4—741no—
145C2×D4—1482no—
146C2×D4C4×D3711yescharacteristic
147C22×C4—371no—
148C22×C4—371no—
149C22×C4—371no—
150C22×C4—741no—
151M16—744no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—741no—
155C2×C8—741no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C22⋊C4—741no—
163C22⋊C4—741no—
164C42—371no—
165C42—371no—
166C42—371no—
167C42C22×D3711yescharacteristic
168C23—21no—
169C23—371no—
170C23—741no—
171C23—1482no—
172C23—1482no—
173C23—1482no—
174Q8—41no—
175Q8—1481no—
176Q8—1482no—
177D4—41no—
178D4—1481no—
179D4—1482no—
180C2×C4—21no—
181C2×C4—371no—
182C2×C4—371no—
183C2×C4—371no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4—741no—
187C2×C4—1481no—
188C2×C4—1482no—
189C2×C4C2×C4×D3711yescharacteristic
190C2×C4D4×D3711yescharacteristic
191C2×C4D4×D3711yescharacteristic
192C8—22no—
193C8—41no—
194C8—742no—
195C8—1481no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—372no—
200C22—2964no—
201C22—741no—
202C22—741no—
203C22—1481no—
204C22—1481no—
205C22—1481no—
206C22C22⋊C4×D3711yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—372no—
212C4—741no—
213C4—741no—
214C4—1481no—
215C2—81no—
216C2—2961no—
217C2—742no—
218C2#100×D3711yescharacteristic
219C2#104×D3711yescharacteristic
220C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C4
cosocleC42×C37C23
hypercenter#329D37
hypocenterC37#1527
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. #14557485C2semidirect
4. #14557273C2semidirect
5. #14557272C2semidirect
6. #14557272C2semidirect
7. C37×#329C2semidirect
21. #11924447C22semidirect
22. #11924447C22semidirect
25. #97×C37C22semidirect
26. #97×C37C22semidirect
117. #329D37semidirect
118. C37#1527semidirect
135. #97C2×D37semidirect
136. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#124×D372
#145575882
#145574852
#145572732
#145572722
C37×#3292
#152737