Finite Group Databasebeta

← #17993262

Subgroups — #17993262

Order 4736.

344 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 75 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#127×D37C211yesmaximal, characteristic
2#14557585C211yesmaximal, characteristic, complemented
3#14557555C211yesmaximal, characteristic, complemented
4#14557277C211yesmaximal, characteristic, complemented
5#14557276C211yesmaximal, characteristic, complemented
6#14557276C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×D4×D37—21no—
9C2×D4×D37—21no—
10C2×D4×D37C412yes—
11C2×#10596929—21no—
12#11924533C2211yescharacteristic
13#11924532—21no—
14#11924532—21no—
15#11924532C412yes—
16C42×D37C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic, complemented
18C4⋊#64436C2211yescharacteristic, complemented
19#11924465—21no—
20#11924448—21no—
21C8×Dic37—21no—
22#127×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic, complemented
24C4⋊C8×C37C2211yescharacteristic, complemented
25C23×D37—22no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37C2×C412yes—
29C2×C22⋊D37—22no—
30C2×C22⋊D37—22no—
31C2×C22⋊D37—22no—
32D4×D37—42no—
33D4×D37—42no—
34D4×D37—44no—
35D4×D37—42no—
36D4×D37—42no—
37C2×D148—21no—
38C2×D148—21no—
39C2×D148C2×C412yes—
40C2×C4×D37C2×C411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C8×C37—21no—
44C2×C8×C37—21no—
45C42×C37C2311yescharacteristic
46C4×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C2×#64436—21no—
50C2×#64436—21no—
51#10596929—42no—
52C23×C37—22no—
53C22×D37—22no—
54C22×D37—44no—
55C22×D37—44no—
56C22×D37—44no—
57C22×D37C22⋊C411yescharacteristic
58D4×C37—42no—
59D4×C37—41no—
60D4×C37—41no—
61D4×C37—41no—
62D4×C37—41no—
63C2×C4×C37C22×C411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C22⋊D37—44no—
67C22⋊D37—44no—
68C22⋊D37—44no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C22⋊C411yescharacteristic
72D148—42no—
73D148—41no—
74D148—41no—
75D148—41no—
76D148—41no—
77C4×D37—21no—
78C4×D37—21no—
79C4×D37—22no—
80C4×D37D812yes—
81C4×D37SD1612yes—
82C8×C37—41no—
83C8×C37—41no—
84#64436—41no—
85#64436—41no—
86C22×C37—42no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37C2×C22⋊C411yescharacteristic
90C2×D37—21no—
91C2×D37—21no—
92C2×D37—42no—
93C2×D37—42no—
94C2×D37—42no—
95C2×D37—88no—
96C2×D37#10212yes—
97C4×C37—21no—
98C4×C37C2×D811yescharacteristic
99C4×C37C2×SD1611yescharacteristic
100C4×C37AGL(1,ℤ/8)11yescharacteristic
101C4×C37AGL(1,ℤ/8)11yescharacteristic
102Dic37—21no—
103Dic37#10012yes—
104Dic37#10212yes—
105#1545—371nomaximal, Sylow
106C2×C37—82no—
107C2×C37C2×#10011yescharacteristic
108C2×C37C2×#10211yescharacteristic
109C2×C37#41811yescharacteristic
110D37—22no—
111D37—82no—
112C2×#127—371no—
113#431—371no—
114#423—371no—
115#331—371no—
116#331—371no—
117#331—371no—
118#331D3711yescharacteristic, complemented
119C37#154511yescharacteristic, complemented, Sylow
120C22×D4—372no—
121C22×D4—741no—
122C22×D4—741no—
123C2×M16—741no—
124#127—372no—
125#127—371no—
126#127—741no—
127#127—741no—
128#127C2×D3711yescharacteristic
129C2×C42—371no—
130C4⋊C8—371no—
131C4⋊C8—371no—
132C4⋊C8—741no—
133C4⋊C8C2×D3711yescharacteristic, complemented
134C4⋊C8C2×D3711yescharacteristic, complemented
135C22⋊C8—741no—
136C4×C8—741no—
137C24—742no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—372no—
141C2×D4—742no—
142C2×D4—742no—
143C2×D4—742no—
144C2×D4—741no—
145C2×D4—741no—
146C2×D4—1482no—
147C2×D4—1482no—
148C2×D4—1482no—
149C2×D4—1482no—
150C2×D4—1484no—
151C2×D4C4×D3712yes—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—371no—
155M16—1482no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—741no—
159C2×C8—741no—
160C42—371no—
161C42—371no—
162C42—371no—
163C42C22×D3711yescharacteristic
164C23—22no—
165C23—371no—
166C23—742no—
167C23—1484no—
168C23—1484no—
169C23—1484no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—1482no—
176D4—1484no—
177D4—1484no—
178D4—1484no—
179D4—1481no—
180D4—1481no—
181D4—1481no—
182D4—1481no—
183C2×C4—371no—
184C2×C4—371no—
185C2×C4—372no—
186C2×C4—372no—
187C2×C4—371no—
188C2×C4—742no—
189C2×C4—741no—
190C2×C4—741no—
191C2×C4C2×C4×D3711yescharacteristic
192C2×C4D4×D3711yescharacteristic
193C2×C4D4×D3711yescharacteristic
194C8—41no—
195C8—41no—
196C8—1481no—
197C8—1481no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—372no—
202C22—2968no—
203C22—741no—
204C22—741no—
205C22—1482no—
206C22—1482no—
207C22—1482no—
208C22C22⋊C4×D3711yescharacteristic
209C4—21no—
210C4—372no—
211C4—372no—
212C4—741no—
213C4D8×D3711yescharacteristic
214C4SD16×D3711yescharacteristic
215C4#1192456011yescharacteristic
216C4#1192456311yescharacteristic
217C2—82no—
218C2—2962no—
219C2—742no—
220C2#100×D3711yescharacteristic
221C2#102×D3711yescharacteristic
222C2#1455753611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#331C2
socleC22×C37C2×C22⋊C4
prime radical#127×D37C2
cosocleC42×C37C23
hypercenter#331D37
hypocenterC37#1545
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14557585C2semidirect
3. #14557555C2semidirect
4. #14557277C2semidirect
5. #14557276C2semidirect
6. #14557276C2semidirect
7. C37×#331C2semidirect
17. C4⋊#64436C22semidirect
18. C4⋊#64436C22semidirect
23. C4⋊C8×C37C22semidirect
24. C4⋊C8×C37C22semidirect
118. #331D37semidirect
119. C37#1545semidirect
133. C4⋊C8C2×D37semidirect
134. C4⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#127×D372
#145575852
#145575552
#145572772
#145572762
C37×#3312
#154537