Finite Group Databasebeta

← #17995190

Subgroups — #17995190

Order 4736.

230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 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#14557432C211yesmaximal, characteristic
2C4⋊C4×Dic37C211yesmaximal, characteristic
3#14557296C211yesmaximal, characteristic
4#14557295C211yesmaximal, characteristic
5#14557295C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic
7C2×#107×C37C211yesmaximal, characteristic
8C22×#64436C2211yescharacteristic
9C2×C4⋊Dic37—21no—
10C2×C4⋊Dic37C2211yescharacteristic
11C2×C4⋊Dic37C2211yescharacteristic
12C2×C4×Dic37—21no—
13C2×C4×Dic37C2211yescharacteristic
14#11924443—21no—
15#11924443—21no—
16C22×C8×C37C2211yescharacteristic
17C2×C4⋊C4×C37C2211yescharacteristic
18C2×C4⋊C4×C37C2211yescharacteristic
19#107×C37C414yescomplemented
20C22×C4×C37—21no—
21C22×C4×C37—21no—
22C22×C4×C37C2311yescharacteristic
23C22×Dic37—21no—
24C22×Dic37—21no—
25C22×Dic37D411yescharacteristic
26C22×Dic37D411yescharacteristic
27C2×C8×C37—21no—
28C2×C8×C37—21no—
29C2×C8×C37C2×C412yes—
30C4⋊C4×C37—21no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37C2×C412yes—
33C4⋊C4×C37C2×C412yes—
34C4⋊Dic37—21no—
35C4⋊Dic37—21no—
36C4⋊Dic37—21no—
37C4⋊Dic37—42no—
38C4⋊Dic37Q812yes—
39C4×Dic37—21no—
40C4×Dic37—21no—
41C4×Dic37—42no—
42C2×#64436—21no—
43C2×#64436—21no—
44C2×#64436—21no—
45C23×C37C2×D411yescharacteristic
46C2×C4×C37—22no—
47C2×C4×C37—22no—
48C2×C4×C37—41no—
49C2×C4×C37—41no—
50C2×C4×C37—41no—
51C2×C4×C37—41no—
52C2×C4×C37C22×C411yescharacteristic
53C2×C4×C37C2×Q811yescharacteristic
54C2×C4×C37#4111yescharacteristic
55C2×C4×C37#4111yescharacteristic
56C2×C4×C37#4111yescharacteristic
57C2×C4×C37#4111yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—22no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—41no—
65C2×Dic37—41no—
66C2×Dic37—41no—
67C2×Dic37—41no—
68C2×Dic37—41no—
69C2×Dic37Q1612yes—
70C8×C37—22no—
71#64436—41no—
72C22×C37C4×D411yescharacteristic
73C22×C37C22⋊Q811yescharacteristic
74C22×C37#12311yescharacteristic
75C22×C37C2×Q1611yescharacteristic
76C22×C37#13511yescharacteristic
77C22×C37AGL(1,ℤ/8)11yescharacteristic
78C22×C37AGL(1,ℤ/8)11yescharacteristic
79C4×C37—42no—
80C4×C37—42no—
81C4×C37#11711yescharacteristic
82C4×C37C4×Q811yescharacteristic
83C4×C37#12511yescharacteristic
84C4×C37#12611yescharacteristic
85Dic37—22no—
86Dic37—42no—
87Dic37—41no—
88Dic37—81no—
89#1921—371nomaximal, Sylow
90C2×C37#38711yescharacteristic
91C2×C37C4×Q1611yescharacteristic
92C2×C37#44211yescharacteristic
93C2×C37#47711yescharacteristic
94C2×C37#47811yescharacteristic
95C2×C37#48211yescharacteristic
96C2×C37#48411yescharacteristic
97C2×#107D3711yescharacteristic
98#389—371no—
99C4×C4⋊C4—371no—
100#340—371no—
101#340—371no—
102#340—371no—
103#336—371no—
104C37#192111yescharacteristic, complemented, Sylow
105C22×C8—371no—
106C22×C8C2×D3711yescharacteristic
107C2×C4⋊C4—371no—
108C2×C4⋊C4—371no—
109C2×C4⋊C4—741no—
110C2×C4⋊C4C2×D3711yescharacteristic
111C2×C4⋊C4C2×D3711yescharacteristic
112C2×C42—371no—
113C2×C42—741no—
114#107Dic3714yescomplemented
115#95—741no—
116#95—741no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—741no—
122C22×C4—741no—
123C22×C4C22×D3711yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—741no—
127C2×C8—741no—
128C2×C8—741no—
129C2×C8C2×Dic3712yes—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—372no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4—741no—
136C4⋊C4—1482no—
137C4⋊C4C2×Dic3712yes—
138C4⋊C4C2×Dic3712yes—
139C42—741no—
140C42—741no—
141C42—1482no—
142C23D4×D3711yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—372no—
150C2×C4—741no—
151C2×C4—741no—
152C2×C4—742no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—1481no—
157C2×C4—1481no—
158C2×C4—1481no—
159C2×C4—1481no—
160C2×C4—1481no—
161C2×C4#1059696211yescharacteristic
162C2×C4#1059696211yescharacteristic
163C2×C4#1059696411yescharacteristic
164C2×C4Q8×D3711yescharacteristic
165C2×C4#1059696611yescharacteristic
166C2×C4C22×Dic3711yescharacteristic
167C8—22no—
168C8—1481no—
169C22D4×Dic3711yescharacteristic
170C22#1192451411yescharacteristic
171C22#1192452111yescharacteristic
172C22Q16×D3711yescharacteristic
173C22#1192455911yescharacteristic
174C22#1192456011yescharacteristic
175C22#1192456011yescharacteristic
176C4—42no—
177C4—42no—
178C4—2961no—
179C4—742no—
180C4—1482no—
181C4—1481no—
182C4#1192449511yescharacteristic
183C4Q8×Dic3711yescharacteristic
184C4#1192452611yescharacteristic
185C4#1192453111yescharacteristic
186C2#1455741911yescharacteristic
187C2Q16×Dic3711yescharacteristic
188C2#1455764511yescharacteristic
189C2#1455782711yescharacteristic
190C2#1455783611yescharacteristic
191C2#1455786011yescharacteristic
192C2#1455787011yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#107×C37C2
socle, prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenterC2×#107D37
hypocenterC37#1921
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
19. #107×C37C4semidirect
104. C37#1921semidirect
114. #107Dic37semidirect

Maximal subgroups

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

subgroupindex
#145574322
C4⋊C4×Dic372
#145572962
#145572952
#145572872
C2×#107×C372
#192137