Finite Group Databasebeta

← #17995030

Subgroups — #17995030

Order 4736.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C22×#10596934C211yesmaximal, characteristic
2C2×#11924460C212yesmaximal, complemented
3#14557393C211yesmaximal, characteristic
4#14557295C212yesmaximal, complemented
5C2×C22⋊Q8×C37C211yesmaximal, characteristic
6C2×#10596934—22no—
7C2×#10596934—24no—
8C22×#64436C2212yes—
9C2×C4⋊Dic37C2212yes—
10C2×C22⋊Dic37—21no—
11#11924460—24no—
12#11924443—21no—
13C22×Q8×C37C2211yescharacteristic
14C23×C4×C37C2211yescharacteristic
15C22⋊Q8×C37—22no—
16C22⋊Q8×C37C414yescomplemented
17C2×C4⋊C4×C37—21no—
18C2×C4⋊C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37—21no—
20C24×C37D411yescharacteristic
21C2×Q8×C37—21no—
22C2×Q8×C37—22no—
23C2×Q8×C37—22no—
24C2×Q8×C37C2×C412yes—
25C22×C4×C37—22no—
26C22×C4×C37—22no—
27C22×C4×C37—21no—
28C22×C4×C37—21no—
29C22×C4×C37C2×C412yes—
30C22×C4×C37D411yescharacteristic
31C22×C4×C37D412yes—
32C22×C4×C37C2311yescharacteristic
33C22×Dic37—22no—
34C4⋊C4×C37—24no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C412yes—
37C22⋊C4×C37—24no—
38C22⋊Dic37—42no—
39C4⋊Dic37—22no—
40C4⋊Dic37—22no—
41#10596934—28no—
42C2×#64436—22no—
43C2×#64436—22no—
44C2×#64436D414yes—
45C23×C37—22no—
46C23×C37—21no—
47C23×C37—21no—
48C23×C37—22no—
49C23×C37C22⋊C412yes—
50C23×C37C2×D411yescharacteristic
51Q8×C37—24no—
52Q8×C37—41no—
53Q8×C37—41no—
54C2×C4×C37—22no—
55C2×C4×C37—24no—
56C2×C4×C37—22no—
57C2×C4×C37—22no—
58C2×C4×C37—22no—
59C2×C4×C37—22no—
60C2×C4×C37—42no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37C22⋊C412yes—
64C2×C4×C37C22×C411yescharacteristic
65C2×C4×C37C2×D412yes—
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37#4112yes—
68C2×Dic37—42no—
69C2×Dic37—42no—
70C2×Dic37—42no—
71#64436—24no—
72C22×C37—22no—
73C22×C37—22no—
74C22×C37—22no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37C2×C22⋊C411yescharacteristic
78C22×C37#12112yes—
79C22×C37AGL(1,ℤ/8)11yescharacteristic
80C22×C37#13711yescharacteristic
81C22×C37#13712yes—
82C4×C37—22no—
83C4×C37—42no—
84C4×C37—42no—
85C4×C37C4×D412yes—
86C4×C37#12011yescharacteristic
87C4×C37#12311yescharacteristic
88Dic37—82no—
89#1894—371nomaximal, Sylow
90C2×C37—42no—
91C2×C37#38611yescharacteristic
92C2×C37#41711yescharacteristic
93C2×C37#41911yescharacteristic
94C2×C37#46812yes—
95C2×C37#47012yes—
96C22×M16—371no—
97C2×C22⋊Q8D3711yescharacteristic
98C2×#103—372no—
99#380—371no—
100#340—372no—
101C37#189411yescharacteristic, complemented, Sylow
102C22×Q8C2×D3711yescharacteristic
103C23×C4C2×D3711yescharacteristic
104C2×M16—744no—
105C2×M16—742no—
106C22×C8—372no—
107C22⋊Q8—22no—
108C22⋊Q8Dic3714yescomplemented
109C2×C4⋊C4—21no—
110C2×C4⋊C4—372no—
111C2×C4⋊C4C2×D3711yescharacteristic
112C2×C22⋊C4—21no—
113C2×C22⋊C4—741no—
114#103—744no—
115#95—741no—
116C24C22⋊D3711yescharacteristic
117C2×Q8—21no—
118C2×Q8—22no—
119C2×Q8—22no—
120C2×Q8C2×Dic3712yes—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—742no—
126C22×C4C2×Dic3712yes—
127C22×C4C22⋊D3711yescharacteristic
128C22×C4C22⋊D3712yes—
129C22×C4C22×D3711yescharacteristic
130M16—748no—
131C2×C8—374no—
132C2×C8—742no—
133C2×C8—742no—
134C4⋊C4—24no—
135C4⋊C4—21no—
136C4⋊C4—742no—
137C4⋊C4—742no—
138C4⋊C4C2×Dic3712yes—
139C22⋊C4—24no—
140C22⋊C4—1482no—
141C23—22no—
142C23—21no—
143C23—21no—
144C23—22no—
145C23C22⋊Dic3712yes—
146C23C2×C22⋊D3711yescharacteristic
147Q8—24no—
148Q8—41no—
149Q8—41no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—1482no—
160C2×C4—1482no—
161C2×C4—1482no—
162C2×C4C22⋊Dic3712yes—
163C2×C4D4×D3712yes—
164C2×C4#1059696412yes—
165C2×C4C22×Dic3711yescharacteristic
166C2×C4C2×C22⋊D3711yescharacteristic
167C8—744no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22C2×C22⋊Dic3711yescharacteristic
174C22#1192450812yes—
175C22#1192456111yescharacteristic
176C22#1192456611yescharacteristic
177C22#1192456712yes—
178C4—22no—
179C4—42no—
180C4—42no—
181C4—2962no—
182C4D4×Dic3712yes—
183C4#1192450411yescharacteristic
184C4#1192451711yescharacteristic
185C2—42no—
186C2#1455741311yescharacteristic
187C2#1455753411yescharacteristic
188C2#1455754211yescharacteristic
189C2#1455778112yes—
190C2#1455778912yes—
subgroupG/H
centerC23C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×C22⋊Q8×C37C2
socleC23×C37C2×D4
prime radicalC24×C37D4
cosocleC22×C4×C37C23
hypercenterC2×C22⋊Q8D37
hypocenterC37#1894
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11924460C2semidirect
4. #14557295C2semidirect
16. C22⋊Q8×C37C4semidirect
101. C37#1894semidirect
108. C22⋊Q8Dic37semidirect

Maximal subgroups

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

subgroupindex
C22×#105969342
C2×#119244602
#145573932
#145572952
C2×C22⋊Q8×C372
#189437