Finite Group Databasebeta

← #18006057

Subgroups — #18006057

Order 4736.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#14558154C212yesmaximal, complemented
2#14557829C212yesmaximal, complemented
3#14557814C212yesmaximal, complemented
4#14557779C212yesmaximal, complemented
5#14557774C211yesmaximal, characteristic, complemented
6#14557769C211yesmaximal, characteristic
7#14557756C212yesmaximal, complemented
8#14557749C212yesmaximal, complemented
9C37×#424C211yesmaximal, characteristic, complemented
10C2×Dic148C2211yescharacteristic
11C2×#10596930C2212yes—
12C2×D296C2211yescharacteristic
13#11924536C2212yes—
14#11924531—22no—
15#11924524C2212yes—
16#11924522—22no—
17#11924518—22no—
18#11924515C2212yes—
19#11924514—22no—
20#11924510C2212yes—
21C4×Dic74C2212yes—
22C4×D148C2212yes—
23#11924470C2211yescharacteristic
24#11924470C2211yescharacteristic
25#11924470C2212yes—
26#11924461C2212yes—
27#11924461C2212yes—
28#11924458C2212yes—
29#11924458C2212yes—
30C2×M16×C37C2211yescharacteristic
31C22×C8×C37C2211yescharacteristic
32#117×C37C2211yescharacteristic
33C4⋊C8×C37C2212yes—
34C4⋊C8×C37C2212yes—
35C22×C4×C37C2311yescharacteristic
36C2×C22⋊D37—22no—
37C2×D148C2312yes—
38C2×C4×D37—22no—
39C2×Dic74—22no—
40C2×Dic74C2312yes—
41M16×C37—41no—
42C2×C8×C37—41no—
43C2×C8×C37C2311yescharacteristic
44C2×C8×C37C2312yes—
45C2×C8×C37C2311yescharacteristic
46C4⋊C4×C37D411yescharacteristic
47C4⋊C4×C37D411yescharacteristic
48C22⋊C4×C37D412yes—
49C42×C37C2312yes—
50C22⋊Dic37—22no—
51#10596938—22no—
52#10596938—22no—
53#10596938—22no—
54#10596938—22no—
55C4⋊Dic37—22no—
56C4⋊Dic37C2312yes—
57C4⋊Dic37C2312yes—
58#10596936—22no—
59#10596936—22no—
60C4×Dic37—22no—
61Dic148—41no—
62D296—41no—
63#10596930—42no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37C2×D412yes—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D412yes—
71C2×C4×C37C2411yescharacteristic
72C22⋊D37—82no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76D148—22no—
77D148—22no—
78C4×D37—82no—
79Dic74—22no—
80Dic74—22no—
81Dic74—82no—
82C8×C37—22no—
83C8×C37—21no—
84C8×C37—21no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37C22×D411yescharacteristic
89C2×D37—42no—
90C2×D37—42no—
91C2×D37—42no—
92C4×C37—21no—
93C4×C37—22no—
94C4×C37—22no—
95C4×C37H(5,𝔽2)11yescharacteristic
96C4×C372−1+411yescharacteristic
97Dic37—42no—
98Dic37—42no—
99Dic37—42no—
100#3262—371nomaximal, Sylow
101C2×C37—41no—
102C2×C37#53711yescharacteristic
103C2×C37#57611yescharacteristic
104C2×C37#57811yescharacteristic
105D37—82no—
106#542—372no—
107#477—372no—
108#474—372no—
109#468—372no—
110#467—371no—
111#466—371no—
112#464—372no—
113#463—372no—
114#424D3711yescharacteristic, complemented
115C37#326211yescharacteristic, complemented, Sylow
116C2×Q16—371no—
117C2×SD16—372no—
118C2×D8—371no—
119C2×M16C2×D3711yescharacteristic
120C22×C8C2×D3711yescharacteristic
121C4⋊Q8—372no—
122#126—742no—
123#124—372no—
124#124—742no—
125#123—742no—
126C22⋊Q8—372no—
127C22⋊Q8—742no—
128#121—372no—
129C4×Q8—372no—
130C4×D4—372no—
131#117C2×D3711yescharacteristic
132#107—371no—
133#107—371no—
134#107—372no—
135C4⋊C8C2×D3712yes—
136C4⋊C8C2×D3712yes—
137#103—372no—
138#103—372no—
139#102—372no—
140#102—372no—
141C2×Q8—372no—
142C2×Q8—742no—
143C2×D4—372no—
144C2×D4—742no—
145C22×C4—742no—
146C22×C4C22×D3711yescharacteristic
147Q16—1481no—
148SD16—1482no—
149D8—1481no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D3711yescharacteristic
153C2×C8C22×D3712yes—
154C2×C8C22×D3711yescharacteristic
155C4⋊C4—372no—
156C4⋊C4—372no—
157C4⋊C4—742no—
158C4⋊C4—742no—
159C4⋊C4—742no—
160C4⋊C4D14811yescharacteristic
161C4⋊C4D14811yescharacteristic
162C22⋊C4—742no—
163C22⋊C4—742no—
164C22⋊C4—742no—
165C22⋊C4—742no—
166C22⋊C4—742no—
167C22⋊C4D14812yes—
168C42—742no—
169C42C22×D3712yes—
170C23—742no—
171C23C2×D14811yescharacteristic
172Q8—2962no—
173Q8—742no—
174Q8—742no—
175D4—2962no—
176D4—742no—
177D4—742no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—2962no—
181C2×C4—742no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4C2×D14812yes—
185C2×C4C2×D14812yes—
186C2×C4C2×D14811yescharacteristic
187C2×C4C23×D3711yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—1482no—
195C22—1482no—
196C22—1482no—
197C22C22×D14811yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—1482no—
202C4—1482no—
203C4—1482no—
204C4#1192458111yescharacteristic
205C4#1192458411yescharacteristic
206C2—41no—
207C2—2962no—
208C2#1455811411yescharacteristic
209C2#1455833811yescharacteristic
210C2#1455835011yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#424C2
socleC22×C37C22×D4
prime radical#14557769C2
hypercenter#424D37
hypocenterC37#3262
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14557829C2semidirect
3. #14557814C2semidirect
4. #14557779C2semidirect
5. #14557774C2semidirect
7. #14557756C2semidirect
8. #14557749C2semidirect
9. C37×#424C2semidirect
114. #424D37semidirect
115. C37#3262semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145578292
#145578142
#145577792
#145577742
#145577692
#145577562
#145577492
C37×#4242
#326237