Finite Group Databasebeta

← #18004397

Subgroups — #18004397

Order 4736.

376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×C4×Dic74C211yesmaximal, characteristic
2#14557837C214yesmaximal, complemented
3#14557825C212yesmaximal, complemented
4#14557815C212yesmaximal, complemented
5#14557576C212yesmaximal
6#14557557C211yesmaximal, characteristic
7#14557541C212yesmaximal
8C37×#533C211yesmaximal, characteristic
9C22×Dic74C2211yescharacteristic
10C2×#10596934C2212yes—
11C4×Dic74—21no—
12C4×Dic74—21no—
13C4×Dic74C2212yes—
14C4×Dic74C2212yes—
15C2×C4⋊Dic37C2211yescharacteristic
16C2×#10596936—21no—
17C2×C4×Dic37—21no—
18#11924469C2214yes—
19#11924467C2214yes—
20C4⋊#64436C2212yes—
21C4⋊#64436C2212yes—
22#11924459C2214yes—
23#11924459C2214yes—
24C4⋊Q8×C37C2211yescharacteristic
25C4⋊Q8×C37C2211yescharacteristic
26#125×C37C2212yes—
27C22⋊Q8×C37—21no—
28C22⋊Q8×C37—21no—
29C4×Q8×C37—21no—
30C4×Q8×C37—21no—
31#117×C37C2212yes—
32C2×C42×C37C2211yescharacteristic
33C2×Q8×C37—21no—
34C2×Q8×C37—21no—
35C22×C4×C37D411yescharacteristic
36C22×C4×C37D411yescharacteristic
37C22×C4×C37C2311yescharacteristic
38C22×Dic37—21no—
39C22×Dic37—21no—
40C2×Dic74—21no—
41C2×Dic74—22no—
42C2×Dic74Q814yescomplemented
43C2×Dic74C2312yes—
44C4⋊C4×C37—22no—
45C4⋊C4×C37—22no—
46C4⋊C4×C37—21no—
47C4⋊C4×C37—21no—
48C4⋊C4×C37C2312yes—
49C4⋊C4×C37C2312yes—
50C22⋊C4×C37—22no—
51C42×C37—22no—
52C42×C37D411yescharacteristic
53C42×C37D411yescharacteristic
54C42×C37C2311yescharacteristic
55C42×C37C2311yescharacteristic
56C4⋊Dic37—21no—
57C4⋊Dic37C2312yes—
58#10596936—22no—
59#10596936—22no—
60C4×Dic37—22no—
61C4×Dic37—22no—
62#10596934—24no—
63C2×#64436C2314yes—
64C23×C37C2×D411yescharacteristic
65Q8×C37—42no—
66Q8×C37—42no—
67C2×C4×C37—22no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—41no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×Q812yes—
77C2×C4×C37#4112yes—
78C2×C4×C37C2411yescharacteristic
79C2×Dic37—24no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—42no—
83Dic74—24no—
84Dic74—22no—
85Dic74C2×Q814yes—
86#64436—24no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37C22⋊Q812yes—
90C22×C37C22×D411yescharacteristic
91C4×C37—21no—
92C4×C37—21no—
93C4×C37—21no—
94C4×C37—42no—
95C4×C37—42no—
96C4×C37C22⋊Q812yes—
97C4×C37#13712yes—
98C4×C37C22×Q811yescharacteristic
99C4×C37C2×#4111yescharacteristic
100Dic37—24no—
101Dic37—42no—
102#3078—371nomaximal, Sylow
103C2×C37—22no—
104C2×C37C2×C22⋊Q811yescharacteristic
105C2×C37C2×#13711yescharacteristic
106C2×C37#57511yescharacteristic
107#533D3711yescharacteristic
108C2×C4×Q8—371no—
109#479—374no—
110#477—372no—
111#475—372no—
112#428—372no—
113#423—371no—
114#419—372no—
115C37#307811yescharacteristic, complemented, Sylow
116C22×Q8—371no—
117C2×M16—372no—
118C4⋊Q8C2×D3711yescharacteristic
119C4⋊Q8C2×D3711yescharacteristic
120#125C2×D3712yes—
121C22⋊Q8—21no—
122C22⋊Q8—21no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—372no—
126C4×Q8—372no—
127C4×Q8—741no—
128C4×Q8—741no—
129#117C2×D3712yes—
130C2×C4⋊C4—371no—
131C2×C4⋊C4—741no—
132C2×C42—741no—
133C2×C42C2×D3711yescharacteristic
134#107—374no—
135#106—374no—
136C4⋊C8—372no—
137C4⋊C8—372no—
138#103—374no—
139#103—374no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—374no—
143C2×Q8—372no—
144C2×Q8—742no—
145C2×Q8—741no—
146C22×C4—741no—
147C22×C4—741no—
148C22×C4C22⋊D3711yescharacteristic
149C22×C4C22⋊D3711yescharacteristic
150C22×C4C22×D3711yescharacteristic
151M16—744no—
152C2×C8—374no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—372no—
158C4⋊C4—742no—
159C4⋊C4—742no—
160C4⋊C4—741no—
161C4⋊C4C22×D3712yes—
162C4⋊C4C22×D3712yes—
163C22⋊C4—22no—
164C42—22no—
165C42—742no—
166C42—742no—
167C42C22⋊D3711yescharacteristic
168C42C22⋊D3711yescharacteristic
169C42C22×D3711yescharacteristic
170C42C22×D3711yescharacteristic
171C23C2×C22⋊D3711yescharacteristic
172Q8—42no—
173Q8—42no—
174Q8—374no—
175Q8—744no—
176Q8—742no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—744no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4—1482no—
185C2×C4Q8×D3712yes—
186C2×C4#1059696612yes—
187C2×C4C2×C22⋊D3711yescharacteristic
188C2×C4C2×C22⋊D3711yescharacteristic
189C2×C4C2×C22⋊D3711yescharacteristic
190C2×C4C2×C22⋊D3711yescharacteristic
191C2×C4C2×C22⋊D3711yescharacteristic
192C2×C4C23×D3711yescharacteristic
193C8—744no—
194C22—21no—
195C22—21no—
196C22#1192451212yes—
197C22C22×C22⋊D3711yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—42no—
202C4—42no—
203C4—744no—
204C4—1482no—
205C4#1192451212yes—
206C4#1192456612yes—
207C4C2×Q8×D3711yescharacteristic
208C4C2×#1059696611yescharacteristic
209C2—22no—
210C2C2×#1192451211yescharacteristic
211C2C2×#1192456611yescharacteristic
212C2#1455833111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#533C2
socleC22×C37C22×D4
prime radicalC23×C37C2×D4
hypercenter#533D37
hypocenterC37#3078
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14557837C2semidirect
3. #14557825C2semidirect
4. #14557815C2semidirect
42. C2×Dic74Q8semidirect
115. C37#3078semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic742
#145578372
#145578252
#145578152
#145575762
#145575572
#145575412
C37×#5332
#307837