Finite Group Databasebeta

← #18004401

Subgroups — #18004401

Order 4736.

376 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 153 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#14558090C211yesmaximal, characteristic
2#14557840C214yesmaximal, complemented
3#14557828C212yesmaximal, complemented
4#14557818C212yesmaximal, complemented
5#14557573C212yesmaximal
6#14557557C211yesmaximal, characteristic
7#14557542C212yesmaximal
8C2×C4×Q8×C37C211yesmaximal, characteristic
9C2×#10596934C2212yes—
10#11924536C2211yescharacteristic
11#11924536C2211yescharacteristic
12#11924528C2212yes—
13#11924515—21no—
14#11924515—21no—
15C4×Dic74—21no—
16C4×Dic74—21no—
17#11924495C2212yes—
18#11924469C2214yes—
19#11924467C2214yes—
20C4⋊#64436C2212yes—
21C4⋊#64436C2212yes—
22#11924460C2214yes—
23#11924460C2214yes—
24C22×Q8×C37C2211yescharacteristic
25C4×Q8×C37—21no—
26C4×Q8×C37—21no—
27C4×Q8×C37C2212yes—
28C4×Q8×C37C2212yes—
29C2×C4⋊C4×C37—21no—
30C2×C4⋊C4×C37C2211yescharacteristic
31C2×C42×C37—21no—
32C2×C42×C37C2211yescharacteristic
33C2×Q8×C37—21no—
34C2×Q8×C37—22no—
35C2×Q8×C37Q814yescomplemented
36C2×Q8×C37C2312yes—
37C22×C4×C37—21no—
38C22×C4×C37—21no—
39C22×C4×C37D411yescharacteristic
40C22×C4×C37D411yescharacteristic
41C22×C4×C37C2311yescharacteristic
42C2×Dic74—21no—
43C2×Dic74—21no—
44C4⋊C4×C37—22no—
45C4⋊C4×C37—22no—
46C4⋊C4×C37—21no—
47C4⋊C4×C37C2312yes—
48C42×C37—22no—
49C42×C37—22no—
50C42×C37D411yescharacteristic
51C42×C37D411yescharacteristic
52C42×C37C2311yescharacteristic
53C42×C37C2311yescharacteristic
54C22⋊Dic37—22no—
55C4⋊Dic37—21no—
56C4⋊Dic37—21no—
57C4⋊Dic37C2312yes—
58C4⋊Dic37C2312yes—
59#10596936—22no—
60#10596936—22no—
61C4×Dic37—22no—
62#10596934—24no—
63C2×#64436C2314yes—
64C23×C37C2×D411yescharacteristic
65Q8×C37—24no—
66Q8×C37—22no—
67Q8×C37C2×Q814yes—
68C2×C4×C37—24no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37—41no—
73C2×C4×C37—42no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×Q812yes—
80C2×C4×C37#4112yes—
81C2×C4×C37C2411yescharacteristic
82C2×Dic37—22no—
83C2×Dic37—22no—
84Dic74—42no—
85Dic74—42no—
86#64436—24no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37C22⋊Q812yes—
90C22×C37C22×D411yescharacteristic
91C4×C37—24no—
92C4×C37—21no—
93C4×C37—21no—
94C4×C37—21no—
95C4×C37—42no—
96C4×C37C22⋊Q812yes—
97C4×C37#13712yes—
98C4×C37C22×Q811yescharacteristic
99C4×C37C2×#4111yescharacteristic
100Dic37—42no—
101Dic37—42no—
102#3078—371nomaximal, Sylow
103C2×C37—22no—
104C2×C37C2×C22⋊Q811yescharacteristic
105C2×C37C2×#13711yescharacteristic
106C2×C37#57511yescharacteristic
107#533—371no—
108C2×C4×Q8D3711yescharacteristic
109#479—374no—
110#477—372no—
111#475—372no—
112#428—372no—
113#423—371no—
114#419—372no—
115C37#307811yescharacteristic, complemented, Sylow
116C22×Q8C2×D3711yescharacteristic
117C2×M16—372no—
118C4⋊Q8—371no—
119C4⋊Q8—371no—
120#125—372no—
121C22⋊Q8—741no—
122C22⋊Q8—741no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—741no—
126C4×Q8—741no—
127C4×Q8C2×D3712yes—
128C4×Q8C2×D3712yes—
129#117—372no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4C2×D3711yescharacteristic
132C2×C42—21no—
133C2×C42C2×D3711yescharacteristic
134#107—374no—
135#106—374no—
136C4⋊C8—372no—
137C4⋊C8—372no—
138#103—374no—
139#103—374no—
140C2×Q8—22no—
141C2×Q8—21no—
142C2×Q8—741no—
143C2×Q8—741no—
144C2×Q8Dic7414yescomplemented
145C2×Q8C22×D3712yes—
146C22×C4—21no—
147C22×C4—21no—
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—372no—
157C4⋊C4—372no—
158C4⋊C4—742no—
159C4⋊C4—742no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C4⋊C4C22×D3712yes—
163C22⋊C4—742no—
164C42—22no—
165C42—22no—
166C42—742no—
167C42C22⋊D3711yescharacteristic
168C42C22⋊D3711yescharacteristic
169C42C22×D3711yescharacteristic
170C42C22×D3711yescharacteristic
171C23C2×C22⋊D3711yescharacteristic
172Q8—24no—
173Q8—22no—
174Q8—1482no—
175Q8—1482no—
176Q8C2×Dic7414yes—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4C2×Dic7412yes—
186C2×C4#1059696212yes—
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#1192451512yes—
197C22C22×C22⋊D3711yescharacteristic
198C4—24no—
199C4—21no—
200C4—21no—
201C4—21no—
202C4—42no—
203C4—1482no—
204C4—1482no—
205C4#1192451512yes—
206C4#1192456712yes—
207C4C22×Dic7411yescharacteristic
208C4C2×#1059696211yescharacteristic
209C2—22no—
210C2C2×#1192451511yescharacteristic
211C2C2×#1192456711yescharacteristic
212C2#1455833111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×C4×Q8×C37C2
socleC22×C37C22×D4
prime radicalC23×C37C2×D4
hypercenterC2×C4×Q8D37
hypocenterC37#3078
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #14557840C2semidirect
3. #14557828C2semidirect
4. #14557818C2semidirect
35. C2×Q8×C37Q8semidirect
115. C37#3078semidirect
144. C2×Q8Dic74semidirect

Maximal subgroups

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

subgroupindex
#145580902
#145578402
#145578282
#145578182
#145575732
#145575572
#145575422
C2×C4×Q8×C372
#307837