Finite Group Databasebeta

← #17995089

Subgroups — #17995089

Order 4736.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×#11924569C211yesmaximal, characteristic
2#14558010C211yesmaximal, characteristic, complemented
3#14557549C211yesmaximal, characteristic
4#14557543C211yesmaximal, characteristic, complemented
5#14557506C211yesmaximal, characteristic
6#14557290C211yesmaximal, characteristic, complemented
7C37×#344C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924569—22no—
11#11924569—22no—
12C2×Dic148C412yescomplemented
13C2×#10596930C412yescomplemented
14C4×Dic74—22no—
15#11924501—22no—
16#11924495C2211yescharacteristic
17#11924495C2211yescharacteristic
18#11924492—22no—
19#11924462—22no—
20#11924461—22no—
21#11924450—22no—
22C2×M16×C37C2211yescharacteristic
23C2×M16×C37C2211yescharacteristic
24#117×C37C2211yescharacteristic
25C22×C4×C37C2311yescharacteristic
26C2×C22⋊D37—21no—
27C22×Dic37—21no—
28#10596962—21no—
29#10596962—21no—
30#10596962—21no—
31#10596962—21no—
32C2×D148C2×C411yescharacteristic
33C2×C4×D37—21no—
34C2×Dic74—21no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74C2×C411yescharacteristic
38C2×Dic74C2×C412yes—
39C2×Dic74D412yes—
40C2×Dic74D412yes—
41M16×C37—21no—
42M16×C37—21no—
43M16×C37—21no—
44M16×C37—21no—
45C2×C8×C37—21no—
46C2×C8×C37C2×C412yes—
47C4⋊C4×C37—21no—
48C22⋊C4×C37D412yes—
49C42×C37—21no—
50C22⋊Dic37—21no—
51C22⋊Dic37—21no—
52C4⋊Dic37—21no—
53C4⋊Dic37—21no—
54#10596936—24no—
55C4×Dic37—24no—
56C4×Dic37—21no—
57C4×Dic37D412yes—
58Dic148—24no—
59#10596930—24no—
60C23×C37C2×D411yescharacteristic
61C22×D37—21no—
62C2×C4×C37—22no—
63C2×C4×C37C22×C411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37#4111yescharacteristic
68C2×C4×C37#4111yescharacteristic
69C22⋊D37—41no—
70C22⋊D37—41no—
71C2×Dic37—22no—
72C2×Dic37—22no—
73C2×Dic37—22no—
74C2×Dic37—21no—
75C2×Dic37—22no—
76C2×Dic37—41no—
77D148—21no—
78D148—21no—
79C4×D37—41no—
80C4×D37—41no—
81Dic74—22no—
82Dic74—22no—
83Dic74—22no—
84Dic74—21no—
85Dic74—21no—
86Dic74C22⋊C414yes—
87C8×C37—22no—
88C8×C37—41no—
89C22×C37—41no—
90C22×C37C4×D411yescharacteristic
91C22×C37#12011yescharacteristic
92C22×C37#12111yescharacteristic
93C2×D37—41no—
94C2×D37—81no—
95C4×C37—42no—
96C4×C37C2×C22⋊C411yescharacteristic
97C4×C37C4×D411yescharacteristic
98C4×C37#12111yescharacteristic
99C4×C37#12311yescharacteristic
100Dic37—24no—
101Dic37—42no—
102Dic37—41no—
103Dic37—81no—
104#1905—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—21no—
107C2×C37—21no—
108C2×C37#38611yescharacteristic
109D37—81no—
110C2×#137—371no—
111#519—371no—
112#421—371no—
113#419—371no—
114#410—371no—
115#344D3711yescharacteristic, complemented
116H(3,ℤ/4)—371no—
117C37#190511yescharacteristic, complemented, Sylow
118C2×#41—371no—
119C22×Q8—371no—
120#137—742no—
121#137—742no—
122C2×Q16—372no—
123C2×SD16—372no—
124C2×M16C2×D3711yescharacteristic
125C2×M16C2×D3711yescharacteristic
126C4×Q8—742no—
127C4×Q8—742no—
128#117—371no—
129#117—371no—
130#117—742no—
131#117C2×D3711yescharacteristic
132#104—742no—
133#103—742no—
134#99—742no—
135#41—741no—
136#41—741no—
137#41—741no—
138#41—741no—
139C2×Q8—372no—
140C2×Q8—371no—
141C2×Q8—372no—
142C2×Q8—372no—
143C2×Q8—741no—
144C2×Q8—741no—
145C2×Q8—741no—
146C2×D4—371no—
147C2×D4—741no—
148C22×C4—741no—
149C22×C4—741no—
150C22×C4C22×D3711yescharacteristic
151Q16—744no—
152SD16—744no—
153M16—21no—
154M16—21no—
155M16—21no—
156M16—21no—
157C2×C8—21no—
158C2×C8C4×D3712yes—
159C4⋊C4—21no—
160C4⋊C4—744no—
161C4⋊C4—741no—
162C4⋊C4—741no—
163C22⋊C4—741no—
164C22⋊C4—741no—
165C22⋊C4D14812yes—
166C42—21no—
167C42—372no—
168C42—744no—
169C42—741no—
170C23—741no—
171C23C2×D14811yescharacteristic
172Q8—374no—
173Q8—742no—
174Q8—742no—
175Q8—742no—
176Q8—741no—
177Q8—741no—
178D4—741no—
179D4—741no—
180D4—1481no—
181D4—1481no—
182C2×C4—22no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4—741no—
187C2×C4—742no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4—1481no—
191C2×C4C2×C4×D3711yescharacteristic
192C2×C4#1059696211yescharacteristic
193C2×C4D4×D3711yescharacteristic
194C2×C4D4×D3711yescharacteristic
195C2×C4D4×D3711yescharacteristic
196C2×C4#1059696611yescharacteristic
197C8—22no—
198C8—41no—
199C22—41no—
200C22—2961no—
201C22—1481no—
202C22C4×D14811yescharacteristic
203C22#1192450611yescharacteristic
204C22#1192451111yescharacteristic
205C4—42no—
206C4—2961no—
207C4—744no—
208C4—1482no—
209C4—1481no—
210C4C22⋊C4×D3711yescharacteristic
211C4#1192449811yescharacteristic
212C4#1192450911yescharacteristic
213C4#1192452111yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—2961no—
218C2#1455741111yescharacteristic
subgroupG/H
centerC2#14557411
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#344C2
socleC2×C37#386
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#344D37
hypocenterC37#1905
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #14558010C2semidirect
4. #14557543C2semidirect
6. #14557290C2semidirect
7. C37×#344C2semidirect
12. C2×Dic148C4semidirect
13. C2×#10596930C4semidirect
115. #344D37semidirect
117. C37#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
#145580102
#145575492
#145575432
#145575062
#145572902
C37×#3442
#190537