Finite Group Databasebeta

← #17995087

Subgroups — #17995087

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×#11924566C211yesmaximal, characteristic
2#14558010C211yesmaximal, characteristic, complemented
3#14557543C211yesmaximal, characteristic, complemented
4#14557507C211yesmaximal, characteristic
5#14557305C211yesmaximal, characteristic, complemented
6#14557289C211yesmaximal, characteristic, complemented
7C37×#421C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9#11924566—22no—
10#11924566—22no—
11C2×#10596942C412yescomplemented
12C2×#10596940C412yescomplemented
13C2×#10596934C2211yescharacteristic
14C4×Dic74—22no—
15#11924501—22no—
16#11924495C2211yescharacteristic
17#11924495C2211yescharacteristic
18#11924492—22no—
19#11924461—22no—
20#11924451—22no—
21C2×#41×C37C2211yescharacteristic
22C2×M16×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24#104×C37—22no—
25#41×C37—21no—
26#41×C37—21no—
27#41×C37—21no—
28#41×C37—21no—
29C2×Q8×C37C2×C411yescharacteristic
30C2×D4×C37—21no—
31C2×D4×C37C2×C411yescharacteristic
32C22×C4×C37—21no—
33C22×C4×C37C2311yescharacteristic
34C22×Dic37—21no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74C2×C412yes—
39C2×Dic74D412yes—
40C2×Dic74D412yes—
41M16×C37—21no—
42M16×C37—21no—
43C2×C8×C37—21no—
44C4⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C42×C37D412yes—
47C22⋊Dic37—21no—
48C22⋊Dic37D412yes—
49#10596942—24no—
50#10596940—24no—
51C4⋊Dic37—21no—
52C4⋊Dic37—21no—
53#10596936—24no—
54C4×Dic37—24no—
55C4×Dic37—21no—
56C4×Dic37—21no—
57#10596934—21no—
58#10596934—21no—
59C2×#64436C2×C412yes—
60C23×C37—21no—
61C23×C37C2×D411yescharacteristic
62Q8×C37—21no—
63Q8×C37—21no—
64D4×C37—21no—
65D4×C37—21no—
66D4×C37—41no—
67D4×C37—41no—
68C2×C4×C37—21no—
69C2×C4×C37—22no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37C22×C411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37#4111yescharacteristic
77C2×C4×C37#4111yescharacteristic
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—41no—
83Dic74—22no—
84Dic74—22no—
85Dic74—22no—
86Dic74C22⋊C414yes—
87C8×C37—41no—
88#64436—22no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37—81no—
92C22×C37C4×D411yescharacteristic
93C22×C37#12011yescharacteristic
94C22×C37#12111yescharacteristic
95C4×C37—42no—
96C4×C37—41no—
97C4×C37C2×C22⋊C411yescharacteristic
98C4×C37C4×D411yescharacteristic
99C4×C37#12111yescharacteristic
100C4×C37#12311yescharacteristic
101Dic37—24no—
102Dic37—42no—
103Dic37—81no—
104#1905—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—21no—
107C2×C37—21no—
108C2×C37—81no—
109C2×C37#38611yescharacteristic
110C2×#137—371no—
111#519—371no—
112#421D3711yescharacteristic
113#419—371no—
114#410—371no—
115#344—371no—
116H(3,ℤ/4)—371no—
117C37#190511yescharacteristic, complemented, Sylow
118C2×#41C2×D3711yescharacteristic
119C22×Q8—371no—
120#137—742no—
121#137—742no—
122C2×Q16—372no—
123C2×SD16—372no—
124C2×M16—371no—
125C2×M16C2×D3711yescharacteristic
126C4×Q8—742no—
127C4×Q8—742no—
128#117—371no—
129#117—371no—
130#117—742no—
131#117C2×D3711yescharacteristic
132#104—22no—
133#103—742no—
134#99—742no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—372no—
140C2×Q8—372no—
141C2×Q8—372no—
142C2×Q8—741no—
143C2×Q8—741no—
144C2×Q8—741no—
145C2×Q8C4×D3711yescharacteristic
146C2×D4—21no—
147C2×D4C4×D3711yescharacteristic
148C22×C4—21no—
149C22×C4—741no—
150C22×C4C22×D3711yescharacteristic
151Q16—744no—
152SD16—744no—
153M16—21no—
154M16—21no—
155M16—741no—
156M16—741no—
157C2×C8—21no—
158C2×C8—372no—
159C4⋊C4—21no—
160C4⋊C4—744no—
161C4⋊C4—741no—
162C4⋊C4—741no—
163C22⋊C4—21no—
164C22⋊C4—372no—
165C22⋊C4—741no—
166C42—744no—
167C42—741no—
168C42—741no—
169C42C22⋊D3712yes—
170C23—21no—
171C23D4×D3711yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—374no—
175Q8—742no—
176Q8—742no—
177Q8—742no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—742no—
189C2×C4—742no—
190C2×C4—1481no—
191C2×C4C2×C4×D3711yescharacteristic
192C2×C4#1059696211yescharacteristic
193C2×C4D4×D3711yescharacteristic
194C2×C4D4×D3711yescharacteristic
195C2×C4#1059696411yescharacteristic
196C2×C4C2×C22⋊D3711yescharacteristic
197C8—41no—
198C8—742no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22#1192449611yescharacteristic
203C22#1192450411yescharacteristic
204C22#1192450911yescharacteristic
205C4—42no—
206C4—41no—
207C4—2961no—
208C4—744no—
209C4—1482no—
210C4C22⋊C4×D3711yescharacteristic
211C4C4×C22⋊D3711yescharacteristic
212C4#1192450711yescharacteristic
213C4#1192451811yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1455740911yescharacteristic
subgroupG/H
centerC2#14557409
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#421C2
socleC2×C37#386
prime radicalC2×#41×C37C22
cosocleC22×C4×C37C23
hypercenter#421D37
hypocenterC37#1905
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #14558010C2semidirect
3. #14557543C2semidirect
5. #14557305C2semidirect
6. #14557289C2semidirect
11. C2×#10596942C4semidirect
12. C2×#10596940C4semidirect
117. C37#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
#145580102
#145575432
#145575072
#145573052
#145572892
C37×#4212
#190537