Finite Group Databasebeta

← #17995090

Subgroups — #17995090

Order 4736.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11924567C211yesmaximal, characteristic
2#14557551C211yesmaximal, characteristic
3#14557542C211yesmaximal, characteristic, complemented
4#14557506C211yesmaximal, characteristic
5#14557303C211yesmaximal, characteristic, complemented
6#14557289C211yesmaximal, characteristic, complemented
7C37×#519C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—22no—
10#11924567—22no—
11C2×#10596942C412yescomplemented
12C2×#10596941C412yescomplemented
13C2×#10596934C2211yescharacteristic
14C2×#10596934C2211yescharacteristic
15#11924495C2211yescharacteristic
16#11924464—22no—
17#11924460—22no—
18#11924450—22no—
19C22×Q8×C37C2211yescharacteristic
20C4×Q8×C37—22no—
21C4×Q8×C37—22no—
22#117×C37—22no—
23#117×C37C2211yescharacteristic
24#117×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27C2×Q8×C37—21no—
28C2×Q8×C37C2×C412yes—
29C2×Q8×C37D412yes—
30C2×Q8×C37D412yes—
31C22×C4×C37—21no—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—21no—
34#10596962—21no—
35#10596962—21no—
36#10596962—21no—
37#10596962—21no—
38C2×D148C2×C411yescharacteristic
39C2×C4×D37—21no—
40C2×Dic74C2×C411yescharacteristic
41C4⋊C4×C37—24no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37—21no—
44C22⋊C4×C37—21no—
45C22⋊C4×C37D412yes—
46C42×C37—24no—
47C42×C37—21no—
48C42×C37D412yes—
49C22⋊Dic37—21no—
50#10596942—24no—
51#10596941—24no—
52C4⋊Dic37—21no—
53C4×Dic37—21no—
54#10596934—21no—
55#10596934—21no—
56#10596934—21no—
57#10596934—21no—
58C2×#64436—21no—
59C2×#64436C2×C412yes—
60C23×C37C2×D411yescharacteristic
61C22×D37—21no—
62Q8×C37—22no—
63Q8×C37—22no—
64Q8×C37—22no—
65Q8×C37C22⋊C414yes—
66C2×C4×C37—22no—
67C2×C4×C37—22no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37C22×C411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37#4111yescharacteristic
76C2×C4×C37#4111yescharacteristic
77C22⋊D37—41no—
78C22⋊D37—41no—
79C2×Dic37—21no—
80C2×Dic37—41no—
81D148—21no—
82D148—21no—
83C4×D37—41no—
84C4×D37—41no—
85Dic74—21no—
86Dic74—21no—
87#64436—22no—
88#64436—41no—
89C22×C37—41no—
90C22×C37C4×D411yescharacteristic
91C22×C37#12011yescharacteristic
92C22×C37#12111yescharacteristic
93C2×D37—41no—
94C2×D37—81no—
95C4×C37—24no—
96C4×C37—42no—
97C4×C37—42no—
98C4×C37C2×C22⋊C411yescharacteristic
99C4×C37C4×D411yescharacteristic
100C4×C37#12111yescharacteristic
101C4×C37#12311yescharacteristic
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#519D3711yescharacteristic, complemented
112#421—371no—
113#419—371no—
114#410—371no—
115#344—371no—
116H(3,ℤ/4)—371no—
117C37#190511yescharacteristic, complemented, Sylow
118C2×#41—371no—
119C22×Q8C2×D3711yescharacteristic
120#137—742no—
121#137—742no—
122C2×Q16—372no—
123C2×SD16—372no—
124C2×M16—371no—
125C2×M16—371no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129#117—371no—
130#117C2×D3711yescharacteristic
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—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—371no—
143C2×Q8C4×D3712yes—
144C2×Q8D14812yes—
145C2×Q8C22⋊D3712yes—
146C2×D4—371no—
147C2×D4—741no—
148C22×C4—21no—
149C22×C4—741no—
150C22×C4C22×D3711yescharacteristic
151Q16—744no—
152SD16—744no—
153M16—741no—
154M16—741no—
155M16—741no—
156M16—741no—
157C2×C8—372no—
158C2×C8—741no—
159C4⋊C4—24no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—741no—
163C22⋊C4—21no—
164C22⋊C4—741no—
165C22⋊C4C22⋊D3712yes—
166C42—24no—
167C42—21no—
168C42—741no—
169C42C22⋊D3712yes—
170C23—741no—
171C23C2×C22⋊D3711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—741no—
176Q8—741no—
177Q8#1059693814yes—
178D4—741no—
179D4—741no—
180D4—1481no—
181D4—1481no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—741no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4—1481no—
191C2×C4C2×C4×D3711yescharacteristic
192C2×C4C2×D14811yescharacteristic
193C2×C4#1059696211yescharacteristic
194C2×C4#1059696211yescharacteristic
195C2×C4C2×C22⋊D3711yescharacteristic
196C2×C4C2×C22⋊D3711yescharacteristic
197C8—742no—
198C8—1481no—
199C22—41no—
200C22—2961no—
201C22—1481no—
202C22C4×C22⋊D3711yescharacteristic
203C22#1192450511yescharacteristic
204C22#1192451011yescharacteristic
205C4—24no—
206C4—42no—
207C4—42no—
208C4—2961no—
209C4—1481no—
210C4C2×#1059693811yescharacteristic
211C4C4×C22⋊D3711yescharacteristic
212C4#1192451011yescharacteristic
213C4#1192451911yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—2961no—
218C2#1455741211yescharacteristic
subgroupG/H
centerC2#14557412
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#519C2
socleC2×C37#386
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#519D37
hypocenterC37#1905
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. #14557542C2semidirect
5. #14557303C2semidirect
6. #14557289C2semidirect
7. C37×#519C2semidirect
11. C2×#10596942C4semidirect
12. C2×#10596941C4semidirect
111. #519D37semidirect
117. C37#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
#145575512
#145575422
#145575062
#145573032
#145572892
C37×#5192
#190537