Finite Group Databasebeta

← #17994571

Subgroups — #17994571

Order 4736.

536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 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#14557550C212yesmaximal, complemented
2#14557542C212yesmaximal, complemented
3#14557517C211yesmaximal, characteristic, complemented
4#14557507C211yesmaximal, characteristic, complemented
5C2×2−1+4×C37C211yesmaximal, characteristic
6C2×#10596934C2212yes—
7#11924495C2212yes—
8#11924463—24no—
9#11924460—24no—
10#11924455—21no—
11#11924453—21no—
12#11924451—22no—
132−1+4×C37—24no—
142−1+4×C37—24no—
15C2×#41×C37—21no—
16C2×#41×C37—22no—
17C2×#41×C37C412yescomplemented
18C2×#41×C37C2211yescharacteristic
19C2×#41×C37C2211yescharacteristic
20C22×Q8×C37—21no—
21C22×Q8×C37C412yescomplemented
22C22×Q8×C37C2211yescharacteristic
23#41×C37—216no—
24#41×C37—28no—
25#41×C37—24no—
26#41×C37—24no—
27#41×C37—22no—
28#41×C37—22no—
29#41×C37—22no—
30#41×C37D414yes—
31C2×Q8×C37—28no—
32C2×Q8×C37—24no—
33C2×Q8×C37—24no—
34C2×Q8×C37—22no—
35C2×Q8×C37—21no—
36C2×Q8×C37—22no—
37C2×Q8×C37C2×C411yescharacteristic
38C2×Q8×C37C2×C412yes—
39C2×Q8×C37D414yes—
40C2×Q8×C37D411yescharacteristic
41C2×D4×C37—22no—
42C2×D4×C37—21no—
43C2×D4×C37C2×C411yescharacteristic
44C2×D4×C37D412yes—
45C2×D4×C37D411yescharacteristic
46C22×C4×C37—22no—
47C22×C4×C37—21no—
48C22×C4×C37—22no—
49C22×C4×C37—21no—
50C22×C4×C37C2×C412yes—
51C22×C4×C37C2311yescharacteristic
52C22⋊Dic37—22no—
53C4⋊Dic37—22no—
54C4×Dic37—22no—
55#10596934—22no—
56#10596934—22no—
57C2×#64436—22no—
58C23×C37—21no—
59C23×C37C22⋊C412yes—
60C23×C37C2×D411yescharacteristic
61Q8×C37—28no—
62Q8×C37—21no—
63Q8×C37—22no—
64Q8×C37—24no—
65Q8×C37—22no—
66Q8×C37C22⋊C412yes—
67Q8×C37C22⋊C414yes—
68D4×C37—28no—
69D4×C37—24no—
70D4×C37—24no—
71D4×C37—21no—
72D4×C37—22no—
73D4×C37C22⋊C412yes—
74C2×C4×C37—28no—
75C2×C4×C37—28no—
76C2×C4×C37—21no—
77C2×C4×C37—22no—
78C2×C4×C37—24no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—24no—
82C2×C4×C37C22⋊C412yes—
83C2×C4×C37C22×C411yescharacteristic
84C2×C4×C37C2×D412yes—
85C2×C4×C37C2×D412yes—
86C2×C4×C37C2×D411yescharacteristic
87C2×Dic37—42no—
88#64436—42no—
89C22×C37—22no—
90C22×C37—22no—
91C22×C37—41no—
92C22×C37—42no—
93C22×C37—42no—
94C22×C37C2×C22⋊C411yescharacteristic
95C22×C37#12012yes—
96C4×C37—24no—
97C4×C37—22no—
98C4×C37—22no—
99C4×C37C2×C22⋊C411yescharacteristic
100C4×C37C2×C22⋊C411yescharacteristic
101C4×C37#12012yes—
102Dic37—82no—
103#1796—371nomaximal, Sylow
104C2×C37—22no—
105C2×C37—21no—
106C2×C37—42no—
107C2×C37—42no—
108C2×C37#37911yescharacteristic
109C2×2−1+4D3711yescharacteristic
110#421—372no—
111#419—372no—
112#413—371no—
113#410—371no—
114C37#179611yescharacteristic, complemented, Sylow
1152−1+4—24no—
1162−1+4—24no—
117C2×#41—21no—
118C2×#41—22no—
119C2×#41Dic3712yescomplemented
120C2×#41C2×D3711yescharacteristic
121C2×#41C2×D3711yescharacteristic
122C22×Q8—21no—
123C22×Q8Dic3712yescomplemented
124C22×Q8C2×D3711yescharacteristic
125C2×M16—372no—
126#117—372no—
127#104—744no—
128#103—744no—
129#101—741no—
130#100—741no—
131#99—742no—
132#41—216no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—22no—
137#41—22no—
138#41—22no—
139#41C22⋊D3714yes—
140C2×Q8—28no—
141C2×Q8—24no—
142C2×Q8—24no—
143C2×Q8—22no—
144C2×Q8—21no—
145C2×Q8—22no—
146C2×Q8C2×Dic3711yescharacteristic
147C2×Q8C2×Dic3712yes—
148C2×Q8C22⋊D3714yes—
149C2×Q8C22⋊D3711yescharacteristic
150C2×D4—22no—
151C2×D4—21no—
152C2×D4C2×Dic3711yescharacteristic
153C2×D4C22⋊D3712yes—
154C2×D4C22⋊D3711yescharacteristic
155C22×C4—22no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—21no—
159C22×C4C2×Dic3712yes—
160C22×C4C22×D3711yescharacteristic
161M16—742no—
162M16—742no—
163C2×C8—742no—
164C4⋊C4—742no—
165C22⋊C4—742no—
166C42—742no—
167C23—21no—
168C23C22⋊Dic3712yes—
169C23C2×C22⋊D3711yescharacteristic
170Q8—28no—
171Q8—21no—
172Q8—22no—
173Q8—24no—
174Q8—22no—
175Q8C22⋊Dic3712yes—
176Q8C22⋊Dic3714yes—
177D4—28no—
178D4—24no—
179D4—24no—
180D4—21no—
181D4—22no—
182D4C22⋊Dic3712yes—
183C2×C4—28no—
184C2×C4—28no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—1482no—
192C2×C4C22⋊Dic3712yes—
193C2×C4C22×Dic3711yescharacteristic
194C2×C4C2×C22⋊D3712yes—
195C2×C4C2×C22⋊D3712yes—
196C2×C4C2×C22⋊D3711yescharacteristic
197C8—1482no—
198C22—22no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22C2×C22⋊Dic3711yescharacteristic
204C22#1192450512yes—
205C4—24no—
206C4—22no—
207C4—22no—
208C4—2962no—
209C4C2×C22⋊Dic3711yescharacteristic
210C4C2×C22⋊Dic3711yescharacteristic
211C4#1192450512yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—42no—
216C2#1455738911yescharacteristic
subgroupG/H
centerC2#14557389
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC2×2−1+4×C37C2
socleC2×C37#379
cosocleC22×C4×C37C23
hypercenterC2×2−1+4D37
hypocenterC37#1796
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #14557550C2semidirect
2. #14557542C2semidirect
3. #14557517C2semidirect
4. #14557507C2semidirect
17. C2×#41×C37C4semidirect
21. C22×Q8×C37C4semidirect
114. C37#1796semidirect
119. C2×#41Dic37semidirect
123. C22×Q8Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575502
#145575422
#145575172
#145575072
C2×2−1+4×C372
#179637