Finite Group Databasebeta

← #17994569

Subgroups — #17994569

Order 4736.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11924583C211yesmaximal, characteristic
2#14557551C212yesmaximal, complemented
3#14557541C212yesmaximal, complemented
4#14557517C211yesmaximal, characteristic, complemented
5C37×#410C211yesmaximal, characteristic, complemented
6#11924583—24no—
7#11924583—24no—
8C2×#10596962C412yescomplemented
9C2×#10596962C2211yescharacteristic
10C2×#10596964—22no—
11C2×#10596964—21no—
12C22×Dic74C412yescomplemented
13C22×Dic74C2211yescharacteristic
14C2×Q8×D37—21no—
15C2×#10596934C2212yes—
16#11924464—24no—
17#11924459—24no—
18#11924455—21no—
19#11924453—21no—
20C2×#41×C37C2211yescharacteristic
21#117×C37C2212yes—
22#99×C37—22no—
23#41×C37—22no—
24#41×C37—22no—
25C2×Q8×C37D411yescharacteristic
26C2×D4×C37D411yescharacteristic
27C2×D4×C37D412yes—
28C22×C4×C37C2×C412yes—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—22no—
31C2×C22⋊D37—21no—
32C22×Dic37—22no—
33C22×Dic37—21no—
34Q8×D37—28no—
35#10596964—216no—
36#10596964—28no—
37#10596962—22no—
38#10596962—24no—
39#10596962—24no—
40#10596962D414yes—
41C2×D148C2×C411yescharacteristic
42C2×C4×D37—22no—
43C2×C4×D37—21no—
44C2×Dic74—22no—
45C2×Dic74—21no—
46C2×Dic74—22no—
47C2×Dic74—24no—
48C2×Dic74—24no—
49C2×Dic74C2×C411yescharacteristic
50C2×Dic74C2×C412yes—
51C2×Dic74D414yes—
52C4⋊C4×C37—22no—
53C22⋊C4×C37—22no—
54C42×C37—22no—
55#10596934—22no—
56#10596934—22no—
57C2×#64436—22no—
58C23×C37C22⋊C412yes—
59C23×C37C2×D411yescharacteristic
60C22×D37—21no—
61Q8×C37—22no—
62D4×C37—24no—
63D4×C37—22no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—42no—
67C2×C4×C37C22⋊C412yes—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D412yes—
71C2×C4×C37C2×D412yes—
72C22⋊D37—28no—
73C22⋊D37—24no—
74C2×Dic37—28no—
75C2×Dic37—21no—
76C2×Dic37—22no—
77C2×Dic37—24no—
78D148—21no—
79D148C22⋊C412yes—
80C4×D37—28no—
81C4×D37—24no—
82Dic74—28no—
83Dic74—22no—
84Dic74—21no—
85Dic74—24no—
86Dic74C22⋊C412yes—
87Dic74C22⋊C414yes—
88#64436—42no—
89C22×C37—22no—
90C22×C37—41no—
91C22×C37—42no—
92C22×C37C2×C22⋊C411yescharacteristic
93C22×C37#12012yes—
94C2×D37—22no—
95C2×D37—42no—
96C4×C37—22no—
97C4×C37—82no—
98C4×C37C2×C22⋊C411yescharacteristic
99C4×C37C2×C22⋊C411yescharacteristic
100C4×C37#12012yes—
101Dic37—22no—
102Dic37—24no—
103#1796—371nomaximal, Sylow
104C2×C37—22no—
105C2×C37—21no—
106C2×C37—42no—
107C2×C37#37911yescharacteristic
108D37—42no—
109C2×2−1+4—371no—
110#421—372no—
111#419—372no—
112#413—371no—
113#410D3711yescharacteristic, complemented
114C37#179611yescharacteristic, complemented, Sylow
1152−1+4—744no—
1162−1+4—744no—
117C2×#41—372no—
118C2×#41—371no—
119C2×#41—741no—
120C2×#41—742no—
121C2×#41C2×D3711yescharacteristic
122C22×Q8—372no—
123C22×Q8—371no—
124C22×Q8—741no—
125C2×M16—372no—
126#117C2×D3712yes—
127#104—744no—
128#103—744no—
129#101—741no—
130#100—741no—
131#99—22no—
132#41—22no—
133#41—22no—
134#41—374no—
135#41—744no—
136#41—744no—
137#41—7416no—
138#41—748no—
139#41—742no—
140C2×Q8—372no—
141C2×Q8—371no—
142C2×Q8—374no—
143C2×Q8—744no—
144C2×Q8—744no—
145C2×Q8—748no—
146C2×Q8—742no—
147C2×Q8—741no—
148C2×Q8—742no—
149C2×Q8D14811yescharacteristic
150C2×D4—371no—
151C2×D4—742no—
152C2×D4—741no—
153C2×D4D14811yescharacteristic
154C2×D4C22⋊D3712yes—
155C22×C4—742no—
156C22×C4—741no—
157C22×C4—742no—
158C22×C4—741no—
159C22×C4C4×D3712yes—
160C22×C4C22×D3711yescharacteristic
161M16—742no—
162M16—742no—
163C2×C8—742no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—741no—
168C23#1059693812yes—
169C23C2×C22⋊D3711yescharacteristic
170Q8—22no—
171Q8—374no—
172Q8—372no—
173Q8—748no—
174Q8—742no—
175Q8—741no—
176Q8—744no—
177D4—24no—
178D4—22no—
179D4—372no—
180D4—748no—
181D4—744no—
182D4—741no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—748no—
187C2×C4—748no—
188C2×C4—741no—
189C2×C4—742no—
190C2×C4—744no—
191C2×C4—744no—
192C2×C4#1059693812yes—
193C2×C4C2×C4×D3711yescharacteristic
194C2×C4C2×D14811yescharacteristic
195C2×C4D4×D3712yes—
196C2×C4D4×D3712yes—
197C8—1482no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—742no—
202C22—1482no—
203C22C2×#1059693811yescharacteristic
204C22#1192450412yes—
205C4—22no—
206C4—82no—
207C4—744no—
208C4—742no—
209C4C22⋊C4×D3711yescharacteristic
210C4C22⋊C4×D3711yescharacteristic
211C4#1192450612yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—1482no—
216C2#1455738811yescharacteristic
subgroupG/H
centerC2#14557388
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#410C2
socleC2×C37#379
prime radicalC2×#11924583C2
cosocleC22×C4×C37C23
hypercenter#410D37
hypocenterC37#1796
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14557551C2semidirect
3. #14557541C2semidirect
4. #14557517C2semidirect
5. C37×#410C2semidirect
8. C2×#10596962C4semidirect
12. C22×Dic74C4semidirect
113. #410D37semidirect
114. C37#1796semidirect

Maximal subgroups

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

subgroupindex
C2×#119245832
#145575512
#145575412
#145575172
C37×#4102
#179637