Finite Group Databasebeta

← #17996259

Subgroups — #17996259

Order 4736.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558079C211yesmaximal, characteristic
2#14557507C211yesmaximal, characteristic, complemented
3#14557327C212yesmaximal, complemented
4#14557325C212yesmaximal, complemented
5C37×#410C211yesmaximal, characteristic, complemented
6C2×#10596962C411yescharacteristic, complemented
7#11924534C411yescharacteristic, complemented
8#11924532C2211yescharacteristic
9#11924525C411yescharacteristic, complemented
10#11924523C2211yescharacteristic
11#11924508—21no—
12#11924508—21no—
13C4×C22⋊D37—21no—
14C4×C22⋊D37—21no—
15#11924495—21no—
16C2×C4×Dic37C411yescharacteristic, complemented
17#11924451—21no—
18#11924451C2212yes—
19C2×#41×C37C2211yescharacteristic
20#117×C37—21no—
21#99×C37—21no—
22#99×C37C2212yes—
23#41×C37—41no—
24#41×C37—41no—
25C2×Q8×C37C2×C411yescharacteristic
26C2×D4×C37D411yescharacteristic
27C2×D4×C37D411yescharacteristic
28C2×D4×C37C2311yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37D411yescharacteristic
31C22×C4×C37D411yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C22×Dic37—21no—
36#10596962—41no—
37#10596962—41no—
38C2×D148C2×C411yescharacteristic
39C2×C4×D37—21no—
40C2×Dic74C2×C411yescharacteristic
41C4⋊C4×C37—41no—
42C22⋊C4×C37—22no—
43C42×C37—41no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46C22⋊Dic37—22no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37—41no—
50#10596936—21no—
51#10596936—21no—
52C4×Dic37—21no—
53C4×Dic37—41no—
54C4×Dic37C2×C411yescharacteristic
55C4×Dic37C2×C411yescharacteristic
56C23×C37C22⋊C411yescharacteristic
57C23×C37C2×D411yescharacteristic
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60Q8×C37—41no—
61D4×C37—41no—
62D4×C37—41no—
63D4×C37—41no—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—42no—
71C2×C4×C37C22⋊C411yescharacteristic
72C2×C4×C37C22⋊C411yescharacteristic
73C2×C4×C37C22⋊C411yescharacteristic
74C2×C4×C37C22×C411yescharacteristic
75C22⋊D37—42no—
76C22⋊D37—42no—
77C22⋊D37—42no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—42no—
82C2×Dic37—42no—
83D148—41no—
84C4×D37—41no—
85C4×D37—41no—
86Dic74—41no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37C2×C22⋊C411yescharacteristic
94C2×D37—41no—
95C2×D37—41no—
96C2×D37—41no—
97C4×C37—21no—
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—82no—
101C4×C37#9911yescharacteristic
102C4×C37#9911yescharacteristic
103Dic37—22no—
104Dic37—41no—
105Dic37—41no—
106Dic37—82no—
107#2126—371nomaximal, Sylow
108C2×C37—21no—
109C2×C37—41no—
110C2×C37—41no—
111C2×C37—41no—
112C2×C37C2×#9911yescharacteristic
113D37—81no—
114#532—371no—
115#410—371no—
116#410D3711yescharacteristic, complemented
117#354—372no—
118#353—372no—
119C37#212611yescharacteristic, complemented, Sylow
120C2×#41—371no—
121C2×#41C2×D3711yescharacteristic
122C4⋊Q8—371no—
123#127—371no—
124#124—371no—
125#124—371no—
126#121—741no—
127#121—741no—
128C4×D4—741no—
129C4×D4—741no—
130#117—21no—
131#117—741no—
132C2×C42—371no—
133#99—21no—
134#99—372no—
135#99—741no—
136#99C2×D3712yes—
137#41—41no—
138#41—41no—
139#41—1481no—
140#41—1481no—
141C2×Q8—371no—
142C2×Q8C4×D3711yescharacteristic
143C2×D4—371no—
144C2×D4—741no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4D14811yescharacteristic
148C2×D4C22⋊D3711yescharacteristic
149C2×D4C22×D3711yescharacteristic
150C22×C4—741no—
151C22×C4—741no—
152C22×C4C4×D3711yescharacteristic
153C22×C4D14811yescharacteristic
154C22×C4C22⋊D3711yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—741no—
157C4⋊C4—741no—
158C4⋊C4—1481no—
159C22⋊C4—22no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C22⋊C4—741no—
163C22⋊C4—741no—
164C22⋊C4—742no—
165C42—41no—
166C42—371no—
167C42—371no—
168C42—741no—
169C42—1481no—
170C23—741no—
171C23#1059693811yescharacteristic
172C23C2×D14811yescharacteristic
173C23C2×C22⋊D3711yescharacteristic
174Q8—41no—
175Q8—1481no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—1481no—
180D4—1482no—
181D4—1482no—
182D4—1482no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—741no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—1482no—
194C2×C4—1482no—
195C2×C4—1481no—
196C2×C4—1481no—
197C2×C4#1059693811yescharacteristic
198C2×C4#1059693811yescharacteristic
199C2×C4#1059693811yescharacteristic
200C2×C4C2×C4×D3711yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—1481no—
208C22—1481no—
209C22—1481no—
210C22C2×#1059693811yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—2962no—
216C4—742no—
217C4—1481no—
218C4—1481no—
219C4#1192445011yescharacteristic
220C4#1192445011yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—2961no—
226C2C2×#1192445011yescharacteristic
subgroupG/H
centerC4#11924450
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#410C2
socleC2×C37C2×#99
prime radical#14558079C2
cosocleC2×D4×C37C23
hypercenter#410D37
hypocenterC37#2126
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14557507C2semidirect
3. #14557327C2semidirect
4. #14557325C2semidirect
5. C37×#410C2semidirect
6. C2×#10596962C4semidirect
7. #11924534C4semidirect
9. #11924525C4semidirect
16. C2×C4×Dic37C4semidirect
116. #410D37semidirect
119. C37#2126semidirect

Maximal subgroups

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

subgroupindex
#145580792
#145575072
#145573272
#145573252
C37×#4102
#212637