Finite Group Databasebeta

← #17995774

Subgroups — #17995774

Order 4736.

278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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#14558159C211yesmaximal, characteristic, complemented
2C2×#11924450C211yesmaximal, characteristic
3C2×#11924450C211yesmaximal, characteristic
4C2×#11924450C211yesmaximal, characteristic
5#14557300C211yesmaximal, characteristic, complemented
6#14557299C211yesmaximal, characteristic, complemented
7C37×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C2211yescharacteristic
9#11924515—22no—
10#11924513—22no—
11#11924513—22no—
12C2×C22⋊Dic37C2211yescharacteristic
13C2×C22⋊Dic37C2211yescharacteristic
14C2×C22⋊Dic37C2211yescharacteristic
15#11924450—22no—
16#11924450—22no—
17#11924450—22no—
18C2×C22⋊C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37C2211yescharacteristic
20C2×C22⋊C4×C37C2211yescharacteristic
21C24×C37C2311yescharacteristic
22C23×D37Q811yescharacteristic, complemented
23C22×C4×C37—21no—
24C22×C4×C37—21no—
25C22×C4×C37—21no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C22×Dic37—21no—
33C22×Dic37—21no—
34C22×Dic37—21no—
35C22×Dic37Q811yescharacteristic, complemented
36C2×Dic74—22no—
37C22⋊C4×C37—21no—
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37D412yes—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46C22⋊Dic37—21no—
47C22⋊Dic37D412yes—
48C22⋊Dic37D412yes—
49C4⋊Dic37—22no—
50#10596936—24no—
51C23×C37—81no—
52C23×C37C2×D411yescharacteristic
53C23×C37C2×D411yescharacteristic
54C23×C37C2×D411yescharacteristic
55C23×C37C2×Q811yescharacteristic
56C23×C37#4111yescharacteristic
57C23×C37#4111yescharacteristic
58C23×C37#4111yescharacteristic
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—21no—
62C22×D37—81no—
63C2×C4×C37—22no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—81no—
67C2×C4×C37—81no—
68C2×C4×C37—81no—
69C22⋊D37—41no—
70C22⋊D37—41no—
71C22⋊D37—41no—
72C22⋊D37—41no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—41no—
79C2×Dic37—81no—
80C2×Dic37—81no—
81C2×Dic37—81no—
82Dic74—82no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37—41no—
88C22×C37—41no—
89C22×C37—41no—
90C22×C37#12011yescharacteristic
91C22×C37C22⋊Q811yescharacteristic
92C22×C37C22⋊Q811yescharacteristic
93C22×C37C22⋊Q811yescharacteristic
94C22×C37#12411yescharacteristic
95C22×C37#12411yescharacteristic
96C22×C37#12411yescharacteristic
97C2×D37—41no—
98C2×D37—81no—
99C2×D37—81no—
100C2×D37—81no—
101C4×C37—42no—
102C4×C37—81no—
103C4×C37—81no—
104Dic37—42no—
105Dic37—42no—
106Dic37—41no—
107Dic37—81no—
108#2032—371nomaximal, Sylow
109C2×C37—21no—
110C2×C37—21no—
111C2×C37—21no—
112C2×C37—21no—
113C2×C37—21no—
114C2×C37—21no—
115C2×C37—21no—
116C2×C37#39311yescharacteristic
117D37—81no—
118#543—371no—
119C2×#99—371no—
120C2×#99—371no—
121C2×#99—371no—
122#342—371no—
123#342—371no—
124#342D3711yescharacteristic, complemented
125C37#203211yescharacteristic, complemented, Sylow
126C22×D4—371no—
127C22⋊Q8—742no—
128C22⋊Q8—742no—
129C22⋊Q8—742no—
130C2×C22⋊C4—371no—
131C2×C22⋊C4—371no—
132C2×C22⋊C4—371no—
133C2×C22⋊C4C2×D3711yescharacteristic
134C2×C22⋊C4C2×D3711yescharacteristic
135C2×C22⋊C4C2×D3711yescharacteristic
136#99—742no—
137#99—742no—
138#99—742no—
139C24—371no—
140C24C22×D3711yescharacteristic
141C2×Q8—742no—
142C2×D4—741no—
143C2×D4—741no—
144C2×D4—741no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4—741no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—371no—
152C22×C4—741no—
153C22×C4—741no—
154C22×C4—741no—
155C4⋊C4—744no—
156C4⋊C4—742no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—372no—
163C22⋊C4—372no—
164C22⋊C4—741no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C22⋊C4D14812yes—
169C23—81no—
170C23—2961no—
171C23—741no—
172C23—741no—
173C23—741no—
174C23C2×D14811yescharacteristic
175C23#1059696211yescharacteristic
176C23#1059696211yescharacteristic
177C23D4×D3711yescharacteristic
178C23D4×D3711yescharacteristic
179C23#1059696411yescharacteristic
180C23Q8×D3711yescharacteristic
181Q8—2962no—
182D4—1481no—
183D4—1481no—
184D4—1481no—
185D4—1481no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—2961no—
193C2×C4—2961no—
194C2×C4—2961no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4—741no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—1481no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—2961no—
209C22—2961no—
210C22—2961no—
211C22—1481no—
212C22#1192450611yescharacteristic
213C22#1192451411yescharacteristic
214C22#1192451411yescharacteristic
215C22#1192451611yescharacteristic
216C22#1192452211yescharacteristic
217C22#1192452211yescharacteristic
218C22#1192452411yescharacteristic
219C4—42no—
220C4—81no—
221C4—81no—
222C4—2961no—
223C4—1482no—
224C4—1482no—
225C4—1481no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—2961no—
234C2#1455744611yescharacteristic
subgroupG/H
centerC2#14557446
commutator, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC37×#342C2
socleC2×C37#393
prime radicalC22×C22⋊D37C22
hypercenter#342D37
hypocenterC37#2032
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #14558159C2semidirect
5. #14557300C2semidirect
6. #14557299C2semidirect
7. C37×#342C2semidirect
22. C23×D37Q8semidirect
35. C22×Dic37Q8semidirect
124. #342D37semidirect
125. C37#2032semidirect

Maximal subgroups

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

subgroupindex
#145581592
C2×#119244502
#145573002
#145572992
C37×#3422
#203237