Finite Group Databasebeta

← #17995773

Subgroups — #17995773

Order 4736.

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

normal subgroups only

This group has 278 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#14558159C211yesmaximal, characteristic, complemented
2C2×#11924451C211yesmaximal, characteristic
3C2×#11924451C211yesmaximal, characteristic
4#14557300C211yesmaximal, characteristic, complemented
5#14557299C211yesmaximal, characteristic, complemented
6#14557299C211yesmaximal, characteristic, complemented
7C2×#99×C37C211yesmaximal, characteristic
8#11924515—22no—
9#11924513—22no—
10#11924513—22no—
11C2×C22⋊Dic37C2211yescharacteristic
12C2×C22⋊Dic37C2211yescharacteristic
13C2×C22⋊Dic37C2211yescharacteristic
14C2×C22⋊Dic37C2211yescharacteristic
15#11924451—22no—
16#11924451—22no—
17C22×D4×C37C2211yescharacteristic
18C2×C22⋊C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37C2211yescharacteristic
20#99×C37—22no—
21C24×C37Q811yescharacteristic, complemented
22C24×C37C2311yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37—21no—
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37—21no—
31C22×C4×C37Q811yescharacteristic, complemented
32C22×Dic37—21no—
33C22×Dic37—21no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36C2×Dic74—22no—
37C22⋊C4×C37—21no—
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37D412yes—
41C22⋊Dic37—21no—
42C22⋊Dic37—21no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46C22⋊Dic37—21no—
47C22⋊Dic37D412yes—
48C22⋊Dic37D412yes—
49C4⋊Dic37—22no—
50#10596936—24no—
51C23×C37—21no—
52C23×C37—21no—
53C23×C37—21no—
54C23×C37—81no—
55C23×C37—81no—
56C23×C37C2×D411yescharacteristic
57C23×C37C2×D411yescharacteristic
58C23×C37C2×D411yescharacteristic
59C23×C37C2×Q811yescharacteristic
60C23×C37#4111yescharacteristic
61C23×C37#4111yescharacteristic
62C23×C37#4111yescharacteristic
63D4×C37—41no—
64D4×C37—41no—
65D4×C37—41no—
66D4×C37—41no—
67C2×C4×C37—22no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37—81no—
73C2×C4×C37—81no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—41no—
77C2×Dic37—41no—
78C2×Dic37—81no—
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—41no—
91C22×C37—81no—
92C22×C37—81no—
93C22×C37—81no—
94C22×C37#12011yescharacteristic
95C22×C37C22⋊Q811yescharacteristic
96C22×C37C22⋊Q811yescharacteristic
97C22×C37C22⋊Q811yescharacteristic
98C22×C37#12411yescharacteristic
99C22×C37#12411yescharacteristic
100C22×C37#12411yescharacteristic
101C4×C37—42no—
102C4×C37—41no—
103C4×C37—81no—
104Dic37—42no—
105Dic37—42no—
106Dic37—81no—
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—81no—
117C2×C37#39311yescharacteristic
118#543—371no—
119C2×#99—371no—
120C2×#99—371no—
121C2×#99D3711yescharacteristic
122#342—371no—
123#342—371no—
124#342—371no—
125C37#203211yescharacteristic, complemented, Sylow
126C22×D4C2×D3711yescharacteristic
127C22⋊Q8—742no—
128C22⋊Q8—742no—
129C22⋊Q8—742no—
130C2×C22⋊C4—371no—
131C2×C22⋊C4—371no—
132C2×C22⋊C4—371no—
133C2×C22⋊C4—371no—
134C2×C22⋊C4C2×D3711yescharacteristic
135C2×C22⋊C4C2×D3711yescharacteristic
136#99—22no—
137#99—742no—
138#99—742no—
139C24Dic7411yescharacteristic, complemented
140C24C22×D3711yescharacteristic
141C2×Q8—742no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—741no—
151C22×C4—741no—
152C22×C4—741no—
153C22×C4—741no—
154C22×C4Dic7411yescharacteristic, complemented
155C4⋊C4—744no—
156C4⋊C4—742no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—372no—
161C22⋊C4—372no—
162C22⋊C4—741no—
163C22⋊C4—741no—
164C22⋊C4—741no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C22⋊C4C22⋊D3712yes—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—81no—
173C23—81no—
174C23C2×Dic7411yescharacteristic
175C23#1059696211yescharacteristic
176C23D4×D3711yescharacteristic
177C23D4×D3711yescharacteristic
178C23#1059696411yescharacteristic
179C23#1059696411yescharacteristic
180C23C2×C22⋊D3711yescharacteristic
181Q8—2962no—
182D4—41no—
183D4—41no—
184D4—41no—
185D4—41no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—2961no—
194C2×C4—2961no—
195C2×C4—2961no—
196C2×C4—2961no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—1481no—
200C2×C4—1481no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22#1192450411yescharacteristic
213C22#1192451311yescharacteristic
214C22#1192451311yescharacteristic
215C22#1192451511yescharacteristic
216C22#1192452211yescharacteristic
217C22#1192452211yescharacteristic
218C22#1192452311yescharacteristic
219C4—42no—
220C4—41no—
221C4—81no—
222C4—2961no—
223C4—2961no—
224C4—1482no—
225C4—1482no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—81no—
234C2#1455744511yescharacteristic
subgroupG/H
centerC2#14557445
commutator, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC2×#99×C37C2
socleC2×C37#393
prime radicalC22×D4×C37C22
hypercenterC2×#99D37
hypocenterC37#2032
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. #14558159C2semidirect
4. #14557300C2semidirect
5. #14557299C2semidirect
6. #14557299C2semidirect
21. C24×C37Q8semidirect
31. C22×C4×C37Q8semidirect
125. C37#2032semidirect
139. C24Dic74semidirect
154. C22×C4Dic74semidirect

Maximal subgroups

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

subgroupindex
#145581592
C2×#119244512
#145573002
#145572992
C2×#99×C372
#203237