Finite Group Databasebeta

← #17995680

Subgroups — #17995680

Order 4736.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#10596930C211yesmaximal, characteristic
2C22×#10596941C211yesmaximal, characteristic
3C2×#11924534C211yesmaximal, characteristic, complemented
4C2×#11924459C211yesmaximal, characteristic, complemented
5#14557434C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic, complemented
7C2×#103×C37C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C22×D148C2211yescharacteristic
10C2×#10596930—22no—
11C2×#10596930—22no—
12C2×#10596930—22no—
13C2×#10596941—22no—
14C2×#10596941—22no—
15C2×#10596941—22no—
16C22×#64436C2211yescharacteristic
17#11924534—22no—
18#11924534—22no—
19C2×#10596936—22no—
20C2×#10596938—22no—
21C2×C4×Dic37C2211yescharacteristic
22#11924459—22no—
23C22×Q8×C37C2211yescharacteristic
24C22×C8×C37C2211yescharacteristic
25C2×C4⋊C4×C37C2211yescharacteristic
26#103×C37—22no—
27C23×D37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37—21no—
30C2×Q8×C37—21no—
31C2×Q8×C37—21no—
32C2×Q8×C37—21no—
33C2×Q8×C37D412yes—
34C22×C4×C37—21no—
35C22×C4×C37—21no—
36C22×C4×C37C2311yescharacteristic
37C22×Dic37—21no—
38C22×Dic37D412yes—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148—21no—
42C2×D148—21no—
43C2×D148—21no—
44C2×D148D412yes—
45C2×Dic74—21no—
46C2×Dic74—21no—
47C2×Dic74—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×Dic74D412yes—
51C2×C8×C37—21no—
52C2×C8×C37—21no—
53C2×C8×C37D412yes—
54C4⋊C4×C37—21no—
55C4⋊C4×C37—21no—
56#10596941—28no—
57#10596938—44no—
58#10596936—28no—
59C4×Dic37—21no—
60C4×Dic37—21no—
61C2×#64436—21no—
62C2×#64436—21no—
63C2×#64436D412yes—
64#10596930—28no—
65C23×C37C2×D411yescharacteristic
66C22×D37—22no—
67C22×D37—41no—
68C22×D37—41no—
69C22×D37—42no—
70C22×D37—42no—
71Q8×C37—22no—
72Q8×C37—22no—
73Q8×C37—41no—
74Q8×C37—41no—
75C2×C4×C37—22no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37—42no—
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37#4111yescharacteristic
86C2×Dic37—22no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89C2×Dic37—41no—
90C2×Dic37—41no—
91C2×Dic37SD1614yescomplemented
92D148—22no—
93D148—22no—
94D148—41no—
95D148—41no—
96Dic74—22no—
97Dic74—22no—
98Dic74—41no—
99Dic74—41no—
100C8×C37—22no—
101#64436—22no—
102C22×C37#12011yescharacteristic
103C22×C37#12111yescharacteristic
104C22×C37#12711yescharacteristic
105C22×C37C2×SD1612yes—
106C22×C37#13712yes—
107C2×D37—42no—
108C2×D37—44no—
109C2×D37—82no—
110C2×D37—81no—
111C2×D37—81no—
112C4×C37—42no—
113C4×C37—81no—
114C4×C37#12011yescharacteristic
115C4×C37#12011yescharacteristic
116C4×C37#12111yescharacteristic
117C4×C37#12111yescharacteristic
118Dic37—24no—
119Dic37—42no—
120#2013—371nomaximal, Sylow
121C2×C37#39211yescharacteristic
122C2×C37#44812yes—
123C2×C37#46112yes—
124C2×C37#49211yescharacteristic
125C2×C37#49711yescharacteristic
126D37—82no—
127C22×SD16—371no—
128C22×SD16—371no—
129C2×C4⋊Q8—371no—
130C2×#103—371no—
131C2×#103D3711yescharacteristic, complemented
132#390—371no—
133#336—371no—
134C37#201311yescharacteristic, complemented, Sylow
135C22×Q8—371no—
136C22×Q8C2×D3711yescharacteristic
137C22×D4—371no—
138C2×SD16—742no—
139C2×SD16—742no—
140C2×SD16—742no—
141C2×SD16—742no—
142C2×SD16—742no—
143C2×SD16—742no—
144C22×C8—371no—
145C22×C8C2×D3711yescharacteristic
146C4⋊Q8—742no—
147C4⋊Q8—742no—
148C2×C4⋊C4—742no—
149C2×C4⋊C4C2×D3711yescharacteristic
150C2×C22⋊C4—742no—
151C2×C42—371no—
152#103—22no—
153#103—742no—
154C24—741no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—372no—
161C2×Q8—741no—
162C2×Q8—741no—
163C2×Q8—741no—
164C2×Q8—741no—
165C2×Q8—741no—
166C2×Q8D14812yes—
167C2×D4—372no—
168C2×D4—741no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—372no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178SD16—748no—
179SD16—748no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—372no—
183C2×C8—741no—
184C2×C8—741no—
185C2×C8C22⋊D3712yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—748no—
189C22⋊C4—1484no—
190C42—741no—
191C42—741no—
192C23—742no—
193C23—1481no—
194C23—1481no—
195C23—1482no—
196C23—1482no—
197C23D4×D3711yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—742no—
203Q8—742no—
204Q8—1481no—
205Q8—1481no—
206D4—742no—
207D4—742no—
208D4—1481no—
209D4—1481no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—374no—
216C2×C4—742no—
217C2×C4—742no—
218C2×C4—742no—
219C2×C4—1481no—
220C2×C4—1481no—
221C2×C4C2×D14811yescharacteristic
222C2×C4#1059696211yescharacteristic
223C2×C4D4×D3711yescharacteristic
224C2×C4D4×D3711yescharacteristic
225C2×C4D4×D3711yescharacteristic
226C2×C4C2×C22⋊D3711yescharacteristic
227C8—22no—
228C8—742no—
229C22—2961no—
230C22—2961no—
231C22—2962no—
232C22—1482no—
233C22—1484no—
234C22#1192450611yescharacteristic
235C22#1192450911yescharacteristic
236C22#1192453211yescharacteristic
237C22SD16×D3712yes—
238C22#1192456812yes—
239C4—42no—
240C4—81no—
241C4—744no—
242C4—1482no—
243C4#1192450411yescharacteristic
244C4#1192450611yescharacteristic
245C4#1192450911yescharacteristic
246C4#1192451011yescharacteristic
247C2—2962no—
248C2#1455744211yescharacteristic
249C2#1455767312yes—
250C2#1455773712yes—
251C2#1455790411yescharacteristic
252C2#1455792611yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#103×C37C2
socleC23×C37C2×D4
prime radicalC22×D148C22
hypercenterC2×#103D37
hypocenterC37#2013
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#11924534C2semidirect
4. C2×#11924459C2semidirect
6. #14557287C2semidirect
7. C2×#103×C37C2semidirect
91. C2×Dic37SD16semidirect
131. C2×#103D37semidirect
134. C37#2013semidirect

Maximal subgroups

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

subgroupindex
C22×#105969302
C22×#105969412
C2×#119245342
C2×#119244592
#145574342
#145572872
C2×#103×C372
#201337