Finite Group Databasebeta

← #17995824

Subgroups — #17995824

Order 4736.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558111C211yesmaximal, characteristic
2C2×#11924464C211yesmaximal, characteristic, complemented
3#14557535C211yesmaximal, characteristic, complemented
4#14557534C211yesmaximal, characteristic, complemented
5#14557399C211yesmaximal, characteristic, complemented
6#14557301C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924515—21no—
11#11924512—21no—
12#11924510—21no—
13#11924508—22no—
14#11924507—21no—
15C2×C4⋊Dic37C2211yescharacteristic
16C2×C4⋊Dic37C2211yescharacteristic
17#11924464—22no—
18#11924461—21no—
19#11924460—21no—
20#11924458—21no—
21#11924457—21no—
22#11924443—22no—
23C2×#41×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25C2×C42×C37C2211yescharacteristic
26#104×C37—22no—
27#41×C37—21no—
28#41×C37—21no—
29#41×C37—21no—
30#41×C37—21no—
31C2×Q8×C37D411yescharacteristic
32C2×D4×C37—21no—
33C2×D4×C37D411yescharacteristic
34C22×C4×C37—21no—
35C22×C4×C37—21no—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—21no—
38C2×C22⋊D37—22no—
39C22×Dic37—21no—
40C22×Dic37D412yes—
41#10596962—21no—
42#10596962—21no—
43#10596962—21no—
44#10596962—21no—
45C2×D148D411yescharacteristic
46C2×C4×D37—21no—
47C2×Dic74D411yescharacteristic
48M16×C37—21no—
49M16×C37—21no—
50C2×C8×C37—21no—
51C42×C37—21no—
52C42×C37D412yescomplemented
53C22⋊Dic37—22no—
54#10596938—22no—
55C4⋊Dic37—21no—
56C4⋊Dic37—21no—
57C4⋊Dic37—21no—
58C4⋊Dic37—21no—
59#10596936—22no—
60#10596934—21no—
61#10596934—21no—
62C2×#64436—21no—
63C23×C37—21no—
64C23×C37C2×D411yescharacteristic
65C22×D37—21no—
66Q8×C37—21no—
67Q8×C37—21no—
68D4×C37—21no—
69D4×C37—21no—
70D4×C37—41no—
71D4×C37—41no—
72C2×C4×C37—21no—
73C2×C4×C37—22no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C2×C4×C37#4111yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C22⋊D37—41no—
85C22⋊D37—41no—
86C22⋊D37—82no—
87C2×Dic37—21no—
88C2×Dic37—22no—
89C2×Dic37—42no—
90C2×Dic37—42no—
91C2×Dic37—41no—
92D148—21no—
93D148—21no—
94C4×D37—41no—
95C4×D37—41no—
96Dic74—21no—
97Dic74—21no—
98C8×C37—41no—
99#64436—41no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—41no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37#12011yescharacteristic
106C22×C37#12111yescharacteristic
107C22×C37#12411yescharacteristic
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—41no—
111C4×C37—42no—
112C4×C37—41no—
113C4×C37#12111yescharacteristic
114C4×C37#12111yescharacteristic
115C4×C37#12311yescharacteristic
116C4×C37#12311yescharacteristic
117Dic37—41no—
118Dic37—42no—
119Dic37—81no—
120#2040—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—21no—
123C2×C37—81no—
124C2×C37#39411yescharacteristic
125C2×C37#45411yescharacteristic
126C2×C37#45511yescharacteristic
127D37—81no—
128#537—371no—
129C2×#104—371no—
130C2×#104D3711yescharacteristic, complemented
131#417—371no—
132#417—371no—
133#382—371no—
134#343—371no—
135C37#204011yescharacteristic, complemented, Sylow
136C2×#41—371no—
137C2×#41C2×D3711yescharacteristic
138C2×M16—371no—
139C2×M16C2×D3711yescharacteristic
140C22⋊Q8—741no—
141C22⋊Q8—741no—
142#121—741no—
143#121—742no—
144#121—741no—
145C2×C4⋊C4—371no—
146C2×C4⋊C4—371no—
147C2×C42C2×D3711yescharacteristic
148#104—22no—
149#104—742no—
150#103—741no—
151#103—741no—
152#102—741no—
153#102—741no—
154#95—742no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—741no—
160#41—741no—
161#41—741no—
162#41—741no—
163C2×Q8—371no—
164C2×Q8D14811yescharacteristic
165C2×D4—21no—
166C2×D4—371no—
167C2×D4—742no—
168C2×D4—741no—
169C2×D4D14811yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—372no—
173C22×C4—741no—
174C22×C4—741no—
175C22×C4C22×D3711yescharacteristic
176M16—21no—
177M16—21no—
178M16—741no—
179M16—741no—
180C2×C8—21no—
181C2×C8—741no—
182C4⋊C4—742no—
183C4⋊C4—741no—
184C4⋊C4—741no—
185C4⋊C4—741no—
186C4⋊C4—741no—
187C22⋊C4—742no—
188C22⋊C4—742no—
189C42—21no—
190C42C22⋊D3712yescomplemented
191C23—21no—
192C23—741no—
193C23D4×D3711yescharacteristic
194Q8—21no—
195Q8—21no—
196Q8—741no—
197Q8—741no—
198D4—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—2962no—
203D4—741no—
204D4—741no—
205D4—1481no—
206D4—1481no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—742no—
214C2×C4—741no—
215C2×C4—1482no—
216C2×C4—1481no—
217C2×C4—1481no—
218C2×C4—1481no—
219C2×C4—1482no—
220C2×C4C2×D14811yescharacteristic
221C2×C4#1059696211yescharacteristic
222C2×C4D4×D3711yescharacteristic
223C2×C4#1059696411yescharacteristic
224C2×C4#1059696411yescharacteristic
225C2×C4C2×C22⋊D3711yescharacteristic
226C8—41no—
227C8—1481no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—1481no—
234C22—1481no—
235C22—1481no—
236C22#1192450611yescharacteristic
237C22#1192450811yescharacteristic
238C22#1192452211yescharacteristic
239C4—42no—
240C4—41no—
241C4—2961no—
242C4—1481no—
243C4—1482no—
244C4#1192450711yescharacteristic
245C4#1192451011yescharacteristic
246C4#1192451811yescharacteristic
247C4#1192452011yescharacteristic
248C2—21no—
249C2—21no—
250C2—81no—
251C2—2961no—
252C2#1455744911yescharacteristic
253C2#1455770711yescharacteristic
254C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37#120
prime radical#14558111C2
hypercenterC2×#104D37
hypocenterC37#2040
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11924464C2semidirect
3. #14557535C2semidirect
4. #14557534C2semidirect
5. #14557399C2semidirect
6. #14557301C2semidirect
7. C2×#104×C37C2semidirect
52. C42×C37D4semidirect
130. C2×#104D37semidirect
135. C37#2040semidirect
190. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145581112
C2×#119244642
#145575352
#145575342
#145573992
#145573012
C2×#104×C372
#204037