Finite Group Databasebeta

← #18005146

Subgroups — #18005146

Order 4736.

348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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#14558086C211yesmaximal, characteristic
2C2×#11924527C211yesmaximal, characteristic
3#14557941C212yesmaximal, complemented
4#14557940C212yesmaximal, complemented
5#14557934C212yesmaximal, complemented
6#14557933C212yesmaximal, complemented
7#14557576C211yesmaximal, characteristic
8#14557575C211yesmaximal, characteristic
9#14557573C211yesmaximal, characteristic
10M16×Dic37C211yesmaximal, characteristic
11C37×#428C211yesmaximal, characteristic
12C2×#10596934C2211yescharacteristic
13#11924535C2211yescharacteristic
14#11924535C2211yescharacteristic
15#11924527—21no—
16#11924527—21no—
17#11924527C2212yes—
18#11924527C2212yes—
19#11924527C2211yescharacteristic
20#11924527C2211yescharacteristic
21#11924513—21no—
22#11924513—21no—
23C4×Dic74—21no—
24C4×Dic74—21no—
25#11924495C2211yescharacteristic
26C2×C4⋊Dic37—21no—
27C2×C4⋊Dic37C2211yescharacteristic
28C2×#10596936—21no—
29C2×C4×Dic37C2211yescharacteristic
30#11924470C2212yes—
31#11924469C2212yes—
32#11924469C2212yes—
33#11924468C2212yes—
34#11924467C2212yes—
35#11924467C2212yes—
36#11924446C2212yes—
37C8×Dic37C2212yes—
38C2×M16×C37C2211yescharacteristic
39#117×C37C2211yescharacteristic
40C2×C4⋊C4×C37C2211yescharacteristic
41#107×C37C2212yes—
42#106×C37C2212yes—
43C22×C4×C37—21no—
44C22×C4×C37C2311yescharacteristic
45C22×Dic37—21no—
46C22×Dic37D411yescharacteristic
47C22×Dic37D411yescharacteristic
48C2×Dic74—21no—
49C2×Dic74—21no—
50M16×C37Q814yescomplemented
51C2×C8×C37C2312yes—
52C4⋊C4×C37—21no—
53C4⋊C4×C37C2312yes—
54C4⋊C4×C37C2311yescharacteristic
55C4⋊C4×C37C2311yescharacteristic
56C22⋊C4×C37—21no—
57C42×C37—21no—
58C22⋊Dic37—21no—
59C4⋊Dic37—21no—
60C4⋊Dic37—22no—
61C4⋊Dic37—22no—
62C4⋊Dic37—21no—
63C4⋊Dic37—21no—
64C4⋊Dic37C2312yes—
65C4⋊Dic37C2311yescharacteristic
66C4⋊Dic37C2311yescharacteristic
67#10596936—22no—
68#10596936—22no—
69#10596936—21no—
70#10596936—21no—
71#10596936—21no—
72#10596936—21no—
73C4×Dic37—21no—
74C4×Dic37D411yescharacteristic
75C4×Dic37D411yescharacteristic
76C4×Dic37C2311yescharacteristic
77C4×Dic37C2311yescharacteristic
78#10596934Q814yescomplemented
79C2×#64436C2312yes—
80C23×C37C2×D411yescharacteristic
81C2×C4×C37—22no—
82C2×C4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37—42no—
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2×Q812yes—
87C2×C4×C37C2×Q812yes—
88C2×C4×C37C2411yescharacteristic
89C2×Dic37—21no—
90C2×Dic37—21no—
91C2×Dic37—22no—
92C2×Dic37—41no—
93C2×Dic37—41no—
94C2×Dic37—42no—
95C2×Dic37C2×D411yescharacteristic
96C2×Dic37C2×D411yescharacteristic
97C2×Dic37C2×D411yescharacteristic
98C2×Dic37C2×D411yescharacteristic
99Dic74—42no—
100Dic74—42no—
101C8×C37C2×Q814yes—
102#64436C2×Q814yes—
103C22×C37—21no—
104C22×C37—21no—
105C22×C37C4⋊Q812yes—
106C22×C37C22×D411yescharacteristic
107C4×C37—41no—
108C4×C37—41no—
109C4×C37—42no—
110C4×C37C4⋊Q812yes—
111C4×C37C22×Q811yescharacteristic
112C4×C37C22×Q811yescharacteristic
113Dic37—21no—
114Dic37—21no—
115Dic37—21no—
116Dic37—21no—
117Dic37—41no—
118Dic37—41no—
119Dic37—42no—
120#3166—371nomaximal, Sylow
121C2×C37—22no—
122C2×C37C2×C4⋊Q811yescharacteristic
123C2×C37#57511yescharacteristic
124C2×C37#57511yescharacteristic
125#533—371no—
126C2×#125—371no—
127#501—372no—
128#501—372no—
129#499—372no—
130#499—372no—
131#428—371no—
132#428—371no—
133#428—371no—
134#428D3711yescharacteristic
135C4×M16—371no—
136C37#316611yescharacteristic, complemented, Sylow
137C2×M16—371no—
138C2×M16C2×D3711yescharacteristic
139C4⋊Q8—371no—
140C4⋊Q8—371no—
141#125—372no—
142#125—372no—
143#125—371no—
144#125—371no—
145#125—741no—
146#125—741no—
147C22⋊Q8—741no—
148C22⋊Q8—741no—
149C4×Q8—741no—
150C4×Q8—741no—
151#117—371no—
152#117C2×D3711yescharacteristic
153C2×C4⋊C4—371no—
154C2×C4⋊C4—741no—
155C2×C4⋊C4—741no—
156C2×C4⋊C4C2×D3711yescharacteristic
157C2×C42—371no—
158#107—372no—
159#107—372no—
160#107—372no—
161#107C2×D3712yes—
162#106—372no—
163#106—372no—
164#106—372no—
165#106C2×D3712yes—
166#97—372no—
167C4×C8—372no—
168C2×Q8—741no—
169C2×Q8—741no—
170C22×C4—21no—
171C22×C4—371no—
172C22×C4—371no—
173C22×C4—741no—
174C22×C4C22×D3711yescharacteristic
175M16—374no—
176M16Dic7414yescomplemented
177C2×C8—372no—
178C2×C8C22×D3712yes—
179C4⋊C4—21no—
180C4⋊C4—372no—
181C4⋊C4—371no—
182C4⋊C4—371no—
183C4⋊C4—742no—
184C4⋊C4—742no—
185C4⋊C4—741no—
186C4⋊C4—741no—
187C4⋊C4—741no—
188C4⋊C4—741no—
189C4⋊C4—742no—
190C4⋊C4—742no—
191C4⋊C4—741no—
192C4⋊C4—741no—
193C4⋊C4—741no—
194C4⋊C4C22×D3711yescharacteristic
195C4⋊C4C22×D3712yes—
196C4⋊C4C22×D3711yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—741no—
199C42—21no—
200C42—371no—
201C42—371no—
202C42—371no—
203C42—371no—
204C42—741no—
205C23D4×D3711yescharacteristic
206Q8—1482no—
207Q8—1482no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—371no—
213C2×C4—371no—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—741no—
217C2×C4—741no—
218C2×C4—742no—
219C2×C4—1481no—
220C2×C4—1481no—
221C2×C4—1482no—
222C2×C4C2×Dic7412yes—
223C2×C4D4×D3711yescharacteristic
224C2×C4Q8×D3712yes—
225C2×C4C23×D3711yescharacteristic
226C8—374no—
227C8C2×Dic7414yes—
228C22—21no—
229C22—21no—
230C22#1192453512yes—
231C22C2×D4×D3711yescharacteristic
232C4—42no—
233C4—41no—
234C4—41no—
235C4—741no—
236C4—741no—
237C4—741no—
238C4—741no—
239C4—1481no—
240C4—1482no—
241C4—1481no—
242C4#1192453512yes—
243C4C2×Q8×D3711yescharacteristic
244C4C22×Dic7411yescharacteristic
245C2—22no—
246C2C2×#1192453511yescharacteristic
247C2#1455832911yescharacteristic
248C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#428C2
socleC22×C37C22×D4
prime radicalC23×C37C2×D4
hypercenter#428D37
hypocenterC37#3166
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #14557941C2semidirect
4. #14557940C2semidirect
5. #14557934C2semidirect
6. #14557933C2semidirect
50. M16×C37Q8semidirect
78. #10596934Q8semidirect
136. C37#3166semidirect
176. M16Dic74semidirect

Maximal subgroups

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

subgroupindex
#145580862
C2×#119245272
#145579412
#145579402
#145579342
#145579332
#145575762
#145575752
#145575732
M16×Dic372
C37×#4282
#316637