Finite Group Databasebeta

← #18004082

Subgroups — #18004082

Order 4736.

480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#11924569C211yesmaximal, characteristic
2C2×#11924567C211yesmaximal, characteristic
3C2×#11924534C211yesmaximal, characteristic, complemented
4#14558001C211yesmaximal, characteristic
5#14557742C214yesmaximal, complemented
6#14557737C214yesmaximal, complemented
7#14557556C211yesmaximal, characteristic, complemented
8#14557541C211yesmaximal, characteristic, complemented
9C37×#419C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C22×Dic74C2211yescharacteristic
12#11924569—24no—
13#11924567—24no—
14C2×Dic148C2212yes—
15C2×#10596942C2212yes—
16C2×#10596930C2212yes—
17C2×#10596941C2212yes—
18C2×#10596934C2211yescharacteristic
19#11924534—21no—
20#11924534—21no—
21#11924534C2214yes—
22#11924501C2212yes—
23#11924498C2212yes—
24#11924496—22no—
25#11924493—21no—
26C2×#10596936—22no—
27C2×C4×Dic37C2211yescharacteristic
28C42×D37—21no—
29#11924465C2214yes—
30#11924459C2214yes—
31C22×Q8×C37C2211yescharacteristic
32C2×M16×C37C2211yescharacteristic
33#117×C37C2211yescharacteristic
34#103×C37C2214yes—
35C2×Q8×C37—21no—
36C2×Q8×C37—22no—
37C2×Q8×C37—22no—
38C2×Q8×C37C2312yes—
39C22×C4×C37—21no—
40C22×C4×C37C2311yescharacteristic
41C2×C22⋊D37—21no—
42C22×Dic37—21no—
43C22×Dic37D412yes—
44#10596962—22no—
45#10596962D414yes—
46C2×D148C2311yescharacteristic
47C2×C4×D37—21no—
48C2×C4×D37—22no—
49C2×Dic74—22no—
50C2×Dic74—22no—
51C2×Dic74—21no—
52C2×Dic74C2312yes—
53C2×Dic74C2311yescharacteristic
54M16×C37—22no—
55C2×C8×C37C2312yes—
56C4⋊C4×C37C2312yes—
57C22⋊C4×C37—21no—
58C42×C37—21no—
59#10596942—24no—
60#10596941—24no—
61#10596938—22no—
62#10596936—24no—
63#10596936—24no—
64#10596936—22no—
65C4×Dic37—22no—
66C4×Dic37D411yescharacteristic
67C4×Dic37D411yescharacteristic
68C4×Dic37C2312yes—
69#10596934—22no—
70C2×#64436C2312yes—
71Dic148—24no—
72#10596930—24no—
73C23×C37C2×D411yescharacteristic
74C22×D37—21no—
75Q8×C37—22no—
76Q8×C37—22no—
77Q8×C37—42no—
78C2×C4×C37—22no—
79C2×C4×C37—22no—
80C2×C4×C37—42no—
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D412yes—
83C2×C4×C37#4112yes—
84C2×C4×C37C2411yescharacteristic
85C22⋊D37—24no—
86C2×Dic37—21no—
87C2×Dic37—24no—
88C2×Dic37—22no—
89C2×Dic37—42no—
90C2×Dic37C2×D412yes—
91C2×Dic37C2×D412yes—
92D148—21no—
93D148C2×D412yes—
94C4×D37—24no—
95C4×D37—44no—
96Dic74—21no—
97Dic74—22no—
98Dic74—22no—
99Dic74—42no—
100Dic74C2×D412yes—
101C8×C37—22no—
102#64436—22no—
103C22×C37—22no—
104C22×C37#12112yes—
105C22×C37C22×D411yescharacteristic
106C2×D37—22no—
107C2×D37—42no—
108C4×C37—42no—
109C4×C37—42no—
110C4×C37#12112yes—
111C4×C37C22×D411yescharacteristic
112C4×C37C2×#4111yescharacteristic
113Dic37—22no—
114Dic37—22no—
115Dic37—42no—
116Dic37#13714yescomplemented
117#3039—371nomaximal, Sylow
118C2×C37—22no—
119C2×C37C2×#12111yescharacteristic
120C2×C37C2×#13712yes—
121D37—42no—
122C2×#137—371no—
123C2×#137—371no—
124C2×C4⋊Q8—371no—
125C4×#41—371no—
126#462—374no—
127#461—374no—
128#423—371no—
129#419—371no—
130#419D3711yescharacteristic, complemented
131C37#303911yescharacteristic, complemented, Sylow
132C2×#41—371no—
133C22×Q8—371no—
134C22×Q8C2×D3711yescharacteristic
135#137—744no—
136#137—744no—
137C2×Q16—372no—
138C2×Q16—372no—
139C2×SD16—372no—
140C2×SD16—372no—
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143C4⋊Q8—374no—
144C4⋊Q8—741no—
145C4⋊Q8—741no—
146C4×Q8—372no—
147C4×D4—372no—
148C4×D4—742no—
149#117—741no—
150#117C2×D3711yescharacteristic
151C2×C4⋊C4—742no—
152C2×C42—371no—
153C2×C42—741no—
154C4⋊C8—374no—
155#103—374no—
156#103C2×D3714yes—
157#41—374no—
158#41—742no—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—371no—
163C2×Q8—372no—
164C2×Q8—741no—
165C2×Q8—742no—
166C2×Q8—742no—
167C2×Q8C22×D3712yes—
168C2×D4—371no—
169C2×D4—741no—
170C22×C4—21no—
171C22×C4—372no—
172C22×C4—742no—
173C22×C4—741no—
174C22×C4—741no—
175C22×C4C22×D3711yescharacteristic
176Q16—744no—
177Q16—744no—
178SD16—744no—
179SD16—744no—
180M16—22no—
181M16—742no—
182C2×C8—372no—
183C2×C8C22×D3712yes—
184C4⋊C4—744no—
185C4⋊C4—744no—
186C4⋊C4—742no—
187C4⋊C4C22×D3712yes—
188C22⋊C4—21no—
189C22⋊C4—742no—
190C42—21no—
191C42—371no—
192C42—371no—
193C42—372no—
194C42—742no—
195C23—741no—
196C23D4×D3711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—42no—
200Q8—372no—
201Q8—741no—
202Q8—742no—
203Q8—742no—
204Q8—1482no—
205D4—372no—
206D4—744no—
207D4—741no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—372no—
212C2×C4—372no—
213C2×C4—744no—
214C2×C4—741no—
215C2×C4—744no—
216C2×C4—742no—
217C2×C4—1484no—
218C2×C4—1482no—
219C2×C4#1059696212yes—
220C2×C4D4×D3711yescharacteristic
221C2×C4D4×D3712yes—
222C2×C4C23×D3711yescharacteristic
223C8—22no—
224C8—742no—
225C22—22no—
226C22—742no—
227C22—1482no—
228C22#1192450912yes—
229C22C2×D4×D3711yescharacteristic
230C4—42no—
231C4—42no—
232C4—374no—
233C4—742no—
234C4—742no—
235C4—1482no—
236C4#1192450912yes—
237C4C2×D4×D3711yescharacteristic
238C4C2×#1059696211yescharacteristic
239C2—22no—
240C2—1482no—
241C2C2×#1192450911yescharacteristic
242C2#137×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#419C2
socleC22×C37C22×D4
prime radicalC2×#10596962C22
hypercenter#419D37
hypocenterC37#3039
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C2×#11924534C2semidirect
5. #14557742C2semidirect
6. #14557737C2semidirect
7. #14557556C2semidirect
8. #14557541C2semidirect
9. C37×#419C2semidirect
116. Dic37#137semidirect
130. #419D37semidirect
131. C37#3039semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C2×#119245672
C2×#119245342
#145580012
#145577422
#145577372
#145575562
#145575412
C37×#4192
#303937