Finite Group Databasebeta

← #18005353

Subgroups — #18005353

Order 4736.

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

normal subgroups only

This group has 468 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×#11924515C211yesmaximal, characteristic, complemented
2#14557863C212yesmaximal, complemented
3#14557849C212yesmaximal, complemented
4#14557760C214yesmaximal, complemented
5#14557684C212yesmaximal, complemented
6#14557671C212yesmaximal, complemented
7C2×C22⋊#64436C211yesmaximal, characteristic, complemented
8C2×#121×C37C211yesmaximal, characteristic
9C22×Dic74C2211yescharacteristic, complemented
10C2×#10596940C2214yescomplemented
11C22×#64436C2212yescomplemented
12#11924515—21no—
13#11924515—21no—
14#11924515C2212yes—
15#11924515C2212yescomplemented
16C2×C4⋊Dic37C2211yescharacteristic, complemented
17C2×#10596936—21no—
18C2×C22⋊Dic37—21no—
19#11924467C2214yescomplemented
20#11924459C2214yescomplemented
21#11924457C2214yescomplemented
22C22⋊#64436C2212yes—
23C22⋊#64436C2212yescomplemented
24C22×D4×C37—21no—
25C22×D4×C37C2211yescharacteristic
26C23×C4×C37C2211yescharacteristic
27#121×C37—21no—
28#121×C37—21no—
29#121×C37C2212yes—
30#121×C37C2212yes—
31C2×C4⋊C4×C37C2211yescharacteristic
32C2×C22⋊C4×C37—21no—
33C24×C37—21no—
34C24×C37D411yescharacteristic
35C2×D4×C37—22no—
36C2×D4×C37—22no—
37C2×D4×C37—21no—
38C2×D4×C37—42no—
39C2×D4×C37—44no—
40C2×D4×C37C2312yes—
41C22×C4×C37—21no—
42C22×C4×C37—42no—
43C22×C4×C37D411yescharacteristic
44C22×C4×C37D411yescharacteristic
45C22×C4×C37D411yescharacteristic
46C22×C4×C37C2311yescharacteristic
47C22×C4×C37C2311yescharacteristic
48C22×C4×C37C2311yescharacteristic
49C22×Dic37—21no—
50C22×Dic37—21no—
51C2×Dic74—21no—
52C2×Dic74—42no—
53C2×Dic74C2312yes—
54C4⋊C4×C37—21no—
55C4⋊C4×C37C2312yes—
56C22⋊C4×C37—22no—
57C22⋊C4×C37—22no—
58C22⋊Dic37—22no—
59C22⋊Dic37—22no—
60#10596940—44no—
61C4⋊Dic37—21no—
62C4⋊Dic37C2312yes—
63#10596936—22no—
64#10596936—22no—
65C2×#64436—42no—
66C2×#64436C2314yes—
67C23×C37—22no—
68C23×C37—41no—
69C23×C37—41no—
70C23×C37—42no—
71C23×C37—42no—
72C23×C37—42no—
73C23×C37SD1614yescomplemented
74C23×C37C2×D411yescharacteristic
75C23×C37C2×D411yescharacteristic
76C23×C37C2×D411yescharacteristic
77D4×C37—24no—
78D4×C37—42no—
79D4×C37—44no—
80D4×C37—44no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—41no—
86C2×C4×C37—41no—
87C2×C4×C37—41no—
88C2×C4×C37—42no—
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2411yescharacteristic
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—42no—
96C2×Dic37—42no—
97Dic74—24no—
98Dic74—42no—
99#64436—24no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37—21no—
104C22×C37—21no—
105C22×C37—21no—
106C22×C37—44no—
107C22×C37—42no—
108C22×C37—42no—
109C22×C37—42no—
110C22×C37—84no—
111C22×C37C2×SD1612yes—
112C22×C37C2×SD1612yes—
113C22×C37C2×SD1612yes—
114C22×C37C22×D411yescharacteristic
115C4×C37—21no—
116C4×C37—21no—
117C4×C37—21no—
118C4×C37—42no—
119C4×C37H(5,𝔽2)12yes—
120Dic37—42no—
121Dic37—42no—
122#3187—371nomaximal, Sylow
123C2×C37—22no—
124C2×C37—22no—
125C2×C37—22no—
126C2×C37—82no—
127C2×C37#53411yescharacteristic
128C2×C37C22×SD1611yescharacteristic
129C2×C37#57511yescharacteristic
130C2×C22⋊Q8—371no—
131C2×#121D3711yescharacteristic
132#483—372no—
133#481—372no—
134#465—374no—
135#450—372no—
136#448—372no—
137C2×C22⋊C8—371no—
138C37#318711yescharacteristic, complemented, Sylow
139C22×Q8—371no—
140C22×D4—21no—
141C22×D4C2×D3711yescharacteristic
142C23×C4C2×D3711yescharacteristic
143C2×SD16—374no—
144C22×C8—372no—
145C22⋊Q8—372no—
146C22⋊Q8—372no—
147C22⋊Q8—741no—
148C22⋊Q8—741no—
149#121—21no—
150#121—21no—
151#121C2×D3712yes—
152#121C2×D3712yes—
153C2×C4⋊C4—371no—
154C2×C4⋊C4—741no—
155C2×C4⋊C4C2×D3711yescharacteristic
156C2×C22⋊C4—21no—
157C2×C22⋊C4—741no—
158#106—374no—
159#103—374no—
160#102—374no—
161C22⋊C8—372no—
162C22⋊C8—372no—
163C24—21no—
164C24C22⋊D3711yescharacteristic
165C2×Q8—372no—
166C2×Q8—741no—
167C2×Q8—1482no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—42no—
172C2×D4—44no—
173C2×D4C22×D3712yes—
174C22×C4—21no—
175C22×C4—42no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4C22⋊D3711yescharacteristic
179C22×C4C22⋊D3711yescharacteristic
180C22×C4C22⋊D3711yescharacteristic
181C22×C4C22×D3711yescharacteristic
182C22×C4C22×D3711yescharacteristic
183C22×C4C22×D3711yescharacteristic
184SD16—1484no—
185C2×C8—374no—
186C2×C8—1482no—
187C4⋊C4—21no—
188C4⋊C4—372no—
189C4⋊C4—742no—
190C4⋊C4—742no—
191C4⋊C4—741no—
192C4⋊C4C22×D3712yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—742no—
196C22⋊C4—742no—
197C23—22no—
198C23—41no—
199C23—41no—
200C23—42no—
201C23—42no—
202C23—42no—
203C23#1059694014yescomplemented
204C23C2×C22⋊D3711yescharacteristic
205C23C2×C22⋊D3711yescharacteristic
206C23C2×C22⋊D3711yescharacteristic
207Q8—744no—
208Q8—1482no—
209D4—24no—
210D4—42no—
211D4—44no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—742no—
222C2×C4—742no—
223C2×C4—1482no—
224C2×C4—1482no—
225C2×C4C2×C22⋊D3711yescharacteristic
226C2×C4C2×C22⋊D3711yescharacteristic
227C2×C4C2×C22⋊D3711yescharacteristic
228C2×C4C23×D3711yescharacteristic
229C8—744no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—44no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—84no—
241C22C2×#1059694012yes—
242C22C2×#1059694012yes—
243C22C2×#1059694012yes—
244C22C22×C22⋊D3711yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—1482no—
250C4—1482no—
251C4#1192458112yes—
252C2—22no—
253C2—22no—
254C2—22no—
255C2—82no—
256C2#1455809211yescharacteristic
257C2C22×#1059694011yescharacteristic
258C2#1455833111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC2×#121×C37C2
socleC22×C37C22×D4
hypercenterC2×#121D37
hypocenterC37#3187
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11924515C2semidirect
2. #14557863C2semidirect
3. #14557849C2semidirect
4. #14557760C2semidirect
5. #14557684C2semidirect
6. #14557671C2semidirect
7. C2×C22⋊#64436C2semidirect
9. C22×Dic74C22semidirect
10. C2×#10596940C22semidirect
11. C22×#64436C22semidirect
15. #11924515C22semidirect
16. C2×C4⋊Dic37C22semidirect
19. #11924467C22semidirect
20. #11924459C22semidirect
21. #11924457C22semidirect
23. C22⋊#64436C22semidirect
73. C23×C37SD16semidirect
138. C37#3187semidirect
203. C23#10596940semidirect

Maximal subgroups

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

subgroupindex
C2×#119245152
#145578632
#145578492
#145577602
#145576842
#145576712
C2×C22⋊#644362
C2×#121×C372
#318737