Finite Group Databasebeta

← #18006331

Subgroups — #18006331

Order 4736.

482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×Q16×D37C211yesmaximal, characteristic, complemented
2#14558190C212yesmaximal, complemented
3#14557916C211yesmaximal, characteristic, complemented
4#14557774C211yesmaximal, characteristic, complemented
5#14557766C211yesmaximal, characteristic, complemented
6#14557753C212yesmaximal, complemented
7#14557695C212yesmaximal, complemented
8#14557670C212yesmaximal, complemented
9Q16×Dic37C211yesmaximal, characteristic, complemented
10C8×C22⋊D37C211yesmaximal, characteristic, complemented
11C2×#135×C37C211yesmaximal, characteristic, complemented
12C2×Q8×D37C2212yes—
13C2×Dic148C2211yescharacteristic
14C2×#10596942C2212yes—
15Q16×D37—24no—
16C2×#10596940C2212yes—
17C2×C8×D37C2211yescharacteristic
18#11924523—22no—
19#11924523C2212yes—
20#11924515—22no—
21#11924515C2212yes—
22#11924507—22no—
23#11924507C2212yes—
24Q8×Dic37C2212yes—
25C4×C22⋊D37—22no—
26C4×C22⋊D37C2211yescharacteristic
27#11924470C2211yescharacteristic
28#11924465C2211yescharacteristic
29#11924461C2212yes—
30#11924460C2212yes—
31#11924457C2212yes—
32C22⋊#64436C2211yescharacteristic
33#11924448C2211yescharacteristic
34C8×Dic37C2211yescharacteristic
35C2×#41×C37C2212yes—
36#135×C37—24no—
37C2×Q16×C37C2211yescharacteristic
38C2×SD16×C37C2212yes—
39C2×D8×C37C2211yescharacteristic
40C22×C8×C37C2211yescharacteristic
41#41×C37—24no—
42#41×C37—42no—
43C2×Q8×C37C2312yes—
44C2×D4×C37—22no—
45C2×D4×C37C2312yes—
46C22×C4×C37—22no—
47C22×C4×C37C2311yescharacteristic
48C2×C22⋊D37—22no—
49C2×C22⋊D37D411yescharacteristic
50Q8×D37—24no—
51Q8×D37—42no—
52C2×C4×D37—22no—
53C2×C4×D37C2311yescharacteristic
54C2×Dic74—22no—
55C2×Dic74C2312yes—
56Q16×C37D414yescomplemented
57SD16×C37—24no—
58D8×C37—22no—
59C2×C8×C37—22no—
60C2×C8×C37C2311yescharacteristic
61C2×C8×C37C2311yescharacteristic
62C22⋊Dic37—22no—
63C22⋊Dic37—22no—
64C22⋊Dic37—22no—
65C22⋊Dic37—22no—
66C22⋊Dic37D411yescharacteristic
67#10596942—24no—
68#10596940—42no—
69#10596938D411yescharacteristic
70C4⋊Dic37—22no—
71C4⋊Dic37C2312yes—
72#10596936—22no—
73#10596936D411yescharacteristic
74C4×Dic37—22no—
75C4×Dic37C2311yescharacteristic
76C2×#64436C2311yescharacteristic
77C2×#64436C2311yescharacteristic
78Dic148—22no—
79C8×D37—22no—
80C23×C37—22no—
81C23×C37C2×D411yescharacteristic
82C22×D37C2×D411yescharacteristic
83Q8×C37—22no—
84Q8×C37C2×D414yes—
85D4×C37—22no—
86D4×C37—22no—
87D4×C37—44no—
88C2×C4×C37—22no—
89C2×C4×C37—21no—
90C2×C4×C37—21no—
91C2×C4×C37—44no—
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—22no—
95C22⋊D37—44no—
96C2×Dic37—22no—
97C2×Dic37—22no—
98C2×Dic37C2×D411yescharacteristic
99C2×Dic37C2×D411yescharacteristic
100C2×Dic37C2×D411yescharacteristic
101C4×D37—21no—
102C4×D37—21no—
103C4×D37—44no—
104Dic74—22no—
105Dic74—22no—
106Dic74—44no—
107C8×C37—21no—
108C8×C37C2×D412yes—
109#64436—21no—
110#64436—21no—
111C22×C37—21no—
112C22×C37—21no—
113C22×C37—21no—
114C22×C37—42no—
115C22×C37—42no—
116C22×C37—42no—
117C22×C37C22×D411yescharacteristic
118C2×D37—21no—
119C2×D37—21no—
120C2×D37#13512yescomplemented
121C4×C37—24no—
122C4×C37—21no—
123C4×C37C22×D411yescharacteristic
124C4×C37H(5,𝔽2)11yescharacteristic
125Dic37—21no—
126Dic37—21no—
127Dic37—21no—
128Dic37—42no—
129Dic37—42no—
130#3285—371nomaximal, Sylow
131C2×C37—41no—
132C2×C37—82no—
133C2×C37D4211yescharacteristic
134C2×C37C2×#13511yescharacteristic
135C2×C37#57811yescharacteristic
136D37—22no—
137C2×#135D3711yescharacteristic, complemented
138C22×Q16—371no—
139#548—372no—
140#495—371no—
141#467—371no—
142#466—371no—
143#464—372no—
144#452—372no—
145#448—372no—
146C4×Q16—371no—
147C8×D4—371no—
148C37#328511yescharacteristic, complemented, Sylow
149C2×#41C2×D3712yes—
150C22×Q8—372no—
151#135—24no—
152C2×Q16—372no—
153C2×Q16—371no—
154C2×Q16—744no—
155C2×Q16C2×D3711yescharacteristic
156C2×SD16—372no—
157C2×SD16C2×D3712yes—
158C2×D8C2×D3711yescharacteristic
159C22×C8—371no—
160C22×C8C2×D3711yescharacteristic
161#124—372no—
162#124—742no—
163C22⋊Q8—372no—
164C22⋊Q8—742no—
165#121—372no—
166#121—742no—
167C4×Q8—372no—
168C4×D4—371no—
169C4×D4—742no—
170#107—371no—
171C4⋊C8—371no—
172#103—372no—
173#103—372no—
174#102—372no—
175C22⋊C8—371no—
176C22⋊C8—371no—
177C4×C8—371no—
178#41—24no—
179#41—42no—
180C2×Q8—372no—
181C2×Q8—742no—
182C2×Q8—744no—
183C2×Q8—1482no—
184C2×Q8C22×D3712yes—
185C2×D4—22no—
186C2×D4—371no—
187C2×D4—742no—
188C2×D4C22×D3712yes—
189C22×C4—22no—
190C22×C4—371no—
191C22×C4—742no—
192C22×C4C22×D3711yescharacteristic
193Q16—744no—
194Q16—742no—
195Q16C22⋊D3714yescomplemented
196SD16—24no—
197SD16—1482no—
198D8—22no—
199C2×C8—22no—
200C2×C8—371no—
201C2×C8—371no—
202C2×C8—742no—
203C2×C8C22×D3711yescharacteristic
204C2×C8C22×D3711yescharacteristic
205C4⋊C4—371no—
206C4⋊C4—372no—
207C4⋊C4—742no—
208C4⋊C4—742no—
209C22⋊C4—371no—
210C22⋊C4—371no—
211C22⋊C4—742no—
212C22⋊C4—742no—
213C22⋊C4—742no—
214C22⋊C4—742no—
215C42—371no—
216C42—742no—
217C23—22no—
218C23—371no—
219C23D4×D3711yescharacteristic
220Q8—22no—
221Q8—742no—
222Q8—742no—
223Q8—1484no—
224Q8C2×C22⋊D3714yes—
225D4—22no—
226D4—22no—
227D4—44no—
228D4—742no—
229D4—1484no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—44no—
234C2×C4—371no—
235C2×C4—371no—
236C2×C4—371no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—742no—
240C2×C4—742no—
241C2×C4—1484no—
242C2×C4D4×D3711yescharacteristic
243C2×C4C23×D3711yescharacteristic
244C8—21no—
245C8—741no—
246C8—741no—
247C8C2×C22⋊D3712yes—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—372no—
255C22—741no—
256C22—741no—
257C22C2×D4×D3711yescharacteristic
258C4—21no—
259C4—24no—
260C4—741no—
261C4—741no—
262C4—741no—
263C4—1482no—
264C4—1482no—
265C4C22×C22⋊D3711yescharacteristic
266C4#1192458111yescharacteristic
267C2—41no—
268C2—82no—
269C2—742no—
270C2D4×C22⋊D3711yescharacteristic
271C2#135×D3711yescharacteristic
272C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#135×C37C2
socleC22×C37C22×D4
hypercenterC2×#135D37
hypocenterC37#3285
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D37C2semidirect
2. #14558190C2semidirect
3. #14557916C2semidirect
4. #14557774C2semidirect
5. #14557766C2semidirect
6. #14557753C2semidirect
7. #14557695C2semidirect
8. #14557670C2semidirect
9. Q16×Dic37C2semidirect
10. C8×C22⋊D37C2semidirect
11. C2×#135×C37C2semidirect
56. Q16×C37D4semidirect
120. C2×D37#135semidirect
137. C2×#135D37semidirect
148. C37#3285semidirect
195. Q16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D372
#145581902
#145579162
#145577742
#145577662
#145577532
#145576952
#145576702
Q16×Dic372
C8×C22⋊D372
C2×#135×C372
#328537