Finite Group Databasebeta

← #18006336

Subgroups — #18006336

Order 4736.

482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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×#11924555C211yesmaximal, characteristic, complemented
2C2×Q16×D37C211yesmaximal, characteristic, complemented
3#14558191C212yesmaximal, complemented
4#14557771C211yesmaximal, characteristic, complemented
5#14557766C211yesmaximal, characteristic, complemented
6#14557752C212yesmaximal, complemented
7#14557692C212yesmaximal, complemented
8#14557670C212yesmaximal, complemented
9C4×Dic148C211yesmaximal, characteristic, complemented
10C8×D148C211yesmaximal, characteristic, complemented
11C37×#495C211yesmaximal, characteristic, complemented
12C2×#10596964C2212yes—
13C2×Q8×D37C2212yes—
14#11924555—24no—
15C2×Dic148C2211yescharacteristic
16C2×#10596942C2212yes—
17Q16×D37—24no—
18C2×#10596940C2212yes—
19C2×C8×D37C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924522—22no—
22#11924513—22no—
23#11924512C2212yes—
24#11924509—22no—
25#11924507C2212yes—
26C4×Dic74C2212yes—
27C4×D148C2211yescharacteristic
28#11924496—22no—
29#11924470C2211yescharacteristic
30C4⋊#64436C2211yescharacteristic
31#11924461C2212yes—
32#11924460C2212yes—
33#11924457C2212yes—
34#11924448C2211yescharacteristic
35#11924448C2211yescharacteristic
36C2×Q16×C37C2211yescharacteristic
37C2×SD16×C37C2212yes—
38C2×D8×C37C2211yescharacteristic
39#124×C37C2212yes—
40C4×C8×C37C2211yescharacteristic
41C2×Q8×C37C2312yes—
42C2×D4×C37C2312yes—
43C2×C22⋊D37—22no—
44C2×C22⋊D37—22no—
45C22×Dic37—22no—
46Q8×D37—24no—
47Q8×D37—42no—
48#10596964—24no—
49#10596964—42no—
50C2×D148D411yescharacteristic
51C2×C4×D37—22no—
52C2×C4×D37C2311yescharacteristic
53C2×C4×D37C2311yescharacteristic
54C2×Dic74—22no—
55C2×Dic74C2312yes—
56Q16×C37—22no—
57SD16×C37—42no—
58D8×C37—22no—
59C2×C8×C37C2311yescharacteristic
60C2×C8×C37C2311yescharacteristic
61C22⋊C4×C37—22no—
62C22⋊C4×C37—22no—
63C42×C37C2311yescharacteristic
64C22⋊Dic37—22no—
65#10596942—24no—
66#10596940—24no—
67#10596938—22no—
68#10596938D411yescharacteristic
69#10596938D411yescharacteristic
70C4⋊Dic37D411yescharacteristic
71C4⋊Dic37C2312yes—
72#10596936—22no—
73#10596936—22no—
74C4×Dic37—22no—
75C2×#64436C2311yescharacteristic
76C2×#64436C2311yescharacteristic
77Dic148D414yescomplemented
78C8×D37—22no—
79C8×D37—22no—
80C23×C37—22no—
81C22×D37C2×D411yescharacteristic
82C22×D37C2×D411yescharacteristic
83Q8×C37—22no—
84Q8×C37—22no—
85D4×C37—22no—
86D4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2411yescharacteristic
91C22⋊D37—44no—
92C22⋊D37—44no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—44no—
96C2×Dic37C2×D411yescharacteristic
97C2×Dic37C2×D411yescharacteristic
98D148—22no—
99C4×D37—21no—
100C4×D37—21no—
101C4×D37—21no—
102C4×D37—21no—
103C4×D37—44no—
104Dic74—22no—
105Dic74—44no—
106Dic74C2×D414yes—
107C8×C37—21no—
108C8×C37C2×D412yes—
109#64436—21no—
110#64436—21no—
111C22×C37—42no—
112C22×C37—42no—
113C22×C37—42no—
114C22×C37C22×D411yescharacteristic
115C2×D37—21no—
116C2×D37—21no—
117C2×D37—21no—
118C2×D37—21no—
119C2×D37—21no—
120C2×D37#13512yescomplemented
121C4×C37—21no—
122C4×C37—21no—
123C4×C37—42no—
124C4×C37C22×D411yescharacteristic
125C4×C37H(5,𝔽2)11yescharacteristic
126Dic37—24no—
127Dic37—21no—
128Dic37—21no—
129Dic37—42no—
130#3285—371nomaximal, Sylow
131C2×C37—82no—
132C2×C37D4211yescharacteristic
133C2×C37C2×#13511yescharacteristic
134C2×C37#57811yescharacteristic
135D37—22no—
136D37—41no—
137C2×#135—371no—
138C22×Q16—371no—
139#548—372no—
140#495D3711yescharacteristic, complemented
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×#41—372no—
150C22×Q8—372no—
151#135—744no—
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×C8—371no—
161#124—742no—
162#124C2×D3712yes—
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×C8C2×D3711yescharacteristic
178#41—744no—
179#41—1482no—
180C2×Q8—372no—
181C2×Q8—742no—
182C2×Q8—744no—
183C2×Q8—1482no—
184C2×Q8C22×D3712yes—
185C2×D4—371no—
186C2×D4—742no—
187C2×D4—742no—
188C2×D4C22×D3712yes—
189C22×C4—371no—
190C22×C4—371no—
191C22×C4—742no—
192C22×C4—742no—
193Q16—22no—
194Q16—374no—
195Q16—744no—
196SD16—42no—
197SD16—744no—
198D8—22no—
199C2×C8—371no—
200C2×C8—371no—
201C2×C8—742no—
202C2×C8—742no—
203C2×C8C22×D3711yescharacteristic
204C2×C8C22×D3711yescharacteristic
205C4⋊C4—371no—
206C4⋊C4—372no—
207C4⋊C4—742no—
208C4⋊C4—742no—
209C22⋊C4—22no—
210C22⋊C4—22no—
211C22⋊C4—371no—
212C22⋊C4—371no—
213C22⋊C4—742no—
214C22⋊C4—742no—
215C42—742no—
216C42C22×D3711yescharacteristic
217C23—22no—
218C23—371no—
219C23—371no—
220Q8—22no—
221Q8—22no—
222Q8—374no—
223Q8—742no—
224Q8—1484no—
225D4—22no—
226D4—22no—
227D4—742no—
228D4—1484no—
229D4—1484no—
230C2×C4—22no—
231C2×C4—371no—
232C2×C4—371no—
233C2×C4—742no—
234C2×C4—741no—
235C2×C4—741no—
236C2×C4—741no—
237C2×C4—741no—
238C2×C4—742no—
239C2×C4—1484no—
240C2×C4—1484no—
241C2×C4D4×D3711yescharacteristic
242C2×C4D4×D3711yescharacteristic
243C2×C4C23×D3711yescharacteristic
244C8—21no—
245C8—741no—
246C8—741no—
247C8D4×D3712yes—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—372no—
252C22—741no—
253C22—741no—
254C22—741no—
255C22—741no—
256C22—741no—
257C22C2×D4×D3711yescharacteristic
258C4—21no—
259C4—21no—
260C4—42no—
261C4—741no—
262C4—741no—
263C4—744no—
264C4—1482no—
265C4C2×D4×D3711yescharacteristic
266C4#1192458111yescharacteristic
267C2—82no—
268C2—742no—
269C2—1481no—
270C2#1455816811yescharacteristic
271C2#135×D3711yescharacteristic
272C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#495C2
socleC22×C37C22×D4
hypercenter#495D37
hypocenterC37#3285
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#11924555C2semidirect
2. C2×Q16×D37C2semidirect
3. #14558191C2semidirect
4. #14557771C2semidirect
5. #14557766C2semidirect
6. #14557752C2semidirect
7. #14557692C2semidirect
8. #14557670C2semidirect
9. C4×Dic148C2semidirect
10. C8×D148C2semidirect
11. C37×#495C2semidirect
77. Dic148D4semidirect
120. C2×D37#135semidirect
140. #495D37semidirect
148. C37#3285semidirect

Maximal subgroups

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

subgroupindex
C2×#119245552
C2×Q16×D372
#145581912
#145577712
#145577662
#145577522
#145576922
#145576702
C4×Dic1482
C8×D1482
C37×#4952
#328537