Finite Group Databasebeta

← #18005040

Subgroups — #18005040

Order 4736.

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

normal subgroups only

This group has 564 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×#11924559C212yesmaximal, complemented
2C2×#11924557C212yesmaximal, complemented
3#14558084C211yesmaximal, characteristic, complemented
4#14558082C211yesmaximal, characteristic, complemented
5#14557926C212yesmaximal, complemented
6#14557925C211yesmaximal, characteristic, complemented
7#14557923C211yesmaximal, characteristic, complemented
8#14557922C211yesmaximal, characteristic, complemented
9#14557919C212yesmaximal, complemented
10#97×D37C211yesmaximal, characteristic, complemented
11C37×#497C211yesmaximal, characteristic, complemented
12C2×#10596966C2212yes—
13C2×#10596966C2211yescharacteristic
14C2×#10596964C2211yescharacteristic
15#11924559—28no—
16#11924557—28no—
17C2×#10596942C2212yes—
18C2×#10596930C2212yes—
19C2×#10596941C2212yes—
20C2×#10596941C2212yes—
21C2×D296C2212yes—
22C2×#10596939C2212yes—
23C2×C8×D37C2212yes—
24#11924534C2211yescharacteristic
25#11924533C2211yescharacteristic
26#11924532C2211yescharacteristic
27#11924525C2212yes—
28#11924524C2211yescharacteristic
29#11924511—22no—
30#11924509—22no—
31#11924498—22no—
32#11924496—22no—
33C42×D37C2211yescharacteristic
34#11924447C2211yescharacteristic
35#11924446C2212yes—
36C2×Q16×C37C2212yes—
37C2×SD16×C37C2212yes—
38C4⋊Q8×C37C2211yescharacteristic
39#124×C37C2211yescharacteristic
40#97×C37C2211yescharacteristic
41C2×Q8×C37C2312yes—
42C2×Q8×C37C2311yescharacteristic
43C2×D4×C37C2311yescharacteristic
44C2×C22⋊D37—21no—
45C2×C22⋊D37—22no—
46C22×Dic37—21no—
47#10596966—24no—
48#10596966—24no—
49#10596966—24no—
50#10596964—24no—
51C2×D148—21no—
52C2×D148—22no—
53C2×D148—22no—
54C2×D148C2311yescharacteristic
55C2×D148C2312yes—
56C2×C4×D37—21no—
57C2×C4×D37—22no—
58C2×C4×D37D412yes—
59C2×C4×D37C2311yescharacteristic
60C2×Dic74C2311yescharacteristic
61Q16×C37—24no—
62SD16×C37—24no—
63C2×C8×C37C2312yes—
64C4⋊C4×C37—22no—
65C22⋊C4×C37—22no—
66C42×C37C2311yescharacteristic
67#10596942—24no—
68#10596941—24no—
69#10596941—24no—
70#10596939—24no—
71#10596938—22no—
72#10596938—24no—
73#10596936—22no—
74C4×Dic37D412yes—
75C4×Dic37C2311yescharacteristic
76C2×#64436C2312yes—
77D296—24no—
78#10596930—24no—
79C8×D37D418yescomplemented
80C23×C37—21no—
81C22×D37—22no—
82C22×D37—21no—
83C22×D37C2×D411yescharacteristic
84Q8×C37—22no—
85Q8×C37—22no—
86Q8×C37—22no—
87D4×C37—22no—
88C2×C4×C37—21no—
89C2×C4×C37—22no—
90C2×C4×C37C2×D412yes—
91C2×C4×C37C2411yescharacteristic
92C22⋊D37—44no—
93C22⋊D37—42no—
94C2×Dic37—21no—
95C2×Dic37—42no—
96C2×Dic37C2×D412yes—
97C2×Dic37C2×D411yescharacteristic
98D148—22no—
99D148—22no—
100D148—22no—
101D148—44no—
102D148—42no—
103D148—44no—
104C4×D37—42no—
105C4×D37—42no—
106C4×D37—44no—
107C4×D37C2×D414yes—
108Dic74—22no—
109C8×C37C2×D414yes—
110#64436C2×D414yes—
111C22×C37—41no—
112C22×C37—42no—
113C22×C37C22×D411yescharacteristic
114C2×D37—22no—
115C2×D37—42no—
116C2×D37—41no—
117C2×D37—44no—
118C2×D37—42no—
119C2×D37#12712yes—
120C4×C37—22no—
121C4×C37—41no—
122C4×C37—42no—
123C4×C37C22×D412yes—
124Dic37—22no—
125Dic37—41no—
126Dic37#12712yes—
127#3150—371nomaximal, Sylow
128C2×C37—81no—
129C2×C37C2×#12711yescharacteristic
130C2×C37#57512yes—
131D37—22no—
132D37—82no—
133D37—81no—
134C2×#135—372no—
135C2×#135—372no—
136#532—371no—
137#532—371no—
138#497—372no—
139#497—371no—
140#497D3711yescharacteristic, complemented
141#496—372no—
142#496—371no—
143#496—371no—
144C2×#97—371no—
145C37#315011yescharacteristic, complemented, Sylow
146C2×#41—372no—
147C2×#41—371no—
148C2×#41—371no—
149#135—748no—
150#135—748no—
151C2×Q16—372no—
152C2×Q16C2×D3712yes—
153C2×SD16—372no—
154C2×SD16—372no—
155C2×SD16—372no—
156C2×SD16C2×D3712yes—
157C2×D8—372no—
158C2×D8—372no—
159C22×C8—372no—
160C4⋊Q8—371no—
161C4⋊Q8C2×D3711yescharacteristic
162#127—371no—
163#127—371no—
164#124—372no—
165#124—371no—
166#124C2×D3711yescharacteristic
167#121—742no—
168#121—742no—
169C4×D4—742no—
170C4×D4—742no—
171C2×C42—371no—
172#97—372no—
173#97—371no—
174#97C2×D3711yescharacteristic
175#41—744no—
176#41—744no—
177#41—744no—
178#41—744no—
179C2×Q8—371no—
180C2×Q8C22×D3712yes—
181C2×Q8C22×D3711yescharacteristic
182C2×D4—371no—
183C2×D4—372no—
184C2×D4—741no—
185C2×D4—742no—
186C2×D4—742no—
187C2×D4—741no—
188C2×D4—742no—
189C2×D4C22×D3711yescharacteristic
190C22×C4—371no—
191C22×C4—372no—
192C22×C4—741no—
193C22×C4—742no—
194C22×C4—741no—
195Q16—24no—
196Q16—744no—
197SD16—24no—
198SD16—744no—
199SD16—744no—
200SD16—744no—
201D8—744no—
202D8—744no—
203C2×C8—372no—
204C2×C8—378no—
205C2×C8C22×D3712yes—
206C4⋊C4—22no—
207C4⋊C4—742no—
208C22⋊C4—22no—
209C22⋊C4—744no—
210C22⋊C4—742no—
211C42—372no—
212C42—371no—
213C42C22×D3711yescharacteristic
214C23—21no—
215C23—371no—
216C23—742no—
217C23—741no—
218Q8—22no—
219Q8—22no—
220Q8—22no—
221Q8—742no—
222D4—22no—
223D4—742no—
224D4—742no—
225D4—742no—
226D4—1484no—
227D4—1482no—
228D4—1484no—
229D4—1484no—
230D4—1482no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—371no—
234C2×C4—374no—
235C2×C4—372no—
236C2×C4—741no—
237C2×C4—1482no—
238C2×C4—1482no—
239C2×C4—1484no—
240C2×C4—1482no—
241C2×C4D4×D3712yes—
242C2×C4C23×D3711yescharacteristic
243C8—374no—
244C8D4×D3714yes—
245C22—41no—
246C22—42no—
247C22—372no—
248C22—742no—
249C22—1482no—
250C22—1481no—
251C22—1484no—
252C22—1482no—
253C22C2×D4×D3711yescharacteristic
254C4—22no—
255C4—41no—
256C4—42no—
257C4—372no—
258C4—742no—
259C4—1481no—
260C4C2×D4×D3712yes—
261C2—81no—
262C2—2962no—
263C2—2961no—
264C2—742no—
265C2#127×D3711yescharacteristic
266C2#1455833212yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#497C2
socleC22×C37C22×D4
hypercenter#497D37
hypocenterC37#3150
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#11924559C2semidirect
2. C2×#11924557C2semidirect
3. #14558084C2semidirect
4. #14558082C2semidirect
5. #14557926C2semidirect
6. #14557925C2semidirect
7. #14557923C2semidirect
8. #14557922C2semidirect
9. #14557919C2semidirect
10. #97×D37C2semidirect
11. C37×#497C2semidirect
79. C8×D37D4semidirect
140. #497D37semidirect
145. C37#3150semidirect

Maximal subgroups

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

subgroupindex
C2×#119245592
C2×#119245572
#145580842
#145580822
#145579262
#145579252
#145579232
#145579222
#145579192
#97×D372
C37×#4972
#315037