Finite Group Databasebeta

← #18004762

Subgroups — #18004762

Order 4736.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#14558064C211yesmaximal, characteristic
2C2×Q8×Dic37C211yesmaximal, characteristic, complemented
3#14557869C211yesmaximal, characteristic, complemented
4#14557849C211yesmaximal, characteristic
5#14557842C212yesmaximal, complemented
6#14557753C212yesmaximal, complemented
7#14557689C211yesmaximal, characteristic, complemented
8#14557637C212yesmaximal, complemented
9#14557634C212yesmaximal, complemented
10#14557587C211yesmaximal, characteristic, complemented
11C37×#448C211yesmaximal, characteristic
12C2×#10596942C2212yes—
13#11924529—21no—
14#11924527C2211yescharacteristic
15#11924523C2211yescharacteristic
16#11924517—21no—
17#11924515C2211yescharacteristic
18Q8×Dic37—21no—
19Q8×Dic37—21no—
20Q8×Dic37C2212yes—
21Q8×Dic37C2212yes—
22#11924501C2211yescharacteristic
23D4×Dic37—21no—
24D4×Dic37C2211yescharacteristic
25#11924492—21no—
26C2×C4⋊Dic37—21no—
27C2×C4⋊Dic37C2211yescharacteristic
28C2×C4×Dic37—21no—
29C2×C4×Dic37C2211yescharacteristic
30#11924470C2212yes—
31#11924467C2212yes—
32#11924465C2212yes—
33#11924461C2212yes—
34#11924460C2212yes—
35#11924457C2212yes—
36C22⋊#64436C2211yescharacteristic
37#11924446C2212yes—
38C22×Q8×C37C2211yescharacteristic
39C2×SD16×C37C2212yes—
40#121×C37C2211yescharacteristic
41#103×C37C2212yes—
42C22⋊C8×C37C2211yescharacteristic
43C2×Q8×C37—24no—
44C2×Q8×C37—21no—
45C2×Q8×C37C2312yes—
46C2×D4×C37—21no—
47C2×D4×C37C2311yescharacteristic
48C22×C4×C37—21no—
49C22×C4×C37C2311yescharacteristic
50C22×Dic37—21no—
51C22×Dic37—21no—
52C22×Dic37D411yescharacteristic
53C22×Dic37D411yescharacteristic
54C2×Dic74C2311yescharacteristic
55SD16×C37—24no—
56C2×C8×C37C2312yes—
57C4⋊C4×C37C2311yescharacteristic
58C22⋊C4×C37—21no—
59C22⋊Dic37—21no—
60C22⋊Dic37—21no—
61C22⋊Dic37—21no—
62C22⋊Dic37—21no—
63#10596942—24no—
64C4⋊Dic37—21no—
65C4⋊Dic37—22no—
66C4⋊Dic37—22no—
67C4⋊Dic37—21no—
68C4⋊Dic37C2312yes—
69C4⋊Dic37C2311yescharacteristic
70#10596936—21no—
71#10596936—21no—
72#10596936—21no—
73C4×Dic37—22no—
74C4×Dic37—22no—
75C4×Dic37—21no—
76C4×Dic37D411yescharacteristic
77C4×Dic37D411yescharacteristic
78C4×Dic37C2311yescharacteristic
79C4×Dic37C2311yescharacteristic
80C2×#64436C2312yes—
81C23×C37—21no—
82C23×C37C2×D411yescharacteristic
83Q8×C37—24no—
84Q8×C37—22no—
85Q8×C37#4114yes—
86D4×C37—22no—
87D4×C37—42no—
88C2×C4×C37—24no—
89C2×C4×C37—22no—
90C2×C4×C37—22no—
91C2×C4×C37—21no—
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2411yescharacteristic
94C2×Dic37—22no—
95C2×Dic37—22no—
96C2×Dic37—21no—
97C2×Dic37—21no—
98C2×Dic37—41no—
99C2×Dic37—42no—
100C2×Dic37—42no—
101C2×Dic37C2×D411yescharacteristic
102C2×Dic37C2×D411yescharacteristic
103C2×Dic37C2×D411yescharacteristic
104C2×Dic37C2×D411yescharacteristic
105Dic74—22no—
106C8×C37—22no—
107#64436—22no—
108C22×C37—21no—
109C22×C37—21no—
110C22×C37—41no—
111C22×C37—41no—
112C22×C37—41no—
113C22×C37#13712yes—
114C22×C37C22×D411yescharacteristic
115C4×C37—24no—
116C4×C37—21no—
117C4×C37—41no—
118C4×C37C2×#4112yes—
119Dic37—21no—
120Dic37—21no—
121Dic37—21no—
122Dic37—21no—
123Dic37—41no—
124Dic37—42no—
125Dic37—41no—
126#3117—371nomaximal, Sylow
127C2×C37—22no—
128C2×C37—81no—
129C2×C37#52511yescharacteristic
130C2×C37C2×#13711yescharacteristic
131C2×C37#57511yescharacteristic
132#529—371no—
133C2×C4×Q8—371no—
134#484—371no—
135#481—371no—
136#479—372no—
137#464—372no—
138#451—371no—
139#448D3711yescharacteristic
140#441—372no—
141#440—372no—
142#432—371no—
143C37#311711yescharacteristic, complemented, Sylow
144C22×Q8C2×D3711yescharacteristic
145C2×Q16—372no—
146C2×SD16C2×D3712yes—
147#126—741no—
148#125—371no—
149#124—371no—
150#123—741no—
151C22⋊Q8—371no—
152#121C2×D3711yescharacteristic
153C4×Q8—372no—
154C4×Q8—372no—
155C4×Q8—371no—
156C4×Q8—741no—
157C4×Q8—741no—
158C4×D4—371no—
159C4×D4—741no—
160#117—741no—
161C2×C4⋊C4—371no—
162C2×C4⋊C4—741no—
163C2×C42—371no—
164C2×C42—741no—
165#107—372no—
166#106—372no—
167C4⋊C8—372no—
168#103—372no—
169#103—372no—
170#103C2×D3712yes—
171#102—372no—
172C22⋊C8—371no—
173C22⋊C8C2×D3711yescharacteristic
174#97—372no—
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8—371no—
178C2×Q8C22×D3712yes—
179C2×D4—21no—
180C2×D4C22×D3711yescharacteristic
181C22×C4—21no—
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—741no—
185C22×C4—741no—
186C22×C4C22×D3711yescharacteristic
187Q16—744no—
188SD16—24no—
189C2×C8—372no—
190C2×C8C22×D3712yes—
191C4⋊C4—372no—
192C4⋊C4—371no—
193C4⋊C4—741no—
194C4⋊C4—741no—
195C4⋊C4—742no—
196C4⋊C4—742no—
197C4⋊C4—741no—
198C4⋊C4—741no—
199C4⋊C4—741no—
200C4⋊C4C22×D3711yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—741no—
203C22⋊C4—741no—
204C22⋊C4—741no—
205C22⋊C4—741no—
206C42—371no—
207C42—371no—
208C42—371no—
209C42—371no—
210C42—742no—
211C42—742no—
212C42—741no—
213C23—21no—
214C23D4×D3711yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—742no—
218Q8#1059696414yes—
219D4—22no—
220D4—42no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—371no—
226C2×C4—371no—
227C2×C4—371no—
228C2×C4—371no—
229C2×C4—742no—
230C2×C4—742no—
231C2×C4—741no—
232C2×C4—741no—
233C2×C4—1481no—
234C2×C4—1482no—
235C2×C4—1482no—
236C2×C4D4×D3711yescharacteristic
237C2×C4C23×D3711yescharacteristic
238C8—22no—
239C8—742no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#1192456512yes—
246C22C2×D4×D3711yescharacteristic
247C4—24no—
248C4—21no—
249C4—41no—
250C4—741no—
251C4—741no—
252C4—741no—
253C4—741no—
254C4—1481no—
255C4—1482no—
256C4—1481no—
257C4C2×#1059696412yes—
258C2—22no—
259C2—81no—
260C2#1455803911yescharacteristic
261C2C2×#1192456511yescharacteristic
262C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#448C2
socleC22×C37C22×D4
prime radical#121×C37C22
hypercenter#448D37
hypocenterC37#3117
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic37C2semidirect
3. #14557869C2semidirect
5. #14557842C2semidirect
6. #14557753C2semidirect
7. #14557689C2semidirect
8. #14557637C2semidirect
9. #14557634C2semidirect
10. #14557587C2semidirect
143. C37#3117semidirect

Maximal subgroups

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

subgroupindex
#145580642
C2×Q8×Dic372
#145578692
#145578492
#145578422
#145577532
#145576892
#145576372
#145576342
#145575872
C37×#4482
#311737