Finite Group Databasebeta

← #18004080

Subgroups — #18004080

Order 4736.

480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11924568C212yesmaximal
2C4⋊Q8×D37C211yesmaximal, characteristic, complemented
3C4×#10596966C211yesmaximal, characteristic
4#14557743C211yesmaximal, characteristic, complemented
5#14557741C212yesmaximal, complemented
6#14557739C211yesmaximal, characteristic, complemented
7#14557737C212yesmaximal, complemented
8#14557735C211yesmaximal, characteristic, complemented
9#14557555C211yesmaximal, characteristic, complemented
10#14557540C212yesmaximal, complemented
11C37×#462C211yesmaximal, characteristic, complemented
12C2×#10596966C2211yescharacteristic
13C2×Q8×D37C2212yes—
14#11924568—28no—
15C2×#10596942C2212yes—
16C2×#10596930C2212yes—
17C2×#10596941C2212yes—
18C2×#10596929C2212yes—
19#11924536C2211yescharacteristic
20#11924535—21no—
21#11924535—21no—
22#11924534C2212yes—
23Q8×Dic37C2211yescharacteristic
24C4×D148—21no—
25C4×D148C2211yescharacteristic
26#11924498—21no—
27#11924498C2211yescharacteristic
28#11924494—21no—
29#11924494C2211yescharacteristic
30C4⋊C4×D37—21no—
31C4⋊C4×D37—21no—
32C42×D37—21no—
33C42×D37C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35#11924465C2212yes—
36#11924461C2212yes—
37#11924460C2212yes—
38#11924459C2212yes—
39C2×Q16×C37C2212yes—
40C4⋊Q8×C37C2211yescharacteristic
41C4×Q8×C37C2211yescharacteristic
42C4⋊C8×C37C2211yescharacteristic
43#103×C37C2212yes—
44C2×Q8×C37C2312yes—
45C2×Q8×C37C2311yescharacteristic
46#10596966—22no—
47#10596966D414yes—
48Q8×D37—24no—
49Q8×D37—24no—
50C2×D148—21no—
51C2×D148C2311yescharacteristic
52C2×C4×D37—21no—
53C2×C4×D37—22no—
54C2×C4×D37—21no—
55C2×C4×D37—21no—
56C2×C4×D37D411yescharacteristic
57C2×C4×D37D411yescharacteristic
58C2×C4×D37C2311yescharacteristic
59C2×Dic74—22no—
60C2×Dic74C2312yes—
61Q16×C37—24no—
62C2×C8×C37C2312yes—
63C4⋊C4×C37—21no—
64C4⋊C4×C37—21no—
65C4⋊C4×C37—21no—
66C4⋊C4×C37C2311yescharacteristic
67C42×C37—21no—
68C42×C37C2311yescharacteristic
69#10596942—24no—
70#10596941—24no—
71#10596938—21no—
72#10596938—21no—
73#10596938—21no—
74C4⋊Dic37—21no—
75C4⋊Dic37—21no—
76C4⋊Dic37—21no—
77C4⋊Dic37C2311yescharacteristic
78#10596936—22no—
79#10596936—22no—
80C4×Dic37—21no—
81C4×Dic37—21no—
82C4×Dic37D411yescharacteristic
83C4×Dic37D411yescharacteristic
84C4×Dic37C2311yescharacteristic
85C2×#64436C2312yes—
86#10596930—24no—
87#10596929—24no—
88C22×D37—21no—
89C22×D37C2×D411yescharacteristic
90Q8×C37—21no—
91Q8×C37—22no—
92Q8×C37—22no—
93Q8×C37C2×D412yes—
94C2×C4×C37—21no—
95C2×C4×C37—21no—
96C2×C4×C37—22no—
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2411yescharacteristic
100C2×Dic37—21no—
101C2×Dic37—22no—
102C2×Dic37C2×D411yescharacteristic
103C2×Dic37C2×D411yescharacteristic
104C2×Dic37C2×D411yescharacteristic
105D148—24no—
106D148—21no—
107D148C2×D412yes—
108C4×D37—22no—
109C4×D37—24no—
110C4×D37—22no—
111C4×D37—44no—
112C4×D37—42no—
113C4×D37—42no—
114C4×D37C2×D412yes—
115C4×D37#4112yes—
116Dic74—22no—
117Dic74—22no—
118Dic74—44no—
119C8×C37—22no—
120#64436—22no—
121C22×C37C22×D411yescharacteristic
122C2×D37—21no—
123C2×D37—21no—
124C2×D37—22no—
125C2×D37—41no—
126C2×D37—41no—
127C2×D37#12112yes—
128C4×C37—22no—
129C4×C37—21no—
130C4×C37—42no—
131C4×C37—41no—
132C4×C37#13712yescomplemented
133C4×C37C22×D411yescharacteristic
134C4×C37C2×#4111yescharacteristic
135Dic37—21no—
136Dic37—42no—
137Dic37—41no—
138Dic37#12112yes—
139Dic37#13712yescomplemented
140#3039—371nomaximal, Sylow
141C2×C37C2×#12111yescharacteristic
142C2×C37C2×#13711yescharacteristic
143C2×C37C2×#13711yescharacteristic
144D37—22no—
145D37—42no—
146C2×#137—372no—
147C2×C4⋊Q8—371no—
148C4×#41—371no—
149#462—372no—
150#462—371no—
151#462D3711yescharacteristic, complemented
152#461—371no—
153#461—371no—
154#461—372no—
155#423—371no—
156#419—372no—
157C37#303911yescharacteristic, complemented, Sylow
158C2×#41—371no—
159C22×Q8—372no—
160#137—748no—
161C2×Q16—372no—
162C2×Q16C2×D3712yes—
163C2×SD16—372no—
164C2×SD16—372no—
165C2×M16—372no—
166C4⋊Q8—372no—
167C4⋊Q8—371no—
168C4⋊Q8—741no—
169C4⋊Q8—741no—
170C4⋊Q8C2×D3711yescharacteristic
171C4×Q8—371no—
172C4×Q8C2×D3711yescharacteristic
173C4×D4—371no—
174C4×D4—371no—
175C4×D4—741no—
176C4×D4—741no—
177#117—371no—
178#117—741no—
179C2×C4⋊C4—741no—
180C2×C4⋊C4—741no—
181C2×C42—371no—
182C2×C42—741no—
183C4⋊C8—372no—
184C4⋊C8—371no—
185C4⋊C8C2×D3711yescharacteristic
186#103—372no—
187#103—372no—
188#103—372no—
189#103C2×D3712yes—
190#41—374no—
191#41—742no—
192C2×Q8—372no—
193C2×Q8—742no—
194C2×Q8—744no—
195C2×Q8—744no—
196C2×Q8C22×D3712yes—
197C2×Q8C22×D3711yescharacteristic
198C2×D4—371no—
199C2×D4—741no—
200C22×C4—371no—
201C22×C4—371no—
202C22×C4—371no—
203C22×C4—741no—
204C22×C4—741no—
205C22×C4—742no—
206C22×C4—741no—
207Q16—24no—
208Q16—744no—
209SD16—744no—
210SD16—744no—
211M16—744no—
212C2×C8—372no—
213C2×C8C22×D3712yes—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—371no—
218C4⋊C4—742no—
219C4⋊C4—742no—
220C4⋊C4—741no—
221C4⋊C4—741no—
222C4⋊C4—741no—
223C4⋊C4C22×D3711yescharacteristic
224C22⋊C4—741no—
225C22⋊C4—741no—
226C22⋊C4—741no—
227C42—21no—
228C42—371no—
229C42—371no—
230C42—371no—
231C42—741no—
232C42—741no—
233C42C22×D3711yescharacteristic
234C23—371no—
235C23—741no—
236Q8—21no—
237Q8—22no—
238Q8—22no—
239Q8—742no—
240Q8—742no—
241Q8—1484no—
242Q8D4×D3712yes—
243D4—372no—
244D4—744no—
245D4—741no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—371no—
250C2×C4—371no—
251C2×C4—372no—
252C2×C4—372no—
253C2×C4—371no—
254C2×C4—742no—
255C2×C4—744no—
256C2×C4—742no—
257C2×C4—741no—
258C2×C4—742no—
259C2×C4—1482no—
260C2×C4—1484no—
261C2×C4—1482no—
262C2×C4D4×D3711yescharacteristic
263C2×C4D4×D3711yescharacteristic
264C2×C4C23×D3711yescharacteristic
265C8—22no—
266C8—742no—
267C22—372no—
268C22—741no—
269C22—741no—
270C22—742no—
271C22—1481no—
272C22—1481no—
273C22C2×D4×D3711yescharacteristic
274C4—22no—
275C4—21no—
276C4—42no—
277C4—41no—
278C4—372no—
279C4—372no—
280C4—741no—
281C4—1482no—
282C4—1481no—
283C4#1192456812yescomplemented
284C4C2×D4×D3711yescharacteristic
285C4#41×D3711yescharacteristic
286C2—742no—
287C2—1482no—
288C2#121×D3711yescharacteristic
289C2#137×D3711yescharacteristic
290C2C2×#1192456811yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#462C2
socleC22×C37C22×D4
prime radicalC2×#10596966C22
hypercenter#462D37
hypocenterC37#3039
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D37C2semidirect
4. #14557743C2semidirect
5. #14557741C2semidirect
6. #14557739C2semidirect
7. #14557737C2semidirect
8. #14557735C2semidirect
9. #14557555C2semidirect
10. #14557540C2semidirect
11. C37×#462C2semidirect
132. C4×C37#137semidirect
139. Dic37#137semidirect
151. #462D37semidirect
157. C37#3039semidirect
283. C4#11924568semidirect

Maximal subgroups

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

subgroupindex
C2×#119245682
C4⋊Q8×D372
C4×#105969662
#145577432
#145577412
#145577392
#145577372
#145577352
#145575552
#145575402
C37×#4622
#303937