Finite Group Databasebeta

← #18007305

Subgroups — #18007305

Order 4736.

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

normal subgroups only

This group has 396 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
1#14558243C211yesmaximal, characteristic, complemented
2#14558205C211yesmaximal, characteristic, complemented
3#14557898C212yesmaximal, complemented
4#14557880C211yesmaximal, characteristic, complemented
5#14557834C212yesmaximal, complemented
6#14557824C211yesmaximal, characteristic, complemented
7#14557729C211yesmaximal, characteristic, complemented
8#14557729C212yesmaximal, complemented
9#14557646C212yesmaximal, complemented
10C4×D296C211yesmaximal, characteristic, complemented
11C37×#446C211yesmaximal, characteristic, complemented
12C2×#10596966—21no—
13C2×D296C2211yescharacteristic
14C2×D296C2212yes—
15#11924536C2211yescharacteristic
16#11924533C2211yescharacteristic
17#11924533C2212yes—
18#11924528C2212yes—
19#11924514—22no—
20#11924512—21no—
21#11924511—21no—
22#11924511—22no—
23C4×D148C2211yescharacteristic
24C4×D148C2212yes—
25C4×D148C2211yescharacteristic
26C4×D148C2212yes—
27C4⋊C4×D37—21no—
28#11924470C2211yescharacteristic
29#11924468C2212yes—
30#11924458C2212yes—
31#11924458C2212yes—
32#11924458C2212yes—
33#11924458C2211yescharacteristic
34#11924458C2211yescharacteristic
35#11924458C2212yes—
36C4×Q8×C37C2211yescharacteristic
37C4⋊C8×C37C2211yescharacteristic
38C4⋊C8×C37C2212yes—
39#97×C37C2212yes—
40C4×C8×C37C2211yescharacteristic
41C2×Q8×C37D411yescharacteristic
42#10596966—44no—
43C2×D148—22no—
44C2×D148—21no—
45C2×D148—22no—
46C2×D148—21no—
47C2×D148C2311yescharacteristic
48C2×D148C2312yes—
49C2×D148C2311yescharacteristic
50C2×C4×D37—21no—
51C2×C4×D37—22no—
52C2×C4×D37—21no—
53C2×C4×D37—22no—
54C2×Dic74—21no—
55C2×C8×C37C2311yescharacteristic
56C2×C8×C37C2312yes—
57C2×C8×C37C2311yescharacteristic
58C4⋊C4×C37D411yescharacteristic
59C4⋊C4×C37D412yes—
60C42×C37C2312yes—
61C42×C37C2311yescharacteristic
62#10596938—22no—
63#10596938—21no—
64#10596938—22no—
65#10596938—21no—
66C4⋊Dic37—21no—
67C4⋊Dic37C2311yescharacteristic
68C4⋊Dic37C2311yescharacteristic
69C4⋊Dic37C2312yes—
70#10596936—22no—
71#10596936—22no—
72D296—22no—
73D296—24no—
74C22×D37—21no—
75C22×D37—22no—
76C22×D37—21no—
77Q8×C37—22no—
78C2×C4×C37C2×D412yes—
79C2×C4×C37C2×D412yes—
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2411yescharacteristic
83C2×Dic37—21no—
84C2×Dic37—22no—
85C2×Dic37—21no—
86D148—21no—
87D148—22no—
88D148—21no—
89D148—21no—
90D148—22no—
91D148—44no—
92D148—42no—
93D148—81no—
94D148—82no—
95D148#4112yescomplemented
96C4×D37—44no—
97C4×D37—42no—
98C4×D37—42no—
99C4×D37—82no—
100Dic74—81no—
101C8×C37—21no—
102C8×C37—22no—
103C8×C37—21no—
104C22×C37C22×D411yescharacteristic
105C2×D37—22no—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—42no—
109C2×D37—41no—
110C2×D37—42no—
111C2×D37—41no—
112C2×D37—42no—
113C2×D37—41no—
114C4×C37—22no—
115C4×C37—21no—
116C4×C37—22no—
117C4×C37AGL(1,ℤ/8)12yes—
118C4×C37C2×#4111yescharacteristic
119C4×C372−1+411yescharacteristic
120Dic37—41no—
121Dic37—41no—
122Dic37—42no—
123#3366—371nomaximal, Sylow
124C2×C37#54811yescharacteristic
125C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C37#57611yescharacteristic
127D37—42no—
128D37—82no—
129D37—81no—
130#554—371no—
131#550—371no—
132#490—372no—
133#486—371no—
134#478—372no—
135#476—371no—
136#459—372no—
137#459—371no—
138#446D3711yescharacteristic, complemented
139#442—372no—
140C4×D8—371no—
141C37#336611yescharacteristic, complemented, Sylow
142C2×#41—741no—
143C2×D8—371no—
144C2×D8—372no—
145C4⋊Q8—371no—
146#127—371no—
147#127—372no—
148#125—372no—
149C22⋊Q8—741no—
150C22⋊Q8—742no—
151#121—741no—
152#121—742no—
153C4×Q8C2×D3711yescharacteristic
154C4×D4—371no—
155C4×D4—372no—
156C4×D4—371no—
157C4×D4—372no—
158C2×C4⋊C4—741no—
159#107—371no—
160#106—372no—
161C4⋊C8C2×D3711yescharacteristic
162C4⋊C8C2×D3712yes—
163#102—371no—
164#102—371no—
165#102—372no—
166#102—372no—
167#102—372no—
168#102—372no—
169#97C2×D3712yes—
170C4×C8C2×D3711yescharacteristic
171#41—1484no—
172C2×Q8—741no—
173C2×Q8D14811yescharacteristic
174C2×D4—371no—
175C2×D4—371no—
176C2×D4—372no—
177C2×D4—741no—
178C2×D4—742no—
179C2×D4—742no—
180C2×D4—741no—
181C22×C4—742no—
182C22×C4—741no—
183C22×C4—742no—
184C22×C4—741no—
185D8—742no—
186D8—744no—
187C2×C8C22×D3711yescharacteristic
188C2×C8C22×D3711yescharacteristic
189C2×C8C22×D3712yes—
190C4⋊C4—372no—
191C4⋊C4—371no—
192C4⋊C4—371no—
193C4⋊C4—742no—
194C4⋊C4—742no—
195C4⋊C4—741no—
196C4⋊C4D14811yescharacteristic
197C4⋊C4D14812yes—
198C22⋊C4—741no—
199C22⋊C4—742no—
200C22⋊C4—741no—
201C22⋊C4—742no—
202C42C22×D3711yescharacteristic
203C42C22×D3712yes—
204C23—741no—
205C23—742no—
206C23—741no—
207Q8—22no—
208Q8—2961no—
209D4—372no—
210D4—2962no—
211D4—2961no—
212D4—741no—
213D4—742no—
214D4—741no—
215D4—741no—
216D4—742no—
217D4—1484no—
218D4—1482no—
219C2×C4—2962no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—742no—
223C2×C4—1484no—
224C2×C4—1482no—
225C2×C4—1482no—
226C2×C4C2×D14811yescharacteristic
227C2×C4C2×D14812yes—
228C2×C4C2×D14812yes—
229C2×C4C2×D14811yescharacteristic
230C2×C4C23×D3711yescharacteristic
231C8—21no—
232C8—22no—
233C8—21no—
234C22—742no—
235C22—1482no—
236C22—1481no—
237C22—1481no—
238C22—1482no—
239C22—1482no—
240C22—1481no—
241C22—1481no—
242C22—1481no—
243C22C22×D14811yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—1481no—
248C4—1481no—
249C4—1482no—
250C4#1192456412yes—
251C4#41×D3711yescharacteristic
252C4#1192458411yescharacteristic
253C2—2962no—
254C2—2961no—
255C2—1482no—
256C2#1455819511yescharacteristic
257C2C2×#1192456411yescharacteristic
258C2#1455833811yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#446C2
socleC22×C37C22×D4
hypercenter#446D37
hypocenterC37#3366
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #14558243C2semidirect
2. #14558205C2semidirect
3. #14557898C2semidirect
4. #14557880C2semidirect
5. #14557834C2semidirect
6. #14557824C2semidirect
7. #14557729C2semidirect
8. #14557729C2semidirect
9. #14557646C2semidirect
10. C4×D296C2semidirect
11. C37×#446C2semidirect
95. D148#41semidirect
138. #446D37semidirect
141. C37#3366semidirect

Maximal subgroups

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

subgroupindex
#145582432
#145582052
#145578982
#145578802
#145578342
#145578242
#145577292
#145576462
C4×D2962
C37×#4462
#336637