Finite Group Databasebeta

← #17996243

Subgroups — #17996243

Order 4736.

280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558092C211yesmaximal, characteristic
2C2×#11924451C211yesmaximal, characteristic, complemented
3#14557324C212yesmaximal, complemented
4#14557321C212yesmaximal, complemented
5C2×#100×C37C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C411yescharacteristic, complemented
7#11924519—21no—
8#11924517C411yescharacteristic, complemented
9#11924517C2211yescharacteristic
10#11924508—21no—
11#11924508—21no—
12#11924505—21no—
13#11924504C411yescharacteristic, complemented
14#11924504C2211yescharacteristic
15C2×C22⋊Dic37—21no—
16C2×C22⋊Dic37C411yescharacteristic, complemented
17#11924451—21no—
18#11924451C2212yes—
19C22×D4×C37C2211yescharacteristic
20C2×M16×C37—21no—
21#100×C37—21no—
22#100×C37C2212yes—
23C24×C37C2×C411yescharacteristic
24C24×C37D411yescharacteristic
25C23×D37C2×C411yescharacteristic, complemented
26C2×D4×C37—41no—
27C2×D4×C37—41no—
28C2×D4×C37C2×C411yescharacteristic
29C2×D4×C37D411yescharacteristic
30C2×D4×C37D411yescharacteristic
31C2×D4×C37C2311yescharacteristic
32C22×C4×C37D411yescharacteristic
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C2×C22⋊D37—21no—
37C2×C22⋊D37—41no—
38C2×C22⋊D37—41no—
39C22×Dic37—21no—
40C22×Dic37—41no—
41C22×Dic37C2×C411yescharacteristic, complemented
42M16×C37—22no—
43M16×C37—41no—
44C2×C8×C37—41no—
45C22⋊Dic37—21no—
46C22⋊Dic37—21no—
47C22⋊Dic37—21no—
48C22⋊Dic37—22no—
49C22⋊Dic37—41no—
50C22⋊Dic37C2×C411yescharacteristic, complemented
51C22⋊Dic37C2×C411yescharacteristic, complemented
52#10596938—21no—
53#10596938—21no—
54#10596936—21no—
55#10596936—21no—
56C23×C37—21no—
57C23×C37—21no—
58C23×C37—21no—
59C23×C37—21no—
60C23×C37—81no—
61C23×C37—81no—
62C23×C37C22⋊C411yescharacteristic
63C23×C37C22⋊C411yescharacteristic
64C23×C37C22⋊C411yescharacteristic
65C23×C37C22×C411yescharacteristic
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68C22×D37—41no—
69C22×D37—81no—
70D4×C37—41no—
71D4×C37—41no—
72D4×C37—41no—
73D4×C37—41no—
74C2×C4×C37—21no—
75C2×C4×C37—21no—
76C2×C4×C37C22⋊C411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C22⋊D37—42no—
79C22⋊D37—41no—
80C22⋊D37—41no—
81C22⋊D37—81no—
82C22⋊D37—81no—
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37—21no—
86C2×Dic37—41no—
87C2×Dic37—42no—
88C2×Dic37—81no—
89C2×Dic37—82no—
90C8×C37—42no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37—41no—
100C22×C37—42no—
101C22×C37—81no—
102C22×C37—81no—
103C22×C37—81no—
104C22×C37#9911yescharacteristic
105C22×C37#9911yescharacteristic
106C22×C37C2×C22⋊C411yescharacteristic
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—82no—
111C4×C37—21no—
112C4×C37—21no—
113Dic37—41no—
114Dic37—41no—
115Dic37—41no—
116Dic37—82no—
117#2121—371nomaximal, Sylow
118C2×C37—21no—
119C2×C37—21no—
120C2×C37—21no—
121C2×C37—41no—
122C2×C37—41no—
123C2×C37—41no—
124C2×C37—41no—
125C2×C37C2×#9911yescharacteristic
126D37—81no—
127#534—371no—
128C2×#100D3711yescharacteristic, complemented
129C2×#99—371no—
130#352—372no—
131AΣL(1,𝔽16)—372no—
132C37#212111yescharacteristic, complemented, Sylow
133C22×D4—371no—
134C22×D4C2×D3711yescharacteristic
135C2×M16—21no—
136#123—371no—
137#123—371no—
138#123—741no—
139#121—741no—
140#121—741no—
141#120—371no—
142#120—371no—
143#120—741no—
144C2×C22⋊C4—371no—
145C2×C22⋊C4—741no—
146#100—21no—
147#100C2×D3712yes—
148#99—372no—
149#99—741no—
150C24—371no—
151C24C4×D3711yescharacteristic
152C24D14811yescharacteristic
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—741no—
156C2×D4—741no—
157C2×D4—741no—
158C2×D4—741no—
159C2×D4—1481no—
160C2×D4—1481no—
161C2×D4C4×D3711yescharacteristic
162C2×D4D14811yescharacteristic
163C2×D4C22⋊D3711yescharacteristic
164C2×D4C22×D3711yescharacteristic
165C22×C4—371no—
166C22×C4—741no—
167C22×C4—1481no—
168C22×C4C22⋊D3711yescharacteristic
169M16—22no—
170M16—41no—
171C2×C8—41no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C22⋊C4—371no—
175C22⋊C4—371no—
176C22⋊C4—741no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4—741no—
181C22⋊C4—742no—
182C22⋊C4—1481no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—81no—
188C23—81no—
189C23—2961no—
190C23—741no—
191C23—1481no—
192C23#1059693811yescharacteristic
193C23#1059693811yescharacteristic
194C23#1059693811yescharacteristic
195C23C2×C4×D3711yescharacteristic
196C23C2×D14811yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—2961no—
202D4—2961no—
203D4—1482no—
204D4—1481no—
205D4—1481no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—2962no—
209C2×C4—2961no—
210C2×C4—741no—
211C2×C4—741no—
212C2×C4—741no—
213C2×C4—1482no—
214C2×C4—1481no—
215C2×C4#1059693811yescharacteristic
216C2×C4C2×C22⋊D3711yescharacteristic
217C8—42no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—81no—
229C22—81no—
230C22—81no—
231C22—2962no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22#1192445011yescharacteristic
236C22#1192445011yescharacteristic
237C22C2×#1059693811yescharacteristic
238C4—21no—
239C4—21no—
240C4—2962no—
241C4—1481no—
242C4—1481no—
243C4—1481no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—2961no—
252C2C2×#1192445011yescharacteristic
subgroupG/H
centerC2C2×#11924450
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC2×#100×C37C2
socleC2×C37C2×#99
prime radical#14558092C2
cosocleC2×D4×C37C23
hypercenterC2×#100D37
hypocenterC37#2121
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#11924451C2semidirect
3. #14557324C2semidirect
4. #14557321C2semidirect
5. C2×#100×C37C2semidirect
6. C22×C22⋊D37C4semidirect
8. #11924517C4semidirect
13. #11924504C4semidirect
16. C2×C22⋊Dic37C4semidirect
25. C23×D37C2×C4semidirect
41. C22×Dic37C2×C4semidirect
50. C22⋊Dic37C2×C4semidirect
51. C22⋊Dic37C2×C4semidirect
128. C2×#100D37semidirect
132. C37#2121semidirect

Maximal subgroups

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

subgroupindex
#145580922
C2×#119244512
#145573242
#145573212
C2×#100×C372
#212137