Finite Group Databasebeta

← #17994605

Subgroups — #17994605

Order 4736.

356 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11924498C211yesmaximal, characteristic
2C2×#11924465C211yesmaximal, characteristic, complemented
3C2×#11924458C211yesmaximal, characteristic
4C2×#11924456C211yesmaximal, characteristic
5#14557398C211yesmaximal, characteristic, complemented
6#14557295C211yesmaximal, characteristic, complemented
7C37×#340C211yesmaximal, characteristic, complemented
8C22×D148C2211yescharacteristic
9C22×C4×D37—21no—
10C22×#64436C2211yescharacteristic
11#11924498—22no—
12#11924498C414yescomplemented
13C2×C4⋊Dic37C2211yescharacteristic
14C2×#10596938—21no—
15C2×C4×Dic37C2211yescharacteristic
16#11924465—22no—
17#11924458—22no—
18#11924456—22no—
19#11924443—21no—
20#11924443—21no—
21C22×C8×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
24C23×D37—21no—
25C22×C4×C37—21no—
26C22×C4×C37—21no—
27C22×C4×C37C2311yescharacteristic
28C22×Dic37—21no—
29C22×Dic37D411yescharacteristic
30C22×Dic37D411yescharacteristic
31C2×D148—21no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148C2×C412yes—
35C2×D148D412yes—
36C2×D148Q812yes—
37C2×C4×D37—24no—
38C2×C4×D37—42no—
39C2×C4×D37—42no—
40C2×C8×C37—21no—
41C2×C8×C37—21no—
42C2×C8×C37—21no—
43C4⋊C4×C37—21no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37—21no—
46C4⋊C4×C37C2×C412yes—
47#10596938—24no—
48C4⋊Dic37—21no—
49C4⋊Dic37—21no—
50C4×Dic37C2×C412yes—
51C4×Dic37D412yes—
52C2×#64436—21no—
53C2×#64436—21no—
54C2×#64436—21no—
55C23×C37C2×D411yescharacteristic
56C22×D37—22no—
57C22×D37—22no—
58C22×D37—22no—
59C22×D37—41no—
60C22×D37—41no—
61C22×D37—41no—
62C22×D37—41no—
63C2×C4×C37—22no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C22×C411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×Q811yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C2×C4×C37#4111yescharacteristic
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82C2×Dic37C22⋊C412yes—
83C2×Dic37C22⋊C412yes—
84D148—22no—
85D148—22no—
86D148—22no—
87D148C4⋊C414yes—
88C4×D37—48no—
89C8×C37—41no—
90#64436—41no—
91C22×C37C2×C22⋊C411yescharacteristic
92C22×C37#12111yescharacteristic
93C22×C37C22⋊Q811yescharacteristic
94C22×C37#13511yescharacteristic
95C22×C37#13511yescharacteristic
96C22×C37AGL(1,ℤ/8)11yescharacteristic
97C22×C37AGL(1,ℤ/8)11yescharacteristic
98C2×D37—24no—
99C2×D37—42no—
100C2×D37—42no—
101C2×D37—42no—
102C2×D37—42no—
103C2×D37—42no—
104C2×D37—42no—
105C4×C37—42no—
106C4×C37—81no—
107C4×C37C2×C4⋊C411yescharacteristic
108C4×C37#11711yescharacteristic
109C4×C37#12111yescharacteristic
110C4×C37C22⋊Q811yescharacteristic
111Dic37—22no—
112Dic37—22no—
113Dic37—81no—
114#1804—371nomaximal, Sylow
115C2×C37#38011yescharacteristic
116C2×C37#41611yescharacteristic
117C2×C37#41811yescharacteristic
118C2×C37#46311yescharacteristic
119C2×C37#46311yescharacteristic
120C2×C37#47811yescharacteristic
121C2×C37#47811yescharacteristic
122D37—44no—
123C2×C4×D4—371no—
124C2×C4⋊C8—371no—
125C2×#102—371no—
126C2×#102—371no—
127#382—371no—
128#340—371no—
129#340D3711yescharacteristic, complemented
130C37#180411yescharacteristic, complemented, Sylow
131C22×D4—371no—
132C23×C4—741no—
133C22×C8—371no—
134C22×C8C2×D3711yescharacteristic
135C4×D4—374no—
136C4×D4—742no—
137C2×C4⋊C4—371no—
138C2×C4⋊C4C2×D3711yescharacteristic
139C2×C4⋊C4C2×D3711yescharacteristic
140C2×C22⋊C4—741no—
141C2×C42—371no—
142C4⋊C8—742no—
143#102—742no—
144#102—742no—
145#95—741no—
146#95—741no—
147C24—741no—
148C2×D4—372no—
149C2×D4—372no—
150C2×D4—372no—
151C2×D4—741no—
152C2×D4—741no—
153C2×D4—741no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—744no—
159C22×C4—741no—
160C22×C4—1482no—
161C22×C4—1482no—
162C22×C4C22×D3711yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—741no—
167C2×C8—741no—
168C2×C8—741no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C4⋊C4C4×D3712yes—
175C22⋊C4—744no—
176C42—372no—
177C42—372no—
178C23—742no—
179C23—742no—
180C23—742no—
181C23—1481no—
182C23—1481no—
183C23—1481no—
184C23—1481no—
185C23D4×D3711yescharacteristic
186D4—374no—
187D4—742no—
188D4—742no—
189D4—742no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—372no—
197C2×C4—372no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—741no—
201C2×C4—741no—
202C2×C4—1488no—
203C2×C4—1481no—
204C2×C4—1481no—
205C2×C4—1481no—
206C2×C4C2×C4×D3711yescharacteristic
207C2×C4#1059696211yescharacteristic
208C2×C4#1059696211yescharacteristic
209C2×C4D4×D3711yescharacteristic
210C2×C4D4×D3711yescharacteristic
211C2×C4Q8×D3711yescharacteristic
212C8—41no—
213C8—1481no—
214C22—744no—
215C22—1482no—
216C22—1482no—
217C22—1482no—
218C22—1482no—
219C22—1482no—
220C22—1482no—
221C22C22⋊C4×D3711yescharacteristic
222C22#1192450911yescharacteristic
223C22#1192451411yescharacteristic
224C22#1192455711yescharacteristic
225C22#1192455911yescharacteristic
226C22#1192456011yescharacteristic
227C22#1192456311yescharacteristic
228C4—42no—
229C4—81no—
230C4—2961no—
231C4—742no—
232C4—742no—
233C4C4⋊C4×D3711yescharacteristic
234C4#1192449311yescharacteristic
235C4#1192450911yescharacteristic
236C4#1192451411yescharacteristic
237C2—1484no—
238C2#1455739211yescharacteristic
239C2#1455752811yescharacteristic
240C2#1455753611yescharacteristic
241C2#1455774711yescharacteristic
242C2#1455775111yescharacteristic
243C2#1455783211yescharacteristic
244C2#1455783611yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#340C2
socleC23×C37C2×D4
prime radicalC22×D148C22
cosocleC22×C4×C37C23
hypercenter#340D37
hypocenterC37#1804
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#11924465C2semidirect
5. #14557398C2semidirect
6. #14557295C2semidirect
7. C37×#340C2semidirect
12. #11924498C4semidirect
129. #340D37semidirect
130. C37#1804semidirect

Maximal subgroups

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

subgroupindex
C2×#119244982
C2×#119244652
C2×#119244582
C2×#119244562
#145573982
#145572952
C37×#3402
#180437