Finite Group Databasebeta

← #17994902

Subgroups — #17994902

Order 4736.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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×#11924516C211yesmaximal, characteristic
2C2×C4⋊C4×D37C211yesmaximal, characteristic
3C2×#11924461C211yesmaximal, characteristic, complemented
4C2×#11924459C211yesmaximal, characteristic, complemented
5C2×#11924448C211yesmaximal, characteristic
6#14557295C211yesmaximal, characteristic, complemented
7C37×#340C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C22×C4×D37—21no—
10C22×C4×D37C2211yescharacteristic
11C22×#64436C2211yescharacteristic
12#11924516—22no—
13#11924516C414yescomplemented
14C2×C4⋊Dic37—21no—
15C2×C4⋊Dic37C2211yescharacteristic
16C2×#10596936—21no—
17C4⋊C4×D37—22no—
18C4⋊C4×D37—22no—
19C2×#10596938—21no—
20#11924461—22no—
21#11924459—22no—
22#11924448—22no—
23C22×C8×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25C2×C4⋊C4×C37C2211yescharacteristic
26C23×D37D411yescharacteristic
27C22×C4×C37—21no—
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—24no—
38C2×C4×D37—42no—
39C2×C4×D37—42no—
40C2×C4×D37C2×C412yes—
41C2×C4×D37D412yes—
42C2×Dic74—21no—
43C2×Dic74—21no—
44C2×Dic74—21no—
45C2×Dic74—21no—
46C2×Dic74—21no—
47C2×Dic74C2×C412yescomplemented
48C2×C8×C37—21no—
49C2×C8×C37—21no—
50C2×C8×C37—21no—
51C4⋊C4×C37—21no—
52C4⋊C4×C37—21no—
53C4⋊C4×C37C2×C412yescomplemented
54C4⋊C4×C37D412yes—
55#10596938—24no—
56C4⋊Dic37—21no—
57C4⋊Dic37—24no—
58C4⋊Dic37D412yes—
59#10596936—24no—
60C2×#64436—21no—
61C2×#64436—21no—
62C2×#64436—21no—
63C23×C37C2×D411yescharacteristic
64C22×D37—21no—
65C22×D37—21no—
66C22×D37—21no—
67C22×D37—21no—
68C22×D37C22⋊C412yes—
69C22×D37SD1612yes—
70C22×D37Q1612yes—
71C2×C4×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37—41no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37C22×C411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C2×C4×C37#4111yescharacteristic
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37—22no—
86C2×Dic37—22no—
87C2×Dic37—41no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90C2×Dic37—41no—
91C2×Dic37C22⋊C412yes—
92C4×D37—22no—
93C4×D37—22no—
94C4×D37—22no—
95C4×D37—22no—
96C4×D37—48no—
97Dic74—22no—
98Dic74—22no—
99Dic74—41no—
100Dic74—41no—
101C8×C37—41no—
102#64436—41no—
103C22×C37C2×C22⋊C411yescharacteristic
104C22×C37#12011yescharacteristic
105C22×C37#12311yescharacteristic
106C22×C37C2×SD1611yescharacteristic
107C22×C37C2×Q1611yescharacteristic
108C22×C37AGL(1,ℤ/8)11yescharacteristic
109C22×C37#13711yescharacteristic
110C2×D37—22no—
111C2×D37—22no—
112C2×D37—22no—
113C2×D37—22no—
114C2×D37—22no—
115C2×D37—22no—
116C2×D37#10314yescomplemented
117C4×C37—42no—
118C4×C37—42no—
119C4×C37C4×D411yescharacteristic
120C4×C37C4×D411yescharacteristic
121C4×C37#12111yescharacteristic
122C4×C37#12111yescharacteristic
123Dic37—22no—
124Dic37—42no—
125Dic37—42no—
126#1872—371nomaximal, Sylow
127C2×C37#38611yescharacteristic
128C2×C37C2×#10311yescharacteristic
129C2×C37#41711yescharacteristic
130C2×C37#45011yescharacteristic
131C2×C37#45111yescharacteristic
132C2×C37#48311yescharacteristic
133C2×C37#48411yescharacteristic
134D37—24no—
135C2×C22⋊Q8—371no—
136C22×C4⋊C4—371no—
137C2×#103—371no—
138C2×#103—371no—
139C2×C22⋊C8—371no—
140#340—371no—
141#340D3711yescharacteristic, complemented
142C37#187211yescharacteristic, complemented, Sylow
143C22×Q8—371no—
144C23×C4—371no—
145C23×C4—741no—
146C22×C8—371no—
147C22×C8C2×D3711yescharacteristic
148C22⋊Q8—374no—
149C22⋊Q8—742no—
150C2×C4⋊C4—371no—
151C2×C4⋊C4—742no—
152C2×C4⋊C4—741no—
153C2×C4⋊C4—741no—
154C2×C4⋊C4—742no—
155C2×C4⋊C4C2×D3711yescharacteristic
156C2×C4⋊C4C2×D3711yescharacteristic
157C2×C22⋊C4—741no—
158#103—742no—
159#103—742no—
160C22⋊C8—742no—
161C24—371no—
162C2×Q8—372no—
163C2×Q8—741no—
164C2×Q8—741no—
165C2×Q8—741no—
166C2×Q8—741no—
167C2×Q8—741no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—371no—
171C22×C4—372no—
172C22×C4—372no—
173C22×C4—744no—
174C22×C4—741no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4—741no—
179C22×C4—741no—
180C22×C4—1482no—
181C22×C4—1482no—
182C22×C4C22×D3711yescharacteristic
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—741no—
187C2×C8—741no—
188C2×C8—741no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—372no—
192C4⋊C4—744no—
193C4⋊C4—744no—
194C4⋊C4—741no—
195C4⋊C4C4×D3712yescomplemented
196C4⋊C4D14812yes—
197C22⋊C4—744no—
198C23—372no—
199C23—372no—
200C23—372no—
201C23—741no—
202C23—741no—
203C23—741no—
204C23—741no—
205C23D4×D3711yescharacteristic
206Q8—742no—
207Q8—742no—
208Q8—1481no—
209Q8—1481no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—372no—
217C2×C4—741no—
218C2×C4—741no—
219C2×C4—742no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—742no—
223C2×C4—742no—
224C2×C4—742no—
225C2×C4—1488no—
226C2×C4—1481no—
227C2×C4—1481no—
228C2×C4—1481no—
229C2×C4—1481no—
230C2×C4C2×C4×D3711yescharacteristic
231C2×C4C2×D14811yescharacteristic
232C2×C4#1059696211yescharacteristic
233C2×C4D4×D3711yescharacteristic
234C2×C4D4×D3711yescharacteristic
235C2×C4#1059696611yescharacteristic
236C8—41no—
237C8—1481no—
238C22—374no—
239C22—742no—
240C22—742no—
241C22—742no—
242C22—742no—
243C22—742no—
244C22—742no—
245C22C22⋊C4×D3711yescharacteristic
246C22#1192450611yescharacteristic
247C22#1192452111yescharacteristic
248C22SD16×D3711yescharacteristic
249C22Q16×D3711yescharacteristic
250C22#1192456011yescharacteristic
251C22#1192456511yescharacteristic
252C4—42no—
253C4—42no—
254C4—742no—
255C4—1482no—
256C4—1482no—
257C4#1192449811yescharacteristic
258C4C4×D14811yescharacteristic
259C4#1192450911yescharacteristic
260C4#1192451111yescharacteristic
261C2—744no—
262C2#1455741111yescharacteristic
263C2#103×D3711yescharacteristic
264C2#1455753111yescharacteristic
265C2#1455768511yescharacteristic
266C2#1455769011yescharacteristic
267C2#1455786511yescharacteristic
268C2#1455787011yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#340C2
socleC23×C37C2×D4
prime radicalC23×D37D4
cosocleC22×C4×C37C23
hypercenter#340D37
hypocenterC37#1872
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
3. C2×#11924461C2semidirect
4. C2×#11924459C2semidirect
6. #14557295C2semidirect
7. C37×#340C2semidirect
13. #11924516C4semidirect
47. C2×Dic74C2×C4semidirect
53. C4⋊C4×C37C2×C4semidirect
116. C2×D37#103semidirect
141. #340D37semidirect
142. C37#1872semidirect
195. C4⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245162
C2×C4⋊C4×D372
C2×#119244612
C2×#119244592
C2×#119244482
#145572952
C37×#3402
#187237