Finite Group Databasebeta

← #17994952

Subgroups — #17994952

Order 4736.

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

normal subgroups only

This group has 374 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
1C22×#10596930C211yesmaximal, characteristic
2C2×#11924501C211yesmaximal, characteristic, complemented
3C2×#11924459C211yesmaximal, characteristic, complemented
4C2×#11924456C211yesmaximal, characteristic
5#14557434C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic, complemented
7C37×#340C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C22×D148C2211yescharacteristic
10C2×#10596930—22no—
11C2×#10596930—22no—
12C2×#10596930C414yescomplemented
13C22×#64436C2211yescharacteristic
14#11924501—22no—
15#11924501—22no—
16C2×#10596936—21no—
17C2×#10596938—21no—
18C2×#10596938—21no—
19C2×C4×Dic37—21no—
20C2×C4×Dic37C2211yescharacteristic
21#11924459—22no—
22#11924456—22no—
23C22×C8×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25C2×C4⋊C4×C37C2211yescharacteristic
26C23×D37—21no—
27C22×C4×C37—21no—
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C22×Dic37D411yescharacteristic
33C2×D148—21no—
34C2×D148—21no—
35C2×D148—21no—
36C2×D148—21no—
37C2×D148—21no—
38C2×D148C2×C412yes—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74—21no—
42C2×Dic74C2×C412yes—
43C2×Dic74D412yes—
44C2×Dic74D412yes—
45C2×C8×C37—21no—
46C2×C8×C37—21no—
47C2×C8×C37C2×C412yes—
48C4⋊C4×C37—21no—
49C4⋊C4×C37—21no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37D412yes—
52#10596938—42no—
53#10596938—42no—
54#10596936—24no—
55C4×Dic37—24no—
56C4×Dic37—21no—
57C4×Dic37—21no—
58C2×#64436—21no—
59C2×#64436—21no—
60C2×#64436—21no—
61#10596930—28no—
62C23×C37C2×D411yescharacteristic
63C22×D37—22no—
64C22×D37—41no—
65C22×D37—41no—
66C22×D37—41no—
67C22×D37—41no—
68C22×D37—41no—
69C22×D37—41no—
70C2×C4×C37—22no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37—41no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37C22×C411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37#4111yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C2×Dic37—22no—
83C2×Dic37—21no—
84C2×Dic37—22no—
85C2×Dic37—22no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37—21no—
89C2×Dic37—21no—
90C2×Dic37SD1612yescomplemented
91D148—22no—
92D148—22no—
93D148—41no—
94D148—41no—
95Dic74—22no—
96Dic74—22no—
97Dic74—22no—
98Dic74C22⋊C414yescomplemented
99C8×C37—22no—
100#64436—41no—
101C22×C37C4×D411yescharacteristic
102C22×C37#12011yescharacteristic
103C22×C37#12111yescharacteristic
104C22×C37C2×SD1611yescharacteristic
105C22×C37#13511yescharacteristic
106C22×C37AGL(1,ℤ/8)11yescharacteristic
107C22×C37#13711yescharacteristic
108C2×D37—42no—
109C2×D37—42no—
110C2×D37—42no—
111C2×D37—81no—
112C2×D37—81no—
113C2×D37—81no—
114C2×D37—81no—
115C4×C37—42no—
116C4×C37—81no—
117C4×C37C2×C22⋊C411yescharacteristic
118C4×C37C4×D411yescharacteristic
119C4×C37#12111yescharacteristic
120C4×C37#12311yescharacteristic
121Dic37—24no—
122Dic37—22no—
123Dic37—41no—
124#1880—371nomaximal, Sylow
125C2×C37#38611yescharacteristic
126C2×C37C4×SD1611yescharacteristic
127C2×C37#44011yescharacteristic
128C2×C37#44811yescharacteristic
129C2×C37#44911yescharacteristic
130C2×C37#46011yescharacteristic
131C2×C37#46411yescharacteristic
132D37—82no—
133C22×SD16—371no—
134C2×C4×Q8—371no—
135C2×#103—371no—
136C2×#102—371no—
137#390—371no—
138#340D3711yescharacteristic, complemented
139#336—371no—
140C37#188011yescharacteristic, complemented, Sylow
141C22×Q8—371no—
142C22×D4—371no—
143C2×SD16—374no—
144C2×SD16—742no—
145C2×SD16—742no—
146C22×C8—371no—
147C22×C8C2×D3711yescharacteristic
148C4×Q8—742no—
149C4×Q8—742no—
150C2×C4⋊C4—741no—
151C2×C4⋊C4C2×D3711yescharacteristic
152C2×C4⋊C4C2×D3711yescharacteristic
153C2×C22⋊C4—741no—
154C2×C22⋊C4—741no—
155C2×C42—371no—
156C2×C42—741no—
157#103—742no—
158#102—742no—
159C24—741no—
160C2×Q8—372no—
161C2×Q8—372no—
162C2×Q8—372no—
163C2×Q8—741no—
164C2×Q8—741no—
165C2×Q8—741no—
166C2×D4—372no—
167C2×D4—741no—
168C2×D4—741no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—741no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—371no—
175C22×C4—371no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178SD16—748no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—741no—
182C2×C8—741no—
183C2×C8—741no—
184C2×C8C4×D3712yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—744no—
189C4⋊C4D14812yes—
190C22⋊C4—1482no—
191C22⋊C4—1482no—
192C42—744no—
193C42—741no—
194C42—741no—
195C23—742no—
196C23—1481no—
197C23—1481no—
198C23—1481no—
199C23—1481no—
200C23—1481no—
201C23—1481no—
202C23D4×D3711yescharacteristic
203Q8—374no—
204Q8—742no—
205Q8—742no—
206Q8—742no—
207D4—742no—
208D4—742no—
209D4—1481no—
210D4—1481no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—372no—
218C2×C4—742no—
219C2×C4—741no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4C2×C4×D3711yescharacteristic
227C2×C4C2×D14811yescharacteristic
228C2×C4#1059696211yescharacteristic
229C2×C4D4×D3711yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C2×C4#1059696611yescharacteristic
232C8—22no—
233C8—1481no—
234C22—2961no—
235C22—2961no—
236C22—2961no—
237C22—2961no—
238C22—1482no—
239C22—1482no—
240C22—1482no—
241C22#1192449811yescharacteristic
242C22#1192450611yescharacteristic
243C22#1192450911yescharacteristic
244C22SD16×D3711yescharacteristic
245C22#1192455711yescharacteristic
246C22#1192456011yescharacteristic
247C22#1192456811yescharacteristic
248C4—42no—
249C4—81no—
250C4—744no—
251C4—742no—
252C4—1481no—
253C4C22⋊C4×D3711yescharacteristic
254C4C4×D14811yescharacteristic
255C4#1192451111yescharacteristic
256C4#1192452111yescharacteristic
257C2—2962no—
258C2#1455741111yescharacteristic
259C2#1455762011yescharacteristic
260C2#1455763211yescharacteristic
261C2#1455767311yescharacteristic
262C2#1455767911yescharacteristic
263C2#1455773211yescharacteristic
264C2#1455775811yescharacteristic
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#1880
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×#11924501C2semidirect
3. C2×#11924459C2semidirect
6. #14557287C2semidirect
7. C37×#340C2semidirect
12. C2×#10596930C4semidirect
90. C2×Dic37SD16semidirect
98. Dic74C22⋊C4semidirect
138. #340D37semidirect
140. C37#1880semidirect

Maximal subgroups

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

subgroupindex
C22×#105969302
C2×#119245012
C2×#119244592
C2×#119244562
#145574342
#145572872
C37×#3402
#188037