Finite Group Databasebeta

← #17996248

Subgroups — #17996248

Order 4736.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558105C211yesmaximal, characteristic
2#14557514C211yesmaximal, characteristic
3#14557505C211yesmaximal, characteristic
4#14557324C211yesmaximal, characteristic, complemented
5#14557323C211yesmaximal, characteristic, complemented
6#14557322C211yesmaximal, characteristic, complemented
7C37×#352C211yesmaximal, characteristic, complemented
8C2×#10596964C2211yescharacteristic
9C22×Dic74C411yescharacteristic, complemented
10M16×D37—21no—
11#11924535—21no—
12#11924522—21no—
13#11924520C411yescharacteristic, complemented
14#11924519C411yescharacteristic, complemented
15#11924517C2211yescharacteristic
16#11924514—21no—
17#11924513—21no—
18#11924492—21no—
19#11924492C411yescharacteristic, complemented
20#11924454—21no—
21#11924453C2211yescharacteristic
22#11924451C2211yescharacteristic
23#11924450—21no—
24#123×C37C2211yescharacteristic
25#100×C37C2211yescharacteristic
26#99×C37C2211yescharacteristic
27C2×D4×C37C2311yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37C2×C411yescharacteristic
30C2×C22⋊D37D411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37D411yescharacteristic
34#10596964—41no—
35#10596964—41no—
36C2×C4×D37D411yescharacteristic
37C2×Dic74—21no—
38C2×Dic74—21no—
39C2×Dic74—41no—
40C2×Dic74—41no—
41C2×Dic74D411yescharacteristic
42M16×C37—21no—
43C4⋊C4×C37—21no—
44C22⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C22⋊C4×C37C2×C411yescharacteristic
47C22⋊Dic37—21no—
48C22⋊Dic37—21no—
49C22⋊Dic37C2×C411yescharacteristic
50#10596938—21no—
51#10596938—21no—
52C4⋊Dic37—21no—
53#10596936—21no—
54#10596936—21no—
55#10596936—21no—
56#10596936—41no—
57C4×Dic37—21no—
58C4×Dic37—41no—
59#10596934—21no—
60#10596929—41no—
61C8×D37—41no—
62C23×C37C22×C411yescharacteristic
63C23×C37C2×D411yescharacteristic
64C22×D37C22⋊C411yescharacteristic
65D4×C37—41no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37C2×D411yescharacteristic
71C22⋊D37—41no—
72C22⋊D37—41no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37C22⋊C411yescharacteristic
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C22⋊C411yescharacteristic
84C4×D37—21no—
85C4×D37—21no—
86Dic74—41no—
87Dic74—42no—
88Dic74—41no—
89Dic74—41no—
90C8×C37—41no—
91#64436—41no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—41no—
95C22×C37—41no—
96C22×C37C2×C22⋊C411yescharacteristic
97C2×D37—21no—
98C2×D37—41no—
99C4×C37—21no—
100C4×C37—41no—
101C4×C37—41no—
102C4×C37—81no—
103Dic37—21no—
104Dic37—21no—
105Dic37—41no—
106Dic37—41no—
107Dic37—81no—
108Dic37#9911yescharacteristic
109Dic37#9911yescharacteristic
110#2123—371nomaximal, Sylow
111C2×C37—21no—
112C2×C37—41no—
113C2×C37—41no—
114C2×C37C2×#9911yescharacteristic
115D37—41no—
116#536—371no—
117#413—371no—
118#410—371no—
119#352—371no—
120#352—371no—
121#352—371no—
122#352D3711yescharacteristic, complemented
123C37#212311yescharacteristic, complemented, Sylow
124C2×#41—371no—
125C22×Q8—371no—
126C2×M16—741no—
127C4⋊Q8—741no—
128#124—741no—
129#123—371no—
130#123—371no—
131#123—371no—
132#123C2×D3711yescharacteristic
133C22⋊Q8—741no—
134C22⋊Q8—741no—
135#117—371no—
136#117—741no—
137#101—741no—
138#100—371no—
139#100C2×D3711yescharacteristic
140#99—371no—
141#99—741no—
142#99C2×D3711yescharacteristic
143#41—1481no—
144#41—1481no—
145C2×Q8—371no—
146C2×Q8—741no—
147C2×Q8—741no—
148C2×Q8—1481no—
149C2×Q8—1481no—
150C2×D4—371no—
151C2×D4—371no—
152C2×D4C22×D3711yescharacteristic
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4C4×D3711yescharacteristic
158M16—21no—
159M16—741no—
160M16—1481no—
161C2×C8—1481no—
162C4⋊C4—21no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4—741no—
166C4⋊C4—741no—
167C4⋊C4—1481no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—371no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C22⋊C4—741no—
174C22⋊C4—741no—
175C22⋊C4C4×D3711yescharacteristic
176C42—741no—
177C42—1481no—
178C23—371no—
179C23C2×C4×D3711yescharacteristic
180C23D4×D3711yescharacteristic
181Q8—1481no—
182Q8—1481no—
183Q8—1481no—
184Q8—1482no—
185D4—41no—
186D4—1481no—
187D4—1481no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—371no—
193C2×C4—371no—
194C2×C4—371no—
195C2×C4—741no—
196C2×C4—741no—
197C2×C4—741no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—741no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—1481no—
204C2×C4—1481no—
205C2×C4D4×D3711yescharacteristic
206C8—41no—
207C8—1481no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—741no—
213C22—1481no—
214C22C22⋊C4×D3711yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—371no—
220C4—371no—
221C4—2961no—
222C4—741no—
223C4—741no—
224C4—1481no—
225C4—1481no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—1481no—
230C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#352C2
socleC2×C37C2×#99
prime radicalC2×#10596964C22
cosocleC2×D4×C37C23
hypercenter#352D37
hypocenterC37#2123
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #14557324C2semidirect
5. #14557323C2semidirect
6. #14557322C2semidirect
7. C37×#352C2semidirect
9. C22×Dic74C4semidirect
13. #11924520C4semidirect
14. #11924519C4semidirect
19. #11924492C4semidirect
122. #352D37semidirect
123. C37#2123semidirect

Maximal subgroups

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

subgroupindex
#145581052
#145575142
#145575052
#145573242
#145573232
#145573222
C37×#3522
#212337