Finite Group Databasebeta

← #18010011

Subgroups — #18010011

Order 4736.

286 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558504C211yesmaximal, characteristic, complemented
2#14558475C211yesmaximal, characteristic, complemented
3#14558387C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#14558040C211yesmaximal, characteristic
6C2×#10596953—21no—
7C2×C4⋊#3866—21no—
8C2×C22⋊#3866—21no—
9#11924593C2212yes—
10C22⋊#64438—21no—
11(C2×#3866)⋊C4C2212yes—
12C22×C4×D37C2211yescharacteristic
13#11924517—21no—
14#11924512C411yescharacteristic, complemented
15#11924512C2211yescharacteristic
16#11924507C411yescharacteristic, complemented
17#11924507C2211yescharacteristic
18#11924504—21no—
19C4×C22⋊D37—21no—
20C4×C22⋊D37—21no—
21#11924495C411yescharacteristic, complemented
22C2×#41×C37C411yescharacteristic, complemented
23C23×D37D411yescharacteristic
24C22×#3866—22no—
25#41×C37—42no—
26C2×Q8×C37C2×C411yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2×C411yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C22×Dic37D411yescharacteristic
34C2×C4×D37—42no—
35C2×C4×D37C2×C411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37C2311yescharacteristic
39C22⋊#3866—42no—
40C2×#64438—22no—
41C4⋊#3866—42no—
42#10596953—42no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46#10596938—21no—
47#10596938—21no—
48C4⋊Dic37C2×C411yescharacteristic
49C4⋊Dic37C2×C411yescharacteristic
50#10596936—21no—
51#10596936—21no—
52C4×Dic37—21no—
53C23×C37—21no—
54C23×C37C22⋊C411yescharacteristic
55C22×D37—21no—
56C22×D37—21no—
57C22×D37—41no—
58C22×D37—41no—
59C22×D37C22⋊C411yescharacteristic
60C22×D37C2×D411yescharacteristic
61C2×#3866—42no—
62C2×#3866—42no—
63C2×#3866—42no—
64Q8×C37—41no—
65D4×C37—41no—
66D4×C37—42no—
67C2×C4×C37—22no—
68C2×C4×C37—21no—
69C2×C4×C37—42no—
70C2×C4×C37C22⋊C411yescharacteristic
71C2×C4×C37C22×C411yescharacteristic
72C22⋊D37—42no—
73C22⋊D37—41no—
74C22⋊D37—41no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—41no—
78C2×Dic37C22⋊C411yescharacteristic
79C2×Dic37C2×D411yescharacteristic
80C4×D37—22no—
81C4×D37—22no—
82C4×D37—41no—
83C4×D37—41no—
84#64438—42no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—41no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37C2×C22⋊C411yescharacteristic
92C2×D37—21no—
93C2×D37—21no—
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—42no—
98C2×D37—42no—
99C2×D37AGL(1,ℤ/8)11yescharacteristic
100C2×D37#13711yescharacteristic
101#3866—82no—
102C4×C37—21no—
103C4×C37—41no—
104C4×C37#9912yes—
105Dic37—21no—
106Dic37—21no—
107Dic37—41no—
108Dic37—41no—
109#1513—371nomaximal, Sylow
110C2×C37—41no—
111C2×C37—81no—
112C2×C37C2×#9911yescharacteristic
113C2×C37#41711yescharacteristic
114C2×C37#42111yescharacteristic
115D37—21no—
116D37—21no—
117D37—41no—
118#525—371no—
119#407—371no—
120#380—371no—
121#328—372no—
122#327—372no—
123C37#151311yescharacteristic, complemented, Sylow
124C2×#41#386611yescharacteristic, complemented
125C23×C4—371no—
126C2×M16—741no—
127#123—741no—
128C22⋊Q8—371no—
129C22⋊Q8—371no—
130#121—371no—
131#121—371no—
132#120—741no—
133C4×D4—741no—
134C4×D4—741no—
135#117—371no—
136C2×C4⋊C4—741no—
137C2×C22⋊C4—741no—
138C22⋊C8—372no—
139C22⋊C8—741no—
140#95—372no—
141C24—371no—
142#41—42no—
143C2×Q8C2×#386611yescharacteristic
144C2×D4—21no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4C2×#386611yescharacteristic
148C22×C4—21no—
149C22×C4—371no—
150C22×C4—371no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—742no—
155C22×C4—1482no—
156C22×C4C2×#386611yescharacteristic
157M16—1482no—
158C2×C8—742no—
159C4⋊C4—371no—
160C4⋊C4—371no—
161C4⋊C4—741no—
162C4⋊C4—741no—
163C4⋊C4—1482no—
164C22⋊C4—741no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—1482no—
170C42—741no—
171C23—21no—
172C23—371no—
173C23—371no—
174C23—741no—
175C23—741no—
176C23—1481no—
177C23—1481no—
178C23C22⋊#386611yescharacteristic
179Q8—41no—
180D4—41no—
181D4—42no—
182D4—1481no—
183D4—1481no—
184D4—1482no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—42no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—742no—
191C2×C4—742no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4—1482no—
197C2×C4—1482no—
198C2×C4—1482no—
199C2×C4—1481no—
200C2×C4C22⋊#386611yescharacteristic
201C2×C4C22×#386611yescharacteristic
202C8—1482no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—371no—
210C22—371no—
211C22—741no—
212C22—741no—
213C22—741no—
214C22—741no—
215C22—741no—
216C22—1482no—
217C22—1482no—
218C22C2×C22⋊#386611yescharacteristic
219C4—21no—
220C4—41no—
221C4—2962no—
222C4—741no—
223C4—741no—
224C4—1481no—
225C4—1481no—
226C4#1192459412yes—
227C2—41no—
228C2—81no—
229C2—741no—
230C2—741no—
231C2—1481no—
232C2C2×#1192459411yescharacteristic
233C2#1455852411yescharacteristic
234C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558040C2
cosocleC2×C4×D37C23
hypercenterC2×#41#3866
hypocenterC37#1513
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14558504C2semidirect
2. #14558475C2semidirect
3. #14558387C2semidirect
4. #14558384C2semidirect
14. #11924512C4semidirect
16. #11924507C4semidirect
21. #11924495C4semidirect
22. C2×#41×C37C4semidirect
123. C37#1513semidirect
124. C2×#41#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
#145584752
#145583872
#145583842
#145580402
#151337