Finite Group Databasebeta

← #18010856

Subgroups — #18010856

Order 4736.

266 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 52 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#14558520C211yesmaximal, characteristic, complemented
2#14558513C211yesmaximal, characteristic, complemented
3#14558434C212yesmaximal, complemented
4#14558433C212yesmaximal, complemented
5#14558098C211yesmaximal, characteristic
6C2×#10596957—21no—
7#11924615—21no—
8#11924597—21no—
9#11924596C2212yes—
10#11924594—21no—
11#11924594C2212yes—
12C2×#10596964C2211yescharacteristic
13C22×C22⋊D37C411yescharacteristic, complemented
14#11924532—21no—
15#11924522—21no—
16#11924509—21no—
17#11924508—21no—
18#11924506C2211yescharacteristic
19#11924505C2211yescharacteristic
20#11924504C411yescharacteristic, complemented
21#11924492C411yescharacteristic, complemented
22#120×C37C411yescharacteristic, complemented
23C24×C37C2×C411yescharacteristic
24C23×D37C2×C411yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37C2×C411yescharacteristic
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—41no—
32C2×C22⋊D37—41no—
33C2×C22⋊D37D411yescharacteristic
34C2×C22⋊D37C2311yescharacteristic
35C22×Dic37C2×C411yescharacteristic
36C22×Dic37D411yescharacteristic
37#10596964—41no—
38#10596964—41no—
39C2×D148—21no—
40C2×C4×D37D411yescharacteristic
41C2×Dic74D411yescharacteristic
42C22⋊#3866—22no—
43#10596957—22no—
44#10596957—41no—
45C2×#64438—41no—
46C4⋊#3866—41no—
47C4×#3866—41no—
48C22⋊C4×C37—21no—
49C22⋊C4×C37C2×C411yescharacteristic
50C22⋊Dic37—21no—
51C22⋊Dic37C2×C411yescharacteristic
52#10596938—21no—
53#10596938—21no—
54#10596936—21no—
55C4×Dic37—21no—
56C23×C37—21no—
57C23×C37—41no—
58C23×C37—81no—
59C23×C37C22⋊C411yescharacteristic
60C23×C37C22×C411yescharacteristic
61C22×D37—21no—
62C22×D37—41no—
63C22×D37—81no—
64C22×D37C2×D411yescharacteristic
65C2×#3866—42no—
66D4×C37—41no—
67D4×C37—81no—
68C2×C4×C37—21no—
69C2×C4×C37C22⋊C411yescharacteristic
70C22⋊D37—41no—
71C22⋊D37—41no—
72C22⋊D37—42no—
73C22⋊D37—41no—
74C22⋊D37—41no—
75C22⋊D37—81no—
76C22⋊D37—81no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C22⋊C411yescharacteristic
84C2×Dic37C2×D411yescharacteristic
85D148—81no—
86C4×D37—21no—
87C4×D37—21no—
88Dic74—41no—
89#64438—42no—
90C22×C37—21no—
91C22×C37—21no—
92C22×C37—41no—
93C22×C37—41no—
94C22×C37—41no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37—82no—
98C22×C37C2×C22⋊C411yescharacteristic
99C2×D37—21no—
100C2×D37—41no—
101C2×D37—41no—
102C2×D37—41no—
103C2×D37—41no—
104C2×D37—82no—
105#3866—82no—
106C4×C37—21no—
107C4×C37—41no—
108Dic37—21no—
109Dic37—21no—
110Dic37—41no—
111Dic37#9911yescharacteristic
112Dic37#9911yescharacteristic
113#2122—371nomaximal, Sylow
114C2×C37—21no—
115C2×C37—41no—
116C2×C37—41no—
117C2×C37—81no—
118C2×C37C2×#9911yescharacteristic
119D37—41no—
120D37—81no—
121#535—371no—
122#413—371no—
123#410—371no—
124AΣL(1,𝔽16)—372no—
125AΣL(1,𝔽16)—372no—
126C37#212211yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C22×D4—371no—
129C2×M16—741no—
130#127—741no—
131#124—741no—
132#121—741no—
133#121—741no—
134#120—371no—
135#120—371no—
136#120—371no—
137#120#386611yescharacteristic, complemented
138#117—371no—
139#117—741no—
140#101—741no—
141#100—372no—
142#99—372no—
143#99—741no—
144C24—371no—
145C24C2×#386611yescharacteristic
146#41—1481no—
147#41—1481no—
148C2×Q8—371no—
149C2×D4—21no—
150C2×D4—371no—
151C2×D4—371no—
152C2×D4—741no—
153C2×D4—741no—
154C2×D4—741no—
155C2×D4—741no—
156C2×D4—741no—
157C2×D4—1481no—
158C2×D4—1481no—
159C2×D4C2×#386611yescharacteristic
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163M16—742no—
164M16—1481no—
165C2×C8—1481no—
166C4⋊C4—741no—
167C4⋊C4—1481no—
168C22⋊C4—21no—
169C22⋊C4—371no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C22⋊C4—742no—
174C22⋊C4C2×#386611yescharacteristic
175C42—741no—
176C42—1481no—
177C23—21no—
178C23—41no—
179C23—81no—
180C23—371no—
181C23—2961no—
182C23—741no—
183C23—1481no—
184C23C22⋊#386611yescharacteristic
185C23C22×#386611yescharacteristic
186Q8—1481no—
187D4—41no—
188D4—81no—
189D4—2961no—
190D4—2961no—
191D4—2961no—
192D4—1481no—
193D4—1481no—
194D4—1481no—
195D4—1481no—
196D4—1482no—
197C2×C4—21no—
198C2×C4—371no—
199C2×C4—371no—
200C2×C4—371no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—741no—
204C2×C4—741no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—741no—
208C2×C4—1482no—
209C2×C4C22⋊#386611yescharacteristic
210C8—1482no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—82no—
219C22—2962no—
220C22—741no—
221C22—1481no—
222C22—1481no—
223C22—1481no—
224C22—1481no—
225C22C2×C22⋊#386611yescharacteristic
226C4—21no—
227C4—41no—
228C4—371no—
229C4—371no—
230C4—2962no—
231C4—741no—
232C4—741no—
233C4—1481no—
234C2—21no—
235C2—41no—
236C2—41no—
237C2—81no—
238C2—2961no—
239C2—1481no—
240C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#120×C37C4
socleC2×C37C2×#99
prime radical#14558098C2
cosocleC2×C22⋊D37C23
hypercenter#120#3866
hypocenterC37#2122
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #14558520C2semidirect
2. #14558513C2semidirect
3. #14558434C2semidirect
4. #14558433C2semidirect
13. C22×C22⋊D37C4semidirect
20. #11924504C4semidirect
21. #11924492C4semidirect
22. #120×C37C4semidirect
126. C37#2122semidirect
137. #120#3866semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145585132
#145584342
#145584332
#145580982
#212237