Finite Group Databasebeta

← C137×#7657 #46857043

Subgroups — C137×#7657 #46857043

Order 35072.

370 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2864×C137C211yesmaximal, characteristic
2#1839×C137C211yesmaximal, characteristic
3#1744×C137C211yesmaximal, characteristic
4#1271×C137C212yesmaximal
5#1271×C137C212yesmaximal
6C2×C4×C8×C137—21no—
7#389×C137C411yescharacteristic
8#389×C137C411yescharacteristic
9#389×C137C2211yescharacteristic
10#389×C137C2211yescharacteristic
11#387×C137—21no—
12#387×C137—21no—
13#387×C137—21no—
14#387×C137—21no—
15#382×C137C411yescharacteristic
16#382×C137C411yescharacteristic
17C43×C137C2211yescharacteristic
18#336×C137—21no—
19#336×C137—21no—
20#336×C137—21no—
21#336×C137C2212yes—
22#336×C137C2212yes—
23C22×C8×C137—22no—
24C22×C8×C137—22no—
25C2×C4⋊C4×C137—21no—
26C2×C4⋊C4×C137—21no—
27C2×C4⋊C4×C137—21no—
28C2×C4⋊C4×C137—21no—
29C2×C4⋊C4×C137C2×C411yescharacteristic
30C2×C4⋊C4×C137C2×C411yescharacteristic
31C2×C4⋊C4×C137C2×C411yescharacteristic
32C2×C4⋊C4×C137C2×C411yescharacteristic
33C2×C42×C137C2×C411yescharacteristic
34C2×C42×C137C2×C411yescharacteristic
35C2×C42×C137D411yescharacteristic
36C2×C42×C137D411yescharacteristic
37C2×C42×C137D411yescharacteristic
38C2×C42×C137D411yescharacteristic
39C2×C42×C137C2311yescharacteristic
40C4×C8×C137—24no—
41#95×C137—21no—
42#95×C137—21no—
43#95×C137—21no—
44#95×C137—21no—
45#95×C137—21no—
46#95×C137—21no—
47#95×C137—21no—
48#95×C137—21no—
49C22×C4×C137—21no—
50C22×C4×C137—21no—
51C22×C4×C137—21no—
52C22×C4×C137—21no—
53C22×C4×C137C22⋊C411yescharacteristic
54C22×C4×C137C22⋊C411yescharacteristic
55C22×C4×C137C22⋊C411yescharacteristic
56C22×C4×C137C22⋊C411yescharacteristic
57C22×C4×C137C22×C411yescharacteristic
58C22×C4×C137C2×D411yescharacteristic
59C22×C4×C137C2×D411yescharacteristic
60C2×C8×C137—24no—
61C2×C8×C137—42no—
62C2×C8×C137—42no—
63C2×C8×C137—42no—
64C2×C8×C137—42no—
65C2×C8×C137—42no—
66C4⋊C4×C137—22no—
67C4⋊C4×C137—22no—
68C4⋊C4×C137—41no—
69C4⋊C4×C137—41no—
70C4⋊C4×C137—42no—
71C4⋊C4×C137—42no—
72C4⋊C4×C137—42no—
73C4⋊C4×C137—42no—
74C42×C137—22no—
75C42×C137—22no—
76C42×C137—22no—
77C42×C137—22no—
78C42×C137—22no—
79C42×C137—41no—
80C42×C137—41no—
81C23×C137C2×C22⋊C411yescharacteristic
82C2×C4×C137—21no—
83C2×C4×C137—21no—
84C2×C4×C137—21no—
85C2×C4×C137—21no—
86C2×C4×C137—21no—
87C2×C4×C137—21no—
88C2×C4×C137—21no—
89C2×C4×C137—21no—
90C2×C4×C137—21no—
91C2×C4×C137—21no—
92C2×C4×C137—21no—
93C2×C4×C137—21no—
94C2×C4×C137—21no—
95C2×C4×C137—21no—
96C2×C4×C137—21no—
97C2×C4×C137—21no—
98C2×C4×C137—41no—
99C2×C4×C137—41no—
100C2×C4×C137—41no—
101C2×C4×C137—41no—
102C2×C4×C137—41no—
103C2×C4×C137—41no—
104C2×C4×C137—41no—
105C2×C4×C137—41no—
106C2×C4×C137—41no—
107C2×C4×C137—41no—
108C2×C4×C137—41no—
109C2×C4×C137—41no—
110C2×C4×C137#10112yes—
111C2×C4×C137#10412yes—
112C2×C4×C137#13112yes—
113C2×C4×C137#13512yes—
114C2×C4×C137#13512yes—
115C8×C137—44no—
116C8×C137—82no—
117C22×C137#40811yescharacteristic
118C22×C137#41011yescharacteristic
119C22×C137C2×#10111yescharacteristic
120C22×C137#41611yescharacteristic
121C22×C137#41611yescharacteristic
122C22×C137C2×#10411yescharacteristic
123C22×C137#42111yescharacteristic
124C4×C137—22no—
125C4×C137—22no—
126C4×C137—22no—
127C4×C137—22no—
128C4×C137—22no—
129C4×C137—41no—
130C4×C137—41no—
131C4×C137—81no—
132C4×C137—81no—
133C4×C137—81no—
134C4×C137—81no—
135C2×C137#147011yescharacteristic
136C2×C137#148211yescharacteristic
137C2×C137#149411yescharacteristic
138C2×C137#150011yescharacteristic
139C2×C137#152111yescharacteristic
140C2×C137#153111yescharacteristic
141C2×C137#154411yescharacteristic
142#7657C13711yesmaximal, characteristic, direct product factor, Sylow
143C137#765711yescharacteristic, direct product factor, Sylow
144#2864C2×C13711yescharacteristic
145#1839C2×C13711yescharacteristic
146#1744C2×C13711yescharacteristic
147#1271C2×C13712yes—
148#1271C2×C13712yes—
149C2×C4×C8—21no—
150#389C4×C13711yescharacteristic
151#389C4×C13711yescharacteristic
152#389C22×C13711yescharacteristic
153#389C22×C13711yescharacteristic
154#387—21no—
155#387—21no—
156#387—21no—
157#387—21no—
158#382C4×C13711yescharacteristic
159#382C4×C13711yescharacteristic
160C43C22×C13711yescharacteristic
161#336—21no—
162#336—21no—
163#336—21no—
164#336C22×C13712yes—
165#336C22×C13712yes—
166C22×C8—22no—
167C22×C8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C2×C4×C13711yescharacteristic
173C2×C4⋊C4C2×C4×C13711yescharacteristic
174C2×C4⋊C4C2×C4×C13711yescharacteristic
175C2×C4⋊C4C2×C4×C13711yescharacteristic
176C2×C42C2×C4×C13711yescharacteristic
177C2×C42C2×C4×C13711yescharacteristic
178C2×C42D4×C13711yescharacteristic
179C2×C42D4×C13711yescharacteristic
180C2×C42D4×C13711yescharacteristic
181C2×C42D4×C13711yescharacteristic
182C2×C42C23×C13711yescharacteristic
183C4×C8—24no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4C22⋊C4×C13711yescharacteristic
197C22×C4C22⋊C4×C13711yescharacteristic
198C22×C4C22⋊C4×C13711yescharacteristic
199C22×C4C22⋊C4×C13711yescharacteristic
200C22×C4C22×C4×C13711yescharacteristic
201C22×C4C2×D4×C13711yescharacteristic
202C22×C4C2×D4×C13711yescharacteristic
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C42—22no—
218C42—22no—
219C42—22no—
220C42—22no—
221C42—22no—
222C42—41no—
223C42—41no—
224C23C2×C22⋊C4×C13711yescharacteristic
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4#101×C13712yes—
254C2×C4#104×C13712yes—
255C2×C4#131×C13712yes—
256C2×C4#135×C13712yes—
257C2×C4#135×C13712yes—
258C8—44no—
259C8—82no—
260C22#408×C13711yescharacteristic
261C22#410×C13711yescharacteristic
262C22C2×#101×C13711yescharacteristic
263C22#416×C13711yescharacteristic
264C22#416×C13711yescharacteristic
265C22C2×#104×C13711yescharacteristic
266C22#421×C13711yescharacteristic
267C4—22no—
268C4—22no—
269C4—22no—
270C4—22no—
271C4—22no—
272C4—41no—
273C4—41no—
274C4—81no—
275C4—81no—
276C4—81no—
277C4—81no—
278C2#1470×C13711yescharacteristic
279C2#1482×C13711yescharacteristic
280C2#1494×C13711yescharacteristic
281C2#1500×C13711yescharacteristic
282C2#1521×C13711yescharacteristic
283C2#1531×C13711yescharacteristic
284C2#1544×C13711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C137C2×C22⋊C4
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C42C23×C137
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C43×C137 ◁ G

Complements

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

NH ≅ G/Ntype
142. #7657C137direct (N × H)
143. C137#7657direct (N × H)

Maximal subgroups

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

subgroupindex
#2864×C1372
#1839×C1372
#1744×C1372
#1271×C1372
#7657137