Finite Group Databasebeta

← C137×#20360 #46869746

Subgroups — C137×#20360 #46869746

Order 35072.

1996 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C137C211yesmaximal, characteristic
2C2×#568×C137C211yesmaximal, characteristic
3#3428×C137C211yesmaximal, characteristic
4C2×#344×C137C2112yesmaximal, complemented
5C22×#41×C137C2211yescharacteristic
6#568×C137—24no—
7#568×C137—24no—
8#568×C137—24no—
9#568×C137C418yescomplemented
10C2×#131×C137—24no—
11C2×#131×C137C418yescomplemented
12C22×M16×C137C2216yes—
13C22×M16×C137C2216yes—
14#520×C137—24no—
15#519×C137C412yes—
16#518×C137C416yes—
17C4×#41×C137—24no—
18C2×#117×C137C2216yes—
19#344×C137C22116yes—
20C2×#41×C137C2×C414yes—
21C2×#41×C137C2×C414yes—
22C2×#41×C137D414yes—
23C2×#41×C137D414yes—
24C2×#41×C137D414yes—
25C2×#41×C137Q814yes—
26C22×Q8×C137C2×C411yescharacteristic
27C22×D4×C137C2×C413yes—
28C23×C4×C137C2313yes—
29#131×C137—232no—
30#131×C137—232no—
31C2×M16×C137—26no—
32C2×M16×C137—212no—
33C2×M16×C137—212no—
34C2×M16×C137—212no—
35C2×M16×C137C2×C4124yescomplemented
36C2×M16×C137C2×C4112yescomplemented
37C2×M16×C137C2314yes—
38C2×M16×C137C2314yes—
39C22×C8×C137—26no—
40C22×C8×C137C2×C4112yescomplemented
41C4×Q8×C137—28no—
42C4×D4×C137—224no—
43#117×C137—26no—
44#117×C137—26no—
45#117×C137C2×C4112yes—
46#117×C137C2314yes—
47C2×C4⋊C4×C137—26no—
48C2×C22⋊C4×C137C2×C4112yes—
49C2×C42×C137—26no—
50C24×C137C22×C413yes—
51#41×C137C22⋊C4116yes—
52#41×C137C22⋊C4116yes—
53#41×C137C4⋊C4116yes—
54#41×C137C4⋊C4116yes—
55C2×Q8×C137C4214yes—
56C2×Q8×C137C22⋊C414yes—
57C2×Q8×C137C4⋊C414yes—
58C2×D4×C137C42112yes—
59C2×D4×C137C22⋊C4112yes—
60C2×D4×C137C4⋊C4112yes—
61C22×C4×C137—212no—
62C22×C4×C137C22×C413yes—
63C22×C4×C137C22×C416yes—
64C22×C4×C137C22×C416yes—
65C22×C4×C137C2×D416yes—
66C22×C4×C137C2×D416yes—
67C22×C4×C137C2×D416yes—
68C22×C4×C137C2×Q816yes—
69C22×C4×C137C2411yescharacteristic
70M16×C137—224no—
71M16×C137—224no—
72M16×C137—24no—
73M16×C137—24no—
74M16×C137—24no—
75M16×C137C22×C418yes—
76C2×C8×C137—224no—
77C2×C8×C137—224no—
78C2×C8×C137—24no—
79C2×C8×C137C22×C418yes—
80C4⋊C4×C137—212no—
81C4⋊C4×C137—24no—
82C22⋊C4×C137—212no—
83C22⋊C4×C137C22×C418yes—
84C42×C137—212no—
85C42×C137—24no—
86C23×C137—83no—
87C23×C137C2×C4216yes—
88C23×C137C2×C22⋊C416yes—
89C23×C137C2×C4⋊C416yes—
90C23×C137C23×C411yescharacteristic
91Q8×C137#95116yes—
92D4×C137#95148yes—
93C2×C4×C137—28no—
94C2×C4×C137—812no—
95C2×C4×C137C2×C4216yes—
96C2×C4×C137C2×C22⋊C4112yes—
97C2×C4×C137C2×C22⋊C4112yes—
98C2×C4×C137C2×C22⋊C416yes—
99C2×C4×C137C2×C4⋊C4112yes—
100C2×C4×C137C2×C4⋊C4112yes—
101C2×C4×C137C2×C4⋊C416yes—
102C2×C4×C137C23×C411yescharacteristic
103C2×C4×C137C23×C411yescharacteristic
104C2×C4×C137C22×D411yescharacteristic
105C2×C4×C137C22×D411yescharacteristic
106C2×C4×C137C22×D411yescharacteristic
107C2×C4×C137C22×Q811yescharacteristic
108C8×C137—28no—
109C8×C137—28no—
110C22×C137—46no—
111C22×C137—41no—
112C22×C137—46no—
113C22×C137—46no—
114C22×C137C2×#95112yes—
115C22×C137C22×C4211yescharacteristic
116C22×C137C22×C22⋊C411yescharacteristic
117C22×C137C22×C4⋊C411yescharacteristic
118C4×C137—48no—
119C4×C137C2×#95112yes—
120C4×C137C22×C22⋊C411yescharacteristic
121C4×C137C22×C22⋊C411yescharacteristic
122C4×C137C22×C4⋊C411yescharacteristic
123C4×C137C22×C4⋊C411yescharacteristic
124C2×C137—21no—
125C2×C137—21no—
126C2×C137—21no—
127C2×C137—212no—
128C2×C137C22×#9511yescharacteristic
129#20360C13711yesmaximal, characteristic, direct product factor, Sylow
130C137#2036011yescharacteristic, direct product factor, Sylow
131C2×#568C2×C13711yescharacteristic
132C2×#568C2×C13711yescharacteristic
133#3428C2×C13711yescharacteristic
134C2×#344C2×C137112yescomplemented
135C22×#41C22×C13711yescharacteristic
136#568—24no—
137#568—24no—
138#568—24no—
139#568C4×C13718yescomplemented
140C2×#131—24no—
141C2×#131C4×C13718yescomplemented
142C22×M16C22×C13716yes—
143C22×M16C22×C13716yes—
144#520—24no—
145#519C4×C13712yes—
146#518C4×C13716yes—
147C4×#41—24no—
148C2×#117C22×C13716yes—
149#344C22×C137116yes—
150C2×#41C2×C4×C13714yes—
151C2×#41C2×C4×C13714yes—
152C2×#41D4×C13714yes—
153C2×#41D4×C13714yes—
154C2×#41D4×C13714yes—
155C2×#41Q8×C13714yes—
156C22×Q8C2×C4×C13711yescharacteristic
157C22×D4C2×C4×C13713yes—
158C23×C4C23×C13713yes—
159#131—232no—
160#131—232no—
161C2×M16—26no—
162C2×M16—212no—
163C2×M16—212no—
164C2×M16—212no—
165C2×M16C2×C4×C137124yescomplemented
166C2×M16C2×C4×C137112yescomplemented
167C2×M16C23×C13714yes—
168C2×M16C23×C13714yes—
169C22×C8—26no—
170C22×C8C2×C4×C137112yescomplemented
171C4×Q8—28no—
172C4×D4—224no—
173#117—26no—
174#117—26no—
175#117C2×C4×C137112yes—
176#117C23×C13714yes—
177C2×C4⋊C4—26no—
178C2×C22⋊C4C2×C4×C137112yes—
179C2×C42—26no—
180C24C22×C4×C13713yes—
181#41C22⋊C4×C137116yes—
182#41C22⋊C4×C137116yes—
183#41C4⋊C4×C137116yes—
184#41C4⋊C4×C137116yes—
185C2×Q8C42×C13714yes—
186C2×Q8C22⋊C4×C13714yes—
187C2×Q8C4⋊C4×C13714yes—
188C2×D4C42×C137112yes—
189C2×D4C22⋊C4×C137112yes—
190C2×D4C4⋊C4×C137112yes—
191C22×C4—212no—
192C22×C4C22×C4×C13713yes—
193C22×C4C22×C4×C13716yes—
194C22×C4C22×C4×C13716yes—
195C22×C4C2×D4×C13716yes—
196C22×C4C2×D4×C13716yes—
197C22×C4C2×D4×C13716yes—
198C22×C4C2×Q8×C13716yes—
199C22×C4C24×C13711yescharacteristic
200M16—224no—
201M16—224no—
202M16—24no—
203M16—24no—
204M16—24no—
205M16C22×C4×C13718yes—
206C2×C8—224no—
207C2×C8—224no—
208C2×C8—24no—
209C2×C8C22×C4×C13718yes—
210C4⋊C4—212no—
211C4⋊C4—24no—
212C22⋊C4—212no—
213C22⋊C4C22×C4×C13718yes—
214C42—212no—
215C42—24no—
216C23—83no—
217C23C2×C42×C13716yes—
218C23C2×C22⋊C4×C13716yes—
219C23C2×C4⋊C4×C13716yes—
220C23C23×C4×C13711yescharacteristic
221Q8#95×C137116yes—
222D4#95×C137148yes—
223C2×C4—28no—
224C2×C4—812no—
225C2×C4C2×C42×C13716yes—
226C2×C4C2×C22⋊C4×C13716yes—
227C2×C4C2×C22⋊C4×C137112yes—
228C2×C4C2×C22⋊C4×C137112yes—
229C2×C4C2×C4⋊C4×C13716yes—
230C2×C4C2×C4⋊C4×C137112yes—
231C2×C4C2×C4⋊C4×C137112yes—
232C2×C4C23×C4×C13711yescharacteristic
233C2×C4C23×C4×C13711yescharacteristic
234C2×C4C22×D4×C13711yescharacteristic
235C2×C4C22×D4×C13711yescharacteristic
236C2×C4C22×D4×C13711yescharacteristic
237C2×C4C22×Q8×C13711yescharacteristic
238C8—28no—
239C8—28no—
240C22—46no—
241C22—41no—
242C22—46no—
243C22—46no—
244C22C2×#95×C137112yes—
245C22C22×C42×C13711yescharacteristic
246C22C22×C22⋊C4×C13711yescharacteristic
247C22C22×C4⋊C4×C13711yescharacteristic
248C4—48no—
249C4C2×#95×C137112yes—
250C4C22×C22⋊C4×C13711yescharacteristic
251C4C22×C22⋊C4×C13711yescharacteristic
252C4C22×C4⋊C4×C13711yescharacteristic
253C4C22×C4⋊C4×C13711yescharacteristic
254C2—21no—
255C2—21no—
256C2—21no—
257C2—212no—
258C2C22×#95×C13711yescharacteristic
subgroupG/H
centerC4×C137C22×C22⋊C4
commutatorC22C22×C42×C137
Frattini, cosocleC22×C4C24×C137
socleC2×C137C22×#95
prime radicalC22×#41×C137C22
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C137 ◁ C22×#41×C137 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#344×C137C2semidirect
9. #568×C137C4semidirect
11. C2×#131×C137C4semidirect
35. C2×M16×C137C2×C4semidirect
36. C2×M16×C137C2×C4semidirect
40. C22×C8×C137C2×C4semidirect
129. #20360C137direct (N × H)
130. C137#20360direct (N × H)
134. C2×#344C2×C137semidirect
139. #568C4×C137semidirect
141. C2×#131C4×C137semidirect
165. C2×M16C2×C4×C137semidirect
166. C2×M16C2×C4×C137semidirect
170. C22×C8C2×C4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C1372
#3428×C1372
C2×#344×C1372
#20360137