Finite Group Databasebeta

← C22×#343×C137 #46869742

Subgroups — C22×#343×C137 #46869742

Order 35072.

2494 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C137C212yesmaximal
2C23×C4⋊C4×C137C211yesmaximal, characteristic
3C2×#343×C137C2112yesmaximal, direct product factor
4C24×C4×C137C412yes—
5C24×C4×C137C2211yescharacteristic
6C22×M16×C137—28no—
7C22×M16×C137—26no—
8C22×M16×C137C4116yescomplemented
9C22×M16×C137C22112yes—
10C23×C8×C137—22no—
11C22×C4⋊C4×C137—26no—
12C22×C4⋊C4×C137—22no—
13C22×C4⋊C4×C137C416yes—
14C22×C4⋊C4×C137C2216yes—
15#343×C137C22116yesdirect product factor
16C25×C137C2×C411yescharacteristic
17C23×C4×C137—26no—
18C23×C4×C137—22no—
19C23×C4×C137—48no—
20C23×C4×C137C2×C4112yes—
21C23×C4×C137C2×C413yes—
22C23×C4×C137C2×C418yes—
23C23×C4×C137D414yes—
24C23×C4×C137D416yes—
25C23×C4×C137D412yes—
26C23×C4×C137Q814yes—
27C23×C4×C137C2313yes—
28C2×M16×C137—248no—
29C2×M16×C137—224no—
30C2×M16×C137—212no—
31C2×M16×C137C2×C4148yescomplemented
32C2×M16×C137C2318yes—
33C22×C8×C137—216no—
34C22×C8×C137—212no—
35C2×C4⋊C4×C137—212no—
36C2×C4⋊C4×C137—212no—
37C2×C4⋊C4×C137—212no—
38C2×C4⋊C4×C137—212no—
39C2×C4⋊C4×C137C2×C4112yes—
40C2×C4⋊C4×C137C2314yes—
41C24×C137—24no—
42C24×C137—24no—
43C24×C137C4214yes—
44C24×C137C22⋊C413yes—
45C24×C137C22⋊C411yescharacteristic
46C24×C137C4⋊C414yes—
47C24×C137C22×C413yes—
48C22×C4×C137—212no—
49C22×C4×C137—212no—
50C22×C4×C137—424no—
51C22×C4×C137—48no—
52C22×C4×C137—424no—
53C22×C4×C137C42112yes—
54C22×C4×C137C22⋊C416yes—
55C22×C4×C137C22⋊C416yes—
56C22×C4×C137C22⋊C418yes—
57C22×C4×C137C22⋊C4124yes—
58C22×C4×C137C4⋊C4112yes—
59C22×C4×C137C4⋊C4124yes—
60C22×C4×C137C4⋊C418yes—
61C22×C4×C137C22×C418yes—
62C22×C4×C137C22×C413yes—
63C22×C4×C137C22×C4112yes—
64C22×C4×C137C2×D416yes—
65C22×C4×C137C2×D416yes—
66C22×C4×C137C2×D416yes—
67C22×C4×C137C2×Q816yes—
68C22×C4×C137C2411yescharacteristic
69M16×C137—248no—
70M16×C137—28no—
71M16×C137C22×C4116yescomplemented
72C2×C8×C137—248no—
73C2×C8×C137—28no—
74C4⋊C4×C137—224no—
75C4⋊C4×C137—28no—
76C23×C137—216no—
77C23×C137—216no—
78C23×C137—26no—
79C23×C137—26no—
80C23×C137—26no—
81C23×C137—26no—
82C23×C137#95112yes—
83C23×C137#9514yes—
84C23×C137#10014yes—
85C23×C137#10114yes—
86C23×C137C2×C4216yes—
87C23×C137C2×C22⋊C413yes—
88C23×C137C2×C22⋊C413yes—
89C23×C137C2×C4⋊C416yes—
90C23×C137C23×C411yescharacteristic
91C2×C4×C137—28no—
92C2×C4×C137—424no—
93C2×C4×C137—424no—
94C2×C4×C137—48no—
95C2×C4×C137#95124yes—
96C2×C4×C137#95124yes—
97C2×C4×C137C2×C4216yes—
98C2×C4×C137C2×C22⋊C4112yes—
99C2×C4×C137C2×C22⋊C4112yes—
100C2×C4×C137C2×C22⋊C416yes—
101C2×C4×C137C2×C4⋊C4112yes—
102C2×C4×C137C2×C4⋊C4112yes—
103C2×C4×C137C2×C4⋊C416yes—
104C2×C4×C137C23×C412yes—
105C2×C4×C137C22×D411yescharacteristic
106C2×C4×C137C22×D412yes—
107C2×C4×C137C22×Q811yescharacteristic
108C8×C137—216no—
109C22×C137—23no—
110C22×C137—21no—
111C22×C137—23no—
112C22×C137—21no—
113C22×C137—224no—
114C22×C137—212no—
115C22×C137—212no—
116C22×C137#343116yesdirect product factor
117C22×C137C2×#9516yes—
118C22×C137C2×#9516yes—
119C22×C137C2×#10016yes—
120C22×C137C2×#10116yes—
121C22×C137C22×C4211yescharacteristic
122C22×C137C22×C22⋊C411yescharacteristic
123C22×C137C22×C4⋊C411yescharacteristic
124C4×C137—48no—
125C4×C137C2×#95112yes—
126C4×C137C22×C22⋊C412yes—
127C4×C137C22×C4⋊C412yes—
128C2×C137—21no—
129C2×C137—26no—
130C2×C137—21no—
131C2×C137C2×#343112yesdirect product factor
132C2×C137C22×#9511yescharacteristic
133C2×C137C22×#10011yescharacteristic
134C2×C137C22×#10111yescharacteristic
135C22×#343C13711yesmaximal, characteristic, direct product factor, Sylow
136C137C22×#34311yescharacteristic, direct product factor, Sylow
137C23×M16C2×C13712yes—
138C23×C4⋊C4C2×C13711yescharacteristic
139C2×#343C2×C137112yesdirect product factor
140C24×C4C4×C13712yes—
141C24×C4C22×C13711yescharacteristic
142C22×M16—28no—
143C22×M16—26no—
144C22×M16C4×C137116yescomplemented
145C22×M16C22×C137112yes—
146C23×C8—22no—
147C22×C4⋊C4—22no—
148C22×C4⋊C4—26no—
149C22×C4⋊C4C4×C13716yes—
150C22×C4⋊C4C22×C13716yes—
151#343C22×C137116yesdirect product factor
152C25C2×C4×C13711yescharacteristic
153C23×C4—26no—
154C23×C4—22no—
155C23×C4—48no—
156C23×C4C2×C4×C137112yes—
157C23×C4C2×C4×C13713yes—
158C23×C4C2×C4×C13718yes—
159C23×C4D4×C13714yes—
160C23×C4D4×C13712yes—
161C23×C4D4×C13716yes—
162C23×C4Q8×C13714yes—
163C23×C4C23×C13713yes—
164C2×M16—248no—
165C2×M16—224no—
166C2×M16—212no—
167C2×M16C2×C4×C137148yescomplemented
168C2×M16C23×C13718yes—
169C22×C8—216no—
170C22×C8—212no—
171C2×C4⋊C4—212no—
172C2×C4⋊C4—212no—
173C2×C4⋊C4—212no—
174C2×C4⋊C4—212no—
175C2×C4⋊C4C2×C4×C137112yes—
176C2×C4⋊C4C23×C13714yes—
177C24—24no—
178C24—24no—
179C24C42×C13714yes—
180C24C22⋊C4×C13713yes—
181C24C22⋊C4×C13711yescharacteristic
182C24C4⋊C4×C13714yes—
183C24C22×C4×C13713yes—
184C22×C4—212no—
185C22×C4—212no—
186C22×C4—424no—
187C22×C4—48no—
188C22×C4—424no—
189C22×C4C42×C137112yes—
190C22×C4C22⋊C4×C13716yes—
191C22×C4C22⋊C4×C13716yes—
192C22×C4C22⋊C4×C13718yes—
193C22×C4C22⋊C4×C137124yes—
194C22×C4C4⋊C4×C137112yes—
195C22×C4C4⋊C4×C137124yes—
196C22×C4C4⋊C4×C13718yes—
197C22×C4C22×C4×C13718yes—
198C22×C4C22×C4×C13713yes—
199C22×C4C22×C4×C137112yes—
200C22×C4C2×D4×C13716yes—
201C22×C4C2×D4×C13716yes—
202C22×C4C2×D4×C13716yes—
203C22×C4C2×Q8×C13716yes—
204C22×C4C24×C13711yescharacteristic
205M16—248no—
206M16—28no—
207M16C22×C4×C137116yescomplemented
208C2×C8—248no—
209C2×C8—28no—
210C4⋊C4—224no—
211C4⋊C4—28no—
212C23—26no—
213C23—26no—
214C23—26no—
215C23—26no—
216C23—216no—
217C23—216no—
218C23#95×C137112yes—
219C23#95×C13714yes—
220C23#100×C13714yes—
221C23#101×C13714yes—
222C23C2×C42×C13716yes—
223C23C2×C22⋊C4×C13713yes—
224C23C2×C22⋊C4×C13713yes—
225C23C2×C4⋊C4×C13716yes—
226C23C23×C4×C13711yescharacteristic
227C2×C4—28no—
228C2×C4—424no—
229C2×C4—424no—
230C2×C4—48no—
231C2×C4#95×C137124yes—
232C2×C4#95×C137124yes—
233C2×C4C2×C42×C13716yes—
234C2×C4C2×C22⋊C4×C13716yes—
235C2×C4C2×C22⋊C4×C137112yes—
236C2×C4C2×C22⋊C4×C137112yes—
237C2×C4C2×C4⋊C4×C13716yes—
238C2×C4C2×C4⋊C4×C137112yes—
239C2×C4C2×C4⋊C4×C137112yes—
240C2×C4C23×C4×C13712yes—
241C2×C4C22×D4×C13711yescharacteristic
242C2×C4C22×D4×C13712yes—
243C2×C4C22×Q8×C13711yescharacteristic
244C8—216no—
245C22—23no—
246C22—21no—
247C22—23no—
248C22—21no—
249C22—224no—
250C22—212no—
251C22—212no—
252C22#343×C137116yesdirect product factor
253C22C2×#95×C13716yes—
254C22C2×#95×C13716yes—
255C22C2×#100×C13716yes—
256C22C2×#101×C13716yes—
257C22C22×C42×C13711yescharacteristic
258C22C22×C22⋊C4×C13711yescharacteristic
259C22C22×C4⋊C4×C13711yescharacteristic
260C4—48no—
261C4C2×#95×C137112yes—
262C4C22×C22⋊C4×C13712yes—
263C4C22×C4⋊C4×C13712yes—
264C2—26no—
265C2—21no—
266C2—21no—
267C2C2×#343×C137112yesdirect product factor
268C2C22×#95×C13711yescharacteristic
269C2C22×#100×C13711yescharacteristic
270C2C22×#101×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C22⋊C4
commutatorC22C22×C42×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC25×C137C2×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C24×C137 ◁ C24×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#343×C137C2direct (N × H)
8. C22×M16×C137C4semidirect
15. #343×C137C22direct (N × H)
31. C2×M16×C137C2×C4semidirect
71. M16×C137C22×C4semidirect
116. C22×C137#343direct (N × H)
131. C2×C137C2×#343direct (N × H)
135. C22×#343C137direct (N × H)
136. C137C22×#343direct (N × H)
139. C2×#343C2×C137direct (N × H)
144. C22×M16C4×C137semidirect
151. #343C22×C137direct (N × H)
167. C2×M16C2×C4×C137semidirect
207. M16C22×C4×C137semidirect
252. C22#343×C137direct (N × H)
267. C2C2×#343×C137direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C1372
C23×C4⋊C4×C1372
C2×#343×C1372
C22×#343137