Finite Group Databasebeta

← C103×#33381 #39938656

Subgroups — C103×#33381 #39938656

Order 26368.

1176 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C103C211yesmaximal, characteristic
2C2×#504×C103C211yesmaximal, characteristic, complemented
3C103×#2913C211yesmaximal, characteristic, complemented
4C103×#2140C213yesmaximal, complemented
5C103×#2139C213yesmaximal, complemented
6C103×#2138C213yesmaximal, complemented
7C2×#357×C103C213yesmaximal, complemented
8C2×H(5,𝔽2)×C103—21no—
9#576×C103—24no—
10#576×C103C418yescomplemented
11C2×AGL(1,ℤ/8)×C103—23no—
12C2×#135×C103C2213yes—
13C22×D8×C103C2213yes—
14C2×#131×C103C2211yescharacteristic
15#520×C103—21no—
16#504×C103—24no—
17C2×M32×C103C2213yescomplemented
18C22×C16×C103C2213yescomplemented
19#428×C103—23no—
20#427×C103C2213yescomplemented
21C2×#107×C103C2213yescomplemented
22#358×C103C2211yescharacteristic, complemented
23#358×C103C2213yescomplemented
24#357×C103C2213yescomplemented
25#357×C103C2216yescomplemented
26#357×C103C2213yescomplemented
27H(5,𝔽2)×C103—28no—
28H(5,𝔽2)×C103—44no—
29C2×#41×C103—23no—
30C2×#41×C103—41no—
31C2×#41×C103D411yescharacteristic
32C22×D4×C103—23no—
33C22×D4×C103—43no—
34AGL(1,ℤ/8)×C103—224no—
35#135×C103—26no—
36#135×C103C2×C4112yescomplemented
37C2×Q16×C103C2311yescharacteristic
38C2×SD16×C103—23no—
39C2×D8×C103—23no—
40C2×D8×C103—26no—
41C2×D8×C103C2×C4112yescomplemented
42C2×D8×C103C2313yes—
43#131×C103C2×C414yes—
44#131×C103D414yes—
45C2×M16×C103D413yes—
46C22×C8×C103C2313yes—
47C4×Q8×C103—41no—
48C4×D4×C103—43no—
49#117×C103—23no—
50C2×C4⋊C4×C103—23no—
51M32×C103—26no—
52C2×C16×C103—26no—
53C2×C16×C103C2311yescharacteristic
54C2×C16×C103C2313yes—
55#107×C103—23no—
56#107×C103C2313yes—
57#107×C103C2311yescharacteristic
58#106×C103—23no—
59C24×C103—43no—
60#41×C103—212no—
61#41×C103—48no—
62#41×C103—46no—
63#41×C103C22⋊C414yes—
64#41×C103SD1614yes—
65C2×Q8×C103—21no—
66C2×Q8×C103D811yescharacteristic
67C2×D4×C103—212no—
68C2×D4×C103—23no—
69C2×D4×C103—43no—
70C2×D4×C103—424no—
71C2×D4×C103—43no—
72C2×D4×C103—46no—
73C2×D4×C103D813yes—
74C22×C4×C103—43no—
75C22×C4×C103—43no—
76C22×C4×C103C2×D413yes—
77Q16×C103—21no—
78Q16×C103C22×C412yes—
79SD16×C103—212no—
80D8×C103—212no—
81D8×C103—23no—
82D8×C103C22×C416yes—
83M16×C103C22⋊C4112yes—
84C2×C8×C103C22×C416yes—
85C2×C8×C103C2×D413yes—
86C2×C8×C103C2×D416yes—
87C2×C8×C103C2411yescharacteristic
88C4⋊C4×C103—21no—
89C4⋊C4×C103—23no—
90C4⋊C4×C103—43no—
91C22⋊C4×C103—43no—
92C42×C103—43no—
93C16×C103—21no—
94C16×C103—23no—
95C23×C103—43no—
96C23×C103—412no—
97C23×C103—163no—
98C23×C103—163no—
99C23×C103C2×D813yes—
100Q8×C103—22no—
101Q8×C103—41no—
102Q8×C103#10214yes—
103D4×C103—26no—
104D4×C103—412no—
105D4×C103—43no—
106D4×C103—412no—
107D4×C103#102112yes—
108C2×C4×C103—41no—
109C2×C4×C103—412no—
110C2×C4×C103—41no—
111C2×C4×C103—43no—
112C2×C4×C103—163no—
113C2×C4×C103C2×C22⋊C416yes—
114C2×C4×C103C2×D813yes—
115C2×C4×C103C2×SD1616yes—
116C2×C4×C103C22×D411yescharacteristic
117C8×C103C2×C22⋊C416yes—
118C8×C103C23×C411yescharacteristic
119C8×C103C22×D411yescharacteristic
120C22×C103—23no—
121C22×C103—23no—
122C22×C103—46no—
123C22×C103—83no—
124C22×C103—83no—
125C22×C103—1612no—
126C22×C103C2×#10216yes—
127C22×C103C22×D811yescharacteristic
128C4×C103—42no—
129C4×C103—83no—
130C4×C103—81no—
131C4×C103C2×#10216yes—
132C4×C103C22×C22⋊C411yescharacteristic
133C4×C103C22×SD1611yescharacteristic
134#33381C10311yesmaximal, characteristic, direct product factor, Sylow
135C2×C103—26no—
136C2×C103—86no—
137C2×C103C22×#10211yescharacteristic
138C2×C103#341511yescharacteristic
139C2×C103#341611yescharacteristic
140C2×#576C2×C10311yescharacteristic
141C2×#504C2×C10311yescharacteristic, complemented
142#2913C2×C10311yescharacteristic, complemented
143#2140C2×C10313yescomplemented
144#2139C2×C10313yescomplemented
145#2138C2×C10313yescomplemented
146C2×#357C2×C10313yescomplemented
147C103#3338111yescharacteristic, direct product factor, Sylow
148C2×H(5,𝔽2)—21no—
149#576—24no—
150#576C4×C10318yescomplemented
151C2×AGL(1,ℤ/8)—23no—
152C2×#135C22×C10313yes—
153C22×D8C22×C10313yes—
154C2×#131C22×C10311yescharacteristic
155#520—21no—
156#504—24no—
157C2×M32C22×C10313yescomplemented
158C22×C16C22×C10313yescomplemented
159#428—23no—
160#427C22×C10313yescomplemented
161C2×#107C22×C10313yescomplemented
162#358C22×C10311yescharacteristic, complemented
163#358C22×C10313yescomplemented
164#357C22×C10313yescomplemented
165#357C22×C10316yescomplemented
166#357C22×C10313yescomplemented
167H(5,𝔽2)—28no—
168H(5,𝔽2)—44no—
169C2×#41—23no—
170C2×#41—41no—
171C2×#41D4×C10311yescharacteristic
172C22×D4—23no—
173C22×D4—43no—
174AGL(1,ℤ/8)—224no—
175#135—26no—
176#135C2×C4×C103112yescomplemented
177C2×Q16C23×C10311yescharacteristic
178C2×SD16—23no—
179C2×D8—23no—
180C2×D8—26no—
181C2×D8C2×C4×C103112yescomplemented
182C2×D8C23×C10313yes—
183#131C2×C4×C10314yes—
184#131D4×C10314yes—
185C2×M16D4×C10313yes—
186C22×C8C23×C10313yes—
187C4×Q8—41no—
188C4×D4—43no—
189#117—23no—
190C2×C4⋊C4—23no—
191M32—26no—
192C2×C16—26no—
193C2×C16C23×C10311yescharacteristic
194C2×C16C23×C10313yes—
195#107—23no—
196#107C23×C10313yes—
197#107C23×C10311yescharacteristic
198#106—23no—
199C24—43no—
200#41—212no—
201#41—48no—
202#41—46no—
203#41C22⋊C4×C10314yes—
204#41SD16×C10314yes—
205C2×Q8—21no—
206C2×Q8D8×C10311yescharacteristic
207C2×D4—212no—
208C2×D4—23no—
209C2×D4—43no—
210C2×D4—424no—
211C2×D4—43no—
212C2×D4—46no—
213C2×D4D8×C10313yes—
214C22×C4—43no—
215C22×C4—43no—
216C22×C4C2×D4×C10313yes—
217Q16—21no—
218Q16C22×C4×C10312yes—
219SD16—212no—
220D8—212no—
221D8—23no—
222D8C22×C4×C10316yes—
223M16C22⋊C4×C103112yes—
224C2×C8C22×C4×C10316yes—
225C2×C8C2×D4×C10313yes—
226C2×C8C2×D4×C10316yes—
227C2×C8C24×C10311yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—23no—
230C4⋊C4—43no—
231C22⋊C4—43no—
232C42—43no—
233C16—21no—
234C16—23no—
235C23—43no—
236C23—412no—
237C23—163no—
238C23—163no—
239C23C2×D8×C10313yes—
240Q8—22no—
241Q8—41no—
242Q8#102×C10314yes—
243D4—26no—
244D4—412no—
245D4—412no—
246D4—43no—
247D4#102×C103112yes—
248C2×C4—41no—
249C2×C4—412no—
250C2×C4—41no—
251C2×C4—43no—
252C2×C4—163no—
253C2×C4C2×C22⋊C4×C10316yes—
254C2×C4C2×D8×C10313yes—
255C2×C4C2×SD16×C10316yes—
256C2×C4C22×D4×C10311yescharacteristic
257C8C2×C22⋊C4×C10316yes—
258C8C23×C4×C10311yescharacteristic
259C8C22×D4×C10311yescharacteristic
260C22—23no—
261C22—23no—
262C22—46no—
263C22—83no—
264C22—83no—
265C22—1612no—
266C22C2×#102×C10316yes—
267C22C22×D8×C10311yescharacteristic
268C4—42no—
269C4—83no—
270C4—81no—
271C4C2×#102×C10316yes—
272C4C22×C22⋊C4×C10311yescharacteristic
273C4C22×SD16×C10311yescharacteristic
274C2—26no—
275C2—86no—
276C2C22×#102×C10311yescharacteristic
277C2C103×#341511yescharacteristic
278C2C103×#341611yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutatorC8C23×C4×C103
Frattini, cosocleC2×C8C24×C103
prime radicalC2×#576×C103C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×#41×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#504×C103C2semidirect
3. C103×#2913C2semidirect
4. C103×#2140C2semidirect
5. C103×#2139C2semidirect
6. C103×#2138C2semidirect
7. C2×#357×C103C2semidirect
10. #576×C103C4semidirect
17. C2×M32×C103C22semidirect
18. C22×C16×C103C22semidirect
20. #427×C103C22semidirect
21. C2×#107×C103C22semidirect
22. #358×C103C22semidirect
23. #358×C103C22semidirect
24. #357×C103C22semidirect
25. #357×C103C22semidirect
26. #357×C103C22semidirect
36. #135×C103C2×C4semidirect
41. C2×D8×C103C2×C4semidirect
134. #33381C103direct (N × H)
141. C2×#504C2×C103semidirect
142. #2913C2×C103semidirect
143. #2140C2×C103semidirect
144. #2139C2×C103semidirect
145. #2138C2×C103semidirect
146. C2×#357C2×C103semidirect
147. C103#33381direct (N × H)
150. #576C4×C103semidirect
157. C2×M32C22×C103semidirect
158. C22×C16C22×C103semidirect
160. #427C22×C103semidirect
161. C2×#107C22×C103semidirect
162. #358C22×C103semidirect
163. #358C22×C103semidirect
164. #357C22×C103semidirect
165. #357C22×C103semidirect
166. #357C22×C103semidirect
176. #135C2×C4×C103semidirect
181. C2×D8C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C1032
C2×#504×C1032
C103×#29132
C103×#21402
C103×#21392
C103×#21382
C2×#357×C1032
#33381103