Finite Group Databasebeta

← C103×#21359 #39926634

Subgroups — C103×#21359 #39926634

Order 26368.

1002 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#431×C103C211yesmaximal, characteristic
2C103×#2285C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C103C211yesmaximal, characteristic
4C103×#1948C214yesmaximal, complemented
5C103×#1853C214yesmaximal
6C4×#106×C103C214yesmaximal, complemented
7C2×#117×C103—21no—
8C22×C4⋊C4×C103C2212yes—
9C22×C42×C103—21no—
10C22×C42×C103C2211yescharacteristic
11#431×C103C418yescomplemented
12C2×#106×C103C2218yes—
13C2×C4⋊C8×C103C2212yes—
14C2×C22⋊C8×C103C2212yes—
15C2×C4×C8×C103C2212yes—
16#384×C103C2212yes—
17#382×C103—21no—
18#380×C103—21no—
19#380×C103C2212yes—
20C4×C4⋊C4×C103—21no—
21C4×C4⋊C4×C103—21no—
22C4×C4⋊C4×C103—21no—
23C4×C4⋊C4×C103C2212yes—
24C4×C4⋊C4×C103C2212yes—
25C4×C4⋊C4×C103C2212yes—
26C2×#95×C103—21no—
27#340×C103C2218yes—
28C23×C4×C103—22no—
29C23×C4×C103D411yescharacteristic
30C23×C4×C103D411yescharacteristic
31C23×C4×C103C2311yescharacteristic
32C22×C8×C103C2314yes—
33#117×C103—44no—
34C2×C4⋊C4×C103—22no—
35C2×C4⋊C4×C103—28no—
36C2×C4⋊C4×C103—22no—
37C2×C4⋊C4×C103—22no—
38C2×C4⋊C4×C103C2314yes—
39C2×C4⋊C4×C103C2314yes—
40C2×C22⋊C4×C103—22no—
41C2×C42×C103—22no—
42C2×C42×C103—22no—
43C2×C42×C103—22no—
44C2×C42×C103—44no—
45C2×C42×C103C2×C414yes—
46C2×C42×C103D411yescharacteristic
47C2×C42×C103D411yescharacteristic
48C2×C42×C103Q814yes—
49C2×C42×C103C2311yescharacteristic
50C2×C42×C103C2311yescharacteristic
51#106×C103—216no—
52C4⋊C8×C103C2×C418yescomplemented
53C22⋊C8×C103C2×C418yes—
54C4×C8×C103C2×C418yescomplemented
55#95×C103—22no—
56#95×C103—22no—
57#95×C103—22no—
58#95×C103—22no—
59C24×C103C2×D411yescharacteristic
60C22×C4×C103—24no—
61C22×C4×C103—28no—
62C22×C4×C103—24no—
63C22×C4×C103—24no—
64C22×C4×C103—42no—
65C22×C4×C103—44no—
66C22×C4×C103—44no—
67C22×C4×C103C4⋊C414yes—
68C22×C4×C103C4⋊C414yes—
69C22×C4×C103SD1614yes—
70C22×C4×C103SD1614yes—
71C22×C4×C103C22×C412yes—
72C22×C4×C103C2×D411yescharacteristic
73C22×C4×C103C2×D411yescharacteristic
74C22×C4×C103C2×D411yescharacteristic
75C22×C4×C103C2×D411yescharacteristic
76C22×C4×C103C2×D411yescharacteristic
77C22×C4×C103C2×Q812yes—
78C22×C4×C103C2411yescharacteristic
79C2×C8×C103—28no—
80C2×C8×C103C22×C418yes—
81C4⋊C4×C103—28no—
82C4⋊C4×C103—24no—
83C4⋊C4×C103—28no—
84C4⋊C4×C103—44no—
85C4⋊C4×C103—44no—
86C4⋊C4×C103#4118yes—
87C22⋊C4×C103—44no—
88C42×C103—44no—
89C42×C103—44no—
90C42×C103—44no—
91C42×C103C4⋊C414yes—
92C42×C103C4⋊C414yes—
93C42×C103C22×C412yes—
94C42×C103C22×C412yes—
95C42×C103C2×Q812yes—
96C42×C103C2×Q812yes—
97C23×C103—22no—
98C23×C103—22no—
99C23×C103C2×C4⋊C412yes—
100C23×C103C2×SD1612yes—
101C23×C103C2×SD1612yes—
102C23×C103C22×D411yescharacteristic
103C2×C4×C103—22no—
104C2×C4×C103—22no—
105C2×C4×C103—22no—
106C2×C4×C103—24no—
107C2×C4×C103—24no—
108C2×C4×C103—28no—
109C2×C4×C103—44no—
110C2×C4×C103—416no—
111C2×C4×C103—44no—
112C2×C4×C103—44no—
113C2×C4×C103—44no—
114C2×C4×C103—44no—
115C2×C4×C103—44no—
116C2×C4×C103#106116yescomplemented
117C2×C4×C103C2×C4⋊C412yes—
118C2×C4×C103C2×C4⋊C412yes—
119C2×C4×C103C2×C4⋊C412yes—
120C2×C4×C103C2×C4⋊C412yes—
121C2×C4×C103C2×C4⋊C412yes—
122C2×C4×C103C2×SD1612yes—
123C2×C4×C103C2×SD1612yes—
124C2×C4×C103C2×SD1612yes—
125C2×C4×C103C2×SD1612yes—
126C2×C4×C103C23×C411yescharacteristic
127C2×C4×C103C22×Q811yescharacteristic
128C2×C4×C103C2×#4114yes—
129C8×C103—28no—
130C22×C103—24no—
131C22×C103—24no—
132C22×C103—22no—
133C22×C103—22no—
134C22×C103C2×#10614yes—
135C22×C103C22×C4⋊C411yescharacteristic
136C22×C103#52512yes—
137C22×C103C22×SD1611yescharacteristic
138C22×C103C22×SD1611yescharacteristic
139C22×C103#57512yes—
140C4×C103—22no—
141C4×C103—22no—
142C4×C103—22no—
143C4×C103—48no—
144C4×C103—84no—
145C4×C103C2×#10614yes—
146C4×C103C2×#10614yes—
147C4×C103C4×#4112yes—
148C4×C103#53312yes—
149#21359C10311yesmaximal, characteristic, direct product factor, Sylow
150C2×C103—24no—
151C2×C103#229611yescharacteristic
152C2×C103C22×#10611yescharacteristic
153C2×C103#291111yescharacteristic
154C2×C103#310112yes—
155C2×C103#310312yes—
156C2×#431C2×C10311yescharacteristic
157#2285C2×C10311yescharacteristic
158C2×C4×C4⋊C4C2×C10311yescharacteristic
159#1948C2×C10314yescomplemented
160#1853C2×C10314yes—
161C4×#106C2×C10314yescomplemented
162C103#2135911yescharacteristic, direct product factor, Sylow
163C2×#117—21no—
164C22×C4⋊C4C22×C10312yes—
165C22×C42—21no—
166C22×C42C22×C10311yescharacteristic
167#431C4×C10318yescomplemented
168C2×#106C22×C10318yes—
169C2×C4⋊C8C22×C10312yes—
170C2×C22⋊C8C22×C10312yes—
171C2×C4×C8C22×C10312yes—
172#384C22×C10312yes—
173#382—21no—
174#380—21no—
175#380C22×C10312yes—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4C22×C10312yes—
180C4×C4⋊C4C22×C10312yes—
181C4×C4⋊C4C22×C10312yes—
182C2×#95—21no—
183#340C22×C10318yes—
184C23×C4—22no—
185C23×C4D4×C10311yescharacteristic
186C23×C4D4×C10311yescharacteristic
187C23×C4C23×C10311yescharacteristic
188C22×C8C23×C10314yes—
189#117—44no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—28no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4C23×C10314yes—
195C2×C4⋊C4C23×C10314yes—
196C2×C22⋊C4—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—44no—
201C2×C42C2×C4×C10314yes—
202C2×C42D4×C10311yescharacteristic
203C2×C42D4×C10311yescharacteristic
204C2×C42Q8×C10314yes—
205C2×C42C23×C10311yescharacteristic
206C2×C42C23×C10311yescharacteristic
207#106—216no—
208C4⋊C8C2×C4×C10318yescomplemented
209C22⋊C8C2×C4×C10318yes—
210C4×C8C2×C4×C10318yescomplemented
211#95—22no—
212#95—22no—
213#95—22no—
214#95—22no—
215C24C2×D4×C10311yescharacteristic
216C22×C4—24no—
217C22×C4—28no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4—44no—
222C22×C4—44no—
223C22×C4C4⋊C4×C10314yes—
224C22×C4C4⋊C4×C10314yes—
225C22×C4SD16×C10314yes—
226C22×C4SD16×C10314yes—
227C22×C4C22×C4×C10312yes—
228C22×C4C2×D4×C10311yescharacteristic
229C22×C4C2×D4×C10311yescharacteristic
230C22×C4C2×D4×C10311yescharacteristic
231C22×C4C2×D4×C10311yescharacteristic
232C22×C4C2×D4×C10311yescharacteristic
233C22×C4C2×Q8×C10312yes—
234C22×C4C24×C10311yescharacteristic
235C2×C8—28no—
236C2×C8C22×C4×C10318yes—
237C4⋊C4—28no—
238C4⋊C4—24no—
239C4⋊C4—28no—
240C4⋊C4—44no—
241C4⋊C4—44no—
242C4⋊C4#41×C10318yes—
243C22⋊C4—44no—
244C42—44no—
245C42—44no—
246C42—44no—
247C42C4⋊C4×C10314yes—
248C42C4⋊C4×C10314yes—
249C42C22×C4×C10312yes—
250C42C22×C4×C10312yes—
251C42C2×Q8×C10312yes—
252C42C2×Q8×C10312yes—
253C23—22no—
254C23—22no—
255C23C2×C4⋊C4×C10312yes—
256C23C2×SD16×C10312yes—
257C23C2×SD16×C10312yes—
258C23C22×D4×C10311yescharacteristic
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—28no—
265C2×C4—44no—
266C2×C4—416no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4#106×C103116yescomplemented
273C2×C4C2×C4⋊C4×C10312yes—
274C2×C4C2×C4⋊C4×C10312yes—
275C2×C4C2×C4⋊C4×C10312yes—
276C2×C4C2×C4⋊C4×C10312yes—
277C2×C4C2×C4⋊C4×C10312yes—
278C2×C4C2×SD16×C10312yes—
279C2×C4C2×SD16×C10312yes—
280C2×C4C2×SD16×C10312yes—
281C2×C4C2×SD16×C10312yes—
282C2×C4C23×C4×C10311yescharacteristic
283C2×C4C22×Q8×C10311yescharacteristic
284C2×C4C2×#41×C10314yes—
285C8—28no—
286C22—22no—
287C22—24no—
288C22—24no—
289C22—22no—
290C22C2×#106×C10314yes—
291C22C22×C4⋊C4×C10311yescharacteristic
292C22#525×C10312yes—
293C22C22×SD16×C10311yescharacteristic
294C22C22×SD16×C10311yescharacteristic
295C22#575×C10312yes—
296C4—22no—
297C4—22no—
298C4—22no—
299C4—48no—
300C4—84no—
301C4C2×#106×C10314yes—
302C4C2×#106×C10314yes—
303C4C4×#41×C10312yes—
304C4#533×C10312yes—
305C2—24no—
306C2C103×#229611yescharacteristic
307C2C22×#106×C10311yescharacteristic
308C2C103×#291111yescharacteristic
309C2C103×#310112yes—
310C2C103×#310312yes—
subgroupG/H
centerC22×C4×C103C2×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC23×C103C22×D4
prime radicalC24×C103C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1948C2semidirect
6. C4×#106×C103C2semidirect
11. #431×C103C4semidirect
52. C4⋊C8×C103C2×C4semidirect
54. C4×C8×C103C2×C4semidirect
116. C2×C4×C103#106semidirect
149. #21359C103direct (N × H)
159. #1948C2×C103semidirect
161. C4×#106C2×C103semidirect
162. C103#21359direct (N × H)
167. #431C4×C103semidirect
208. C4⋊C8C2×C4×C103semidirect
210. C4×C8C2×C4×C103semidirect
272. C2×C4#106×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#431×C1032
C103×#22852
C2×C4×C4⋊C4×C1032
C103×#19482
C103×#18532
C4×#106×C1032
#21359103