Finite Group Databasebeta

← C103×#20476 #39925751

Subgroups — C103×#20476 #39925751

Order 26368.

990 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#432×C103C211yesmaximal, characteristic
2C22×C4×C8×C103C211yesmaximal, characteristic
3C103×#2283C211yesmaximal, characteristic
4C103×#1770C212yesmaximal, complemented
5C8×C4⋊C4×C103C212yesmaximal, complemented
6C103×#1752C212yesmaximal
7C8×C22⋊C4×C103C212yesmaximal
8C103×#1746C212yesmaximal, complemented
9C103×#1726C212yesmaximal, complemented
10C23×C8×C103C2211yescharacteristic
11C23×C8×C103C2211yescharacteristic
12C22×C42×C103C2211yescharacteristic
13#432×C103C418yescomplemented
14C2×C4⋊C8×C103C2212yes—
15C2×C22⋊C8×C103C2212yes—
16C2×#97×C103C2214yes—
17C2×#97×C103C2212yes—
18C2×C4×C8×C103C418yescomplemented
19C2×C4×C8×C103C2214yes—
20C2×C4×C8×C103C2211yescharacteristic
21C2×C4×C8×C103C2211yescharacteristic
22C2×C4×C8×C103C2211yescharacteristic
23C2×C4×C8×C103C2211yescharacteristic
24#383×C103C412yes—
25#382×C103C412yes—
26#381×C103C412yes—
27#380×C103C412yes—
28C4×C4⋊C4×C103C2212yes—
29C4×C22⋊C4×C103C2212yes—
30#376×C103C2212yes—
31#336×C103C2214yes—
32#336×C103C2214yes—
33C23×C4×C103C2×C411yescharacteristic
34C23×C4×C103C2×C411yescharacteristic
35C23×C4×C103C2311yescharacteristic
36C22×C8×C103—24no—
37C22×C8×C103—24no—
38C22×C8×C103C2×C414yes—
39C22×C8×C103C2×C414yes—
40C22×C8×C103C2311yescharacteristic
41C22×C8×C103C2311yescharacteristic
42C22×C8×C103C2314yes—
43C22×C8×C103C2311yescharacteristic
44C22×C8×C103C2311yescharacteristic
45C2×C4⋊C4×C103C2×C414yes—
46C2×C22⋊C4×C103C2×C414yes—
47C2×C42×C103C2×C411yescharacteristic
48C2×C42×C103C2×C411yescharacteristic
49C2×C42×C103C2×C414yes—
50C2×C42×C103C2×C414yes—
51C2×C42×C103C2314yes—
52C2×C42×C103C2311yescharacteristic
53C2×C42×C103C2311yescharacteristic
54C4⋊C8×C103C2×C418yes—
55C22⋊C8×C103C2×C418yes—
56#97×C103—28no—
57#97×C103C2×C418yes—
58C4×C8×C103—28no—
59C4×C8×C103C2×C414yes—
60C4×C8×C103C2×C414yes—
61C4×C8×C103C2×C414yes—
62C4×C8×C103C2×C414yes—
63#95×C103C2×C414yes—
64#95×C103C2×C414yes—
65#95×C103C2×C414yes—
66#95×C103C2×C414yes—
67C24×C103C22×C411yescharacteristic
68C22×C4×C103—24no—
69C22×C4×C103—24no—
70C22×C4×C103—22no—
71C22×C4×C103—22no—
72C22×C4×C103C4214yes—
73C22×C4×C103C4214yes—
74C22×C4×C103C22×C418yes—
75C22×C4×C103C22×C411yescharacteristic
76C22×C4×C103C22×C411yescharacteristic
77C22×C4×C103C22×C411yescharacteristic
78C22×C4×C103C22×C411yescharacteristic
79C22×C4×C103C22×C412yes—
80C22×C4×C103C22×C412yes—
81C22×C4×C103C22×C411yescharacteristic
82C22×C4×C103C2411yescharacteristic
83C2×C8×C103—24no—
84C2×C8×C103—24no—
85C2×C8×C103—22no—
86C2×C8×C103—22no—
87C2×C8×C103—28no—
88C2×C8×C103—28no—
89C2×C8×C103C22×C412yes—
90C2×C8×C103C22×C412yes—
91C2×C8×C103C22×C418yes—
92C2×C8×C103C22×C412yes—
93C2×C8×C103C22×C412yes—
94C2×C8×C103#4114yes—
95C2×C8×C103#4114yes—
96C4⋊C4×C103—28no—
97C22⋊C4×C103—28no—
98C42×C103—24no—
99C42×C103—24no—
100C42×C103C4214yes—
101C42×C103C4214yes—
102C42×C103C22×C412yes—
103C42×C103C22×C412yes—
104C42×C103C22×C412yes—
105C42×C103C22×C412yes—
106C23×C103—22no—
107C23×C103—22no—
108C23×C103C2×C4212yes—
109C23×C103#13114yes—
110C23×C103C23×C411yescharacteristic
111C2×C4×C103—22no—
112C2×C4×C103—22no—
113C2×C4×C103—22no—
114C2×C4×C103—22no—
115C2×C4×C103—28no—
116C2×C4×C103—22no—
117C2×C4×C103—22no—
118C2×C4×C103—24no—
119C2×C4×C103—28no—
120C2×C4×C103—28no—
121C2×C4×C103—28no—
122C2×C4×C103—28no—
123C2×C4×C103C2×C4212yes—
124C2×C4×C103C2×C4212yes—
125C2×C4×C103C2×C4212yes—
126C2×C4×C103C2×C4212yes—
127C2×C4×C103C2×C4212yes—
128C2×C4×C103#13114yes—
129C2×C4×C103C23×C411yescharacteristic
130C2×C4×C103C23×C411yescharacteristic
131C2×C4×C103C2×#4112yes—
132C2×C4×C103C2×#4112yes—
133C8×C103—22no—
134C8×C103—22no—
135C8×C103—28no—
136C8×C103#11714yes—
137C8×C103#11714yes—
138C22×C103—22no—
139C22×C103—28no—
140C22×C103—22no—
141C22×C103#40514yes—
142C22×C103C22×C4211yescharacteristic
143C22×C103C4×#4112yes—
144C22×C103C2×#13112yes—
145C22×C103C2×#13112yes—
146C4×C103—22no—
147C4×C103—22no—
148C4×C103—22no—
149C4×C103—22no—
150C4×C103—48no—
151C4×C103#40514yes—
152C4×C103C2×#11711yescharacteristic
153C4×C103C2×#11711yescharacteristic
154C4×C103C4×#4112yes—
155#20476C10311yesmaximal, characteristic, direct product factor, Sylow
156C2×C103—24no—
157C2×C103C4×#11711yescharacteristic
158C2×C103C2×#40511yescharacteristic
159C2×C103C2×#40511yescharacteristic
160C2×C103#296614yes—
161C2×#432C2×C10311yescharacteristic
162C22×C4×C8C2×C10311yescharacteristic
163#2283C2×C10311yescharacteristic
164#1770C2×C10312yescomplemented
165C8×C4⋊C4C2×C10312yescomplemented
166#1752C2×C10312yes—
167C8×C22⋊C4C2×C10312yes—
168#1746C2×C10312yescomplemented
169#1726C2×C10312yescomplemented
170C103#2047611yescharacteristic, direct product factor, Sylow
171C23×C8C22×C10311yescharacteristic
172C23×C8C22×C10311yescharacteristic
173C22×C42C22×C10311yescharacteristic
174#432C4×C10318yescomplemented
175C2×C4⋊C8C22×C10312yes—
176C2×C22⋊C8C22×C10312yes—
177C2×#97C22×C10314yes—
178C2×#97C22×C10312yes—
179C2×C4×C8C4×C10318yescomplemented
180C2×C4×C8C22×C10314yes—
181C2×C4×C8C22×C10311yescharacteristic
182C2×C4×C8C22×C10311yescharacteristic
183C2×C4×C8C22×C10311yescharacteristic
184C2×C4×C8C22×C10311yescharacteristic
185#383C4×C10312yes—
186#382C4×C10312yes—
187#381C4×C10312yes—
188#380C4×C10312yes—
189C4×C4⋊C4C22×C10312yes—
190C4×C22⋊C4C22×C10312yes—
191#376C22×C10312yes—
192#336C22×C10314yes—
193#336C22×C10314yes—
194C23×C4C2×C4×C10311yescharacteristic
195C23×C4C2×C4×C10311yescharacteristic
196C23×C4C23×C10311yescharacteristic
197C22×C8—24no—
198C22×C8—24no—
199C22×C8C2×C4×C10314yes—
200C22×C8C2×C4×C10314yes—
201C22×C8C23×C10311yescharacteristic
202C22×C8C23×C10311yescharacteristic
203C22×C8C23×C10314yes—
204C22×C8C23×C10311yescharacteristic
205C22×C8C23×C10311yescharacteristic
206C2×C4⋊C4C2×C4×C10314yes—
207C2×C22⋊C4C2×C4×C10314yes—
208C2×C42C2×C4×C10311yescharacteristic
209C2×C42C2×C4×C10311yescharacteristic
210C2×C42C2×C4×C10314yes—
211C2×C42C2×C4×C10314yes—
212C2×C42C23×C10314yes—
213C2×C42C23×C10311yescharacteristic
214C2×C42C23×C10311yescharacteristic
215C4⋊C8C2×C4×C10318yes—
216C22⋊C8C2×C4×C10318yes—
217#97—28no—
218#97C2×C4×C10318yes—
219C4×C8—28no—
220C4×C8C2×C4×C10314yes—
221C4×C8C2×C4×C10314yes—
222C4×C8C2×C4×C10314yes—
223C4×C8C2×C4×C10314yes—
224#95C2×C4×C10314yes—
225#95C2×C4×C10314yes—
226#95C2×C4×C10314yes—
227#95C2×C4×C10314yes—
228C24C22×C4×C10311yescharacteristic
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4C42×C10314yes—
234C22×C4C42×C10314yes—
235C22×C4C22×C4×C10318yes—
236C22×C4C22×C4×C10311yescharacteristic
237C22×C4C22×C4×C10311yescharacteristic
238C22×C4C22×C4×C10311yescharacteristic
239C22×C4C22×C4×C10311yescharacteristic
240C22×C4C22×C4×C10312yes—
241C22×C4C22×C4×C10312yes—
242C22×C4C22×C4×C10311yescharacteristic
243C22×C4C24×C10311yescharacteristic
244C2×C8—24no—
245C2×C8—24no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—28no—
249C2×C8—28no—
250C2×C8C22×C4×C10312yes—
251C2×C8C22×C4×C10312yes—
252C2×C8C22×C4×C10318yes—
253C2×C8C22×C4×C10312yes—
254C2×C8C22×C4×C10312yes—
255C2×C8#41×C10314yes—
256C2×C8#41×C10314yes—
257C4⋊C4—28no—
258C22⋊C4—28no—
259C42—24no—
260C42—24no—
261C42C42×C10314yes—
262C42C42×C10314yes—
263C42C22×C4×C10312yes—
264C42C22×C4×C10312yes—
265C42C22×C4×C10312yes—
266C42C22×C4×C10312yes—
267C23—22no—
268C23—22no—
269C23C2×C42×C10312yes—
270C23#131×C10314yes—
271C23C23×C4×C10311yescharacteristic
272C2×C4—28no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—28no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—28no—
282C2×C4—28no—
283C2×C4—28no—
284C2×C4C2×C42×C10312yes—
285C2×C4C2×C42×C10312yes—
286C2×C4C2×C42×C10312yes—
287C2×C4C2×C42×C10312yes—
288C2×C4C2×C42×C10312yes—
289C2×C4#131×C10314yes—
290C2×C4C23×C4×C10311yescharacteristic
291C2×C4C23×C4×C10311yescharacteristic
292C2×C4C2×#41×C10312yes—
293C2×C4C2×#41×C10312yes—
294C8—22no—
295C8—22no—
296C8—28no—
297C8#117×C10314yes—
298C8#117×C10314yes—
299C22—28no—
300C22—22no—
301C22—22no—
302C22#405×C10314yes—
303C22C22×C42×C10311yescharacteristic
304C22C4×#41×C10312yes—
305C22C2×#131×C10312yes—
306C22C2×#131×C10312yes—
307C4—22no—
308C4—22no—
309C4—22no—
310C4—22no—
311C4—48no—
312C4#405×C10314yes—
313C4C2×#117×C10311yescharacteristic
314C4C2×#117×C10311yescharacteristic
315C4C4×#41×C10312yes—
316C2—24no—
317C2C4×#117×C10311yescharacteristic
318C2C2×#405×C10311yescharacteristic
319C2C2×#405×C10311yescharacteristic
320C2C103×#296614yes—
subgroupG/H
centerC22×C8×C103C23
commutatorC22C22×C42×C103
Frattini, cosocleC22×C4C24×C103
socleC23×C103C23×C4
prime radicalC24×C103C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1770C2semidirect
5. C8×C4⋊C4×C103C2semidirect
8. C103×#1746C2semidirect
9. C103×#1726C2semidirect
13. #432×C103C4semidirect
18. C2×C4×C8×C103C4semidirect
155. #20476C103direct (N × H)
164. #1770C2×C103semidirect
165. C8×C4⋊C4C2×C103semidirect
168. #1746C2×C103semidirect
169. #1726C2×C103semidirect
170. C103#20476direct (N × H)
174. #432C4×C103semidirect
179. C2×C4×C8C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#432×C1032
C22×C4×C8×C1032
C103×#22832
C103×#17702
C8×C4⋊C4×C1032
C103×#17522
C8×C22⋊C4×C1032
C103×#17462
C103×#17262
#20476103