Finite Group Databasebeta

← C103×#3194 #27192560

Subgroups — C103×#3194 #27192560

Order 13184.

466 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×C103C211yesmaximal, characteristic, complemented
2C2×#121×C103C211yesmaximal, characteristic, complemented
3#483×C103C211yesmaximal, characteristic, complemented
4#482×C103C212yesmaximal, complemented
5#480×C103C211yesmaximal, characteristic, complemented
6#469×C103C212yesmaximal, complemented
7#468×C103C212yesmaximal, complemented
8#450×C103C211yesmaximal, characteristic, complemented
9#449×C103C212yesmaximal, complemented
10#447×C103C211yesmaximal, characteristic, complemented
11#407×C103C211yesmaximal, characteristic, complemented
12C2×#41×C103C2211yescharacteristic, complemented
13C22×D4×C103—21no—
14C22×D4×C103C2211yescharacteristic
15C23×C4×C103C2211yescharacteristic
16C2×SD16×C103C2212yescomplemented
17C2×D8×C103C2212yescomplemented
18C2×M16×C103C2212yescomplemented
19#123×C103—21no—
20C22⋊Q8×C103C2211yescharacteristic
21C22⋊Q8×C103C2211yescharacteristic, complemented
22#121×C103—21no—
23#121×C103—21no—
24#121×C103C2211yescharacteristic
25#121×C103C2212yes—
26#121×C103C2212yes—
27#121×C103C2211yescharacteristic, complemented
28#120×C103—21no—
29C4×D4×C103—21no—
30C4×D4×C103—21no—
31#117×C103C2211yescharacteristic, complemented
32C2×C4⋊C4×C103C2211yescharacteristic
33C2×C22⋊C4×C103—21no—
34#107×C103C2212yescomplemented
35#106×C103C2212yescomplemented
36#103×C103C2212yescomplemented
37#102×C103C2212yescomplemented
38#102×C103C2212yescomplemented
39#102×C103C2212yescomplemented
40C22⋊C8×C103C2211yescharacteristic
41C22⋊C8×C103C2211yescharacteristic
42C22⋊C8×C103C2212yescomplemented
43C24×C103—21no—
44C24×C103D411yescharacteristic
45#41×C103—42no—
46C2×Q8×C103C2311yescharacteristic
47C2×D4×C103—21no—
48C2×D4×C103—21no—
49C2×D4×C103—21no—
50C2×D4×C103—22no—
51C2×D4×C103—22no—
52C2×D4×C103—21no—
53C2×D4×C103—42no—
54C2×D4×C103—44no—
55C2×D4×C103C2312yes—
56C2×D4×C103C2311yescharacteristic
57C22×C4×C103—21no—
58C22×C4×C103—21no—
59C22×C4×C103—42no—
60C22×C4×C103D411yescharacteristic
61C22×C4×C103D411yescharacteristic
62C22×C4×C103D411yescharacteristic
63C22×C4×C103C2311yescharacteristic
64C22×C4×C103C2311yescharacteristic
65C22×C4×C103C2311yescharacteristic
66SD16×C103—42no—
67D8×C103—42no—
68M16×C103—42no—
69C2×C8×C103C2312yes—
70C2×C8×C103C2312yes—
71C4⋊C4×C103—21no—
72C4⋊C4×C103—21no—
73C4⋊C4×C103—21no—
74C4⋊C4×C103C2311yescharacteristic
75C4⋊C4×C103C2311yescharacteristic
76C4⋊C4×C103C2312yes—
77C22⋊C4×C103—21no—
78C22⋊C4×C103—21no—
79C22⋊C4×C103—21no—
80C22⋊C4×C103—22no—
81C22⋊C4×C103—22no—
82C22⋊C4×C103—21no—
83C22⋊C4×C103—21no—
84C42×C103—21no—
85C23×C103—22no—
86C23×C103—21no—
87C23×C103—22no—
88C23×C103—41no—
89C23×C103—41no—
90C23×C103—42no—
91C23×C103—42no—
92C23×C103—42no—
93C23×C103C2×D411yescharacteristic
94C23×C103C2×D411yescharacteristic
95C23×C103C2×D411yescharacteristic
96Q8×C103—22no—
97D4×C103—22no—
98D4×C103—22no—
99D4×C103—22no—
100D4×C103—42no—
101D4×C103—42no—
102D4×C103—44no—
103D4×C103—44no—
104D4×C103—42no—
105D4×C103—42no—
106C2×C4×C103—22no—
107C2×C4×C103—22no—
108C2×C4×C103—22no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—22no—
113C2×C4×C103—41no—
114C2×C4×C103—41no—
115C2×C4×C103—41no—
116C2×C4×C103—42no—
117C2×C4×C103—42no—
118C2×C4×C103C2×D411yescharacteristic
119C2×C4×C103C2×D411yescharacteristic
120C2×C4×C103C2×D411yescharacteristic
121C2×C4×C103C2411yescharacteristic
122C8×C103—22no—
123C8×C103—22no—
124C22×C103—21no—
125C22×C103—21no—
126C22×C103—21no—
127C22×C103—21no—
128C22×C103—21no—
129C22×C103—21no—
130C22×C103—21no—
131C22×C103—21no—
132C22×C103—44no—
133C22×C103—41no—
134C22×C103—42no—
135C22×C103—42no—
136C22×C103—41no—
137C22×C103—41no—
138C22×C103—42no—
139C22×C103—84no—
140C22×C103AGL(1,ℤ/8)12yes—
141C22×C103C22×D411yescharacteristic
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—21no—
145C4×C103—41no—
146C4×C103—42no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103H(5,𝔽2)12yes—
150C2×C103—22no—
151C2×C103—41no—
152C2×C103—41no—
153C2×C103—81no—
154C2×C103—82no—
155C2×C103#53411yescharacteristic
156C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
157C2×C103#57511yescharacteristic
158#3194C10311yesmaximal, characteristic, direct product factor, Sylow
159C103#319411yescharacteristic, direct product factor, Sylow
160#525C2×C10311yescharacteristic, complemented
161C2×#121C2×C10311yescharacteristic, complemented
162#483C2×C10311yescharacteristic, complemented
163#482C2×C10312yescomplemented
164#480C2×C10311yescharacteristic, complemented
165#469C2×C10312yescomplemented
166#468C2×C10312yescomplemented
167#450C2×C10311yescharacteristic, complemented
168#449C2×C10312yescomplemented
169#447C2×C10311yescharacteristic, complemented
170#407C2×C10311yescharacteristic, complemented
171C2×#41C22×C10311yescharacteristic, complemented
172C22×D4—21no—
173C22×D4C22×C10311yescharacteristic
174C23×C4C22×C10311yescharacteristic
175C2×SD16C22×C10312yescomplemented
176C2×D8C22×C10312yescomplemented
177C2×M16C22×C10312yescomplemented
178#123—21no—
179C22⋊Q8C22×C10311yescharacteristic
180C22⋊Q8C22×C10311yescharacteristic, complemented
181#121—21no—
182#121—21no—
183#121C22×C10312yes—
184#121C22×C10312yes—
185#121C22×C10311yescharacteristic
186#121C22×C10311yescharacteristic, complemented
187#120—21no—
188C4×D4—21no—
189C4×D4—21no—
190#117C22×C10311yescharacteristic, complemented
191C2×C4⋊C4C22×C10311yescharacteristic
192C2×C22⋊C4—21no—
193#107C22×C10312yescomplemented
194#106C22×C10312yescomplemented
195#103C22×C10312yescomplemented
196#102C22×C10312yescomplemented
197#102C22×C10312yescomplemented
198#102C22×C10312yescomplemented
199C22⋊C8C22×C10311yescharacteristic
200C22⋊C8C22×C10311yescharacteristic
201C22⋊C8C22×C10312yescomplemented
202C24—21no—
203C24D4×C10311yescharacteristic
204#41—42no—
205C2×Q8C23×C10311yescharacteristic
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—42no—
213C2×D4—44no—
214C2×D4C23×C10312yes—
215C2×D4C23×C10311yescharacteristic
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4D4×C10311yescharacteristic
220C22×C4D4×C10311yescharacteristic
221C22×C4D4×C10311yescharacteristic
222C22×C4C23×C10311yescharacteristic
223C22×C4C23×C10311yescharacteristic
224C22×C4C23×C10311yescharacteristic
225SD16—42no—
226D8—42no—
227M16—42no—
228C2×C8C23×C10312yes—
229C2×C8C23×C10312yes—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4C23×C10311yescharacteristic
234C4⋊C4C23×C10311yescharacteristic
235C4⋊C4C23×C10312yes—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—22no—
240C22⋊C4—22no—
241C22⋊C4—21no—
242C22⋊C4—21no—
243C42—21no—
244C23—22no—
245C23—21no—
246C23—22no—
247C23—41no—
248C23—41no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23C2×D4×C10311yescharacteristic
253C23C2×D4×C10311yescharacteristic
254C23C2×D4×C10311yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—44no—
261D4—44no—
262D4—42no—
263D4—42no—
264D4—42no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4C2×D4×C10311yescharacteristic
278C2×C4C2×D4×C10311yescharacteristic
279C2×C4C2×D4×C10311yescharacteristic
280C2×C4C24×C10311yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—41no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—84no—
299C22AGL(1,ℤ/8)×C10312yes—
300C22C22×D4×C10311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—42no—
306C4—41no—
307C4—41no—
308C4H(5,𝔽2)×C10312yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2—81no—
314C2#534×C10311yescharacteristic
315C2C2×AGL(1,ℤ/8)×C10311yescharacteristic
316C2#575×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C22×D4
commutator, Frattini, cosocleC2×C4C24×C103
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. #525×C103C2semidirect
2. C2×#121×C103C2semidirect
3. #483×C103C2semidirect
4. #482×C103C2semidirect
5. #480×C103C2semidirect
6. #469×C103C2semidirect
7. #468×C103C2semidirect
8. #450×C103C2semidirect
9. #449×C103C2semidirect
10. #447×C103C2semidirect
11. #407×C103C2semidirect
12. C2×#41×C103C22semidirect
16. C2×SD16×C103C22semidirect
17. C2×D8×C103C22semidirect
18. C2×M16×C103C22semidirect
21. C22⋊Q8×C103C22semidirect
27. #121×C103C22semidirect
31. #117×C103C22semidirect
34. #107×C103C22semidirect
35. #106×C103C22semidirect
36. #103×C103C22semidirect
37. #102×C103C22semidirect
38. #102×C103C22semidirect
39. #102×C103C22semidirect
42. C22⋊C8×C103C22semidirect
158. #3194C103direct (N × H)
159. C103#3194direct (N × H)
160. #525C2×C103semidirect
161. C2×#121C2×C103semidirect
162. #483C2×C103semidirect
163. #482C2×C103semidirect
164. #480C2×C103semidirect
165. #469C2×C103semidirect
166. #468C2×C103semidirect
167. #450C2×C103semidirect
168. #449C2×C103semidirect
169. #447C2×C103semidirect
170. #407C2×C103semidirect
171. C2×#41C22×C103semidirect
175. C2×SD16C22×C103semidirect
176. C2×D8C22×C103semidirect
177. C2×M16C22×C103semidirect
180. C22⋊Q8C22×C103semidirect
186. #121C22×C103semidirect
190. #117C22×C103semidirect
193. #107C22×C103semidirect
194. #106C22×C103semidirect
195. #103C22×C103semidirect
196. #102C22×C103semidirect
197. #102C22×C103semidirect
198. #102C22×C103semidirect
201. C22⋊C8C22×C103semidirect

Maximal subgroups

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

subgroupindex
#525×C1032
C2×#121×C1032
#483×C1032
#482×C1032
#480×C1032
#469×C1032
#468×C1032
#450×C1032
#449×C1032
#447×C1032
#407×C1032
#3194103