Finite Group Databasebeta

← C103×#3243 #27192609

Subgroups — C103×#3243 #27192609

Order 13184.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#544×C103C211yesmaximal, characteristic, complemented
2#542×C103C211yesmaximal, characteristic
3#501×C103C211yesmaximal, characteristic, complemented
4#500×C103C211yesmaximal, characteristic, complemented
5#489×C103C211yesmaximal, characteristic, complemented
6#488×C103C211yesmaximal, characteristic, complemented
7#485×C103C211yesmaximal, characteristic, complemented
8#484×C103C211yesmaximal, characteristic, complemented
9#482×C103C211yesmaximal, characteristic
10#480×C103C211yesmaximal, characteristic
11#479×C103C211yesmaximal, characteristic, complemented
12#478×C103C211yesmaximal, characteristic, complemented
13#477×C103C211yesmaximal, characteristic, complemented
14#474×C103C211yesmaximal, characteristic, complemented
15#433×C103C211yesmaximal, characteristic, complemented
16C4⋊Q8×C103—21no—
17C4⋊Q8×C103C2211yescharacteristic
18C4⋊Q8×C103C2211yescharacteristic
19C4⋊Q8×C103C2211yescharacteristic
20#126×C103—21no—
21#125×C103—21no—
22#125×C103C2211yescharacteristic
23#125×C103C2211yescharacteristic
24#124×C103—21no—
25#124×C103C2211yescharacteristic
26#123×C103—21no—
27C22⋊Q8×C103—21no—
28C22⋊Q8×C103—21no—
29C22⋊Q8×C103—21no—
30C22⋊Q8×C103C2211yescharacteristic
31#121×C103C2211yescharacteristic
32C4×Q8×C103C2211yescharacteristic
33C4×D4×C103C2211yescharacteristic
34#117×C103C2211yescharacteristic
35#117×C103C2211yescharacteristic
36C2×C4⋊C4×C103C2211yescharacteristic
37#107×C103C2211yescharacteristic
38#107×C103C2211yescharacteristic
39#107×C103C2211yescharacteristic
40#107×C103C2211yescharacteristic
41#107×C103C2211yescharacteristic
42#107×C103C2211yescharacteristic
43#106×C103C2211yescharacteristic
44#106×C103C2211yescharacteristic
45C4⋊C8×C103C2211yescharacteristic
46C4⋊C8×C103C2211yescharacteristic
47#103×C103C2211yescharacteristic
48#103×C103C2211yescharacteristic
49#103×C103C2211yescharacteristic
50#103×C103C2211yescharacteristic
51#102×C103C2211yescharacteristic
52#102×C103C2211yescharacteristic
53#102×C103C2211yescharacteristic
54#102×C103C2211yescharacteristic
55C22⋊C8×C103C2211yescharacteristic
56C22⋊C8×C103C2211yescharacteristic
57#97×C103C2211yescharacteristic
58C4×C8×C103C2211yescharacteristic
59C2×Q8×C103—21no—
60C2×Q8×C103—21no—
61C2×Q8×C103—21no—
62C2×Q8×C103C2311yescharacteristic
63C2×D4×C103—21no—
64C2×D4×C103C2311yescharacteristic
65C22×C4×C103—21no—
66C22×C4×C103—21no—
67C22×C4×C103C2311yescharacteristic
68C2×C8×C103C2311yescharacteristic
69C2×C8×C103C2311yescharacteristic
70C2×C8×C103C2311yescharacteristic
71C2×C8×C103C2311yescharacteristic
72C4⋊C4×C103—21no—
73C4⋊C4×C103—21no—
74C4⋊C4×C103—21no—
75C4⋊C4×C103—21no—
76C4⋊C4×C103—21no—
77C4⋊C4×C103—21no—
78C4⋊C4×C103—21no—
79C4⋊C4×C103—21no—
80C4⋊C4×C103—21no—
81C4⋊C4×C103—21no—
82C4⋊C4×C103D411yescharacteristic
83C4⋊C4×C103D411yescharacteristic
84C4⋊C4×C103C2311yescharacteristic
85C4⋊C4×C103C2311yescharacteristic
86C4⋊C4×C103C2311yescharacteristic
87C4⋊C4×C103C2311yescharacteristic
88C4⋊C4×C103C2311yescharacteristic
89C4⋊C4×C103C2311yescharacteristic
90C22⋊C4×C103—21no—
91C22⋊C4×C103—21no—
92C22⋊C4×C103—21no—
93C22⋊C4×C103—21no—
94C22⋊C4×C103—21no—
95C22⋊C4×C103—21no—
96C22⋊C4×C103D411yescharacteristic
97C22⋊C4×C103D411yescharacteristic
98C42×C103—21no—
99C42×C103—21no—
100C42×C103C2311yescharacteristic
101C42×C103C2311yescharacteristic
102C23×C103—21no—
103C23×C103C2×D411yescharacteristic
104Q8×C103—21no—
105Q8×C103—21no—
106Q8×C103—81no—
107Q8×C103—81no—
108Q8×C103—81no—
109D4×C103—21no—
110D4×C103—21no—
111D4×C103—81no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—81no—
122C2×C4×C103—81no—
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2411yescharacteristic
129C8×C103—21no—
130C8×C103—21no—
131C8×C103—21no—
132C8×C103—21no—
133C22×C103—21no—
134C22×C103—21no—
135C22×C103—21no—
136C22×C103—41no—
137C22×C103—41no—
138C22×C103—41no—
139C22×C103C22×D411yescharacteristic
140C4×C103—21no—
141C4×C103—21no—
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—21no—
145C4×C103—41no—
146C4×C103—41no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103—41no—
151C4×C103—41no—
152C4×C1032−1+411yescharacteristic
153C4×C1032−1+411yescharacteristic
154C2×C103—41no—
155C2×C103—81no—
156C2×C103#53611yescharacteristic
157C2×C103#57611yescharacteristic
158C2×C103#57811yescharacteristic
159#3243C10311yesmaximal, characteristic, direct product factor, Sylow
160C103#324311yescharacteristic, direct product factor, Sylow
161#544C2×C10311yescharacteristic, complemented
162#542C2×C10311yescharacteristic
163#501C2×C10311yescharacteristic, complemented
164#500C2×C10311yescharacteristic, complemented
165#489C2×C10311yescharacteristic, complemented
166#488C2×C10311yescharacteristic, complemented
167#485C2×C10311yescharacteristic, complemented
168#484C2×C10311yescharacteristic, complemented
169#482C2×C10311yescharacteristic
170#480C2×C10311yescharacteristic
171#479C2×C10311yescharacteristic, complemented
172#478C2×C10311yescharacteristic, complemented
173#477C2×C10311yescharacteristic, complemented
174#474C2×C10311yescharacteristic, complemented
175#433C2×C10311yescharacteristic, complemented
176C4⋊Q8—21no—
177C4⋊Q8C22×C10311yescharacteristic
178C4⋊Q8C22×C10311yescharacteristic
179C4⋊Q8C22×C10311yescharacteristic
180#126—21no—
181#125—21no—
182#125C22×C10311yescharacteristic
183#125C22×C10311yescharacteristic
184#124—21no—
185#124C22×C10311yescharacteristic
186#123—21no—
187C22⋊Q8—21no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190C22⋊Q8C22×C10311yescharacteristic
191#121C22×C10311yescharacteristic
192C4×Q8C22×C10311yescharacteristic
193C4×D4C22×C10311yescharacteristic
194#117C22×C10311yescharacteristic
195#117C22×C10311yescharacteristic
196C2×C4⋊C4C22×C10311yescharacteristic
197#107C22×C10311yescharacteristic
198#107C22×C10311yescharacteristic
199#107C22×C10311yescharacteristic
200#107C22×C10311yescharacteristic
201#107C22×C10311yescharacteristic
202#107C22×C10311yescharacteristic
203#106C22×C10311yescharacteristic
204#106C22×C10311yescharacteristic
205C4⋊C8C22×C10311yescharacteristic
206C4⋊C8C22×C10311yescharacteristic
207#103C22×C10311yescharacteristic
208#103C22×C10311yescharacteristic
209#103C22×C10311yescharacteristic
210#103C22×C10311yescharacteristic
211#102C22×C10311yescharacteristic
212#102C22×C10311yescharacteristic
213#102C22×C10311yescharacteristic
214#102C22×C10311yescharacteristic
215C22⋊C8C22×C10311yescharacteristic
216C22⋊C8C22×C10311yescharacteristic
217#97C22×C10311yescharacteristic
218C4×C8C22×C10311yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8C23×C10311yescharacteristic
223C2×D4—21no—
224C2×D4C23×C10311yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4C23×C10311yescharacteristic
228C2×C8C23×C10311yescharacteristic
229C2×C8C23×C10311yescharacteristic
230C2×C8C23×C10311yescharacteristic
231C2×C8C23×C10311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4D4×C10311yescharacteristic
243C4⋊C4D4×C10311yescharacteristic
244C4⋊C4C23×C10311yescharacteristic
245C4⋊C4C23×C10311yescharacteristic
246C4⋊C4C23×C10311yescharacteristic
247C4⋊C4C23×C10311yescharacteristic
248C4⋊C4C23×C10311yescharacteristic
249C4⋊C4C23×C10311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4D4×C10311yescharacteristic
257C22⋊C4D4×C10311yescharacteristic
258C42—21no—
259C42—21no—
260C42C23×C10311yescharacteristic
261C42C23×C10311yescharacteristic
262C23—21no—
263C23C2×D4×C10311yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—81no—
267Q8—81no—
268Q8—81no—
269D4—21no—
270D4—21no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4C2×D4×C10311yescharacteristic
284C2×C4C2×D4×C10311yescharacteristic
285C2×C4C2×D4×C10311yescharacteristic
286C2×C4C2×D4×C10311yescharacteristic
287C2×C4C2×D4×C10311yescharacteristic
288C2×C4C24×C10311yescharacteristic
289C8—21no—
290C8—21no—
291C8—21no—
292C8—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C22×D4×C10311yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C42−1+4×C10311yescharacteristic
313C42−1+4×C10311yescharacteristic
314C2—41no—
315C2—81no—
316C2#536×C10311yescharacteristic
317C2#576×C10311yescharacteristic
318C2#578×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C22×D4
commutator, Frattini, cosocleC2×C4C24×C103
prime radical#121×C103C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ #117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. #544×C103C2semidirect
3. #501×C103C2semidirect
4. #500×C103C2semidirect
5. #489×C103C2semidirect
6. #488×C103C2semidirect
7. #485×C103C2semidirect
8. #484×C103C2semidirect
11. #479×C103C2semidirect
12. #478×C103C2semidirect
13. #477×C103C2semidirect
14. #474×C103C2semidirect
15. #433×C103C2semidirect
159. #3243C103direct (N × H)
160. C103#3243direct (N × H)
161. #544C2×C103semidirect
163. #501C2×C103semidirect
164. #500C2×C103semidirect
165. #489C2×C103semidirect
166. #488C2×C103semidirect
167. #485C2×C103semidirect
168. #484C2×C103semidirect
171. #479C2×C103semidirect
172. #478C2×C103semidirect
173. #477C2×C103semidirect
174. #474C2×C103semidirect
175. #433C2×C103semidirect

Maximal subgroups

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

subgroupindex
#544×C1032
#542×C1032
#501×C1032
#500×C1032
#489×C1032
#488×C1032
#485×C1032
#484×C1032
#482×C1032
#480×C1032
#479×C1032
#478×C1032
#477×C1032
#474×C1032
#433×C1032
#3243103