Finite Group Databasebeta

← C103×#8697 #39913972

Subgroups — C103×#8697 #39913972

Order 26368.

384 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2966C211yesmaximal, characteristic
2C4×#107×C103C211yesmaximal, characteristic, complemented
3C103×#1568C211yesmaximal, characteristic, complemented
4C103×#1509C212yesmaximal
5C103×#1285C212yesmaximal, complemented
6#529×C103C2211yescharacteristic
7#446×C103C411yescharacteristic, complemented
8C8×Q8×C103C411yescharacteristic, complemented
9#436×C103C411yescharacteristic, complemented
10#435×C103—21no—
11C8×D4×C103—21no—
12C8×D4×C103C411yescharacteristic, complemented
13#433×C103—21no—
14#432×C103C2212yes—
15#432×C103C2211yescharacteristic
16C2×#107×C103—21no—
17#405×C103—21no—
18C2×C4×C8×C103C2211yescharacteristic
19C4×C4⋊C4×C103C2212yes—
20#340×C103—21no—
21#335×C103—21no—
22#334×C103—21no—
23#328×C103—22no—
24#327×C103—22no—
25C2×M16×C103—21no—
26C22×C8×C103—21no—
27C22×C8×C103D411yescharacteristic
28C22×C8×C103D411yescharacteristic
29#126×C103—21no—
30#125×C103Q811yescharacteristic
31#124×C103Q811yescharacteristic
32#123×C103—21no—
33C22⋊Q8×C103D411yescharacteristic
34#121×C103D411yescharacteristic
35C4×Q8×C103C2×C411yescharacteristic
36C4×D4×C103—21no—
37C4×D4×C103C2×C411yescharacteristic
38#117×C103—21no—
39C2×C4⋊C4×C103—22no—
40C2×C42×C103—22no—
41C2×C42×C103C2311yescharacteristic
42#107×C103—24no—
43C4⋊C8×C103—21no—
44C4⋊C8×C103—21no—
45C4⋊C8×C103—22no—
46C4⋊C8×C103C2×C411yescharacteristic
47C4⋊C8×C103C2×C411yescharacteristic
48C22⋊C8×C103—21no—
49C22⋊C8×C103—21no—
50C22⋊C8×C103—21no—
51C22⋊C8×C103—22no—
52#97×C103—21no—
53#97×C103—21no—
54#97×C103—22no—
55C4×C8×C103—21no—
56C4×C8×C103C2×C411yescharacteristic
57C4×C8×C103C2×C411yescharacteristic
58C4×C8×C103D411yescharacteristic
59C4×C8×C103D411yescharacteristic
60#95×C103—22no—
61C2×Q8×C103C4⋊C411yescharacteristic
62C2×D4×C103—21no—
63C2×D4×C103C4⋊C411yescharacteristic
64C22×C4×C103—21no—
65C22×C4×C103—42no—
66C22×C4×C103C2×D411yescharacteristic
67C22×C4×C103C2×D411yescharacteristic
68C22×C4×C103#4111yescharacteristic
69M16×C103—42no—
70C2×C8×C103—22no—
71C2×C8×C103—21no—
72C2×C8×C103—21no—
73C2×C8×C103—41no—
74C2×C8×C103—42no—
75C2×C8×C103—42no—
76C2×C8×C103C22⋊C411yescharacteristic
77C2×C8×C103C22⋊C411yescharacteristic
78C2×C8×C103C22⋊C411yescharacteristic
79C2×C8×C103C22⋊C411yescharacteristic
80C4⋊C4×C103—21no—
81C4⋊C4×C103—21no—
82C4⋊C4×C103—21no—
83C4⋊C4×C103—21no—
84C4⋊C4×C103—24no—
85C4⋊C4×C103—42no—
86C4⋊C4×C103C4⋊C411yescharacteristic
87C4⋊C4×C103C4⋊C411yescharacteristic
88C22⋊C4×C103—21no—
89C22⋊C4×C103—21no—
90C22⋊C4×C103—21no—
91C22⋊C4×C103—21no—
92C22⋊C4×C103—21no—
93C42×C103—21no—
94C42×C103—82no—
95C42×C103C22×C411yescharacteristic
96C42×C103C2×D411yescharacteristic
97C42×C103C2×Q811yescharacteristic
98C42×C103#4111yescharacteristic
99C23×C103—21no—
100C23×C103#12111yescharacteristic
101Q8×C103—41no—
102D4×C103—41no—
103D4×C103—41no—
104D4×C103—41no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—41no—
113C2×C4×C103—41no—
114C2×C4×C103—41no—
115C2×C4×C103—44no—
116C2×C4×C103—82no—
117C2×C4×C103—82no—
118C2×C4×C103C2×C22⋊C411yescharacteristic
119C2×C4×C103C2×C4⋊C411yescharacteristic
120C2×C4×C103#11711yescharacteristic
121C2×C4×C103#12111yescharacteristic
122C2×C4×C103C22⋊Q811yescharacteristic
123C2×C4×C103C22⋊Q811yescharacteristic
124C8×C103—21no—
125C8×C103—21no—
126C8×C103—21no—
127C8×C103—41no—
128C8×C103—41no—
129C8×C103—82no—
130C8×C103#10412yes—
131C22×C103—21no—
132C22×C103—21no—
133C22×C103—41no—
134C22×C103—41no—
135C22×C103—41no—
136C22×C103#38011yescharacteristic
137C22×C103#47211yescharacteristic
138C22×C103#47311yescharacteristic
139C4×C103—21no—
140C4×C103—21no—
141C4×C103—21no—
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—41no—
145C4×C103—41no—
146C4×C103—41no—
147C4×C103—84no—
148C4×C103C2×#10411yescharacteristic
149C4×C103#42111yescharacteristic
150#8697C10311yesmaximal, characteristic, direct product factor, Sylow
151C2×C103—21no—
152C2×C103—21no—
153C2×C103—81no—
154C2×C103#180611yescharacteristic
155C2×C103#181211yescharacteristic
156C2×C103#181611yescharacteristic
157#2966C2×C10311yescharacteristic
158C4×#107C2×C10311yescharacteristic, complemented
159#1568C2×C10311yescharacteristic, complemented
160#1509C2×C10312yes—
161#1285C2×C10312yescomplemented
162C103#869711yescharacteristic, direct product factor, Sylow
163#529C22×C10311yescharacteristic
164#446C4×C10311yescharacteristic, complemented
165C8×Q8C4×C10311yescharacteristic, complemented
166#436C4×C10311yescharacteristic, complemented
167#435—21no—
168C8×D4—21no—
169C8×D4C4×C10311yescharacteristic, complemented
170#433—21no—
171#432C22×C10312yes—
172#432C22×C10311yescharacteristic
173C2×#107—21no—
174#405—21no—
175C2×C4×C8C22×C10311yescharacteristic
176C4×C4⋊C4C22×C10312yes—
177#340—21no—
178#335—21no—
179#334—21no—
180#328—22no—
181#327—22no—
182C2×M16—21no—
183C22×C8—21no—
184C22×C8D4×C10311yescharacteristic
185C22×C8D4×C10311yescharacteristic
186#126—21no—
187#125Q8×C10311yescharacteristic
188#124Q8×C10311yescharacteristic
189#123—21no—
190C22⋊Q8D4×C10311yescharacteristic
191#121D4×C10311yescharacteristic
192C4×Q8C2×C4×C10311yescharacteristic
193C4×D4—21no—
194C4×D4C2×C4×C10311yescharacteristic
195#117—21no—
196C2×C4⋊C4—22no—
197C2×C42—22no—
198C2×C42C23×C10311yescharacteristic
199#107—24no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—22no—
203C4⋊C8C2×C4×C10311yescharacteristic
204C4⋊C8C2×C4×C10311yescharacteristic
205C22⋊C8—21no—
206C22⋊C8—21no—
207C22⋊C8—21no—
208C22⋊C8—22no—
209#97—21no—
210#97—21no—
211#97—22no—
212C4×C8—21no—
213C4×C8C2×C4×C10311yescharacteristic
214C4×C8C2×C4×C10311yescharacteristic
215C4×C8D4×C10311yescharacteristic
216C4×C8D4×C10311yescharacteristic
217#95—22no—
218C2×Q8C4⋊C4×C10311yescharacteristic
219C2×D4—21no—
220C2×D4C4⋊C4×C10311yescharacteristic
221C22×C4—21no—
222C22×C4—42no—
223C22×C4C2×D4×C10311yescharacteristic
224C22×C4C2×D4×C10311yescharacteristic
225C22×C4#41×C10311yescharacteristic
226M16—42no—
227C2×C8—22no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8C22⋊C4×C10311yescharacteristic
234C2×C8C22⋊C4×C10311yescharacteristic
235C2×C8C22⋊C4×C10311yescharacteristic
236C2×C8C22⋊C4×C10311yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—24no—
242C4⋊C4—42no—
243C4⋊C4C4⋊C4×C10311yescharacteristic
244C4⋊C4C4⋊C4×C10311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—21no—
249C22⋊C4—21no—
250C42—21no—
251C42—82no—
252C42C22×C4×C10311yescharacteristic
253C42C2×D4×C10311yescharacteristic
254C42C2×Q8×C10311yescharacteristic
255C42#41×C10311yescharacteristic
256C23—21no—
257C23#121×C10311yescharacteristic
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—41no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4C2×C22⋊C4×C10311yescharacteristic
276C2×C4C2×C4⋊C4×C10311yescharacteristic
277C2×C4#117×C10311yescharacteristic
278C2×C4#121×C10311yescharacteristic
279C2×C4C22⋊Q8×C10311yescharacteristic
280C2×C4C22⋊Q8×C10311yescharacteristic
281C8—21no—
282C8—21no—
283C8—21no—
284C8—41no—
285C8—41no—
286C8—82no—
287C8#104×C10312yes—
288C22—21no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22#380×C10311yescharacteristic
294C22#472×C10311yescharacteristic
295C22#473×C10311yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—84no—
305C4C2×#104×C10311yescharacteristic
306C4#421×C10311yescharacteristic
307C2—21no—
308C2—21no—
309C2—81no—
310C2C103×#180611yescharacteristic
311C2C103×#181211yescharacteristic
312C2C103×#181611yescharacteristic
subgroupG/H
center, socleC22×C103#380
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radical#121×C103D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#107×C103C2semidirect
3. C103×#1568C2semidirect
5. C103×#1285C2semidirect
7. #446×C103C4semidirect
8. C8×Q8×C103C4semidirect
9. #436×C103C4semidirect
12. C8×D4×C103C4semidirect
150. #8697C103direct (N × H)
158. C4×#107C2×C103semidirect
159. #1568C2×C103semidirect
161. #1285C2×C103semidirect
162. C103#8697direct (N × H)
164. #446C4×C103semidirect
165. C8×Q8C4×C103semidirect
166. #436C4×C103semidirect
169. C8×D4C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#29662
C4×#107×C1032
C103×#15682
C103×#15092
C103×#12852
#8697103