Finite Group Databasebeta

← C103×#12951 #39918226

Subgroups — C103×#12951 #39918226

Order 26368.

406 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#135×C103C211yesmaximal, characteristic
2C103×#2155C211yesmaximal, characteristic, complemented
3C103×#2148C211yesmaximal, characteristic
4C103×#2145C211yesmaximal, characteristic
5C103×#1945C211yesmaximal, characteristic, complemented
6C103×#1384C211yesmaximal, characteristic, complemented
7C103×#1376C211yesmaximal, characteristic, complemented
8C2×#135×C103C2211yescharacteristic
9C4×#41×C103—21no—
10C2×M32×C103C2211yescharacteristic
11C2×M32×C103C2211yescharacteristic
12C4×Q16×C103—21no—
13C4×SD16×C103—22no—
14C4×D8×C103—21no—
15C2×#108×C103C2211yescharacteristic
16#427×C103C2211yescharacteristic
17#427×C103C2211yescharacteristic
18#424×C103—21no—
19#416×C103—21no—
20C2×C4×C8×C103C2211yescharacteristic
21#365×C103—22no—
22#362×C103—21no—
23#361×C103—21no—
24#360×C103C414yescomplemented
25#339×C103—21no—
26C2×#41×C103—21no—
27#135×C103—21no—
28#135×C103—21no—
29#135×C103C2×C412yes—
30#135×C103Q812yes—
31C2×Q16×C103D411yescharacteristic
32C2×SD16×C103—21no—
33C2×D8×C103D411yescharacteristic
34C2×M16×C103—21no—
35C22×C8×C103D411yescharacteristic
36C22×C8×C103C2311yescharacteristic
37C4×Q8×C103—22no—
38C4×D4×C103—22no—
39C4×D4×C103—42no—
40#117×C103—21no—
41#117×C103—21no—
42#117×C103—41no—
43C2×C42×C103—41no—
44C2×C42×C103D411yescharacteristic
45M32×C103—21no—
46M32×C103—21no—
47M32×C103—21no—
48M32×C103C2×C412yescomplemented
49C2×C16×C103—21no—
50C2×C16×C103—21no—
51#108×C103—21no—
52#108×C103—21no—
53#107×C103—21no—
54#107×C103—21no—
55#106×C103C2×C412yescomplemented
56#106×C103D412yes—
57C4⋊C8×C103—42no—
58#103×C103—22no—
59#102×C103—22no—
60C4×C8×C103—21no—
61C4×C8×C103—21no—
62#41×C103—22no—
63#41×C103—22no—
64#41×C103—41no—
65#41×C103—41no—
66C2×Q8×C103—21no—
67C2×D4×C103—21no—
68C2×D4×C103—41no—
69C22×C4×C103—21no—
70C22×C4×C103—42no—
71C22×C4×C103—41no—
72C22×C4×C103C2×D411yescharacteristic
73Q16×C103—21no—
74Q16×C103C4⋊C412yes—
75SD16×C103—22no—
76SD16×C103—22no—
77D8×C103—21no—
78D8×C103C4⋊C412yes—
79M16×C103—41no—
80M16×C103—41no—
81C2×C8×C103—21no—
82C2×C8×C103—21no—
83C2×C8×C103—21no—
84C2×C8×C103—41no—
85C2×C8×C103C22×C411yescharacteristic
86C2×C8×C103C2×D411yescharacteristic
87C2×C8×C103C2×D411yescharacteristic
88C2×C8×C103C2×Q811yescharacteristic
89C2×C8×C103#4111yescharacteristic
90C2×C8×C103#4111yescharacteristic
91C4⋊C4×C103—22no—
92C4⋊C4×C103—22no—
93C4⋊C4×C103—42no—
94C22⋊C4×C103—42no—
95C22⋊C4×C103—41no—
96C22⋊C4×C103—41no—
97C42×C103—21no—
98C42×C103—42no—
99C42×C103—41no—
100C42×C103—41no—
101C42×C103SD1611yescharacteristic
102C42×C103SD1611yescharacteristic
103C16×C103—22no—
104C16×C103—41no—
105C23×C103—41no—
106C23×C103AGL(1,ℤ/8)11yescharacteristic
107Q8×C103—22no—
108Q8×C103—41no—
109D4×C103—22no—
110D4×C103—42no—
111D4×C103—42no—
112D4×C103—41no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—42no—
116C2×C4×C103—41no—
117C2×C4×C103—42no—
118C2×C4×C103—42no—
119C2×C4×C103—42no—
120C2×C4×C103—42no—
121C2×C4×C103—84no—
122C2×C4×C103C4×D411yescharacteristic
123C2×C4×C103#12011yescharacteristic
124C2×C4×C103C22⋊Q811yescharacteristic
125C2×C4×C103C2×SD1611yescharacteristic
126C2×C4×C103#13511yescharacteristic
127C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
128C8×C103—41no—
129C8×C103—81no—
130C8×C103C2×C4⋊C411yescharacteristic
131C8×C103C4×D411yescharacteristic
132C8×C103C22⋊Q811yescharacteristic
133C8×C103#12311yescharacteristic
134C22×C103—41no—
135C22×C103—42no—
136C22×C103—82no—
137C22×C103#44211yescharacteristic
138C22×C103#45011yescharacteristic
139C22×C103#47811yescharacteristic
140C4×C103—22no—
141C4×C103—41no—
142C4×C103—42no—
143C4×C103—82no—
144C4×C103—82no—
145C4×C103#38511yescharacteristic
146C4×C103C4×SD1611yescharacteristic
147C4×C103#44911yescharacteristic
148C4×C103#47611yescharacteristic
149#12951C10311yesmaximal, characteristic, direct product factor, Sylow
150C2×C103—21no—
151C2×C103—21no—
152C2×C103—21no—
153C2×C103—82no—
154C2×C103#186411yescharacteristic
155C4×#135C2×C10311yescharacteristic
156#2155C2×C10311yescharacteristic, complemented
157#2148C2×C10311yescharacteristic
158#2145C2×C10311yescharacteristic
159#1945C2×C10311yescharacteristic, complemented
160#1384C2×C10311yescharacteristic, complemented
161#1376C2×C10311yescharacteristic, complemented
162C103#1295111yescharacteristic, direct product factor, Sylow
163C2×#135C22×C10311yescharacteristic
164C4×#41—21no—
165C2×M32C22×C10311yescharacteristic
166C2×M32C22×C10311yescharacteristic
167C4×Q16—21no—
168C4×SD16—22no—
169C4×D8—21no—
170C2×#108C22×C10311yescharacteristic
171#427C22×C10311yescharacteristic
172#427C22×C10311yescharacteristic
173#424—21no—
174#416—21no—
175C2×C4×C8C22×C10311yescharacteristic
176#365—22no—
177#362—21no—
178#361—21no—
179#360C4×C10314yescomplemented
180#339—21no—
181C2×#41—21no—
182#135—21no—
183#135—21no—
184#135C2×C4×C10312yes—
185#135Q8×C10312yes—
186C2×Q16D4×C10311yescharacteristic
187C2×SD16—21no—
188C2×D8D4×C10311yescharacteristic
189C2×M16—21no—
190C22×C8D4×C10311yescharacteristic
191C22×C8C23×C10311yescharacteristic
192C4×Q8—22no—
193C4×D4—22no—
194C4×D4—42no—
195#117—21no—
196#117—21no—
197#117—41no—
198C2×C42—41no—
199C2×C42D4×C10311yescharacteristic
200M32—21no—
201M32—21no—
202M32—21no—
203M32C2×C4×C10312yescomplemented
204C2×C16—21no—
205C2×C16—21no—
206#108—21no—
207#108—21no—
208#107—21no—
209#107—21no—
210#106C2×C4×C10312yescomplemented
211#106D4×C10312yes—
212C4⋊C8—42no—
213#103—22no—
214#102—22no—
215C4×C8—21no—
216C4×C8—21no—
217#41—22no—
218#41—22no—
219#41—41no—
220#41—41no—
221C2×Q8—21no—
222C2×D4—21no—
223C2×D4—41no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4C2×D4×C10311yescharacteristic
228Q16—21no—
229Q16C4⋊C4×C10312yes—
230SD16—22no—
231SD16—22no—
232D8—21no—
233D8C4⋊C4×C10312yes—
234M16—41no—
235M16—41no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—41no—
240C2×C8C22×C4×C10311yescharacteristic
241C2×C8C2×D4×C10311yescharacteristic
242C2×C8C2×D4×C10311yescharacteristic
243C2×C8C2×Q8×C10311yescharacteristic
244C2×C8#41×C10311yescharacteristic
245C2×C8#41×C10311yescharacteristic
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C42—21no—
253C42—42no—
254C42—41no—
255C42—41no—
256C42SD16×C10311yescharacteristic
257C42SD16×C10311yescharacteristic
258C16—22no—
259C16—41no—
260C23—41no—
261C23AGL(1,ℤ/8)×C10311yescharacteristic
262Q8—22no—
263Q8—41no—
264D4—22no—
265D4—42no—
266D4—42no—
267D4—41no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—84no—
277C2×C4C4×D4×C10311yescharacteristic
278C2×C4#120×C10311yescharacteristic
279C2×C4C22⋊Q8×C10311yescharacteristic
280C2×C4C2×SD16×C10311yescharacteristic
281C2×C4#135×C10311yescharacteristic
282C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
283C8—41no—
284C8—81no—
285C8C2×C4⋊C4×C10311yescharacteristic
286C8C4×D4×C10311yescharacteristic
287C8C22⋊Q8×C10311yescharacteristic
288C8#123×C10311yescharacteristic
289C22—41no—
290C22—42no—
291C22—82no—
292C22#442×C10311yescharacteristic
293C22#450×C10311yescharacteristic
294C22#478×C10311yescharacteristic
295C4—22no—
296C4—41no—
297C4—42no—
298C4—82no—
299C4—82no—
300C4#385×C10311yescharacteristic
301C4C4×SD16×C10311yescharacteristic
302C4#449×C10311yescharacteristic
303C4#476×C10311yescharacteristic
304C2—21no—
305C2—21no—
306C2—21no—
307C2—82no—
308C2C103×#186411yescharacteristic
subgroupG/H
centerC4×C103#476
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
socleC2×C103#1864
prime radicalC2×#135×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C4×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2155C2semidirect
5. C103×#1945C2semidirect
6. C103×#1384C2semidirect
7. C103×#1376C2semidirect
24. #360×C103C4semidirect
48. M32×C103C2×C4semidirect
55. #106×C103C2×C4semidirect
149. #12951C103direct (N × H)
156. #2155C2×C103semidirect
159. #1945C2×C103semidirect
160. #1384C2×C103semidirect
161. #1376C2×C103semidirect
162. C103#12951direct (N × H)
179. #360C4×C103semidirect
203. M32C2×C4×C103semidirect
210. #106C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C4×#135×C1032
C103×#21552
C103×#21482
C103×#21452
C103×#19452
C103×#13842
C103×#13762
#12951103