Finite Group Databasebeta

← C103×#11978 #39917253

Subgroups — C103×#11978 #39917253

Order 26368.

312 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3168C211yesmaximal, characteristic
2C2×C4⋊C16×C103C211yesmaximal, characteristic, complemented
3C103×#1568C211yesmaximal, characteristic, complemented
4C103×#1363C212yesmaximal, complemented
5C103×#1360C212yesmaximal, complemented
6#529×C103—21no—
7C22×C16×C103—21no—
8#499×C103C2211yescharacteristic
9#495×C103C2211yescharacteristic
10#488×C103—21no—
11#467×C103C411yescharacteristic
12#466×C103C411yescharacteristic
13#465×C103—21no—
14C4×Q16×C103C411yescharacteristic
15C4×SD16×C103—21no—
16C4×D8×C103C411yescharacteristic
17#432×C103—21no—
18C2×C4×C8×C103C2211yescharacteristic
19C4⋊C16×C103—21no—
20C4⋊C16×C103C2212yes—
21#335×C103—21no—
22#334×C103C2212yes—
23C2×Q16×C103C2×C411yescharacteristic
24C2×SD16×C103—21no—
25C2×D8×C103C2×C411yescharacteristic
26C22×C8×C103C2×C411yescharacteristic
27C22×C8×C103D411yescharacteristic
28#126×C103—41no—
29#125×C103—21no—
30#124×C103—21no—
31#123×C103—41no—
32C22⋊Q8×C103—21no—
33#121×C103—21no—
34C4×Q8×C103—21no—
35C4×D4×C103—21no—
36C4×D4×C103—41no—
37#117×C103—41no—
38C2×C42×C103D411yescharacteristic
39C2×C16×C103—22no—
40C2×C16×C103—42no—
41#107×C103C2×C411yescharacteristic
42#107×C103C2×C411yescharacteristic
43#106×C103—21no—
44C4⋊C8×C103—22no—
45#103×C103—21no—
46#103×C103—21no—
47#102×C103—21no—
48#102×C103—21no—
49C22⋊C8×C103—41no—
50#97×C103—41no—
51C4×C8×C103C2×C411yescharacteristic
52C4×C8×C103D411yescharacteristic
53C4×C8×C103D411yescharacteristic
54C4×C8×C103C2311yescharacteristic
55C2×Q8×C103—21no—
56C2×D4×C103—21no—
57C2×D4×C103—41no—
58C22×C4×C103—41no—
59C22×C4×C103C22⋊C411yescharacteristic
60C22×C4×C103D811yescharacteristic
61C22×C4×C103SD1611yescharacteristic
62Q16×C103—41no—
63SD16×C103—41no—
64SD16×C103—41no—
65D8×C103—41no—
66C2×C8×C103—21no—
67C2×C8×C103—21no—
68C2×C8×C103—41no—
69C2×C8×C103—42no—
70C2×C8×C103C22⋊C411yescharacteristic
71C2×C8×C103C22⋊C411yescharacteristic
72C2×C8×C103C22×C411yescharacteristic
73C2×C8×C103C2×D411yescharacteristic
74C4⋊C4×C103—21no—
75C4⋊C4×C103—21no—
76C4⋊C4×C103—41no—
77C4⋊C4×C103—41no—
78C4⋊C4×C103—41no—
79C4⋊C4×C103—41no—
80C22⋊C4×C103—41no—
81C22⋊C4×C103—41no—
82C22⋊C4×C103—41no—
83C22⋊C4×C103—41no—
84C22⋊C4×C103—41no—
85C42×C103—41no—
86C42×C103C22⋊C411yescharacteristic
87C42×C103D811yescharacteristic
88C42×C103SD1611yescharacteristic
89C42×C103C2×D411yescharacteristic
90C16×C103—42no—
91C23×C103—41no—
92C23×C103#10211yescharacteristic
93Q8×C103—41no—
94Q8×C103—41no—
95D4×C103—41no—
96D4×C103—41no—
97D4×C103—82no—
98C2×C4×C103—22no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—41no—
102C2×C4×C103—41no—
103C2×C4×C103—41no—
104C2×C4×C103—41no—
105C2×C4×C103—82no—
106C2×C4×C103#10211yescharacteristic
107C2×C4×C103#10211yescharacteristic
108C2×C4×C103#10211yescharacteristic
109C2×C4×C103C2×C22⋊C411yescharacteristic
110C2×C4×C103C2×D811yescharacteristic
111C2×C4×C103C2×SD1611yescharacteristic
112C8×C103—21no—
113C8×C103—21no—
114C8×C103—21no—
115C8×C103—82no—
116C8×C103AGL(1,ℤ/8)11yescharacteristic
117C8×C103#13711yescharacteristic
118C22×C103—21no—
119C22×C103—21no—
120C22×C103—81no—
121C22×C103—81no—
122C22×C103—81no—
123C22×C103#35912yes—
124C22×C103C2×#10211yescharacteristic
125C4×C103—21no—
126C4×C103—21no—
127C4×C103—21no—
128C4×C103—21no—
129C4×C103—21no—
130C4×C103—81no—
131C4×C103—81no—
132C4×C103—81no—
133C4×C103#41311yescharacteristic
134C4×C103#41711yescharacteristic
135#11978C10311yesmaximal, characteristic, direct product factor, Sylow
136C2×C103—22no—
137C2×C103—161no—
138C2×C103#154711yescharacteristic
139C2×C103C2×#35911yescharacteristic
140C2×C103#214511yescharacteristic
141#3168C2×C10311yescharacteristic
142C2×C4⋊C16C2×C10311yescharacteristic, complemented
143#1568C2×C10311yescharacteristic, complemented
144#1363C2×C10312yescomplemented
145#1360C2×C10312yescomplemented
146C103#1197811yescharacteristic, direct product factor, Sylow
147#529—21no—
148C22×C16—21no—
149#499C22×C10311yescharacteristic
150#495C22×C10311yescharacteristic
151#488—21no—
152#467C4×C10311yescharacteristic
153#466C4×C10311yescharacteristic
154#465—21no—
155C4×Q16C4×C10311yescharacteristic
156C4×SD16—21no—
157C4×D8C4×C10311yescharacteristic
158#432—21no—
159C2×C4×C8C22×C10311yescharacteristic
160C4⋊C16—21no—
161C4⋊C16C22×C10312yes—
162#335—21no—
163#334C22×C10312yes—
164C2×Q16C2×C4×C10311yescharacteristic
165C2×SD16—21no—
166C2×D8C2×C4×C10311yescharacteristic
167C22×C8C2×C4×C10311yescharacteristic
168C22×C8D4×C10311yescharacteristic
169#126—41no—
170#125—21no—
171#124—21no—
172#123—41no—
173C22⋊Q8—21no—
174#121—21no—
175C4×Q8—21no—
176C4×D4—21no—
177C4×D4—41no—
178#117—41no—
179C2×C42D4×C10311yescharacteristic
180C2×C16—22no—
181C2×C16—42no—
182#107C2×C4×C10311yescharacteristic
183#107C2×C4×C10311yescharacteristic
184#106—21no—
185C4⋊C8—22no—
186#103—21no—
187#103—21no—
188#102—21no—
189#102—21no—
190C22⋊C8—41no—
191#97—41no—
192C4×C8C2×C4×C10311yescharacteristic
193C4×C8D4×C10311yescharacteristic
194C4×C8D4×C10311yescharacteristic
195C4×C8C23×C10311yescharacteristic
196C2×Q8—21no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—41no—
200C22×C4C22⋊C4×C10311yescharacteristic
201C22×C4D8×C10311yescharacteristic
202C22×C4SD16×C10311yescharacteristic
203Q16—41no—
204SD16—41no—
205SD16—41no—
206D8—41no—
207C2×C8—21no—
208C2×C8—21no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8C22⋊C4×C10311yescharacteristic
212C2×C8C22⋊C4×C10311yescharacteristic
213C2×C8C22×C4×C10311yescharacteristic
214C2×C8C2×D4×C10311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C42—41no—
227C42C22⋊C4×C10311yescharacteristic
228C42D8×C10311yescharacteristic
229C42SD16×C10311yescharacteristic
230C42C2×D4×C10311yescharacteristic
231C16—42no—
232C23—41no—
233C23#102×C10311yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—82no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—82no—
247C2×C4#102×C10311yescharacteristic
248C2×C4#102×C10311yescharacteristic
249C2×C4#102×C10311yescharacteristic
250C2×C4C2×C22⋊C4×C10311yescharacteristic
251C2×C4C2×D8×C10311yescharacteristic
252C2×C4C2×SD16×C10311yescharacteristic
253C8—21no—
254C8—21no—
255C8—21no—
256C8—82no—
257C8AGL(1,ℤ/8)×C10311yescharacteristic
258C8#137×C10311yescharacteristic
259C22—21no—
260C22—21no—
261C22—81no—
262C22—81no—
263C22—81no—
264C22#359×C10312yes—
265C22C2×#102×C10311yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—81no—
272C4—81no—
273C4—81no—
274C4#413×C10311yescharacteristic
275C4#417×C10311yescharacteristic
276C2—22no—
277C2—161no—
278C2C103×#154711yescharacteristic
279C2C2×#359×C10311yescharacteristic
280C2C103×#214511yescharacteristic
subgroupG/H
center, socleC22×C103C2×#102
commutatorC2×C8C22×C4×C103
Frattini, cosocleC4×C8C23×C103
prime radical#466×C103C4
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C16×C103C2semidirect
3. C103×#1568C2semidirect
4. C103×#1363C2semidirect
5. C103×#1360C2semidirect
135. #11978C103direct (N × H)
142. C2×C4⋊C16C2×C103semidirect
143. #1568C2×C103semidirect
144. #1363C2×C103semidirect
145. #1360C2×C103semidirect
146. C103#11978direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31682
C2×C4⋊C16×C1032
C103×#15682
C103×#13632
C103×#13602
#11978103