Finite Group Databasebeta

← C103×#11682 #39916957

Subgroups — C103×#11682 #39916957

Order 26368.

322 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3168C211yesmaximal, characteristic
2C4×M32×C103C211yesmaximal, characteristic, complemented
3C103×#1568C211yesmaximal, characteristic, complemented
4C103×#1334C212yesmaximal, complemented
5C103×#1333C212yesmaximal, complemented
6#529×C103—21no—
7C2×M32×C103—21no—
8#499×C103C411yescharacteristic
9#495×C103C411yescharacteristic
10#488×C103—21no—
11#467×C103C411yescharacteristic
12#466×C103C411yescharacteristic
13#465×C103—21no—
14C4×Q16×C103C2211yescharacteristic
15C4×SD16×C103—21no—
16C4×D8×C103C2211yescharacteristic
17#432×C103—21no—
18C2×C4×C8×C103C2211yescharacteristic
19#346×C103C2212yes—
20C4×C16×C103—21no—
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
39M32×C103—24no—
40C2×C16×C103—22no—
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—22no—
63SD16×C103—42no—
64D8×C103—22no—
65C2×C8×C103—22no—
66C2×C8×C103—22no—
67C2×C8×C103—42no—
68C2×C8×C103C22⋊C411yescharacteristic
69C2×C8×C103C22⋊C411yescharacteristic
70C2×C8×C103C22×C411yescharacteristic
71C2×C8×C103C2×D411yescharacteristic
72C4⋊C4×C103—21no—
73C4⋊C4×C103—21no—
74C4⋊C4×C103—41no—
75C4⋊C4×C103—41no—
76C4⋊C4×C103—41no—
77C4⋊C4×C103—41no—
78C22⋊C4×C103—41no—
79C22⋊C4×C103—41no—
80C22⋊C4×C103—41no—
81C22⋊C4×C103—41no—
82C22⋊C4×C103—41no—
83C42×C103—41no—
84C42×C103C22⋊C411yescharacteristic
85C42×C103D811yescharacteristic
86C42×C103SD1611yescharacteristic
87C42×C103C2×D411yescharacteristic
88C16×C103—24no—
89C23×C103—41no—
90C23×C103#10211yescharacteristic
91Q8×C103—41no—
92Q8×C103—41no—
93D4×C103—41no—
94D4×C103—41no—
95D4×C103—82no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—41no—
99C2×C4×C103—41no—
100C2×C4×C103—41no—
101C2×C4×C103—41no—
102C2×C4×C103—41no—
103C2×C4×C103—82no—
104C2×C4×C103#10211yescharacteristic
105C2×C4×C103#10211yescharacteristic
106C2×C4×C103#10211yescharacteristic
107C2×C4×C103C2×C22⋊C411yescharacteristic
108C2×C4×C103C2×D811yescharacteristic
109C2×C4×C103C2×SD1611yescharacteristic
110C8×C103—21no—
111C8×C103—21no—
112C8×C103—82no—
113C8×C103#10412yes—
114C8×C103#13112yes—
115C22×C103—21no—
116C22×C103—21no—
117C22×C103—21no—
118C22×C103—81no—
119C22×C103—81no—
120C22×C103—81no—
121C22×C103C2×#10211yescharacteristic
122C4×C103—21no—
123C4×C103—21no—
124C4×C103—21no—
125C4×C103—21no—
126C4×C103—21no—
127C4×C103—81no—
128C4×C103—81no—
129C4×C103—81no—
130C4×C103#40811yescharacteristic
131C4×C103C2×#10411yescharacteristic
132#11682C10311yesmaximal, characteristic, direct product factor, Sylow
133C2×C103—41no—
134C2×C103—161no—
135C2×C103#149211yescharacteristic
136C2×C103#214511yescharacteristic
137C2×C103#214811yescharacteristic
138#3168C2×C10311yescharacteristic
139C4×M32C2×C10311yescharacteristic, complemented
140#1568C2×C10311yescharacteristic, complemented
141#1334C2×C10312yescomplemented
142#1333C2×C10312yescomplemented
143C103#1168211yescharacteristic, direct product factor, Sylow
144#529—21no—
145C2×M32—21no—
146#499C4×C10311yescharacteristic
147#495C4×C10311yescharacteristic
148#488—21no—
149#467C4×C10311yescharacteristic
150#466C4×C10311yescharacteristic
151#465—21no—
152C4×Q16C22×C10311yescharacteristic
153C4×SD16—21no—
154C4×D8C22×C10311yescharacteristic
155#432—21no—
156C2×C4×C8C22×C10311yescharacteristic
157#346C22×C10312yes—
158C4×C16—21no—
159#335—21no—
160#334C22×C10312yes—
161C2×Q16C2×C4×C10311yescharacteristic
162C2×SD16—21no—
163C2×D8C2×C4×C10311yescharacteristic
164C22×C8C2×C4×C10311yescharacteristic
165C22×C8D4×C10311yescharacteristic
166#126—41no—
167#125—21no—
168#124—21no—
169#123—41no—
170C22⋊Q8—21no—
171#121—21no—
172C4×Q8—21no—
173C4×D4—21no—
174C4×D4—41no—
175#117—41no—
176C2×C42D4×C10311yescharacteristic
177M32—24no—
178C2×C16—22no—
179#107C2×C4×C10311yescharacteristic
180#107C2×C4×C10311yescharacteristic
181#106—21no—
182C4⋊C8—22no—
183#103—21no—
184#103—21no—
185#102—21no—
186#102—21no—
187C22⋊C8—41no—
188#97—41no—
189C4×C8C2×C4×C10311yescharacteristic
190C4×C8D4×C10311yescharacteristic
191C4×C8D4×C10311yescharacteristic
192C4×C8C23×C10311yescharacteristic
193C2×Q8—21no—
194C2×D4—21no—
195C2×D4—41no—
196C22×C4—41no—
197C22×C4C22⋊C4×C10311yescharacteristic
198C22×C4D8×C10311yescharacteristic
199C22×C4SD16×C10311yescharacteristic
200Q16—22no—
201SD16—42no—
202D8—22no—
203C2×C8—22no—
204C2×C8—22no—
205C2×C8—42no—
206C2×C8C22⋊C4×C10311yescharacteristic
207C2×C8C22⋊C4×C10311yescharacteristic
208C2×C8C22×C4×C10311yescharacteristic
209C2×C8C2×D4×C10311yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C42—41no—
222C42C22⋊C4×C10311yescharacteristic
223C42D8×C10311yescharacteristic
224C42SD16×C10311yescharacteristic
225C42C2×D4×C10311yescharacteristic
226C16—24no—
227C23—41no—
228C23#102×C10311yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—41no—
232D4—41no—
233D4—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—82no—
242C2×C4#102×C10311yescharacteristic
243C2×C4#102×C10311yescharacteristic
244C2×C4#102×C10311yescharacteristic
245C2×C4C2×C22⋊C4×C10311yescharacteristic
246C2×C4C2×D8×C10311yescharacteristic
247C2×C4C2×SD16×C10311yescharacteristic
248C8—21no—
249C8—21no—
250C8—82no—
251C8#104×C10312yes—
252C8#131×C10312yes—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—81no—
257C22—81no—
258C22—81no—
259C22C2×#102×C10311yescharacteristic
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—81no—
266C4—81no—
267C4—81no—
268C4#408×C10311yescharacteristic
269C4C2×#104×C10311yescharacteristic
270C2—41no—
271C2—161no—
272C2C103×#149211yescharacteristic
273C2C103×#214511yescharacteristic
274C2C103×#214811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#102
commutatorC2×C8C22×C4×C103
Frattini, cosocleC4×C8C23×C103
prime radical#466×C103C4
LCSG ▷ C2×C8 ▷ 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. C4×M32×C103C2semidirect
3. C103×#1568C2semidirect
4. C103×#1334C2semidirect
5. C103×#1333C2semidirect
132. #11682C103direct (N × H)
139. C4×M32C2×C103semidirect
140. #1568C2×C103semidirect
141. #1334C2×C103semidirect
142. #1333C2×C103semidirect
143. C103#11682direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31682
C4×M32×C1032
C103×#15682
C103×#13342
C103×#13332
#11682103