Finite Group Databasebeta

← C103×#13146 #39918421

Subgroups — C103×#13146 #39918421

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×#2148C211yesmaximal, characteristic
2C2×#359×C103C211yesmaximal, characteristic
3C103×#2108C211yesmaximal, characteristic, complemented
4C103×#1976C211yesmaximal, characteristic
5C103×#1953C211yesmaximal, characteristic, complemented
6C103×#1389C211yesmaximal, characteristic, complemented
7C103×#1382C211yesmaximal, characteristic, complemented
8C2×#135×C103C2211yescharacteristic
9C2×M32×C103C2211yescharacteristic
10C22×C16×C103C2211yescharacteristic
11#430×C103—21no—
12C2×#108×C103C2211yescharacteristic
13C2×#108×C103C2211yescharacteristic
14#427×C103C2211yescharacteristic
15#421×C103—21no—
16#410×C103—21no—
17#405×C103C2211yescharacteristic
18#362×C103C412yescomplemented
19#361×C103C412yescomplemented
20#359×C103—21no—
21#359×C103—21no—
22#346×C103—21no—
23C4×C16×C103—21no—
24#344×C103—21no—
25C2×#41×C103—21no—
26#135×C103—21no—
27#135×C103—21no—
28#135×C103—21no—
29#135×C103—21no—
30C2×Q16×C103C2×C411yescharacteristic
31C2×SD16×C103—21no—
32C2×D8×C103C2×C411yescharacteristic
33C2×M16×C103—21no—
34C2×M16×C103—21no—
35C2×M16×C103D411yescharacteristic
36C22×C8×C103C2311yescharacteristic
37#117×C103—21no—
38#117×C103D411yescharacteristic
39M32×C103—21no—
40M32×C103C2×C412yes—
41C2×C16×C103—21no—
42C2×C16×C103—21no—
43C2×C16×C103—21no—
44C2×C16×C103D411yescharacteristic
45C2×C16×C103D411yescharacteristic
46#108×C103—21no—
47#108×C103—21no—
48#108×C103—21no—
49#108×C103—42no—
50#108×C103C2×C412yes—
51#107×C103—21no—
52#106×C103—21no—
53#104×C103—42no—
54#99×C103—42no—
55#97×C103—21no—
56C4×C8×C103—21no—
57#41×C103—41no—
58#41×C103—41no—
59#41×C103—41no—
60#41×C103—41no—
61C2×Q8×C103—21no—
62C2×D4×C103—21no—
63C2×D4×C103—41no—
64C22×C4×C103—41no—
65C22×C4×C103C2×D411yescharacteristic
66Q16×C103—21no—
67Q16×C103—21no—
68SD16×C103—41no—
69SD16×C103—41no—
70D8×C103—21no—
71D8×C103—21no—
72M16×C103—21no—
73M16×C103—22no—
74M16×C103—41no—
75M16×C103—41no—
76M16×C103—41no—
77M16×C103D812yes—
78C2×C8×C103—21no—
79C2×C8×C103—41no—
80C2×C8×C103—41no—
81C2×C8×C103C22×C411yescharacteristic
82C2×C8×C103C2×D411yescharacteristic
83C2×C8×C103#4111yescharacteristic
84C2×C8×C103#4111yescharacteristic
85C2×C8×C103#4111yescharacteristic
86C2×C8×C103#4111yescharacteristic
87C4⋊C4×C103—21no—
88C4⋊C4×C103—41no—
89C22⋊C4×C103—41no—
90C22⋊C4×C103SD1612yes—
91C42×C103—21no—
92C42×C103—41no—
93C16×C103—22no—
94C16×C103—21no—
95C16×C103—21no—
96C23×C103—41no—
97C23×C103C2×SD1611yescharacteristic
98Q8×C103—41no—
99Q8×C103—41no—
100D4×C103—41no—
101D4×C103—41no—
102D4×C103—81no—
103D4×C103—81no—
104C2×C4×C103—22no—
105C2×C4×C103—41no—
106C2×C4×C103—81no—
107C2×C4×C103—81no—
108C2×C4×C103—81no—
109C2×C4×C103C4×D411yescharacteristic
110C2×C4×C103#12111yescharacteristic
111C2×C4×C103#12411yescharacteristic
112C2×C4×C103C2×D811yescharacteristic
113C2×C4×C103#13511yescharacteristic
114C2×C4×C103#13511yescharacteristic
115C8×C103—22no—
116C8×C103—42no—
117C8×C103—81no—
118C8×C103#11711yescharacteristic
119C8×C103C4×D411yescharacteristic
120C8×C103#12311yescharacteristic
121C8×C103#12611yescharacteristic
122C22×C103—41no—
123C22×C103—81no—
124C22×C103—161no—
125C22×C103C4×SD1611yescharacteristic
126C22×C103#46511yescharacteristic
127C22×C103#48611yescharacteristic
128C4×C103—42no—
129C4×C103—81no—
130C4×C103—161no—
131C4×C103#38811yescharacteristic
132C4×C103C4×D811yescharacteristic
133C4×C103#46611yescharacteristic
134C4×C103#48811yescharacteristic
135#13146C10311yesmaximal, characteristic, direct product factor, Sylow
136C2×C103—21no—
137C2×C103—21no—
138C2×C103—21no—
139C2×C103—161no—
140C2×C103#193411yescharacteristic
141#2148C2×C10311yescharacteristic
142C2×#359C2×C10311yescharacteristic
143#2108C2×C10311yescharacteristic, complemented
144#1976C2×C10311yescharacteristic
145#1953C2×C10311yescharacteristic, complemented
146#1389C2×C10311yescharacteristic, complemented
147#1382C2×C10311yescharacteristic, complemented
148C103#1314611yescharacteristic, direct product factor, Sylow
149C2×#135C22×C10311yescharacteristic
150C2×M32C22×C10311yescharacteristic
151C22×C16C22×C10311yescharacteristic
152#430—21no—
153C2×#108C22×C10311yescharacteristic
154C2×#108C22×C10311yescharacteristic
155#427C22×C10311yescharacteristic
156#421—21no—
157#410—21no—
158#405C22×C10311yescharacteristic
159#362C4×C10312yescomplemented
160#361C4×C10312yescomplemented
161#359—21no—
162#359—21no—
163#346—21no—
164C4×C16—21no—
165#344—21no—
166C2×#41—21no—
167#135—21no—
168#135—21no—
169#135—21no—
170#135—21no—
171C2×Q16C2×C4×C10311yescharacteristic
172C2×SD16—21no—
173C2×D8C2×C4×C10311yescharacteristic
174C2×M16—21no—
175C2×M16—21no—
176C2×M16D4×C10311yescharacteristic
177C22×C8C23×C10311yescharacteristic
178#117—21no—
179#117D4×C10311yescharacteristic
180M32—21no—
181M32C2×C4×C10312yes—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—21no—
185C2×C16D4×C10311yescharacteristic
186C2×C16D4×C10311yescharacteristic
187#108—21no—
188#108—21no—
189#108—21no—
190#108—42no—
191#108C2×C4×C10312yes—
192#107—21no—
193#106—21no—
194#104—42no—
195#99—42no—
196#97—21no—
197C4×C8—21no—
198#41—41no—
199#41—41no—
200#41—41no—
201#41—41no—
202C2×Q8—21no—
203C2×D4—21no—
204C2×D4—41no—
205C22×C4—41no—
206C22×C4C2×D4×C10311yescharacteristic
207Q16—21no—
208Q16—21no—
209SD16—41no—
210SD16—41no—
211D8—21no—
212D8—21no—
213M16—21no—
214M16—22no—
215M16—41no—
216M16—41no—
217M16—41no—
218M16D8×C10312yes—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C22×C4×C10311yescharacteristic
223C2×C8C2×D4×C10311yescharacteristic
224C2×C8#41×C10311yescharacteristic
225C2×C8#41×C10311yescharacteristic
226C2×C8#41×C10311yescharacteristic
227C2×C8#41×C10311yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4SD16×C10312yes—
232C42—21no—
233C42—41no—
234C16—22no—
235C16—21no—
236C16—21no—
237C23—41no—
238C23C2×SD16×C10311yescharacteristic
239Q8—41no—
240Q8—41no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4C4×D4×C10311yescharacteristic
251C2×C4#121×C10311yescharacteristic
252C2×C4#124×C10311yescharacteristic
253C2×C4C2×D8×C10311yescharacteristic
254C2×C4#135×C10311yescharacteristic
255C2×C4#135×C10311yescharacteristic
256C8—22no—
257C8—42no—
258C8—81no—
259C8#117×C10311yescharacteristic
260C8C4×D4×C10311yescharacteristic
261C8#123×C10311yescharacteristic
262C8#126×C10311yescharacteristic
263C22—41no—
264C22—81no—
265C22—161no—
266C22C4×SD16×C10311yescharacteristic
267C22#465×C10311yescharacteristic
268C22#486×C10311yescharacteristic
269C4—42no—
270C4—81no—
271C4—161no—
272C4#388×C10311yescharacteristic
273C4C4×D8×C10311yescharacteristic
274C4#466×C10311yescharacteristic
275C4#488×C10311yescharacteristic
276C2—21no—
277C2—21no—
278C2—21no—
279C2—161no—
280C2C103×#193411yescharacteristic
subgroupG/H
centerC4×C103#466
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
socleC2×C103#1934
prime radicalC2×#135×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C4×C103 ◁ #405×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2108C2semidirect
5. C103×#1953C2semidirect
6. C103×#1389C2semidirect
7. C103×#1382C2semidirect
18. #362×C103C4semidirect
19. #361×C103C4semidirect
135. #13146C103direct (N × H)
143. #2108C2×C103semidirect
145. #1953C2×C103semidirect
146. #1389C2×C103semidirect
147. #1382C2×C103semidirect
148. C103#13146direct (N × H)
159. #362C4×C103semidirect
160. #361C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#21482
C2×#359×C1032
C103×#21082
C103×#19762
C103×#19532
C103×#13892
C103×#13822
#13146103