Finite Group Databasebeta

← C103×#8596 #39913871

Subgroups — C103×#8596 #39913871

Order 26368.

598 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C8×C103C211yesmaximal, characteristic
2C103×#1797C212yesmaximal
3C2×#335×C103C212yesmaximal, complemented
4C103×#1277C212yesmaximal, complemented
5C23×C8×C103C411yescharacteristic
6C23×C8×C103C411yescharacteristic
7C22×C42×C103C2211yescharacteristic
8C2×C4⋊C8×C103C2214yes—
9C2×C22⋊C8×C103—22no—
10C2×C4×C8×C103—24no—
11C2×C4×C8×C103C411yescharacteristic
12C2×C4×C8×C103C411yescharacteristic
13C2×C4×C8×C103C2211yescharacteristic
14C2×C4×C8×C103C2211yescharacteristic
15#336×C103—22no—
16#335×C103—24no—
17C23×C4×C103C2×C411yescharacteristic
18C23×C4×C103D411yescharacteristic
19C23×C4×C103Q811yescharacteristic
20C22×C8×C103—22no—
21C22×C8×C103—22no—
22C22×C8×C103—22no—
23C22×C8×C103—22no—
24C22×C8×C103—22no—
25C22×C8×C103—24no—
26C22×C8×C103C814yescomplemented
27C22×C8×C103C2×C411yescharacteristic
28C22×C8×C103C2×C411yescharacteristic
29C22×C8×C103C2×C411yescharacteristic
30C22×C8×C103C2×C411yescharacteristic
31C2×C42×C103—22no—
32C2×C42×C103—22no—
33C2×C42×C103C2×C411yescharacteristic
34C2×C42×C103D411yescharacteristic
35C2×C42×C103Q811yescharacteristic
36C2×C42×C103C2311yescharacteristic
37C4⋊C8×C103—24no—
38C4⋊C8×C103—24no—
39C22⋊C8×C103—44no—
40C4×C8×C103—22no—
41C4×C8×C103—22no—
42C4×C8×C103—22no—
43C4×C8×C103D414yes—
44C24×C103C4⋊C411yescharacteristic
45C22×C4×C103—22no—
46C22×C4×C103—22no—
47C22×C4×C103—21no—
48C22×C4×C103—21no—
49C22×C4×C103—22no—
50C22×C4×C103—22no—
51C22×C4×C103—21no—
52C22×C4×C103—21no—
53C22×C4×C103—22no—
54C22×C4×C103C4⋊C411yescharacteristic
55C22×C4×C103C4⋊C411yescharacteristic
56C22×C4×C103C4⋊C411yescharacteristic
57C22×C4×C103C2×C812yes—
58C22×C4×C103M1612yes—
59C22×C4×C103D812yes—
60C22×C4×C103Q1612yes—
61C22×C4×C103C22×C411yescharacteristic
62C22×C4×C103C2×D411yescharacteristic
63C22×C4×C103C2×Q811yescharacteristic
64C2×C8×C103—28no—
65C2×C8×C103—21no—
66C2×C8×C103—21no—
67C2×C8×C103—21no—
68C2×C8×C103—21no—
69C2×C8×C103—21no—
70C2×C8×C103—21no—
71C2×C8×C103—28no—
72C2×C8×C103—44no—
73C2×C8×C103—44no—
74C2×C8×C103—44no—
75C2×C8×C103C22⋊C412yes—
76C2×C8×C103C22⋊C412yes—
77C2×C8×C103C2×C812yes—
78C2×C8×C103C2×C812yes—
79C2×C8×C103M1612yes—
80C2×C8×C103M1612yes—
81C42×C103—21no—
82C42×C103—21no—
83C42×C103—22no—
84C42×C103—22no—
85C42×C103C2×D412yes—
86C42×C103#4112yes—
87C23×C103—21no—
88C23×C103—21no—
89C23×C103—21no—
90C23×C103—21no—
91C23×C103C4⋊C812yes—
92C23×C103#10712yes—
93C23×C103#10812yes—
94C23×C103C2×C4⋊C411yescharacteristic
95C2×C4×C103—28no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—22no—
105C2×C4×C103—22no—
106C2×C4×C103—22no—
107C2×C4×C103—22no—
108C2×C4×C103—24no—
109C2×C4×C103—24no—
110C2×C4×C103C4⋊C812yes—
111C2×C4×C103#10712yes—
112C2×C4×C103#10812yes—
113C2×C4×C103C2×C22⋊C411yescharacteristic
114C2×C4×C103#11711yescharacteristic
115C2×C4×C103#12112yes—
116C2×C4×C103C22⋊Q812yes—
117C2×C4×C103C22×C811yescharacteristic
118C2×C4×C103C2×M1611yescharacteristic
119C2×C4×C103C2×M1611yescharacteristic
120C2×C4×C103C2×M1611yescharacteristic
121C2×C4×C103C2×D811yescharacteristic
122C2×C4×C103C2×Q1611yescharacteristic
123C2×C4×C103#13512yes—
124C8×C103—22no—
125C8×C103—22no—
126C8×C103—22no—
127C8×C103—84no—
128C8×C103C22⋊C814yescomplemented
129C22×C103—22no—
130C22×C103—22no—
131C22×C103—22no—
132C22×C103—22no—
133C22×C103—22no—
134C22×C103—22no—
135C22×C103#33514yescomplemented
136C22×C103#38011yescharacteristic
137C22×C103C2×C4⋊C811yescharacteristic
138C22×C103#42311yescharacteristic
139C22×C103C2×#10711yescharacteristic
140C22×C103#42711yescharacteristic
141C22×C103C2×#10811yescharacteristic
142C22×C103C2×#10811yescharacteristic
143C4×C103—22no—
144C4×C103—22no—
145C4×C103—22no—
146C4×C103—22no—
147C4×C103C2×C22⋊C811yescharacteristic
148C4×C103#40711yescharacteristic
149C4×C103#43111yescharacteristic
150C4×C103#43211yescharacteristic
151C4×C103#46612yes—
152C4×C103#46712yes—
153#8596C10311yesmaximal, characteristic, direct product factor, Sylow
154C2×C103—24no—
155C2×C103C2×#33511yescharacteristic
156C2×C103#156411yescharacteristic
157C2×C103#156711yescharacteristic
158C2×C103#156811yescharacteristic
159C2×C103#179711yescharacteristic
160C2×C103#180811yescharacteristic
161C2×C103#181011yescharacteristic
162C22×C4×C8C2×C10311yescharacteristic
163#1797C2×C10312yes—
164C2×#335C2×C10312yescomplemented
165#1277C2×C10312yescomplemented
166C103#859611yescharacteristic, direct product factor, Sylow
167C23×C8C4×C10311yescharacteristic
168C23×C8C4×C10311yescharacteristic
169C22×C42C22×C10311yescharacteristic
170C2×C4⋊C8C22×C10314yes—
171C2×C22⋊C8—22no—
172C2×C4×C8—24no—
173C2×C4×C8C4×C10311yescharacteristic
174C2×C4×C8C4×C10311yescharacteristic
175C2×C4×C8C22×C10311yescharacteristic
176C2×C4×C8C22×C10311yescharacteristic
177#336—22no—
178#335—24no—
179C23×C4C2×C4×C10311yescharacteristic
180C23×C4D4×C10311yescharacteristic
181C23×C4Q8×C10311yescharacteristic
182C22×C8—22no—
183C22×C8—22no—
184C22×C8—22no—
185C22×C8—22no—
186C22×C8—22no—
187C22×C8—24no—
188C22×C8C8×C10314yescomplemented
189C22×C8C2×C4×C10311yescharacteristic
190C22×C8C2×C4×C10311yescharacteristic
191C22×C8C2×C4×C10311yescharacteristic
192C22×C8C2×C4×C10311yescharacteristic
193C2×C42—22no—
194C2×C42—22no—
195C2×C42C2×C4×C10311yescharacteristic
196C2×C42D4×C10311yescharacteristic
197C2×C42Q8×C10311yescharacteristic
198C2×C42C23×C10311yescharacteristic
199C4⋊C8—24no—
200C4⋊C8—24no—
201C22⋊C8—44no—
202C4×C8—22no—
203C4×C8—22no—
204C4×C8—22no—
205C4×C8D4×C10314yes—
206C24C4⋊C4×C10311yescharacteristic
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4C4⋊C4×C10311yescharacteristic
217C22×C4C4⋊C4×C10311yescharacteristic
218C22×C4C4⋊C4×C10311yescharacteristic
219C22×C4C2×C8×C10312yes—
220C22×C4M16×C10312yes—
221C22×C4D8×C10312yes—
222C22×C4Q16×C10312yes—
223C22×C4C22×C4×C10311yescharacteristic
224C22×C4C2×D4×C10311yescharacteristic
225C22×C4C2×Q8×C10311yescharacteristic
226C2×C8—28no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—28no—
234C2×C8—44no—
235C2×C8—44no—
236C2×C8—44no—
237C2×C8C22⋊C4×C10312yes—
238C2×C8C22⋊C4×C10312yes—
239C2×C8C2×C8×C10312yes—
240C2×C8C2×C8×C10312yes—
241C2×C8M16×C10312yes—
242C2×C8M16×C10312yes—
243C42—21no—
244C42—21no—
245C42—22no—
246C42—22no—
247C42C2×D4×C10312yes—
248C42#41×C10312yes—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23C4⋊C8×C10312yes—
254C23#107×C10312yes—
255C23#108×C10312yes—
256C23C2×C4⋊C4×C10311yescharacteristic
257C2×C4—28no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4C4⋊C8×C10312yes—
273C2×C4#107×C10312yes—
274C2×C4#108×C10312yes—
275C2×C4C2×C22⋊C4×C10311yescharacteristic
276C2×C4#117×C10311yescharacteristic
277C2×C4#121×C10312yes—
278C2×C4C22⋊Q8×C10312yes—
279C2×C4C22×C8×C10311yescharacteristic
280C2×C4C2×M16×C10311yescharacteristic
281C2×C4C2×M16×C10311yescharacteristic
282C2×C4C2×M16×C10311yescharacteristic
283C2×C4C2×D8×C10311yescharacteristic
284C2×C4C2×Q16×C10311yescharacteristic
285C2×C4#135×C10312yes—
286C8—22no—
287C8—22no—
288C8—22no—
289C8—84no—
290C8C22⋊C8×C10314yescomplemented
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22#335×C10314yescomplemented
298C22#380×C10311yescharacteristic
299C22C2×C4⋊C8×C10311yescharacteristic
300C22#423×C10311yescharacteristic
301C22C2×#107×C10311yescharacteristic
302C22#427×C10311yescharacteristic
303C22C2×#108×C10311yescharacteristic
304C22C2×#108×C10311yescharacteristic
305C4—22no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4C2×C22⋊C8×C10311yescharacteristic
310C4#407×C10311yescharacteristic
311C4#431×C10311yescharacteristic
312C4#432×C10311yescharacteristic
313C4#466×C10312yes—
314C4#467×C10312yes—
315C2—24no—
316C2C2×#335×C10311yescharacteristic
317C2C103×#156411yescharacteristic
318C2C103×#156711yescharacteristic
319C2C103×#156811yescharacteristic
320C2C103×#179711yescharacteristic
321C2C103×#180811yescharacteristic
322C2C103×#181011yescharacteristic
subgroupG/H
centerC22×C4×C103C2×D4
commutatorC2×C4C22×C8×C103
Frattini, cosocleC2×C42C23×C103
socleC23×C103C2×C4⋊C4
prime radicalC24×C103C4⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#335×C103C2semidirect
4. C103×#1277C2semidirect
26. C22×C8×C103C8semidirect
128. C8×C103C22⋊C8semidirect
135. C22×C103#335semidirect
153. #8596C103direct (N × H)
164. C2×#335C2×C103semidirect
165. #1277C2×C103semidirect
166. C103#8596direct (N × H)
188. C22×C8C8×C103semidirect
290. C8C22⋊C8×C103semidirect
297. C22#335×C103semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C8×C1032
C103×#17972
C2×#335×C1032
C103×#12772
#8596103