Finite Group Databasebeta

← C103×#20667 #39925942

Subgroups — C103×#20667 #39925942

Order 26368.

1438 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
1C23×M16×C103C211yesmaximal, characteristic
2C2×#430×C103C212yesmaximal, complemented
3C2×#407×C103C212yesmaximal
4C103×#1811C214yesmaximal, complemented
5C103×#1810C214yesmaximal, complemented
6C103×#1738C212yesmaximal, complemented
7C24×C4×C103C2211yescharacteristic
8C22×M16×C103—28no—
9C22×M16×C103C418yes—
10C22×M16×C103C2214yes—
11C22×M16×C103C2211yescharacteristic
12C22×M16×C103C2212yes—
13C22×M16×C103C2211yescharacteristic
14C23×C8×C103C2212yes—
15#430×C103—28no—
16C2×#108×C103C2218yescomplemented
17#407×C103—24no—
18#407×C103C2214yes—
19#407×C103C2214yes—
20C2×C22⋊C8×C103—24no—
21#341×C103C2218yescomplemented
22C25×C103Q811yescharacteristic
23C23×C4×C103—24no—
24C23×C4×C103—24no—
25C23×C4×C103C2×C414yes—
26C23×C4×C103D414yes—
27C23×C4×C103Q811yescharacteristic
28C23×C4×C103Q811yescharacteristic
29C23×C4×C103Q811yescharacteristic
30C23×C4×C103C2311yescharacteristic
31C23×C4×C103C2311yescharacteristic
32C23×C4×C103C2311yescharacteristic
33C2×M16×C103—24no—
34C2×M16×C103—232no—
35C2×M16×C103—24no—
36C2×M16×C103—28no—
37C2×M16×C103—28no—
38C2×M16×C103—28no—
39C2×M16×C103C2×C414yes—
40C2×M16×C103C2×C418yes—
41C2×M16×C103C2×C414yes—
42C2×M16×C103D418yes—
43C2×M16×C103C2318yes—
44C22×C8×C103—28no—
45C22×C8×C103—24no—
46C22×C8×C103C2×C418yes—
47C22×C8×C103C2312yes—
48C22×C8×C103C2312yes—
49#108×C103—216no—
50C22⋊C8×C103—28no—
51C22⋊C8×C103—28no—
52C24×C103—24no—
53C24×C103—44no—
54C24×C103C4⋊C414yes—
55C24×C103C2×Q811yescharacteristic
56C24×C103C2×Q811yescharacteristic
57C24×C103C2×Q811yescharacteristic
58C22×C4×C103—24no—
59C22×C4×C103—28no—
60C22×C4×C103—28no—
61C22×C4×C103—216no—
62C22×C4×C103—24no—
63C22×C4×C103—24no—
64C22×C4×C103—22no—
65C22×C4×C103—22no—
66C22×C4×C103—22no—
67C22×C4×C103—22no—
68C22×C4×C103C4⋊C414yes—
69C22×C4×C103C4⋊C414yes—
70C22×C4×C103C4⋊C414yes—
71C22×C4×C103C22×C412yes—
72C22×C4×C103C22×C412yes—
73C22×C4×C103C22×C412yes—
74C22×C4×C103C2×D412yes—
75C22×C4×C103C2×D412yes—
76C22×C4×C103C2×D414yes—
77C22×C4×C103C2×D412yes—
78C22×C4×C103C2×Q811yescharacteristic
79C22×C4×C103C2×Q811yescharacteristic
80C22×C4×C103C2×Q811yescharacteristic
81C22×C4×C103#4114yes—
82C22×C4×C103C2411yescharacteristic
83M16×C103—28no—
84M16×C103—216no—
85M16×C103—28no—
86M16×C103—28no—
87M16×C103—48no—
88M16×C103C22⋊C4116yes—
89C2×C8×C103—24no—
90C2×C8×C103—216no—
91C2×C8×C103—28no—
92C2×C8×C103—48no—
93C2×C8×C103C22×C414yes—
94C2×C8×C103C22×C414yes—
95C2×C8×C103C2×D418yes—
96C23×C103—22no—
97C23×C103—24no—
98C23×C103—22no—
99C23×C103—28no—
100C23×C103—28no—
101C23×C103—44no—
102C23×C103—42no—
103C23×C103—42no—
104C23×C103—416no—
105C23×C103C2×C4⋊C412yes—
106C23×C103C2×C4⋊C412yes—
107C23×C103C2×C4⋊C412yes—
108C23×C103C22⋊Q814yes—
109C23×C103C22×Q811yescharacteristic
110C2×C4×C103—22no—
111C2×C4×C103—22no—
112C2×C4×C103—28no—
113C2×C4×C103—22no—
114C2×C4×C103—22no—
115C2×C4×C103—22no—
116C2×C4×C103—22no—
117C2×C4×C103—24no—
118C2×C4×C103—24no—
119C2×C4×C103—28no—
120C2×C4×C103—28no—
121C2×C4×C103C2×C22⋊C414yes—
122C2×C4×C103C2×C4⋊C412yes—
123C2×C4×C103C2×C4⋊C412yes—
124C2×C4×C103C2×C4⋊C412yes—
125C2×C4×C103#11714yes—
126C2×C4×C103#12118yes—
127C2×C4×C103C22⋊Q814yes—
128C2×C4×C103C23×C411yescharacteristic
129C2×C4×C103C22×D412yes—
130C2×C4×C103C22×D411yescharacteristic
131C2×C4×C103C2×#4112yes—
132C8×C103—24no—
133C8×C103—48no—
134C8×C103C2×C22⋊C418yes—
135C22×C103—28no—
136C22×C103—22no—
137C22×C103—24no—
138C22×C103—22no—
139C22×C103—22no—
140C22×C103—24no—
141C22×C103—22no—
142C22×C103—44no—
143C22×C103—416no—
144C22×C103—44no—
145C22×C103#38014yes—
146C22×C103#43014yescomplemented
147C22×C103C22×C4⋊C411yescharacteristic
148C22×C103C2×C22⋊Q812yes—
149C4×C103—22no—
150C4×C103—22no—
151C4×C103#38014yes—
152C4×C103C22×C22⋊C411yescharacteristic
153C4×C103C2×#11711yescharacteristic
154C4×C103C2×#12112yes—
155#20667C10311yesmaximal, characteristic, direct product factor, Sylow
156C2×C103—22no—
157C2×C103—24no—
158C2×C103—24no—
159C2×C103—42no—
160C2×C103C2×#38011yescharacteristic
161C2×C103C2×#43012yes—
162C23×M16C2×C10311yescharacteristic
163C2×#430C2×C10312yescomplemented
164C2×#407C2×C10312yes—
165#1811C2×C10314yescomplemented
166#1810C2×C10314yescomplemented
167#1738C2×C10312yescomplemented
168C103#2066711yescharacteristic, direct product factor, Sylow
169C24×C4C22×C10311yescharacteristic
170C22×M16—28no—
171C22×M16C4×C10318yes—
172C22×M16C22×C10314yes—
173C22×M16C22×C10312yes—
174C22×M16C22×C10311yescharacteristic
175C22×M16C22×C10311yescharacteristic
176C23×C8C22×C10312yes—
177#430—28no—
178C2×#108C22×C10318yescomplemented
179#407—24no—
180#407C22×C10314yes—
181#407C22×C10314yes—
182C2×C22⋊C8—24no—
183#341C22×C10318yescomplemented
184C25Q8×C10311yescharacteristic
185C23×C4—24no—
186C23×C4—24no—
187C23×C4C2×C4×C10314yes—
188C23×C4D4×C10314yes—
189C23×C4Q8×C10311yescharacteristic
190C23×C4Q8×C10311yescharacteristic
191C23×C4Q8×C10311yescharacteristic
192C23×C4C23×C10311yescharacteristic
193C23×C4C23×C10311yescharacteristic
194C23×C4C23×C10311yescharacteristic
195C2×M16—24no—
196C2×M16—232no—
197C2×M16—24no—
198C2×M16—28no—
199C2×M16—28no—
200C2×M16—28no—
201C2×M16C2×C4×C10314yes—
202C2×M16C2×C4×C10318yes—
203C2×M16C2×C4×C10314yes—
204C2×M16D4×C10318yes—
205C2×M16C23×C10318yes—
206C22×C8—28no—
207C22×C8—24no—
208C22×C8C2×C4×C10318yes—
209C22×C8C23×C10312yes—
210C22×C8C23×C10312yes—
211#108—216no—
212C22⋊C8—28no—
213C22⋊C8—28no—
214C24—24no—
215C24—44no—
216C24C4⋊C4×C10314yes—
217C24C2×Q8×C10311yescharacteristic
218C24C2×Q8×C10311yescharacteristic
219C24C2×Q8×C10311yescharacteristic
220C22×C4—24no—
221C22×C4—28no—
222C22×C4—28no—
223C22×C4—216no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4C4⋊C4×C10314yes—
231C22×C4C4⋊C4×C10314yes—
232C22×C4C4⋊C4×C10314yes—
233C22×C4C22×C4×C10312yes—
234C22×C4C22×C4×C10312yes—
235C22×C4C22×C4×C10312yes—
236C22×C4C2×D4×C10312yes—
237C22×C4C2×D4×C10312yes—
238C22×C4C2×D4×C10314yes—
239C22×C4C2×D4×C10312yes—
240C22×C4C2×Q8×C10311yescharacteristic
241C22×C4C2×Q8×C10311yescharacteristic
242C22×C4C2×Q8×C10311yescharacteristic
243C22×C4#41×C10314yes—
244C22×C4C24×C10311yescharacteristic
245M16—28no—
246M16—216no—
247M16—28no—
248M16—28no—
249M16—48no—
250M16C22⋊C4×C103116yes—
251C2×C8—24no—
252C2×C8—216no—
253C2×C8—28no—
254C2×C8—48no—
255C2×C8C22×C4×C10314yes—
256C2×C8C22×C4×C10314yes—
257C2×C8C2×D4×C10318yes—
258C23—24no—
259C23—22no—
260C23—28no—
261C23—28no—
262C23—22no—
263C23—44no—
264C23—42no—
265C23—42no—
266C23—416no—
267C23C2×C4⋊C4×C10312yes—
268C23C2×C4⋊C4×C10312yes—
269C23C2×C4⋊C4×C10312yes—
270C23C22⋊Q8×C10314yes—
271C23C22×Q8×C10311yescharacteristic
272C2×C4—28no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—28no—
276C2×C4—28no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4C2×C22⋊C4×C10314yes—
284C2×C4C2×C4⋊C4×C10312yes—
285C2×C4C2×C4⋊C4×C10312yes—
286C2×C4C2×C4⋊C4×C10312yes—
287C2×C4#117×C10314yes—
288C2×C4#121×C10318yes—
289C2×C4C22⋊Q8×C10314yes—
290C2×C4C23×C4×C10311yescharacteristic
291C2×C4C22×D4×C10312yes—
292C2×C4C22×D4×C10311yescharacteristic
293C2×C4C2×#41×C10312yes—
294C8—24no—
295C8—48no—
296C8C2×C22⋊C4×C10318yes—
297C22—28no—
298C22—22no—
299C22—22no—
300C22—24no—
301C22—22no—
302C22—22no—
303C22—24no—
304C22—44no—
305C22—416no—
306C22—44no—
307C22#380×C10314yes—
308C22#430×C10314yescomplemented
309C22C22×C4⋊C4×C10311yescharacteristic
310C22C2×C22⋊Q8×C10312yes—
311C4—22no—
312C4—22no—
313C4#380×C10314yes—
314C4C22×C22⋊C4×C10311yescharacteristic
315C4C2×#117×C10311yescharacteristic
316C4C2×#121×C10312yes—
317C2—24no—
318C2—22no—
319C2—24no—
320C2—42no—
321C2C2×#380×C10311yescharacteristic
322C2C2×#430×C10312yes—
subgroupG/H
centerC2×C4×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC22×C103C22×C4⋊C4
prime radicalC25×C103Q8
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C24×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#430×C103C2semidirect
4. C103×#1811C2semidirect
5. C103×#1810C2semidirect
6. C103×#1738C2semidirect
16. C2×#108×C103C22semidirect
21. #341×C103C22semidirect
146. C22×C103#430semidirect
155. #20667C103direct (N × H)
163. C2×#430C2×C103semidirect
165. #1811C2×C103semidirect
166. #1810C2×C103semidirect
167. #1738C2×C103semidirect
168. C103#20667direct (N × H)
178. C2×#108C22×C103semidirect
183. #341C22×C103semidirect
308. C22#430×C103semidirect

Maximal subgroups

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

subgroupindex
C23×M16×C1032
C2×#430×C1032
C2×#407×C1032
C103×#18112
C103×#18102
C103×#17382
#20667103