Finite Group Databasebeta

← C103×#20673 #39925948

Subgroups — C103×#20673 #39925948

Order 26368.

1292 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C103C211yesmaximal, characteristic
2C2×#430×C103C212yesmaximal, complemented
3C2×#413×C103C212yesmaximal
4C103×#1813C218yesmaximal, complemented
5C2×#338×C103C212yesmaximal, complemented
6C22×#41×C103C2211yescharacteristic
7#568×C103—28no—
8C2×#131×C103C414yes—
9C2×#131×C103C2214yes—
10C22×M16×C103C414yes—
11C22×M16×C103C2214yes—
12C22×M16×C103C2211yescharacteristic
13C22×M16×C103C2211yescharacteristic
14#430×C103—28no—
15C2×#108×C103C2218yescomplemented
16#413×C103—24no—
17#413×C103C2218yes—
18C2×#101×C103—22no—
19C2×#100×C103—22no—
20#338×C103C2218yescomplemented
21C2×#41×C103—24no—
22C2×#41×C103—24no—
23C2×#41×C103C2×C412yes—
24C2×#41×C103D412yes—
25C2×#41×C103Q812yes—
26C2×#41×C103C2312yes—
27C22×Q8×C103D411yescharacteristic
28C22×D4×C103D411yescharacteristic
29C22×D4×C103Q812yes—
30C23×C4×C103C2×C412yes—
31C23×C4×C103C2311yescharacteristic
32#131×C103—216no—
33#131×C103—216no—
34C2×M16×C103—24no—
35C2×M16×C103—216no—
36C2×M16×C103—24no—
37C2×M16×C103—24no—
38C2×M16×C103—24no—
39C2×M16×C103—24no—
40C2×M16×C103—24no—
41C2×M16×C103C2×C412yes—
42C2×M16×C103C2×C418yes—
43C2×M16×C103C2×C412yes—
44C2×M16×C103C2×C412yes—
45C2×M16×C103D418yes—
46C2×M16×C103C2318yes—
47C2×M16×C103C2312yes—
48C22×C8×C103—24no—
49C22×C8×C103C2×C418yes—
50C22×C8×C103C2×C412yes—
51C22×C8×C103C2312yes—
52#108×C103—216no—
53#101×C103—28no—
54#100×C103—28no—
55C24×C103C4⋊C412yes—
56C24×C103C2×Q811yescharacteristic
57#41×C103—24no—
58#41×C103—24no—
59#41×C103—28no—
60#41×C103—28no—
61#41×C103—24no—
62#41×C103—24no—
63C2×Q8×C103—24no—
64C2×Q8×C103C4⋊C412yes—
65C2×Q8×C103C2×D412yes—
66C2×D4×C103—28no—
67C2×D4×C103—24no—
68C2×D4×C103C4⋊C412yes—
69C2×D4×C103C4⋊C414yes—
70C2×D4×C103C2×D412yes—
71C2×D4×C103C2×Q814yes—
72C22×C4×C103—24no—
73C22×C4×C103—24no—
74C22×C4×C103C4⋊C412yes—
75C22×C4×C103C4⋊C414yes—
76C22×C4×C103C22×C414yes—
77C22×C4×C103C22×C411yescharacteristic
78C22×C4×C103C22×C411yescharacteristic
79C22×C4×C103C2×D414yes—
80C22×C4×C103C2×D411yescharacteristic
81C22×C4×C103C2×D411yescharacteristic
82C22×C4×C103C2×Q811yescharacteristic
83C22×C4×C103#4114yes—
84C22×C4×C103C2411yescharacteristic
85M16×C103—24no—
86M16×C103—24no—
87M16×C103—216no—
88M16×C103—28no—
89M16×C103—28no—
90M16×C103—44no—
91M16×C103—44no—
92M16×C103C22⋊C418yes—
93M16×C103C22⋊C418yes—
94C2×C8×C103—24no—
95C2×C8×C103—216no—
96C2×C8×C103—28no—
97C2×C8×C103—44no—
98C2×C8×C103—44no—
99C2×C8×C103C22×C414yes—
100C2×C8×C103C22×C414yes—
101C2×C8×C103C2×D418yes—
102C23×C103—24no—
103C23×C103—81no—
104C23×C103—82no—
105C23×C103C2×C4⋊C414yes—
106C23×C103C2×C4⋊C411yescharacteristic
107C23×C103C2×C4⋊C411yescharacteristic
108C23×C103C22⋊Q814yes—
109C23×C103C22×Q811yescharacteristic
110Q8×C103—24no—
111Q8×C103—24no—
112D4×C103—28no—
113D4×C103—28no—
114D4×C103—24no—
115D4×C103—24no—
116C2×C4×C103—24no—
117C2×C4×C103—24no—
118C2×C4×C103—24no—
119C2×C4×C103—28no—
120C2×C4×C103C2×C22⋊C412yes—
121C2×C4×C103C2×C22⋊C412yes—
122C2×C4×C103C2×C4⋊C414yes—
123C2×C4×C103C2×C4⋊C411yescharacteristic
124C2×C4×C103C2×C4⋊C411yescharacteristic
125C2×C4×C103#11712yes—
126C2×C4×C103#11712yes—
127C2×C4×C103#12114yes—
128C2×C4×C103#12114yes—
129C2×C4×C103C22⋊Q814yes—
130C2×C4×C103C23×C411yescharacteristic
131C2×C4×C103C22×D412yes—
132C2×C4×C103C22×D411yescharacteristic
133C2×C4×C103C2×#4112yes—
134C8×C103—24no—
135C8×C103—48no—
136C8×C103C2×C22⋊C418yes—
137C22×C103—24no—
138C22×C103—41no—
139C22×C103—41no—
140C22×C103—44no—
141C22×C103—41no—
142C22×C103—44no—
143C22×C103—84no—
144C22×C103#38012yes—
145C22×C103#38012yes—
146C22×C103C22×C4⋊C411yescharacteristic
147C22×C103C2×C22⋊Q812yes—
148C4×C103—24no—
149C4×C103#38012yes—
150C4×C103#38012yes—
151C4×C103C22×C22⋊C411yescharacteristic
152C4×C103C2×#11711yescharacteristic
153C4×C103C2×#12112yes—
154#20673C10311yesmaximal, characteristic, direct product factor, Sylow
155C2×C103—21no—
156C2×C103—22no—
157C2×C103—22no—
158C2×C103—22no—
159C2×C103—44no—
160C2×C103C2×#38011yescharacteristic
161C2×#568C2×C10311yescharacteristic
162C2×#430C2×C10312yescomplemented
163C2×#413C2×C10312yes—
164#1813C2×C10318yescomplemented
165C2×#338C2×C10312yescomplemented
166C103#2067311yescharacteristic, direct product factor, Sylow
167C22×#41C22×C10311yescharacteristic
168#568—28no—
169C2×#131C4×C10314yes—
170C2×#131C22×C10314yes—
171C22×M16C4×C10314yes—
172C22×M16C22×C10314yes—
173C22×M16C22×C10311yescharacteristic
174C22×M16C22×C10311yescharacteristic
175#430—28no—
176C2×#108C22×C10318yescomplemented
177#413—24no—
178#413C22×C10318yes—
179C2×#101—22no—
180C2×#100—22no—
181#338C22×C10318yescomplemented
182C2×#41—24no—
183C2×#41—24no—
184C2×#41C2×C4×C10312yes—
185C2×#41D4×C10312yes—
186C2×#41Q8×C10312yes—
187C2×#41C23×C10312yes—
188C22×Q8D4×C10311yescharacteristic
189C22×D4D4×C10311yescharacteristic
190C22×D4Q8×C10312yes—
191C23×C4C2×C4×C10312yes—
192C23×C4C23×C10311yescharacteristic
193#131—216no—
194#131—216no—
195C2×M16—24no—
196C2×M16—216no—
197C2×M16—24no—
198C2×M16—24no—
199C2×M16—24no—
200C2×M16—24no—
201C2×M16—24no—
202C2×M16C2×C4×C10312yes—
203C2×M16C2×C4×C10318yes—
204C2×M16C2×C4×C10312yes—
205C2×M16C2×C4×C10312yes—
206C2×M16D4×C10318yes—
207C2×M16C23×C10318yes—
208C2×M16C23×C10312yes—
209C22×C8—24no—
210C22×C8C2×C4×C10318yes—
211C22×C8C2×C4×C10312yes—
212C22×C8C23×C10312yes—
213#108—216no—
214#101—28no—
215#100—28no—
216C24C4⋊C4×C10312yes—
217C24C2×Q8×C10311yescharacteristic
218#41—24no—
219#41—24no—
220#41—28no—
221#41—28no—
222#41—24no—
223#41—24no—
224C2×Q8—24no—
225C2×Q8C4⋊C4×C10312yes—
226C2×Q8C2×D4×C10312yes—
227C2×D4—28no—
228C2×D4—24no—
229C2×D4C4⋊C4×C10312yes—
230C2×D4C4⋊C4×C10314yes—
231C2×D4C2×D4×C10312yes—
232C2×D4C2×Q8×C10314yes—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4C4⋊C4×C10312yes—
236C22×C4C4⋊C4×C10314yes—
237C22×C4C22×C4×C10314yes—
238C22×C4C22×C4×C10311yescharacteristic
239C22×C4C22×C4×C10311yescharacteristic
240C22×C4C2×D4×C10314yes—
241C22×C4C2×D4×C10311yescharacteristic
242C22×C4C2×D4×C10311yescharacteristic
243C22×C4C2×Q8×C10311yescharacteristic
244C22×C4#41×C10314yes—
245C22×C4C24×C10311yescharacteristic
246M16—24no—
247M16—24no—
248M16—216no—
249M16—28no—
250M16—28no—
251M16—44no—
252M16—44no—
253M16C22⋊C4×C10318yes—
254M16C22⋊C4×C10318yes—
255C2×C8—24no—
256C2×C8—216no—
257C2×C8—28no—
258C2×C8—44no—
259C2×C8—44no—
260C2×C8C22×C4×C10314yes—
261C2×C8C22×C4×C10314yes—
262C2×C8C2×D4×C10318yes—
263C23—24no—
264C23—81no—
265C23—82no—
266C23C2×C4⋊C4×C10314yes—
267C23C2×C4⋊C4×C10311yescharacteristic
268C23C2×C4⋊C4×C10311yescharacteristic
269C23C22⋊Q8×C10314yes—
270C23C22×Q8×C10311yescharacteristic
271Q8—24no—
272Q8—24no—
273D4—28no—
274D4—28no—
275D4—24no—
276D4—24no—
277C2×C4—24no—
278C2×C4—28no—
279C2×C4—24no—
280C2×C4—24no—
281C2×C4C2×C22⋊C4×C10312yes—
282C2×C4C2×C22⋊C4×C10312yes—
283C2×C4C2×C4⋊C4×C10314yes—
284C2×C4C2×C4⋊C4×C10311yescharacteristic
285C2×C4C2×C4⋊C4×C10311yescharacteristic
286C2×C4#117×C10312yes—
287C2×C4#117×C10312yes—
288C2×C4#121×C10314yes—
289C2×C4#121×C10314yes—
290C2×C4C22⋊Q8×C10314yes—
291C2×C4C23×C4×C10311yescharacteristic
292C2×C4C22×D4×C10312yes—
293C2×C4C22×D4×C10311yescharacteristic
294C2×C4C2×#41×C10312yes—
295C8—24no—
296C8—48no—
297C8C2×C22⋊C4×C10318yes—
298C22—24no—
299C22—41no—
300C22—41no—
301C22—44no—
302C22—41no—
303C22—44no—
304C22—84no—
305C22#380×C10312yes—
306C22#380×C10312yes—
307C22C22×C4⋊C4×C10311yescharacteristic
308C22C2×C22⋊Q8×C10312yes—
309C4—24no—
310C4#380×C10312yes—
311C4#380×C10312yes—
312C4C22×C22⋊C4×C10311yescharacteristic
313C4C2×#117×C10311yescharacteristic
314C4C2×#121×C10312yes—
315C2—21no—
316C2—22no—
317C2—22no—
318C2—22no—
319C2—44no—
320C2C2×#380×C10311yescharacteristic
subgroupG/H
centerC4×C103C2×#117
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC2×C103C2×#380
prime radicalC22×#41×C103C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×M16×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#430×C103C2semidirect
4. C103×#1813C2semidirect
5. C2×#338×C103C2semidirect
15. C2×#108×C103C22semidirect
20. #338×C103C22semidirect
154. #20673C103direct (N × H)
162. C2×#430C2×C103semidirect
164. #1813C2×C103semidirect
165. C2×#338C2×C103semidirect
166. C103#20673direct (N × H)
176. C2×#108C22×C103semidirect
181. #338C22×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C1032
C2×#430×C1032
C2×#413×C1032
C103×#18132
C2×#338×C1032
#20673103