Finite Group Databasebeta

← C103×#23505 #39928780

Subgroups — C103×#23505 #39928780

Order 26368.

2134 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#127×C103C211yesmaximal, characteristic
2C2×#418×C103C212yesmaximal, complemented
3C2×#418×C103C212yesmaximal, complemented
4C103×#2296C211yesmaximal, characteristic, complemented
5C103×#2041C218yesmaximal, complemented
6C103×#1728C211yesmaximal, characteristic, complemented
7C23×D4×C103—22no—
8C23×D4×C103C2212yes—
9C22×M16×C103C2212yes—
10C2×#127×C103—28no—
11C2×#127×C103—22no—
12C2×#127×C103C2214yes—
13C2×#117×C103C2211yescharacteristic
14C2×#117×C103C2211yescharacteristic
15C22×C42×C103C2211yescharacteristic
16#418×C103—28no—
17#418×C103—28no—
18C2×#102×C103C2218yescomplemented
19C2×#102×C103C2218yescomplemented
20#389×C103C2214yescomplemented
21#385×C103—22no—
22C4×C4⋊C4×C103—22no—
23#336×C103C2214yescomplemented
24C25×C103—22no—
25C22×D4×C103—216no—
26C22×D4×C103—24no—
27C22×D4×C103—22no—
28C22×D4×C103—24no—
29C22×D4×C103—28no—
30C22×D4×C103—24no—
31C22×D4×C103—24no—
32C22×D4×C103—24no—
33C22×D4×C103—416no—
34C22×D4×C103D418yes—
35C22×D4×C103C2314yes—
36C23×C4×C103D412yes—
37C23×C4×C103C2311yescharacteristic
38C2×M16×C103—24no—
39C2×M16×C103—24no—
40C2×M16×C103—24no—
41C22×C8×C103C2314yes—
42#127×C103—216no—
43#127×C103—216no—
44#117×C103—22no—
45#117×C103—24no—
46#117×C103D414yescomplemented
47C2×C4⋊C4×C103—24no—
48C2×C4⋊C4×C103C2312yes—
49C2×C4⋊C4×C103C2312yes—
50C2×C22⋊C4×C103—21no—
51C2×C22⋊C4×C103—21no—
52C2×C42×C103—21no—
53C2×C42×C103—24no—
54C2×C42×C103—21no—
55C2×C42×C103D412yes—
56C2×C42×C103C2312yes—
57#102×C103—216no—
58#102×C103—216no—
59#95×C103—24no—
60C24×C103—28no—
61C24×C103—24no—
62C24×C103—416no—
63C24×C103—44no—
64C24×C103—44no—
65C24×C103C2×D411yescharacteristic
66C2×D4×C103—232no—
67C2×D4×C103—28no—
68C2×D4×C103—216no—
69C2×D4×C103—216no—
70C2×D4×C103—24no—
71C2×D4×C103—24no—
72C2×D4×C103—24no—
73C2×D4×C103—24no—
74C2×D4×C103—24no—
75C2×D4×C103—464no—
76C2×D4×C103—416no—
77C2×D4×C103—48no—
78C2×D4×C103—44no—
79C2×D4×C103—48no—
80C2×D4×C103—44no—
81C2×D4×C103—416no—
82C2×D4×C103C2×D418yes—
83C22×C4×C103—24no—
84C22×C4×C103—28no—
85C22×C4×C103—22no—
86C22×C4×C103—22no—
87C22×C4×C103C2×D414yes—
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103C2×D414yes—
90C22×C4×C103C2×D412yes—
91C22×C4×C103#4114yes—
92C22×C4×C103#4112yes—
93C22×C4×C103C2411yescharacteristic
94M16×C103—48no—
95C2×C8×C103—24no—
96C2×C8×C103—24no—
97C2×C8×C103—24no—
98C4⋊C4×C103—22no—
99C4⋊C4×C103—24no—
100C4⋊C4×C103—48no—
101C4⋊C4×C103C2×D414yescomplemented
102C22⋊C4×C103—24no—
103C22⋊C4×C103—42no—
104C42×C103—24no—
105C42×C103—24no—
106C42×C103—24no—
107C42×C103—42no—
108C23×C103—24no—
109C23×C103—28no—
110C23×C103—432no—
111C23×C103—44no—
112C23×C103—44no—
113C23×C103—416no—
114C23×C103—416no—
115C23×C103—816no—
116C23×C103—816no—
117C23×C103#12012yes—
118C23×C103#12112yes—
119C23×C103#12412yes—
120C23×C103C22×D411yescharacteristic
121D4×C103—28no—
122D4×C103—28no—
123D4×C103—464no—
124D4×C103—44no—
125D4×C103—44no—
126D4×C103—416no—
127C2×C4×C103—216no—
128C2×C4×C103—24no—
129C2×C4×C103—24no—
130C2×C4×C103—24no—
131C2×C4×C103—44no—
132C2×C4×C103—42no—
133C2×C4×C103—44no—
134C2×C4×C103#12012yes—
135C2×C4×C103#12118yes—
136C2×C4×C103#12112yes—
137C2×C4×C103#12318yes—
138C2×C4×C103#12412yes—
139C2×C4×C103AGL(1,ℤ/8)18yes—
140C2×C4×C103C22×D411yescharacteristic
141C2×C4×C103C22×D412yes—
142C2×C4×C103C2×#4112yes—
143C2×C4×C103C2×#4111yescharacteristic
144C8×C103—44no—
145C22×C103—24no—
146C22×C103—24no—
147C22×C103—24no—
148C22×C103—48no—
149C22×C103—416no—
150C22×C103—832no—
151C22×C103—88no—
152C22×C103—88no—
153C22×C103#39414yes—
154C22×C103C2×#12011yescharacteristic
155C22×C103C2×#12111yescharacteristic
156C22×C103C2×#12411yescharacteristic
157C22×C103C2×AGL(1,ℤ/8)14yes—
158C4×C103—28no—
159C4×C103—44no—
160C4×C103—82no—
161C4×C103#39414yes—
162C4×C103C2×#12112yes—
163C4×C103C2×#12312yes—
164#23505C10311yesmaximal, characteristic, direct product factor, Sylow
165C2×C103—24no—
166C2×C103—88no—
167C2×C103C2×#39411yescharacteristic
168C2×C103#300312yes—
169C2×C103#303812yes—
170C2×C103#313812yes—
171C22×#127C2×C10311yescharacteristic
172C2×#418C2×C10312yescomplemented
173C2×#418C2×C10312yescomplemented
174#2296C2×C10311yescharacteristic, complemented
175#2041C2×C10318yescomplemented
176#1728C2×C10311yescharacteristic, complemented
177C103#2350511yescharacteristic, direct product factor, Sylow
178C23×D4—22no—
179C23×D4C22×C10312yes—
180C22×M16C22×C10312yes—
181C2×#127—28no—
182C2×#127—22no—
183C2×#127C22×C10314yes—
184C2×#117C22×C10311yescharacteristic
185C2×#117C22×C10311yescharacteristic
186C22×C42C22×C10311yescharacteristic
187#418—28no—
188#418—28no—
189C2×#102C22×C10318yescomplemented
190C2×#102C22×C10318yescomplemented
191#389C22×C10314yescomplemented
192#385—22no—
193C4×C4⋊C4—22no—
194#336C22×C10314yescomplemented
195C25—22no—
196C22×D4—216no—
197C22×D4—24no—
198C22×D4—22no—
199C22×D4—24no—
200C22×D4—28no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—416no—
205C22×D4D4×C10318yes—
206C22×D4C23×C10314yes—
207C23×C4D4×C10312yes—
208C23×C4C23×C10311yescharacteristic
209C2×M16—24no—
210C2×M16—24no—
211C2×M16—24no—
212C22×C8C23×C10314yes—
213#127—216no—
214#127—216no—
215#117—22no—
216#117—24no—
217#117D4×C10314yescomplemented
218C2×C4⋊C4—24no—
219C2×C4⋊C4C23×C10312yes—
220C2×C4⋊C4C23×C10312yes—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C42—21no—
224C2×C42—24no—
225C2×C42—21no—
226C2×C42D4×C10312yes—
227C2×C42C23×C10312yes—
228#102—216no—
229#102—216no—
230#95—24no—
231C24—28no—
232C24—24no—
233C24—416no—
234C24—44no—
235C24—44no—
236C24C2×D4×C10311yescharacteristic
237C2×D4—232no—
238C2×D4—28no—
239C2×D4—216no—
240C2×D4—216no—
241C2×D4—24no—
242C2×D4—24no—
243C2×D4—24no—
244C2×D4—24no—
245C2×D4—24no—
246C2×D4—464no—
247C2×D4—416no—
248C2×D4—44no—
249C2×D4—48no—
250C2×D4—48no—
251C2×D4—44no—
252C2×D4—416no—
253C2×D4C2×D4×C10318yes—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4C2×D4×C10314yes—
259C22×C4C2×D4×C10311yescharacteristic
260C22×C4C2×D4×C10314yes—
261C22×C4C2×D4×C10312yes—
262C22×C4#41×C10314yes—
263C22×C4#41×C10312yes—
264C22×C4C24×C10311yescharacteristic
265M16—48no—
266C2×C8—24no—
267C2×C8—24no—
268C2×C8—24no—
269C4⋊C4—22no—
270C4⋊C4—24no—
271C4⋊C4—48no—
272C4⋊C4C2×D4×C10314yescomplemented
273C22⋊C4—24no—
274C22⋊C4—42no—
275C42—24no—
276C42—24no—
277C42—24no—
278C42—42no—
279C23—24no—
280C23—28no—
281C23—432no—
282C23—416no—
283C23—44no—
284C23—44no—
285C23—416no—
286C23—816no—
287C23—816no—
288C23#120×C10312yes—
289C23#121×C10312yes—
290C23#124×C10312yes—
291C23C22×D4×C10311yescharacteristic
292D4—28no—
293D4—28no—
294D4—464no—
295D4—416no—
296D4—44no—
297D4—44no—
298C2×C4—216no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—44no—
305C2×C4#120×C10312yes—
306C2×C4#121×C10312yes—
307C2×C4#121×C10318yes—
308C2×C4#123×C10318yes—
309C2×C4#124×C10312yes—
310C2×C4AGL(1,ℤ/8)×C10318yes—
311C2×C4C22×D4×C10311yescharacteristic
312C2×C4C22×D4×C10312yes—
313C2×C4C2×#41×C10312yes—
314C2×C4C2×#41×C10311yescharacteristic
315C8—44no—
316C22—24no—
317C22—24no—
318C22—24no—
319C22—416no—
320C22—48no—
321C22—832no—
322C22—88no—
323C22—88no—
324C22#394×C10314yes—
325C22C2×#120×C10311yescharacteristic
326C22C2×#121×C10311yescharacteristic
327C22C2×#124×C10311yescharacteristic
328C22C2×AGL(1,ℤ/8)×C10314yes—
329C4—28no—
330C4—44no—
331C4—82no—
332C4#394×C10314yes—
333C4C2×#121×C10312yes—
334C4C2×#123×C10312yes—
335C2—24no—
336C2—88no—
337C2C2×#394×C10311yescharacteristic
338C2C103×#300312yes—
339C2C103×#303812yes—
340C2C103×#313812yes—
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×#127×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#418×C103C2semidirect
3. C2×#418×C103C2semidirect
4. C103×#2296C2semidirect
5. C103×#2041C2semidirect
6. C103×#1728C2semidirect
18. C2×#102×C103C22semidirect
19. C2×#102×C103C22semidirect
20. #389×C103C22semidirect
23. #336×C103C22semidirect
46. #117×C103D4semidirect
101. C4⋊C4×C103C2×D4semidirect
164. #23505C103direct (N × H)
172. C2×#418C2×C103semidirect
173. C2×#418C2×C103semidirect
174. #2296C2×C103semidirect
175. #2041C2×C103semidirect
176. #1728C2×C103semidirect
177. C103#23505direct (N × H)
189. C2×#102C22×C103semidirect
190. C2×#102C22×C103semidirect
191. #389C22×C103semidirect
194. #336C22×C103semidirect
217. #117D4×C103semidirect
272. C4⋊C4C2×D4×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#127×C1032
C2×#418×C1032
C103×#22962
C103×#20412
C103×#17282
#23505103