Finite Group Databasebeta

← C2×#21447127 #29707939

Subgroups — C2×#21447127 #29707939

Order 15616.

1918 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519706C211yesmaximal, characteristic, complemented
2C22×#14519698C212yesmaximal, complemented
3C2×#16839665C212yesmaximal, complemented
4#21447127C218yesmaximal, direct product factor
5C2×#16839525C211yesmaximal, characteristic, complemented
6C23×D8×C61C211yesmaximal, characteristic
7C23×#92418C2211yescharacteristic
8C22×C4⋊Dic61C2212yes—
9C22×C22⋊Dic61—22no—
10C22×C22⋊Dic61—22no—
11C22×C4×Dic61C2211yescharacteristic
12C2×#14519706—24no—
13C2×#14519706C2214yescomplemented
14C2×#14519698—28no—
15C2×#14519698C2218yescomplemented
16#16839665—24no—
17#16839665C2218yescomplemented
18#16839525C2214yescomplemented
19C23×D4×C61C2212yes—
20C22×D8×C61—28no—
21C22×D8×C61—24no—
22C22×D8×C61C2214yes—
23C23×C8×C61C2211yescharacteristic
24C23×Dic61—22no—
25C23×Dic61D411yescharacteristic
26C23×Dic61D411yescharacteristic
27C22×#92418—24no—
28C22×#92418—22no—
29C22×#92418C2312yes—
30C2×C4⋊Dic61—24no—
31C2×C4⋊Dic61—24no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61C2314yes—
34C2×C22⋊Dic61—28no—
35C2×C22⋊Dic61—28no—
36C2×C22⋊Dic61—48no—
37C2×C22⋊Dic61—48no—
38C2×C4×Dic61—22no—
39C2×C4×Dic61—22no—
40C2×C4×Dic61D412yes—
41C2×C4×Dic61C2312yes—
42#14519706—28no—
43#14519698—216no—
44C25×C61—22no—
45C22×D4×C61—24no—
46C22×D4×C61—24no—
47C22×D4×C61—22no—
48C22×D4×C61—24no—
49C22×D4×C61—24no—
50C22×D4×C61—24no—
51C22×D4×C61D418yes—
52C22×D4×C61C2314yes—
53C23×C4×C61C2311yescharacteristic
54C2×D8×C61—232no—
55C2×D8×C61—216no—
56C2×D8×C61—28no—
57C22×C8×C61—24no—
58C22×C8×C61D414yes—
59C22×C8×C61C2312yes—
60C24×C61—28no—
61C24×C61—24no—
62C24×C61—44no—
63C24×C61—44no—
64C24×C61—44no—
65C24×C61—44no—
66C24×C61—44no—
67C24×C61—44no—
68C24×C61C2×D411yescharacteristic
69C2×D4×C61—216no—
70C2×D4×C61—28no—
71C2×D4×C61—216no—
72C2×D4×C61—24no—
73C2×D4×C61—24no—
74C2×D4×C61—24no—
75C2×D4×C61—24no—
76C2×D4×C61—24no—
77C2×D4×C61—44no—
78C2×D4×C61—44no—
79C2×D4×C61—48no—
80C2×D4×C61—48no—
81C2×D4×C61C2×D418yes—
82C22×C4×C61C2×D414yes—
83C22×C4×C61C2×D412yes—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4112yes—
86C22×C4×C61#4114yes—
87C22×C4×C61C2411yescharacteristic
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—22no—
91C22×Dic61—24no—
92C22×Dic61—24no—
93C22×Dic61—44no—
94C22×Dic61—44no—
95C22×Dic61—44no—
96C22×Dic61D814yescomplemented
97C22×Dic61C2×D412yes—
98C22×Dic61C2×D412yes—
99D8×C61—232no—
100C2×C8×C61—28no—
101C2×C8×C61—24no—
102C2×C8×C61C2×D414yes—
103C22⋊Dic61—416no—
104C22⋊Dic61—416no—
105C4⋊Dic61—24no—
106C4⋊Dic61—24no—
107C4⋊Dic61—44no—
108C4×Dic61—24no—
109C4×Dic61—22no—
110C4×Dic61—22no—
111C2×#92418—24no—
112C2×#92418—22no—
113C2×#92418—44no—
114C23×C61—28no—
115C23×C61—44no—
116C23×C61—44no—
117C23×C61—44no—
118C23×C61—44no—
119C23×C61—44no—
120C23×C61—44no—
121C23×C61—416no—
122C23×C61—416no—
123C23×C61—416no—
124C23×C61—88no—
125C23×C61—88no—
126C23×C61—88no—
127C23×C61—88no—
128C23×C61#12114yes—
129C23×C61#12112yes—
130C23×C61C2×D812yes—
131C23×C61#13512yes—
132C23×C61AGL(1,ℤ/8)14yes—
133C23×C61C22×D411yescharacteristic
134D4×C61—28no—
135D4×C61—28no—
136D4×C61—44no—
137D4×C61—44no—
138D4×C61—416no—
139C2×C4×C61#12014yes—
140C2×C4×C61#12112yes—
141C2×C4×C61#12114yes—
142C2×C4×C61#12318yes—
143C2×C4×C61#12414yes—
144C2×C4×C61C22×D412yes—
145C2×C4×C61C22×D411yescharacteristic
146C2×C4×C61C2×#4111yescharacteristic
147C2×C4×C61C2×#4112yes—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—28no—
151C2×Dic61—22no—
152C2×Dic61—24no—
153C2×Dic61—44no—
154C2×Dic61—44no—
155C2×Dic61—44no—
156C2×Dic61—44no—
157C2×Dic61—88no—
158C2×Dic61C2×D814yescomplemented
159C8×C61—24no—
160#92418—42no—
161C2×#2054—611nomaximal, Sylow
162C22×C61—48no—
163C22×C61—48no—
164C22×C61—48no—
165C22×C61—832no—
166C22×C61—84no—
167C22×C61—84no—
168C22×C61—84no—
169C22×C61—84no—
170C22×C61#39414yes—
171C22×C61#45918yes—
172C22×C61#46318yes—
173C22×C61#46614yes—
174C22×C61#46914yes—
175C22×C61C2×#12111yescharacteristic
176C22×C61C2×#12112yes—
177C22×C61C22×D811yescharacteristic
178C22×C61C2×#13511yescharacteristic
179C22×C61C2×AGL(1,ℤ/8)12yes—
180C4×C61#39414yes—
181C4×C61C2×#12011yescharacteristic
182C4×C61C2×#12312yes—
183C4×C61C2×#12411yescharacteristic
184Dic61—24no—
185Dic61—42no—
186Dic61—84no—
187C23×D8D6111yescharacteristic
188C22×C4⋊C8—611no—
189C22×#102—612no—
190C2×#390—612no—
191#2054—618no—
192C2×#340—611no—
193C2×C61—88no—
194C2×C61#205418yescomplemented
195C2×C61C2×#39411yescharacteristic
196C2×C61C2×#45912yes—
197C2×C61C2×#46312yes—
198C2×C61C2×#46611yescharacteristic
199C2×C61C2×#46911yescharacteristic
200C23×D4C2×D6112yes—
201C22×D8—28no—
202C22×D8—24no—
203C22×D8C2×D6114yes—
204C23×C8—611no—
205C23×C8C2×D6111yescharacteristic
206C22×C4⋊C4—612no—
207C22×C22⋊C4—1222no—
208C22×C22⋊C4—1222no—
209C22×C42—611no—
210C2×C4⋊C8—614no—
211C2×C4⋊C8—1224no—
212C2×#102—618no—
213C2×#102—1228no—
214#390—618no—
215#390—1224no—
216#340—614no—
217C61C2×#205411yescharacteristic, complemented, Sylow
218C25—22no—
219C22×D4—22no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4C22⋊D6118yes—
226C22×D4C22×D6114yes—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—1222no—
230C23×C4C22×D6111yescharacteristic
231C2×D8—232no—
232C2×D8—216no—
233C2×D8—28no—
234C22×C8—24no—
235C22×C8—612no—
236C22×C8—1224no—
237C22×C8—1222no—
238C22×C8C22⋊D6114yes—
239C22×C8C22×D6112yes—
240C2×C4⋊C4—614no—
241C2×C4⋊C4—1224no—
242C2×C4⋊C4—1224no—
243C2×C4⋊C4—1222no—
244C2×C22⋊C4—1228no—
245C2×C22⋊C4—1228no—
246C2×C22⋊C4—2448no—
247C2×C22⋊C4—2448no—
248C2×C42—612no—
249C2×C42—612no—
250C2×C42—1222no—
251C2×C42—1222no—
252C4⋊C8—1228no—
253#102—12216no—
254C24—24no—
255C24—28no—
256C24—44no—
257C24—44no—
258C24—44no—
259C24—44no—
260C24—44no—
261C24—44no—
262C24D4×D6111yescharacteristic
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—24no—
268C2×D4—216no—
269C2×D4—28no—
270C2×D4—216no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—48no—
274C2×D4—48no—
275C2×D4C2×C22⋊D6118yes—
276C22×C4—612no—
277C22×C4—614no—
278C22×C4—612no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1224no—
283C22×C4—1224no—
284C22×C4—2444no—
285C22×C4—2444no—
286C22×C4—2444no—
287C22×C4D4×D6111yescharacteristic
288C22×C4#1175822412yes—
289C22×C4#1175822414yes—
290C22×C4C2×C22⋊D6112yes—
291C22×C4C2×C22⋊D6114yes—
292C22×C4C23×D6111yescharacteristic
293D8—232no—
294C2×C8—24no—
295C2×C8—28no—
296C2×C8—1224no—
297C2×C8—1222no—
298C2×C8—2444no—
299C2×C8C2×C22⋊D6114yes—
300C4⋊C4—1224no—
301C4⋊C4—1224no—
302C4⋊C4—2444no—
303C22⋊C4—24416no—
304C22⋊C4—24416no—
305C42—1222no—
306C42—1222no—
307C42—1224no—
308C23—28no—
309C23—416no—
310C23—416no—
311C23—44no—
312C23—44no—
313C23—44no—
314C23—44no—
315C23—44no—
316C23—44no—
317C23—416no—
318C23—88no—
319C23—88no—
320C23—88no—
321C23—88no—
322C23#1451974812yes—
323C23#1451974914yes—
324C23D8×D6112yes—
325C23#1451979612yes—
326C23#1451980114yes—
327C23C2×D4×D6111yescharacteristic
328D4—28no—
329D4—28no—
330D4—44no—
331D4—44no—
332D4—416no—
333C2×C4—614no—
334C2×C4—1228no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1224no—
339C2×C4—4888no—
340C2×C4—2444no—
341C2×C4—2444no—
342C2×C4—2444no—
343C2×C4—2444no—
344C2×C4#1451974614yes—
345C2×C4#1451974812yes—
346C2×C4#1451974914yes—
347C2×C4#1451975818yes—
348C2×C4#1451976414yes—
349C2×C4C22×C22⋊D6112yes—
350C2×C4C22×C22⋊D6111yescharacteristic
351C2×C4C2×#1175822411yescharacteristic
352C2×C4C2×#1175822412yes—
353C8—24no—
354C8—2442no—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—84no—
359C22—84no—
360C22—84no—
361C22—84no—
362C22—832no—
363C22#1683967614yes—
364C22#1683995518yes—
365C22#1683997518yes—
366C22#1683999514yes—
367C22#1684001214yes—
368C22C2×#1451974811yescharacteristic
369C22C2×#1451974912yes—
370C22C2×D8×D6111yescharacteristic
371C22C2×#1451979611yescharacteristic
372C22C2×#1451980112yes—
373C4—1224no—
374C4—4884no—
375C4—2442no—
376C4#1683967614yes—
377C4C2×#1451974611yescharacteristic
378C4C2×#1451975812yes—
379C4C2×#1451976411yescharacteristic
380C2—88no—
381C2#2144712718yesdirect product factor
382C2C2×#1683967611yescharacteristic
383C2C2×#1683995512yes—
384C2C2×#1683997512yes—
385C2C2×#1683999511yescharacteristic
386C2C2×#1684001211yescharacteristic
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC23×D8×C61C2
socleC24×C61C2×D4
hypercenterC23×D8D61
hypocenterC61C2×#2054
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C22×#14519706C2semidirect
2. C22×#14519698C2semidirect
3. C2×#16839665C2semidirect
4. #21447127C2direct (N × H)
5. C2×#16839525C2semidirect
13. C2×#14519706C22semidirect
15. C2×#14519698C22semidirect
17. #16839665C22semidirect
18. #16839525C22semidirect
96. C22×Dic61D8semidirect
158. C2×Dic61C2×D8semidirect
194. C2×C61#2054semidirect
217. C61C2×#2054semidirect
381. C2#21447127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197062
C22×#145196982
C2×#168396652
#214471272
C2×#168395252
C23×D8×C612
C2×#205461