Finite Group Databasebeta

← C2×#21444935 #29655623

Subgroups — C2×#21444935 #29655623

Order 15616.

1722 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840134C211yesmaximal, characteristic, complemented
2C2×#16840052C212yesmaximal, complemented
3#21444935C218yesmaximal, direct product factor
4C2×#16839506C211yesmaximal, characteristic, complemented
5C2×D4⋊#92418C212yesmaximal, complemented
6C2×D42×C61C211yesmaximal, characteristic
7C22×#11758200—22no—
8C2×#14519777C2211yescharacteristic, complemented
9#16840134—22no—
10#16840134C2214yescomplemented
11#16840052—24no—
12#16840052C2218yescomplemented
13C2×#14519708—22no—
14C2×C4⋊#92418C2212yescomplemented
15C2×#14519698—22no—
16C2×C4×#92418C2211yescharacteristic, complemented
17#16839506C2214yescomplemented
18D4⋊#92418C2218yescomplemented
19C23×D4×C61—22no—
20D42×C61—22no—
21D42×C61—24no—
22D42×C61C2214yes—
23C2×#127×C61C2211yescharacteristic
24C2×#121×C61—22no—
25C2×#120×C61—22no—
26C2×C4×D4×C61C2212yes—
27C22×Dic122—21no—
28C2×#11758200—28no—
29C2×#11758200—48no—
30C22×#92418—21no—
31C22×#92418—22no—
32#14519777—22no—
33#14519777—21no—
34#14519777C2312yescomplemented
35C2×C4⋊Dic61—22no—
36#14519708—28no—
37C4⋊#92418—22no—
38C4⋊#92418C2314yescomplemented
39#14519698—28no—
40C4×#92418—21no—
41C4×#92418C2312yescomplemented
42C25×C61—22no—
43C22×D4×C61—28no—
44C22×D4×C61—24no—
45C22×D4×C61—28no—
46C22×D4×C61—22no—
47C22×D4×C61—48no—
48C22×D4×C61—48no—
49C22×D4×C61D412yes—
50C22×D4×C61D412yes—
51C23×C4×C61—22no—
52#127×C61—22no—
53#127×C61D412yes—
54#127×C61C2312yes—
55#121×C61—28no—
56#121×C61—28no—
57#120×C61—28no—
58#120×C61—28no—
59C4×D4×C61—22no—
60C4×D4×C61—22no—
61C4×D4×C61D414yes—
62C4×D4×C61C2314yes—
63C2×C4⋊C4×C61D412yes—
64C2×C22⋊C4×C61—22no—
65C2×C22⋊C4×C61—22no—
66C2×C42×C61C2311yescharacteristic
67C24×C61—22no—
68C24×C61—28no—
69C24×C61—22no—
70C24×C61—416no—
71C24×C61—84no—
72C2×D4×C61—216no—
73C2×D4×C61—22no—
74C2×D4×C61—24no—
75C2×D4×C61—22no—
76C2×D4×C61—24no—
77C2×D4×C61—24no—
78C2×D4×C61—44no—
79C2×D4×C61—416no—
80C2×D4×C61—432no—
81C2×D4×C61—416no—
82C2×D4×C61—416no—
83C2×D4×C61—44no—
84C2×D4×C61—44no—
85C2×D4×C61SD1618yescomplemented
86C2×D4×C61C2×D414yes—
87C2×D4×C61C2×D414yes—
88C22×C4×C61—22no—
89C22×C4×C61—24no—
90C22×C4×C61—24no—
91C22×C4×C61—44no—
92C22×C4×C61—44no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D412yes—
95C22×Dic61—41no—
96C2×Dic122—22no—
97C2×Dic122—44no—
98C2×Dic122—41no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61C2×D414yes—
101C22⋊C4×C61—28no—
102C22⋊C4×C61—24no—
103C22⋊C4×C61—24no—
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D412yes—
106C42×C61C2411yescharacteristic
107#11758200—416no—
108C4⋊Dic61—24no—
109C4⋊Dic61—42no—
110C2×#92418—24no—
111C2×#92418—22no—
112C2×#92418—24no—
113C2×#92418—44no—
114C23×C61—24no—
115C23×C61—28no—
116C23×C61—24no—
117C23×C61—432no—
118C23×C61—44no—
119C23×C61—44no—
120C23×C61—48no—
121C23×C61—44no—
122C23×C61—88no—
123C23×C61—832no—
124C23×C61#12011yescharacteristic
125D4×C61—24no—
126D4×C61—28no—
127D4×C61—44no—
128D4×C61—432no—
129D4×C61—44no—
130D4×C61—44no—
131D4×C61—48no—
132D4×C61—82no—
133D4×C61C2×SD1618yescomplemented
134C2×C4×C61—22no—
135C2×C4×C61—24no—
136C2×C4×C61—44no—
137C2×C4×C61—44no—
138C2×C4×C61—44no—
139C2×C4×C61—48no—
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12012yes—
142C2×C4×C61C2×SD1614yes—
143C2×C4×C61AGL(1,ℤ/8)14yes—
144C2×C4×C61C22×D411yescharacteristic
145C2×C4×C61C22×D412yes—
146C2×Dic61—42no—
147C2×Dic61—82no—
148Dic122—44no—
149Dic122—82no—
150#92418—24no—
151#92418—44no—
152C2×#1629—611nomaximal, Sylow
153C22×C61—28no—
154C22×C61—416no—
155C22×C61—44no—
156C22×C61—44no—
157C22×C61—48no—
158C22×C61—44no—
159C22×C61—832no—
160C22×C61—88no—
161C22×C61#45014yes—
162C22×C61#45312yes—
163C22×C61C2×#12011yescharacteristic
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—44no—
167C4×C61#45014yes—
168C4×C61C22×SD1612yes—
169C4×C61C2×AGL(1,ℤ/8)12yes—
170Dic61—82no—
171C2×D42D6111yescharacteristic
172C2×#492—611no—
173C2×#476—612no—
174#1629—618no—
175C2×#331—611no—
176C2×D4⋊C8—612no—
177C2×C61—48no—
178C2×C61—84no—
179C2×C61#162914yescomplemented
180C2×C61C2×#45012yes—
181C2×C61C2×#45311yescharacteristic
182C23×D4—22no—
183C22×SD16—1222no—
184D42—22no—
185D42—24no—
186D42C2×D6114yes—
187C2×C4⋊Q8—611no—
188C2×#127C2×D6111yescharacteristic
189C2×#121—22no—
190C2×#120—22no—
191C2×C4×D4C2×D6112yes—
192#492—614no—
193#492—1222no—
194#476—618no—
195#476—1224no—
196C2×#106—1222no—
197C2×C4⋊C8—612no—
198C2×#102—1222no—
199C2×C4×C8—611no—
200#331—614no—
201D4⋊C8—618no—
202C61C2×#162911yescharacteristic, complemented, Sylow
203C25—22no—
204C22×Q8—1221no—
205C22×D4—24no—
206C22×D4—28no—
207C22×D4—28no—
208C22×D4—22no—
209C22×D4—48no—
210C22×D4—48no—
211C22×D4C22⋊D6112yes—
212C22×D4C22⋊D6112yes—
213C23×C4—22no—
214C2×SD16—1228no—
215C2×SD16—2448no—
216C22×C8—1221no—
217C22×C8—1222no—
218C4⋊Q8—612no—
219C4⋊Q8—1222no—
220C4⋊Q8—1221no—
221#127—22no—
222#127C22⋊D6112yes—
223#127C22×D6112yes—
224#121—28no—
225#121—28no—
226#120—28no—
227#120—28no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4C22⋊D6114yes—
231C4×D4C22×D6114yes—
232C2×C4⋊C4—1222no—
233C2×C4⋊C4C22⋊D6112yes—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C42C22×D6111yescharacteristic
237#106—1228no—
238C4⋊C8—614no—
239C4⋊C8—1222no—
240#102—1228no—
241C4×C8—612no—
242C4×C8—1221no—
243C24—22no—
244C24—28no—
245C24—22no—
246C24—416no—
247C24—84no—
248C2×Q8—1222no—
249C2×Q8—2444no—
250C2×Q8—2441no—
251C2×D4—216no—
252C2×D4—24no—
253C2×D4—22no—
254C2×D4—24no—
255C2×D4—22no—
256C2×D4—24no—
257C2×D4—44no—
258C2×D4—416no—
259C2×D4—432no—
260C2×D4—416no—
261C2×D4—416no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4#1175820018yescomplemented
265C2×D4C2×C22⋊D6114yes—
266C2×D4C2×C22⋊D6114yes—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—2441no—
273C22×C4C2×C22⋊D6111yescharacteristic
274C22×C4C2×C22⋊D6112yes—
275SD16—24416no—
276C2×C8—1224no—
277C2×C8—1222no—
278C2×C8—1224no—
279C2×C8—2444no—
280C4⋊C4—22no—
281C4⋊C4—1224no—
282C4⋊C4—2442no—
283C4⋊C4C2×C22⋊D6114yes—
284C22⋊C4—28no—
285C22⋊C4—24no—
286C22⋊C4—24no—
287C42C2×C22⋊D6111yescharacteristic
288C42C2×C22⋊D6112yes—
289C42C23×D6111yescharacteristic
290C23—24no—
291C23—28no—
292C23—24no—
293C23—432no—
294C23—44no—
295C23—44no—
296C23—48no—
297C23—44no—
298C23—88no—
299C23—832no—
300C23#1451974611yescharacteristic
301Q8—4882no—
302Q8—2444no—
303D4—24no—
304D4—28no—
305D4—44no—
306D4—432no—
307D4—44no—
308D4—44no—
309D4—48no—
310D4—82no—
311D4C2×#1175820018yescomplemented
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—48no—
318C2×C4—4882no—
319C2×C4—2442no—
320C2×C4#1451974611yescharacteristic
321C2×C4#1451974612yes—
322C2×C4C2×#1175820014yes—
323C2×C4#1451980314yes—
324C2×C4C22×C22⋊D6111yescharacteristic
325C2×C4C22×C22⋊D6112yes—
326C8—1224no—
327C8—2444no—
328C22—28no—
329C22—44no—
330C22—416no—
331C22—44no—
332C22—44no—
333C22—48no—
334C22—832no—
335C22—88no—
336C22#1683991314yes—
337C22#1683993012yes—
338C22C2×#1451974611yescharacteristic
339C4—21no—
340C4—21no—
341C4—44no—
342C4—4882no—
343C4#1683991314yes—
344C4C22×#1175820012yes—
345C4C2×#1451980312yes—
346C2—48no—
347C2—84no—
348C2#2144493514yesdirect product factor
349C2C2×#1683991312yes—
350C2C2×#1683993011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC2×D42×C61C2
socleC23×C61#120
hypercenterC2×D42D61
hypocenterC61C2×#1629
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#16840134C2semidirect
2. C2×#16840052C2semidirect
3. #21444935C2direct (N × H)
4. C2×#16839506C2semidirect
5. C2×D4⋊#92418C2semidirect
8. C2×#14519777C22semidirect
10. #16840134C22semidirect
12. #16840052C22semidirect
14. C2×C4⋊#92418C22semidirect
16. C2×C4×#92418C22semidirect
17. #16839506C22semidirect
18. D4⋊#92418C22semidirect
34. #14519777C23semidirect
38. C4⋊#92418C23semidirect
41. C4×#92418C23semidirect
85. C2×D4×C61SD16semidirect
133. D4×C61C2×SD16semidirect
179. C2×C61#1629semidirect
202. C61C2×#1629semidirect
264. C2×D4#11758200semidirect
311. D4C2×#11758200semidirect
348. C2#21444935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401342
C2×#168400522
#214449352
C2×#168395062
C2×D4⋊#924182
C2×D42×C612
C2×#162961