Finite Group Databasebeta

← C2×#19133650 #25072202

Subgroups — C2×#19133650 #25072202

Order 11008.

1838 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 219 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×#14583534C211yesmaximal, characteristic, complemented
2C2×#14583275C211yesmaximal, characteristic, complemented
3C2×#14583095C212yesmaximal, complemented
4#19133650C218yesmaximal, direct product factor
5C2×#14582626C212yesmaximal, complemented
6C2×C43×#331C211yesmaximal, characteristic, complemented
7C22×D4×D43—22no—
8C22×D344—22no—
9C22×#10621882—22no—
10#14583534—24no—
11#14583534—22no—
12#14583534C2214yescomplemented
13C2×#13063322C2211yescharacteristic, complemented
14C2×#13063296—22no—
15C2×#13063293—22no—
16C2×C4×D172C2212yes—
17#14583275—22no—
18#14583275C2214yescomplemented
19#14583095—24no—
20#14583095C2218yescomplemented
21C2×#13063247—22no—
22C2×C4×C43⋊C8C2211yescharacteristic, complemented
23#14582626C2218yescomplemented
24C2×#127×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2212yescomplemented
26C43×#331C2214yescomplemented
27C24×D43—22no—
28C22×D172—22no—
29C22×D172—21no—
30C22×D172D412yes—
31C22×C22⋊D43—24no—
32C2×D4×D43—28no—
33C2×D4×D43—28no—
34C2×D4×D43—48no—
35C2×D4×D43—48no—
36C22×C4×D43—22no—
37C2×D344—28no—
38C2×D344—48no—
39C2×#10621882—28no—
40C2×#10621882—48no—
41C22×C43⋊C8—21no—
42#13063322—22no—
43#13063322—21no—
44#13063322C2312yescomplemented
45#13063296—28no—
46#13063296—28no—
47#13063293—28no—
48#13063293—28no—
49C4×D172—22no—
50C4×D172—22no—
51C4×D172D414yes—
52C4×D172C2314yes—
53C2×C4⋊Dic43D412yes—
54C2×C22⋊Dic43—22no—
55C2×(C2×D43)⋊C4—22no—
56#13063247—28no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8C2312yescomplemented
59C22×D4×C43—22no—
60C22×D4×C43D412yes—
61C22×C8×C43—22no—
62#127×C43—22no—
63#127×C43D412yes—
64#127×C43C2312yes—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—22no—
67C4⋊C8×C43C2314yescomplemented
68C24×C43—22no—
69C23×D43—22no—
70C23×D43—28no—
71C23×D43—416no—
72C23×D43—41no—
73C23×D43—84no—
74C2×D4×C43—24no—
75C2×D4×C43—22no—
76C2×D4×C43—24no—
77C2×D4×C43—44no—
78C2×D4×C43—44no—
79C2×D4×C43—44no—
80C2×D4×C43C2×D414yes—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D412yes—
83C2×C22⋊D43—216no—
84C2×C22⋊D43—416no—
85C22×Dic43—22no—
86D4×D43—416no—
87D4×D43—432no—
88D4×D43—416no—
89C2×D172—22no—
90C2×D172—24no—
91C2×D172—24no—
92C2×D172—22no—
93C2×D172—41no—
94C2×D172—42no—
95C2×D172—44no—
96C2×D172—44no—
97C2×D172—44no—
98C2×D172D818yescomplemented
99C2×D172C2×D414yes—
100C2×C4×D43—24no—
101C2×C4×D43—24no—
102C2×C4×D43—44no—
103C2×C4×D43—44no—
104C2×C8×C43—24no—
105C2×C8×C43—44no—
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D412yes—
108C42×C43C2411yescharacteristic
109C22⋊Dic43—28no—
110#10621882—416no—
111(C2×D43)⋊C4—24no—
112(C2×D43)⋊C4—24no—
113C4⋊Dic43—22no—
114C4⋊Dic43C2×D414yes—
115C2×C43⋊C8—24no—
116C2×C43⋊C8—22no—
117D344—416no—
118C23×C43—24no—
119C23×C43—48no—
120C23×C43—44no—
121C23×C43#12011yescharacteristic
122C22×D43—24no—
123C22×D43—28no—
124C22×D43—432no—
125C22×D43—44no—
126C22×D43—44no—
127C22×D43—42no—
128C22×D43—88no—
129C22×D43—832no—
130C22×D43—84no—
131C22×D43—82no—
132D4×C43—44no—
133D4×C43—44no—
134D4×C43—44no—
135D4×C43—48no—
136D4×C43—82no—
137C2×C4×C43—22no—
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43#12012yes—
140C2×C4×C43C2×D814yes—
141C2×C4×C43AGL(1,ℤ/8)14yes—
142C2×C4×C43C22×D412yes—
143C2×C4×C43C22×D411yescharacteristic
144C22⋊D43—432no—
145C2×Dic43—24no—
146C2×Dic43—44no—
147D172—24no—
148D172—28no—
149D172—44no—
150D172—44no—
151D172—44no—
152D172—82no—
153D172—84no—
154D172C2×D818yescomplemented
155C4×D43—44no—
156C4×D43—44no—
157C4×D43—48no—
158C8×C43—44no—
159C43⋊C8—24no—
160C2×#1619—431nomaximal, Sylow
161C22×C43—48no—
162C22×C43—44no—
163C22×C43—88no—
164C22×C43#44714yes—
165C22×C43#45312yes—
166C22×C43C2×#12011yescharacteristic
167C2×D43—28no—
168C2×D43—416no—
169C2×D43—44no—
170C2×D43—44no—
171C2×D43—832no—
172C2×D43—84no—
173C2×D43—82no—
174C2×D43—164no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43#44714yes—
178C4×C43C22×D812yes—
179C4×C43C2×AGL(1,ℤ/8)12yes—
180Dic43—44no—
181C2×D42—431no—
182C2×#493—431no—
183C2×#459—432no—
184#1619—438no—
185C2×#331D4311yescharacteristic, complemented
186C2×D4⋊C8—432no—
187C2×C43—84no—
188C2×C43#161914yescomplemented
189C2×C43C2×#44712yes—
190C2×C43C2×#45311yescharacteristic
191D43—48no—
192D43—162no—
193C23×D4—862no—
194C22×D8—862no—
195C22×D8—862no—
196D42—434no—
197D42—864no—
198D42—862no—
199C2×#127—431no—
200C2×#127C2×D4311yescharacteristic
201C2×#121—862no—
202C2×#120—862no—
203C2×C4×D4—432no—
204#493—434no—
205#493—862no—
206#459—438no—
207#459—864no—
208C2×C4⋊C8C2×D4312yescomplemented
209C2×#102—862no—
210C2×C4×C8—431no—
211#331C2×D4314yescomplemented
212D4⋊C8—438no—
213C43C2×#161911yescharacteristic, complemented, Sylow
214C25—862no—
215C22×D4—22no—
216C22×D4—432no—
217C22×D4—868no—
218C22×D4—868no—
219C22×D4—864no—
220C22×D4—861no—
221C22×D4—862no—
222C22×D4—1728no—
223C22×D4—1728no—
224C22×D4D17212yes—
225C23×C4—862no—
226C2×D8—868no—
227C2×D8—868no—
228C2×D8—1728no—
229C2×D8—1728no—
230C22×C8—22no—
231C22×C8—861no—
232#127—22no—
233#127—432no—
234#127—861no—
235#127—862no—
236#127D17212yes—
237#127C22×D4312yes—
238#121—868no—
239#121—868no—
240#120—868no—
241#120—868no—
242C4×D4—434no—
243C4×D4—434no—
244C4×D4—862no—
245C4×D4—862no—
246C2×C4⋊C4—432no—
247C2×C22⋊C4—862no—
248C2×C22⋊C4—862no—
249C2×C42C22×D4311yescharacteristic
250C4⋊C8—22no—
251C4⋊C8C22×D4314yescomplemented
252#102—868no—
253C4×C8—432no—
254C4×C8—861no—
255C24—22no—
256C24—868no—
257C24—862no—
258C24—3444no—
259C24—17216no—
260C24—1721no—
261C2×D4—24no—
262C2×D4—22no—
263C2×D4—24no—
264C2×D4—44no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—438no—
268C2×D4—434no—
269C2×D4—8616no—
270C2×D4—862no—
271C2×D4—864no—
272C2×D4—864no—
273C2×D4—862no—
274C2×D4—1724no—
275C2×D4—17216no—
276C2×D4—17216no—
277C2×D4—17232no—
278C2×D4—17216no—
279C2×D4—1721no—
280C2×D4—1722no—
281C2×D4—1724no—
282C2×D4—1724no—
283C2×D4C2×D17214yes—
284C22×C4—862no—
285C22×C4—864no—
286C22×C4—864no—
287C22×C4—1724no—
288C22×C4—1724no—
289C22×C4C2×D17211yescharacteristic
290C22×C4D4×D4312yes—
291D8—17216no—
292D8—17216no—
293C2×C8—24no—
294C2×C8—44no—
295C2×C8—864no—
296C2×C8—862no—
297C4⋊C4—434no—
298C4⋊C4—862no—
299C22⋊C4—868no—
300C22⋊C4—864no—
301C22⋊C4—864no—
302C42C2×D17211yescharacteristic
303C42D4×D4312yes—
304C42C23×D4311yescharacteristic
305C23—24no—
306C23—44no—
307C23—48no—
308C23—864no—
309C23—868no—
310C23—3448no—
311C23—34432no—
312C23—3442no—
313C23—3444no—
314C23—17232no—
315C23—1722no—
316C23—1724no—
317C23—1724no—
318C23#1306329511yescharacteristic
319D4—44no—
320D4—44no—
321D4—44no—
322D4—48no—
323D4—82no—
324D4—438no—
325D4—864no—
326D4—868no—
327D4—3442no—
328D4—3444no—
329D4—1724no—
330D4—17232no—
331D4—1724no—
332D4—1724no—
333C2×C4—22no—
334C2×C4—864no—
335C2×C4—1724no—
336C2×C4—1724no—
337C2×C4—1724no—
338C2×C4—1728no—
339C2×C4#1306329511yescharacteristic
340C2×C4#1306329512yes—
341C2×C4D8×D4314yes—
342C2×C4#1306335214yes—
343C2×C4C2×D4×D4312yes—
344C2×C4C22×D17211yescharacteristic
345C8—44no—
346C8—864no—
347C22—48no—
348C22—44no—
349C22—88no—
350C22—868no—
351C22—34432no—
352C22—3444no—
353C22—3442no—
354C22—1724no—
355C22—17216no—
356C22—1724no—
357C22—6884no—
358C22#1458303414yes—
359C22#1458306912yes—
360C22C2×#1306329511yescharacteristic
361C4—21no—
362C4—21no—
363C4—1724no—
364C4#1458303414yes—
365C4C2×D8×D4312yes—
366C4C2×#1306335212yes—
367C2—84no—
368C2—1728no—
369C2—6882no—
370C2#1913365014yesdirect product factor
371C2C2×#1458303412yes—
372C2C2×#1458306911yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#331C2
socleC23×C43#120
hypercenterC2×#331D43
hypocenterC43C2×#1619
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. C2×#14583534C2semidirect
2. C2×#14583275C2semidirect
3. C2×#14583095C2semidirect
4. #19133650C2direct (N × H)
5. C2×#14582626C2semidirect
6. C2×C43×#331C2semidirect
12. #14583534C22semidirect
13. C2×#13063322C22semidirect
18. #14583275C22semidirect
20. #14583095C22semidirect
22. C2×C4×C43⋊C8C22semidirect
23. #14582626C22semidirect
25. C2×C4⋊C8×C43C22semidirect
26. C43×#331C22semidirect
44. #13063322C23semidirect
58. C4×C43⋊C8C23semidirect
67. C4⋊C8×C43C23semidirect
98. C2×D172D8semidirect
154. D172C2×D8semidirect
185. C2×#331D43semidirect
188. C2×C43#1619semidirect
208. C2×C4⋊C8C2×D43semidirect
211. #331C2×D43semidirect
213. C43C2×#1619semidirect
251. C4⋊C8C22×D43semidirect
370. C2#19133650direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835342
C2×#145832752
C2×#145830952
#191336502
C2×#145826262
C2×C43×#3312
C2×#161943