Finite Group Databasebeta

← C2×#19133712 #25072208

Subgroups — C2×#19133712 #25072208

Order 11008.

1722 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1722 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
2C2×#14583271C211yesmaximal, characteristic, complemented
3C2×#14583190C212yesmaximal, complemented
4#19133712C218yesmaximal, direct product factor
5C2×#14582626C212yesmaximal, complemented
6C2×C43×#331C211yesmaximal, characteristic, complemented
7C22×D4×D43—22no—
8C22×#10621883—22no—
9#14583534—24no—
10#14583534—22no—
11#14583534C2214yes—
12C2×#13063325C2211yescharacteristic, complemented
13C2×#13063296—22no—
14C2×#13063293—22no—
15C2×C4×D172C2212yes—
16#14583271—22no—
17#14583271C2214yescomplemented
18#14583190—24no—
19#14583190C2218yescomplemented
20C2×#13063257—22no—
21C2×#13063247—22no—
22C2×C4×C43⋊C8C2211yescharacteristic, complemented
23#14582626C2218yescomplemented
24C2×#127×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2212yescomplemented
26C43×#331C2214yescomplemented
27C24×D43—22no—
28C22×Dic86—21no—
29C22×D172D412yes—
30C22×C22⋊D43—24no—
31C2×D4×D43—28no—
32C2×D4×D43—28no—
33C2×D4×D43—48no—
34C2×D4×D43—48no—
35C22×C4×D43—22no—
36C2×#10621883—28no—
37C2×#10621883—48no—
38C22×C43⋊C8—21no—
39#13063325—22no—
40#13063325—21no—
41#13063325C2312yescomplemented
42#13063296—28no—
43#13063296—28no—
44#13063293—28no—
45#13063293—28no—
46C4×D172—22no—
47C4×D172—22no—
48C4×D172D414yes—
49C4×D172C2314yes—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43D412yes—
52C2×C22⋊Dic43—22no—
53C2×(C2×D43)⋊C4—22no—
54#13063257—28no—
55#13063247—28no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8C2312yescomplemented
58C22×D4×C43—22no—
59C22×D4×C43D412yes—
60C22×C8×C43—22no—
61#127×C43—22no—
62#127×C43D412yes—
63#127×C43C2312yes—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—22no—
66C4⋊C8×C43C2314yescomplemented
67C24×C43—22no—
68C23×D43—22no—
69C23×D43—28no—
70C23×D43—416no—
71C23×D43—84no—
72C2×D4×C43—24no—
73C2×D4×C43—22no—
74C2×D4×C43—24no—
75C2×D4×C43—44no—
76C2×D4×C43—44no—
77C2×D4×C43—44no—
78C2×D4×C43C2×D414yes—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D412yes—
81C2×C22⋊D43—216no—
82C2×C22⋊D43—416no—
83C22×Dic43—22no—
84C22×Dic43—41no—
85D4×D43—416no—
86D4×D43—432no—
87D4×D43—416no—
88C2×D172—22no—
89C2×D172—24no—
90C2×D172SD1618yescomplemented
91C2×D172C2×D414yes—
92C2×C4×D43—24no—
93C2×C4×D43—24no—
94C2×C4×D43—44no—
95C2×C4×D43—44no—
96C2×Dic86—22no—
97C2×Dic86—44no—
98C2×Dic86—41no—
99C2×C8×C43—24no—
100C2×C8×C43—44no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D412yes—
103C42×C43C2411yescharacteristic
104C22⋊Dic43—28no—
105#10621883—416no—
106(C2×D43)⋊C4—24no—
107(C2×D43)⋊C4—24no—
108C4⋊Dic43—22no—
109C4⋊Dic43—24no—
110C4⋊Dic43—42no—
111C4⋊Dic43C2×D414yes—
112C2×C43⋊C8—24no—
113C2×C43⋊C8—22no—
114C23×C43—24no—
115C23×C43—48no—
116C23×C43—44no—
117C23×C43#12011yescharacteristic
118C22×D43—24no—
119C22×D43—28no—
120C22×D43—432no—
121C22×D43—44no—
122C22×D43—44no—
123C22×D43—88no—
124C22×D43—832no—
125D4×C43—44no—
126D4×C43—44no—
127D4×C43—44no—
128D4×C43—48no—
129D4×C43—82no—
130C2×C4×C43—22no—
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43#12012yes—
133C2×C4×C43C2×SD1614yes—
134C2×C4×C43AGL(1,ℤ/8)14yes—
135C2×C4×C43C22×D412yes—
136C2×C4×C43C22×D411yescharacteristic
137C22⋊D43—432no—
138C2×Dic43—24no—
139C2×Dic43—44no—
140C2×Dic43—42no—
141C2×Dic43—82no—
142D172—24no—
143D172—28no—
144D172C2×SD1618yescomplemented
145C4×D43—44no—
146C4×D43—44no—
147C4×D43—48no—
148Dic86—44no—
149Dic86—82no—
150C8×C43—44no—
151C43⋊C8—24no—
152C2×#1629—431nomaximal, Sylow
153C22×C43—48no—
154C22×C43—44no—
155C22×C43—88no—
156C22×C43#45014yes—
157C22×C43#45312yes—
158C22×C43C2×#12011yescharacteristic
159C2×D43—28no—
160C2×D43—416no—
161C2×D43—44no—
162C2×D43—44no—
163C2×D43—832no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43#45014yes—
167C4×C43C22×SD1612yes—
168C4×C43C2×AGL(1,ℤ/8)12yes—
169Dic43—44no—
170Dic43—82no—
171C2×D42—431no—
172C2×#492—431no—
173C2×#476—432no—
174#1629—438no—
175C2×#331D4311yescharacteristic, complemented
176C2×D4⋊C8—432no—
177C2×C43—84no—
178C2×C43#162914yescomplemented
179C2×C43C2×#45012yes—
180C2×C43C2×#45311yescharacteristic
181D43—48no—
182C23×D4—862no—
183C22×SD16—862no—
184D42—434no—
185D42—864no—
186D42—862no—
187C2×C4⋊Q8—431no—
188C2×#127C2×D4311yescharacteristic
189C2×#121—862no—
190C2×#120—862no—
191C2×C4×D4—432no—
192#492—434no—
193#492—862no—
194#476—438no—
195#476—864no—
196C2×#106—862no—
197C2×C4⋊C8C2×D4312yescomplemented
198C2×#102—862no—
199C2×C4×C8—431no—
200#331C2×D4314yescomplemented
201D4⋊C8—438no—
202C43C2×#162911yescharacteristic, complemented, Sylow
203C25—862no—
204C22×Q8—861no—
205C22×D4—22no—
206C22×D4—432no—
207C22×D4—868no—
208C22×D4—868no—
209C22×D4—864no—
210C22×D4—1728no—
211C22×D4—1728no—
212C22×D4D17212yes—
213C23×C4—862no—
214C2×SD16—868no—
215C2×SD16—1728no—
216C22×C8—22no—
217C22×C8—861no—
218C4⋊Q8—432no—
219C4⋊Q8—861no—
220C4⋊Q8—862no—
221#127—22no—
222#127D17212yes—
223#127C22×D4312yes—
224#121—868no—
225#121—868no—
226#120—868no—
227#120—868no—
228C4×D4—434no—
229C4×D4—434no—
230C4×D4—862no—
231C4×D4—862no—
232C2×C4⋊C4—432no—
233C2×C4⋊C4—862no—
234C2×C22⋊C4—862no—
235C2×C22⋊C4—862no—
236C2×C42C22×D4311yescharacteristic
237#106—868no—
238C4⋊C8—22no—
239C4⋊C8C22×D4314yescomplemented
240#102—868no—
241C4×C8—432no—
242C4×C8—861no—
243C24—22no—
244C24—868no—
245C24—862no—
246C24—3444no—
247C24—17216no—
248C2×Q8—862no—
249C2×Q8—1724no—
250C2×Q8—1721no—
251C2×D4—24no—
252C2×D4—22no—
253C2×D4—24no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—438no—
258C2×D4—434no—
259C2×D4—8616no—
260C2×D4—862no—
261C2×D4—864no—
262C2×D4—17216no—
263C2×D4—17232no—
264C2×D4—17216no—
265C2×D4—17216no—
266C2×D4C2×D17214yes—
267C22×C4—862no—
268C22×C4—864no—
269C22×C4—864no—
270C22×C4—1721no—
271C22×C4—1724no—
272C22×C4—1724no—
273C22×C4C2×D17211yescharacteristic
274C22×C4D4×D4312yes—
275SD16—17216no—
276C2×C8—24no—
277C2×C8—44no—
278C2×C8—864no—
279C2×C8—862no—
280C4⋊C4—434no—
281C4⋊C4—862no—
282C4⋊C4—864no—
283C4⋊C4—1722no—
284C22⋊C4—868no—
285C22⋊C4—864no—
286C22⋊C4—864no—
287C42C2×D17211yescharacteristic
288C42D4×D4312yes—
289C42C23×D4311yescharacteristic
290C23—24no—
291C23—48no—
292C23—44no—
293C23—868no—
294C23—864no—
295C23—3448no—
296C23—34432no—
297C23—17232no—
298C23—1724no—
299C23—1724no—
300C23#1306329511yescharacteristic
301Q8—3442no—
302Q8—1724no—
303D4—44no—
304D4—48no—
305D4—44no—
306D4—44no—
307D4—82no—
308D4—438no—
309D4—868no—
310D4—864no—
311D4—17232no—
312C2×C4—22no—
313C2×C4—864no—
314C2×C4—3442no—
315C2×C4—1722no—
316C2×C4—1724no—
317C2×C4—1728no—
318C2×C4—1724no—
319C2×C4—1724no—
320C2×C4#1306329511yescharacteristic
321C2×C4#1306329512yes—
322C2×C4SD16×D4314yes—
323C2×C4#1306334914yes—
324C2×C4C2×D4×D4312yes—
325C2×C4C22×D17211yescharacteristic
326C8—44no—
327C8—864no—
328C22—48no—
329C22—44no—
330C22—88no—
331C22—868no—
332C22—34432no—
333C22—17216no—
334C22—1724no—
335C22—1724no—
336C22#1458305114yes—
337C22#1458306912yes—
338C22C2×#1306329511yescharacteristic
339C4—21no—
340C4—21no—
341C4—3442no—
342C4—1724no—
343C4#1458305114yes—
344C4C2×SD16×D4312yes—
345C4C2×#1306334912yes—
346C2—84no—
347C2—1728no—
348C2#1913371214yesdirect product factor
349C2C2×#1458305112yes—
350C2C2×#1458306911yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#331C2
socleC23×C43#120
prime radicalC2×#14583534C2
hypercenterC2×#331D43
hypocenterC43C2×#1629
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
2. C2×#14583271C2semidirect
3. C2×#14583190C2semidirect
4. #19133712C2direct (N × H)
5. C2×#14582626C2semidirect
6. C2×C43×#331C2semidirect
12. C2×#13063325C22semidirect
17. #14583271C22semidirect
19. #14583190C22semidirect
22. C2×C4×C43⋊C8C22semidirect
23. #14582626C22semidirect
25. C2×C4⋊C8×C43C22semidirect
26. C43×#331C22semidirect
41. #13063325C23semidirect
57. C4×C43⋊C8C23semidirect
66. C4⋊C8×C43C23semidirect
90. C2×D172SD16semidirect
144. D172C2×SD16semidirect
175. C2×#331D43semidirect
178. C2×C43#1629semidirect
197. C2×C4⋊C8C2×D43semidirect
200. #331C2×D43semidirect
202. C43C2×#1629semidirect
239. C4⋊C8C22×D43semidirect
348. C2#19133712direct (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×#145832712
C2×#145831902
#191337122
C2×#145826262
C2×C43×#3312
C2×#162943