Finite Group Databasebeta

← C2×#19134232 #25084335

Subgroups — C2×#19134232 #25084335

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583275C211yesmaximal, characteristic
2C2×#14583251C211yesmaximal, characteristic, complemented
3C2×#14583247C211yesmaximal, characteristic, complemented
4C2×#14583246C211yesmaximal, characteristic, complemented
5C2×#14583245C211yesmaximal, characteristic, complemented
6#19134232C218yesmaximal, direct product factor
7C2×#14582621C211yesmaximal, characteristic, complemented
8C2×C43×#492C211yesmaximal, characteristic, complemented
9C22×#10621882—22no—
10C2×#13063325C2211yescharacteristic
11C2×#13063322C2211yescharacteristic
12#14583275—22no—
13#14583275C2214yes—
14#14583251—22no—
15#14583251C2214yescomplemented
16#14583247—22no—
17#14583247C2214yescomplemented
18#14583246—22no—
19#14583246C2214yescomplemented
20#14583245—22no—
21#14583245C2214yescomplemented
22C2×#13063248—22no—
23C2×#13063247—22no—
24C2×#13063246—22no—
25C2×#13063245—22no—
26C2×C4×C43⋊C8C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582621C2214yescomplemented
29C22×SD16×C43—22no—
30C2×C4⋊Q8×C43C2211yescharacteristic
31C2×#127×C43C2211yescharacteristic
32C43×#492—22no—
33C43×#492C2214yescomplemented
34C2×C4×C8×C43C2211yescharacteristic
35C22×Dic86—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C2×#10621882—28no—
40C2×#10621882—48no—
41C22×C43⋊C8D412yes—
42C22×C43⋊C8D412yes—
43#13063325—21no—
44#13063325—21no—
45#13063325—21no—
46#13063325C2312yes—
47#13063322—21no—
48#13063322—21no—
49#13063322—21no—
50#13063322C2312yes—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53#13063248—28no—
54#13063247—28no—
55#13063246—28no—
56#13063245—28no—
57C4×C43⋊C8D412yes—
58C4×C43⋊C8D412yes—
59C4×C43⋊C8C2312yes—
60C4×C43⋊C8C2312yes—
61C22×Q8×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C2×SD16×C43—28no—
66C2×SD16×C43—48no—
67C22×C8×C43D412yes—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43—21no—
70C4⋊Q8×C43—21no—
71C4⋊Q8×C43C2312yes—
72#127×C43—21no—
73#127×C43—21no—
74#127×C43—21no—
75#127×C43C2312yes—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4×C8×C43D412yes—
80C4×C8×C43C2312yes—
81C24×C43—41no—
82C23×D43—41no—
83C2×Q8×C43—22no—
84C2×Q8×C43—41no—
85C2×Q8×C43—44no—
86C2×D4×C43—22no—
87C2×D4×C43—22no—
88C2×D4×C43—22no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—44no—
93C2×D4×C43—44no—
94C2×D4×C43—44no—
95C22×C4×C43—41no—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×Dic43—41no—
100C2×D172—22no—
101C2×D172—22no—
102C2×D172—22no—
103C2×D172—41no—
104C2×D172—41no—
105C2×D172—41no—
106C2×D172—44no—
107C2×D172—44no—
108C2×D172—44no—
109C2×Dic86—22no—
110C2×Dic86—44no—
111C2×Dic86—41no—
112SD16×C43—416no—
113C2×C8×C43—24no—
114C2×C8×C43C2×D414yes—
115C4⋊C4×C43—22no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43C2411yescharacteristic
123#10621882—416no—
124C4⋊Dic43—22no—
125C4⋊Dic43—22no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C2×C43⋊C8—24no—
129C2×C43⋊C8—24no—
130C2×C43⋊C8C2×D414yes—
131C2×C43⋊C8C2×D414yes—
132C23×C43—42no—
133C23×C43—82no—
134C23×C43—82no—
135C23×C43—82no—
136C23×C43#12711yescharacteristic
137C22×D43—42no—
138C22×D43—82no—
139C22×D43—82no—
140C22×D43—82no—
141Q8×C43—44no—
142Q8×C43—82no—
143D4×C43—44no—
144D4×C43—44no—
145D4×C43—44no—
146D4×C43—82no—
147D4×C43—82no—
148D4×C43—82no—
149C2×C4×C43—42no—
150C2×C4×C43—82no—
151C2×C4×C43#12711yescharacteristic
152C2×C4×C43#12711yescharacteristic
153C2×C4×C43#12711yescharacteristic
154C2×C4×C43#13514yes—
155C2×C4×C43AGL(1,ℤ/8)14yes—
156C2×C4×C43AGL(1,ℤ/8)14yes—
157C2×C4×C43C22×D411yescharacteristic
158C2×C4×C43C22×D411yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×Dic43—42no—
161C2×Dic43—82no—
162D172—44no—
163D172—44no—
164D172—44no—
165D172—82no—
166D172—82no—
167D172—82no—
168Dic86—44no—
169Dic86—82no—
170C8×C43—24no—
171C43⋊C8—24no—
172C43⋊C8—24no—
173C2×#1717—431nomaximal, Sylow
174C22×C43—82no—
175C22×C43—82no—
176C22×C43—82no—
177C22×C43—164no—
178C22×C43#49512yes—
179C22×C43#49612yes—
180C22×C43#49612yes—
181C22×C43C2×#12711yescharacteristic
182C2×D43—82no—
183C2×D43—82no—
184C2×D43—82no—
185C2×D43—164no—
186C4×C43—82no—
187C4×C43#49512yes—
188C4×C43#49612yes—
189C4×C43#49612yes—
190C4×C43C2×#13512yes—
191C4×C43C2×AGL(1,ℤ/8)12yes—
192C4×C43C2×AGL(1,ℤ/8)12yes—
193Dic43—82no—
194C2×#493—431no—
195C2×#492D4311yescharacteristic, complemented
196C2×#487—431no—
197C2×#486—431no—
198C2×#486—431no—
199C2×#486—431no—
200#1717—438no—
201C2×#322—431no—
202C2×C43—162no—
203C2×C43#171714yescomplemented
204C2×C43C2×#49511yescharacteristic
205C2×C43C2×#49611yescharacteristic
206C2×C43C2×#49611yescharacteristic
207D43—162no—
208C22×SD16—22no—
209C22×D8—862no—
210C2×C4⋊Q8—431no—
211C2×C4⋊Q8C2×D4311yescharacteristic
212C2×#127—431no—
213C2×#127C2×D4311yescharacteristic
214#493—434no—
215#493—862no—
216#492—22no—
217#492C2×D4314yescomplemented
218#487—434no—
219#487—862no—
220#486—434no—
221#486—434no—
222#486—434no—
223#486—862no—
224#486—862no—
225#486—862no—
226C2×#103—862no—
227C2×#102—862no—
228C2×#102—862no—
229C2×#102—862no—
230C2×C4×C8—431no—
231C2×C4×C8—431no—
232C2×C4×C8C2×D4311yescharacteristic
233#322—434no—
234C43C2×#171711yescharacteristic, complemented, Sylow
235C22×Q8—21no—
236C22×Q8—861no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—861no—
241C22×D4—861no—
242C22×D4—861no—
243C2×SD16—28no—
244C2×SD16—48no—
245C2×D8—868no—
246C2×D8—1728no—
247C22×C8—432no—
248C22×C8—432no—
249C22×C8C22⋊D4312yes—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—432no—
254C4⋊Q8—861no—
255C4⋊Q8—861no—
256C4⋊Q8—861no—
257C4⋊Q8C22×D4312yes—
258#127—21no—
259#127—21no—
260#127—21no—
261#127—432no—
262#127—861no—
263#127—861no—
264#127—861no—
265#127C22×D4312yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C42C22×D4311yescharacteristic
271#103—868no—
272#102—868no—
273#102—868no—
274#102—868no—
275C4×C8—432no—
276C4×C8—432no—
277C4×C8—432no—
278C4×C8—432no—
279C4×C8C22⋊D4312yes—
280C4×C8C22×D4312yes—
281C24—41no—
282C24—1721no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—44no—
286C2×Q8—862no—
287C2×Q8—1724no—
288C2×Q8—1721no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—44no—
296C2×D4—44no—
297C2×D4—44no—
298C2×D4—862no—
299C2×D4—862no—
300C2×D4—862no—
301C2×D4—1721no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1724no—
305C2×D4—1724no—
306C2×D4—1724no—
307C22×C4—41no—
308C22×C4—1721no—
309C22×C4D4×D4311yescharacteristic
310C22×C4D4×D4311yescharacteristic
311C22×C4C2×C22⋊D4311yescharacteristic
312SD16—416no—
313D8—17216no—
314C2×C8—24no—
315C2×C8—434no—
316C2×C8—434no—
317C2×C8—864no—
318C2×C8—864no—
319C2×C8C2×C22⋊D4314yes—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—862no—
325C4⋊C4—862no—
326C4⋊C4—1721no—
327C4⋊C4—1721no—
328C42D4×D4311yescharacteristic
329C42D4×D4311yescharacteristic
330C42C2×C22⋊D4311yescharacteristic
331C42C23×D4311yescharacteristic
332C23—42no—
333C23—82no—
334C23—82no—
335C23—82no—
336C23—3442no—
337C23—3442no—
338C23—3442no—
339C23—1722no—
340C23#1306332111yescharacteristic
341Q8—44no—
342Q8—82no—
343Q8—3442no—
344Q8—1724no—
345D4—44no—
346D4—44no—
347D4—44no—
348D4—82no—
349D4—82no—
350D4—82no—
351D4—3442no—
352D4—3442no—
353D4—3442no—
354D4—1724no—
355D4—1724no—
356D4—1724no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—3442no—
360C2×C4—1722no—
361C2×C4#1306332111yescharacteristic
362C2×C4#1306332111yescharacteristic
363C2×C4#1306332111yescharacteristic
364C2×C4#1306334614yes—
365C2×C4#1306335114yes—
366C2×C4#1306335214yes—
367C2×C4C2×D4×D4311yescharacteristic
368C2×C4C2×D4×D4311yescharacteristic
369C2×C4C22×C22⋊D4311yescharacteristic
370C8—24no—
371C8—864no—
372C8—864no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—164no—
377C22—3442no—
378C22—3442no—
379C22—3442no—
380C22—6884no—
381C22#1458328012yes—
382C22#1458328512yes—
383C22#1458328612yes—
384C22C2×#1306332111yescharacteristic
385C4—82no—
386C4—3442no—
387C4#1458328012yes—
388C4#1458328512yes—
389C4#1458328612yes—
390C4C2×#1306334612yes—
391C4C2×#1306335112yes—
392C4C2×#1306335212yes—
393C2—162no—
394C2—6882no—
395C2#1913423214yesdirect product factor
396C2C2×#1458328011yescharacteristic
397C2C2×#1458328511yescharacteristic
398C2C2×#1458328611yescharacteristic
subgroupG/H
centerC23#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#492C2
socleC23×C43#127
prime radicalC2×#14583275C2
hypercenterC2×#492D43
hypocenterC43C2×#1717
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
2. C2×#14583251C2semidirect
3. C2×#14583247C2semidirect
4. C2×#14583246C2semidirect
5. C2×#14583245C2semidirect
6. #19134232C2direct (N × H)
7. C2×#14582621C2semidirect
8. C2×C43×#492C2semidirect
15. #14583251C22semidirect
17. #14583247C22semidirect
19. #14583246C22semidirect
21. #14583245C22semidirect
28. #14582621C22semidirect
33. C43×#492C22semidirect
195. C2×#492D43semidirect
203. C2×C43#1717semidirect
217. #492C2×D43semidirect
234. C43C2×#1717semidirect
395. C2#19134232direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832752
C2×#145832512
C2×#145832472
C2×#145832462
C2×#145832452
#191342322
C2×#145826212
C2×C43×#4922
C2×#171743