Finite Group Databasebeta

← C2×#19134199 #25084263

Subgroups — C2×#19134199 #25084263

Order 11008.

982 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×#14583278C211yesmaximal, characteristic, complemented
2C2×#14583275C211yesmaximal, characteristic
3C2×#14583247C211yesmaximal, characteristic, complemented
4C2×#14583246C211yesmaximal, characteristic, complemented
5C2×#14583245C211yesmaximal, characteristic, complemented
6#19134199C218yesmaximal, direct product factor
7C2×C8×C43⋊C8C211yesmaximal, characteristic, complemented
8C2×C43×#486C211yesmaximal, characteristic, complemented
9C22×#10621885—22no—
10C22×#10621882—22no—
11C2×#13063325C2211yescharacteristic
12C2×#13063322C2211yescharacteristic
13#14583278—22no—
14#14583278C2214yescomplemented
15#14583275—22no—
16#14583275C2214yes—
17#14583247—22no—
18#14583247C2214yescomplemented
19#14583246—22no—
20#14583246C2214yescomplemented
21#14583245—22no—
22#14583245C2214yescomplemented
23C2×#13063247—22no—
24C2×#13063246—22no—
25C2×#13063245—22no—
26C2×C4×C43⋊C8C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28C8×C43⋊C8C2214yescomplemented
29C2×C4⋊Q8×C43C2211yescharacteristic
30C2×#127×C43C2211yescharacteristic
31C43×#486—22no—
32C43×#486C2214yescomplemented
33C2×#102×C43—22no—
34C2×C4×C8×C43C2211yescharacteristic
35C22×Dic86—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C2×#10621885—28no—
40C2×#10621885—48no—
41C2×#10621882—28no—
42C2×#10621882—48no—
43C22×C43⋊C8D412yes—
44C22×C43⋊C8D412yes—
45#13063325—21no—
46#13063325—21no—
47#13063325—21no—
48#13063325C2312yes—
49#13063322—21no—
50#13063322—21no—
51#13063322—21no—
52#13063322C2312yes—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55#13063247—28no—
56#13063246—28no—
57#13063245—28no—
58C4×C43⋊C8D412yes—
59C4×C43⋊C8D412yes—
60C4×C43⋊C8C2312yes—
61C4×C43⋊C8C2312yes—
62C22×Q8×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×C8×C43D412yes—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43—21no—
70C4⋊Q8×C43C2312yes—
71#127×C43—21no—
72#127×C43—21no—
73#127×C43—21no—
74#127×C43C2312yes—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C42×C43C2311yescharacteristic
78#102×C43—28no—
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—
112C2×C8×C43—24no—
113C2×C8×C43C2×D414yes—
114C4⋊C4×C43—22no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2411yescharacteristic
122#10621885—416no—
123#10621882—416no—
124C4⋊Dic43—22no—
125C4⋊Dic43—22no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C2×C43⋊C8—24no—
129C2×C43⋊C8D818yes—
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×C43C2×D814yes—
155C2×C4×C43#13514yes—
156C2×C4×C43#13514yes—
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⋊C8C2×D818yes—
173C2×#1709—431nomaximal, Sylow
174C22×C43—82no—
175C22×C43—82no—
176C22×C43—82no—
177C22×C43—164no—
178C22×C43#49312yes—
179C22×C43#49512yes—
180C22×C43#49512yes—
181C22×C43C2×#12711yescharacteristic
182C2×D43—82no—
183C2×D43—82no—
184C2×D43—82no—
185C2×D43—164no—
186C4×C43—82no—
187C4×C43#49312yes—
188C4×C43#49512yes—
189C4×C43#49512yes—
190C4×C43C22×D812yes—
191C4×C43C2×#13512yes—
192C4×C43C2×#13512yes—
193Dic43—82no—
194C2×#494—431no—
195C2×#493—431no—
196C2×#486—431no—
197C2×#486—431no—
198C2×#486—431no—
199C2×#486D4311yescharacteristic, complemented
200#1709—438no—
201C2×C82—431no—
202C2×C43—162no—
203C2×C43#170914yescomplemented
204C2×C43C2×#49311yescharacteristic
205C2×C43C2×#49511yescharacteristic
206C2×C43C2×#49511yescharacteristic
207D43—162no—
208C22×Q16—862no—
209C22×D8—862no—
210C2×C4⋊Q8—431no—
211C2×C4⋊Q8C2×D4311yescharacteristic
212C2×#127—431no—
213C2×#127C2×D4311yescharacteristic
214#494—434no—
215#494—862no—
216#493—434no—
217#493—862no—
218#486—22no—
219#486—434no—
220#486—434no—
221#486—434no—
222#486—862no—
223#486—862no—
224#486—862no—
225#486C2×D4314yescomplemented
226C2×#102—22no—
227C2×#102—862no—
228C2×#102—862no—
229C2×#102—862no—
230C2×C4×C8—431no—
231C2×C4×C8—431no—
232C2×C4×C8C2×D4311yescharacteristic
233C82—434no—
234C43C2×#170911yescharacteristic, 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×Q16—868no—
244C2×Q16—1728no—
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#102—28no—
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
312Q16—17216no—
313D8—17216no—
314C2×C8—24no—
315C2×C8—438no—
316C2×C8—434no—
317C2×C8—434no—
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×C4D8×D4314yes—
365C2×C4#1306334514yes—
366C2×C4#1306334614yes—
367C2×C4C2×D4×D4311yescharacteristic
368C2×C4C2×D4×D4311yescharacteristic
369C2×C4C22×C22⋊D4311yescharacteristic
370C8—24no—
371C8—438no—
372C8—864no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—164no—
377C22—3442no—
378C22—3442no—
379C22—3442no—
380C22—6884no—
381C22#1458327412yes—
382C22#1458328012yes—
383C22#1458328112yes—
384C22C2×#1306332111yescharacteristic
385C4—82no—
386C4—3442no—
387C4#1458327412yes—
388C4#1458328012yes—
389C4#1458328112yes—
390C4C2×D8×D4312yes—
391C4C2×#1306334512yes—
392C4C2×#1306334612yes—
393C2—162no—
394C2—6882no—
395C2#1913419914yesdirect product factor
396C2C2×#1458327411yescharacteristic
397C2C2×#1458328011yescharacteristic
398C2C2×#1458328111yescharacteristic
subgroupG/H
centerC23#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#486C2
socleC23×C43#127
prime radicalC2×#14583275C2
hypercenterC2×#486D43
hypocenterC43C2×#1709
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#14583278C2semidirect
3. C2×#14583247C2semidirect
4. C2×#14583246C2semidirect
5. C2×#14583245C2semidirect
6. #19134199C2direct (N × H)
7. C2×C8×C43⋊C8C2semidirect
8. C2×C43×#486C2semidirect
14. #14583278C22semidirect
18. #14583247C22semidirect
20. #14583246C22semidirect
22. #14583245C22semidirect
28. C8×C43⋊C8C22semidirect
32. C43×#486C22semidirect
199. C2×#486D43semidirect
203. C2×C43#1709semidirect
225. #486C2×D43semidirect
234. C43C2×#1709semidirect
395. C2#19134199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832782
C2×#145832752
C2×#145832472
C2×#145832462
C2×#145832452
#191341992
C2×C8×C43⋊C82
C2×C43×#4862
C2×#170943