Finite Group Databasebeta

← C2×#19145175 #25966334

Subgroups — C2×#19145175 #25966334

Order 11008.

2566 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583450C212yesmaximal, complemented
2#19145175C2116yesmaximal, direct product factor
3C2×#14583276C211yesmaximal, characteristic, complemented
4C2×#14583247C212yesmaximal, complemented
5C2×#14583136C214yesmaximal, complemented
6C2×#14582981C214yesmaximal, complemented
7C2×C4×C8×D43C211yesmaximal, characteristic, complemented
8C2×C43×#500C211yesmaximal, characteristic, complemented
9C22×#10621902—22no—
10C22×D344C2214yes—
11C22×C8×D43C2212yes—
12#14583450—28no—
13#14583450C22116yescomplemented
14C2×#13063322C2212yes—
15C2×#13063314—22no—
16C2×#13063300—22no—
17C2×#13063300C2214yes—
18C2×#13063287—22no—
19C2×#13063287C2214yes—
20C2×C42×D43C2211yescharacteristic
21#14583276C2218yescomplemented
22#14583247C22116yescomplemented
23#14583136C22132yescomplemented
24#14582981C22132yescomplemented
25C2×#13063245C2218yes—
26C2×C4×C43⋊C8C2211yescharacteristic
27C2×C8×Dic43C2212yes—
28C4×C8×D43C2218yescomplemented
29C2×C4⋊Q8×C43C2212yes—
30C43×#500C2218yescomplemented
31C2×#107×C43C2214yes—
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621902—216no—
34C2×#10621902—416no—
35C22×D172—24no—
36C22×D172—22no—
37C22×D172—22no—
38C22×D172C2314yes—
39C22×C4×D43—24no—
40C22×C4×D43D411yescharacteristic
41C22×C4×D43D411yescharacteristic
42C22×C4×D43C2311yescharacteristic
43C2×D344—216no—
44C2×D344C23116yes—
45C22×C43⋊C8C2312yes—
46C2×C8×D43—28no—
47C2×C8×D43C2318yes—
48#13063322—24no—
49#13063322C2318yes—
50#13063314—216no—
51#13063300—216no—
52#13063300—28no—
53#13063300C23116yes—
54#13063287—216no—
55#13063287—28no—
56#13063287C23116yes—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—24no—
59C2×C4×Dic43D411yescharacteristic
60C2×C4×Dic43D411yescharacteristic
61C2×C4×Dic43C2311yescharacteristic
62C42×D43D414yes—
63C42×D43C2314yes—
64#13063245C23132yes—
65C4×C43⋊C8C2314yes—
66C8×Dic43C2318yes—
67C22×Q8×C43—22no—
68C22×C8×C43C2312yes—
69C4⋊Q8×C43—24no—
70C4⋊Q8×C43C2318yes—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43C2314yes—
73C2×C42×C43C2311yescharacteristic
74#107×C43C23116yes—
75C4×C8×C43C2314yes—
76C23×D43—24no—
77C23×D43C2×D411yescharacteristic
78C2×Q8×C43—28no—
79C2×Q8×C43—48no—
80C22×C4×C43—24no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2411yescharacteristic
84C22×Dic43C2×D411yescharacteristic
85C22×Dic43C2×D411yescharacteristic
86C22×Dic43C2×D411yescharacteristic
87#10621902—464no—
88C2×D172—24no—
89C2×D172—28no—
90C2×D172—28no—
91C2×D172—216no—
92C2×D172—216no—
93C2×D172—48no—
94C2×D172—48no—
95C2×D172—416no—
96C2×D172C2418yes—
97C2×C4×D43—24no—
98C2×C4×D43—24no—
99C2×C4×D43—216no—
100C2×C4×D43—416no—
101C2×C4×D43D818yescomplemented
102C2×C4×D43C2×D412yes—
103C2×C4×D43C2×D414yes—
104C2×C4×D43C2×D414yes—
105C2×C4×D43C2412yes—
106C2×C8×C43#4118yescomplemented
107C2×C8×C43C2414yes—
108C4⋊C4×C43—28no—
109C4⋊C4×C43—24no—
110C4⋊C4×C43C2418yes—
111C42×C43C2×D412yes—
112C42×C43C2412yes—
113(C2×D43)⋊C4—216no—
114(C2×D43)⋊C4—216no—
115C4×Dic43C2×D412yes—
116C4×Dic43C2×D414yes—
117C4×Dic43C2×D414yes—
118C4×Dic43C2412yes—
119C2×C43⋊C8—24no—
120C2×C43⋊C8C2414yes—
121D344—232no—
122C8×D43—216no—
123C23×C43C22×D411yescharacteristic
124C22×D43—22no—
125C22×D43—22no—
126C22×D43—28no—
127C22×D43—48no—
128C22×D43—48no—
129C22×D43—48no—
130C22×D43C2×D814yes—
131C22×D43C22×D412yes—
132Q8×C43—416no—
133C2×C4×C43—28no—
134C2×C4×C43—48no—
135C2×C4×C43C2×D814yes—
136C2×C4×C43#13514yes—
137C2×C4×C43C22×D411yescharacteristic
138C2×C4×C43C22×D412yes—
139C2×C4×C43C22×D412yes—
140C2×C4×C43C2×#4114yes—
141C2×C4×C43C2511yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43C2×D814yes—
145C2×Dic43C22×D412yes—
146C2×Dic43C22×D412yes—
147C2×Dic43C22×D412yes—
148D172—216no—
149D172—432no—
150D172—48no—
151D172—416no—
152D172—416no—
153C4×D43—24no—
154C4×D43—28no—
155C4×D43—24no—
156C4×D43—432no—
157C4×D43C2×D8116yescomplemented
158C8×C43C2×#4118yescomplemented
159C43⋊C8—24no—
160C2×#3169—431nomaximal, Sylow
161C22×C43#53212yes—
162C22×C43C22×D812yes—
163C22×C43C2×#13512yes—
164C22×C43C23×D411yescharacteristic
165C2×D43—28no—
166C2×D43—22no—
167C2×D43—22no—
168C2×D43—48no—
169C2×D43—48no—
170C2×D43—48no—
171C2×D43—816no—
172C2×D43C22×D814yes—
173C4×C43—48no—
174C4×C43#53212yes—
175C4×C43C22×D814yes—
176C4×C43C2×#13514yes—
177C4×C43C22×#4112yes—
178Dic43—22no—
179Dic43—22no—
180Dic43C22×D814yes—
181C2×#532—432no—
182#3169—4316no—
183C2×#500D4311yescharacteristic, complemented
184C2×#493—431no—
185C2×#486—432no—
186C2×#466—434no—
187C2×C4×D8—434no—
188C22×C4×C8—431no—
189C2×C43#316914yescomplemented
190C2×C43C2×#53211yescharacteristic
191C2×C43C23×D811yescharacteristic
192C2×C43C22×#13511yescharacteristic
193D43—24no—
194D43—88no—
195C22×#41—862no—
196C22×D8—434no—
197C23×C8—432no—
198#532—4316no—
199#532—868no—
200C2×C4⋊Q8C2×D4312yes—
201C2×#127—432no—
202C2×#124—862no—
203C2×#121—434no—
204C2×#121—862no—
205C2×C4×D4—434no—
206C2×C4×D4—862no—
207C22×C42—431no—
208#500C2×D4318yescomplemented
209#493—438no—
210#486—4316no—
211#466—4332no—
212C4×D8—4332no—
213C2×#107C2×D4314yes—
214C2×#102—438no—
215C2×C4×C8—432no—
216C2×C4×C8—431no—
217C2×C4×C8—438no—
218C2×C4×C8C2×D4311yescharacteristic
219C43C2×#316911yescharacteristic, complemented, Sylow
220C2×#41—8616no—
221C2×#41—17216no—
222C22×Q8—22no—
223C22×D4—434no—
224C22×D4—864no—
225C22×D4—862no—
226C22×D4—862no—
227C23×C4—431no—
228C23×C4—431no—
229C23×C4—431no—
230C23×C4—864no—
231C2×D8—4316no—
232C2×D8—8616no—
233C22×C8—432no—
234C22×C8—438no—
235C22×C8—868no—
236C22×C8C22×D4312yes—
237C4⋊Q8—24no—
238C4⋊Q8C22×D4318yes—
239#127—438no—
240#127—864no—
241#124—8616no—
242#121—4316no—
243#121—868no—
244#121—8616no—
245C4×D4—4316no—
246C4×D4—868no—
247C4×D4—8616no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C22×D4314yes—
250C2×C22⋊C4—864no—
251C2×C22⋊C4—864no—
252C2×C42—431no—
253C2×C42—431no—
254C2×C42—431no—
255C2×C42—434no—
256C2×C42—434no—
257C2×C42C22×D4311yescharacteristic
258#107C22×D43116yes—
259#102—4332no—
260C4×C8—438no—
261C4×C8—434no—
262C4×C8C22×D4314yes—
263C24—431no—
264C24—864no—
265#41—17264no—
266C2×Q8—28no—
267C2×Q8—48no—
268C2×D4—438no—
269C2×D4—8616no—
270C2×D4—868no—
271C2×D4—864no—
272C2×D4—868no—
273C2×D4—8616no—
274C2×D4—17216no—
275C2×D4—1728no—
276C2×D4—1728no—
277C22×C4—24no—
278C22×C4—431no—
279C22×C4—438no—
280C22×C4—434no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—434no—
284C22×C4—432no—
285C22×C4—432no—
286C22×C4—8616no—
287C22×C4—864no—
288C22×C4—864no—
289C22×C4—17216no—
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4C23×D4311yescharacteristic
293D8—8632no—
294C2×C8—434no—
295C2×C8—864no—
296C2×C8—8616no—
297C2×C8#1062190218yescomplemented
298C2×C8C23×D4314yes—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4C23×D4318yes—
302C22⋊C4—8616no—
303C22⋊C4—8616no—
304C42—434no—
305C42—432no—
306C42—434no—
307C42—432no—
308C42D4×D4312yes—
309C42C23×D4312yes—
310C23—434no—
311C23—432no—
312C23—862no—
313C23—862no—
314C23—868no—
315C23—1728no—
316C23—1728no—
317C23—1728no—
318C23C2×D4×D4311yescharacteristic
319Q8—416no—
320D4—8616no—
321D4—17232no—
322D4—17216no—
323D4—17216no—
324D4—1728no—
325C2×C4—28no—
326C2×C4—48no—
327C2×C4—434no—
328C2×C4—432no—
329C2×C4—4316no—
330C2×C4—432no—
331C2×C4—432no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—868no—
335C2×C4—864no—
336C2×C4—864no—
337C2×C4—17232no—
338C2×C4D8×D4314yes—
339C2×C4#1306334814yes—
340C2×C4C2×D4×D4312yes—
341C2×C4C2×D4×D4312yes—
342C2×C4C2×D4×D4311yescharacteristic
343C2×C4C2×#1062190214yes—
344C2×C4C24×D4311yescharacteristic
345C8—864no—
346C8C2×#1062190218yescomplemented
347C22—434no—
348C22—862no—
349C22—862no—
350C22—868no—
351C22—34416no—
352C22—1728no—
353C22—1728no—
354C22—1728no—
355C22#1458345012yes—
356C22C2×D8×D4312yes—
357C22C2×#1306334812yes—
358C22C22×D4×D4311yescharacteristic
359C4—48no—
360C4—434no—
361C4—862no—
362C4—862no—
363C4#1458345012yes—
364C4C2×D8×D4314yes—
365C4C2×#1306334814yes—
366C4C22×#1062190212yes—
367C2—864no—
368C2—3448no—
369C2#1914517514yesdirect product factor
370C2C2×#1458345011yescharacteristic
371C2C22×D8×D4311yescharacteristic
372C2C22×#1306334811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#500C2
socleC23×C43C22×D4
hypercenterC2×#500D43
hypocenterC43C2×#3169
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#14583450C2semidirect
2. #19145175C2direct (N × H)
3. C2×#14583276C2semidirect
4. C2×#14583247C2semidirect
5. C2×#14583136C2semidirect
6. C2×#14582981C2semidirect
7. C2×C4×C8×D43C2semidirect
8. C2×C43×#500C2semidirect
13. #14583450C22semidirect
21. #14583276C22semidirect
22. #14583247C22semidirect
23. #14583136C22semidirect
24. #14582981C22semidirect
28. C4×C8×D43C22semidirect
30. C43×#500C22semidirect
101. C2×C4×D43D8semidirect
106. C2×C8×C43#41semidirect
157. C4×D43C2×D8semidirect
158. C8×C43C2×#41semidirect
183. C2×#500D43semidirect
189. C2×C43#3169semidirect
208. #500C2×D43semidirect
219. C43C2×#3169semidirect
297. C2×C8#10621902semidirect
346. C8C2×#10621902semidirect
369. C2#19145175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834502
#191451752
C2×#145832762
C2×#145832472
C2×#145831362
C2×#145829812
C2×C4×C8×D432
C2×C43×#5002
C2×#316943