Finite Group Databasebeta

← C2×#19145172 #25966331

Subgroups — C2×#19145172 #25966331

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×#14583447C212yesmaximal, complemented
2#19145172C2116yesmaximal, direct product factor
3C2×#14583304C211yesmaximal, characteristic, complemented
4C2×#14583245C212yesmaximal, complemented
5C2×#14583132C214yesmaximal, complemented
6C2×D8×Dic43C214yesmaximal, complemented
7C2×C4×C8×D43C211yesmaximal, characteristic, complemented
8C2×C43×#493C211yesmaximal, characteristic, complemented
9C22×#10621900—22no—
10C22×C8×D43C2212yes—
11#14583447—28no—
12#14583447C22116yescomplemented
13C2×#13063325C2212yes—
14C2×#13063312—22no—
15C2×#13063296—22no—
16C2×#13063296C2214yes—
17C2×D4×Dic43—22no—
18C2×D4×Dic43C2214yes—
19C2×C42×D43C2211yescharacteristic
20#14583304C2218yescomplemented
21#14583245C22116yescomplemented
22#14583132C22132yescomplemented
23D8×Dic43C22132yescomplemented
24C2×#13063259C2214yes—
25C2×#13063246C2218yes—
26C2×C4×C43⋊C8C2211yescharacteristic
27C2×C8×Dic43C2212yes—
28C4×C8×D43C2218yescomplemented
29C22×D8×C43C2214yes—
30C2×#127×C43C2212yes—
31C43×#493C2218yescomplemented
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621900—216no—
34C2×#10621900—416no—
35C22×Dic86—22no—
36C22×C22⋊D43—24no—
37C23×Dic43—24no—
38C22×C4×D43D411yescharacteristic
39C22×C4×D43D411yescharacteristic
40C22×C4×D43C2311yescharacteristic
41C22×C43⋊C8C2312yes—
42C2×C8×D43—28no—
43C2×C8×D43C2318yes—
44#13063325—24no—
45#13063325C2318yes—
46#13063312—216no—
47#13063296—216no—
48#13063296—28no—
49#13063296C23116yes—
50D4×Dic43—216no—
51D4×Dic43—28no—
52D4×Dic43C23116yes—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43C2314yes—
55C2×C22⋊Dic43—24no—
56C2×C22⋊Dic43—24no—
57C2×C4×Dic43D411yescharacteristic
58C2×C4×Dic43D411yescharacteristic
59C2×C4×Dic43C2311yescharacteristic
60C42×D43D414yes—
61C42×D43C2314yes—
62#13063259C23116yes—
63#13063246C23132yes—
64C4×C43⋊C8C2314yes—
65C8×Dic43C2318yes—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43C2314yes—
69C2×D8×C43—216no—
70C2×D8×C43C23116yes—
71C22×C8×C43C2312yes—
72#127×C43—24no—
73#127×C43C2318yes—
74C2×C42×C43C2311yescharacteristic
75C4×C8×C43C2314yes—
76C24×C43—24no—
77C23×D43C2×D411yescharacteristic
78C2×D4×C43—24no—
79C2×D4×C43—28no—
80C2×D4×C43—28no—
81C2×D4×C43—216no—
82C2×D4×C43—48no—
83C2×D4×C43—48no—
84C2×D4×C43C2418yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2411yescharacteristic
88C2×C22⋊D43—216no—
89C2×C22⋊D43—416no—
90C22×Dic43—216no—
91C22×Dic43—24no—
92C22×Dic43—416no—
93C22×Dic43C2×D411yescharacteristic
94C22×Dic43C2×D411yescharacteristic
95C22×Dic43C2×D411yescharacteristic
96#10621900—464no—
97C2×C4×D43—24no—
98C2×C4×D43—24no—
99C2×C4×D43D818yescomplemented
100C2×C4×D43C2×D412yes—
101C2×C4×D43C2×D414yes—
102C2×C4×D43C2×D414yes—
103C2×C4×D43C2412yes—
104C2×Dic86—28no—
105C2×Dic86—48no—
106D8×C43—232no—
107C2×C8×C43#4118yescomplemented
108C2×C8×C43C2414yes—
109C42×C43C2×D412yes—
110C42×C43C2412yes—
111C22⋊Dic43—216no—
112C22⋊Dic43—216no—
113C4⋊Dic43—28no—
114C4⋊Dic43—24no—
115C4⋊Dic43C2418yes—
116C4×Dic43C2×D412yes—
117C4×Dic43C2×D414yes—
118C4×Dic43C2×D414yes—
119C4×Dic43C2412yes—
120C2×C43⋊C8—24no—
121C2×C43⋊C8C2414yes—
122C8×D43—216no—
123C23×C43—28no—
124C23×C43—48no—
125C23×C43—48no—
126C23×C43—48no—
127C23×C43C22×D411yescharacteristic
128C22×D43—22no—
129C22×D43—22no—
130C22×D43C2×D814yes—
131C22×D43C22×D412yes—
132D4×C43—216no—
133D4×C43—48no—
134D4×C43—416no—
135D4×C43—416no—
136C2×C4×C43C2×D814yes—
137C2×C4×C43#13514yes—
138C2×C4×C43C22×D411yescharacteristic
139C2×C4×C43C22×D412yes—
140C2×C4×C43C22×D412yes—
141C2×C4×C43C2×#4114yes—
142C2×C4×C43C2511yescharacteristic
143C22⋊D43—432no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—28no—
147C2×Dic43—48no—
148C2×Dic43—432no—
149C2×Dic43C2×D814yes—
150C2×Dic43C22×D412yes—
151C2×Dic43C22×D412yes—
152C2×Dic43C22×D412yes—
153C4×D43—24no—
154C4×D43—28no—
155C4×D43—24no—
156C4×D43C2×D8116yescomplemented
157Dic86—416no—
158C8×C43C2×#4118yescomplemented
159C43⋊C8—24no—
160C2×#3169—431nomaximal, Sylow
161C22×C43—48no—
162C22×C43—48no—
163C22×C43—48no—
164C22×C43—816no—
165C22×C43#53212yes—
166C22×C43C22×D812yes—
167C22×C43C2×#13512yes—
168C22×C43C23×D411yescharacteristic
169C2×D43—28no—
170C2×D43—22no—
171C2×D43—22no—
172C2×D43C22×D814yes—
173C4×C43#53212yes—
174C4×C43C22×D814yes—
175C4×C43C2×#13514yes—
176C4×C43C22×#4112yes—
177Dic43—22no—
178Dic43—22no—
179Dic43—48no—
180Dic43C22×D814yes—
181C2×#532—432no—
182#3169—4316no—
183C2×#500—431no—
184C2×#493D4311yescharacteristic, complemented
185C2×#486—432no—
186C2×#466—434no—
187C2×C4×D8—434no—
188C22×C4×C8—431no—
189C2×C43—88no—
190C2×C43#316914yescomplemented
191C2×C43C2×#53211yescharacteristic
192C2×C43C23×D811yescharacteristic
193C2×C43C22×#13511yescharacteristic
194D43—24no—
195C22×#41—862no—
196C22×D8C2×D4314yes—
197C23×C8—432no—
198#532—4316no—
199#532—868no—
200C2×C4⋊Q8—432no—
201C2×#127C2×D4312yes—
202C2×#124—862no—
203C2×#121—434no—
204C2×#121—862no—
205C2×C4×D4—434no—
206C2×C4×D4—862no—
207C22×C42—431no—
208#500—438no—
209#493C2×D4318yescomplemented
210#486—4316no—
211#466—4332no—
212C4×D8—4332no—
213C2×#107—434no—
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—862no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—864no—
226C22×D4C22×D4314yes—
227C23×C4—431no—
228C23×C4—431no—
229C23×C4—431no—
230C23×C4—864no—
231C2×D8—216no—
232C2×D8C22×D43116yes—
233C22×C8—432no—
234C22×C8—438no—
235C22×C8—868no—
236C22×C8C22×D4312yes—
237C4⋊Q8—438no—
238C4⋊Q8—864no—
239#127—24no—
240#127C22×D4318yes—
241#124—8616no—
242#121—4316no—
243#121—868no—
244#121—8616no—
245C4×D4—4316no—
246C4×D4—868no—
247C4×D4—8616no—
248C2×C4⋊C4—434no—
249C2×C4⋊C4—862no—
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#107—4316no—
259#102—4332no—
260C4×C8—438no—
261C4×C8—434no—
262C4×C8C22×D4314yes—
263C24—24no—
264C24—431no—
265#41—17264no—
266C2×Q8—868no—
267C2×Q8—1728no—
268C2×D4—24no—
269C2×D4—28no—
270C2×D4—28no—
271C2×D4—216no—
272C2×D4—48no—
273C2×D4—48no—
274C2×D4—8616no—
275C2×D4—17216no—
276C2×D4C23×D4318yes—
277C22×C4—431no—
278C22×C4—438no—
279C22×C4—434no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—434no—
283C22×C4—432no—
284C22×C4—432no—
285C22×C4—8616no—
286C22×C4—864no—
287C22×C4—864no—
288C22×C4—864no—
289C22×C4—17216no—
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4C23×D4311yescharacteristic
293D8—232no—
294C2×C8—434no—
295C2×C8—864no—
296C2×C8—8616no—
297C2×C8#1062190018yescomplemented
298C2×C8C23×D4314yes—
299C4⋊C4—438no—
300C4⋊C4—864no—
301C4⋊C4—868no—
302C22⋊C4—8616no—
303C22⋊C4—8616no—
304C42—434no—
305C42—432no—
306C42—434no—
307C42—432no—
308C42D4×D4312yes—
309C42C23×D4312yes—
310C23—28no—
311C23—48no—
312C23—48no—
313C23—48no—
314C23—434no—
315C23—432no—
316C23—862no—
317C23—862no—
318C23C2×D4×D4311yescharacteristic
319Q8—17216no—
320D4—216no—
321D4—416no—
322D4—416no—
323D4—48no—
324D4—17232no—
325C2×C4—434no—
326C2×C4—432no—
327C2×C4—4316no—
328C2×C4—432no—
329C2×C4—432no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—868no—
333C2×C4—864no—
334C2×C4—864no—
335C2×C4—868no—
336C2×C4—17232no—
337C2×C4—1728no—
338C2×C4D8×D4314yes—
339C2×C4#1306334414yes—
340C2×C4C2×D4×D4312yes—
341C2×C4C2×D4×D4312yes—
342C2×C4C2×D4×D4311yescharacteristic
343C2×C4C2×#1062190014yes—
344C2×C4C24×D4311yescharacteristic
345C8—864no—
346C8C2×#1062190018yescomplemented
347C22—48no—
348C22—48no—
349C22—48no—
350C22—816no—
351C22—434no—
352C22—862no—
353C22—862no—
354C22—868no—
355C22#1458344712yes—
356C22C2×D8×D4312yes—
357C22C2×#1306334412yes—
358C22C22×D4×D4311yescharacteristic
359C4—434no—
360C4—862no—
361C4—862no—
362C4—1728no—
363C4#1458344712yes—
364C4C2×D8×D4314yes—
365C4C2×#1306334414yes—
366C4C22×#1062190012yes—
367C2—88no—
368C2—864no—
369C2#1914517214yesdirect product factor
370C2C2×#1458344711yescharacteristic
371C2C22×D8×D4311yescharacteristic
372C2C22×#1306334411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#493C2
socleC23×C43C22×D4
hypercenterC2×#493D43
hypocenterC43C2×#3169
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#14583447C2semidirect
2. #19145172C2direct (N × H)
3. C2×#14583304C2semidirect
4. C2×#14583245C2semidirect
5. C2×#14583132C2semidirect
6. C2×D8×Dic43C2semidirect
7. C2×C4×C8×D43C2semidirect
8. C2×C43×#493C2semidirect
12. #14583447C22semidirect
20. #14583304C22semidirect
21. #14583245C22semidirect
22. #14583132C22semidirect
23. D8×Dic43C22semidirect
28. C4×C8×D43C22semidirect
31. C43×#493C22semidirect
99. C2×C4×D43D8semidirect
107. C2×C8×C43#41semidirect
156. C4×D43C2×D8semidirect
158. C8×C43C2×#41semidirect
184. C2×#493D43semidirect
190. C2×C43#3169semidirect
209. #493C2×D43semidirect
219. C43C2×#3169semidirect
297. C2×C8#10621900semidirect
346. C8C2×#10621900semidirect
369. C2#19145172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834472
#191451722
C2×#145833042
C2×#145832452
C2×#145831322
C2×D8×Dic432
C2×C4×C8×D432
C2×C43×#4932
C2×#316943