Finite Group Databasebeta

← C2×#19134097 #25079121

Subgroups — C2×#19134097 #25079121

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583295C211yesmaximal, characteristic, complemented
2C2×#14583186C211yesmaximal, characteristic
3C2×#14583105C211yesmaximal, characteristic
4C2×#14582976C211yesmaximal, characteristic
5#19134097C218yesmaximal, direct product factor
6C2×#14582651C211yesmaximal, characteristic, complemented
7C2×#14582644C211yesmaximal, characteristic, complemented
8C2×C43×#333C211yesmaximal, characteristic, complemented
9C22×#10621873—21no—
10C22×#10621872—21no—
11C2×#13063325C2211yescharacteristic
12C2×C4×D172C2211yescharacteristic
13#14583295—22no—
14#14583295C2214yescomplemented
15#14583186—22no—
16#14583186C2214yes—
17#14583105—22no—
18#14583105C2214yes—
19#14582976—22no—
20#14582976C2214yes—
21C2×#13063256—21no—
22C2×#13063256—21no—
23C2×#13063256—21no—
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063250—21no—
26C2×#13063245—21no—
27C2×(C2×D43)⋊C8—21no—
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582651C2214yescomplemented
30#14582644C2214yescomplemented
31C2×C4⋊Q8×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×C4⋊C8×C43C2211yescharacteristic
34C43×#333C2214yescomplemented
35C22×Dic86—21no—
36C22×D172D411yescharacteristic
37C22×C4×D43—21no—
38C2×#10621873—24no—
39C2×#10621873—44no—
40C2×#10621872—24no—
41C2×#10621872—44no—
42C22×C43⋊C8—21no—
43C22×C43⋊C8D411yescharacteristic
44C22×C43⋊C8D411yescharacteristic
45#13063325—21no—
46#13063325—21no—
47#13063325—21no—
48#13063325C2312yes—
49C4×D172—21no—
50C4×D172—21no—
51C4×D172D412yes—
52C4×D172C2312yes—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D411yescharacteristic
56C2×(C2×D43)⋊C4—21no—
57#13063256—24no—
58#13063256—24no—
59#13063256—24no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)C2312yes—
62#13063250—24no—
63#13063245—24no—
64(C2×D43)⋊C8—24no—
65C4×C43⋊C8D412yes—
66C4×C43⋊C8C2312yes—
67C22×Q8×C43—21no—
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C4⋊Q8×C43—21no—
71C4⋊Q8×C43—21no—
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43C2312yes—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C4⋊C8×C43—21no—
79C4⋊C8×C43C2312yes—
80C4⋊C8×C43C2312yes—
81C23×D43—21no—
82C2×Q8×C43—22no—
83C2×Q8×C43—41no—
84C2×Q8×C43—82no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×Dic43—21no—
90C22×Dic43—41no—
91C2×D172—21no—
92C2×D172—22no—
93C2×D172—22no—
94C2×D172C2×D412yes—
95C2×C4×D43—22no—
96C2×C4×D43—22no—
97C2×C4×D43—42no—
98C2×C4×D43—42no—
99C2×Dic86—22no—
100C2×Dic86—42no—
101C2×Dic86—42no—
102C2×Dic86—41no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—42no—
106C2×C8×C43—42no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C42×C43C2411yescharacteristic
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117C4⋊Dic43—21no—
118C4⋊Dic43—22no—
119C4⋊Dic43—22no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122C4⋊Dic43C2×D412yes—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—42no—
126C2×C43⋊C8SD1614yescomplemented
127C2×C43⋊C8C2×D412yes—
128C2×C43⋊C8C2×D412yes—
129#10621873—48no—
130#10621872—48no—
131C23×C43#12111yescharacteristic
132C22×D43—22no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—42no—
136Q8×C43—82no—
137Q8×C43—82no—
138C2×C4×C43—22no—
139C2×C4×C43—42no—
140C2×C4×C43—82no—
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43C2×SD1612yes—
145C2×C4×C43AGL(1,ℤ/8)12yes—
146C2×C4×C43#13712yes—
147C2×C4×C43#13712yes—
148C2×C4×C43C22×D411yescharacteristic
149C2×C4×C43C22×D411yescharacteristic
150C2×C4×C43C2×#4111yescharacteristic
151C2×Dic43—22no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—82no—
155D172—22no—
156D172—22no—
157D172—42no—
158C4×D43—42no—
159C4×D43—42no—
160C4×D43—44no—
161Dic86—42no—
162Dic86—42no—
163Dic86—82no—
164C8×C43—42no—
165C8×C43—42no—
166C43⋊C8—22no—
167C43⋊C8—42no—
168C43⋊C8C2×SD1614yescomplemented
169C2×#1691—431nomaximal, Sylow
170C22×C43#46112yes—
171C22×C43#46812yes—
172C22×C43#47112yes—
173C22×C43C2×#12111yescharacteristic
174C2×D43—42no—
175C2×D43—42no—
176C2×D43—42no—
177C2×D43—84no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—82no—
181C4×C43#46112yes—
182C4×C43#46812yes—
183C4×C43C22×SD1611yescharacteristic
184C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
185C4×C43C2×#13711yescharacteristic
186C4×C43C2×#13711yescharacteristic
187Dic43—42no—
188Dic43—82no—
189C2×#498—431no—
190C2×#476—431no—
191C2×#461—431no—
192C2×#436—431no—
193#1691—438no—
194C2×#335—431no—
195C2×#333D4311yescharacteristic, complemented
196C2×#332—431no—
197C2×C43#169114yescomplemented
198C2×C43C2×#46111yescharacteristic
199C2×C43C2×#46811yescharacteristic
200C2×C43C2×#47111yescharacteristic
201D43—82no—
202C22×SD16—861no—
203C22×M16—861no—
204C2×C4⋊Q8—431no—
205C2×C4⋊Q8C2×D4311yescharacteristic
206C2×C4×D4—431no—
207#498—434no—
208#498—862no—
209#476—434no—
210#476—862no—
211#461—434no—
212#461—862no—
213#436—434no—
214#436—862no—
215C2×#106—861no—
216C2×#106—861no—
217C2×#106—861no—
218C2×C4⋊C8—431no—
219C2×C4⋊C8C2×D4311yescharacteristic
220C2×C4⋊C8C2×D4311yescharacteristic
221C2×#103—861no—
222C2×#102—861no—
223C2×C22⋊C8—861no—
224C2×C4×C8—431no—
225#335—434no—
226#333C2×D4314yescomplemented
227#332—434no—
228C43C2×#169111yescharacteristic, complemented, Sylow
229C22×Q8—21no—
230C22×Q8—861no—
231C22×D4—431no—
232C23×C4—861no—
233C2×SD16—864no—
234C2×SD16—1724no—
235C2×M16—864no—
236C2×M16—1724no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—431no—
240C22×C8—431no—
241C22×C8—861no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—432no—
246C4⋊Q8—861no—
247C4⋊Q8—861no—
248C4⋊Q8—861no—
249C4⋊Q8C22×D4312yes—
250C4×D4—432no—
251C4×D4—432no—
252C4×D4—861no—
253C4×D4—861no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—861no—
258C2×C4⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C42C22×D4311yescharacteristic
261#106—864no—
262#106—864no—
263#106—864no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—432no—
267C4⋊C8—861no—
268C4⋊C8C22×D4312yes—
269C4⋊C8C22×D4312yes—
270#103—864no—
271#102—864no—
272C22⋊C8—864no—
273C4×C8—432no—
274C4×C8—432no—
275C24—861no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—82no—
279C2×Q8—862no—
280C2×Q8—1722no—
281C2×Q8—1722no—
282C2×Q8—1721no—
283C2×D4—432no—
284C2×D4—861no—
285C2×D4—862no—
286C2×D4—862no—
287C22×C4—41no—
288C22×C4—861no—
289C22×C4—862no—
290C22×C4—862no—
291C22×C4—1721no—
292C22×C4—1722no—
293C22×C4—1722no—
294C22×C4#1062189811yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4D4×D4311yescharacteristic
297SD16—1728no—
298M16—1728no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—434no—
304C2×C8—432no—
305C2×C8—432no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8—1722no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—432no—
314C4⋊C4—861no—
315C4⋊C4—862no—
316C4⋊C4—862no—
317C4⋊C4—1721no—
318C4⋊C4—1721no—
319C22⋊C4—862no—
320C22⋊C4—862no—
321C42#1062189811yescharacteristic
322C42D4×D4311yescharacteristic
323C42D4×D4311yescharacteristic
324C42C23×D4311yescharacteristic
325C23—862no—
326C23—1722no—
327C23—1722no—
328C23—1722no—
329C23#1306329811yescharacteristic
330Q8—82no—
331Q8—82no—
332Q8—3442no—
333Q8—1722no—
334Q8—1722no—
335D4—862no—
336D4—862no—
337D4—1722no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—862no—
342C2×C4—3442no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1724no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4#1306329811yescharacteristic
349C2×C4#1306329811yescharacteristic
350C2×C4#1306329811yescharacteristic
351C2×C4SD16×D4312yes—
352C2×C4#1306335212yes—
353C2×C4#1306335712yes—
354C2×C4#1306335712yes—
355C2×C4C2×D4×D4311yescharacteristic
356C2×C4C2×D4×D4311yescharacteristic
357C2×C4C2×#1062189811yescharacteristic
358C8—42no—
359C8—42no—
360C8—434no—
361C8—862no—
362C8—1722no—
363C22—3444no—
364C22—1722no—
365C22—1722no—
366C22—1722no—
367C22#1458310312yes—
368C22#1458314812yes—
369C22#1458316112yes—
370C22C2×#1306329811yescharacteristic
371C4—21no—
372C4—21no—
373C4—82no—
374C4—3442no—
375C4—1722no—
376C4#1458310312yes—
377C4#1458314812yes—
378C4C2×SD16×D4311yescharacteristic
379C4C2×#1306335211yescharacteristic
380C4C2×#1306335711yescharacteristic
381C4C2×#1306335711yescharacteristic
382C2—3442no—
383C2#1913409714yesdirect product factor
384C2C2×#1458310311yescharacteristic
385C2C2×#1458314811yescharacteristic
386C2C2×#1458316111yescharacteristic
subgroupG/H
centerC23#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#333C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenterC2×#333D43
hypocenterC43C2×#1691
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. C2×#14583295C2semidirect
5. #19134097C2direct (N × H)
6. C2×#14582651C2semidirect
7. C2×#14582644C2semidirect
8. C2×C43×#333C2semidirect
14. #14583295C22semidirect
29. #14582651C22semidirect
30. #14582644C22semidirect
34. C43×#333C22semidirect
126. C2×C43⋊C8SD16semidirect
168. C43⋊C8C2×SD16semidirect
195. C2×#333D43semidirect
197. C2×C43#1691semidirect
226. #333C2×D43semidirect
228. C43C2×#1691semidirect
383. C2#19134097direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832952
C2×#145831862
C2×#145831052
C2×#145829762
#191340972
C2×#145826512
C2×#145826442
C2×C43×#3332
C2×#169143