Finite Group Databasebeta

← C2×#19134163 #25079261

Subgroups — C2×#19134163 #25079261

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583246C211yesmaximal, characteristic
2C2×#14583109C211yesmaximal, characteristic, complemented
3C2×#14583099C211yesmaximal, characteristic
4#19134163C218yesmaximal, direct product factor
5C2×#14582650C211yesmaximal, characteristic, complemented
6C2×#14582644C211yesmaximal, characteristic, complemented
7C2×#14582642C211yesmaximal, characteristic
8C2×C43×#446C211yesmaximal, characteristic, complemented
9C22×#10621885—21no—
10C22×#10621884—21no—
11C2×#13063325C2211yescharacteristic
12C2×#13063322C2211yescharacteristic
13#14583246—22no—
14#14583246C2214yes—
15#14583109—22no—
16#14583109C2214yescomplemented
17#14583099—22no—
18#14583099C2214yes—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063248—21no—
22C2×#13063247—21no—
23C2×#13063247—21no—
24C2×#13063245—21no—
25#14582650C2214yescomplemented
26#14582644C2214yescomplemented
27#14582642C2214yes—
28C2×C4×Q8×C43C2211yescharacteristic
29C43×#446—22no—
30C43×#446C2214yescomplemented
31C2×C4⋊C8×C43—21no—
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×#97×C43—21no—
34C2×C4×C8×C43C2211yescharacteristic
35C22×Dic86—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C2×#10621885—24no—
40C2×#10621885—44no—
41C2×#10621884—24no—
42C2×#10621884—44no—
43C22×C43⋊C8—21no—
44C22×C43⋊C8—21no—
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—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)—21no—
57C4⋊(C43⋊C8)C2312yes—
58C4⋊(C43⋊C8)C2312yes—
59#13063248—24no—
60#13063247—24no—
61#13063247—24no—
62#13063245—24no—
63C22×Q8×C43D411yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43D411yescharacteristic
66C22×C8×C43D411yescharacteristic
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43D412yes—
70C4×Q8×C43C2312yes—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—24no—
76C4⋊C8×C43—21no—
77C4⋊C8×C43C2312yes—
78#97×C43—24no—
79C4×C8×C43D412yes—
80C4×C8×C43C2312yes—
81C23×D43—41no—
82C2×Q8×C43—21no—
83C2×Q8×C43—22no—
84C2×Q8×C43—22no—
85C2×Q8×C43C2×D412yes—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×Dic43—41no—
92C2×D172—22no—
93C2×D172—22no—
94C2×D172—22no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98C2×D172—42no—
99C2×D172—42no—
100C2×D172—42no—
101C2×D172—42no—
102C2×D172—82no—
103C2×Dic86—22no—
104C2×Dic86—42no—
105C2×Dic86—42no—
106C2×Dic86—41no—
107C2×C8×C43—22no—
108C2×C8×C43—22no—
109C2×C8×C43—22no—
110C2×C8×C43—42no—
111C2×C8×C43C2×D412yes—
112C2×C8×C43C2×D412yes—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43C2×D412yes—
117C42×C43—22no—
118C42×C43—22no—
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C42×C43C2411yescharacteristic
123#10621885—48no—
124#10621884—48no—
125C4⋊Dic43—22no—
126C4⋊Dic43—22no—
127C4⋊Dic43—41no—
128C4⋊Dic43—41no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—42no—
132C2×C43⋊C8—42no—
133C23×C43#12111yescharacteristic
134C22×D43—42no—
135C22×D43—82no—
136C22×D43—82no—
137C22×D43—82no—
138Q8×C43—22no—
139Q8×C43—22no—
140Q8×C43—42no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#13512yes—
150C2×C4×C43AGL(1,ℤ/8)12yes—
151C2×C4×C43AGL(1,ℤ/8)12yes—
152C2×C4×C43#13712yes—
153C2×C4×C43C22×D411yescharacteristic
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C2×#4111yescharacteristic
156C2×Dic43—42no—
157C2×Dic43—82no—
158D172—42no—
159D172—42no—
160D172—42no—
161D172—42no—
162D172—82no—
163D172—82no—
164D172—82no—
165D172—82no—
166Dic86—42no—
167Dic86—42no—
168Dic86—82no—
169C8×C43—22no—
170C8×C43—22no—
171C8×C43—42no—
172C43⋊C8—42no—
173C43⋊C8—42no—
174C2×#1702—431nomaximal, Sylow
175C22×C43#46412yes—
176C22×C43#46912yes—
177C22×C43#47112yes—
178C22×C43C2×#12111yescharacteristic
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—82no—
182C2×D43—164no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—42no—
186C4×C43—42no—
187C4×C43#46412yes—
188C4×C43#46912yes—
189C4×C43C2×#13511yescharacteristic
190C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
191C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
192C4×C43C2×#13711yescharacteristic
193Dic43—82no—
194C2×#486—431no—
195C2×#462—431no—
196C2×#460—431no—
197C2×#446D4311yescharacteristic, complemented
198#1702—438no—
199C2×#334—431no—
200C2×#332—431no—
201C2×#331—431no—
202C2×C43#170214yescomplemented
203C2×C43C2×#46411yescharacteristic
204C2×C43C2×#46911yescharacteristic
205C2×C43C2×#47111yescharacteristic
206D43—162no—
207C22×Q16—861no—
208C22×SD16—861no—
209C2×C4⋊Q8—431no—
210C2×#127—431no—
211C2×C4×Q8C2×D4311yescharacteristic
212#486—434no—
213#486—862no—
214#462—434no—
215#462—862no—
216#460—434no—
217#460—862no—
218#446—22no—
219#446C2×D4314yescomplemented
220C2×C4⋊C8—21no—
221C2×C4⋊C8—431no—
222C2×C4⋊C8—431no—
223C2×C4⋊C8C2×D4311yescharacteristic
224C2×#103—861no—
225C2×#102—861no—
226C2×#102—861no—
227C2×#102—861no—
228C2×#97—21no—
229C2×C4×C8C2×D4311yescharacteristic
230#334—434no—
231#332—434no—
232#331—434no—
233C43C2×#170211yescharacteristic, complemented, Sylow
234C22×Q8—861no—
235C22×Q8D17211yescharacteristic
236C22×D4—861no—
237C22×D4—861no—
238C22×D4—861no—
239C2×Q16—864no—
240C2×Q16—1724no—
241C2×SD16—864no—
242C2×SD16—1724no—
243C22×C8—21no—
244C22×C8—861no—
245C22×C8—861no—
246C22×C8C22⋊D4311yescharacteristic
247C22×C8C22⋊D4311yescharacteristic
248C4⋊Q8—432no—
249C4⋊Q8—861no—
250C4⋊Q8—861no—
251C4⋊Q8—861no—
252#127—432no—
253#127—861no—
254#127—861no—
255#127—861no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8D17212yes—
259C4×Q8C22×D4312yes—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4D17211yescharacteristic
264C2×C42—21no—
265C2×C42C22×D4311yescharacteristic
266C4⋊C8—24no—
267C4⋊C8—21no—
268C4⋊C8—432no—
269C4⋊C8—432no—
270C4⋊C8—861no—
271C4⋊C8—861no—
272C4⋊C8C22×D4312yes—
273#103—864no—
274#102—864no—
275#102—864no—
276#102—864no—
277#97—24no—
278C4×C8C22⋊D4312yes—
279C4×C8C22×D4312yes—
280C24—1721no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—862no—
285C2×Q8—1722no—
286C2×Q8—1722no—
287C2×Q8—1721no—
288C2×Q8C2×D17212yes—
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—862no—
292C2×D4—3442no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1722no—
297C2×D4—1722no—
298C2×D4—1722no—
299C2×D4—1722no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—1721no—
303C22×C4C2×D17211yescharacteristic
304C22×C4#1062189811yescharacteristic
305C22×C4C2×C22⋊D4311yescharacteristic
306Q16—1728no—
307SD16—1728no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—42no—
312C2×C8—862no—
313C2×C8—862no—
314C2×C8—1722no—
315C2×C8—1722no—
316C2×C8C2×C22⋊D4312yes—
317C2×C8C2×C22⋊D4312yes—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—862no—
322C4⋊C4—862no—
323C4⋊C4—1721no—
324C4⋊C4—1721no—
325C4⋊C4C2×D17212yes—
326C42—22no—
327C42—22no—
328C42C2×D17211yescharacteristic
329C42#1062189811yescharacteristic
330C42C2×C22⋊D4311yescharacteristic
331C42C23×D4311yescharacteristic
332C23—3442no—
333C23—3442no—
334C23—3442no—
335C23—1722no—
336C23#1306329911yescharacteristic
337Q8—22no—
338Q8—22no—
339Q8—42no—
340Q8—3442no—
341Q8—1722no—
342Q8—1722no—
343D4—3442no—
344D4—3442no—
345D4—3442no—
346D4—3442no—
347D4—1722no—
348D4—1722no—
349D4—1722no—
350D4—1722no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—3442no—
357C2×C4—1722no—
358C2×C4#1306329911yescharacteristic
359C2×C4#1306329911yescharacteristic
360C2×C4#1306329911yescharacteristic
361C2×C4#1306334512yes—
362C2×C4#1306335312yes—
363C2×C4#1306335312yes—
364C2×C4#1306335612yes—
365C2×C4C22×C22⋊D4311yescharacteristic
366C2×C4C22×D17211yescharacteristic
367C2×C4C2×#1062189811yescharacteristic
368C8—22no—
369C8—22no—
370C8—42no—
371C8—1722no—
372C8—1722no—
373C22—3442no—
374C22—3442no—
375C22—3442no—
376C22—6884no—
377C22#1458312112yes—
378C22#1458315212yes—
379C22#1458316212yes—
380C22C2×#1306329911yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—42no—
385C4—3442no—
386C4#1458312112yes—
387C4#1458315212yes—
388C4C2×#1306334511yescharacteristic
389C4C2×#1306335311yescharacteristic
390C4C2×#1306335311yescharacteristic
391C4C2×#1306335611yescharacteristic
392C2—6882no—
393C2#1913416314yesdirect product factor
394C2C2×#1458312111yescharacteristic
395C2C2×#1458315211yescharacteristic
396C2C2×#1458316211yescharacteristic
subgroupG/H
centerC23#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#446C2
socleC23×C43#121
prime radicalC2×#13063322C22
hypercenterC2×#446D43
hypocenterC43C2×#1702
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#14583109C2semidirect
4. #19134163C2direct (N × H)
5. C2×#14582650C2semidirect
6. C2×#14582644C2semidirect
8. C2×C43×#446C2semidirect
16. #14583109C22semidirect
25. #14582650C22semidirect
26. #14582644C22semidirect
30. C43×#446C22semidirect
197. C2×#446D43semidirect
202. C2×C43#1702semidirect
219. #446C2×D43semidirect
233. C43C2×#1702semidirect
393. C2#19134163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832462
C2×#145831092
C2×#145830992
#191341632
C2×#145826502
C2×#145826442
C2×#145826422
C2×C43×#4462
C2×#170243