Finite Group Databasebeta

← C2×#19149050 #26004361

Subgroups — C2×#19149050 #26004361

Order 11008.

6566 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149050C2132yesmaximal, direct product factor
2C2×C43⋊#564C211yesmaximal, characteristic, complemented
3C2×#14583649C212yesmaximal, complemented
4C2×#14583603C214yesmaximal, complemented
5C2×#14583596C214yesmaximal, complemented
6C2×#14583586C214yesmaximal, complemented
7C2×#14583509C214yesmaximal, complemented
8C2×#14583494C214yesmaximal, complemented
9C2×#14583492C214yesmaximal, complemented
10C2×#14583428C212yesmaximal, complemented
11C2×#125×D43C211yesmaximal, characteristic, complemented
12C2×C43×#562C211yesmaximal, characteristic, complemented
13C43⋊#564C22116yescomplemented
14#14583649C22132yescomplemented
15#14583603C22164yescomplemented
16#14583596C22164yescomplemented
17#14583586C22164yescomplemented
18#14583509C22164yescomplemented
19#14583494C22164yescomplemented
20#14583492C22164yescomplemented
21C2×#13063323C2214yes—
22#14583428C22132yescomplemented
23C2×#13063318C2214yes—
24C2×#13063318C2214yes—
25C2×#13063318C2214yes—
26C2×#13063318C2214yes—
27C2×#13063318C2214yes—
28C2×#13063317C2211yescharacteristic
29C2×#13063317C2212yes—
30C2×#13063316C2212yes—
31C2×#13063316C2214yes—
32C2×#13063316C2214yes—
33C2×#13063315C2214yes—
34C2×#13063315C2214yes—
35C2×#13063315C2214yes—
36C2×#13063315C2214yes—
37#125×D43C22116yescomplemented
38C2×#13063307C2214yes—
39C2×#13063306C2214yes—
40C2×#13063306C2214yes—
41C2×#13063306C2214yes—
42C2×#13063304C2214yes—
43C2×#13063303C2214yes—
44C2×#13063302C2214yes—
45C2×#13063302C2214yes—
46C2×#13063302C2214yes—
47C2×#13063301C2212yes—
48C2×#13063296C2212yes—
49C2×#13063296C2214yes—
50C2×Q8×Dic43C2212yes—
51C2×#13063290C2214yes—
52C2×D4×Dic43C2214yes—
53C2×D4×Dic43C2212yes—
54C2×C4×C22⋊D43C2214yes—
55C2×(C22⋊D43)⋊C4C2214yes—
56C2×(C22⋊D43)⋊C4C2214yes—
57C2×#13063284C2214yes—
58C2×#13063281C2214yes—
59C22×Dic43⋊C4C2214yes—
60C2×C4⋊C4×D43C2214yes—
61C2×C4⋊C4×D43C2212yes—
62C2×C42×D43C2211yescharacteristic
63C43×#562C22116yescomplemented
64C2×#125×C43C2211yescharacteristic
65C2×#124×C43C2212yes—
66C2×#123×C43C2214yes—
67C2×C22⋊Q8×C43C2214yes—
68C2×#121×C43C2214yes—
69C22×Dic86C2314yes—
70C22×C22⋊D43C2314yes—
71C23×Dic43C2314yes—
72C23×Dic43C2314yes—
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2312yes—
75C22×C4×D43C2314yes—
76#13063323C23132yes—
77#13063318C23132yes—
78#13063318C23132yes—
79#13063318C23132yes—
80#13063318C23132yes—
81#13063318C23132yes—
82#13063317C2318yes—
83#13063317C23116yes—
84#13063316C23116yes—
85#13063316C23132yes—
86#13063316C23132yes—
87#13063315C23132yes—
88#13063315C23132yes—
89#13063315C23132yes—
90#13063315C23132yes—
91#13063307C23132yes—
92#13063306C23132yes—
93#13063306C23132yes—
94#13063306C23132yes—
95#13063304C23132yes—
96#13063303C23132yes—
97#13063302C23132yes—
98#13063302C23132yes—
99#13063302C23132yes—
100#13063301C23116yes—
101#13063296C23116yes—
102#13063296C23132yes—
103Q8×Dic43C23116yes—
104#13063290C23132yes—
105D4×Dic43C23132yes—
106D4×Dic43C23116yes—
107C4×C22⋊D43C23132yes—
108(C22⋊D43)⋊C4C23132yes—
109(C22⋊D43)⋊C4C23132yes—
110#13063284C23132yes—
111#13063281C23132yes—
112C2×C4⋊Dic43C2314yes—
113C2×C4⋊Dic43C2312yes—
114C2×C4⋊Dic43C2314yes—
115C2×C4⋊Dic43C2312yes—
116C2×C4⋊Dic43C2312yes—
117C2×C4⋊Dic43C2314yes—
118C2×Dic43⋊C4C23132yes—
119C2×Dic43⋊C4C2314yes—
120C2×Dic43⋊C4C2314yes—
121C2×Dic43⋊C4C2314yes—
122C2×Dic43⋊C4C2314yes—
123C2×Dic43⋊C4C2314yes—
124C2×Dic43⋊C4C2314yes—
125C2×Dic43⋊C4C2314yes—
126C2×Dic43⋊C4C2314yes—
127C2×Dic43⋊C4C2314yes—
128C2×Dic43⋊C4C2314yes—
129C4⋊C4×D43C23132yes—
130C4⋊C4×D43C23116yes—
131C2×C22⋊Dic43C2314yes—
132C2×C22⋊Dic43C2314yes—
133C2×C22⋊Dic43C2314yes—
134C2×C22⋊Dic43C2314yes—
135C2×C22⋊Dic43C2314yes—
136C2×(C2×D43)⋊C4C2314yes—
137C2×C4×Dic43C2311yescharacteristic
138C2×C4×Dic43C2312yes—
139C2×C4×Dic43C2314yes—
140C2×C4×Dic43C2314yes—
141C2×C4×Dic43C2314yes—
142C42×D43C2318yes—
143C22×Q8×C43C2312yes—
144C22×D4×C43C2314yes—
145C22×D4×C43C2312yes—
146C23×C4×C43C2314yes—
147#125×C43C2318yes—
148#124×C43C23116yes—
149#123×C43C23132yes—
150C22⋊Q8×C43C23132yes—
151#121×C43C23132yes—
152C2×C4⋊C4×C43C2314yes—
153C2×C4⋊C4×C43C2314yes—
154C2×C4⋊C4×C43C2312yes—
155C2×C22⋊C4×C43C2314yes—
156C2×C22⋊C4×C43C2314yes—
157C2×C22⋊C4×C43C2314yes—
158C2×C42×C43C2311yescharacteristic
159C24×C43C2414yes—
160C23×D43C2411yescharacteristic
161C2×Q8×C43—44no—
162C2×Q8×C43C2418yes—
163C2×D4×C43—48no—
164C2×D4×C43—44no—
165C2×D4×C43C24116yes—
166C2×D4×C43C2418yes—
167C22×C4×C43—48no—
168C22×C4×C43C2411yescharacteristic
169C22×C4×C43C2412yes—
170C22×C4×C43C2414yes—
171C22×C4×C43C2414yes—
172C22×C4×C43C24116yes—
173C2×C22⋊D43—216no—
174C2×C22⋊D43C24116yes—
175C22×Dic43—48no—
176C22×Dic43—48no—
177C22×Dic43C2412yes—
178C22×Dic43C2414yes—
179C22×Dic43C2411yescharacteristic
180C22×Dic43C2414yes—
181C22×Dic43C2414yes—
182C22×Dic43C24116yes—
183C22×Dic43C24116yes—
184C2×C4×D43—24no—
185C2×C4×D43—48no—
186C2×C4×D43—44no—
187C2×C4×D43C2414yes—
188C2×C4×D43C2418yes—
189C2×C4×D43C24116yes—
190C2×Dic86—48no—
191C2×Dic86C24116yes—
192C4⋊C4×C43C24116yes—
193C4⋊C4×C43C24116yes—
194C4⋊C4×C43C2418yes—
195C22⋊C4×C43C24116yes—
196C22⋊C4×C43C24116yes—
197C22⋊C4×C43C24116yes—
198C42×C43C2414yes—
199C22⋊Dic43C24116yes—
200C22⋊Dic43C24116yes—
201C22⋊Dic43C24116yes—
202C22⋊Dic43C24116yes—
203C22⋊Dic43C24116yes—
204(C2×D43)⋊C4C24116yes—
205C4⋊Dic43C24116yes—
206C4⋊Dic43C2418yes—
207C4⋊Dic43C24116yes—
208C4⋊Dic43C2418yes—
209C4⋊Dic43C2418yes—
210C4⋊Dic43C24116yes—
211Dic43⋊C4C24116yes—
212Dic43⋊C4C24116yes—
213Dic43⋊C4C24116yes—
214Dic43⋊C4C24116yes—
215Dic43⋊C4C24116yes—
216Dic43⋊C4C24116yes—
217Dic43⋊C4C24116yes—
218Dic43⋊C4C24116yes—
219Dic43⋊C4C24116yes—
220Dic43⋊C4C24116yes—
221C4×Dic43C2414yes—
222C4×Dic43C2418yes—
223C4×Dic43C24116yes—
224C4×Dic43C24116yes—
225C4×Dic43C24116yes—
226C23×C43—28no—
227C23×C43—28no—
228C23×C43—28no—
229C23×C43C2518yes—
230C23×C43C2511yescharacteristic
231C22×D43—24no—
232C22×D432−1+414yes—
233C22×D43C2512yes—
234Q8×C43—48no—
235D4×C43—416no—
236D4×C43—48no—
237C2×C4×C43—22no—
238C2×C4×C43—28no—
239C2×C4×C43—28no—
240C2×C4×C43—24no—
241C2×C4×C43—416no—
242C2×C4×C43C2518yes—
243C2×C4×C43C2512yes—
244C2×C4×C43C2514yes—
245C2×C4×C43C2518yes—
246C22⋊D43—232no—
247C2×Dic43—22no—
248C2×Dic43—28no—
249C2×Dic43—28no—
250C2×Dic43—28no—
251C2×Dic43—24no—
252C2×Dic43—416no—
253C2×Dic43—416no—
254C2×Dic43C2514yes—
255C2×Dic43C2518yes—
256C2×Dic43C2512yes—
257C2×Dic43C2518yes—
258C2×Dic43C2518yes—
259C4×D43—28no—
260C4×D43—416no—
261C4×D43—48no—
262Dic86—416no—
263C2×#3553—431nomaximal, Sylow
264C22×C43—28no—
265C22×C43—28no—
266C22×C43—28no—
267C22×C43—416no—
268C22×C43C2×2−1+412yes—
269C22×C43#58514yes—
270C22×C43C2611yescharacteristic
271C2×D43—24no—
272C2×D43—28no—
273C2×D43C2×2−1+414yes—
274C4×C43—22no—
275C4×C43—28no—
276C4×C43—28no—
277C4×C43—24no—
278Dic43—22no—
279Dic43—28no—
280Dic43—28no—
281Dic43—28no—
282Dic43—24no—
283#3553—4332no—
284C2×#564—431no—
285C2×#563—432no—
286C2×#562D4311yescharacteristic, complemented
287C2×#554—434no—
288C2×#553—434no—
289C2×#552—434no—
290C2×#541—434no—
291C2×#539—434no—
292C2×#539—434no—
293C2×#529—432no—
294C22×#125—431no—
295C2×C43—48no—
296C2×C43#355314yescomplemented
297C2×C43C22×2−1+411yescharacteristic
298C2×C43C2×#58512yes—
299D43—24no—
300#564—4316no—
301#563—4332no—
302#562C2×D43116yescomplemented
303#554—4364no—
304#553—4364no—
305#552—4364no—
306#541—4364no—
307#539—4364no—
308#539—4364no—
309C2×C4⋊Q8—434no—
310#529—4332no—
311C2×#126—434no—
312C2×#126—434no—
313C2×#126—434no—
314C2×#126—434no—
315C2×#126—434no—
316C2×#125—4316no—
317C2×#125—434no—
318C2×#125—432no—
319C2×#125—434no—
320C2×#125—434no—
321C2×#125—434no—
322C2×#125—434no—
323C2×#125—434no—
324C2×#125—431no—
325C2×#125—432no—
326C2×#125C2×D4311yescharacteristic
327C2×#124C2×D4312yes—
328C2×#123—434no—
329C2×#123—434no—
330C2×#123—434no—
331C2×#123—434no—
332C2×#123C2×D4314yes—
333C2×C22⋊Q8—432no—
334C2×C22⋊Q8—434no—
335C2×C22⋊Q8—434no—
336C2×C22⋊Q8—434no—
337C2×C22⋊Q8—434no—
338C2×C22⋊Q8—434no—
339C2×C22⋊Q8C2×D4314yes—
340C2×#121—432no—
341C2×#121—434no—
342C2×#121C2×D4314yes—
343C2×C4×Q8—432no—
344C2×C4×Q8—434no—
345C2×C4×D4—432no—
346C2×C4×D4—434no—
347C2×C4×D4—434no—
348C2×C4×D4—434no—
349C2×C4×D4—434no—
350C2×#117—434no—
351C2×#117—434no—
352C22×C4⋊C4—434no—
353C22×C4⋊C4—432no—
354C22×C4⋊C4—434no—
355C22×C42—431no—
356C43C2×#355311yescharacteristic, complemented, Sylow
357C22×Q8—434no—
358C22×Q8C22×D4312yes—
359C22×D4—434no—
360C22×D4C22×D4314yes—
361C22×D4C22×D4312yes—
362C23×C4—434no—
363C23×C4—434no—
364C23×C4—431no—
365C23×C4—434no—
366C23×C4—432no—
367C23×C4C22×D4314yes—
368C4⋊Q8—4332no—
369#126—4332no—
370#126—4332no—
371#126—4332no—
372#126—4332no—
373#126—4332no—
374#125—4332no—
375#125—4316no—
376#125—4332no—
377#125—4332no—
378#125—4332no—
379#125—4332no—
380#125—4332no—
381#125—438no—
382#125—4316no—
383#125C22×D4318yes—
384#124C22×D43116yes—
385#123—4332no—
386#123—4332no—
387#123—4332no—
388#123—4332no—
389#123C22×D43132yes—
390C22⋊Q8—4316no—
391C22⋊Q8—4332no—
392C22⋊Q8—4332no—
393C22⋊Q8—4332no—
394C22⋊Q8—4332no—
395C22⋊Q8—4332no—
396C22⋊Q8C22×D43132yes—
397#121—4316no—
398#121—4332no—
399#121C22×D43132yes—
400C4×Q8—4316no—
401C4×Q8—4332no—
402C4×D4—4316no—
403C4×D4—4332no—
404C4×D4—4332no—
405C4×D4—4332no—
406C4×D4—4332no—
407#117—4332no—
408#117—4332no—
409C2×C4⋊C4—434no—
410C2×C4⋊C4—434no—
411C2×C4⋊C4—434no—
412C2×C4⋊C4—434no—
413C2×C4⋊C4—432no—
414C2×C4⋊C4—434no—
415C2×C4⋊C4—434no—
416C2×C4⋊C4—434no—
417C2×C4⋊C4—4332no—
418C2×C4⋊C4—434no—
419C2×C4⋊C4—434no—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—434no—
422C2×C4⋊C4—434no—
423C2×C4⋊C4—434no—
424C2×C4⋊C4—432no—
425C2×C4⋊C4—434no—
426C2×C4⋊C4—4316no—
427C2×C4⋊C4—4332no—
428C2×C4⋊C4C22×D4314yes—
429C2×C4⋊C4C22×D4312yes—
430C2×C4⋊C4C22×D4314yes—
431C2×C22⋊C4—434no—
432C2×C22⋊C4—434no—
433C2×C22⋊C4—434no—
434C2×C22⋊C4—434no—
435C2×C22⋊C4—434no—
436C2×C22⋊C4—434no—
437C2×C22⋊C4C22×D4314yes—
438C2×C22⋊C4C22×D4314yes—
439C2×C22⋊C4C22×D4314yes—
440C2×C42—431no—
441C2×C42—434no—
442C2×C42—434no—
443C2×C42—434no—
444C2×C42—432no—
445C2×C42—438no—
446C2×C42C22×D4311yescharacteristic
447C24—431no—
448C24C23×D4314yes—
449C2×Q8—44no—
450C2×Q8—4316no—
451C2×Q8—1728no—
452C2×Q8C23×D4318yes—
453C2×D4—48no—
454C2×D4—44no—
455C2×D4—4316no—
456C2×D4—8616no—
457C2×D4C23×D43116yes—
458C2×D4C23×D4318yes—
459C22×C4—48no—
460C22×C4—432no—
461C22×C4—434no—
462C22×C4—431no—
463C22×C4—434no—
464C22×C4—434no—
465C22×C4—4316no—
466C22×C4—4316no—
467C22×C4—434no—
468C22×C4—438no—
469C22×C4—4316no—
470C22×C4—864no—
471C22×C4—1728no—
472C22×C4—1724no—
473C22×C4—1728no—
474C22×C4—1728no—
475C22×C4C23×D4314yes—
476C22×C4C23×D4311yescharacteristic
477C22×C4C23×D4312yes—
478C22×C4C23×D4314yes—
479C22×C4C23×D43116yes—
480C4⋊C4—4316no—
481C4⋊C4—4316no—
482C4⋊C4—4316no—
483C4⋊C4—4316no—
484C4⋊C4—438no—
485C4⋊C4—4316no—
486C4⋊C4—4316no—
487C4⋊C4—4316no—
488C4⋊C4—4316no—
489C4⋊C4—4316no—
490C4⋊C4—438no—
491C4⋊C4—4316no—
492C4⋊C4—4316no—
493C4⋊C4—4316no—
494C4⋊C4—438no—
495C4⋊C4—4316no—
496C4⋊C4C23×D43116yes—
497C4⋊C4C23×D4318yes—
498C4⋊C4C23×D43116yes—
499C22⋊C4—4316no—
500C22⋊C4—4316no—
501C22⋊C4—4316no—
502C22⋊C4—4316no—
503C22⋊C4—4316no—
504C22⋊C4—4316no—
505C22⋊C4C23×D43116yes—
506C22⋊C4C23×D43116yes—
507C22⋊C4C23×D43116yes—
508C42—434no—
509C42—438no—
510C42—4316no—
511C42—4316no—
512C42—4316no—
513C42C23×D4314yes—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—434no—
518C23—432no—
519C23—864no—
520C23C24×D4318yes—
521C23C24×D4311yescharacteristic
522Q8—48no—
523Q8—17216no—
524D4—416no—
525D4—48no—
526D4—8632no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—28no—
530C2×C4—24no—
531C2×C4—416no—
532C2×C4—434no—
533C2×C4—438no—
534C2×C4—432no—
535C2×C4—438no—
536C2×C4—438no—
537C2×C4—868no—
538C2×C4—862no—
539C2×C4—868no—
540C2×C4—864no—
541C2×C4—868no—
542C2×C4—868no—
543C2×C4—17216no—
544C2×C4—1728no—
545C2×C4—17216no—
546C2×C4—17216no—
547C2×C4C24×D4318yes—
548C2×C4C24×D4312yes—
549C2×C4C24×D4314yes—
550C2×C4C24×D4318yes—
551C22—28no—
552C22—28no—
553C22—28no—
554C22—416no—
555C22—434no—
556C22—864no—
557C22—868no—
558C222−1+4×D4312yes—
559C22#1458373414yes—
560C22C25×D4311yescharacteristic
561C4—22no—
562C4—28no—
563C4—28no—
564C4—24no—
565C4—862no—
566C4—868no—
567C4—864no—
568C4—868no—
569C4—868no—
570C2—48no—
571C2—864no—
572C2#1914905014yesdirect product factor
573C2C2×2−1+4×D4311yescharacteristic
574C2C2×#1458373412yes—
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#562C2
socleC23×C43C25
hypercenterC2×#562D43
hypocenterC43C2×#3553
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #19149050C2direct (N × H)
2. C2×C43⋊#564C2semidirect
3. C2×#14583649C2semidirect
4. C2×#14583603C2semidirect
5. C2×#14583596C2semidirect
6. C2×#14583586C2semidirect
7. C2×#14583509C2semidirect
8. C2×#14583494C2semidirect
9. C2×#14583492C2semidirect
10. C2×#14583428C2semidirect
11. C2×#125×D43C2semidirect
12. C2×C43×#562C2semidirect
13. C43⋊#564C22semidirect
14. #14583649C22semidirect
15. #14583603C22semidirect
16. #14583596C22semidirect
17. #14583586C22semidirect
18. #14583509C22semidirect
19. #14583494C22semidirect
20. #14583492C22semidirect
22. #14583428C22semidirect
37. #125×D43C22semidirect
63. C43×#562C22semidirect
286. C2×#562D43semidirect
296. C2×C43#3553semidirect
302. #562C2×D43semidirect
356. C43C2×#3553semidirect
572. C2#19149050direct (N × H)

Maximal subgroups

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

subgroupindex
#191490502
C2×C43⋊#5642
C2×#145836492
C2×#145836032
C2×#145835962
C2×#145835862
C2×#145835092
C2×#145834942
C2×#145834922
C2×#145834282
C2×#125×D432
C2×C43×#5622
C2×#355343