Finite Group Databasebeta

← C2×#19133561 #25068697

Subgroups — C2×#19133561 #25068697

Order 11008.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583498C211yesmaximal, characteristic
2C2×#14583054C211yesmaximal, characteristic, complemented
3C2×#14583040C211yesmaximal, characteristic
4C2×#14582820C211yesmaximal, characteristic, complemented
5#19133561C218yesmaximal, direct product factor
6C2×#14582632C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#328C211yesmaximal, characteristic, complemented
9C23×Dic86C2211yescharacteristic
10C22×#10621885—21no—
11C22×#10621873—21no—
12#14583498—22no—
13#14583498—22no—
14#14583498—22no—
15#14583498C2214yes—
16C2×#13063320—21no—
17C2×#13063316—21no—
18C2×#13063310—21no—
19C2×#13063309—21no—
20C2×#13063301—21no—
21C2×#13063299C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C22×C4⋊Dic43—21no—
24C22×Dic43⋊C4C2211yescharacteristic
25#14583054—22no—
26#14583054C2214yescomplemented
27#14583040—22no—
28#14583040C2214yes—
29C2×#13063250—21no—
30C2×#13063248—21no—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582820—22no—
33#14582820C2214yescomplemented
34C2×C43⋊#95—21no—
35#14582632C2214yes—
36#14582624C2214yescomplemented
37C2×C22⋊Q8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C43×#328C2214yescomplemented
41C22×Dic86—21no—
42C22×Dic86—21no—
43C22×Dic86—21no—
44C22×Dic86—21no—
45C22×Dic86—21no—
46C22×Dic86—44no—
47C22×Dic86C2312yes—
48C22×D172D411yescharacteristic
49C22×C22⋊D43—21no—
50C23×Dic43—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C22×C4×D43—21no—
54C2×#10621885—24no—
55C2×#10621885—44no—
56C2×#10621873—24no—
57C2×#10621873—44no—
58C22×C43⋊C8—21no—
59#13063320—24no—
60#13063320—24no—
61#13063316—24no—
62#13063316—24no—
63#13063310—24no—
64#13063310—24no—
65#13063309—24no—
66#13063309—24no—
67#13063301—24no—
68#13063301—24no—
69#13063299—21no—
70#13063299—21no—
71#13063299D412yes—
72#13063299C2312yes—
73(C22⋊D43)⋊C4—24no—
74(C22⋊D43)⋊C4—24no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—24no—
78C2×C4⋊Dic43—44no—
79C2×C4⋊Dic43D411yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D412yes—
86C2×Dic43⋊C4C2312yes—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92#13063250—24no—
93#13063248—24no—
94C22⋊(C43⋊C8)—21no—
95C22⋊(C43⋊C8)C2312yes—
96C43⋊#95—24no—
97C22×Q8×C43D411yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43—21no—
101C22⋊Q8×C43—21no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43D412yes—
104C22⋊Q8×C43C2312yes—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43—21no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110#95×C43—21no—
111#95×C43C2312yes—
112C24×C43C2×D411yescharacteristic
113C23×D43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—42no—
116C2×Q8×C43C2×D412yes—
117C22×C4×C43—24no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
132C2×C22⋊D43—42no—
133C2×C22⋊D43—42no—
134C22×Dic43—24no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—41no—
146C22×Dic43—41no—
147C22×Dic43C2×D412yes—
148C22×Dic43C2×D412yes—
149C2×D172—21no—
150C2×D172—42no—
151C2×D172C2×D412yes—
152C2×C4×D43—24no—
153C2×C4×D43—82no—
154C2×Dic86—24no—
155C2×Dic86—24no—
156C2×Dic86—22no—
157C2×Dic86—22no—
158C2×Dic86—44no—
159C2×Dic86—44no—
160C2×Dic86—44no—
161C2×Dic86—44no—
162C2×Dic86—42no—
163C2×Dic86—42no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×C8×C43—22no—
167C2×C8×C43—42no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43C2×D412yes—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174#10621885—48no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—22no—
179(C2×D43)⋊C4—22no—
180C4⋊Dic43—24no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—48no—
184C4⋊Dic43C2×D412yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—22no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190C4×Dic43—24no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—42no—
193#10621873—48no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43#12011yescharacteristic
197C23×C43#12011yescharacteristic
198C23×C43#13512yes—
199C23×C43#13712yes—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205Q8×C43—42no—
206Q8×C43—81no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—24no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—48no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C22⋊D43—42no—
226C22⋊D43—42no—
227C22⋊D43—44no—
228C2×Dic43—24no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—44no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—44no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—81no—
244D172—42no—
245D172—81no—
246C4×D43—84no—
247Dic86—24no—
248Dic86—24no—
249Dic86—42no—
250Dic86—42no—
251Dic86—44no—
252Dic86—44no—
253C8×C43—42no—
254C43⋊C8—42no—
255C2×#1603—431nomaximal, Sylow
256C22×C43—24no—
257C22×C43—24no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43#45212yes—
263C22×C43#45212yes—
264C22×C43#45612yes—
265C22×C43B(4,𝔽2)12yes—
266C22×C43C2×#12011yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13711yescharacteristic
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—84no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—44no—
278C4×C43—42no—
279C4×C43—42no—
280Dic43—42no—
281Dic43—42no—
282Dic43—44no—
283Dic43—42no—
284C2×#539—431no—
285C2×#451—431no—
286C2×#448—431no—
287C2×#395—431no—
288#1603—438no—
289C2×#328D4311yescharacteristic, complemented
290C2×#327—431no—
291C2×#324—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—22no—
295C2×C43#160314yescomplemented
296C2×C43C2×#45211yescharacteristic
297C2×C43C2×#45611yescharacteristic
298C2×C43C2×B(4,𝔽2)11yescharacteristic
299D43—82no—
300C23×Q8—431no—
301C22×Q16—861no—
302C22×SD16—861no—
303#539—434no—
304#539—862no—
305#539—862no—
306#539—862no—
307C2×#126—861no—
308C2×#125—861no—
309C2×#123—861no—
310C2×#123—861no—
311C2×C22⋊Q8—861no—
312C2×C22⋊Q8C2×D4311yescharacteristic
313C2×#121—431no—
314C2×C4×D4—861no—
315C22×C4⋊C4—431no—
316C22×C4⋊C4—861no—
317#451—434no—
318#451—862no—
319#448—434no—
320#448—862no—
321C2×#103—861no—
322C2×#103—861no—
323C2×C22⋊C8—431no—
324C2×C22⋊C8C2×D4311yescharacteristic
325#395—434no—
326#395—862no—
327C2×#95—861no—
328C2×#95C2×D4311yescharacteristic
329#328C2×D4314yescomplemented
330#327—434no—
331#324—434no—
332C43C2×#160311yescharacteristic, complemented, Sylow
333C22×Q8—432no—
334C22×Q8—861no—
335C22×Q8—861no—
336C22×Q8—861no—
337C22×Q8—861no—
338C22×Q8—861no—
339C22×Q8—1724no—
340C22×Q8D17211yescharacteristic
341C22×D4—431no—
342C22×D4—861no—
343C23×C4—21no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—861no—
347C23×C4—861no—
348C23×C4C22×D4311yescharacteristic
349C2×Q16—864no—
350C2×Q16—1724no—
351C2×SD16—864no—
352C2×SD16—1724no—
353C22×C8—21no—
354C22×C8—861no—
355#126—864no—
356#126—864no—
357#125—864no—
358#125—864no—
359#123—864no—
360#123—864no—
361#123—864no—
362#123—864no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—864no—
366C22⋊Q8—864no—
367C22⋊Q8D17212yes—
368C22⋊Q8C22×D4312yes—
369#121—432no—
370#121—432no—
371#121—861no—
372#121—861no—
373C4×D4—864no—
374C4×D4—864no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—432no—
378C2×C4⋊C4—432no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—1724no—
388C2×C4⋊C4D17211yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C42—861no—
395#103—864no—
396#103—864no—
397C22⋊C8—21no—
398C22⋊C8—432no—
399C22⋊C8—861no—
400C22⋊C8C22×D4312yes—
401#95—21no—
402#95—864no—
403#95C22×D4312yes—
404C24—861no—
405C24D4×D4311yescharacteristic
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8—864no—
409C2×Q8—864no—
410C2×Q8—862no—
411C2×Q8—862no—
412C2×Q8—1722no—
413C2×Q8—1722no—
414C2×Q8—1724no—
415C2×Q8—1724no—
416C2×Q8—1724no—
417C2×Q8—1724no—
418C2×Q8—1721no—
419C2×Q8—1721no—
420C2×Q8C2×D17212yes—
421C2×D4—432no—
422C2×D4—862no—
423C2×D4—862no—
424C2×D4—861no—
425C2×D4—1722no—
426C2×D4—1722no—
427C2×D4—1722no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—864no—
438C22×C4—861no—
439C22×C4—864no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—3442no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4C2×D17211yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458Q16—1728no—
459SD16—1728no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—862no—
463C2×C8—1722no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—432no—
468C4⋊C4—864no—
469C4⋊C4—864no—
470C4⋊C4—864no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—861no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—1728no—
477C4⋊C4C2×D17212yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—864no—
481C22⋊C4—864no—
482C22⋊C4—864no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C42—864no—
486C23—22no—
487C23—22no—
488C23—862no—
489C23—1722no—
490C23—1722no—
491C23—1722no—
492C23#1306329511yescharacteristic
493C23#1306329511yescharacteristic
494C23#1306334612yes—
495C23#1306335712yes—
496C23C2×D4×D4311yescharacteristic
497Q8—42no—
498Q8—81no—
499Q8—864no—
500Q8—864no—
501Q8—1722no—
502Q8—1722no—
503Q8—1724no—
504Q8—1724no—
505D4—3441no—
506D4—1722no—
507D4—1724no—
508D4—1722no—
509D4—1722no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—48no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—864no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—3444no—
531C2×C4—3441no—
532C2×C4—1722no—
533C2×C4—1724no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1724no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4#1306329511yescharacteristic
542C2×C4#1306329511yescharacteristic
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4C22×D17211yescharacteristic
545C8—42no—
546C8—1722no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—24no—
553C22—3444no—
554C22—1722no—
555C22—1722no—
556C22—1722no—
557C22#1458306412yes—
558C22#1458306412yes—
559C22#1458308312yes—
560C22#1458308712yes—
561C22C2×#1306329511yescharacteristic
562C22C2×#1306334611yescharacteristic
563C22C2×#1306335711yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—44no—
569C4—42no—
570C4—42no—
571C4—1722no—
572C4—1724no—
573C4—1722no—
574C4—1722no—
575C2—21no—
576C2—22no—
577C2—21no—
578C2—3442no—
579C2#1913356114yesdirect product factor
580C2C2×#1458306411yescharacteristic
581C2C2×#1458308311yescharacteristic
582C2C2×#1458308711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#328D43
hypocenterC43C2×#1603
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#14583054C2semidirect
4. C2×#14582820C2semidirect
5. #19133561C2direct (N × H)
7. C2×#14582624C2semidirect
8. C2×C43×#328C2semidirect
26. #14583054C22semidirect
33. #14582820C22semidirect
36. #14582624C22semidirect
40. C43×#328C22semidirect
289. C2×#328D43semidirect
295. C2×C43#1603semidirect
329. #328C2×D43semidirect
332. C43C2×#1603semidirect
579. C2#19133561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834982
C2×#145830542
C2×#145830402
C2×#145828202
#191335612
C2×#145826322
C2×#145826242
C2×C43×#3282
C2×#160343