Finite Group Databasebeta

← C2×#19133645 #25068849

Subgroups — C2×#19133645 #25068849

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583487C211yesmaximal, characteristic
2C2×#14583235C211yesmaximal, characteristic, complemented
3C2×#14583218C211yesmaximal, characteristic, complemented
4C2×#14582835C211yesmaximal, characteristic, complemented
5#19133645C218yesmaximal, direct product factor
6C2×#14582637C211yesmaximal, characteristic, complemented
7C2×#14582634C211yesmaximal, characteristic, complemented
8C2×C43×#323C211yesmaximal, characteristic, complemented
9#14583487—22no—
10#14583487—22no—
11#14583487—22no—
12#14583487C2214yes—
13C2×#13063318—21no—
14C2×#13063311—21no—
15C2×#13063307—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×#13063298—21no—
19C2×#13063294—21no—
20C2×C4×C22⋊D43—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4—21no—
23C22×C22⋊Dic43—21no—
24#14583235—22no—
25#14583235C2214yescomplemented
26#14583218—22no—
27#14583218C2214yescomplemented
28C2×#13063259—21no—
29C2×#13063257—21no—
30C2×#13063250—21no—
31C2×#13063247—21no—
32#14582835—22no—
33#14582835C2214yescomplemented
34C2×C43⋊#95C2211yescharacteristic
35#14582637C2214yescomplemented
36#14582634C2214yescomplemented
37C22×C22⋊C4×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C43×#323C2214yescomplemented
41C22×Dic86D411yescharacteristic
42C22×D172D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C22×C22⋊D43—21no—
46C23×Dic43—21no—
47C23×Dic43—21no—
48C22×C4×D43—21no—
49#13063318—24no—
50#13063318—24no—
51#13063311—24no—
52#13063311—24no—
53#13063307—24no—
54#13063307—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063299—21no—
60#13063299—21no—
61#13063299D412yes—
62#13063299C2312yes—
63#13063298—24no—
64#13063298—24no—
65#13063294—24no—
66#13063294—24no—
67C4×C22⋊D43—24no—
68C4×C22⋊D43—24no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43D411yescharacteristic
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43C2312yes—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—24no—
80C2×Dic43⋊C4—44no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—24no—
85C2×C22⋊Dic43—44no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89#13063259—24no—
90#13063257—24no—
91#13063250—24no—
92#13063247—24no—
93C43⋊#95—21no—
94C43⋊#95C2312yes—
95C25×C43D411yescharacteristic
96C23×C4×C43D411yescharacteristic
97C23×C4×C43C2311yescharacteristic
98C22×C8×C43—21no—
99C22×C8×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43D412yes—
105C2×C22⋊C4×C43C2312yes—
106C22⋊C8×C43—21no—
107C22⋊C8×C43—21no—
108C22⋊C8×C43C2312yes—
109C22⋊C8×C43C2312yes—
110C24×C43—21no—
111C24×C43—22no—
112C24×C43—21no—
113C24×C43—22no—
114C24×C43—42no—
115C24×C43—42no—
116C24×C43C2×D411yescharacteristic
117C24×C43C2×D412yes—
118C23×D43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C2×C22⋊D43—24no—
131C2×C22⋊D43—24no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—42no—
135C2×C22⋊D43—42no—
136C2×C22⋊D43—82no—
137C2×C22⋊D43—82no—
138C22×Dic43—24no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C22×Dic43—42no—
150C2×D172—21no—
151C2×D172—42no—
152C2×D172C2×D412yes—
153C2×C4×D43—24no—
154C2×C4×D43—82no—
155C2×Dic86—21no—
156C2×Dic86—42no—
157C2×Dic86C2×D412yes—
158C2×C8×C43—22no—
159C2×C8×C43—22no—
160C2×C8×C43—42no—
161C2×C8×C43—42no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊Dic43—24no—
167C22⋊Dic43—24no—
168C22⋊Dic43—22no—
169C22⋊Dic43—22no—
170C22⋊Dic43—48no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—22no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—41no—
179C4⋊Dic43—41no—
180C4⋊Dic43C2×D412yes—
181C4⋊Dic43C2×D412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—48no—
186C4×Dic43—24no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—48no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—81no—
200C23×C43—81no—
201C23×C43—84no—
202C23×C43#12011yescharacteristic
203C23×C43#12011yescharacteristic
204C23×C43#13512yes—
205C23×C43#13712yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—81no—
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—
228C22⋊D43—84no—
229C22⋊D43—84no—
230C2×Dic43—24no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—48no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—82no—
244C2×Dic43—82no—
245D172—42no—
246D172—81no—
247C4×D43—84no—
248Dic86—42no—
249Dic86—81no—
250C8×C43—42no—
251C8×C43—42no—
252C2×#1618—431nomaximal, Sylow
253C22×C43—24no—
254C22×C43—24no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—44no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—82no—
264C22×C43—84no—
265C22×C43—84no—
266C22×C43#45212yes—
267C22×C43#45212yes—
268C22×C43#45312yes—
269C22×C43#45812yes—
270C22×C43C2×#12011yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—84no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—42no—
282Dic43—44no—
283Dic43—42no—
284Dic43—42no—
285Dic43—42no—
286Dic43—82no—
287C2×#538—431no—
288C2×#484—431no—
289C2×#481—431no—
290C2×#399—431no—
291#1618—438no—
292C2×#328—431no—
293C2×#327—431no—
294C2×#323D4311yescharacteristic, complemented
295C2×C43—21no—
296C2×C43—21no—
297C2×C43—22no—
298C2×C43—82no—
299C2×C43#161814yescomplemented
300C2×C43C2×#45211yescharacteristic
301C2×C43C2×#45311yescharacteristic
302C2×C43C2×#45811yescharacteristic
303D43—82no—
304#538—434no—
305#538—862no—
306#538—862no—
307#538—862no—
308C2×#126—861no—
309C2×#124—861no—
310C2×#123—861no—
311C2×C22⋊Q8—431no—
312C2×#121—431no—
313C2×#121—861no—
314C2×#120—861no—
315C2×C4×D4—861no—
316C22×C4⋊C4—431no—
317C22×C4⋊C4—861no—
318C22×C22⋊C4—861no—
319C22×C22⋊C4C2×D4311yescharacteristic
320#484—434no—
321#484—862no—
322#481—434no—
323#481—862no—
324C2×#107—861no—
325C2×#106—861no—
326C2×#103—861no—
327C2×#102—861no—
328C2×C22⋊C8C2×D4311yescharacteristic
329C2×C22⋊C8C2×D4311yescharacteristic
330#399—434no—
331#399—862no—
332C2×#95—431no—
333#328—434no—
334#327—434no—
335#323C2×D4314yescomplemented
336C43C2×#161811yescharacteristic, complemented, Sylow
337C25D17211yescharacteristic
338C22×Q8—431no—
339C22×D4—431no—
340C22×D4—861no—
341C22×D4—861no—
342C22×D4—861no—
343C23×C4—861no—
344C23×C4—861no—
345C23×C4—861no—
346C23×C4D17211yescharacteristic
347C23×C4C22×D4311yescharacteristic
348C22×C8—21no—
349C22×C8—21no—
350#126—864no—
351#126—864no—
352#124—864no—
353#124—864no—
354#123—864no—
355#123—864no—
356C22⋊Q8—432no—
357C22⋊Q8—432no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360#121—432no—
361#121—432no—
362#121—864no—
363#121—864no—
364#121—861no—
365#121—861no—
366#120—864no—
367#120—864no—
368C4×D4—864no—
369C4×D4—864no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—432no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—864no—
381C2×C4⋊C4—1724no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—864no—
392C2×C22⋊C4—1724no—
393C2×C22⋊C4D17212yes—
394C2×C22⋊C4C22×D4312yes—
395C2×C42—861no—
396#107—864no—
397#106—864no—
398#103—864no—
399#102—864no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8C22×D4312yes—
403C22⋊C8C22×D4312yes—
404#95—432no—
405#95—861no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—22no—
410C24—42no—
411C24—42no—
412C24—861no—
413C24C2×D17211yescharacteristic
414C24C2×D17212yes—
415C2×Q8—432no—
416C2×Q8—861no—
417C2×Q8—1722no—
418C2×D4—432no—
419C2×D4—864no—
420C2×D4—864no—
421C2×D4—862no—
422C2×D4—862no—
423C2×D4—861no—
424C2×D4—3442no—
425C2×D4—3442no—
426C2×D4—1722no—
427C2×D4—1722no—
428C2×D4—1722no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—864no—
434C22×C4—864no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—3442no—
441C22×C4—1722no—
442C22×C4—1722no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4C2×D17212yes—
448C22×C4C2×D17211yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—42no—
457C2×C8—42no—
458C4⋊C4—432no—
459C4⋊C4—432no—
460C4⋊C4—864no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—862no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C4⋊C4—862no—
467C4⋊C4—1728no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—864no—
475C22⋊C4—864no—
476C22⋊C4—864no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C22⋊C4—862no—
480C22⋊C4—862no—
481C22⋊C4—1728no—
482C42—864no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—48no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23—862no—
499C23—1722no—
500C23—1722no—
501C23—1722no—
502C23#1306329511yescharacteristic
503C23#1306329511yescharacteristic
504C23#1306334712yes—
505C23#1306335812yes—
506C23C22×D17211yescharacteristic
507Q8—3441no—
508Q8—1722no—
509D4—3441no—
510D4—3444no—
511D4—3444no—
512D4—1722no—
513D4—1724no—
514D4—1722no—
515D4—1722no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—81no—
526C2×C4—864no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—3444no—
531C2×C4—3442no—
532C2×C4—3442no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1728no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4#1306329511yescharacteristic
543C2×C4#1306329511yescharacteristic
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C2×D4×D4311yescharacteristic
546C8—42no—
547C8—42no—
548C22—21no—
549C22—21no—
550C22—24no—
551C22—24no—
552C22—21no—
553C22—21no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—82no—
559C22—84no—
560C22—84no—
561C22—3444no—
562C22—1722no—
563C22—1722no—
564C22—1722no—
565C22#1458306312yes—
566C22#1458306312yes—
567C22#1458306912yes—
568C22#1458309012yes—
569C22C2×#1306329511yescharacteristic
570C22C2×#1306334711yescharacteristic
571C22C2×#1306335811yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—3442no—
578C4—1724no—
579C4—1722no—
580C4—1722no—
581C4—1722no—
582C2—21no—
583C2—21no—
584C2—22no—
585C2—82no—
586C2—3442no—
587C2#1913364514yesdirect product factor
588C2C2×#1458306311yescharacteristic
589C2C2×#1458306911yescharacteristic
590C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#323C2
socleC23×C43#120
prime radicalC2×#14583487C2
hypercenterC2×#323D43
hypocenterC43C2×#1618
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#14583235C2semidirect
3. C2×#14583218C2semidirect
4. C2×#14582835C2semidirect
5. #19133645C2direct (N × H)
6. C2×#14582637C2semidirect
7. C2×#14582634C2semidirect
8. C2×C43×#323C2semidirect
25. #14583235C22semidirect
27. #14583218C22semidirect
33. #14582835C22semidirect
35. #14582637C22semidirect
36. #14582634C22semidirect
40. C43×#323C22semidirect
294. C2×#323D43semidirect
299. C2×C43#1618semidirect
335. #323C2×D43semidirect
336. C43C2×#1618semidirect
587. C2#19133645direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834872
C2×#145832352
C2×#145832182
C2×#145828352
#191336452
C2×#145826372
C2×#145826342
C2×C43×#3232
C2×#161843