Finite Group Databasebeta

← C2×#19134975 #25098134

Subgroups — C2×#19134975 #25098134

Order 11008.

1794 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2C2×#14583445C211yesmaximal, characteristic
3C2×#14582916C211yesmaximal, characteristic, complemented
4C2×#14582872C211yesmaximal, characteristic, complemented
5#19134975C218yesmaximal, direct product factor
6C2×#14582660C211yesmaximal, characteristic, complemented
7C2×#14582658C211yesmaximal, characteristic, complemented
8C2×C43×#421C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583665—22no—
11#14583665—22no—
12#14583665—22no—
13#14583665C2214yescomplemented
14C2×#13063333—22no—
15C2×#13063331—22no—
16C22×#10621877C2211yescharacteristic
17C2×M16×D43—22no—
18#14583445—22no—
19#14583445—22no—
20#14583445C414yescomplemented
21#14583445C2214yes—
22C2×#13063323C411yescharacteristic, complemented
23C2×#13063321C411yescharacteristic, complemented
24C2×#13063314C411yescharacteristic, complemented
25C2×#13063312C411yescharacteristic, complemented
26C2×#13063297—22no—
27C2×C4×C22⋊D43—22no—
28C2×#13063284C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30#14582916—22no—
31#14582916C2214yescomplemented
32C2×#13063252—22no—
33#14582872—22no—
34#14582872C2214yescomplemented
35C2×#13063239—22no—
36#14582660C2214yescomplemented
37#14582658C2214yescomplemented
38C22×#41×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×#421—22no—
42C43×#421C2214yescomplemented
43C2×#104×C43—22no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898C2×C412yes—
53C2×#10621898D412yes—
54C2×#10621898D412yes—
55C2×#10621898C2312yes—
56C22×Dic86C2×C411yescharacteristic
57C22×D172C2×C411yescharacteristic
58C22×C22⋊D43—22no—
59C22×C22⋊D43D412yes—
60C23×Dic43—21no—
61C22×C4×D43D412yes—
62#13063333—28no—
63#13063333—28no—
64#13063331—28no—
65#13063331—28no—
66C2×#10621877—21no—
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877D412yescomplemented
70C2×#10621877D412yescomplemented
71C2×#10621877C2312yes—
72C2×#10621872—24no—
73M16×D43—28no—
74M16×D43—28no—
75C22×C43⋊C8—21no—
76C2×C8×D43—24no—
77#13063323—22no—
78#13063323C2×C414yescomplemented
79#13063321—22no—
80#13063321C2×C414yescomplemented
81#13063314—22no—
82#13063314C2×C414yescomplemented
83#13063312—22no—
84#13063312C2×C414yescomplemented
85#13063297—28no—
86#13063297—28no—
87C4×C22⋊D43—28no—
88C4×C22⋊D43—28no—
89#13063284—21no—
90#13063284—21no—
91#13063284—21no—
92#13063284C2312yes—
93C2×C4⋊Dic43—21no—
94C2×Dic43⋊C4—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—22no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2×C412yes—
105C2×C4×Dic43C2312yes—
106#13063252—28no—
107#13063239—28no—
108C2×#41×C43—21no—
109C2×#41×C43—21no—
110C2×#41×C43—21no—
111C2×#41×C43—21no—
112C2×#41×C43—21no—
113C2×#41×C43—21no—
114C2×#41×C43—21no—
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117C2×#41×C43—21no—
118C2×#41×C43C2×C412yes—
119C2×#41×C43C2312yes—
120C22×Q8×C43C2×C411yescharacteristic
121C22×D4×C43—21no—
122C22×D4×C43C2×C411yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43D412yescomplemented
129C2×M16×C43D412yescomplemented
130C2×M16×C43C2312yes—
131C22×C8×C43—21no—
132#117×C43—21no—
133#117×C43—21no—
134#117×C43—21no—
135#117×C43C2312yes—
136C2×C4⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139#104×C43—28no—
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43C22⋊C412yes—
143#41×C43—22no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—22no—
147#41×C43—22no—
148#41×C43—22no—
149#41×C43—22no—
150#41×C43—22no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157#41×C43—41no—
158#41×C43—41no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43C22×C412yes—
165C2×D4×C43—21no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43C22×C412yes—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—21no—
180C22×C4×C43—41no—
181C22×C4×C43—41no—
182C22×C4×C43—41no—
183C22×C4×C43—41no—
184C22×C4×C43—41no—
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4111yescharacteristic
195C22×C4×C43#4111yescharacteristic
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43#4111yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—28no—
204C2×C22⋊D43—48no—
205C2×C22⋊D43C22⋊C414yes—
206C2×C22⋊D43C2×D414yes—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—44no—
212C22×Dic43—41no—
213C22×Dic43C22⋊C412yes—
214#10621898—22no—
215#10621898—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—22no—
219#10621898—22no—
220#10621898—22no—
221#10621898—22no—
222#10621898—22no—
223#10621898—22no—
224#10621898—22no—
225#10621898—22no—
226#10621898—22no—
227#10621898—22no—
228#10621898—22no—
229#10621898—22no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172C22⋊C412yes—
235C2×D172C22×C412yes—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43C22⋊C414yes—
241C2×C4×D43C2×D414yes—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86C22⋊C412yes—
247C2×Dic86C22×C412yes—
248M16×C43—22no—
249M16×C43—22no—
250M16×C43—22no—
251M16×C43C2×D414yescomplemented
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43—22no—
255C4⋊C4×C43—22no—
256C4⋊C4×C43—41no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—41no—
259C42×C43—22no—
260C42×C43—41no—
261C22⋊Dic43—28no—
262C22⋊Dic43—22no—
263C22⋊Dic43—41no—
264(C2×D43)⋊C4—28no—
265C4⋊Dic43—22no—
266C4⋊Dic43—41no—
267Dic43⋊C4—28no—
268C4×Dic43—22no—
269C4×Dic43—21no—
270C4×Dic43—21no—
271C4×Dic43—22no—
272C4×Dic43—22no—
273C4×Dic43—41no—
274C4×Dic43C22×C412yes—
275C4×Dic43C22×C412yes—
276#10621877—22no—
277#10621877—22no—
278#10621877—22no—
279#10621877C2×D414yescomplemented
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283#10621872—216no—
284C8×D43—216no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—44no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43C2×C22⋊C411yescharacteristic
291C23×C43C2×C22⋊C411yescharacteristic
292C23×C43#12111yescharacteristic
293C23×C43#12111yescharacteristic
294C23×C43#12111yescharacteristic
295C23×C43#12111yescharacteristic
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—44no—
300C22×D43C2×C22⋊C414yes—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—41no—
304Q8×C43—41no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—42no—
308D4×C43—42no—
309D4×C43—42no—
310D4×C43—42no—
311D4×C43—41no—
312D4×C43—41no—
313C2×C4×C43—22no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—82no—
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C4×D411yescharacteristic
328C2×C4×C43C4×D411yescharacteristic
329C2×C4×C43C4×D411yescharacteristic
330C2×C4×C43C4×D411yescharacteristic
331C2×C4×C43C4×D411yescharacteristic
332C2×C4×C43#12011yescharacteristic
333C2×C4×C43#12011yescharacteristic
334C2×C4×C43#12011yescharacteristic
335C2×C4×C43#12011yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12111yescharacteristic
339C2×C4×C43#12111yescharacteristic
340C2×C4×C43#12311yescharacteristic
341C2×C4×C43#12311yescharacteristic
342C2×C4×C43#12311yescharacteristic
343C2×C4×C43#12311yescharacteristic
344C2×C4×C43C23×C411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C22⋊D43—24no—
351C22⋊D43—24no—
352C22⋊D43—24no—
353C22⋊D43—24no—
354C22⋊D43—416no—
355C2×Dic43—24no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—44no—
361C2×Dic43—44no—
362C2×Dic43—42no—
363C2×Dic43—42no—
364C2×Dic43—82no—
365C2×Dic43C2×C22⋊C414yes—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—22no—
370C4×D43—24no—
371C4×D43—24no—
372C4×D43—24no—
373C4×D43—24no—
374Dic86—22no—
375Dic86—22no—
376Dic86—22no—
377Dic86—22no—
378C8×C43—24no—
379C43⋊C8—24no—
380C2×#1884—431nomaximal, Sylow
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—44no—
389C22×C43—42no—
390C22×C43—82no—
391C22×C43—82no—
392C22×C43#38611yescharacteristic
393C22×C43#38611yescharacteristic
394C22×C43#38611yescharacteristic
395C22×C43#38611yescharacteristic
396C22×C43C22×C22⋊C411yescharacteristic
397C22×C43C2×#12111yescharacteristic
398C22×C43C2×#12111yescharacteristic
399C2×D43—24no—
400C2×D43—44no—
401C2×D43—44no—
402C2×D43—82no—
403C4×C43—42no—
404C4×C43—82no—
405C4×C43#38611yescharacteristic
406C4×C43#38611yescharacteristic
407C4×C43#38611yescharacteristic
408C4×C43#38611yescharacteristic
409C4×C43C2×C4×D411yescharacteristic
410C4×C43C2×C4×D411yescharacteristic
411C4×C43C2×#12011yescharacteristic
412C4×C43C2×#12311yescharacteristic
413Dic43—24no—
414Dic43—24no—
415Dic43—42no—
416Dic43—82no—
417C2×#568—431no—
418C2×#532—431no—
419C2×#421—431no—
420C2×#421D4311yescharacteristic, complemented
421C2×#410—431no—
422#1884—438no—
423C2×#339—431no—
424C2×#339—431no—
425C2×C43—21no—
426C2×C43—21no—
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—21no—
430C2×C43—21no—
431C2×C43—82no—
432C2×C43#188412yescomplemented
433C2×C43C2×#38611yescharacteristic
434D43—44no—
435C22×#41—431no—
436C22×#41C2×D4311yescharacteristic
437#568—434no—
438#568—862no—
439#568—862no—
440#568—862no—
441C2×#131—862no—
442C2×#131—862no—
443C22×M16—431no—
444C22×M16—862no—
445C22×M16C2×D4311yescharacteristic
446#532—434no—
447#532—434no—
448#532—862no—
449#532—862no—
450C2×C4⋊Q8—431no—
451C2×#127—431no—
452C2×#124—431no—
453C2×#124—431no—
454C2×#121—862no—
455C2×C4×D4—862no—
456C2×#117—431no—
457C2×#117C2×D4311yescharacteristic
458C22×C42—431no—
459#421—22no—
460#421—434no—
461#421—862no—
462#421C2×D4314yescomplemented
463C2×#104—22no—
464C2×#104—862no—
465#410—434no—
466#410—862no—
467C2×#99—862no—
468#339—434no—
469#339—434no—
470C43C2×#188411yescharacteristic, complemented, Sylow
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—432no—
482C2×#41—432no—
483C2×#41—432no—
484C2×#41—432no—
485C2×#41—861no—
486C2×#41—861no—
487C2×#41—861no—
488C2×#41—861no—
489C2×#41—861no—
490C2×#41—861no—
491C2×#41—861no—
492C2×#41—861no—
493C2×#41C4×D4312yes—
494C2×#41C22×D4312yes—
495C22×Q8—431no—
496C22×Q8C4×D4311yescharacteristic
497C22×D4—21no—
498C22×D4—432no—
499C22×D4—431no—
500C22×D4—862no—
501C22×D4C4×D4311yescharacteristic
502C23×C4—21no—
503C23×C4—432no—
504C23×C4—861no—
505C23×C4C22×D4311yescharacteristic
506#131—868no—
507#131—868no—
508#131—868no—
509#131—868no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—432no—
514C2×M16—432no—
515C2×M16—432no—
516C2×M16—864no—
517C2×M16—868no—
518C2×M16—868no—
519C2×M16—861no—
520C2×M16—861no—
521C2×M16—861no—
522C2×M16C22⋊D4312yescomplemented
523C2×M16C22⋊D4312yescomplemented
524C2×M16C22×D4312yes—
525C22×C8—21no—
526C22×C8—864no—
527C22×C8—861no—
528C4⋊Q8—434no—
529C4⋊Q8—862no—
530#127—434no—
531#127—862no—
532#124—434no—
533#124—434no—
534#124—862no—
535#124—862no—
536#121—868no—
537#121—868no—
538C4×D4—868no—
539C4×D4—868no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117—432no—
544#117—861no—
545#117—861no—
546#117—861no—
547#117C22×D4312yes—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—862no—
550C2×C4⋊C4—861no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—862no—
553C2×C22⋊C4—862no—
554C2×C22⋊C4—861no—
555C2×C42—21no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—432no—
559C2×C42—432no—
560C2×C42—861no—
561C2×C42—861no—
562C2×C42—861no—
563C2×C42—861no—
564#104—28no—
565#104—868no—
566#99—868no—
567C24—21no—
568C24—432no—
569C24D4×D4311yescharacteristic
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—41no—
586#41—862no—
587#41—862no—
588#41—862no—
589#41—862no—
590#41—862no—
591#41—862no—
592#41—862no—
593#41—862no—
594#41—862no—
595#41—862no—
596#41—862no—
597#41—862no—
598#41—862no—
599#41—862no—
600#41—862no—
601#41—862no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—432no—
608C2×Q8—432no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8C2×C4×D4312yes—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—434no—
626C2×D4—434no—
627C2×D4—432no—
628C2×D4—432no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—862no—
632C2×D4—862no—
633C2×D4—868no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—1728no—
639C2×D4C2×C4×D4312yes—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—432no—
649C22×C4—434no—
650C22×C4—434no—
651C22×C4—861no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—861no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—1724no—
660C22×C4—1721no—
661C22×C4C2×C4×D4311yescharacteristic
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4#1062189811yescharacteristic
664C22×C4#1062189811yescharacteristic
665C22×C4D4×D4311yescharacteristic
666C22×C4D4×D4311yescharacteristic
667C22×C4D4×D4311yescharacteristic
668C22×C4D4×D4311yescharacteristic
669C22×C4D4×D4311yescharacteristic
670C22×C4#1062190011yescharacteristic
671C22×C4#1062190011yescharacteristic
672C22×C4C2×C22⋊D4311yescharacteristic
673C22×C4C2×C22⋊D4311yescharacteristic
674C22×C4C23×D4311yescharacteristic
675M16—22no—
676M16—22no—
677M16—22no—
678M16—434no—
679M16—8616no—
680M16—862no—
681M16—862no—
682M16—862no—
683M16C2×C22⋊D4314yescomplemented
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—8616no—
688C2×C8—862no—
689C2×C8—862no—
690C2×C8—862no—
691C4⋊C4—22no—
692C4⋊C4—41no—
693C4⋊C4—868no—
694C4⋊C4—862no—
695C4⋊C4—1721no—
696C22⋊C4—22no—
697C22⋊C4—41no—
698C22⋊C4—868no—
699C22⋊C4—868no—
700C22⋊C4—862no—
701C22⋊C4—1721no—
702C42—22no—
703C42—41no—
704C42—432no—
705C42—432no—
706C42—862no—
707C42—861no—
708C42—861no—
709C42—862no—
710C42—862no—
711C42—1721no—
712C23—22no—
713C23—42no—
714C23—44no—
715C23—41no—
716C23—41no—
717C23—434no—
718C23—862no—
719C23—862no—
720C23—1724no—
721C23C22⋊C4×D4311yescharacteristic
722C23C22⋊C4×D4311yescharacteristic
723C23#1306329611yescharacteristic
724C23#1306329611yescharacteristic
725C23#1306329811yescharacteristic
726C23#1306329811yescharacteristic
727C23C2×D4×D4311yescharacteristic
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—862no—
733Q8—862no—
734Q8—862no—
735Q8—862no—
736D4—22no—
737D4—22no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—41no—
743D4—41no—
744D4—864no—
745D4—864no—
746D4—864no—
747D4—864no—
748D4—862no—
749D4—862no—
750D4—862no—
751D4—862no—
752D4—17216no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—82no—
762C2×C4—434no—
763C2×C4—864no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—864no—
768C2×C4—864no—
769C2×C4—864no—
770C2×C4—864no—
771C2×C4—862no—
772C2×C4—3442no—
773C2×C4—1724no—
774C2×C4—1724no—
775C2×C4—1722no—
776C2×C4—1722no—
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22⋊C4×D4311yescharacteristic
779C2×C4(C22⋊D43)⋊C411yescharacteristic
780C2×C4(C22⋊D43)⋊C411yescharacteristic
781C2×C4(C22⋊D43)⋊C411yescharacteristic
782C2×C4(C22⋊D43)⋊C411yescharacteristic
783C2×C4C4×C22⋊D4311yescharacteristic
784C2×C4C4×C22⋊D4311yescharacteristic
785C2×C4C4×C22⋊D4311yescharacteristic
786C2×C4C4×C22⋊D4311yescharacteristic
787C2×C4#1306329311yescharacteristic
788C2×C4#1306329311yescharacteristic
789C2×C4#1306329311yescharacteristic
790C2×C4#1306329311yescharacteristic
791C2×C4#1306329611yescharacteristic
792C2×C4#1306329611yescharacteristic
793C2×C4#1306329811yescharacteristic
794C2×C4#1306329811yescharacteristic
795C2×C4#1306330711yescharacteristic
796C2×C4#1306330711yescharacteristic
797C2×C4#1306330711yescharacteristic
798C2×C4#1306330711yescharacteristic
799C2×C4C22×C4×D4311yescharacteristic
800C2×C4C2×D4×D4311yescharacteristic
801C2×C4C2×D4×D4311yescharacteristic
802C2×C4C22×C22⋊D4311yescharacteristic
803C2×C4C2×#1062190011yescharacteristic
804C2×C4C2×#1062189811yescharacteristic
805C8—24no—
806C8—864no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—44no—
815C22—42no—
816C22—82no—
817C22—82no—
818C22—864no—
819C22—3442no—
820C22—1724no—
821C22—1724no—
822C22#1458277511yescharacteristic
823C22#1458277511yescharacteristic
824C22#1458277511yescharacteristic
825C22#1458277511yescharacteristic
826C22C2×C22⋊C4×D4311yescharacteristic
827C22C2×#1306329611yescharacteristic
828C22C2×#1306329811yescharacteristic
829C4—42no—
830C4—82no—
831C4—864no—
832C4—864no—
833C4—3442no—
834C4—1722no—
835C4#1458277511yescharacteristic
836C4#1458277511yescharacteristic
837C4#1458277511yescharacteristic
838C4#1458277511yescharacteristic
839C4C2×(C22⋊D43)⋊C411yescharacteristic
840C4C2×C4×C22⋊D4311yescharacteristic
841C4C2×#1306329311yescharacteristic
842C4C2×#1306330711yescharacteristic
843C2—21no—
844C2—21no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—82no—
850C2—1724no—
851C2#1913497512yesdirect product factor
852C2C2×#1458277511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC22×C43#386
prime radicalC2×#14583445C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43C2×#1884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582916C2semidirect
4. C2×#14582872C2semidirect
5. #19134975C2direct (N × H)
6. C2×#14582660C2semidirect
7. C2×#14582658C2semidirect
8. C2×C43×#421C2semidirect
13. #14583665C22semidirect
20. #14583445C4semidirect
22. C2×#13063323C4semidirect
23. C2×#13063321C4semidirect
24. C2×#13063314C4semidirect
25. C2×#13063312C4semidirect
31. #14582916C22semidirect
34. #14582872C22semidirect
36. #14582660C22semidirect
37. #14582658C22semidirect
42. C43×#421C22semidirect
69. C2×#10621877D4semidirect
70. C2×#10621877D4semidirect
78. #13063323C2×C4semidirect
80. #13063321C2×C4semidirect
82. #13063314C2×C4semidirect
84. #13063312C2×C4semidirect
128. C2×M16×C43D4semidirect
129. C2×M16×C43D4semidirect
251. M16×C43C2×D4semidirect
279. #10621877C2×D4semidirect
420. C2×#421D43semidirect
432. C2×C43#1884semidirect
462. #421C2×D43semidirect
470. C43C2×#1884semidirect
522. C2×M16C22⋊D43semidirect
523. C2×M16C22⋊D43semidirect
683. M16C2×C22⋊D43semidirect
851. C2#19134975direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836652
C2×#145834452
C2×#145829162
C2×#145828722
#191349752
C2×#145826602
C2×#145826582
C2×C43×#4212
C2×#188443