Finite Group Databasebeta

← C2×#19134956 #25098070

Subgroups — C2×#19134956 #25098070

Order 11008.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583699C211yesmaximal, characteristic
2C2×#14583665C211yesmaximal, characteristic, complemented
3C2×#14582917C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5C2×#14582867C211yesmaximal, characteristic, complemented
6#19134956C218yesmaximal, direct product factor
7C2×#14582663C211yesmaximal, characteristic, complemented
8C2×C43×#344C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621898C2211yescharacteristic
11#14583699—22no—
12#14583699—22no—
13#14583699C414yescomplemented
14#14583699C2214yes—
15C2×#13063358—21no—
16C2×#13063358C412yescomplemented
17C2×#13063353—21no—
18C2×#13063353C412yescomplemented
19C2×#13063347—22no—
20#14583665—22no—
21#14583665—22no—
22#14583665—22no—
23#14583665C2214yescomplemented
24C2×#13063333—22no—
25C2×#13063331—22no—
26C22×#10621877C2211yescharacteristic
27C2×M16×D43—22no—
28C23×C43⋊C8C2211yescharacteristic
29#14582917—22no—
30#14582917C2214yescomplemented
31C2×#13063253—22no—
32#14582893—22no—
33#14582893C2214yescomplemented
34C2×#13063248—21no—
35C2×#13063245—21no—
36#14582867—22no—
37#14582867C2214yescomplemented
38C2×(C2×D43)⋊C8—22no—
39#14582663C2214yescomplemented
40C22×M16×C43C2211yescharacteristic
41C22×M16×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C43×#344C2214yescomplemented
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×#10621898—21no—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898—21no—
56C2×#10621898—21no—
57C2×#10621898—21no—
58C2×#10621898—21no—
59C2×#10621898—21no—
60C2×#10621898C2×C412yes—
61C2×#10621898C2×C412yes—
62C2×#10621898C2×C412yes—
63C2×#10621898D412yes—
64C2×#10621898D412yes—
65C2×#10621898D412yes—
66C2×#10621898C2312yes—
67C2×#10621898C2312yes—
68C22×Dic86C2×C411yescharacteristic
69C22×Dic86D411yescharacteristic
70C22×D172C2×C411yescharacteristic
71C22×D172D411yescharacteristic
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76#13063358—24no—
77#13063358—24no—
78#13063358—24no—
79#13063358C2×C418yescomplemented
80#13063353—24no—
81#13063353—24no—
82#13063353—24no—
83#13063353C2×C418yescomplemented
84#13063347—28no—
85#13063347—28no—
86C2×Dic172—22no—
87C2×#10621873—22no—
88C2×#10621873—22no—
89C2×D344—22no—
90#13063333—28no—
91#13063333—28no—
92#13063331—28no—
93#13063331—28no—
94C2×#10621877—21no—
95C2×#10621877—21no—
96C2×#10621877—21no—
97C2×#10621877D412yes—
98C2×#10621877D412yes—
99C2×#10621877C2312yes—
100C2×#10621872—24no—
101M16×D43—28no—
102M16×D43—28no—
103C22×C43⋊C8—21no—
104C22×C43⋊C8—21no—
105C22×C43⋊C8—21no—
106C22×C43⋊C8—21no—
107C22×C43⋊C8—21no—
108C22×C43⋊C8—21no—
109C22×C43⋊C8—21no—
110C22×C43⋊C8C2312yes—
111C2×C8×D43—24no—
112#13063253—28no—
113#13063248—24no—
114#13063245—24no—
115(C2×D43)⋊C8—28no—
116C23×C4×C43C2311yescharacteristic
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43C2×C412yes—
125C2×M16×C43C2×C412yes—
126C2×M16×C43D412yes—
127C2×M16×C43C2312yes—
128C2×M16×C43C2312yes—
129C22×C8×C43—21no—
130C22×C8×C43D412yes—
131#117×C43—21no—
132#117×C43—21no—
133#117×C43—21no—
134#117×C43C2312yes—
135C2×C4⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C42×C43—21no—
138C24×C43#4111yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C22×C4×C43—41no—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170#10621898—22no—
171#10621898—22no—
172#10621898—22no—
173#10621898—22no—
174#10621898—22no—
175#10621898—22no—
176#10621898—22no—
177#10621898—22no—
178#10621898—22no—
179#10621898—22no—
180#10621898—22no—
181#10621898—22no—
182#10621898—22no—
183#10621898—22no—
184#10621898—22no—
185#10621898—22no—
186#10621898—22no—
187#10621898—22no—
188#10621898—22no—
189#10621898—22no—
190#10621898—41no—
191#10621898—41no—
192#10621898—41no—
193#10621898—41no—
194#10621898—41no—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898C22⋊C414yes—
199#10621898C22⋊C414yes—
200#10621898C22×C414yes—
201#10621898C2×D414yes—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172C22⋊C412yes—
211C2×D172C22⋊C412yes—
212C2×D172C22×C412yes—
213C2×D172C2×D412yes—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—41no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C22⋊C412yes—
235C2×Dic86C22⋊C412yes—
236C2×Dic86C22×C412yes—
237C2×Dic86C2×D412yes—
238M16×C43—22no—
239M16×C43—22no—
240M16×C43—22no—
241M16×C43—22no—
242M16×C43—22no—
243M16×C43—22no—
244M16×C43—22no—
245M16×C43C22×C414yes—
246C2×C8×C43—22no—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43C2×D414yes—
252C4⋊C4×C43—22no—
253C4⋊C4×C43—41no—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—41no—
256C42×C43—22no—
257C42×C43—41no—
258#10621877—22no—
259#10621877—22no—
260#10621877—22no—
261#10621877C2×D414yes—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—41no—
269C2×C43⋊C8—41no—
270C2×C43⋊C8—41no—
271C2×C43⋊C8—41no—
272Dic172—28no—
273D344—28no—
274#10621873—28no—
275#10621873—28no—
276#10621872—216no—
277C8×D43—216no—
278C23×C43—42no—
279C23×C43C4×D411yescharacteristic
280C23×C43C4×D411yescharacteristic
281C23×C43#12111yescharacteristic
282C23×C43#12111yescharacteristic
283C23×C43#12311yescharacteristic
284C23×C43#12311yescharacteristic
285C23×C43C2×#4111yescharacteristic
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—44no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—82no—
294C2×C4×C43—42no—
295C2×C4×C43—82no—
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C2×C4×C43C2×C22⋊C411yescharacteristic
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43C4×D411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43C4×D411yescharacteristic
305C2×C4×C43C4×D411yescharacteristic
306C2×C4×C43#12011yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12311yescharacteristic
317C2×C4×C43#12311yescharacteristic
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C22⋊D43—24no—
325C22⋊D43—24no—
326C22⋊D43—24no—
327C22⋊D43—24no—
328C22⋊D43—42no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338D172—22no—
339D172—22no—
340D172—22no—
341D172—22no—
342D172—22no—
343D172—41no—
344D172—41no—
345D172C2×C22⋊C414yes—
346C4×D43—24no—
347C4×D43—24no—
348C4×D43—24no—
349C4×D43—24no—
350C4×D43—42no—
351C4×D43—42no—
352C4×D43—42no—
353C4×D43—42no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—41no—
360Dic86—41no—
361Dic86C2×C22⋊C414yes—
362C8×C43—24no—
363C8×C43—24no—
364C43⋊C8—24no—
365C43⋊C8—42no—
366C2×#1881—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43#38611yescharacteristic
375C22×C43#38611yescharacteristic
376C22×C43#38611yescharacteristic
377C22×C43#38611yescharacteristic
378C22×C43C2×C4×D411yescharacteristic
379C22×C43C2×#12111yescharacteristic
380C22×C43C2×#12311yescharacteristic
381C2×D43—24no—
382C2×D43—44no—
383C2×D43—44no—
384C2×D43—42no—
385C2×D43—82no—
386C2×D43—82no—
387C2×D43—82no—
388C2×D43—82no—
389C4×C43—82no—
390C4×C43#38611yescharacteristic
391C4×C43#38611yescharacteristic
392C4×C43#38611yescharacteristic
393C4×C43#38611yescharacteristic
394C4×C43C22×C22⋊C411yescharacteristic
395C4×C43C2×C4×D411yescharacteristic
396C4×C43C2×#12011yescharacteristic
397C4×C43C2×#12111yescharacteristic
398Dic43—24no—
399Dic43—42no—
400C2×#575—431no—
401C2×#568—431no—
402C2×#421—431no—
403C2×#416—431no—
404C2×#408—431no—
405#1881—438no—
406C2×#344D4311yescharacteristic, complemented
407C2×#341—431no—
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43#188112yescomplemented
415C2×C43C2×#38611yescharacteristic
416D43—44no—
417D43—82no—
418C22×#41—431no—
419C22×#41—431no—
420#575—434no—
421#575—434no—
422#575—862no—
423#575—862no—
424C2×#137—432no—
425C2×#137—861no—
426C2×AGL(1,ℤ/8)—432no—
427C2×AGL(1,ℤ/8)—861no—
428C2×#135—862no—
429#568—434no—
430#568—862no—
431#568—862no—
432#568—862no—
433C2×#131—862no—
434C2×#131—862no—
435C22×M16—431no—
436C22×M16—862no—
437C22×M16C2×D4311yescharacteristic
438C22×M16C2×D4311yescharacteristic
439C23×C8—431no—
440C2×#117C2×D4311yescharacteristic
441#421—434no—
442#421—862no—
443C2×#104—862no—
444#416—434no—
445#416—862no—
446C2×#103—861no—
447C2×#102—861no—
448#408—434no—
449#408—862no—
450C2×C22⋊C8—862no—
451#344C2×D4314yescomplemented
452#341—434no—
453C43C2×#188111yescharacteristic, complemented, Sylow
454C2×#41—432no—
455C2×#41—432no—
456C2×#41—432no—
457C2×#41—432no—
458C2×#41—432no—
459C2×#41—432no—
460C2×#41—432no—
461C2×#41—432no—
462C2×#41—861no—
463C2×#41—861no—
464C2×#41—861no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41—861no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41—861no—
478C22×Q8—431no—
479C22×Q8—431no—
480C22×D4—431no—
481C22×D4—431no—
482C22×D4—861no—
483C22×D4—861no—
484C23×C4—861no—
485C23×C4—861no—
486C23×C4C22×D4311yescharacteristic
487#137—438no—
488#137—864no—
489#137—864no—
490#137—864no—
491AGL(1,ℤ/8)—438no—
492AGL(1,ℤ/8)—864no—
493AGL(1,ℤ/8)—864no—
494AGL(1,ℤ/8)—864no—
495#135—868no—
496#135—868no—
497C2×Q16—862no—
498C2×SD16—862no—
499C2×SD16—862no—
500C2×D8—862no—
501#131—868no—
502#131—868no—
503#131—868no—
504#131—868no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—432no—
513C2×M16—432no—
514C2×M16—432no—
515C2×M16—864no—
516C2×M16—868no—
517C2×M16—868no—
518C2×M16—861no—
519C2×M16—861no—
520C2×M16—861no—
521C2×M16C4×D4312yes—
522C2×M16C4×D4312yes—
523C2×M16D17212yes—
524C2×M16C22×D4312yes—
525C2×M16C22×D4312yes—
526C22×C8—21no—
527C22×C8—432no—
528C22×C8—864no—
529C22×C8—861no—
530C22×C8—861no—
531C22×C8—861no—
532C22×C8—861no—
533C22×C8—861no—
534C22×C8—861no—
535C22×C8—861no—
536C22×C8D17212yes—
537#117—21no—
538#117—21no—
539#117—21no—
540#117C22×D4312yes—
541C2×C4⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C42—21no—
544#104—868no—
545#103—864no—
546#102—864no—
547C22⋊C8—868no—
548C24—861no—
549C24—861no—
550C24#1062189811yescharacteristic
551#41—434no—
552#41—434no—
553#41—434no—
554#41—434no—
555#41—862no—
556#41—862no—
557#41—862no—
558#41—862no—
559#41—862no—
560#41—862no—
561#41—862no—
562#41—862no—
563#41—862no—
564#41—862no—
565#41—862no—
566#41—862no—
567#41—862no—
568#41—862no—
569#41—862no—
570#41—862no—
571#41—862no—
572#41—862no—
573#41—862no—
574#41—862no—
575#41—1721no—
576#41—1721no—
577#41—1721no—
578#41—1721no—
579#41—1721no—
580#41—1721no—
581#41—1721no—
582#41—1721no—
583C2×Q8—432no—
584C2×Q8—432no—
585C2×Q8—432no—
586C2×Q8—432no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8—861no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×D4—432no—
596C2×D4—432no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—862no—
600C2×D4—862no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—1721no—
616C2×D4—1721no—
617C2×D4—1721no—
618C2×D4—1721no—
619C22×C4—41no—
620C22×C4—861no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—861no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—1721no—
631C22×C4—1721no—
632C22×C4—1721no—
633C22×C4—1721no—
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4C2×C4×D4311yescharacteristic
636C22×C4C2×D17211yescharacteristic
637C22×C4C2×D17211yescharacteristic
638C22×C4#1062189811yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4#1062190211yescharacteristic
646C22×C4#1062190211yescharacteristic
647C22×C4C23×D4311yescharacteristic
648Q16—868no—
649SD16—868no—
650SD16—868no—
651D8—868no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—22no—
657M16—22no—
658M16—22no—
659M16—434no—
660M16—8616no—
661M16—862no—
662M16—862no—
663M16—862no—
664M16C2×C4×D4314yes—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—8616no—
671C2×C8—862no—
672C2×C8—862no—
673C2×C8—862no—
674C2×C8—862no—
675C2×C8—862no—
676C2×C8—862no—
677C2×C8—1721no—
678C2×C8—1721no—
679C2×C8—1721no—
680C2×C8—1721no—
681C2×C8C2×D17214yes—
682C4⋊C4—22no—
683C4⋊C4—41no—
684C22⋊C4—22no—
685C22⋊C4—41no—
686C42—22no—
687C42—41no—
688C23—42no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—3442no—
694C23—1724no—
695C23—1721no—
696C23—1721no—
697C23C4×D17211yescharacteristic
698C23C4×D17211yescharacteristic
699C23#1306329811yescharacteristic
700C23#1306329811yescharacteristic
701C23#1306331011yescharacteristic
702C23#1306331011yescharacteristic
703C23C2×#1062189811yescharacteristic
704Q8—434no—
705Q8—862no—
706Q8—862no—
707Q8—862no—
708Q8—862no—
709Q8—862no—
710Q8—1721no—
711Q8—1721no—
712D4—434no—
713D4—864no—
714D4—864no—
715D4—864no—
716D4—864no—
717D4—862no—
718D4—862no—
719D4—862no—
720D4—862no—
721D4—862no—
722D4—1722no—
723D4—1722no—
724D4—1722no—
725D4—1722no—
726D4—1721no—
727D4—1721no—
728C2×C4—42no—
729C2×C4—82no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—864no—
734C2×C4—864no—
735C2×C4—864no—
736C2×C4—864no—
737C2×C4—862no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4C22⋊C4×D4311yescharacteristic
745C2×C4C22⋊C4×D4311yescharacteristic
746C2×C4C22⋊C4×D4311yescharacteristic
747C2×C4C22⋊C4×D4311yescharacteristic
748C2×C4#1306328711yescharacteristic
749C2×C4#1306328711yescharacteristic
750C2×C4#1306328711yescharacteristic
751C2×C4#1306328711yescharacteristic
752C2×C4C4×D17211yescharacteristic
753C2×C4C4×D17211yescharacteristic
754C2×C4#1306329511yescharacteristic
755C2×C4#1306329511yescharacteristic
756C2×C4#1306329511yescharacteristic
757C2×C4#1306329511yescharacteristic
758C2×C4#1306329811yescharacteristic
759C2×C4#1306329811yescharacteristic
760C2×C4#1306330011yescharacteristic
761C2×C4#1306330011yescharacteristic
762C2×C4#1306330011yescharacteristic
763C2×C4#1306330011yescharacteristic
764C2×C4#1306331011yescharacteristic
765C2×C4#1306331011yescharacteristic
766C2×C4C22×C4×D4311yescharacteristic
767C2×C4C2×D4×D4311yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4C22×D17211yescharacteristic
771C2×C4C2×#1062190211yescharacteristic
772C8—24no—
773C8—24no—
774C8—864no—
775C8—1722no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—864no—
784C22—3442no—
785C22—3442no—
786C22—3442no—
787C22—3442no—
788C22—1724no—
789C22—1722no—
790C22—1724no—
791C22#1458277711yescharacteristic
792C22#1458277711yescharacteristic
793C22#1458277711yescharacteristic
794C22#1458277711yescharacteristic
795C22C2×C4×D17211yescharacteristic
796C22C2×#1306329811yescharacteristic
797C22C2×#1306331011yescharacteristic
798C4—82no—
799C4—864no—
800C4—1722no—
801C4#1458277711yescharacteristic
802C4#1458277711yescharacteristic
803C4#1458277711yescharacteristic
804C4#1458277711yescharacteristic
805C4C2×C22⋊C4×D4311yescharacteristic
806C4C2×#1306328711yescharacteristic
807C4C2×#1306329511yescharacteristic
808C4C2×#1306330011yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—3442no—
816C2—1724no—
817C2#1913495612yesdirect product factor
818C2C2×#1458277711yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC2×#14583699C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43C2×#1881
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
2. C2×#14583665C2semidirect
3. C2×#14582917C2semidirect
4. C2×#14582893C2semidirect
5. C2×#14582867C2semidirect
6. #19134956C2direct (N × H)
7. C2×#14582663C2semidirect
8. C2×C43×#344C2semidirect
13. #14583699C4semidirect
16. C2×#13063358C4semidirect
18. C2×#13063353C4semidirect
23. #14583665C22semidirect
30. #14582917C22semidirect
33. #14582893C22semidirect
37. #14582867C22semidirect
39. #14582663C22semidirect
43. C43×#344C22semidirect
79. #13063358C2×C4semidirect
83. #13063353C2×C4semidirect
406. C2×#344D43semidirect
414. C2×C43#1881semidirect
451. #344C2×D43semidirect
453. C43C2×#1881semidirect
817. C2#19134956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836992
C2×#145836652
C2×#145829172
C2×#145828932
C2×#145828672
#191349562
C2×#145826632
C2×C43×#3442
C2×#188143