Finite Group Databasebeta

← C2×#19134977 #25098136

Subgroups — C2×#19134977 #25098136

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×#14583449C211yesmaximal, characteristic
3C2×#14582917C211yesmaximal, characteristic, complemented
4C2×#14582915C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19134977C218yesmaximal, direct product factor
7C2×#14582659C211yesmaximal, characteristic, complemented
8C2×C43×#339C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621898C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yescomplemented
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C2×M16×D43—22no—
19#14583449—22no—
20#14583449—22no—
21#14583449C414yescomplemented
22#14583449C2214yes—
23C2×#13063325C411yescharacteristic, complemented
24C2×#13063322C411yescharacteristic, complemented
25C2×#13063313C411yescharacteristic, complemented
26C2×#13063313C411yescharacteristic, complemented
27C2×#13063299—22no—
28C2×C4×D172—22no—
29C2×#13063284C2211yescharacteristic
30#14582917—22no—
31#14582917C2214yescomplemented
32#14582915—22no—
33#14582915C2214yescomplemented
34C2×#13063253—22no—
35C2×#13063251—22no—
36#14582872—22no—
37#14582872C2214yescomplemented
38C2×#13063239—22no—
39#14582659C2214yescomplemented
40C22×M16×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C22×C42×C43C2211yescharacteristic
43C43×#339C2214yescomplemented
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×#10621898—21no—
61C2×#10621898—21no—
62C2×#10621898C2×C412yes—
63C2×#10621898C2×C412yes—
64C2×#10621898D412yes—
65C2×#10621898D412yes—
66C2×#10621898C2312yes—
67C2×#10621898C2312yes—
68C22×Dic86C2×C411yescharacteristic
69C22×Dic86C2×C411yescharacteristic
70C22×D172—22no—
71C22×D172C2×C411yescharacteristic
72C22×D172C2×C411yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43D412yes—
75C22×C4×D43—21no—
76C22×C4×D43D412yes—
77#13063333—28no—
78#13063333—28no—
79#13063331—28no—
80#13063331—28no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877D412yescomplemented
85C2×#10621877D412yescomplemented
86C2×#10621877C2312yes—
87C2×#10621872—24no—
88M16×D43—28no—
89M16×D43—28no—
90C22×C43⋊C8—21no—
91C2×C8×D43—24no—
92#13063325—22no—
93#13063325C2×C414yescomplemented
94#13063322—22no—
95#13063322C2×C414yescomplemented
96#13063313—22no—
97#13063313—22no—
98#13063313C2×C414yescomplemented
99#13063313C2×C414yescomplemented
100#13063299—28no—
101#13063299—28no—
102C4×D172—28no—
103C4×D172—28no—
104#13063284—21no—
105#13063284—21no—
106#13063284—21no—
107#13063284C2312yes—
108C2×C4⋊Dic43—22no—
109C2×C4⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×C4×Dic43—21no—
114#13063253—28no—
115#13063251—28no—
116#13063239—28no—
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43D412yescomplemented
123C2×M16×C43D412yescomplemented
124C2×M16×C43C2312yes—
125C22×C8×C43—21no—
126#117×C43—21no—
127#117×C43—21no—
128#117×C43—21no—
129#117×C43C2312yes—
130C2×C4⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2×C411yescharacteristic
137C2×C42×C43C2×C411yescharacteristic
138C2×C42×C43C2×C412yes—
139C2×C42×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C23×D43C22⋊C412yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—44no—
148C22×C4×C43—41no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—41no—
170C2×C22⋊D43—41no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43C22⋊C414yes—
174C2×C22⋊D43C2×D414yes—
175C22×Dic43—21no—
176C22×Dic43—41no—
177C22×Dic43C22⋊C412yes—
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—22no—
191#10621898—22no—
192#10621898—22no—
193#10621898—22no—
194#10621898—22no—
195#10621898—22no—
196#10621898—22no—
197#10621898—22no—
198#10621898—22no—
199#10621898—22no—
200#10621898—22no—
201#10621898—22no—
202#10621898—41no—
203#10621898—41no—
204#10621898—41no—
205#10621898—41no—
206#10621898—41no—
207#10621898—41no—
208#10621898—41no—
209#10621898—41no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—28no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—48no—
221C2×D172C22⋊C412yes—
222C2×D172C22×C412yes—
223C2×D172C22×C412yes—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—41no—
231C2×C4×D43—41no—
232C2×C4×D43—41no—
233C2×C4×D43—41no—
234C2×C4×D43C22⋊C414yes—
235C2×C4×D43C2×D414yes—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86C22⋊C412yes—
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—21no—
261C42×C43—21no—
262C42×C43—22no—
263C42×C43—22no—
264C42×C43—41no—
265C42×C43C22×C412yes—
266C42×C43C22×C412yes—
267C22⋊Dic43—22no—
268C22⋊Dic43—41no—
269(C2×D43)⋊C4—28no—
270(C2×D43)⋊C4—28no—
271C4⋊Dic43—28no—
272C4⋊Dic43—22no—
273C4⋊Dic43—41no—
274C4×Dic43—22no—
275C4×Dic43—41no—
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—42no—
286C23×C43C2×C22⋊C411yescharacteristic
287C23×C43C2×C22⋊C411yescharacteristic
288C23×C43#12111yescharacteristic
289C23×C43#12111yescharacteristic
290C23×C43#12111yescharacteristic
291C23×C43#12111yescharacteristic
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43C2×C22⋊C414yes—
301C2×C4×C43—24no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—44no—
305C2×C4×C43—44no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—82no—
309C2×C4×C43C2×C22⋊C411yescharacteristic
310C2×C4×C43C2×C22⋊C411yescharacteristic
311C2×C4×C43C4×D411yescharacteristic
312C2×C4×C43C4×D411yescharacteristic
313C2×C4×C43C4×D411yescharacteristic
314C2×C4×C43C4×D411yescharacteristic
315C2×C4×C43C4×D411yescharacteristic
316C2×C4×C43C4×D411yescharacteristic
317C2×C4×C43C4×D411yescharacteristic
318C2×C4×C43C4×D411yescharacteristic
319C2×C4×C43#12011yescharacteristic
320C2×C4×C43#12011yescharacteristic
321C2×C4×C43#12011yescharacteristic
322C2×C4×C43#12011yescharacteristic
323C2×C4×C43#12111yescharacteristic
324C2×C4×C43#12111yescharacteristic
325C2×C4×C43#12111yescharacteristic
326C2×C4×C43#12111yescharacteristic
327C2×C4×C43#12311yescharacteristic
328C2×C4×C43#12311yescharacteristic
329C2×C4×C43#12311yescharacteristic
330C2×C4×C43#12311yescharacteristic
331C2×C4×C43C23×C411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C22⋊D43—24no—
338C22⋊D43—24no—
339C22⋊D43—24no—
340C22⋊D43—24no—
341C22⋊D43—42no—
342C22⋊D43—42no—
343C22⋊D43—42no—
344C22⋊D43—42no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—42no—
351C2×Dic43—82no—
352C2×Dic43C2×C22⋊C414yes—
353D172—22no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—22no—
358D172—22no—
359D172—416no—
360D172—41no—
361D172—41no—
362C4×D43—24no—
363C4×D43—24no—
364C4×D43—24no—
365C4×D43—24no—
366C4×D43—42no—
367C4×D43—42no—
368C4×D43—42no—
369C4×D43—42no—
370Dic86—22no—
371Dic86—22no—
372Dic86—22no—
373Dic86—22no—
374Dic86—22no—
375Dic86—22no—
376Dic86—41no—
377Dic86—41no—
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#38611yescharacteristic
389C22×C43#38611yescharacteristic
390C22×C43#38611yescharacteristic
391C22×C43#38611yescharacteristic
392C22×C43C22×C22⋊C411yescharacteristic
393C22×C43C2×#12111yescharacteristic
394C22×C43C2×#12111yescharacteristic
395C2×D43—24no—
396C2×D43—44no—
397C2×D43—44no—
398C2×D43—44no—
399C2×D43—42no—
400C2×D43—82no—
401C2×D43—82no—
402C2×D43—82no—
403C4×C43—24no—
404C4×C43—42no—
405C4×C43—82no—
406C4×C43#38611yescharacteristic
407C4×C43#38611yescharacteristic
408C4×C43#38611yescharacteristic
409C4×C43#38611yescharacteristic
410C4×C43C2×C4×D411yescharacteristic
411C4×C43C2×C4×D411yescharacteristic
412C4×C43C2×#12011yescharacteristic
413C4×C43C2×#12311yescharacteristic
414Dic43—24no—
415Dic43—42no—
416Dic43—82no—
417C2×#568—431no—
418C2×#532—431no—
419C2×#421—431no—
420C2×#421—431no—
421C2×#410—431no—
422#1884—438no—
423C2×#339—431no—
424C2×#339D4311yescharacteristic, complemented
425C2×C43—21no—
426C2×C43—21no—
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—21no—
430C2×C43—21no—
431C2×C43#188412yescomplemented
432C2×C43C2×#38611yescharacteristic
433D43—44no—
434D43—82no—
435C22×#41—431no—
436C22×#41—431no—
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×C42C2×D4311yescharacteristic
459#421—434no—
460#421—434no—
461#421—862no—
462#421—862no—
463C2×#104—862no—
464C2×#104—862no—
465#410—434no—
466#410—862no—
467C2×#99—862no—
468#339—434no—
469#339C2×D4314yescomplemented
470C43C2×#188411yescharacteristic, complemented, Sylow
471C2×#41—432no—
472C2×#41—432no—
473C2×#41—432no—
474C2×#41—432no—
475C2×#41—432no—
476C2×#41—432no—
477C2×#41—861no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—861no—
481C2×#41—861no—
482C2×#41—861no—
483C2×#41—861no—
484C2×#41—861no—
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×#41—861no—
494C2×#41—861no—
495C22×Q8—431no—
496C22×Q8—431no—
497C22×D4—432no—
498C22×D4—431no—
499C22×D4—431no—
500C22×D4—862no—
501C22×D4—861no—
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×M16D17212yescomplemented
523C2×M16D17212yescomplemented
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—21no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—861no—
560C2×C42C4×D4311yescharacteristic
561C2×C42C4×D4311yescharacteristic
562C2×C42C4×D4312yes—
563C2×C42C22×D4312yes—
564#104—868no—
565#104—868no—
566#99—868no—
567C24—432no—
568C24—861no—
569C24D4×D4311yescharacteristic
570#41—862no—
571#41—862no—
572#41—862no—
573#41—862no—
574#41—862no—
575#41—862no—
576#41—862no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584#41—862no—
585#41—862no—
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—1721no—
595#41—1721no—
596#41—1721no—
597#41—1721no—
598#41—1721no—
599#41—1721no—
600#41—1721no—
601#41—1721no—
602C2×Q8—432no—
603C2×Q8—432no—
604C2×Q8—432no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×D4—434no—
615C2×D4—434no—
616C2×D4—432no—
617C2×D4—432no—
618C2×D4—432no—
619C2×D4—868no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—1728no—
636C2×D4—1721no—
637C2×D4—1721no—
638C2×D4—1721no—
639C2×D4—1721no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—44no—
645C22×C4—41no—
646C22×C4—432no—
647C22×C4—434no—
648C22×C4—434no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—861no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—1721no—
657C22×C4—1721no—
658C22×C4—1721no—
659C22×C4—1721no—
660C22×C4—1721no—
661C22×C4C2×C4×D4311yescharacteristic
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4C2×D17211yescharacteristic
664C22×C4C2×D17211yescharacteristic
665C22×C4#1062189811yescharacteristic
666C22×C4#1062189811yescharacteristic
667C22×C4D4×D4311yescharacteristic
668C22×C4D4×D4311yescharacteristic
669C22×C4D4×D4311yescharacteristic
670C22×C4D4×D4311yescharacteristic
671C22×C4D4×D4311yescharacteristic
672C22×C4#1062190211yescharacteristic
673C22×C4#1062190211yescharacteristic
674C22×C4C23×D4311yescharacteristic
675M16—22no—
676M16—22no—
677M16—22no—
678M16—434no—
679M16—8616no—
680M16—862no—
681M16—862no—
682M16—862no—
683M16C2×D17214yescomplemented
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—21no—
704C42—21no—
705C42—22no—
706C42—22no—
707C42—41no—
708C42—862no—
709C42—1721no—
710C42C2×C4×D4312yes—
711C42C2×C4×D4312yes—
712C23—42no—
713C23—434no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—1724no—
718C23—1724no—
719C23—1721no—
720C23—1721no—
721C23C22⋊C4×D4311yescharacteristic
722C23C22⋊C4×D4311yescharacteristic
723C23#1306329811yescharacteristic
724C23#1306329811yescharacteristic
725C23#1306330011yescharacteristic
726C23#1306330011yescharacteristic
727C23C2×D4×D4311yescharacteristic
728Q8—862no—
729Q8—862no—
730Q8—862no—
731Q8—862no—
732Q8—862no—
733Q8—862no—
734Q8—1721no—
735Q8—1721no—
736D4—864no—
737D4—864no—
738D4—864no—
739D4—864no—
740D4—862no—
741D4—862no—
742D4—862no—
743D4—862no—
744D4—862no—
745D4—862no—
746D4—17216no—
747D4—1722no—
748D4—1722no—
749D4—1722no—
750D4—1722no—
751D4—1721no—
752D4—1721no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—82no—
761C2×C4—434no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—864no—
765C2×C4—864no—
766C2×C4—864no—
767C2×C4—864no—
768C2×C4—862no—
769C2×C4—3442no—
770C2×C4—1722no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1722no—
774C2×C4—1722no—
775C2×C4—1722no—
776C2×C4—1722no—
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22⋊C4×D4311yescharacteristic
779C2×C4#1306328711yescharacteristic
780C2×C4#1306328711yescharacteristic
781C2×C4#1306328711yescharacteristic
782C2×C4#1306328711yescharacteristic
783C2×C4C4×D17211yescharacteristic
784C2×C4C4×D17211yescharacteristic
785C2×C4C4×D17211yescharacteristic
786C2×C4C4×D17211yescharacteristic
787C2×C4#1306329511yescharacteristic
788C2×C4#1306329511yescharacteristic
789C2×C4#1306329511yescharacteristic
790C2×C4#1306329511yescharacteristic
791C2×C4#1306329811yescharacteristic
792C2×C4#1306329811yescharacteristic
793C2×C4#1306330011yescharacteristic
794C2×C4#1306330011yescharacteristic
795C2×C4#1306331011yescharacteristic
796C2×C4#1306331011yescharacteristic
797C2×C4#1306331011yescharacteristic
798C2×C4#1306331011yescharacteristic
799C2×C4C22×C4×D4311yescharacteristic
800C2×C4C2×D4×D4311yescharacteristic
801C2×C4C2×D4×D4311yescharacteristic
802C2×C4C22×D17211yescharacteristic
803C2×C4C2×#1062189811yescharacteristic
804C2×C4C2×#1062190211yescharacteristic
805C8—24no—
806C8—864no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—864no—
815C22—3442no—
816C22—3442no—
817C22—3442no—
818C22—1724no—
819C22—1724no—
820C22—1722no—
821C22—1724no—
822C22#1458277711yescharacteristic
823C22#1458277711yescharacteristic
824C22#1458277711yescharacteristic
825C22#1458277711yescharacteristic
826C22C2×C22⋊C4×D4311yescharacteristic
827C22C2×#1306329811yescharacteristic
828C22C2×#1306330011yescharacteristic
829C4—24no—
830C4—42no—
831C4—82no—
832C4—864no—
833C4—3442no—
834C4—1722no—
835C4#1458277711yescharacteristic
836C4#1458277711yescharacteristic
837C4#1458277711yescharacteristic
838C4#1458277711yescharacteristic
839C4C2×#1306328711yescharacteristic
840C4C2×C4×D17211yescharacteristic
841C4C2×#1306329511yescharacteristic
842C4C2×#1306331011yescharacteristic
843C2—21no—
844C2—21no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—3442no—
850C2—1724no—
851C2#1913497712yesdirect product factor
852C2C2×#1458277711yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#339C2
socleC22×C43#386
prime radicalC2×#14583449C2
cosocleC22×C4×C43C24
hypercenterC2×#339D43
hypocenterC43C2×#1884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582917C2semidirect
4. C2×#14582915C2semidirect
5. C2×#14582872C2semidirect
6. #19134977C2direct (N × H)
7. C2×#14582659C2semidirect
8. C2×C43×#339C2semidirect
14. #14583665C22semidirect
21. #14583449C4semidirect
23. C2×#13063325C4semidirect
24. C2×#13063322C4semidirect
25. C2×#13063313C4semidirect
26. C2×#13063313C4semidirect
31. #14582917C22semidirect
33. #14582915C22semidirect
37. #14582872C22semidirect
39. #14582659C22semidirect
43. C43×#339C22semidirect
84. C2×#10621877D4semidirect
85. C2×#10621877D4semidirect
93. #13063325C2×C4semidirect
95. #13063322C2×C4semidirect
98. #13063313C2×C4semidirect
99. #13063313C2×C4semidirect
122. C2×M16×C43D4semidirect
123. C2×M16×C43D4semidirect
251. M16×C43C2×D4semidirect
279. #10621877C2×D4semidirect
424. C2×#339D43semidirect
431. C2×C43#1884semidirect
469. #339C2×D43semidirect
470. C43C2×#1884semidirect
522. C2×M16D172semidirect
523. C2×M16D172semidirect
683. M16C2×D172semidirect
851. C2#19134977direct (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×#145834492
C2×#145829172
C2×#145829152
C2×#145828722
#191349772
C2×#145826592
C2×C43×#3392
C2×#188443