Finite Group Databasebeta

← #25098582

Subgroups — #25098582

Order 11008.

1708 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19147928C211yesmaximal, characteristic
3#19143115C211yesmaximal, characteristic, complemented
4#19143112C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19135121C214yesmaximal, complemented
7#19135116C214yesmaximal, complemented
8C2×#14582655C211yesmaximal, characteristic, complemented
9C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C22×#10621898C2211yescharacteristic
12#14583665—22no—
13#14583665—22no—
14#14583665—22no—
15#14583665C2214yes—
16C2×#13063333—22no—
17C2×#13063331—22no—
18C22×#10621877C2211yescharacteristic
19C2×M16×D43—22no—
20#14583480—22no—
21#14583475C412yescomplemented
22#14583475C2212yes—
23#14583468C412yescomplemented
24#14583468C2212yes—
25#14583461—22no—
26#14583449C414yescomplemented
27#14583411—22no—
28#14583411—22no—
29C2×#13063284C2211yescharacteristic
30#14582909C2212yescomplemented
31#14582907C2212yescomplemented
32#14582905C2212yescomplemented
33#14582903C2212yescomplemented
34#14582901—22no—
35#14582898—22no—
36#14582896—22no—
37#14582893—22no—
38#14582872—22no—
39#14582872C2214yes—
40C2×#13063239—22no—
41#14582655C2214yescomplemented
42C22×M16×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C43×H(3,ℤ/4)C2214yescomplemented
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×#10621898—21no—
63C2×#10621898—21no—
64C2×#10621898C2×C412yes—
65C2×#10621898C2×C412yes—
66C2×#10621898C2×C412yes—
67C2×#10621898D412yes—
68C2×#10621898D412yes—
69C2×#10621898C2312yes—
70C22×Dic86C2×C411yescharacteristic
71C22×Dic86C2311yescharacteristic
72C22×D172C2×C411yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C22⋊D43—21no—
75C22×C22⋊D43D412yes—
76C22×C4×D43—21no—
77C22×C4×D43D412yes—
78#13063333—28no—
79#13063333—28no—
80#13063331—28no—
81#13063331—28no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877D412yescomplemented
87C2×#10621877C2312yes—
88C2×#10621872—24no—
89M16×D43—28no—
90M16×D43—28no—
91C22×C43⋊C8D412yescomplemented
92C2×C8×D43—24no—
93#13063325C2×C414yescomplemented
94#13063322C2×C414yescomplemented
95#13063313C2×C414yescomplemented
96#13063313C2×C414yescomplemented
97#13063309—24no—
98#13063309—24no—
99#13063305—24no—
100#13063305—24no—
101#13063300—24no—
102#13063300—24no—
103#13063299—28no—
104#13063295—24no—
105#13063295—24no—
106C4×D172—28no—
107#13063284—21no—
108#13063284—21no—
109#13063284—21no—
110#13063284C2312yes—
111C2×C4⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C4×Dic43—21no—
114#13063250—24no—
115#13063248—24no—
116#13063247—24no—
117#13063245—24no—
118#13063239—28no—
119C23×C4×C43C2311yescharacteristic
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43D412yescomplemented
125C2×M16×C43C2312yes—
126C22×C8×C43D412yescomplemented
127#117×C43—21no—
128#117×C43—21no—
129#117×C43—21no—
130#117×C43—21no—
131#117×C43—21no—
132#117×C43C2×C412yes—
133#117×C43C2312yes—
134#117×C43C2312yes—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43C2×C412yes—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C23×D43C22⋊C412yes—
144C22×C4×C43—22no—
145C22×C4×C43—41no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168C2×C22⋊D43—41no—
169C2×C22⋊D43—41no—
170C2×C22⋊D43C22⋊C414yes—
171C2×C22⋊D43C2×D414yes—
172C22×Dic43—21no—
173C22×Dic43—41no—
174C22×Dic43C22⋊C412yes—
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—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—41no—
200#10621898—41no—
201#10621898—41no—
202#10621898—41no—
203#10621898—41no—
204#10621898—41no—
205#10621898—41no—
206#10621898—41no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—28no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172C22⋊C412yes—
218C2×D172C22×C412yes—
219C2×D172C22×C412yes—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—41no—
227C2×C4×D43—41no—
228C2×C4×D43—41no—
229C2×C4×D43—41no—
230C2×C4×D43C22⋊C414yes—
231C2×C4×D43C2×D414yes—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86C22⋊C412yes—
242C2×Dic86C22×C412yes—
243C2×Dic86C22×C412yes—
244M16×C43—22no—
245M16×C43—22no—
246M16×C43—22no—
247M16×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43C2×D414yes—
251C4⋊C4×C43—22no—
252C4⋊C4×C43—22no—
253C4⋊C4×C43—22no—
254C4⋊C4×C43—41no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—41no—
259C42×C43—22no—
260C42×C43—22no—
261C42×C43—41no—
262C42×C43C22×C414yes—
263C22⋊Dic43—22no—
264C22⋊Dic43—41no—
265(C2×D43)⋊C4—28no—
266(C2×D43)⋊C4—28no—
267C4⋊Dic43—28no—
268C4⋊Dic43—22no—
269C4⋊Dic43—41no—
270C4×Dic43—22no—
271C4×Dic43—41no—
272#10621877—22no—
273#10621877—22no—
274#10621877—22no—
275#10621877—22no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8—22no—
278C2×C43⋊C8C2×D414yes—
279#10621872—216no—
280C8×D43—216no—
281C23×C43—81no—
282C23×C43C2×C22⋊C411yescharacteristic
283C23×C43C2×C22⋊C411yescharacteristic
284C23×C43#12111yescharacteristic
285C23×C43#12111yescharacteristic
286C23×C43#12111yescharacteristic
287C23×C43#12111yescharacteristic
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—82no—
295C22×D43—82no—
296C22×D43C2×C22⋊C414yes—
297C2×C4×C43—24no—
298C2×C4×C43—42no—
299C2×C4×C43—82no—
300C2×C4×C43—82no—
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43C4×D411yescharacteristic
305C2×C4×C43C4×D411yescharacteristic
306C2×C4×C43C4×D411yescharacteristic
307C2×C4×C43C4×D411yescharacteristic
308C2×C4×C43C4×D411yescharacteristic
309C2×C4×C43C4×D411yescharacteristic
310C2×C4×C43C4×D411yescharacteristic
311C2×C4×C43#12011yescharacteristic
312C2×C4×C43#12011yescharacteristic
313C2×C4×C43#12011yescharacteristic
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12311yescharacteristic
320C2×C4×C43#12311yescharacteristic
321C2×C4×C43#12311yescharacteristic
322C2×C4×C43#12311yescharacteristic
323C2×C4×C43C23×C411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C22⋊D43—24no—
330C22⋊D43—24no—
331C22⋊D43—24no—
332C22⋊D43—24no—
333C22⋊D43—42no—
334C22⋊D43—42no—
335C22⋊D43—42no—
336C22⋊D43—42no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—42no—
343C2×Dic43—82no—
344C2×Dic43C2×C22⋊C414yes—
345D172—22no—
346D172—22no—
347D172—22no—
348D172—22no—
349D172—22no—
350D172—22no—
351D172—41no—
352D172—41no—
353D172—88no—
354C4×D43—24no—
355C4×D43—24no—
356C4×D43—24no—
357C4×D43—24no—
358C4×D43—42no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—42no—
362Dic86—22no—
363Dic86—22no—
364Dic86—22no—
365Dic86—22no—
366Dic86—22no—
367Dic86—22no—
368Dic86—41no—
369Dic86—41no—
370C8×C43—24no—
371C43⋊C8—24no—
372#21009—431nomaximal, Sylow
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43#38611yescharacteristic
381C22×C43#38611yescharacteristic
382C22×C43#38611yescharacteristic
383C22×C43#38611yescharacteristic
384C22×C43C22×C22⋊C411yescharacteristic
385C22×C43C2×#12111yescharacteristic
386C22×C43C2×#12111yescharacteristic
387C2×D43—24no—
388C2×D43—44no—
389C2×D43—44no—
390C2×D43—44no—
391C2×D43—42no—
392C2×D43—82no—
393C2×D43—82no—
394C2×D43—82no—
395C4×C43—44no—
396C4×C43—82no—
397C4×C43#38611yescharacteristic
398C4×C43#38611yescharacteristic
399C4×C43#38611yescharacteristic
400C4×C43#38611yescharacteristic
401C4×C43C2×C4×D411yescharacteristic
402C4×C43C2×C4×D411yescharacteristic
403C4×C43C2×#12011yescharacteristic
404C4×C43C2×#12311yescharacteristic
405Dic43—24no—
406Dic43—42no—
407Dic43—82no—
408C2×#568—431no—
409#3449—431no—
410#2896—431no—
411#2896—431no—
412C2×#410—431no—
413#1910—434no—
414#1909—434no—
415C2×H(3,ℤ/4)—431no—
416C2×H(3,ℤ/4)D4311yescharacteristic, complemented
417C2×C43—21no—
418C2×C43—21no—
419C2×C43—21no—
420C2×C43—21no—
421C2×C43—21no—
422C2×C43—21no—
423C2×C43—21no—
424C2×C43C2×#38611yescharacteristic
425D43—44no—
426D43—82no—
427C22×#41—431no—
428C22×#41—431no—
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
438#537—862no—
439#536—432no—
440#536—432no—
441#535—432no—
442#535—432no—
443#534—862no—
444#532—434no—
445#525—862no—
446#525—862no—
447C2×#117—431no—
448C2×#117C2×D4311yescharacteristic
449C2×#117C2×D4311yescharacteristic
450#419—432no—
451#419—432no—
452#418—432no—
453#418—432no—
454#417—862no—
455#417—862no—
456#416—862no—
457#416—862no—
458#410—434no—
459#410—862no—
460C2×#99—862no—
461H(3,ℤ/4)—434no—
462H(3,ℤ/4)C2×D4314yescomplemented
463C43#2100911yescharacteristic, complemented, Sylow
464C2×#41—432no—
465C2×#41—432no—
466C2×#41—432no—
467C2×#41—432no—
468C2×#41—432no—
469C2×#41—432no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
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—
488C22×Q8—431no—
489C22×Q8—431no—
490C22×D4—432no—
491C22×D4—431no—
492C22×D4—431no—
493C22×D4—861no—
494C23×C4—432no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497#131—868no—
498#131—868no—
499#131—868no—
500#131—868no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—432no—
506C2×M16—432no—
507C2×M16—864no—
508C2×M16—868no—
509C2×M16—868no—
510C2×M16—861no—
511C2×M16—861no—
512C2×M16—861no—
513C2×M16—861no—
514C2×M16D17212yescomplemented
515C2×M16C22×D4312yes—
516C22×C8—432no—
517C22×C8—864no—
518C22×C8D17212yescomplemented
519C4⋊Q8—434no—
520#127—434no—
521#124—434no—
522#124—434no—
523#123—864no—
524#123—864no—
525C22⋊Q8—864no—
526C22⋊Q8—864no—
527#121—864no—
528#121—864no—
529#121—868no—
530#120—864no—
531#120—864no—
532C4×D4—868no—
533#117—21no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—432no—
539#117—861no—
540#117—861no—
541#117—861no—
542#117C4×D4312yes—
543#117C22×D4312yes—
544#117C22×D4312yes—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—861no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—861no—
551C2×C42—21no—
552C2×C42—861no—
553C2×C42C4×D4312yes—
554#103—864no—
555#103—864no—
556#102—864no—
557#102—864no—
558#99—868no—
559C24—432no—
560C24—861no—
561C24D4×D4311yescharacteristic
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—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—1721no—
587#41—1721no—
588#41—1721no—
589#41—1721no—
590#41—1721no—
591#41—1721no—
592#41—1721no—
593#41—1721no—
594C2×Q8—432no—
595C2×Q8—432no—
596C2×Q8—432no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—861no—
601C2×Q8—861no—
602C2×Q8—861no—
603C2×Q8—861no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×D4—434no—
607C2×D4—434no—
608C2×D4—432no—
609C2×D4—432no—
610C2×D4—432no—
611C2×D4—868no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—862no—
617C2×D4—862no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—1721no—
628C2×D4—1721no—
629C2×D4—1721no—
630C2×D4—1721no—
631C22×C4—22no—
632C22×C4—41no—
633C22×C4—432no—
634C22×C4—434no—
635C22×C4—434no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—861no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—1721no—
644C22×C4—1721no—
645C22×C4—1721no—
646C22×C4—1721no—
647C22×C4—1721no—
648C22×C4C2×C4×D4311yescharacteristic
649C22×C4C2×C4×D4311yescharacteristic
650C22×C4C2×D17211yescharacteristic
651C22×C4C2×D17211yescharacteristic
652C22×C4#1062189811yescharacteristic
653C22×C4#1062189811yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4D4×D4311yescharacteristic
656C22×C4D4×D4311yescharacteristic
657C22×C4D4×D4311yescharacteristic
658C22×C4D4×D4311yescharacteristic
659C22×C4#1062190211yescharacteristic
660C22×C4#1062190211yescharacteristic
661C22×C4C23×D4311yescharacteristic
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—8616no—
667M16—862no—
668M16—862no—
669M16—862no—
670M16—862no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—434no—
674C2×C8—8616no—
675C2×C8—862no—
676C2×C8—862no—
677C2×C8C2×D17214yes—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—41no—
682C4⋊C4—868no—
683C4⋊C4—862no—
684C4⋊C4—1721no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—41no—
689C22⋊C4—868no—
690C22⋊C4—868no—
691C22⋊C4—862no—
692C22⋊C4—1721no—
693C42—22no—
694C42—22no—
695C42—41no—
696C42—862no—
697C42—1721no—
698C42C2×C4×D4314yes—
699C23—81no—
700C23—434no—
701C23—862no—
702C23—862no—
703C23—862no—
704C23—3442no—
705C23—3442no—
706C23—1721no—
707C23—1721no—
708C23C22⋊C4×D4311yescharacteristic
709C23C22⋊C4×D4311yescharacteristic
710C23#1306329811yescharacteristic
711C23#1306329811yescharacteristic
712C23#1306330011yescharacteristic
713C23#1306330011yescharacteristic
714C23C2×D4×D4311yescharacteristic
715Q8—862no—
716Q8—862no—
717Q8—862no—
718Q8—862no—
719Q8—862no—
720Q8—862no—
721Q8—1721no—
722Q8—1721no—
723D4—864no—
724D4—864no—
725D4—864no—
726D4—864no—
727D4—862no—
728D4—862no—
729D4—862no—
730D4—862no—
731D4—862no—
732D4—862no—
733D4—3448no—
734D4—1722no—
735D4—1722no—
736D4—1722no—
737D4—1722no—
738D4—1721no—
739D4—1721no—
740C2×C4—24no—
741C2×C4—42no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4—434no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—864no—
748C2×C4—864no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—862no—
752C2×C4—3442no—
753C2×C4—1722no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1722no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4C22⋊C4×D4311yescharacteristic
761C2×C4C22⋊C4×D4311yescharacteristic
762C2×C4#1306328711yescharacteristic
763C2×C4#1306328711yescharacteristic
764C2×C4#1306328711yescharacteristic
765C2×C4#1306328711yescharacteristic
766C2×C4C4×D17211yescharacteristic
767C2×C4C4×D17211yescharacteristic
768C2×C4C4×D17211yescharacteristic
769C2×C4C4×D17211yescharacteristic
770C2×C4#1306329511yescharacteristic
771C2×C4#1306329511yescharacteristic
772C2×C4#1306329511yescharacteristic
773C2×C4#1306329511yescharacteristic
774C2×C4#1306329811yescharacteristic
775C2×C4#1306329811yescharacteristic
776C2×C4#1306330011yescharacteristic
777C2×C4#1306330011yescharacteristic
778C2×C4#1306331011yescharacteristic
779C2×C4#1306331011yescharacteristic
780C2×C4#1306331011yescharacteristic
781C2×C4#1306331011yescharacteristic
782C2×C4C22×C4×D4311yescharacteristic
783C2×C4C2×D4×D4311yescharacteristic
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4C22×D17211yescharacteristic
786C2×C4C2×#1062189811yescharacteristic
787C2×C4C2×#1062190211yescharacteristic
788C8—24no—
789C8—864no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—864no—
798C22—3442no—
799C22—3442no—
800C22—3442no—
801C22—1724no—
802C22—1724no—
803C22—1724no—
804C22—1722no—
805C22#1458277711yescharacteristic
806C22#1458277711yescharacteristic
807C22#1458277711yescharacteristic
808C22#1458277711yescharacteristic
809C22C2×C22⋊C4×D4311yescharacteristic
810C22C2×#1306329811yescharacteristic
811C22C2×#1306330011yescharacteristic
812C4—44no—
813C4—82no—
814C4—864no—
815C4—3442no—
816C4—1722no—
817C4#1458277711yescharacteristic
818C4#1458277711yescharacteristic
819C4#1458277711yescharacteristic
820C4#1458277711yescharacteristic
821C4C2×#1306328711yescharacteristic
822C4C2×C4×D17211yescharacteristic
823C4C2×#1306329511yescharacteristic
824C4C2×#1306331011yescharacteristic
825C2—21no—
826C2—21no—
827C2—21no—
828C2—21no—
829C2—21no—
830C2—21no—
831C2—21no—
832C2—3442no—
833C2—1724no—
834C2C2×#1458277711yescharacteristic
subgroupG/H
centerC4#14582777
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC2×C43C2×#386
prime radical#19147928C2
cosocleC22×C4×C43C24
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43#21009
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. #19143115C2semidirect
4. #19143112C2semidirect
5. C2×#14582872C2semidirect
6. #19135121C2semidirect
7. #19135116C2semidirect
8. C2×#14582655C2semidirect
9. C2×C43×H(3,ℤ/4)C2semidirect
21. #14583475C4semidirect
23. #14583468C4semidirect
26. #14583449C4semidirect
30. #14582909C22semidirect
31. #14582907C22semidirect
32. #14582905C22semidirect
33. #14582903C22semidirect
41. #14582655C22semidirect
45. C43×H(3,ℤ/4)C22semidirect
86. C2×#10621877D4semidirect
91. C22×C43⋊C8D4semidirect
93. #13063325C2×C4semidirect
94. #13063322C2×C4semidirect
95. #13063313C2×C4semidirect
96. #13063313C2×C4semidirect
124. C2×M16×C43D4semidirect
126. C22×C8×C43D4semidirect
416. C2×H(3,ℤ/4)D43semidirect
462. H(3,ℤ/4)C2×D43semidirect
463. C43#21009semidirect
514. C2×M16D172semidirect
518. C22×C8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479282
#191431152
#191431122
C2×#145828722
#191351212
#191351162
C2×#145826552
C2×C43×H(3,ℤ/4)2
#2100943