Finite Group Databasebeta

← #25098632

Subgroups — #25098632

Order 11008.

1692 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19147928C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic, complemented
4C2×#14582881C211yesmaximal, characteristic, complemented
5C2×#14582881C211yesmaximal, characteristic, complemented
6#19135146C214yesmaximal, complemented
7#19135141C214yesmaximal, complemented
8C2×#14582669C211yesmaximal, characteristic, complemented
9C2×C43×#344C211yesmaximal, 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
19C22×#10621877C2211yescharacteristic
20C2×M16×D43—22no—
21#14583480—22no—
22#14583475—21no—
23#14583475C2212yes—
24#14583468—21no—
25#14583468C2212yes—
26#14583461C414yes—
27#14583449—22no—
28#14583411—22no—
29#14583411C414yes—
30#14582881—22no—
31#14582881—22no—
32#14582881—22no—
33#14582881—22no—
34#14582881—22no—
35#14582881C2214yes—
36C2×#13063243—21no—
37C2×#13063243C2212yescomplemented
38C2×#13063243C2212yescomplemented
39C2×#13063241—21no—
40C2×#13063241C2212yescomplemented
41C2×#13063241C2212yescomplemented
42#14582669C2214yescomplemented
43C22×M16×C43C2211yescharacteristic
44C22×M16×C43C2211yescharacteristic
45C2×#117×C43C2211yescharacteristic
46C43×#344C2214yescomplemented
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×#10621898—21no—
65C2×#10621898—21no—
66C2×#10621898—21no—
67C2×#10621898C2×C412yes—
68C2×#10621898D412yes—
69C2×#10621898D412yes—
70C2×#10621898C2312yes—
71C22×Dic86D411yescharacteristic
72C22×Dic86C2311yescharacteristic
73C22×D172D411yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43C2×C412yes—
76C22×C22⋊D43C2×C412yes—
77C22×C4×D43C2×C412yes—
78C22×C4×D43D412yes—
79#13063333—28no—
80#13063333—28no—
81#13063331—28no—
82#13063331—28no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877—21no—
87C2×#10621877—21no—
88C2×#10621877—21no—
89C2×#10621877—21no—
90C2×#10621877—21no—
91C2×#10621877D412yescomplemented
92C2×#10621877D412yescomplemented
93C2×#10621877C2312yes—
94C2×#10621877C2312yes—
95C2×#10621872—24no—
96M16×D43—28no—
97M16×D43—28no—
98C22×C43⋊C8—21no—
99C22×C43⋊C8—21no—
100C2×C8×D43—24no—
101#13063325—22no—
102#13063322—22no—
103#13063313—22no—
104#13063313—22no—
105#13063309—24no—
106#13063309C2×C418yes—
107#13063305—24no—
108#13063305—24no—
109#13063300—24no—
110#13063300—24no—
111#13063299—28no—
112#13063295—24no—
113#13063295C2×C418yes—
114C4×D172—28no—
115#13063243—24no—
116#13063243—24no—
117#13063243—24no—
118#13063241—24no—
119#13063241—24no—
120#13063241—24no—
121C23×C4×C43C2311yescharacteristic
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×M16×C43D412yescomplemented
131C2×M16×C43D412yescomplemented
132C2×M16×C43C2312yes—
133C2×M16×C43C2312yes—
134C22×C8×C43—21no—
135C22×C8×C43—21no—
136#117×C43—21no—
137#117×C43—21no—
138#117×C43C2×C412yes—
139#117×C43C2312yes—
140C2×C4⋊C4×C43—21no—
141C2×C22⋊C4×C43C2×C412yes—
142C2×C42×C43—21no—
143C24×C43C22×C411yescharacteristic
144C23×D43C22⋊C412yes—
145C23×D43C22×C412yes—
146C22×C4×C43—22no—
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×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
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—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43C22⋊C414yes—
172C2×C22⋊D43C22×C414yes—
173C22×Dic43C22⋊C412yes—
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—41no—
192#10621898—41no—
193#10621898—41no—
194#10621898—41no—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
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—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—28no—
218C2×D172C22⋊C412yes—
219C2×D172C2×D412yes—
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—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
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×Dic86—21no—
242C2×Dic86C22⋊C412yes—
243C2×Dic86C2×D412yes—
244M16×C43—22no—
245M16×C43—22no—
246M16×C43—22no—
247M16×C43—22no—
248M16×C43—22no—
249M16×C43—41no—
250M16×C43—41no—
251M16×C43C2×D414yes—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43—41no—
257C2×C8×C43—41no—
258C4⋊C4×C43—22no—
259C4⋊C4×C43—22no—
260C22⋊C4×C43—22no—
261C22⋊C4×C43C22×C414yes—
262C42×C43—22no—
263C42×C43—22no—
264(C2×D43)⋊C4—28no—
265(C2×D43)⋊C4—28no—
266C4⋊Dic43—28no—
267#10621877—22no—
268#10621877—22no—
269#10621877—22no—
270#10621877—22no—
271#10621877—22no—
272#10621877—41no—
273#10621877—41no—
274#10621877C2×D414yes—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8—22no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8—41no—
280C2×C43⋊C8—41no—
281#10621872—216no—
282C8×D43—216no—
283C23×C43—81no—
284C23×C43C2×C22⋊C411yescharacteristic
285C23×C43C2×C22⋊C411yescharacteristic
286C23×C43C4×D411yescharacteristic
287C23×C43C4×D411yescharacteristic
288C23×C43C4×D411yescharacteristic
289C23×C43C4×D411yescharacteristic
290C23×C43C23×C411yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—82no—
297C22×D43—82no—
298C22×D43C2×C22⋊C414yes—
299C2×C4×C43—24no—
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×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
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×C43C22×D411yescharacteristic
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—22no—
341C2×Dic43—22no—
342C2×Dic43C2×C22⋊C414yes—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—22no—
347D172—41no—
348D172—41no—
349D172—41no—
350D172—41no—
351D172—88no—
352C4×D43—24no—
353C4×D43—24no—
354C4×D43—24no—
355C4×D43—24no—
356C4×D43—42no—
357C4×D43—42no—
358C4×D43—42no—
359C4×D43—42no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—22no—
364Dic86—41no—
365Dic86—41no—
366Dic86—41no—
367Dic86—41no—
368C8×C43—24no—
369C8×C43—42no—
370C43⋊C8—24no—
371C43⋊C8—42no—
372#21017—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×C4×D411yescharacteristic
386C22×C43C2×C4×D411yescharacteristic
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#38611yescharacteristic
397C4×C43#38611yescharacteristic
398C4×C43#38611yescharacteristic
399C4×C43#38611yescharacteristic
400C4×C43C2×#12011yescharacteristic
401C4×C43C2×#12111yescharacteristic
402C4×C43C2×#12111yescharacteristic
403C4×C43C2×#12311yescharacteristic
404Dic43—24no—
405Dic43—42no—
406C2×#568—431no—
407#3449—431no—
408C2×#413—431no—
409C2×#413—431no—
410C2×#413—431no—
411#1915—434no—
412#1914—434no—
413C2×#344—431no—
414C2×#344D4311yescharacteristic, complemented
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—21no—
419C2×C43—21no—
420C2×C43—21no—
421C2×C43—21no—
422C2×C43C2×#38611yescharacteristic
423D43—44no—
424D43—82no—
425C22×#41—431no—
426C22×#41—431no—
427#568—434no—
428#568—862no—
429#568—862no—
430#568—862no—
431C2×#131—862no—
432C2×#131—862no—
433C22×M16—431no—
434C22×M16—431no—
435C22×M16—862no—
436C22×M16C2×D4311yescharacteristic
437C22×M16C2×D4311yescharacteristic
438#537—862no—
439#536—432no—
440#536—861no—
441#535—432no—
442#535—861no—
443#534—434no—
444#532—862no—
445#525—434no—
446#525—862no—
447C2×#117C2×D4311yescharacteristic
448#413—434no—
449#413—862no—
450#413—862no—
451#413—862no—
452#413—862no—
453#413—862no—
454C2×#101—432no—
455C2×#101—432no—
456C2×#101—861no—
457C2×#100—432no—
458C2×#100—432no—
459C2×#100—861no—
460#344—434no—
461#344C2×D4314yescomplemented
462C43#2101711yescharacteristic, complemented, Sylow
463C2×#41—432no—
464C2×#41—432no—
465C2×#41—432no—
466C2×#41—432no—
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—
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—
487C22×Q8—431no—
488C22×Q8—431no—
489C22×D4—432no—
490C22×D4—432no—
491C22×D4—431no—
492C22×D4—431no—
493C23×C4—432no—
494C23×C4—432no—
495C23×C4C22×D4311yescharacteristic
496#131—868no—
497#131—868no—
498#131—868no—
499#131—868no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—432no—
509C2×M16—432no—
510C2×M16—432no—
511C2×M16—432no—
512C2×M16—864no—
513C2×M16—868no—
514C2×M16—868no—
515C2×M16—861no—
516C2×M16—861no—
517C2×M16—861no—
518C2×M16—861no—
519C2×M16—861no—
520C2×M16—861no—
521C2×M16—861no—
522C2×M16—861no—
523C2×M16D17212yescomplemented
524C2×M16D17212yescomplemented
525C2×M16C22×D4312yes—
526C2×M16C22×D4312yes—
527C22×C8—21no—
528C22×C8—21no—
529C22×C8—864no—
530C22×C8—861no—
531C22×C8—861no—
532C4⋊Q8—862no—
533#127—862no—
534#124—862no—
535#124—862no—
536#123—438no—
537#123—864no—
538C22⋊Q8—864no—
539C22⋊Q8—864no—
540#121—864no—
541#121—864no—
542#121—868no—
543#120—438no—
544#120—864no—
545C4×D4—868no—
546#117—21no—
547#117—21no—
548#117C4×D4312yes—
549#117C22×D4312yes—
550C2×C4⋊C4—21no—
551C2×C22⋊C4C4×D4312yes—
552C2×C42—21no—
553#101—864no—
554#101—864no—
555#101—864no—
556#100—864no—
557#100—864no—
558#100—864no—
559C24—432no—
560C24—432no—
561C24C2×C4×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—1721no—
579#41—1721no—
580#41—1721no—
581#41—1721no—
582#41—1721no—
583#41—1721no—
584#41—1721no—
585#41—1721no—
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—861no—
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—868no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—862no—
617C2×D4—862no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C22×C4—22no—
632C22×C4—432no—
633C22×C4—434no—
634C22×C4—434no—
635C22×C4—432no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4C2×C4×D4311yescharacteristic
647C22×C4C2×D17211yescharacteristic
648C22×C4C2×D17211yescharacteristic
649C22×C4#1062189811yescharacteristic
650C22×C4#1062189811yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4D4×D4311yescharacteristic
656C22×C4D4×D4311yescharacteristic
657C22×C4#1062190211yescharacteristic
658C22×C4#1062190211yescharacteristic
659C22×C4C23×D4311yescharacteristic
660M16—22no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—41no—
666M16—41no—
667M16—434no—
668M16—8616no—
669M16—862no—
670M16—862no—
671M16—862no—
672M16—862no—
673M16—862no—
674M16—1721no—
675M16—1721no—
676M16C2×D17214yes—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—8616no—
684C2×C8—862no—
685C2×C8—862no—
686C2×C8—862no—
687C2×C8—862no—
688C2×C8—1721no—
689C2×C8—1721no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—868no—
693C22⋊C4—22no—
694C22⋊C4—868no—
695C22⋊C4—868no—
696C22⋊C4C2×C4×D4314yes—
697C42—22no—
698C42—22no—
699C23—81no—
700C23—434no—
701C23—862no—
702C23—862no—
703C23—862no—
704C23—862no—
705C23—862no—
706C23—3442no—
707C23—3442no—
708C23C22⋊C4×D4311yescharacteristic
709C23C22⋊C4×D4311yescharacteristic
710C23#1306328711yescharacteristic
711C23#1306328711yescharacteristic
712C23C4×D17211yescharacteristic
713C23C4×D17211yescharacteristic
714C23C22×C4×D4311yescharacteristic
715Q8—862no—
716Q8—862no—
717Q8—862no—
718Q8—862no—
719Q8—1721no—
720Q8—1721no—
721Q8—1721no—
722Q8—1721no—
723D4—864no—
724D4—864no—
725D4—864no—
726D4—864no—
727D4—862no—
728D4—862no—
729D4—862no—
730D4—862no—
731D4—3448no—
732D4—1722no—
733D4—1722no—
734D4—1722no—
735D4—1722no—
736D4—1721no—
737D4—1721no—
738D4—1721no—
739D4—1721no—
740C2×C4—24no—
741C2×C4—82no—
742C2×C4—434no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—864no—
746C2×C4—864no—
747C2×C4—864no—
748C2×C4—864no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—1722no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4C22⋊C4×D4311yescharacteristic
757C2×C4C22⋊C4×D4311yescharacteristic
758C2×C4#1306328711yescharacteristic
759C2×C4#1306328711yescharacteristic
760C2×C4C4×D17211yescharacteristic
761C2×C4C4×D17211yescharacteristic
762C2×C4#1306329511yescharacteristic
763C2×C4#1306329511yescharacteristic
764C2×C4#1306329511yescharacteristic
765C2×C4#1306329511yescharacteristic
766C2×C4#1306329811yescharacteristic
767C2×C4#1306329811yescharacteristic
768C2×C4#1306329811yescharacteristic
769C2×C4#1306329811yescharacteristic
770C2×C4#1306330011yescharacteristic
771C2×C4#1306330011yescharacteristic
772C2×C4#1306330011yescharacteristic
773C2×C4#1306330011yescharacteristic
774C2×C4#1306331011yescharacteristic
775C2×C4#1306331011yescharacteristic
776C2×C4#1306331011yescharacteristic
777C2×C4#1306331011yescharacteristic
778C2×C4C2×D4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C2×C4C22×D17211yescharacteristic
782C2×C4C2×#1062189811yescharacteristic
783C2×C4C2×#1062190211yescharacteristic
784C8—24no—
785C8—42no—
786C8—864no—
787C8—1722no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—864no—
796C22—3442no—
797C22—3442no—
798C22—3442no—
799C22—1724no—
800C22—1724no—
801C22—1724no—
802C22—1722no—
803C22#1458277711yescharacteristic
804C22#1458277711yescharacteristic
805C22#1458277711yescharacteristic
806C22#1458277711yescharacteristic
807C22C2×C22⋊C4×D4311yescharacteristic
808C22C2×#1306328711yescharacteristic
809C22C2×C4×D17211yescharacteristic
810C4—44no—
811C4—864no—
812C4—1722no—
813C4#1458277711yescharacteristic
814C4#1458277711yescharacteristic
815C4#1458277711yescharacteristic
816C4#1458277711yescharacteristic
817C4C2×#1306329511yescharacteristic
818C4C2×#1306329811yescharacteristic
819C4C2×#1306330011yescharacteristic
820C4C2×#1306331011yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—3442no—
829C2—1724no—
830C2C2×#1458277711yescharacteristic
subgroupG/H
centerC4#14582777
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC2×C43C2×#386
prime radical#19147928C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43#21017
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582881C2semidirect
4. C2×#14582881C2semidirect
5. C2×#14582881C2semidirect
6. #19135146C2semidirect
7. #19135141C2semidirect
8. C2×#14582669C2semidirect
9. C2×C43×#344C2semidirect
37. C2×#13063243C22semidirect
38. C2×#13063243C22semidirect
40. C2×#13063241C22semidirect
41. C2×#13063241C22semidirect
42. #14582669C22semidirect
46. C43×#344C22semidirect
91. C2×#10621877D4semidirect
92. C2×#10621877D4semidirect
130. C2×M16×C43D4semidirect
131. C2×M16×C43D4semidirect
414. C2×#344D43semidirect
461. #344C2×D43semidirect
462. C43#21017semidirect
523. C2×M16D172semidirect
524. C2×M16D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479282
C2×#145828812
#191351462
#191351412
C2×#145826692
C2×C43×#3442
#2101743