Finite Group Databasebeta

← #25098629

Subgroups — #25098629

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#19147924C211yesmaximal, characteristic
3C2×#14582883C211yesmaximal, characteristic, complemented
4C2×#14582881C211yesmaximal, characteristic, complemented
5#19135144C214yesmaximal, complemented
6#19135139C214yesmaximal, complemented
7C2×#14582671C211yesmaximal, characteristic, complemented
8C2×#14582670C211yesmaximal, characteristic, complemented
9C2×C43×#413C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yes—
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×M16×D43—22no—
20#14583477—22no—
21#14583473C2212yes—
22#14583470—21no—
23#14583466C2212yes—
24#14583463—21no—
25#14583458C414yes—
26#14583445—22no—
27#14583410C414yes—
28#14583406—22no—
29C2×#13063284C2211yescharacteristic
30#14582883—22no—
31#14582883—22no—
32#14582881—22no—
33#14582881C2214yes—
34C2×#13063244C2212yescomplemented
35C2×#13063243—21no—
36C2×#13063242C2212yescomplemented
37C2×#13063241—21no—
38#14582671C2214yescomplemented
39#14582670C2214yescomplemented
40C22×#41×C43C2211yescharacteristic
41C22×M16×C43C2211yescharacteristic
42C22×M16×C43C2211yescharacteristic
43C43×#413—22no—
44C43×#413—22no—
45C2×#101×C43C2212yescomplemented
46C2×#100×C43C2212yescomplemented
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×#10621898C2×C412yes—
56C2×#10621898D412yes—
57C2×#10621898D412yes—
58C2×#10621898C2312yes—
59C22×Dic86D411yescharacteristic
60C22×D172D411yescharacteristic
61C22×C22⋊D43C2×C412yes—
62C22×C4×D43D412yes—
63#13063333—28no—
64#13063333—28no—
65#13063331—28no—
66#13063331—28no—
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877D412yescomplemented
76C2×#10621877D412yescomplemented
77C2×#10621877C2312yes—
78C2×#10621877C2312yes—
79C2×#10621872—24no—
80M16×D43—28no—
81M16×D43—28no—
82C22×C43⋊C8—21no—
83C22×C43⋊C8—21no—
84C2×C8×D43—24no—
85#13063323—22no—
86#13063321—22no—
87#13063314—22no—
88#13063312—22no—
89#13063308C2×C418yes—
90#13063306—24no—
91#13063304—24no—
92#13063301—24no—
93#13063299—24no—
94#13063297—28no—
95#13063296—24no—
96#13063294C2×C418yes—
97#13063293—24no—
98C4×C22⋊D43—28no—
99#13063284—21no—
100#13063284—21no—
101#13063284C2×C412yes—
102#13063284C2312yes—
103C2×C4⋊Dic43—21no—
104C2×C22⋊Dic43C2×C412yes—
105C2×C4×Dic43—21no—
106#13063244—24no—
107#13063243—24no—
108#13063242—24no—
109#13063241—24no—
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×C43—21no—
119C2×#41×C43—21no—
120C2×#41×C43—21no—
121C2×#41×C43—21no—
122C22×Q8×C43C2311yescharacteristic
123C22×D4×C43C2×C412yes—
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43C2×C412yes—
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×M16×C43—21no—
131C2×M16×C43—21no—
132C2×M16×C43—21no—
133C2×M16×C43—21no—
134C2×M16×C43—21no—
135C2×M16×C43D412yescomplemented
136C2×M16×C43D412yescomplemented
137C2×M16×C43C2312yes—
138C2×M16×C43C2312yes—
139C22×C8×C43—21no—
140C22×C8×C43—21no—
141#101×C43—24no—
142#100×C43—24no—
143C24×C43C22×C412yes—
144C24×C43C22×C411yescharacteristic
145C23×D43C22⋊C412yes—
146#41×C43—41no—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
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—
159#41×C43—41no—
160#41×C43—41no—
161#41×C43—41no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—22no—
175C2×D4×C43—22no—
176C2×D4×C43—22no—
177C2×D4×C43—22no—
178C2×D4×C43—22no—
179C2×D4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43C22×C412yes—
187C22×C4×C43C22×C411yescharacteristic
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×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43#4111yescharacteristic
198C22×C4×C43#4111yescharacteristic
199C22×C4×C43#4111yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—22no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—28no—
206C2×C22⋊D43C22⋊C414yes—
207C2×C22⋊D43C22×C414yes—
208C22×Dic43—22no—
209C22×Dic43C22⋊C412yes—
210#10621898—22no—
211#10621898—22no—
212#10621898—22no—
213#10621898—22no—
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—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172C22⋊C412yes—
231C2×D172C2×D412yes—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43C22⋊C414yes—
237C2×C4×D43C2×D414yes—
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—
258C22⋊Dic43—28no—
259C22⋊Dic43—22no—
260C22⋊Dic43C22×C414yes—
261(C2×D43)⋊C4—28no—
262C4⋊Dic43—22no—
263C4⋊Dic43—22no—
264Dic43⋊C4—28no—
265C4×Dic43—22no—
266C4×Dic43—22no—
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—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—81no—
287C23×C43—82no—
288C23×C43C2×C22⋊C411yescharacteristic
289C23×C43C2×C22⋊C411yescharacteristic
290C23×C43C4×D411yescharacteristic
291C23×C43C4×D411yescharacteristic
292C23×C43C4×D411yescharacteristic
293C23×C43C4×D411yescharacteristic
294C23×C43C23×C411yescharacteristic
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—82no—
298C22×D43C2×C22⋊C414yes—
299Q8×C43—41no—
300Q8×C43—41no—
301Q8×C43—41no—
302Q8×C43—41no—
303D4×C43—42no—
304D4×C43—42no—
305D4×C43—42no—
306D4×C43—42no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C4×D411yescharacteristic
321C2×C4×C43C4×D411yescharacteristic
322C2×C4×C43C4×D411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43#12011yescharacteristic
325C2×C4×C43#12011yescharacteristic
326C2×C4×C43#12011yescharacteristic
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12111yescharacteristic
329C2×C4×C43#12111yescharacteristic
330C2×C4×C43#12111yescharacteristic
331C2×C4×C43#12111yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12311yescharacteristic
337C2×C4×C43#12311yescharacteristic
338C2×C4×C43#12311yescharacteristic
339C2×C4×C43#12311yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C22⋊D43—24no—
347C22⋊D43—24no—
348C22⋊D43—24no—
349C22⋊D43—24no—
350C22⋊D43—88no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—24no—
354C2×Dic43—82no—
355C2×Dic43C2×C22⋊C414yes—
356D172—22no—
357D172—22no—
358D172—22no—
359D172—22no—
360C4×D43—24no—
361C4×D43—24no—
362C4×D43—24no—
363C4×D43—24no—
364Dic86—22no—
365Dic86—22no—
366Dic86—22no—
367Dic86—22no—
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—44no—
381C22×C43—42no—
382C22×C43—82no—
383C22×C43—82no—
384C22×C43#38611yescharacteristic
385C22×C43#38611yescharacteristic
386C22×C43#38611yescharacteristic
387C22×C43#38611yescharacteristic
388C22×C43C22×C22⋊C411yescharacteristic
389C22×C43C2×C4×D411yescharacteristic
390C22×C43C2×C4×D411yescharacteristic
391C2×D43—24no—
392C2×D43—44no—
393C2×D43—44no—
394C2×D43—82no—
395C4×C43—42no—
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—44no—
406C2×#568—431no—
407#3449—431no—
408C2×#413—431no—
409C2×#413—431no—
410C2×#413D4311yescharacteristic, complemented
411#1915—434no—
412#1914—434no—
413C2×#344—431no—
414C2×#344—431no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—21no—
419C2×C43—21no—
420C2×C43—21no—
421C2×C43—21no—
422C2×C43—82no—
423C2×C43C2×#38611yescharacteristic
424D43—44no—
425C22×#41—431no—
426C22×#41C2×D4311yescharacteristic
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×#117—431no—
448#413—22no—
449#413—22no—
450#413—434no—
451#413—862no—
452#413—862no—
453#413—862no—
454C2×#101—432no—
455C2×#101—861no—
456C2×#101C2×D4312yescomplemented
457C2×#100—432no—
458C2×#100—861no—
459C2×#100C2×D4312yescomplemented
460#344—434no—
461#344—434no—
462C43#2101711yescharacteristic, complemented, Sylow
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—432no—
476C2×#41—432no—
477C2×#41—432no—
478C2×#41—432no—
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×Q8C22×D4311yescharacteristic
489C22×D4—432no—
490C22×D4—431no—
491C22×D4C4×D4312yes—
492C22×D4C22×D4311yescharacteristic
493C23×C4—432no—
494C23×C4C4×D4312yes—
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×M16C22⋊D4312yescomplemented
524C2×M16C22⋊D4312yescomplemented
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—432no—
547#117—432no—
548#117—861no—
549#117—861no—
550C2×C4⋊C4—861no—
551C2×C22⋊C4—432no—
552C2×C42—861no—
553#101—24no—
554#101—864no—
555#101—864no—
556#100—24no—
557#100—864no—
558#100—864no—
559C24—432no—
560C24C2×C4×D4312yes—
561C24C2×C4×D4311yescharacteristic
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
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—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—432no—
601C2×Q8—432no—
602C2×Q8—861no—
603C2×Q8—861no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—434no—
619C2×D4—434no—
620C2×D4—432no—
621C2×D4—432no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—868no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—432no—
638C22×C4—434no—
639C22×C4—434no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4C2×C4×D4312yes—
646C22×C4C2×C4×D4311yescharacteristic
647C22×C4#1062189811yescharacteristic
648C22×C4#1062189811yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4D4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4#1062190011yescharacteristic
656C22×C4#1062190011yescharacteristic
657C22×C4C2×C22⋊D4311yescharacteristic
658C22×C4C2×C22⋊D4311yescharacteristic
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×C22⋊D4314yes—
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—868no—
691C4⋊C4—862no—
692C4⋊C4—862no—
693C22⋊C4—434no—
694C22⋊C4—868no—
695C22⋊C4—868no—
696C22⋊C4—862no—
697C42—862no—
698C42—862no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—81no—
703C23—82no—
704C23—434no—
705C23—862no—
706C23—862no—
707C23—3442no—
708C23C22⋊C4×D4311yescharacteristic
709C23C22⋊C4×D4311yescharacteristic
710C23(C22⋊D43)⋊C411yescharacteristic
711C23(C22⋊D43)⋊C411yescharacteristic
712C23C4×C22⋊D4311yescharacteristic
713C23C4×C22⋊D4311yescharacteristic
714C23C22×C4×D4311yescharacteristic
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—862no—
720Q8—862no—
721Q8—862no—
722Q8—862no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—864no—
732D4—864no—
733D4—864no—
734D4—864no—
735D4—862no—
736D4—862no—
737D4—862no—
738D4—862no—
739D4—3448no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—434no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—864no—
751C2×C4—864no—
752C2×C4—864no—
753C2×C4—864no—
754C2×C4—864no—
755C2×C4—3442no—
756C2×C4C22⋊C4×D4311yescharacteristic
757C2×C4C22⋊C4×D4311yescharacteristic
758C2×C4(C22⋊D43)⋊C411yescharacteristic
759C2×C4(C22⋊D43)⋊C411yescharacteristic
760C2×C4C4×C22⋊D4311yescharacteristic
761C2×C4C4×C22⋊D4311yescharacteristic
762C2×C4#1306329311yescharacteristic
763C2×C4#1306329311yescharacteristic
764C2×C4#1306329311yescharacteristic
765C2×C4#1306329311yescharacteristic
766C2×C4#1306329611yescharacteristic
767C2×C4#1306329611yescharacteristic
768C2×C4#1306329611yescharacteristic
769C2×C4#1306329611yescharacteristic
770C2×C4#1306329811yescharacteristic
771C2×C4#1306329811yescharacteristic
772C2×C4#1306329811yescharacteristic
773C2×C4#1306329811yescharacteristic
774C2×C4#1306330711yescharacteristic
775C2×C4#1306330711yescharacteristic
776C2×C4#1306330711yescharacteristic
777C2×C4#1306330711yescharacteristic
778C2×C4C2×D4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C2×C4C22×C22⋊D4311yescharacteristic
782C2×C4C2×#1062190011yescharacteristic
783C2×C4C2×#1062189811yescharacteristic
784C8—24no—
785C8—42no—
786C8—864no—
787C8—1722no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—44no—
796C22—42no—
797C22—82no—
798C22—82no—
799C22—864no—
800C22—3442no—
801C22—1724no—
802C22—1724no—
803C22#1458277511yescharacteristic
804C22#1458277511yescharacteristic
805C22#1458277511yescharacteristic
806C22#1458277511yescharacteristic
807C22C2×C22⋊C4×D4311yescharacteristic
808C22C2×(C22⋊D43)⋊C411yescharacteristic
809C22C2×C4×C22⋊D4311yescharacteristic
810C4—42no—
811C4—864no—
812C4—1724no—
813C4#1458277511yescharacteristic
814C4#1458277511yescharacteristic
815C4#1458277511yescharacteristic
816C4#1458277511yescharacteristic
817C4C2×#1306329311yescharacteristic
818C4C2×#1306329611yescharacteristic
819C4C2×#1306329811yescharacteristic
820C4C2×#1306330711yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—82no—
829C2—1724no—
830C2C2×#1458277511yescharacteristic
subgroupG/H
centerC4#14582775
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#413C2
socleC2×C43C2×#386
prime radical#19147924C2
cosocleC22×C4×C43C24
hypercenterC2×#413D43
hypocenterC43#21017
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582883C2semidirect
4. C2×#14582881C2semidirect
5. #19135144C2semidirect
6. #19135139C2semidirect
7. C2×#14582671C2semidirect
8. C2×#14582670C2semidirect
9. C2×C43×#413C2semidirect
34. C2×#13063244C22semidirect
36. C2×#13063242C22semidirect
38. #14582671C22semidirect
39. #14582670C22semidirect
45. C2×#101×C43C22semidirect
46. C2×#100×C43C22semidirect
75. C2×#10621877D4semidirect
76. C2×#10621877D4semidirect
135. C2×M16×C43D4semidirect
136. C2×M16×C43D4semidirect
410. C2×#413D43semidirect
456. C2×#101C2×D43semidirect
459. C2×#100C2×D43semidirect
462. C43#21017semidirect
523. C2×M16C22⋊D43semidirect
524. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479242
C2×#145828832
C2×#145828812
#191351442
#191351392
C2×#145826712
C2×#145826702
C2×C43×#4132
#2101743