Finite Group Databasebeta

← #36312951

Subgroups — #36312951

Order 21248.

11346 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128538C212yesmaximal, complemented
2#24921254C218yesmaximal, complemented
3#24921247C214yesmaximal, complemented
4#24921240C214yesmaximal, complemented
5#24921234C211yesmaximal, characteristic, complemented
6#24921230C212yesmaximal, complemented
7#24921226C216yesmaximal, complemented
8#24921225C216yesmaximal, complemented
9D4×#13050591C214yesmaximal, complemented
10#24920953C214yesmaximal, complemented
11#24920952C218yesmaximal, complemented
12#24920791C216yesmaximal, complemented
13#532×D83C216yesmaximal, complemented
14C2×C4×#13050591C211yesmaximal, characteristic, complemented
15C83×#3497C211yesmaximal, characteristic, complemented
16#19128538—232no—
17C2×#14581840C2212yescomplemented
18C2×#14581840C2218yescomplemented
19C2×#14581838C22112yescomplemented
20C2×#14581838C2218yescomplemented
21C22×#13050591C2211yescharacteristic
22C22×#13050591C2218yescomplemented
23C2×#41×D83C2218yescomplemented
24C2×#41×D83C22112yescomplemented
25#19128373C2214yescomplemented
26#19128370C2218yescomplemented
27Q8×D332C2214yescomplemented
28Q8×C22⋊D83C2218yescomplemented
29#19128363C2218yescomplemented
30#19128362C2218yescomplemented
31#19128358C2218yescomplemented
32#19128356C22112yescomplemented
33#19128354C22112yescomplemented
34#19128353C22124yescomplemented
35#19128348C22124yescomplemented
36#19128347C22124yescomplemented
37#19128344C22124yescomplemented
38#19128342C22124yescomplemented
39D4×D332C22112yescomplemented
40#19128336C22112yescomplemented
41#19128335C22124yescomplemented
42#19128282C2216yescomplemented
43#19128279C22112yescomplemented
44#19128274C22124yescomplemented
45#19128267C22124yescomplemented
46#19128259C22124yescomplemented
47#19128252C2216yescomplemented
48#19128251C2216yescomplemented
49#19128250C22112yescomplemented
50#19128249C2216yescomplemented
51#19128248C22112yescomplemented
52#19128248C22112yescomplemented
53#19128247C22112yescomplemented
54#19128246C2214yescomplemented
55#19128246C22112yescomplemented
56C4⋊Q8×D83C2216yescomplemented
57#127×D83C2216yescomplemented
58#124×D83C22112yescomplemented
59#19128214C22124yescomplemented
60#19128211C22124yescomplemented
61#121×D83C22112yescomplemented
62#121×D83C22112yescomplemented
63C4×#13050591C2214yescomplemented
64C4×#13050591C2214yescomplemented
65C4×#13050591C2214yescomplemented
66C4×#13050591C2214yescomplemented
67C2×Q8×Dic83C2211yescharacteristic, complemented
68C2×C4×D332C2213yescomplemented
69C2×#14581754C2213yescomplemented
70C4×D4×D83C22112yescomplemented
71C4×D4×D83C22112yescomplemented
72C2×#14581750C2213yescomplemented
73C2×C42×D83C2213yescomplemented
74C2×2−1+4×C83C2212yescomplemented
75#550×C83C2214yescomplemented
76D4×Q8×C83C2214yescomplemented
77#548×C83C2218yescomplemented
78#537×C83C2216yescomplemented
79#532×C83C2216yescomplemented
80C2×C4×Q8×C83C2211yescharacteristic, complemented
81#14581840—264no—
82#14581840—216no—
83#14581838—264no—
84#14581838—296no—
85C2×#13050591—264no—
86C2×#13050591D4116yescomplemented
87C2×#13050591C23124yes—
88C2×#13050591C2318yes—
89C2×#13050591C23112yes—
90C2×#13050591C2314yes—
91C2×#13050591C2314yes—
92C2×#13050590C23124yes—
93C2×#13050590C23112yes—
94C2×#13050590C23124yes—
95C2×#13050589C23112yes—
96C2×#13050589C2318yes—
97#41×D83—264no—
98#41×D83—296no—
99C2×Q8×D83C2318yes—
100C2×Q8×D83C23112yes—
101C22×D332C23124yes—
102C22×D332C2313yes—
103C2×D4×D83C23124yes—
104C2×D4×D83C23124yes—
105C2×D4×D83C23112yes—
106C2×D4×D83C23112yes—
107C2×D4×D83C23112yes—
108C22×C4×D83C23124yes—
109C22×C4×D83C2313yes—
110C22×C4×D83C2313yes—
111C22×C4×D83C2313yes—
112#14581792C2316yes—
113#14581791C2314yes—
114#14581791C23112yes—
115#14581790C23112yes—
116#14581789C2316yes—
117#14581788C23112yes—
118#14581788C2314yes—
119#14581788C23112yes—
120#14581781C23112yes—
121#14581780C23112yes—
122#14581779C23112yes—
123#14581778C2318yes—
124#14581778C23124yes—
125#14581777C23148yes—
126#14581774C23148yes—
127#14581772C23124yes—
128#14581771C23124yes—
129#14581768C23124yes—
130#14581767C23124yes—
131#14581767C23112yes—
132#14581767C23112yes—
133#14581766C23124yes—
134#14581766C2314yes—
135#14581766C23112yes—
136#14581765C23124yes—
137#14581765C23124yes—
138#14581764C2318yes—
139#14581764C23124yes—
140#14581763C23112yes—
141#14581763C23124yes—
142#14581763C23112yes—
143#14581762C23148yes—
144#14581760C23148yes—
145Q8×Dic83C2314yes—
146Q8×Dic83C2314yes—
147C4×D332C23112yes—
148C4×D332C23112yes—
149C4×D332C23112yes—
150C4×D332C23112yes—
151D4×Dic83C2314yes—
152D4×Dic83C23112yes—
153#14581754C23112yes—
154#14581754C23112yes—
155#14581754C2314yes—
156#14581754C23112yes—
157C4×C22⋊D83C23124yes—
158C4×C22⋊D83C23124yes—
159(C22⋊D83)⋊C4C2318yes—
160(C22⋊D83)⋊C4C23124yes—
161#14581750C23112yes—
162#14581750C23112yes—
163C2×C4⋊Dic83C2313yes—
164C4⋊C4×D83C23112yes—
165C4⋊C4×D83C23112yes—
166C2×(C2×D83)⋊C4C2316yes—
167C22⋊C4×D83C23124yes—
168C22⋊C4×D83C23124yes—
169C2×C4×Dic83C2311yescharacteristic
170C2×C4×Dic83C2313yes—
171C2×C4×Dic83C2313yes—
172C42×D83C2316yes—
173C42×D83C2316yes—
174C42×D83C2316yes—
175C42×D83C2316yes—
1762−1+4×C83—216no—
177C2×#41×C83C2318yes—
178C2×#41×C83C23112yes—
179C22×Q8×C83C2318yes—
180C22×Q8×C83C2311yescharacteristic
181C4⋊Q8×C83C2316yes—
182#127×C83C2316yes—
183#124×C83C23112yes—
184C22⋊Q8×C83C23124yes—
185#121×C83C23124yes—
186#121×C83C2314yes—
187#121×C83C23112yes—
188C4×Q8×C83C2314yes—
189C4×Q8×C83C2314yes—
190C4×D4×C83C23112yes—
191C4×D4×C83C23112yes—
192C2×C4⋊C4×C83C2313yes—
193C2×C42×C83C2313yes—
194C23×D83C24124yes—
195C23×D83C2413yes—
196#13050591—232no—
197#13050591—296no—
198#13050591—248no—
199#13050591C2×D4132yescomplemented
200#13050591C2×D4132yescomplemented
201#13050590—248no—
202#13050590—296no—
203#13050590—296no—
204#13050589—232no—
205#13050589—248no—
206C2×Dic166C24112yes—
207C2×Dic166C2418yes—
208Q8×D83—232no—
209Q8×D83—248no—
210C2×D332—296no—
211C2×D332C2×D4124yescomplemented
212C2×D332C24124yes—
213C2×D332C24112yes—
214C2×D332C2414yes—
215C2×D332C24112yes—
216C2×D332C24112yes—
217C2×C22⋊D83C24124yes—
218C2×C22⋊D83C2418yes—
219C2×C22⋊D83C2418yes—
220C2×C22⋊D83C2418yes—
221C2×C22⋊D83C24124yes—
222D4×D83—296no—
223D4×D83—296no—
224D4×D83—248no—
225D4×D83—424no—
226D4×D83—424no—
227C22×Dic83C2411yescharacteristic
228C22×Dic83C2418yes—
229C22×Dic83C2413yes—
230C22×Dic83C2411yescharacteristic
231C2×C4×D83—296no—
232C2×C4×D83—46no—
233C2×C4×D83—46no—
234C2×C4×D83C2×D4124yescomplemented
235C2×C4×D83C2416yes—
236C2×C4×D83C24124yes—
237C2×C4×D83C2416yes—
238C2×C4×D83C24124yes—
239C2×C4×D83C2418yes—
240C2×C4×D83C2416yes—
241C2×C4×D83C2416yes—
242C2×C4×D83C2416yes—
243C2×C4×D83C2416yes—
244C4⋊Dic83C2414yes—
245C4⋊Dic83C24112yes—
246C4⋊Dic83C24112yes—
247Dic83⋊C4C2418yes—
248Dic83⋊C4C24124yes—
249C22⋊Dic83C24124yes—
250C22⋊Dic83C2418yes—
251(C2×D83)⋊C4C24124yes—
252(C2×D83)⋊C4C24124yes—
253(C2×D83)⋊C4C24124yes—
254(C2×D83)⋊C4C2418yes—
255(C2×D83)⋊C4C2418yes—
256C4×Dic83C2411yescharacteristic
257C4×Dic83C2416yes—
258C4×Dic83C2416yes—
259C4×Dic83C2411yescharacteristic
260C4×Dic83C2416yes—
261C4×Dic83C2411yescharacteristic
262C4×Dic83C2411yescharacteristic
263C4×Dic83C2416yes—
264#41×C83—232no—
265#41×C83—248no—
266C2×Q8×C83—232no—
267C2×Q8×C83C2×D418yescomplemented
268C2×Q8×C83C24112yes—
269C2×Q8×C83C2414yes—
270C2×D4×C83C2414yes—
271C2×D4×C83C24112yes—
272C2×D4×C83C2418yes—
273C2×D4×C83C24112yes—
274C22×C4×C83C2411yescharacteristic
275C22×C4×C83C24124yes—
276C22×C4×C83C2413yes—
277C22×C4×C83C2413yes—
278C4⋊C4×C83C2414yes—
279C4⋊C4×C83C24112yes—
280C4⋊C4×C83C24112yes—
281C22⋊C4×C83C24124yes—
282C22⋊C4×C83C2418yes—
283C42×C83C2416yes—
284C42×C83C2416yes—
285C23×C83C2518yes—
286C23×C83C2511yescharacteristic
287C22×D83—248no—
288C22×D83—43no—
289C22×D83—43no—
290C22×D83—424no—
291C22×D83—424no—
292C22×D83C22×D4112yes—
293C22×D83C2518yes—
294C22×D83C2516yes—
295Q8×C83—224no—
296Q8×C83C22×D4116yes—
297D4×C83—216no—
298D4×C83—224no—
299D4×C83—28no—
300D4×C83—412no—
301C2×C4×C83—248no—
302C2×C4×C83—22no—
303C2×C4×C83—43no—
304C2×C4×C83C22×D4112yes—
305C2×C4×C83C2511yescharacteristic
306C2×C4×C83C2516yes—
307C2×C4×C83C2518yes—
308C2×C4×C83C2516yes—
309C2×C4×C83C2511yescharacteristic
310C22⋊D83—216no—
311C22⋊D83—248no—
312C22⋊D83—216no—
313C22⋊D83—216no—
314C22⋊D83—424no—
315C2×Dic83—216no—
316C2×Dic83—22no—
317C2×Dic83—43no—
318C2×Dic83C22×D414yes—
319C2×Dic83C2511yescharacteristic
320C2×Dic83C2516yes—
321C2×Dic83C2518yes—
322C2×Dic83C2511yescharacteristic
323C2×Dic83C2511yescharacteristic
324C2×Dic83C2511yescharacteristic
325D332—248no—
326D332—224no—
327D332—28no—
328D332—412no—
329D332C22×D4148yes—
330C4×D83—248no—
331C4×D83—248no—
332C4×D83—212no—
333C4×D83—216no—
334C4×D83—212no—
335C4×D83—46no—
336C4×D83—46no—
337C4×D83C22×D4124yes—
338C4×D83C22×D4124yes—
339Dic166—224no—
340Dic166—216no—
341C22×C83—21no—
342C22×C83—21no—
343C22×C83—28no—
344C22×C83—28no—
345C22×C83—28no—
346C22×C83C23×D412yes—
347C22×C83C2611yescharacteristic
348C2×D83—26no—
349C2×D83—26no—
350C2×D83—28no—
351C2×D83—28no—
352C2×D83—28no—
353C2×D83—412no—
354C2×D83—848no—
355C2×D83C23×D4112yes—
356C4×C83—28no—
357C4×C83—26no—
358C4×C83—21no—
359C4×C83C23×D4112yes—
360C4×C83#58512yescomplemented
361Dic83—28no—
362Dic83—26no—
363Dic83—21no—
364Dic83C23×D412yes—
365Dic83C23×D412yes—
366Dic83#58512yescomplemented
367#62812—831nomaximal, Sylow
368C2×C83—22no—
369C2×C83—48no—
370C2×C83C24×D411yescharacteristic
371C2×C83C2×#58511yescharacteristic
372C2×C83C2×#58511yescharacteristic
373D83—212no—
374D83—48no—
375C2×#585—832no—
376#3500—838no—
377#3499—834no—
378#3498—834no—
379#3497—832no—
380#3497—831no—
381#3497D8311yescharacteristic, complemented
382#3496—836no—
383#3496—836no—
384D4×#41—834no—
385D4×#41—834no—
386D4×#41—838no—
387#3449—836no—
388C2×#532—836no—
389C2×C4×#41—831no—
390C83#6281211yescharacteristic, complemented, Sylow
391#585—16632no—
392C2×2−1+4—832no—
393C2×2−1+4—838no—
394C2×2−1+4C2×D8312yescomplemented
395C2×H(5,𝔽2)—8312no—
396C2×H(5,𝔽2)—838no—
397C22×#41—8312no—
398C22×#41—838no—
399C22×#41—831no—
400C22×#41—838no—
401#550—838no—
402#550—834no—
403#550C2×D8314yescomplemented
404D4×Q8—838no—
405D4×Q8—834no—
406D4×Q8C2×D8314yescomplemented
407#548—838no—
408#548—838no—
409#548—838no—
410#548C2×D8318yescomplemented
411#547—8312no—
412#547—8324no—
413#547—8312no—
414#546—8324no—
415#546—8324no—
416#546—8324no—
417#546—8324no—
418D42—8312no—
419D42—8324no—
420D42—8312no—
421#537—8312no—
422#537—836no—
423#537C2×D8316yescomplemented
424#536—8324no—
425#535—8324no—
426#534—8324no—
427#532—8312no—
428#532—836no—
429#532—836no—
430#532—8312no—
431#532—834no—
432#532—8312no—
433#532—8312no—
434#532—8312no—
435#532—836no—
436#532C2×D8316yescomplemented
437C2×C4⋊Q8—836no—
438C2×#127—836no—
439C2×#124—8312no—
440#525—8324no—
441#525—8324no—
442C2×#121—8312no—
443C2×#121—8312no—
444C4×#41—834no—
445C4×#41—834no—
446C4×#41—834no—
447C4×#41—834no—
448C2×C4×Q8—831no—
449C2×C4×Q8C2×D8311yescharacteristic, complemented
450C2×C4×D4—8312no—
451C2×C4×D4—8312no—
452C2×C4×D4—833no—
453C2×C4×D4—833no—
454C2×#117—833no—
455C22×C42—833no—
4562−1+4—216no—
4572−1+4—16664no—
4582−1+4—16616no—
459H(5,𝔽2)—16696no—
460H(5,𝔽2)—16664no—
461C2×#41—8316no—
462C2×#41—834no—
463C2×#41—834no—
464C2×#41—8312no—
465C2×#41—8324no—
466C2×#41—838no—
467C2×#41—8312no—
468C2×#41—838no—
469C2×#41—8324no—
470C2×#41—8312no—
471C2×#41—8324no—
472C2×#41—16696no—
473C2×#41—16664no—
474C2×#41—16664no—
475C2×#41C22×D83112yes—
476C2×#41C22×D8318yes—
477C22×Q8—8312no—
478C22×Q8—838no—
479C22×Q8C22×D8318yes—
480C22×Q8C22×D8311yescharacteristic
481C22×D4—8312no—
482C22×D4—8312no—
483C22×D4—8324no—
484C22×D4—8312no—
485C22×D4—8324no—
486C22×D4—833no—
487C22×D4—8324no—
488C23×C4—833no—
489C23×C4—833no—
490C23×C4—833no—
491C23×C4—8324no—
492C4⋊Q8—8312no—
493C4⋊Q8—834no—
494C4⋊Q8—8312no—
495C4⋊Q8—836no—
496C4⋊Q8C22×D8316yes—
497#127—834no—
498#127—8312no—
499#127—8312no—
500#127—836no—
501#127C22×D8316yes—
502#124—8312no—
503#124—8312no—
504#124—838no—
505#124—8324no—
506#124—8312no—
507#124C22×D83112yes—
508#123—8348no—
509#123—8348no—
510C22⋊Q8—8324no—
511C22⋊Q8—8324no—
512C22⋊Q8—8324no—
513C22⋊Q8C22×D83124yes—
514#121—8312no—
515#121—8312no—
516#121—8324no—
517#121—838no—
518#121—8324no—
519#121—834no—
520#121—8312no—
521#121—8324no—
522#121—8312no—
523#121—8312no—
524#121—8324no—
525#121—8324no—
526#121—8324no—
527#121C22×D8314yes—
528#121C22×D83112yes—
529#121C22×D83124yes—
530#120—8348no—
531#120—8348no—
532C4×Q8—834no—
533C4×Q8—834no—
534C4×Q8C22×D8314yes—
535C4×Q8C22×D8314yes—
536C4×D4—834no—
537C4×D4—8312no—
538C4×D4—8324no—
539C4×D4—8324no—
540C4×D4—834no—
541C4×D4—8312no—
542C4×D4—8312no—
543C4×D4—8312no—
544C4×D4—838no—
545C4×D4—8324no—
546C4×D4—8312no—
547C4×D4—8312no—
548C4×D4—8312no—
549C4×D4—8312no—
550C4×D4C22×D83112yes—
551C4×D4C22×D83112yes—
552#117—8312no—
553#117—8312no—
554C2×C4⋊C4—833no—
555C2×C4⋊C4—8312no—
556C2×C4⋊C4—8312no—
557C2×C4⋊C4C22×D8313yes—
558C2×C22⋊C4—836no—
559C2×C22⋊C4—8324no—
560C2×C22⋊C4—8324no—
561C2×C42—833no—
562C2×C42—833no—
563C2×C42—831no—
564C2×C42—836no—
565C2×C42—836no—
566C2×C42—836no—
567C2×C42—836no—
568C2×C42C22×D8313yes—
569C24—833no—
570C24—8324no—
571#41—232no—
572#41—248no—
573#41—8332no—
574#41—8332no—
575#41—16696no—
576#41—16696no—
577#41—16632no—
578#41—16648no—
579#41—16648no—
580#41—16696no—
581#41—16632no—
582#41—16648no—
583C2×Q8—232no—
584C2×Q8—8312no—
585C2×Q8—838no—
586C2×Q8—16648no—
587C2×Q8—16632no—
588C2×Q8D4×D8318yescomplemented
589C2×Q8C23×D83112yes—
590C2×Q8C23×D8314yes—
591C2×D4—33224no—
592C2×D4—33224no—
593C2×D4—8324no—
594C2×D4—838no—
595C2×D4—8324no—
596C2×D4—838no—
597C2×D4—838no—
598C2×D4—8324no—
599C2×D4—8312no—
600C2×D4—8312no—
601C2×D4—834no—
602C2×D4—8324no—
603C2×D4—8312no—
604C2×D4—16696no—
605C2×D4—16648no—
606C2×D4—16696no—
607C2×D4—16696no—
608C2×D4C23×D8314yes—
609C2×D4C23×D8318yes—
610C2×D4C23×D83112yes—
611C2×D4C23×D83112yes—
612C22×C4—3326no—
613C22×C4—3326no—
614C22×C4—833no—
615C22×C4—836no—
616C22×C4—836no—
617C22×C4—831no—
618C22×C4—8324no—
619C22×C4—836no—
620C22×C4—836no—
621C22×C4—831no—
622C22×C4—838no—
623C22×C4—836no—
624C22×C4—836no—
625C22×C4—8324no—
626C22×C4—838no—
627C22×C4—8324no—
628C22×C4—16696no—
629C22×C4C23×D8311yescharacteristic
630C22×C4C23×D83124yes—
631C22×C4C23×D8313yes—
632C22×C4C23×D8313yes—
633C4⋊C4—838no—
634C4⋊C4—834no—
635C4⋊C4—8312no—
636C4⋊C4—8324no—
637C4⋊C4—8312no—
638C4⋊C4C23×D8314yes—
639C4⋊C4C23×D83112yes—
640C4⋊C4C23×D83112yes—
641C22⋊C4—838no—
642C22⋊C4—8324no—
643C22⋊C4—838no—
644C22⋊C4—838no—
645C22⋊C4—8324no—
646C22⋊C4—8324no—
647C22⋊C4—8324no—
648C22⋊C4C23×D8318yes—
649C22⋊C4C23×D83124yes—
650C42—831no—
651C42—831no—
652C42—831no—
653C42—831no—
654C42—836no—
655C42—836no—
656C42—836no—
657C42—836no—
658C42C23×D8316yes—
659C42C23×D8316yes—
660C23—3323no—
661C23—3323no—
662C23—33224no—
663C23—33224no—
664C23—8312no—
665C23—836no—
666C23—838no—
667C23—16648no—
668C23C24×D8318yes—
669C23C24×D8311yescharacteristic
670Q8—224no—
671Q8—16616no—
672Q8—16624no—
673Q8C2×D4×D83116yes—
674D4—216no—
675D4—224no—
676D4—28no—
677D4—412no—
678D4—33212no—
679D4—33224no—
680D4—8348no—
681D4—16648no—
682D4—16616no—
683D4—16616no—
684D4—16648no—
685D4—16616no—
686D4—16624no—
687D4—1668no—
688C2×C4—248no—
689C2×C4—22no—
690C2×C4—43no—
691C2×C4—3326no—
692C2×C4—3326no—
693C2×C4—3323no—
694C2×C4—834no—
695C2×C4—831no—
696C2×C4—831no—
697C2×C4—831no—
698C2×C4—8324no—
699C2×C4—8324no—
700C2×C4—831no—
701C2×C4—836no—
702C2×C4—838no—
703C2×C4—16612no—
704C2×C4—16616no—
705C2×C4—16648no—
706C2×C4—1662no—
707C2×C4—16616no—
708C2×C4—16648no—
709C2×C4—16612no—
710C2×C4C2×D4×D83112yes—
711C2×C4C24×D8311yescharacteristic
712C2×C4C24×D8316yes—
713C2×C4C24×D8318yes—
714C2×C4C24×D8316yes—
715C2×C4C24×D8311yescharacteristic
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—33212no—
722C22—8312no—
723C22—66448no—
724C22—1668no—
725C22—1668no—
726C22—1668no—
727C22—1666no—
728C22—1666no—
729C22C22×D4×D8312yes—
730C22C25×D8311yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—832no—
735C4—832no—
736C4—832no—
737C4—1668no—
738C4—1661no—
739C4—1666no—
740C4C22×D4×D83112yes—
741C4#1912853812yescomplemented
742C2—22no—
743C2—48no—
744C2—3328no—
745C2—16612no—
746C2C23×D4×D8311yescharacteristic
747C2#585×D8311yescharacteristic
748C2C2×#1912853811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3497C2
hypercenter#3497D83
hypocenterC83#62812
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#19128538C2semidirect
2. #24921254C2semidirect
3. #24921247C2semidirect
4. #24921240C2semidirect
5. #24921234C2semidirect
6. #24921230C2semidirect
7. #24921226C2semidirect
8. #24921225C2semidirect
9. D4×#13050591C2semidirect
10. #24920953C2semidirect
11. #24920952C2semidirect
12. #24920791C2semidirect
13. #532×D83C2semidirect
14. C2×C4×#13050591C2semidirect
15. C83×#3497C2semidirect
17. C2×#14581840C22semidirect
18. C2×#14581840C22semidirect
19. C2×#14581838C22semidirect
20. C2×#14581838C22semidirect
22. C22×#13050591C22semidirect
23. C2×#41×D83C22semidirect
24. C2×#41×D83C22semidirect
25. #19128373C22semidirect
26. #19128370C22semidirect
27. Q8×D332C22semidirect
28. Q8×C22⋊D83C22semidirect
29. #19128363C22semidirect
30. #19128362C22semidirect
31. #19128358C22semidirect
32. #19128356C22semidirect
33. #19128354C22semidirect
34. #19128353C22semidirect
35. #19128348C22semidirect
36. #19128347C22semidirect
37. #19128344C22semidirect
38. #19128342C22semidirect
39. D4×D332C22semidirect
40. #19128336C22semidirect
41. #19128335C22semidirect
42. #19128282C22semidirect
43. #19128279C22semidirect
44. #19128274C22semidirect
45. #19128267C22semidirect
46. #19128259C22semidirect
47. #19128252C22semidirect
48. #19128251C22semidirect
49. #19128250C22semidirect
50. #19128249C22semidirect
51. #19128248C22semidirect
52. #19128248C22semidirect
53. #19128247C22semidirect
54. #19128246C22semidirect
55. #19128246C22semidirect
56. C4⋊Q8×D83C22semidirect
57. #127×D83C22semidirect
58. #124×D83C22semidirect
59. #19128214C22semidirect
60. #19128211C22semidirect
61. #121×D83C22semidirect
62. #121×D83C22semidirect
63. C4×#13050591C22semidirect
64. C4×#13050591C22semidirect
65. C4×#13050591C22semidirect
66. C4×#13050591C22semidirect
67. C2×Q8×Dic83C22semidirect
68. C2×C4×D332C22semidirect
69. C2×#14581754C22semidirect
70. C4×D4×D83C22semidirect
71. C4×D4×D83C22semidirect
72. C2×#14581750C22semidirect
73. C2×C42×D83C22semidirect
74. C2×2−1+4×C83C22semidirect
75. #550×C83C22semidirect
76. D4×Q8×C83C22semidirect
77. #548×C83C22semidirect
78. #537×C83C22semidirect
79. #532×C83C22semidirect
80. C2×C4×Q8×C83C22semidirect
86. C2×#13050591D4semidirect
199. #13050591C2×D4semidirect
200. #13050591C2×D4semidirect
211. C2×D332C2×D4semidirect
234. C2×C4×D83C2×D4semidirect
267. C2×Q8×C83C2×D4semidirect
360. C4×C83#585semidirect
366. Dic83#585semidirect
381. #3497D83semidirect
390. C83#62812semidirect
394. C2×2−1+4C2×D83semidirect
403. #550C2×D83semidirect
406. D4×Q8C2×D83semidirect
410. #548C2×D83semidirect
423. #537C2×D83semidirect
436. #532C2×D83semidirect
449. C2×C4×Q8C2×D83semidirect
588. C2×Q8D4×D83semidirect
741. C4#19128538semidirect

Maximal subgroups

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

subgroupindex
C2×#191285382
#249212542
#249212472
#249212402
#249212342
#249212302
#249212262
#249212252
D4×#130505912
#249209532
#249209522
#249207912
#532×D832
C2×C4×#130505912
C83×#34972
#6281283