Finite Group Databasebeta

← #31764378

Subgroups — #31764378

Order 17152.

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×#16864233C212yesmaximal, complemented
2#22574000C218yesmaximal, complemented
3#22573993C214yesmaximal, complemented
4#22573986C214yesmaximal, complemented
5#22573980C211yesmaximal, characteristic, complemented
6#22573976C212yesmaximal, complemented
7#22573972C216yesmaximal, complemented
8#22573971C216yesmaximal, complemented
9D4×#11761629C214yesmaximal, complemented
10#22573699C214yesmaximal, complemented
11#22573698C218yesmaximal, complemented
12#22573537C216yesmaximal, complemented
13#532×D67C216yesmaximal, complemented
14C2×C4×#11761629C211yesmaximal, characteristic, complemented
15C67×#3497C211yesmaximal, characteristic, complemented
16#16864233—232no—
17C2×#14524091C2212yescomplemented
18C2×#14524091C2218yescomplemented
19C2×#14524089C22112yescomplemented
20C2×#14524089C2218yescomplemented
21C22×#11761629C2211yescharacteristic
22C22×#11761629C2218yescomplemented
23C2×#41×D67C2218yescomplemented
24C2×#41×D67C22112yescomplemented
25#16864068C2214yescomplemented
26#16864065C2218yescomplemented
27Q8×D268C2214yescomplemented
28Q8×C22⋊D67C2218yescomplemented
29#16864058C2218yescomplemented
30#16864057C2218yescomplemented
31#16864053C2218yescomplemented
32#16864051C22112yescomplemented
33#16864049C22112yescomplemented
34#16864048C22124yescomplemented
35#16864043C22124yescomplemented
36#16864042C22124yescomplemented
37#16864039C22124yescomplemented
38#16864037C22124yescomplemented
39D4×D268C22112yescomplemented
40#16864031C22112yescomplemented
41#16864030C22124yescomplemented
42#16863977C2216yescomplemented
43#16863974C22112yescomplemented
44#16863969C22124yescomplemented
45#16863962C22124yescomplemented
46#16863954C22124yescomplemented
47#16863947C2216yescomplemented
48#16863946C2216yescomplemented
49#16863945C22112yescomplemented
50#16863944C2216yescomplemented
51#16863943C22112yescomplemented
52#16863943C22112yescomplemented
53#16863942C22112yescomplemented
54#16863941C2214yescomplemented
55#16863941C22112yescomplemented
56C4⋊Q8×D67C2216yescomplemented
57#127×D67C2216yescomplemented
58#124×D67C22112yescomplemented
59#16863909C22124yescomplemented
60#16863906C22124yescomplemented
61#121×D67C22112yescomplemented
62#121×D67C22112yescomplemented
63C4×#11761629C2214yescomplemented
64C4×#11761629C2214yescomplemented
65C4×#11761629C2214yescomplemented
66C4×#11761629C2214yescomplemented
67C2×Q8×Dic67C2211yescharacteristic, complemented
68C2×C4×D268C2213yescomplemented
69C2×#14524005C2213yescomplemented
70C4×D4×D67C22112yescomplemented
71C4×D4×D67C22112yescomplemented
72C2×#14524001C2213yescomplemented
73C2×C42×D67C2213yescomplemented
74C2×2−1+4×C67C2212yescomplemented
75#550×C67C2214yescomplemented
76D4×Q8×C67C2214yescomplemented
77#548×C67C2218yescomplemented
78#537×C67C2216yescomplemented
79#532×C67C2216yescomplemented
80C2×C4×Q8×C67C2211yescharacteristic, complemented
81#14524091—264no—
82#14524091—216no—
83#14524089—264no—
84#14524089—296no—
85C2×#11761629—264no—
86C2×#11761629D4116yescomplemented
87C2×#11761629C23124yes—
88C2×#11761629C2318yes—
89C2×#11761629C23112yes—
90C2×#11761629C2314yes—
91C2×#11761629C2314yes—
92C2×#11761628C23124yes—
93C2×#11761628C23112yes—
94C2×#11761628C23124yes—
95C2×#11761627C23112yes—
96C2×#11761627C2318yes—
97#41×D67—264no—
98#41×D67—296no—
99C2×Q8×D67C2318yes—
100C2×Q8×D67C23112yes—
101C22×D268C23124yes—
102C22×D268C2313yes—
103C2×D4×D67C23124yes—
104C2×D4×D67C23124yes—
105C2×D4×D67C23112yes—
106C2×D4×D67C23112yes—
107C2×D4×D67C23112yes—
108C22×C4×D67C23124yes—
109C22×C4×D67C2313yes—
110C22×C4×D67C2313yes—
111C22×C4×D67C2313yes—
112#14524043C2316yes—
113#14524042C2314yes—
114#14524042C23112yes—
115#14524041C23112yes—
116#14524040C2316yes—
117#14524039C23112yes—
118#14524039C2314yes—
119#14524039C23112yes—
120#14524032C23112yes—
121#14524031C23112yes—
122#14524030C23112yes—
123#14524029C2318yes—
124#14524029C23124yes—
125#14524028C23148yes—
126#14524025C23148yes—
127#14524023C23124yes—
128#14524022C23124yes—
129#14524019C23124yes—
130#14524018C23124yes—
131#14524018C23112yes—
132#14524018C23112yes—
133#14524017C23124yes—
134#14524017C2314yes—
135#14524017C23112yes—
136#14524016C23124yes—
137#14524016C23124yes—
138#14524015C2318yes—
139#14524015C23124yes—
140#14524014C23112yes—
141#14524014C23124yes—
142#14524014C23112yes—
143#14524013C23148yes—
144#14524011C23148yes—
145Q8×Dic67C2314yes—
146Q8×Dic67C2314yes—
147C4×D268C23112yes—
148C4×D268C23112yes—
149C4×D268C23112yes—
150C4×D268C23112yes—
151D4×Dic67C2314yes—
152D4×Dic67C23112yes—
153#14524005C23112yes—
154#14524005C23112yes—
155#14524005C2314yes—
156#14524005C23112yes—
157C4×C22⋊D67C23124yes—
158C4×C22⋊D67C23124yes—
159(C22⋊D67)⋊C4C2318yes—
160(C22⋊D67)⋊C4C23124yes—
161#14524001C23112yes—
162#14524001C23112yes—
163C2×C4⋊Dic67C2313yes—
164C4⋊C4×D67C23112yes—
165C4⋊C4×D67C23112yes—
166C2×(C2×D67)⋊C4C2316yes—
167C22⋊C4×D67C23124yes—
168C22⋊C4×D67C23124yes—
169C2×C4×Dic67C2311yescharacteristic
170C2×C4×Dic67C2313yes—
171C2×C4×Dic67C2313yes—
172C42×D67C2316yes—
173C42×D67C2316yes—
174C42×D67C2316yes—
175C42×D67C2316yes—
1762−1+4×C67—216no—
177C2×#41×C67C2318yes—
178C2×#41×C67C23112yes—
179C22×Q8×C67C2318yes—
180C22×Q8×C67C2311yescharacteristic
181C4⋊Q8×C67C2316yes—
182#127×C67C2316yes—
183#124×C67C23112yes—
184C22⋊Q8×C67C23124yes—
185#121×C67C23124yes—
186#121×C67C2314yes—
187#121×C67C23112yes—
188C4×Q8×C67C2314yes—
189C4×Q8×C67C2314yes—
190C4×D4×C67C23112yes—
191C4×D4×C67C23112yes—
192C2×C4⋊C4×C67C2313yes—
193C2×C42×C67C2313yes—
194C23×D67C24124yes—
195C23×D67C2413yes—
196#11761629—232no—
197#11761629—296no—
198#11761629—248no—
199#11761629C2×D4132yescomplemented
200#11761629C2×D4132yescomplemented
201#11761628—248no—
202#11761628—296no—
203#11761628—296no—
204#11761627—232no—
205#11761627—248no—
206C2×Dic134C24112yes—
207C2×Dic134C2418yes—
208Q8×D67—232no—
209Q8×D67—248no—
210C2×D268—296no—
211C2×D268C2×D4124yescomplemented
212C2×D268C2414yes—
213C2×D268C24124yes—
214C2×D268C24112yes—
215C2×D268C24112yes—
216C2×D268C24112yes—
217C2×C22⋊D67C2418yes—
218C2×C22⋊D67C24124yes—
219C2×C22⋊D67C2418yes—
220C2×C22⋊D67C2418yes—
221C2×C22⋊D67C24124yes—
222D4×D67—296no—
223D4×D67—296no—
224D4×D67—248no—
225D4×D67—424no—
226D4×D67—424no—
227C22×Dic67C2411yescharacteristic
228C22×Dic67C2418yes—
229C22×Dic67C2413yes—
230C22×Dic67C2411yescharacteristic
231C2×C4×D67—296no—
232C2×C4×D67—46no—
233C2×C4×D67—46no—
234C2×C4×D67C2×D4124yescomplemented
235C2×C4×D67C2416yes—
236C2×C4×D67C2416yes—
237C2×C4×D67C24124yes—
238C2×C4×D67C2418yes—
239C2×C4×D67C24124yes—
240C2×C4×D67C2416yes—
241C2×C4×D67C2416yes—
242C2×C4×D67C2416yes—
243C2×C4×D67C2416yes—
244C4⋊Dic67C2414yes—
245C4⋊Dic67C24112yes—
246C4⋊Dic67C24112yes—
247Dic67⋊C4C2418yes—
248Dic67⋊C4C24124yes—
249C22⋊Dic67C2418yes—
250C22⋊Dic67C24124yes—
251(C2×D67)⋊C4C2418yes—
252(C2×D67)⋊C4C2418yes—
253(C2×D67)⋊C4C24124yes—
254(C2×D67)⋊C4C24124yes—
255(C2×D67)⋊C4C24124yes—
256C4×Dic67C2411yescharacteristic
257C4×Dic67C2411yescharacteristic
258C4×Dic67C2411yescharacteristic
259C4×Dic67C2411yescharacteristic
260C4×Dic67C2416yes—
261C4×Dic67C2416yes—
262C4×Dic67C2416yes—
263C4×Dic67C2416yes—
264#41×C67—232no—
265#41×C67—248no—
266C2×Q8×C67—232no—
267C2×Q8×C67C2×D418yescomplemented
268C2×Q8×C67C24112yes—
269C2×Q8×C67C2414yes—
270C2×D4×C67C2414yes—
271C2×D4×C67C2418yes—
272C2×D4×C67C24112yes—
273C2×D4×C67C24112yes—
274C22×C4×C67C2411yescharacteristic
275C22×C4×C67C24124yes—
276C22×C4×C67C2413yes—
277C22×C4×C67C2413yes—
278C4⋊C4×C67C24112yes—
279C4⋊C4×C67C2414yes—
280C4⋊C4×C67C24112yes—
281C22⋊C4×C67C2418yes—
282C22⋊C4×C67C24124yes—
283C42×C67C2416yes—
284C42×C67C2416yes—
285C23×C67C2518yes—
286C23×C67C2511yescharacteristic
287C22×D67—248no—
288C22×D67—43no—
289C22×D67—43no—
290C22×D67—424no—
291C22×D67—424no—
292C22×D67C22×D4112yes—
293C22×D67C2518yes—
294C22×D67C2516yes—
295Q8×C67—224no—
296Q8×C67C22×D4116yes—
297D4×C67—216no—
298D4×C67—224no—
299D4×C67—28no—
300D4×C67—412no—
301C2×C4×C67—248no—
302C2×C4×C67—22no—
303C2×C4×C67—43no—
304C2×C4×C67C22×D4112yes—
305C2×C4×C67C2511yescharacteristic
306C2×C4×C67C2516yes—
307C2×C4×C67C2518yes—
308C2×C4×C67C2516yes—
309C2×C4×C67C2511yescharacteristic
310C22⋊D67—216no—
311C22⋊D67—248no—
312C22⋊D67—216no—
313C22⋊D67—216no—
314C22⋊D67—424no—
315C2×Dic67—216no—
316C2×Dic67—22no—
317C2×Dic67—43no—
318C2×Dic67C22×D414yes—
319C2×Dic67C2511yescharacteristic
320C2×Dic67C2516yes—
321C2×Dic67C2518yes—
322C2×Dic67C2511yescharacteristic
323C2×Dic67C2511yescharacteristic
324C2×Dic67C2511yescharacteristic
325D268—248no—
326D268—224no—
327D268—28no—
328D268—412no—
329D268C22×D4148yes—
330C4×D67—248no—
331C4×D67—248no—
332C4×D67—212no—
333C4×D67—216no—
334C4×D67—212no—
335C4×D67—46no—
336C4×D67—46no—
337C4×D67C22×D4124yes—
338C4×D67C22×D4124yes—
339Dic134—224no—
340Dic134—216no—
341C22×C67—21no—
342C22×C67—21no—
343C22×C67—28no—
344C22×C67—28no—
345C22×C67—28no—
346C22×C67C23×D412yes—
347C22×C67C2611yescharacteristic
348C2×D67—26no—
349C2×D67—26no—
350C2×D67—28no—
351C2×D67—28no—
352C2×D67—28no—
353C2×D67—412no—
354C2×D67—848no—
355C2×D67C23×D4112yes—
356C4×C67—28no—
357C4×C67—26no—
358C4×C67—21no—
359C4×C67C23×D4112yes—
360C4×C67#58512yescomplemented
361Dic67—28no—
362Dic67—26no—
363Dic67—21no—
364Dic67C23×D412yes—
365Dic67C23×D412yes—
366Dic67#58512yescomplemented
367#62812—671nomaximal, Sylow
368C2×C67—22no—
369C2×C67—48no—
370C2×C67C24×D411yescharacteristic
371C2×C67C2×#58511yescharacteristic
372C2×C67C2×#58511yescharacteristic
373D67—212no—
374D67—48no—
375C2×#585—672no—
376#3500—678no—
377#3499—674no—
378#3498—674no—
379#3497—672no—
380#3497—671no—
381#3497D6711yescharacteristic, complemented
382#3496—676no—
383#3496—676no—
384D4×#41—674no—
385D4×#41—674no—
386D4×#41—678no—
387#3449—676no—
388C2×#532—676no—
389C2×C4×#41—671no—
390C67#6281211yescharacteristic, complemented, Sylow
391#585—13432no—
392C2×2−1+4—672no—
393C2×2−1+4—678no—
394C2×2−1+4C2×D6712yescomplemented
395C2×H(5,𝔽2)—6712no—
396C2×H(5,𝔽2)—678no—
397C22×#41—6712no—
398C22×#41—678no—
399C22×#41—671no—
400C22×#41—678no—
401#550—678no—
402#550—674no—
403#550C2×D6714yescomplemented
404D4×Q8—678no—
405D4×Q8—674no—
406D4×Q8C2×D6714yescomplemented
407#548—678no—
408#548—678no—
409#548—678no—
410#548C2×D6718yescomplemented
411#547—6712no—
412#547—6724no—
413#547—6712no—
414#546—6724no—
415#546—6724no—
416#546—6724no—
417#546—6724no—
418D42—6712no—
419D42—6724no—
420D42—6712no—
421#537—6712no—
422#537—676no—
423#537C2×D6716yescomplemented
424#536—6724no—
425#535—6724no—
426#534—6724no—
427#532—6712no—
428#532—676no—
429#532—676no—
430#532—6712no—
431#532—674no—
432#532—6712no—
433#532—6712no—
434#532—6712no—
435#532—676no—
436#532C2×D6716yescomplemented
437C2×C4⋊Q8—676no—
438C2×#127—676no—
439C2×#124—6712no—
440#525—6724no—
441#525—6724no—
442C2×#121—6712no—
443C2×#121—6712no—
444C4×#41—674no—
445C4×#41—674no—
446C4×#41—674no—
447C4×#41—674no—
448C2×C4×Q8—671no—
449C2×C4×Q8C2×D6711yescharacteristic, complemented
450C2×C4×D4—6712no—
451C2×C4×D4—6712no—
452C2×C4×D4—673no—
453C2×C4×D4—673no—
454C2×#117—673no—
455C22×C42—673no—
4562−1+4—216no—
4572−1+4—13464no—
4582−1+4—13416no—
459H(5,𝔽2)—13496no—
460H(5,𝔽2)—13464no—
461C2×#41—6716no—
462C2×#41—674no—
463C2×#41—674no—
464C2×#41—6712no—
465C2×#41—6724no—
466C2×#41—678no—
467C2×#41—6712no—
468C2×#41—678no—
469C2×#41—6724no—
470C2×#41—6712no—
471C2×#41—6724no—
472C2×#41—13496no—
473C2×#41—13464no—
474C2×#41—13464no—
475C2×#41C22×D67112yes—
476C2×#41C22×D6718yes—
477C22×Q8—6712no—
478C22×Q8—678no—
479C22×Q8C22×D6718yes—
480C22×Q8C22×D6711yescharacteristic
481C22×D4—6712no—
482C22×D4—6712no—
483C22×D4—6724no—
484C22×D4—6712no—
485C22×D4—6724no—
486C22×D4—673no—
487C22×D4—6724no—
488C23×C4—673no—
489C23×C4—673no—
490C23×C4—673no—
491C23×C4—6724no—
492C4⋊Q8—6712no—
493C4⋊Q8—674no—
494C4⋊Q8—6712no—
495C4⋊Q8—676no—
496C4⋊Q8C22×D6716yes—
497#127—674no—
498#127—6712no—
499#127—6712no—
500#127—676no—
501#127C22×D6716yes—
502#124—6712no—
503#124—6712no—
504#124—678no—
505#124—6724no—
506#124—6712no—
507#124C22×D67112yes—
508#123—6748no—
509#123—6748no—
510C22⋊Q8—6724no—
511C22⋊Q8—6724no—
512C22⋊Q8—6724no—
513C22⋊Q8C22×D67124yes—
514#121—678no—
515#121—6724no—
516#121—6712no—
517#121—6712no—
518#121—6724no—
519#121—674no—
520#121—6712no—
521#121—6724no—
522#121—6712no—
523#121—6712no—
524#121—6724no—
525#121—6724no—
526#121—6724no—
527#121C22×D6714yes—
528#121C22×D67112yes—
529#121C22×D67124yes—
530#120—6748no—
531#120—6748no—
532C4×Q8—674no—
533C4×Q8—674no—
534C4×Q8C22×D6714yes—
535C4×Q8C22×D6714yes—
536C4×D4—674no—
537C4×D4—6712no—
538C4×D4—6724no—
539C4×D4—6724no—
540C4×D4—674no—
541C4×D4—6712no—
542C4×D4—6712no—
543C4×D4—6712no—
544C4×D4—678no—
545C4×D4—6724no—
546C4×D4—6712no—
547C4×D4—6712no—
548C4×D4—6712no—
549C4×D4—6712no—
550C4×D4C22×D67112yes—
551C4×D4C22×D67112yes—
552#117—6712no—
553#117—6712no—
554C2×C4⋊C4—673no—
555C2×C4⋊C4—6712no—
556C2×C4⋊C4—6712no—
557C2×C4⋊C4C22×D6713yes—
558C2×C22⋊C4—676no—
559C2×C22⋊C4—6724no—
560C2×C22⋊C4—6724no—
561C2×C42—673no—
562C2×C42—673no—
563C2×C42—671no—
564C2×C42—676no—
565C2×C42—676no—
566C2×C42—676no—
567C2×C42—676no—
568C2×C42C22×D6713yes—
569C24—673no—
570C24—6724no—
571#41—232no—
572#41—248no—
573#41—6732no—
574#41—6732no—
575#41—13496no—
576#41—13496no—
577#41—13432no—
578#41—13448no—
579#41—13448no—
580#41—13496no—
581#41—13432no—
582#41—13448no—
583C2×Q8—232no—
584C2×Q8—6712no—
585C2×Q8—678no—
586C2×Q8—13448no—
587C2×Q8—13432no—
588C2×Q8D4×D6718yescomplemented
589C2×Q8C23×D67112yes—
590C2×Q8C23×D6714yes—
591C2×D4—26824no—
592C2×D4—26824no—
593C2×D4—6724no—
594C2×D4—678no—
595C2×D4—6724no—
596C2×D4—678no—
597C2×D4—678no—
598C2×D4—6724no—
599C2×D4—6712no—
600C2×D4—6712no—
601C2×D4—674no—
602C2×D4—6724no—
603C2×D4—6712no—
604C2×D4—13496no—
605C2×D4—13448no—
606C2×D4—13496no—
607C2×D4—13496no—
608C2×D4C23×D6714yes—
609C2×D4C23×D6718yes—
610C2×D4C23×D67112yes—
611C2×D4C23×D67112yes—
612C22×C4—2686no—
613C22×C4—2686no—
614C22×C4—673no—
615C22×C4—676no—
616C22×C4—676no—
617C22×C4—671no—
618C22×C4—6724no—
619C22×C4—676no—
620C22×C4—676no—
621C22×C4—671no—
622C22×C4—678no—
623C22×C4—676no—
624C22×C4—676no—
625C22×C4—6724no—
626C22×C4—678no—
627C22×C4—6724no—
628C22×C4—13496no—
629C22×C4C23×D6711yescharacteristic
630C22×C4C23×D67124yes—
631C22×C4C23×D6713yes—
632C22×C4C23×D6713yes—
633C4⋊C4—678no—
634C4⋊C4—674no—
635C4⋊C4—6712no—
636C4⋊C4—6724no—
637C4⋊C4—6712no—
638C4⋊C4C23×D6714yes—
639C4⋊C4C23×D67112yes—
640C4⋊C4C23×D67112yes—
641C22⋊C4—678no—
642C22⋊C4—6724no—
643C22⋊C4—678no—
644C22⋊C4—678no—
645C22⋊C4—6724no—
646C22⋊C4—6724no—
647C22⋊C4—6724no—
648C22⋊C4C23×D6718yes—
649C22⋊C4C23×D67124yes—
650C42—671no—
651C42—671no—
652C42—671no—
653C42—671no—
654C42—676no—
655C42—676no—
656C42—676no—
657C42—676no—
658C42C23×D6716yes—
659C42C23×D6716yes—
660C23—2683no—
661C23—2683no—
662C23—26824no—
663C23—26824no—
664C23—6712no—
665C23—676no—
666C23—678no—
667C23—13448no—
668C23C24×D6718yes—
669C23C24×D6711yescharacteristic
670Q8—224no—
671Q8—13416no—
672Q8—13424no—
673Q8C2×D4×D67116yes—
674D4—216no—
675D4—224no—
676D4—28no—
677D4—412no—
678D4—26812no—
679D4—26824no—
680D4—6748no—
681D4—13448no—
682D4—13416no—
683D4—13416no—
684D4—13448no—
685D4—13416no—
686D4—13424no—
687D4—1348no—
688C2×C4—248no—
689C2×C4—22no—
690C2×C4—43no—
691C2×C4—2686no—
692C2×C4—2686no—
693C2×C4—2683no—
694C2×C4—674no—
695C2×C4—671no—
696C2×C4—671no—
697C2×C4—671no—
698C2×C4—6724no—
699C2×C4—6724no—
700C2×C4—671no—
701C2×C4—676no—
702C2×C4—678no—
703C2×C4—13412no—
704C2×C4—13416no—
705C2×C4—13448no—
706C2×C4—1342no—
707C2×C4—13416no—
708C2×C4—13448no—
709C2×C4—13412no—
710C2×C4C2×D4×D67112yes—
711C2×C4C24×D6711yescharacteristic
712C2×C4C24×D6716yes—
713C2×C4C24×D6718yes—
714C2×C4C24×D6716yes—
715C2×C4C24×D6711yescharacteristic
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—26812no—
722C22—53648no—
723C22—6712no—
724C22—1348no—
725C22—1348no—
726C22—1348no—
727C22—1346no—
728C22—1346no—
729C22C22×D4×D6712yes—
730C22C25×D6711yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—672no—
735C4—672no—
736C4—672no—
737C4—1348no—
738C4—1341no—
739C4—1346no—
740C4C22×D4×D67112yes—
741C4#1686423312yescomplemented
742C2—22no—
743C2—48no—
744C2—2688no—
745C2—13412no—
746C2C23×D4×D6711yescharacteristic
747C2#585×D6711yescharacteristic
748C2C2×#1686423311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D67
commutator, socle, cosocleC22×C67C26
FittingC67×#3497C2
hypercenter#3497D67
hypocenterC67#62812
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#16864233C2semidirect
2. #22574000C2semidirect
3. #22573993C2semidirect
4. #22573986C2semidirect
5. #22573980C2semidirect
6. #22573976C2semidirect
7. #22573972C2semidirect
8. #22573971C2semidirect
9. D4×#11761629C2semidirect
10. #22573699C2semidirect
11. #22573698C2semidirect
12. #22573537C2semidirect
13. #532×D67C2semidirect
14. C2×C4×#11761629C2semidirect
15. C67×#3497C2semidirect
17. C2×#14524091C22semidirect
18. C2×#14524091C22semidirect
19. C2×#14524089C22semidirect
20. C2×#14524089C22semidirect
22. C22×#11761629C22semidirect
23. C2×#41×D67C22semidirect
24. C2×#41×D67C22semidirect
25. #16864068C22semidirect
26. #16864065C22semidirect
27. Q8×D268C22semidirect
28. Q8×C22⋊D67C22semidirect
29. #16864058C22semidirect
30. #16864057C22semidirect
31. #16864053C22semidirect
32. #16864051C22semidirect
33. #16864049C22semidirect
34. #16864048C22semidirect
35. #16864043C22semidirect
36. #16864042C22semidirect
37. #16864039C22semidirect
38. #16864037C22semidirect
39. D4×D268C22semidirect
40. #16864031C22semidirect
41. #16864030C22semidirect
42. #16863977C22semidirect
43. #16863974C22semidirect
44. #16863969C22semidirect
45. #16863962C22semidirect
46. #16863954C22semidirect
47. #16863947C22semidirect
48. #16863946C22semidirect
49. #16863945C22semidirect
50. #16863944C22semidirect
51. #16863943C22semidirect
52. #16863943C22semidirect
53. #16863942C22semidirect
54. #16863941C22semidirect
55. #16863941C22semidirect
56. C4⋊Q8×D67C22semidirect
57. #127×D67C22semidirect
58. #124×D67C22semidirect
59. #16863909C22semidirect
60. #16863906C22semidirect
61. #121×D67C22semidirect
62. #121×D67C22semidirect
63. C4×#11761629C22semidirect
64. C4×#11761629C22semidirect
65. C4×#11761629C22semidirect
66. C4×#11761629C22semidirect
67. C2×Q8×Dic67C22semidirect
68. C2×C4×D268C22semidirect
69. C2×#14524005C22semidirect
70. C4×D4×D67C22semidirect
71. C4×D4×D67C22semidirect
72. C2×#14524001C22semidirect
73. C2×C42×D67C22semidirect
74. C2×2−1+4×C67C22semidirect
75. #550×C67C22semidirect
76. D4×Q8×C67C22semidirect
77. #548×C67C22semidirect
78. #537×C67C22semidirect
79. #532×C67C22semidirect
80. C2×C4×Q8×C67C22semidirect
86. C2×#11761629D4semidirect
199. #11761629C2×D4semidirect
200. #11761629C2×D4semidirect
211. C2×D268C2×D4semidirect
234. C2×C4×D67C2×D4semidirect
267. C2×Q8×C67C2×D4semidirect
360. C4×C67#585semidirect
366. Dic67#585semidirect
381. #3497D67semidirect
390. C67#62812semidirect
394. C2×2−1+4C2×D67semidirect
403. #550C2×D67semidirect
406. D4×Q8C2×D67semidirect
410. #548C2×D67semidirect
423. #537C2×D67semidirect
436. #532C2×D67semidirect
449. C2×C4×Q8C2×D67semidirect
588. C2×Q8D4×D67semidirect
741. C4#16864233semidirect

Maximal subgroups

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

subgroupindex
C2×#168642332
#225740002
#225739932
#225739862
#225739802
#225739762
#225739722
#225739712
D4×#117616292
#225736992
#225736982
#225735372
#532×D672
C2×C4×#117616292
C67×#34972
#6281267