Finite Group Databasebeta

← #31764377

Subgroups — #31764377

Order 17152.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864233C212yesmaximal, complemented
2#22574003C212yesmaximal, complemented
3#22573998C216yesmaximal, complemented
4#22573992C213yesmaximal, complemented
5#22573987C211yesmaximal, characteristic, complemented
6#22573982C213yesmaximal, complemented
7#22573979C214yesmaximal, complemented
8#22573967C2112yesmaximal, complemented
9D4×#11761629C214yesmaximal, complemented
10#22573696C2112yesmaximal, complemented
11#22573541C216yesmaximal, complemented
12C2×#16863947C213yesmaximal, complemented
13#532×D67C213yesmaximal, complemented
14C4×#41×D67C211yesmaximal, characteristic, complemented
15C67×#3499C211yesmaximal, characteristic, complemented
16#16864233—232no—
17C2×#14524091C2214yescomplemented
18C2×#14524091C2216yescomplemented
19C2×#14524089C22112yescomplemented
20C2×#14524089C2216yescomplemented
21C2×#14524089C2212yescomplemented
22C22×#11761629C2214yescomplemented
23C22×#11761629C2216yescomplemented
24C2×#41×D67C2211yescharacteristic
25C2×#41×D67C22112yescomplemented
26C2×#41×D67C2216yescomplemented
27#16864068C2214yescomplemented
28#16864067C22112yescomplemented
29#16864061C22112yescomplemented
30#16864057C2218yescomplemented
31#16864056C22124yescomplemented
32#16864049C22112yescomplemented
33#16864047C22124yescomplemented
34#16864038C22148yescomplemented
35#16864037C22124yescomplemented
36#16864034C22124yescomplemented
37D4×D268C22112yescomplemented
38D4×D268C22112yescomplemented
39#16864030C22124yescomplemented
40#16863976C22124yescomplemented
41#16863971C22112yescomplemented
42#16863970C2216yescomplemented
43#16863965C2216yescomplemented
44#16863964C22112yescomplemented
45#16863960C2216yescomplemented
46#16863957C22124yescomplemented
47#16863947C22112yescomplemented
48#16863947C22112yescomplemented
49#16863947C2216yescomplemented
50#16863947C2213yescomplemented
51#16863947C2216yescomplemented
52#16863947C2216yescomplemented
53#16863946C2213yescomplemented
54#16863945C2216yescomplemented
55#16863944C2211yescharacteristic, complemented
56#16863943C22112yescomplemented
57#16863942C2216yescomplemented
58#16863941C22112yescomplemented
59C4⋊Q8×D67C2213yescomplemented
60C2×#14524040C2213yescomplemented
61#127×D67C2213yescomplemented
62C2×#14524032C2216yescomplemented
63#124×D67C2216yescomplemented
64#16863909C22124yescomplemented
65#16863904C22124yescomplemented
66C2×#14524018C22112yescomplemented
67#121×D67C22112yescomplemented
68#41×Dic67C2211yescharacteristic, complemented
69C4×#11761629C2212yescomplemented
70C4×#11761628C2213yescomplemented
71#16863864C2213yescomplemented
72C4×#11761627C2216yescomplemented
73C4×Q8×D67C2212yescomplemented
74C2×#14524005C22112yescomplemented
75C4×D4×D67C2216yescomplemented
76C4×D4×D67C22112yescomplemented
77#117×D67C2213yescomplemented
78C2×C42×D67C2213yescomplemented
79C2×2−1+4×C67C2212yescomplemented
80D4×Q8×C67C2214yescomplemented
81#547×C67C22112yescomplemented
82#536×C67C2216yescomplemented
83#532×C67C2213yescomplemented
84C2×C4⋊Q8×C67C2213yescomplemented
85C4×#41×C67C2211yescharacteristic, complemented
86#14524091—248no—
87#14524091—232no—
88#14524089—248no—
89#14524089—296no—
90#14524089—216no—
91C2×#11761629—232no—
92C2×#11761629—248no—
93C2×#11761629C23112yes—
94C2×#11761629C2314yes—
95C2×#11761629C23112yes—
96C2×#11761629C2316yes—
97C2×#11761629C23112yes—
98C2×#11761629C23112yes—
99C2×#11761629C2311yescharacteristic
100C2×#11761628C23124yes—
101C2×#11761628C23112yes—
102C2×#11761628C2316yes—
103C2×#11761628C23112yes—
104C2×#11761628C2313yes—
105C2×#11761627C23112yes—
106C2×#11761627C2312yes—
107C2×#11761627C2313yes—
108#41×D67—296no—
109#41×D67—248no—
110#41×D67D4116yescomplemented
111C2×Q8×D67C23112yes—
112C2×Q8×D67C2316yes—
113C2×Q8×D67C2311yescharacteristic
114C22×D268C23112yes—
115C22×D268C23112yes—
116C22×D268C2316yes—
117C22×D268C23112yes—
118C2×D4×D67C23124yes—
119C2×D4×D67C23112yes—
120C2×D4×D67C23112yes—
121C2×D4×D67C2316yes—
122C2×D4×D67C23112yes—
123C2×D4×D67C2313yes—
124C22×C4×D67C23112yes—
125C22×C4×D67C23112yes—
126C22×C4×D67C2316yes—
127C22×C4×D67C2313yes—
128#14524043C2311yescharacteristic
129#14524042C23112yes—
130#14524041C2316yes—
131#14524040C23112yes—
132#14524040C2313yes—
133#14524040C2316yes—
134#14524039C23112yes—
135#14524039C2316yes—
136#14524032C23124yes—
137#14524032C2316yes—
138#14524032C23112yes—
139#14524031C2316yes—
140#14524030C2312yes—
141#14524029C23124yes—
142#14524028C23148yes—
143#14524026C23124yes—
144#14524021C23148yes—
145#14524019C23124yes—
146#14524018C23124yes—
147#14524018C23124yes—
148#14524018C23124yes—
149#14524018C23112yes—
150#14524018C23124yes—
151#14524017C23112yes—
152#14524017C23124yes—
153#14524016C23148yes—
154#14524016C23124yes—
155#14524015C23124yes—
156#14524014C2314yes—
157#14524013C23148yes—
158#14524013C23124yes—
159#14524011C23124yes—
160Q8×Dic67C2312yes—
161C4×Dic134C2316yes—
162#14524008C2316yes—
163C4×D268C2316yes—
164C4×D268C23112yes—
165D4×Dic67C2316yes—
166D4×Dic67C2314yes—
167#14524005C23124yes—
168#14524005C2316yes—
169#14524005C23124yes—
170#14524005C23112yes—
171#14524005C23124yes—
172C4×C22⋊D67C23112yes—
173C4×C22⋊D67C23124yes—
174(C22⋊D67)⋊C4C23112yes—
175(C22⋊D67)⋊C4C23124yes—
176#14524002C2313yes—
177#14524001C2316yes—
178#14524000C2316yes—
179#14523999C2316yes—
180C4⋊C4×D67C23112yes—
181C4⋊C4×D67C2316yes—
182C2×(C2×D67)⋊C4C23124yes—
183C22⋊C4×D67C23124yes—
184C22⋊C4×D67C2316yes—
185C2×C4×Dic67C2316yes—
186C2×C4×Dic67C2313yes—
187C42×D67C2311yescharacteristic
188C42×D67C2313yes—
189C42×D67C2316yes—
190C42×D67C2316yes—
191C42×D67C2313yes—
192C42×D67C2313yes—
1932−1+4×C67—216no—
194C2×#41×C67C23112yes—
195C2×#41×C67C2316yes—
196C2×#41×C67C2311yescharacteristic
197C22×Q8×C67C2314yes—
198C22×Q8×C67C2316yes—
199C4⋊Q8×C67C23112yes—
200C4⋊Q8×C67C2313yes—
201C4⋊Q8×C67C2316yes—
202#127×C67C2311yescharacteristic
203#124×C67C2316yes—
204#123×C67C23124yes—
205C22⋊Q8×C67C23124yes—
206#121×C67C23112yes—
207C4×Q8×C67C2312yes—
208C4×D4×C67C2316yes—
209C4×D4×C67C23112yes—
210#117×C67C2313yes—
211C2×C4⋊C4×C67C23112yes—
212C2×C42×C67C2313yes—
213C23×D67C24112yes—
214C23×D67C24112yes—
215C23×D67C2413yes—
216#11761629—216no—
217#11761629—248no—
218#11761629—248no—
219#11761629—224no—
220#11761629—248no—
221#11761629—248no—
222#11761629C2×D418yescomplemented
223#11761628—224no—
224#11761628—296no—
225#11761628—248no—
226#11761628—248no—
227#11761628C2×D4124yescomplemented
228#11761627—248no—
229#11761627—28no—
230#11761627C2×D4124yescomplemented
231C2×Dic134C24112yes—
232C2×Dic134C2412yes—
233C2×Dic134C2413yes—
234Q8×D67—224no—
235Q8×D67—248no—
236Q8×D67C2×D418yescomplemented
237C2×D268—248no—
238C2×D268—224no—
239C2×D268—248no—
240C2×D268—424no—
241C2×D268C24112yes—
242C2×D268C24124yes—
243C2×D268C24112yes—
244C2×D268C24112yes—
245C2×D268C2416yes—
246C2×D268C24124yes—
247C2×D268C2413yes—
248C2×C22⋊D67C24112yes—
249C2×C22⋊D67C2414yes—
250C2×C22⋊D67C24112yes—
251C2×C22⋊D67C24124yes—
252C2×C22⋊D67C2416yes—
253D4×D67—248no—
254D4×D67—248no—
255D4×D67—296no—
256D4×D67—224no—
257D4×D67—424no—
258D4×D67C2×D4124yescomplemented
259C22×Dic67C2414yes—
260C22×Dic67C2416yes—
261C22×Dic67C2413yes—
262C2×C4×D67—248no—
263C2×C4×D67—248no—
264C2×C4×D67—412no—
265C2×C4×D67C2×D4124yescomplemented
266C2×C4×D67C2412yes—
267C2×C4×D67C2416yes—
268C2×C4×D67C24112yes—
269C2×C4×D67C24112yes—
270C2×C4×D67C24112yes—
271C2×C4×D67C24124yes—
272C2×C4×D67C2416yes—
273C2×C4×D67C2416yes—
274C2×C4×D67C2411yescharacteristic
275C2×C4×D67C2413yes—
276C2×C4×D67C2413yes—
277C2×C4×D67C2413yes—
278C4⋊Dic67C2414yes—
279C4⋊Dic67C2416yes—
280Dic67⋊C4C24112yes—
281Dic67⋊C4C24124yes—
282C22⋊Dic67C2418yes—
283C22⋊Dic67C2416yes—
284(C2×D67)⋊C4C24124yes—
285(C2×D67)⋊C4C24112yes—
286(C2×D67)⋊C4C24124yes—
287(C2×D67)⋊C4C24148yes—
288C4×Dic67C2412yes—
289C4×Dic67C2411yescharacteristic
290C4×Dic67C2416yes—
291C4×Dic67C2413yes—
292C4×Dic67C2416yes—
293C4×Dic67C2416yes—
294C4×Dic67C2416yes—
295#41×C67—248no—
296#41×C67—224no—
297#41×C67C2×D418yescomplemented
298C2×Q8×C67—216no—
299C2×Q8×C67—224no—
300C2×Q8×C67C24112yes—
301C2×Q8×C67C2416yes—
302C2×Q8×C67C2411yescharacteristic
303C2×D4×C67C2414yes—
304C2×D4×C67C24112yes—
305C2×D4×C67C2412yes—
306C2×D4×C67C2413yes—
307C22×C4×C67C2416yes—
308C22×C4×C67C24112yes—
309C22×C4×C67C24112yes—
310C22×C4×C67C2413yes—
311C4⋊C4×C67C24112yes—
312C4⋊C4×C67C24124yes—
313C4⋊C4×C67C2416yes—
314C22⋊C4×C67C2416yes—
315C22⋊C4×C67C24124yes—
316C42×C67C2411yescharacteristic
317C42×C67C2413yes—
318C42×C67C2416yes—
319C23×C67C2514yes—
320C23×C67C2513yes—
321C22×D67—224no—
322C22×D67—224no—
323C22×D67—46no—
324C22×D67—424no—
325C22×D67—424no—
326C22×D67C22×D4112yes—
327C22×D67C25112yes—
328C22×D67C2513yes—
329C22×D67C2511yescharacteristic
330Q8×C67—212no—
331Q8×C67—224no—
332Q8×C67C22×D414yes—
333D4×C67—224no—
334D4×C67—24no—
335D4×C67—28no—
336D4×C67C22×D4112yes—
337C2×C4×C67—224no—
338C2×C4×C67—224no—
339C2×C4×C67—212no—
340C2×C4×C67C22×D4112yes—
341C2×C4×C67C2516yes—
342C2×C4×C67C25112yes—
343C2×C4×C67C2511yescharacteristic
344C2×C4×C67C2513yes—
345C2×C4×C67C2512yes—
346C22⋊D67—224no—
347C22⋊D67—28no—
348C22⋊D67—224no—
349C22⋊D67—424no—
350C22⋊D67C22×D4124yes—
351C2×Dic67—28no—
352C2×Dic67—46no—
353C2×Dic67C22×D4112yes—
354C2×Dic67C2512yes—
355C2×Dic67C2516yes—
356C2×Dic67C2514yes—
357C2×Dic67C2511yescharacteristic
358C2×Dic67C2513yes—
359D268—248no—
360D268—224no—
361D268—212no—
362D268—224no—
363D268—224no—
364D268—424no—
365D268C22×D4112yes—
366C4×D67—224no—
367C4×D67—224no—
368C4×D67—24no—
369C4×D67—212no—
370C4×D67—224no—
371C4×D67—248no—
372C4×D67—46no—
373C4×D67—46no—
374C4×D67C22×D4112yes—
375C4×D67C22×D414yes—
376C4×D67C22×D4112yes—
377C4×D67C22×D4112yes—
378Dic134—24no—
379Dic134—224no—
380Dic134C22×D4112yes—
381C22×C67—26no—
382C22×C67—24no—
383C22×C67—28no—
384C22×C67C23×D416yes—
385C22×C67C2611yescharacteristic
386C2×D67—22no—
387C2×D67—26no—
388C2×D67—212no—
389C2×D67—224no—
390C2×D67—412no—
391C2×D67—824no—
392C2×D67—824no—
393C2×D67C23×D416yes—
394C2×D67C23×D412yes—
395C4×C67—212no—
396C4×C67—26no—
397C4×C67C23×D412yes—
398C4×C67C23×D416yes—
399C4×C67#58514yescomplemented
400Dic67—24no—
401Dic67—22no—
402Dic67—26no—
403Dic67C23×D416yes—
404Dic67C23×D412yes—
405#62812—671nomaximal, Sylow
406C2×C67—26no—
407C2×C67—44no—
408C2×C67C24×D411yescharacteristic
409C2×C67C2×#58512yes—
410D67—22no—
411D67—26no—
412D67—412no—
413C2×#585—672no—
414#3500—672no—
415#3500—676no—
416#3499—673no—
417#3499D6711yescharacteristic, complemented
418#3498—673no—
419#3498—671no—
420#3497—674no—
421#3496—6712no—
422D4×#41—674no—
423D4×#41—6712no—
424#3449—676no—
425C2×#532—673no—
426C2×#532—673no—
427C2×C4×#41—671no—
428C67#6281211yescharacteristic, complemented, Sylow
429#585—13432no—
430C2×2−1+4—674no—
431C2×2−1+4—676no—
432C2×2−1+4C2×D6712yescomplemented
433C2×H(5,𝔽2)—6712no—
434C2×H(5,𝔽2)—676no—
435C2×H(5,𝔽2)—672no—
436C22×#41—671no—
437C22×#41—676no—
438C22×#41—6712no—
439C22×#41—676no—
440C22×#41—674no—
441#550—674no—
442#550—6712no—
443D4×Q8—6712no—
444D4×Q8C2×D6714yescomplemented
445#548—678no—
446#548—6724no—
447#547—6712no—
448#547—6724no—
449#547C2×D67112yescomplemented
450#546—6724no—
451#546—6748no—
452#546—6724no—
453D42—6724no—
454D42—6712no—
455D42—6712no—
456#537—6724no—
457#536—676no—
458#536—6712no—
459#536C2×D6716yescomplemented
460#535—676no—
461#535—6712no—
462#535—676no—
463#534—6724no—
464#532—676no—
465#532—673no—
466#532—676no—
467#532—6712no—
468#532—6712no—
469#532—676no—
470#532—676no—
471#532—671no—
472#532—676no—
473#532—6712no—
474#532—6712no—
475#532—673no—
476#532C2×D6713yescomplemented
477C2×C4⋊Q8—673no—
478C2×C4⋊Q8C2×D6713yescomplemented
479C2×#127—673no—
480C2×#127—673no—
481C2×#124—676no—
482C2×#124—676no—
483#525—6724no—
484#525—6724no—
485C2×#121—6712no—
486C2×#121—6712no—
487C4×#41—671no—
488C4×#41—672no—
489C4×#41—676no—
490C4×#41—673no—
491C4×#41—673no—
492C4×#41C2×D6711yescharacteristic, complemented
493C2×C4×Q8—672no—
494C2×C4×D4—676no—
495C2×C4×D4—6712no—
496C2×C4×D4—6712no—
497C2×#117—673no—
498C22×C42—673no—
4992−1+4—216no—
5002−1+4—13432no—
5012−1+4—13448no—
502H(5,𝔽2)—13496no—
503H(5,𝔽2)—13448no—
504H(5,𝔽2)—13416no—
505C2×#41—6716no—
506C2×#41—671no—
507C2×#41—6712no—
508C2×#41—676no—
509C2×#41—6712no—
510C2×#41—6712no—
511C2×#41—6712no—
512C2×#41—674no—
513C2×#41—673no—
514C2×#41—6712no—
515C2×#41—672no—
516C2×#41—673no—
517C2×#41—676no—
518C2×#41—6712no—
519C2×#41—6724no—
520C2×#41—6712no—
521C2×#41—13448no—
522C2×#41—13448no—
523C2×#41—13432no—
524C2×#41—13496no—
525C2×#41C22×D6716yes—
526C2×#41C22×D67112yes—
527C2×#41C22×D6711yescharacteristic
528C22×Q8—671no—
529C22×Q8—676no—
530C22×Q8—6712no—
531C22×Q8C22×D6716yes—
532C22×Q8C22×D6714yes—
533C22×D4—6712no—
534C22×D4—673no—
535C22×D4—6712no—
536C22×D4—676no—
537C22×D4—6724no—
538C22×D4—6712no—
539C22×D4—6712no—
540C22×D4—6712no—
541C22×D4—676no—
542C22×D4—6712no—
543C23×C4—676no—
544C23×C4—673no—
545C23×C4—6712no—
546C23×C4—6712no—
547C4⋊Q8—676no—
548C4⋊Q8—6712no—
549C4⋊Q8—671no—
550C4⋊Q8C22×D6713yes—
551C4⋊Q8C22×D6716yes—
552C4⋊Q8C22×D67112yes—
553#127—676no—
554#127—6712no—
555#127—673no—
556#127—676no—
557#127—6712no—
558#127C22×D6711yescharacteristic
559#124—676no—
560#124—6712no—
561#124—6724no—
562#124—672no—
563#124—6724no—
564#124—676no—
565#124C22×D6716yes—
566#123—6724no—
567#123—6748no—
568#123C22×D67124yes—
569C22⋊Q8—6724no—
570C22⋊Q8—6748no—
571C22⋊Q8C22×D67124yes—
572#121—674no—
573#121—6724no—
574#121—6712no—
575#121—6724no—
576#121—6712no—
577#121—6724no—
578#121—6724no—
579#121—6724no—
580#121—6724no—
581#121—6724no—
582#121—6748no—
583#121C22×D67112yes—
584#120—6724no—
585#120—6748no—
586#120—6724no—
587C4×Q8—672no—
588C4×Q8—676no—
589C4×Q8—676no—
590C4×Q8C22×D6712yes—
591C4×D4—674no—
592C4×D4—676no—
593C4×D4—6712no—
594C4×D4—6724no—
595C4×D4—6712no—
596C4×D4—676no—
597C4×D4—6724no—
598C4×D4—6724no—
599C4×D4—6724no—
600C4×D4—6712no—
601C4×D4—6724no—
602C4×D4—676no—
603C4×D4—6712no—
604C4×D4C22×D6716yes—
605C4×D4C22×D67112yes—
606#117—673no—
607#117—676no—
608#117—676no—
609#117—676no—
610#117C22×D6713yes—
611C2×C4⋊C4—676no—
612C2×C4⋊C4—6712no—
613C2×C4⋊C4C22×D67112yes—
614C2×C22⋊C4—6724no—
615C2×C22⋊C4—676no—
616C2×C22⋊C4—6724no—
617C2×C42—676no—
618C2×C42—673no—
619C2×C42—673no—
620C2×C42—676no—
621C2×C42—676no—
622C2×C42—673no—
623C2×C42—673no—
624C2×C42—671no—
625C2×C42C22×D6713yes—
626C24—673no—
627C24—6712no—
628C24—6712no—
629#41—248no—
630#41—224no—
631#41—678no—
632#41—6724no—
633#41—6724no—
634#41—13448no—
635#41—13496no—
636#41—13448no—
637#41—13448no—
638#41—1348no—
639#41—13424no—
640#41—13448no—
641#41—13448no—
642#41—13448no—
643#41—13448no—
644#41—13416no—
645#41—13424no—
646#41D4×D6718yescomplemented
647C2×Q8—216no—
648C2×Q8—224no—
649C2×Q8—678no—
650C2×Q8—673no—
651C2×Q8—6712no—
652C2×Q8—672no—
653C2×Q8—13424no—
654C2×Q8—13448no—
655C2×Q8C23×D67112yes—
656C2×Q8C23×D6716yes—
657C2×Q8C23×D6711yescharacteristic
658C2×D4—26824no—
659C2×D4—26824no—
660C2×D4—6724no—
661C2×D4—676no—
662C2×D4—6724no—
663C2×D4—6712no—
664C2×D4—674no—
665C2×D4—6712no—
666C2×D4—6724no—
667C2×D4—673no—
668C2×D4—6712no—
669C2×D4—6724no—
670C2×D4—6712no—
671C2×D4—6712no—
672C2×D4—676no—
673C2×D4—13448no—
674C2×D4—13448no—
675C2×D4—13424no—
676C2×D4—13496no—
677C2×D4—13448no—
678C2×D4—13448no—
679C2×D4—13424no—
680C2×D4C23×D6714yes—
681C2×D4C23×D67112yes—
682C2×D4C23×D6712yes—
683C2×D4C23×D6713yes—
684C22×C4—26812no—
685C22×C4—676no—
686C22×C4—676no—
687C22×C4—676no—
688C22×C4—673no—
689C22×C4—6724no—
690C22×C4—671no—
691C22×C4—673no—
692C22×C4—673no—
693C22×C4—673no—
694C22×C4—674no—
695C22×C4—672no—
696C22×C4—676no—
697C22×C4—6712no—
698C22×C4—6712no—
699C22×C4—6724no—
700C22×C4—6712no—
701C22×C4—13448no—
702C22×C4—13448no—
703C22×C4C23×D6716yes—
704C22×C4C23×D67112yes—
705C22×C4C23×D67112yes—
706C22×C4C23×D6713yes—
707C4⋊C4—674no—
708C4⋊C4—6712no—
709C4⋊C4—676no—
710C4⋊C4—6724no—
711C4⋊C4C23×D67112yes—
712C4⋊C4C23×D6716yes—
713C4⋊C4C23×D67124yes—
714C22⋊C4—678no—
715C22⋊C4—676no—
716C22⋊C4—6724no—
717C22⋊C4—6712no—
718C22⋊C4—6748no—
719C22⋊C4—6724no—
720C22⋊C4C23×D6716yes—
721C22⋊C4C23×D67124yes—
722C42—672no—
723C42—671no—
724C42—676no—
725C42—673no—
726C42—676no—
727C42—676no—
728C42—676no—
729C42C23×D6711yescharacteristic
730C42C23×D6713yes—
731C42C23×D6716yes—
732C23—2686no—
733C23—26824no—
734C23—26824no—
735C23—6712no—
736C23—673no—
737C23—671no—
738C23—6712no—
739C23—13424no—
740C23—13424no—
741C23C24×D6714yes—
742C23C24×D6713yes—
743Q8—224no—
744Q8—212no—
745Q8—6712no—
746Q8—13424no—
747Q8—1344no—
748Q8C2×D4×D6714yes—
749D4—224no—
750D4—24no—
751D4—28no—
752D4—26824no—
753D4—26824no—
754D4—6724no—
755D4—6712no—
756D4—13424no—
757D4—13448no—
758D4—13424no—
759D4—1348no—
760D4—13424no—
761D4—13424no—
762D4—13412no—
763D4—13424no—
764D4C2×D4×D67112yes—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—212no—
768C2×C4—2686no—
769C2×C4—2686no—
770C2×C4—2686no—
771C2×C4—6712no—
772C2×C4—671no—
773C2×C4—673no—
774C2×C4—674no—
775C2×C4—6712no—
776C2×C4—6712no—
777C2×C4—6712no—
778C2×C4—672no—
779C2×C4—676no—
780C2×C4—674no—
781C2×C4—13424no—
782C2×C4—13448no—
783C2×C4—13424no—
784C2×C4—1348no—
785C2×C4—13424no—
786C2×C4—1344no—
787C2×C4—13412no—
788C2×C4C2×D4×D67112yes—
789C2×C4C24×D6716yes—
790C2×C4C24×D67112yes—
791C2×C4C24×D6711yescharacteristic
792C2×C4C24×D6713yes—
793C2×C4C24×D6712yes—
794C22—26no—
795C22—24no—
796C22—28no—
797C22—26812no—
798C22—53624no—
799C22—53624no—
800C22—672no—
801C22—676no—
802C22—13412no—
803C22—13424no—
804C22—1342no—
805C22—1346no—
806C22C22×D4×D6716yes—
807C22C25×D6711yescharacteristic
808C4—212no—
809C4—26no—
810C4—672no—
811C4—676no—
812C4—1344no—
813C4—1342no—
814C4—1346no—
815C4C22×D4×D6716yes—
816C4C22×D4×D6712yes—
817C4#1686423314yescomplemented
818C2—26no—
819C2—44no—
820C2—26812no—
821C2—1342no—
822C2—1346no—
823C2C23×D4×D6711yescharacteristic
824C2C2×#1686423312yes—
subgroupG/H
center, FrattiniC22C25×D67
commutator, socle, cosocleC22×C67C26
FittingC67×#3499C2
hypercenter#3499D67
hypocenterC67#62812
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#16864233C2semidirect
2. #22574003C2semidirect
3. #22573998C2semidirect
4. #22573992C2semidirect
5. #22573987C2semidirect
6. #22573982C2semidirect
7. #22573979C2semidirect
8. #22573967C2semidirect
9. D4×#11761629C2semidirect
10. #22573696C2semidirect
11. #22573541C2semidirect
12. C2×#16863947C2semidirect
13. #532×D67C2semidirect
14. C4×#41×D67C2semidirect
15. C67×#3499C2semidirect
17. C2×#14524091C22semidirect
18. C2×#14524091C22semidirect
19. C2×#14524089C22semidirect
20. C2×#14524089C22semidirect
21. C2×#14524089C22semidirect
22. C22×#11761629C22semidirect
23. C22×#11761629C22semidirect
25. C2×#41×D67C22semidirect
26. C2×#41×D67C22semidirect
27. #16864068C22semidirect
28. #16864067C22semidirect
29. #16864061C22semidirect
30. #16864057C22semidirect
31. #16864056C22semidirect
32. #16864049C22semidirect
33. #16864047C22semidirect
34. #16864038C22semidirect
35. #16864037C22semidirect
36. #16864034C22semidirect
37. D4×D268C22semidirect
38. D4×D268C22semidirect
39. #16864030C22semidirect
40. #16863976C22semidirect
41. #16863971C22semidirect
42. #16863970C22semidirect
43. #16863965C22semidirect
44. #16863964C22semidirect
45. #16863960C22semidirect
46. #16863957C22semidirect
47. #16863947C22semidirect
48. #16863947C22semidirect
49. #16863947C22semidirect
50. #16863947C22semidirect
51. #16863947C22semidirect
52. #16863947C22semidirect
53. #16863946C22semidirect
54. #16863945C22semidirect
55. #16863944C22semidirect
56. #16863943C22semidirect
57. #16863942C22semidirect
58. #16863941C22semidirect
59. C4⋊Q8×D67C22semidirect
60. C2×#14524040C22semidirect
61. #127×D67C22semidirect
62. C2×#14524032C22semidirect
63. #124×D67C22semidirect
64. #16863909C22semidirect
65. #16863904C22semidirect
66. C2×#14524018C22semidirect
67. #121×D67C22semidirect
68. #41×Dic67C22semidirect
69. C4×#11761629C22semidirect
70. C4×#11761628C22semidirect
71. #16863864C22semidirect
72. C4×#11761627C22semidirect
73. C4×Q8×D67C22semidirect
74. C2×#14524005C22semidirect
75. C4×D4×D67C22semidirect
76. C4×D4×D67C22semidirect
77. #117×D67C22semidirect
78. C2×C42×D67C22semidirect
79. C2×2−1+4×C67C22semidirect
80. D4×Q8×C67C22semidirect
81. #547×C67C22semidirect
82. #536×C67C22semidirect
83. #532×C67C22semidirect
84. C2×C4⋊Q8×C67C22semidirect
85. C4×#41×C67C22semidirect
110. #41×D67D4semidirect
222. #11761629C2×D4semidirect
227. #11761628C2×D4semidirect
230. #11761627C2×D4semidirect
236. Q8×D67C2×D4semidirect
258. D4×D67C2×D4semidirect
265. C2×C4×D67C2×D4semidirect
297. #41×C67C2×D4semidirect
399. C4×C67#585semidirect
417. #3499D67semidirect
428. C67#62812semidirect
432. C2×2−1+4C2×D67semidirect
444. D4×Q8C2×D67semidirect
449. #547C2×D67semidirect
459. #536C2×D67semidirect
476. #532C2×D67semidirect
478. C2×C4⋊Q8C2×D67semidirect
492. C4×#41C2×D67semidirect
646. #41D4×D67semidirect
817. C4#16864233semidirect

Maximal subgroups

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

subgroupindex
C2×#168642332
#225740032
#225739982
#225739922
#225739872
#225739822
#225739792
#225739672
D4×#117616292
#225736962
#225735412
C2×#168639472
#532×D672
C4×#41×D672
C67×#34992
#6281267