Finite Group Databasebeta

← #31764225

Subgroups — #31764225

Order 17152.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574294C212yesmaximal, complemented
2#22574241C216yesmaximal, complemented
3#22574215C212yesmaximal, complemented
4#22574170C216yesmaximal, complemented
5#22574120C213yesmaximal, complemented
6#22574085C213yesmaximal, complemented
7#22574028C211yesmaximal, characteristic, complemented
8#22573987C211yesmaximal, characteristic, complemented
9#22573944C216yesmaximal, complemented
10#22573878C212yesmaximal, complemented
11#22573835C212yesmaximal, complemented
12#22573819C216yesmaximal, complemented
13#22573804C212yesmaximal, complemented
14D4×#11761628C216yesmaximal, complemented
15#22573625C216yesmaximal, complemented
16#22573505C213yesmaximal, complemented
17C2×#16863946C213yesmaximal, complemented
18C4×#14524089C212yesmaximal, complemented
19C2×C4×#41×C67C211yesmaximal, characteristic, complemented
20C2×#14524089C2212yes—
21C22×#11761628C2216yescomplemented
22#16864131C2216yescomplemented
23#16864131C2216yescomplemented
24Q8×Dic134C2212yescomplemented
25#16864125C2212yescomplemented
26#16864119C2216yescomplemented
27#16864111C2216yescomplemented
28#16864109C22112yescomplemented
29#16864106C2216yescomplemented
30#16864103C2216yescomplemented
31#16864094C22112yescomplemented
32#16864092C22112yescomplemented
33#16864090C22112yescomplemented
34#16864070C22124yescomplemented
35#16864068C2212yescomplemented
36#16864068C2212yescomplemented
37#16864067C2216yescomplemented
38#16864067C2216yescomplemented
39#16864065C2214yescomplemented
40D4×Dic134C2216yescomplemented
41#16864057C2214yescomplemented
42#16864055C22112yescomplemented
43#16864051C2216yescomplemented
44#16864047C22112yescomplemented
45#16864042C22112yescomplemented
46#16864042C22112yescomplemented
47#16864036C22124yescomplemented
48#16864034C22112yescomplemented
49D4×D268C2216yescomplemented
50D4×D268C2216yescomplemented
51D4×C22⋊D67C22112yescomplemented
52#16864024C2216yescomplemented
53#16864018C22112yescomplemented
54#16864017C22112yescomplemented
55#16864001C22112yescomplemented
56#16863997C22112yescomplemented
57#16863979C22124yescomplemented
58#16863974C2216yescomplemented
59#16863965C2216yescomplemented
60#16863960C2216yescomplemented
61#16863953C2213yescomplemented
62#16863953C2213yescomplemented
63#16863953C2211yescharacteristic, complemented
64#16863946C2213yescomplemented
65#16863946C2216yescomplemented
66#16863946C2216yescomplemented
67#16863946C2213yescomplemented
68#16863946C2216yescomplemented
69#16863946C2216yescomplemented
70#16863946C2216yescomplemented
71#16863946C2216yescomplemented
72#16863946C2216yescomplemented
73#16863946C2213yescomplemented
74#16863943C22112yescomplemented
75C2×#14524043C2213yescomplemented
76C2×#14524040C2213yescomplemented
77#16863933C22112yescomplemented
78#16863930C2216yescomplemented
79#16863930C2216yescomplemented
80#16863930C2216yescomplemented
81#16863930C2216yescomplemented
82#16863930C2216yescomplemented
83#16863930C2216yescomplemented
84C2×#14524031C2216yescomplemented
85#16863907C2216yescomplemented
86#16863907C2216yescomplemented
87#16863907C2216yescomplemented
88#16863905C22124yescomplemented
89C2×#14524017C2216yescomplemented
90C2×#14524017C2216yescomplemented
91#16863879C2212yes—
92#16863878C2214yescomplemented
93#16863876C2216yescomplemented
94#16863870C2216yescomplemented
95#16863868C22112yescomplemented
96C4×#11761629C2214yescomplemented
97C4×#11761628C2216yescomplemented
98C4×#11761628C2216yescomplemented
99C4×#11761628C2216yescomplemented
100C2×C4×D268C2216yescomplemented
101C2×C4×D268C2216yescomplemented
102C4×D4×D67C22112yescomplemented
103C22×#41×C67C2211yescharacteristic
104C4×#41×C67C2211yescharacteristic
105C4×#41×C67C2211yescharacteristic
106C4×#41×C67C2213yescomplemented
107C4×#41×C67C2211yescharacteristic, complemented
108C4×#41×C67C2213yescomplemented
109C4×#41×C67C2213yescomplemented
110C4×#41×C67C2211yescharacteristic, complemented
111C4×#41×C67C2213yescomplemented
112C2×C4×Q8×C67C2211yescharacteristic, complemented
113C2×C4×Q8×C67C2211yescharacteristic, complemented
114C2×C4×D4×C67C2213yescomplemented
115C2×C4×D4×C67C2213yescomplemented
116C2×#117×C67C2213yescomplemented
117C22×C42×C67C2213yescomplemented
118#14524089—216no—
119C2×#11761629C2314yes—
120C2×#11761628—424no—
121C2×#11761628C2316yes—
122C2×#11761628C2316yes—
123C2×#11761628C23112yes—
124C2×#11761628C2316yes—
125C2×#11761628C23112yes—
126C2×#11761628C23112yes—
127C22×Dic134C2316yes—
128C22×D268C2316yes—
129C22×D268C2316yes—
130C22×D268C2316yes—
131C22×C22⋊D67C23112yes—
132C2×D4×D67C23112yes—
133C22×C4×D67C23112yes—
134#14524043C2316yes—
135#14524043C2316yes—
136#14524043C2316yes—
137#14524043C2313yes—
138#14524043C2311yescharacteristic
139#14524043C2311yescharacteristic
140#14524042C23112yes—
141#14524040C2316yes—
142#14524040C2316yes—
143#14524040C2316yes—
144#14524040C2313yes—
145#14524039C23112yes—
146#14524038C23124yes—
147#14524037C23112yes—
148#14524037C23112yes—
149#14524035C2316yes—
150#14524035C2316yes—
151#14524035C2312yes—
152#14524034C23112yes—
153#14524032C23112yes—
154#14524031C2316yes—
155#14524031C23112yes—
156#14524031C2316yes—
157#14524031C23112yes—
158#14524031C23112yes—
159#14524031C2316yes—
160#14524029C23124yes—
161#14524028C23124yes—
162#14524028C23124yes—
163#14524026C23112yes—
164#14524026C23112yes—
165#14524026C23112yes—
166#14524025C23124yes—
167#14524022C2316yes—
168#14524022C2316yes—
169#14524022C2316yes—
170#14524022C2316yes—
171#14524022C2312yes—
172#14524022C2312yes—
173#14524021C23124yes—
174#14524020C23124yes—
175#14524019C23112yes—
176#14524018C23112yes—
177#14524018C23112yes—
178#14524017C2316yes—
179#14524017C23112yes—
180#14524017C23112yes—
181#14524017C2316yes—
182#14524017C2316yes—
183#14524017C23112yes—
184#14524017C23112yes—
185#14524017C2316yes—
186#14524017C23112yes—
187#14524017C2316yes—
188#14524017C2316yes—
189#14524017C23112yes—
190#14524016C23124yes—
191#14524016C23124yes—
192#14524015C23124yes—
193#14524014C23112yes—
194#14524013C23124yes—
195#14524012C23112yes—
196#14524011C23124yes—
197Q8×Dic67C2314yes—
198C4×Dic134C2316yes—
199C4×Dic134C2316yes—
200C4×Dic134C2316yes—
201C4×Dic134C2316yes—
202C4×Dic134C2312yes—
203C4×Dic134C2312yes—
204C4×D268C2316yes—
205C4×D268C23112yes—
206C4×D268C23112yes—
207C4×D268C2316yes—
208C4×D268C2316yes—
209C4×D268C2316yes—
210C4×D268C23112yes—
211C4×D268C23112yes—
212C4×D268C23112yes—
213C4×D268C2316yes—
214C4×D268C2316yes—
215C4×D268C23112yes—
216D4×Dic67C23112yes—
217#14524005C23112yes—
218#14524005C23112yes—
219C4×C22⋊D67C23112yes—
220C4×C22⋊D67C23112yes—
221C4×C22⋊D67C23112yes—
222C4×C22⋊D67C23112yes—
223C4×C22⋊D67C23112yes—
224C4×C22⋊D67C23112yes—
225(C22⋊D67)⋊C4C23124yes—
226#14524002C2316yes—
227#14524002C2316yes—
228#14524002C2312yes—
229#14524001C23112yes—
230#14524000C23112yes—
231#14524000C23112yes—
232#14524000C23112yes—
233C2×C4⋊Dic67C2316yes—
234C2×C4⋊Dic67C2316yes—
235C4⋊C4×D67C23112yes—
236C2×(C2×D67)⋊C4C23112yes—
237C2×(C2×D67)⋊C4C23112yes—
238C22⋊C4×D67C23124yes—
239C42×D67C23112yes—
240C2×#41×C67—28no—
241C2×#41×C67C2313yes—
242C2×#41×C67C2311yescharacteristic
243C2×#41×C67C2313yes—
244C2×#41×C67C2311yescharacteristic
245C22×Q8×C67C2311yescharacteristic
246C22×D4×C67C2313yes—
247C23×C4×C67C2313yes—
248C23×C4×C67C2313yes—
249C23×C4×C67C2313yes—
250C4×Q8×C67C2313yes—
251C4×Q8×C67C2311yescharacteristic
252C4×Q8×C67C2311yescharacteristic
253C4×Q8×C67C2311yescharacteristic
254C4×Q8×C67C2311yescharacteristic
255C4×Q8×C67C2313yes—
256C4×Q8×C67C2313yes—
257C4×Q8×C67C2313yes—
258C4×D4×C67C2313yes—
259C4×D4×C67C2313yes—
260C4×D4×C67C2316yes—
261C4×D4×C67C2316yes—
262C4×D4×C67C2313yes—
263C4×D4×C67C2313yes—
264C4×D4×C67C2313yes—
265C4×D4×C67C2313yes—
266C4×D4×C67C2316yes—
267C4×D4×C67C2313yes—
268C4×D4×C67C2316yes—
269C4×D4×C67C2313yes—
270#117×C67C2316yes—
271#117×C67C2313yes—
272#117×C67C2313yes—
273#117×C67C2316yes—
274#117×C67C2313yes—
275#117×C67C2313yes—
276C2×C4⋊C4×C67C2313yes—
277C2×C4⋊C4×C67C2313yes—
278C2×C22⋊C4×C67C2316yes—
279C2×C42×C67C2311yescharacteristic
280C2×C42×C67C2313yes—
281C2×C42×C67C2313yes—
282C2×C42×C67C2313yes—
283C2×C42×C67C2313yes—
284C2×C42×C67C2313yes—
285C2×C42×C67C2313yes—
286C2×C42×C67C2313yes—
287C2×C42×C67C2313yes—
288C2×C42×C67C2313yes—
289C2×C42×C67C2313yes—
290C2×C42×C67C2313yes—
291C23×D67C24112yes—
292#11761629—216no—
293#11761628—224no—
294#11761628—224no—
295#11761628—424no—
296#11761628—412no—
297#11761628—424no—
298#11761628—424no—
299C2×Dic134—412no—
300C2×Dic134C2412yes—
301C2×Dic134C2412yes—
302C2×Dic134C2416yes—
303C2×Dic134C24112yes—
304C2×D268—224no—
305C2×D268—412no—
306C2×D268—412no—
307C2×D268C24112yes—
308C2×D268C2416yes—
309C2×D268C2416yes—
310C2×D268C2416yes—
311C2×D268C24112yes—
312C2×D268C24112yes—
313C2×C22⋊D67—424no—
314C2×C22⋊D67C24112yes—
315C2×C22⋊D67C24112yes—
316C2×C22⋊D67C24112yes—
317C2×C22⋊D67C24124yes—
318D4×D67—248no—
319C22×Dic67C24112yes—
320C2×C4×D67—424no—
321C2×C4×D67C24112yes—
322C2×C4×D67C24112yes—
323C2×C4×D67C24112yes—
324C2×C4×D67C24124yes—
325C4⋊Dic67C24112yes—
326C4⋊Dic67C2416yes—
327C4⋊Dic67C2416yes—
328C4⋊Dic67C24112yes—
329C4⋊Dic67C2412yes—
330C4⋊Dic67C2412yes—
331C4⋊Dic67C2412yes—
332C4⋊Dic67C2412yes—
333Dic67⋊C4C24112yes—
334Dic67⋊C4C2414yes—
335Dic67⋊C4C2414yes—
336Dic67⋊C4C24112yes—
337Dic67⋊C4C24112yes—
338Dic67⋊C4C24112yes—
339C22⋊Dic67C24112yes—
340C22⋊Dic67C2414yes—
341C22⋊Dic67C24112yes—
342(C2×D67)⋊C4C24112yes—
343(C2×D67)⋊C4C24124yes—
344(C2×D67)⋊C4C24112yes—
345(C2×D67)⋊C4C24112yes—
346(C2×D67)⋊C4C24124yes—
347(C2×D67)⋊C4C24112yes—
348(C2×D67)⋊C4C24112yes—
349(C2×D67)⋊C4C24112yes—
350C4×Dic67C2414yes—
351C4×Dic67C24112yes—
352C4×Dic67C24112yes—
353C24×C67C2413yes—
354#41×C67—24no—
355#41×C67—212no—
356#41×C67—212no—
357#41×C67#4118yescomplemented
358C2×Q8×C67—24no—
359C2×Q8×C67C2413yes—
360C2×Q8×C67C2411yescharacteristic
361C2×D4×C67—212no—
362C2×D4×C67C2416yes—
363C2×D4×C67C2413yes—
364C2×D4×C67C2413yes—
365C22×C4×C67—212no—
366C22×C4×C67—212no—
367C22×C4×C67—46no—
368C22×C4×C67C2411yescharacteristic
369C22×C4×C67C2411yescharacteristic
370C22×C4×C67C2413yes—
371C22×C4×C67C2413yes—
372C22×C4×C67C2413yes—
373C22×C4×C67C2413yes—
374C22×C4×C67C2413yes—
375C22×C4×C67C2413yes—
376C22×C4×C67C2413yes—
377C22×C4×C67C2413yes—
378C22×C4×C67C2413yes—
379C22×C4×C67C2413yes—
380C22×C4×C67C2413yes—
381C22×C4×C67C2413yes—
382C22×C4×C67C2413yes—
383C22×C4×C67C2413yes—
384C22×C4×C67C2413yes—
385C22×C4×C67C2411yescharacteristic
386C4⋊C4×C67C2413yes—
387C4⋊C4×C67C2413yes—
388C4⋊C4×C67C2413yes—
389C4⋊C4×C67C2413yes—
390C4⋊C4×C67C2416yes—
391C4⋊C4×C67C2416yes—
392C22⋊C4×C67C2416yes—
393C22⋊C4×C67C2416yes—
394C22⋊C4×C67C2416yes—
395C22⋊C4×C67C2416yes—
396C42×C67C2411yescharacteristic
397C42×C67C2411yescharacteristic
398C42×C67C2411yescharacteristic
399C42×C67C2411yescharacteristic
400C42×C67C2413yes—
401C42×C67C2413yes—
402C42×C67C2413yes—
403C42×C67C2413yes—
404C42×C67C2413yes—
405C42×C67C2413yes—
406C42×C67C2413yes—
407C42×C67C2413yes—
408C42×C67C2413yes—
409C42×C67C2413yes—
410C42×C67C2413yes—
411C42×C67C2413yes—
412C23×C67—26no—
413C23×C67—26no—
414C23×C67—43no—
415C23×C67C2513yes—
416C23×C67C2513yes—
417C23×C67C2511yescharacteristic
418C22×D67—224no—
419C22×D67—412no—
420C22×D67—412no—
421C22×D67C25112yes—
422Q8×C67—26no—
423Q8×C67C2×#4114yescomplemented
424D4×C67—212no—
425D4×C67—26no—
426D4×C67C2×#41112yescomplemented
427C2×C4×C67—26no—
428C2×C4×C67—26no—
429C2×C4×C67—22no—
430C2×C4×C67—26no—
431C2×C4×C67—26no—
432C2×C4×C67—26no—
433C2×C4×C67—26no—
434C2×C4×C67—26no—
435C2×C4×C67—26no—
436C2×C4×C67—26no—
437C2×C4×C67—22no—
438C2×C4×C67—26no—
439C2×C4×C67—26no—
440C2×C4×C67—43no—
441C2×C4×C67—43no—
442C2×C4×C67—43no—
443C2×C4×C67C2×#41112yescomplemented
444C2×C4×C67H(5,𝔽2)14yescomplemented
445C2×C4×C67C2511yescharacteristic
446C2×C4×C67C2511yescharacteristic
447C2×C4×C67C2513yes—
448C2×C4×C67C2513yes—
449C2×C4×C67C2513yes—
450C2×C4×C67C2513yes—
451C2×C4×C67C2513yes—
452C2×C4×C67C2511yescharacteristic
453C2×C4×C67C2513yes—
454C2×C4×C67C2511yescharacteristic
455C2×C4×C67C2511yescharacteristic
456C2×C4×C67C2511yescharacteristic
457C22⋊D67—224no—
458C22⋊D67—224no—
459C22⋊D67—424no—
460C22⋊D67—412no—
461C2×Dic67—412no—
462C2×Dic67C2514yes—
463C2×Dic67C2514yes—
464C2×Dic67C25112yes—
465D268—224no—
466D268—212no—
467D268—212no—
468D268—212no—
469D268—412no—
470D268—412no—
471C4×D67—224no—
472C4×D67—224no—
473C4×D67—424no—
474C4×D67—412no—
475Dic134—24no—
476Dic134—212no—
477Dic134—24no—
478Dic134—412no—
479C22×C67—21no—
480C22×C67—23no—
481C22×C67—21no—
482C22×C67—23no—
483C22×C67—23no—
484C22×C67—23no—
485C22×C67—23no—
486C22×C67—412no—
487C22×C67C22×#4116yes—
488C22×C67C2×H(5,𝔽2)12yes—
489C22×C67C2611yescharacteristic
490C2×D67—212no—
491C2×D67—212no—
492C2×D67—212no—
493C2×D67—824no—
494C4×C67—21no—
495C4×C67—23no—
496C4×C67—23no—
497C4×C67—23no—
498C4×C67—23no—
499C4×C67—23no—
500C4×C67—21no—
501C4×C67C22×#4112yes—
502C4×C67C22×#4116yes—
503C4×C67C2×H(5,𝔽2)12yes—
504C4×C67C2×H(5,𝔽2)12yes—
505C4×C67#58512yes—
506Dic67—24no—
507Dic67—212no—
508Dic67—24no—
509#62800—671nomaximal, Sylow
510C2×C67—26no—
511C2×C67—22no—
512C2×C67—43no—
513C2×C67C23×#4111yescharacteristic
514C2×C67C22×H(5,𝔽2)11yescharacteristic
515C2×C67C2×#58511yescharacteristic
516D67—412no—
517#3522—672no—
518#3519—676no—
519#3517—672no—
520#3514—676no—
521#3511—673no—
522#3508—673no—
523#3503—671no—
524#3498—671no—
525#3494—676no—
526#3488—672no—
527#3483—672no—
528#3481—676no—
529#3480—672no—
530D4×#41—676no—
531#3460—676no—
532#3444—673no—
533C2×#532—673no—
534C4×H(5,𝔽2)—672no—
535C2×C4×#41D6711yescharacteristic, complemented
536C67#6280011yescharacteristic, complemented, Sylow
537C2×H(5,𝔽2)—672no—
538C22×#41—676no—
539C22×#41C2×D6711yescharacteristic
540#559—676no—
541#559—676no—
542Q82—672no—
543#557—672no—
544#556—676no—
545#555—676no—
546#555—6712no—
547#554—676no—
548#554—676no—
549#553—6712no—
550#553—6712no—
551#553—6712no—
552#551—6724no—
553#550—674no—
554#550—672no—
555#550—672no—
556#550—676no—
557#550—676no—
558D4×Q8—676no—
559#548—674no—
560#548—6712no—
561#547—676no—
562#547—6712no—
563#546—6712no—
564#546—6712no—
565#546—6712no—
566#546—6724no—
567D42—6712no—
568D42—676no—
569D42—676no—
570#544—676no—
571#542—6712no—
572#542—6712no—
573#540—6712no—
574#540—6712no—
575#538—6724no—
576#537—676no—
577#535—676no—
578#535—676no—
579#533—671no—
580#533—673no—
581#533—673no—
582#532—6712no—
583#532—673no—
584#532—676no—
585#532—676no—
586#532—676no—
587#532—676no—
588#532—676no—
589#532—676no—
590#532—676no—
591#532—673no—
592#532—673no—
593C2×C4⋊Q8—673no—
594C2×#127—673no—
595#529—6712no—
596#529—676no—
597#529—676no—
598#529—676no—
599#529—676no—
600#529—676no—
601#529—676no—
602C2×#124—676no—
603#525—676no—
604#525—676no—
605#525—676no—
606#525—6724no—
607C2×#121—676no—
608C2×#121—676no—
609#520—672no—
610#520—674no—
611#520—676no—
612#518—6712no—
613#518—676no—
614C4×#41—674no—
615C4×#41—676no—
616C4×#41—676no—
617C4×#41—676no—
618C4×#41C2×D6711yescharacteristic
619C4×#41C2×D6711yescharacteristic
620C4×#41C2×D6713yescomplemented
621C4×#41C2×D6713yescomplemented
622C4×#41C2×D6711yescharacteristic, complemented
623C4×#41C2×D6713yescomplemented
624C4×#41C2×D6713yescomplemented
625C4×#41C2×D6711yescharacteristic, complemented
626C2×C4×Q8C2×D6711yescharacteristic, complemented
627C2×C4×Q8C2×D6711yescharacteristic, complemented
628C2×C4×D4—6712no—
629C2×C4×D4—676no—
630C2×C4×D4—676no—
631C2×C4×D4C2×D6713yescomplemented
632C2×C4×D4C2×D6713yescomplemented
633C2×#117C2×D6713yescomplemented
634C22×C42C2×D6713yescomplemented
635H(5,𝔽2)—13416no—
636C2×#41—28no—
637C2×#41—26824no—
638C2×#41—674no—
639C2×#41—676no—
640C2×#41—6712no—
641C2×#41—6712no—
642C2×#41—6712no—
643C2×#41—676no—
644C2×#41—676no—
645C2×#41C22×D6713yes—
646C2×#41C22×D6713yes—
647C2×#41C22×D6711yescharacteristic
648C2×#41C22×D6711yescharacteristic
649C22×Q8—676no—
650C22×Q8C22×D6711yescharacteristic
651C22×D4—6712no—
652C22×D4—6712no—
653C22×D4—676no—
654C22×D4—676no—
655C22×D4—676no—
656C22×D4C22×D6713yes—
657C23×C4—6712no—
658C23×C4C22×D6713yes—
659C23×C4C22×D6713yes—
660C23×C4C22×D6713yes—
661C4⋊Q8—6712no—
662C4⋊Q8—673no—
663C4⋊Q8—676no—
664C4⋊Q8—676no—
665C4⋊Q8—676no—
666C4⋊Q8—671no—
667C4⋊Q8—671no—
668#127—6712no—
669#127—673no—
670#127—676no—
671#127—676no—
672#127—676no—
673#126—6724no—
674#126—6712no—
675#126—6712no—
676#125—6712no—
677#125—672no—
678#125—676no—
679#125—676no—
680#124—6712no—
681#124—6724no—
682#124—676no—
683#124—6712no—
684#124—6712no—
685#124—6712no—
686#124—676no—
687#124—676no—
688#123—6712no—
689#123—6712no—
690#123—6712no—
691#123—6724no—
692#123—6724no—
693#123—6724no—
694C22⋊Q8—6712no—
695C22⋊Q8—672no—
696C22⋊Q8—672no—
697C22⋊Q8—676no—
698C22⋊Q8—676no—
699C22⋊Q8—676no—
700C22⋊Q8—676no—
701C22⋊Q8—6724no—
702C22⋊Q8—6724no—
703#121—6724no—
704#121—6712no—
705#121—676no—
706#121—676no—
707#121—6712no—
708#121—6712no—
709#121—6712no—
710#121—6712no—
711#121—6712no—
712#121—6712no—
713#121—676no—
714#121—676no—
715#121—676no—
716#121—676no—
717#121—6712no—
718#121—6712no—
719#121—6724no—
720#121—6724no—
721#120—6712no—
722#120—6724no—
723#120—6724no—
724C4×Q8—674no—
725C4×Q8—672no—
726C4×Q8—672no—
727C4×Q8—676no—
728C4×Q8—676no—
729C4×Q8—676no—
730C4×Q8—676no—
731C4×Q8C22×D6711yescharacteristic
732C4×Q8C22×D6711yescharacteristic
733C4×Q8C22×D6711yescharacteristic
734C4×Q8C22×D6711yescharacteristic
735C4×Q8C22×D6713yes—
736C4×Q8C22×D6713yes—
737C4×Q8C22×D6713yes—
738C4×Q8C22×D6713yes—
739C4×D4—6712no—
740C4×D4—6712no—
741C4×D4—6712no—
742C4×D4—6712no—
743C4×D4—6712no—
744C4×D4—6712no—
745C4×D4—6712no—
746C4×D4—6712no—
747C4×D4—6712no—
748C4×D4—6724no—
749C4×D4—6712no—
750C4×D4—676no—
751C4×D4—676no—
752C4×D4—6712no—
753C4×D4—6712no—
754C4×D4—6712no—
755C4×D4—6712no—
756C4×D4—6712no—
757C4×D4—676no—
758C4×D4—676no—
759C4×D4—676no—
760C4×D4—676no—
761C4×D4C22×D6713yes—
762C4×D4C22×D6713yes—
763C4×D4C22×D6713yes—
764C4×D4C22×D6713yes—
765C4×D4C22×D6716yes—
766C4×D4C22×D6713yes—
767C4×D4C22×D6716yes—
768C4×D4C22×D6713yes—
769C4×D4C22×D6716yes—
770C4×D4C22×D6716yes—
771C4×D4C22×D6713yes—
772C4×D4C22×D6713yes—
773#117—672no—
774#117—676no—
775#117—676no—
776#117—6712no—
777#117—6712no—
778#117—6712no—
779#117—6712no—
780#117C22×D6713yes—
781#117C22×D6713yes—
782#117C22×D6716yes—
783#117C22×D6716yes—
784#117C22×D6713yes—
785#117C22×D6713yes—
786C2×C4⋊C4—676no—
787C2×C4⋊C4—676no—
788C2×C4⋊C4—6712no—
789C2×C4⋊C4C22×D6713yes—
790C2×C4⋊C4C22×D6713yes—
791C2×C22⋊C4—6712no—
792C2×C22⋊C4—6712no—
793C2×C22⋊C4—6724no—
794C2×C22⋊C4C22×D6716yes—
795C2×C42—6712no—
796C2×C42C22×D6713yes—
797C2×C42C22×D6713yes—
798C2×C42C22×D6713yes—
799C2×C42C22×D6713yes—
800C2×C42C22×D6713yes—
801C2×C42C22×D6713yes—
802C2×C42C22×D6713yes—
803C2×C42C22×D6713yes—
804C2×C42C22×D6713yes—
805C2×C42C22×D6713yes—
806C2×C42C22×D6713yes—
807C2×C42C22×D6711yescharacteristic
808C24—6712no—
809C24C23×D6713yes—
810#41—24no—
811#41—212no—
812#41—212no—
813#41—26824no—
814#41—26812no—
815#41—26824no—
816#41—26824no—
817#41—13416no—
818#41—13424no—
819#41—13424no—
820#41#1176162818yescomplemented
821C2×Q8—24no—
822C2×Q8—26812no—
823C2×Q8—6712no—
824C2×Q8—672no—
825C2×Q8—672no—
826C2×Q8—676no—
827C2×Q8C23×D6713yes—
828C2×Q8C23×D6711yescharacteristic
829C2×D4—212no—
830C2×D4—26812no—
831C2×D4—26812no—
832C2×D4—26824no—
833C2×D4—6712no—
834C2×D4—6724no—
835C2×D4—6712no—
836C2×D4—6712no—
837C2×D4—6712no—
838C2×D4—6712no—
839C2×D4—6712no—
840C2×D4—676no—
841C2×D4—676no—
842C2×D4—676no—
843C2×D4—13448no—
844C2×D4—13424no—
845C2×D4C23×D6716yes—
846C2×D4C23×D6713yes—
847C2×D4C23×D6713yes—
848C22×C4—212no—
849C22×C4—212no—
850C22×C4—46no—
851C22×C4—26824no—
852C22×C4—6712no—
853C22×C4—6712no—
854C22×C4—6724no—
855C22×C4—6712no—
856C22×C4—6712no—
857C22×C4C23×D6711yescharacteristic
858C22×C4C23×D6711yescharacteristic
859C22×C4C23×D6713yes—
860C22×C4C23×D6713yes—
861C22×C4C23×D6713yes—
862C22×C4C23×D6713yes—
863C22×C4C23×D6713yes—
864C22×C4C23×D6713yes—
865C22×C4C23×D6713yes—
866C22×C4C23×D6713yes—
867C22×C4C23×D6713yes—
868C22×C4C23×D6713yes—
869C22×C4C23×D6713yes—
870C22×C4C23×D6713yes—
871C22×C4C23×D6713yes—
872C22×C4C23×D6713yes—
873C22×C4C23×D6713yes—
874C22×C4C23×D6711yescharacteristic
875C4⋊C4—6712no—
876C4⋊C4—676no—
877C4⋊C4—676no—
878C4⋊C4—6712no—
879C4⋊C4—6712no—
880C4⋊C4—672no—
881C4⋊C4—672no—
882C4⋊C4—674no—
883C4⋊C4—674no—
884C4⋊C4—672no—
885C4⋊C4—672no—
886C4⋊C4—6712no—
887C4⋊C4—6712no—
888C4⋊C4—6712no—
889C4⋊C4C23×D6713yes—
890C4⋊C4C23×D6713yes—
891C4⋊C4C23×D6713yes—
892C4⋊C4C23×D6713yes—
893C4⋊C4C23×D6716yes—
894C4⋊C4C23×D6716yes—
895C22⋊C4—6712no—
896C22⋊C4—674no—
897C22⋊C4—6712no—
898C22⋊C4—6712no—
899C22⋊C4—6724no—
900C22⋊C4—6712no—
901C22⋊C4—6712no—
902C22⋊C4—6724no—
903C22⋊C4—6712no—
904C22⋊C4—6712no—
905C22⋊C4—6712no—
906C22⋊C4C23×D6716yes—
907C22⋊C4C23×D6716yes—
908C22⋊C4C23×D6716yes—
909C22⋊C4C23×D6716yes—
910C42—6712no—
911C42—6712no—
912C42—674no—
913C42C23×D6711yescharacteristic
914C42C23×D6711yescharacteristic
915C42C23×D6713yes—
916C42C23×D6713yes—
917C42C23×D6713yes—
918C42C23×D6713yes—
919C42C23×D6713yes—
920C42C23×D6713yes—
921C42C23×D6713yes—
922C42C23×D6713yes—
923C42C23×D6713yes—
924C42C23×D6713yes—
925C42C23×D6713yes—
926C42C23×D6711yescharacteristic
927C42C23×D6711yescharacteristic
928C42C23×D6713yes—
929C23—26no—
930C23—26no—
931C23—43no—
932C23—26812no—
933C23—26812no—
934C23—6712no—
935C23—13424no—
936C23C24×D6713yes—
937C23C24×D6713yes—
938C23C24×D6711yescharacteristic
939Q8—26no—
940Q8—26812no—
941Q8—1344no—
942Q8—13412no—
943Q8—1344no—
944Q8C2×#1176162814yescomplemented
945D4—212no—
946D4—26no—
947D4—26812no—
948D4—26812no—
949D4—26824no—
950D4—26812no—
951D4—13424no—
952D4—13424no—
953D4—13412no—
954D4—13424no—
955D4—13412no—
956D4—13412no—
957D4C2×#11761628112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—22no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—43no—
974C2×C4—26824no—
975C2×C4—26812no—
976C2×C4—26812no—
977C2×C4—674no—
978C2×C4—674no—
979C2×C4—6712no—
980C2×C4—13424no—
981C2×C4—13424no—
982C2×C4C2×#11761628112yescomplemented
983C2×C4#1452408914yescomplemented
984C2×C4C24×D6713yes—
985C2×C4C24×D6711yescharacteristic
986C2×C4C24×D6711yescharacteristic
987C2×C4C24×D6713yes—
988C2×C4C24×D6713yes—
989C2×C4C24×D6713yes—
990C2×C4C24×D6713yes—
991C2×C4C24×D6713yes—
992C2×C4C24×D6711yescharacteristic
993C2×C4C24×D6711yescharacteristic
994C2×C4C24×D6711yescharacteristic
995C2×C4C24×D6711yescharacteristic
996C22—21no—
997C22—23no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—412no—
1004C22—53624no—
1005C22—13412no—
1006C22—13412no—
1007C22—13412no—
1008C22C22×#1176162816yes—
1009C22C2×#1452408912yes—
1010C22C25×D6711yescharacteristic
1011C4—21no—
1012C4—23no—
1013C4—23no—
1014C4—23no—
1015C4—21no—
1016C4—23no—
1017C4—23no—
1018C4—1344no—
1019C4—13412no—
1020C4—1344no—
1021C4C22×#1176162812yes—
1022C4C22×#1176162816yes—
1023C4C2×#1452408912yes—
1024C4C2×#1452408912yes—
1025C4#1686423212yes—
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—26812no—
1030C2C23×#1176162811yescharacteristic
1031C2C22×#1452408911yescharacteristic
1032C2C2×#1686423211yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×C4×#41×C67C2
hypercenterC2×C4×#41D67
hypocenterC67#62800
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22574294C2semidirect
2. #22574241C2semidirect
3. #22574215C2semidirect
4. #22574170C2semidirect
5. #22574120C2semidirect
6. #22574085C2semidirect
7. #22574028C2semidirect
8. #22573987C2semidirect
9. #22573944C2semidirect
10. #22573878C2semidirect
11. #22573835C2semidirect
12. #22573819C2semidirect
13. #22573804C2semidirect
14. D4×#11761628C2semidirect
15. #22573625C2semidirect
16. #22573505C2semidirect
17. C2×#16863946C2semidirect
18. C4×#14524089C2semidirect
19. C2×C4×#41×C67C2semidirect
21. C22×#11761628C22semidirect
22. #16864131C22semidirect
23. #16864131C22semidirect
24. Q8×Dic134C22semidirect
25. #16864125C22semidirect
26. #16864119C22semidirect
27. #16864111C22semidirect
28. #16864109C22semidirect
29. #16864106C22semidirect
30. #16864103C22semidirect
31. #16864094C22semidirect
32. #16864092C22semidirect
33. #16864090C22semidirect
34. #16864070C22semidirect
35. #16864068C22semidirect
36. #16864068C22semidirect
37. #16864067C22semidirect
38. #16864067C22semidirect
39. #16864065C22semidirect
40. D4×Dic134C22semidirect
41. #16864057C22semidirect
42. #16864055C22semidirect
43. #16864051C22semidirect
44. #16864047C22semidirect
45. #16864042C22semidirect
46. #16864042C22semidirect
47. #16864036C22semidirect
48. #16864034C22semidirect
49. D4×D268C22semidirect
50. D4×D268C22semidirect
51. D4×C22⋊D67C22semidirect
52. #16864024C22semidirect
53. #16864018C22semidirect
54. #16864017C22semidirect
55. #16864001C22semidirect
56. #16863997C22semidirect
57. #16863979C22semidirect
58. #16863974C22semidirect
59. #16863965C22semidirect
60. #16863960C22semidirect
61. #16863953C22semidirect
62. #16863953C22semidirect
63. #16863953C22semidirect
64. #16863946C22semidirect
65. #16863946C22semidirect
66. #16863946C22semidirect
67. #16863946C22semidirect
68. #16863946C22semidirect
69. #16863946C22semidirect
70. #16863946C22semidirect
71. #16863946C22semidirect
72. #16863946C22semidirect
73. #16863946C22semidirect
74. #16863943C22semidirect
75. C2×#14524043C22semidirect
76. C2×#14524040C22semidirect
77. #16863933C22semidirect
78. #16863930C22semidirect
79. #16863930C22semidirect
80. #16863930C22semidirect
81. #16863930C22semidirect
82. #16863930C22semidirect
83. #16863930C22semidirect
84. C2×#14524031C22semidirect
85. #16863907C22semidirect
86. #16863907C22semidirect
87. #16863907C22semidirect
88. #16863905C22semidirect
89. C2×#14524017C22semidirect
90. C2×#14524017C22semidirect
92. #16863878C22semidirect
93. #16863876C22semidirect
94. #16863870C22semidirect
95. #16863868C22semidirect
96. C4×#11761629C22semidirect
97. C4×#11761628C22semidirect
98. C4×#11761628C22semidirect
99. C4×#11761628C22semidirect
100. C2×C4×D268C22semidirect
101. C2×C4×D268C22semidirect
102. C4×D4×D67C22semidirect
106. C4×#41×C67C22semidirect
107. C4×#41×C67C22semidirect
108. C4×#41×C67C22semidirect
109. C4×#41×C67C22semidirect
110. C4×#41×C67C22semidirect
111. C4×#41×C67C22semidirect
112. C2×C4×Q8×C67C22semidirect
113. C2×C4×Q8×C67C22semidirect
114. C2×C4×D4×C67C22semidirect
115. C2×C4×D4×C67C22semidirect
116. C2×#117×C67C22semidirect
117. C22×C42×C67C22semidirect
357. #41×C67#41semidirect
423. Q8×C67C2×#41semidirect
426. D4×C67C2×#41semidirect
443. C2×C4×C67C2×#41semidirect
444. C2×C4×C67H(5,𝔽2)semidirect
535. C2×C4×#41D67semidirect
536. C67#62800semidirect
620. C4×#41C2×D67semidirect
621. C4×#41C2×D67semidirect
622. C4×#41C2×D67semidirect
623. C4×#41C2×D67semidirect
624. C4×#41C2×D67semidirect
625. C4×#41C2×D67semidirect
626. C2×C4×Q8C2×D67semidirect
627. C2×C4×Q8C2×D67semidirect
631. C2×C4×D4C2×D67semidirect
632. C2×C4×D4C2×D67semidirect
633. C2×#117C2×D67semidirect
634. C22×C42C2×D67semidirect
820. #41#11761628semidirect
944. Q8C2×#11761628semidirect
957. D4C2×#11761628semidirect
982. C2×C4C2×#11761628semidirect
983. C2×C4#14524089semidirect

Maximal subgroups

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

subgroupindex
#225742942
#225742412
#225742152
#225741702
#225741202
#225740852
#225740282
#225739872
#225739442
#225738782
#225738352
#225738192
#225738042
D4×#117616282
#225736252
#225735052
C2×#168639462
C4×#145240892
C2×C4×#41×C672
#6280067