Finite Group Databasebeta

← #3499×D67 #31764239

Subgroups — #3499×D67 #31764239

Order 17152.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D67C212yesmaximal, complemented
2#22573994C211yesmaximal, characteristic, complemented
3#22573993C214yesmaximal, complemented
4#22573992C213yesmaximal, complemented
5#22573991C216yesmaximal, complemented
6#22573990C212yesmaximal, complemented
7#22573989C213yesmaximal, complemented
8#22573988C2112yesmaximal, complemented
9D4×Q8×D67C214yesmaximal, complemented
10#547×D67C2112yesmaximal, complemented
11#536×D67C216yesmaximal, complemented
12#532×D67C213yesmaximal, complemented
13C2×C4⋊Q8×D67C213yesmaximal, complemented
14C4×#41×D67C211yesmaximal, characteristic, complemented
15C67×#3499C211yesmaximal, characteristic, complemented
16C2×#14524091C2216yescomplemented
17C2×#14524091C2214yescomplemented
18C2×#14524090C22112yescomplemented
19C2×#14524090C2216yescomplemented
20C2×#14524090C2212yescomplemented
212−1+4×D67—232no—
22C2×#41×D67C22112yes—
23C2×#41×D67C2216yes—
24C2×#41×D67C2211yescharacteristic
25C22×Q8×D67C2214yes—
26C22×Q8×D67C2216yes—
27Q8×D268C2214yescomplemented
28D4×Dic134C22112yescomplemented
29#16864061C22112yescomplemented
30Q8×C22⋊D67C2218yescomplemented
31#16864059C22124yescomplemented
32#16864051C22112yescomplemented
33#16864050C22112yescomplemented
34#16864049C22112yescomplemented
35#16864048C22124yescomplemented
36#16864047C22124yescomplemented
37#16864046C22124yescomplemented
38#16864045C22124yescomplemented
39#16864044C22148yescomplemented
40#16863972C2216yescomplemented
41#16863971C22112yescomplemented
42#16863970C2216yescomplemented
43#16863969C22124yescomplemented
44#16863968C22124yescomplemented
45#16863967C2216yescomplemented
46#16863966C22112yescomplemented
47#16863947C2213yescomplemented
48#16863946C2213yescomplemented
49#16863945C2216yescomplemented
50#16863944C2213yescomplemented
51#16863943C22112yescomplemented
52#16863942C2216yescomplemented
53#16863941C22112yescomplemented
54C2×#14524043C2213yescomplemented
55C2×#14524042C22112yescomplemented
56C2×#14524041C2216yescomplemented
57C4⋊Q8×D67C22112yes—
58C4⋊Q8×D67C2213yes—
59C4⋊Q8×D67C2216yes—
60C4⋊Q8×D67C22112yescomplemented
61C4⋊Q8×D67C2216yescomplemented
62C4⋊Q8×D67C2216yescomplemented
63#127×D67C2211yescharacteristic
64#124×D67C2216yes—
65#123×D67C22124yes—
66C22⋊Q8×D67C22124yes—
67#121×D67C22112yes—
68#41×Dic67C2211yescharacteristic, complemented
69C4×#11761629C2212yescomplemented
70C4×#11761628C2213yescomplemented
71#16863864C2213yescomplemented
72C4×#11761627C2216yescomplemented
73C4×Q8×D67C2212yes—
74C4×D4×D67C2216yes—
75C4×D4×D67C22112yes—
76#117×D67C2213yes—
77C2×C4⋊C4×D67C22112yes—
78C2×C42×D67C2213yes—
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—232no—
87#14524091—248no—
88#14524090—248no—
89#14524090—296no—
90#14524090—216no—
91C2×#11761629C23112yes—
92C2×#11761629C2316yes—
93C2×#11761629C2311yescharacteristic
94C2×#11761628C23124yes—
95C2×#11761628C23112yes—
96C2×#11761628C2316yes—
97C2×#11761628C23112yes—
98C2×#11761628C2313yes—
99C2×#11761627C23124yes—
100C2×#11761627C23112yes—
101C2×#11761627C23112yes—
102C2×#11761627C2316yes—
103C2×#11761627C2313yes—
104#41×D67—296no—
105#41×D67—248no—
106#41×D67D4116yescomplemented
107C22×Dic134C23112yes—
108C22×Dic134C2316yes—
109C22×Dic134C23112yes—
110C2×Q8×D67—232no—
111C2×Q8×D67—248no—
112C2×Q8×D67C23112yes—
113C2×Q8×D67C2314yes—
114C2×Q8×D67C23112yes—
115C2×Q8×D67C2316yes—
116C2×Q8×D67C23112yes—
117C2×Q8×D67C23112yes—
118C2×Q8×D67C2311yescharacteristic
119C2×D4×D67C2314yes—
120C2×D4×D67C23112yes—
121C2×D4×D67C2312yes—
122C2×D4×D67C2313yes—
123C22×C4×D67C2316yes—
124C22×C4×D67C23112yes—
125C22×C4×D67C23112yes—
126C22×C4×D67C2313yes—
127#14524043C23112yes—
128#14524043C2313yes—
129#14524043C2316yes—
130#14524042C23124yes—
131#14524042C23124yes—
132#14524042C23112yes—
133#14524042C23124yes—
134#14524041C23124yes—
135#14524041C2316yes—
136#14524041C23112yes—
137#14524040C2311yescharacteristic
138#14524039C2314yes—
139#14524039C2312yes—
140#14524032C2316yes—
141#14524031C2316yes—
142#14524030C2316yes—
143#14524029C23124yes—
144#14524028C23148yes—
145#14524027C23124yes—
146#14524026C23124yes—
147#14524025C23148yes—
148#14524024C23124yes—
149#14524023C23124yes—
150#14524022C23124yes—
151#14524021C23148yes—
152#14524020C23148yes—
153#14524019C23124yes—
154#14524018C23112yes—
155#14524017C23112yes—
156#14524016C23124yes—
157#14524015C23124yes—
158#14524014C23112yes—
159Q8×Dic67C2312yes—
160C4×Dic134C2316yes—
161#14524008C2316yes—
162C4×D268C2316yes—
163C4×D268C23112yes—
164D4×Dic67C2316yes—
165D4×Dic67C23112yes—
166#14524005C23112yes—
167#14524005C2316yes—
168C4×C22⋊D67C23124yes—
169C4×C22⋊D67C23112yes—
170(C22⋊D67)⋊C4C23112yes—
171(C22⋊D67)⋊C4C23124yes—
172#14524002C2313yes—
173#14524001C2316yes—
174#14524000C2316yes—
175#14523999C2316yes—
176C2×C4⋊Dic67C23112yes—
177C2×Dic67⋊C4C23124yes—
178C4⋊C4×D67C23124yes—
179C4⋊C4×D67C23124yes—
180C4⋊C4×D67C23112yes—
181C4⋊C4×D67C23124yes—
182C4⋊C4×D67C2316yes—
183C22⋊C4×D67C2316yes—
184C22⋊C4×D67C23124yes—
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×D67C2414yes—
214C23×D67C2413yes—
215#11761629—248no—
216#11761629—224no—
217#11761629C2×D418yescomplemented
218#11761628—224no—
219#11761628—296no—
220#11761628—248no—
221#11761628—248no—
222#11761628C2×D4124yescomplemented
223#11761627—248no—
224#11761627—296no—
225#11761627—248no—
226#11761627—224no—
227#11761627C2×D4124yescomplemented
228C2×Dic134—224no—
229C2×Dic134—248no—
230C2×Dic134—248no—
231C2×Dic134C24124yes—
232C2×Dic134C24112yes—
233C2×Dic134C24112yes—
234C2×Dic134C2416yes—
235C2×Dic134C2413yes—
236Q8×D67—216no—
237Q8×D67—248no—
238Q8×D67—224no—
239Q8×D67—248no—
240Q8×D67—248no—
241Q8×D67—248no—
242Q8×D67C2×D418yes—
243C2×D268C2414yes—
244C2×D268C24112yes—
245C2×D268C2412yes—
246C2×D268C2413yes—
247C2×C22⋊D67C2418yes—
248C2×C22⋊D67C24112yes—
249C2×C22⋊D67C24112yes—
250C2×C22⋊D67C2414yes—
251C2×C22⋊D67C2416yes—
252D4×D67—248no—
253D4×D67—28no—
254D4×D67—216no—
255D4×D67C2×D4124yes—
256C22×Dic67C2416yes—
257C22×Dic67C24112yes—
258C22×Dic67C24112yes—
259C22×Dic67C2413yes—
260C2×C4×D67—248no—
261C2×C4×D67—248no—
262C2×C4×D67—224no—
263C2×C4×D67C2×D4124yes—
264C2×C4×D67C2416yes—
265C2×C4×D67C2416yes—
266C2×C4×D67C2416yes—
267C2×C4×D67C24112yes—
268C2×C4×D67C24124yes—
269C2×C4×D67C24112yes—
270C2×C4×D67C24112yes—
271C2×C4×D67C2411yescharacteristic
272C2×C4×D67C2413yes—
273C2×C4×D67C2413yes—
274C2×C4×D67C2413yes—
275C2×C4×D67C2412yes—
276C4⋊Dic67C24112yes—
277C4⋊Dic67C24124yes—
278C4⋊Dic67C2416yes—
279Dic67⋊C4C24124yes—
280Dic67⋊C4C24148yes—
281Dic67⋊C4C24112yes—
282C22⋊Dic67C2416yes—
283C22⋊Dic67C24124yes—
284(C2×D67)⋊C4C24112yes—
285(C2×D67)⋊C4C24124yes—
286(C2×D67)⋊C4C24124yes—
287C4×Dic67C2411yescharacteristic
288C4×Dic67C2412yes—
289C4×Dic67C2416yes—
290C4×Dic67C2413yes—
291C4×Dic67C2416yes—
292C4×Dic67C2416yes—
293C4×Dic67C2416yes—
294#41×C67—248no—
295#41×C67—224no—
296#41×C67C2×D418yescomplemented
297C2×Q8×C67—216no—
298C2×Q8×C67—224no—
299C2×Q8×C67C24112yes—
300C2×Q8×C67C2416yes—
301C2×Q8×C67C2411yescharacteristic
302C2×D4×C67C2414yes—
303C2×D4×C67C24112yes—
304C2×D4×C67C2412yes—
305C2×D4×C67C2413yes—
306C22×C4×C67C2416yes—
307C22×C4×C67C24112yes—
308C22×C4×C67C24112yes—
309C22×C4×C67C2413yes—
310C4⋊C4×C67C24112yes—
311C4⋊C4×C67C24124yes—
312C4⋊C4×C67C2416yes—
313C22⋊C4×C67C2416yes—
314C22⋊C4×C67C24124yes—
315C42×C67C2411yescharacteristic
316C42×C67C2413yes—
317C42×C67C2416yes—
318C23×C67C2514yes—
319C23×C67C2513yes—
320C22×D67—212no—
321C22×D67—28no—
322C22×D67—216no—
323C22×D67C22×D4112yes—
324C22×D67C2514yes—
325C22×D67C2513yes—
326C22×D67C2511yescharacteristic
327Q8×C67—212no—
328Q8×C67—224no—
329Q8×C67C22×D414yes—
330D4×C67—224no—
331D4×C67—24no—
332D4×C67—28no—
333D4×C67C22×D4112yes—
334C2×C4×C67—224no—
335C2×C4×C67—224no—
336C2×C4×C67—212no—
337C2×C4×C67C22×D4112yes—
338C2×C4×C67C2516yes—
339C2×C4×C67C25112yes—
340C2×C4×C67C2511yescharacteristic
341C2×C4×C67C2513yes—
342C2×C4×C67C2512yes—
343C22⋊D67—224no—
344C22⋊D67—224no—
345C22⋊D67—28no—
346C22⋊D67—216no—
347C22⋊D67C22×D4124yes—
348C2×Dic67—224no—
349C2×Dic67—224no—
350C2×Dic67—212no—
351C2×Dic67C22×D4112yes—
352C2×Dic67C2516yes—
353C2×Dic67C25112yes—
354C2×Dic67C2511yescharacteristic
355C2×Dic67C2513yes—
356C2×Dic67C2512yes—
357D268—224no—
358D268—24no—
359D268—28no—
360D268C22×D4112yes—
361C4×D67—224no—
362C4×D67—248no—
363C4×D67—212no—
364C4×D67—224no—
365C4×D67—212no—
366C4×D67—224no—
367C4×D67—212no—
368C4×D67C22×D4112yes—
369C4×D67C22×D414yes—
370C4×D67C22×D4112yes—
371C4×D67C22×D4112yes—
372C4×D672−1+418yescomplemented
373Dic134—212no—
374Dic134—224no—
375Dic134—224no—
376Dic134—248no—
377Dic134C22×D4112yes—
378C22×C67—26no—
379C22×C67—24no—
380C22×C67—28no—
381C22×C67C23×D416yes—
382C22×C67C2611yescharacteristic
383C2×D67—26no—
384C2×D67—224no—
385C2×D67—24no—
386C2×D67—28no—
387C2×D67—416no—
388C2×D67C23×D416yes—
389C2×D67C23×D412yes—
390C2×D67C2×2−1+414yes—
391C4×C67—212no—
392C4×C67—26no—
393C4×C67C23×D412yes—
394C4×C67C23×D416yes—
395C4×C67C2×2−1+414yescomplemented
396Dic67—212no—
397Dic67—26no—
398Dic67C23×D412yes—
399Dic67C23×D416yes—
400Dic67C2×2−1+414yescomplemented
401C2×#3499—671nomaximal, Sylow
402C2×C67—26no—
403C2×C67—44no—
404C2×C67C24×D411yescharacteristic
405C2×C67C22×2−1+412yes—
406D67—26no—
407D67—44no—
408D67#349914yesdirect product factor
409C22×2−1+4—672no—
410#3499—672no—
411#3499—674no—
412#3499—6712no—
413#3499—676no—
414#3499—673no—
415#3499—673no—
416#3499—671no—
417#3499D6711yescharacteristic, direct product factor
418C2×D4×Q8—674no—
419C2×#547—6712no—
420C2×#536—676no—
421C2×#532—673no—
422C22×C4⋊Q8—673no—
423C2×C4×#41—671no—
424C67C2×#349911yescharacteristic, complemented, Sylow
425C2×2−1+4—676no—
426C2×2−1+4—6712no—
427C2×2−1+4—672no—
428C2×2−1+4—674no—
429C2×2−1+4—676no—
430C2×2−1+4—13432no—
431C2×2−1+4C2×D6712yescomplemented
432C22×#41—671no—
433C22×#41—676no—
434C22×#41—6712no—
435C23×Q8—676no—
436C23×Q8—674no—
437D4×Q8—678no—
438D4×Q8—6712no—
439D4×Q8—6724no—
440D4×Q8—674no—
441D4×Q8—6712no—
442D4×Q8C2×D6714yescomplemented
443#547—6724no—
444#547—6712no—
445#547—6748no—
446#547—6724no—
447#547—6724no—
448#547—6712no—
449#547—6712no—
450#547—6724no—
451#547C2×D67112yescomplemented
452#536—676no—
453#536—676no—
454#536—6712no—
455#536—6712no—
456#536—6724no—
457#536—6724no—
458#536—676no—
459#536C2×D6716yescomplemented
460#532—676no—
461#532—673no—
462#532—673no—
463#532—676no—
464#532—6712no—
465#532—6712no—
466#532—673no—
467#532C2×D6713yescomplemented
468C2×C4⋊Q8—676no—
469C2×C4⋊Q8—673no—
470C2×C4⋊Q8—676no—
471C2×C4⋊Q8—6712no—
472C2×C4⋊Q8—676no—
473C2×C4⋊Q8—676no—
474C2×C4⋊Q8—6712no—
475C2×C4⋊Q8—6712no—
476C2×C4⋊Q8—673no—
477C2×C4⋊Q8C2×D6713yescomplemented
478C2×#127—671no—
479C2×#124—676no—
480C2×#123—6724no—
481C2×C22⋊Q8—6724no—
482C2×#121—6712no—
483C4×#41—671no—
484C4×#41—672no—
485C4×#41—676no—
486C4×#41—673no—
487C4×#41—673no—
488C4×#41C2×D6711yescharacteristic, complemented
489C2×C4×Q8—672no—
490C2×C4×D4—676no—
491C2×C4×D4—6712no—
492C2×#117—673no—
493C22×C4⋊C4—6712no—
494C22×C42—673no—
4952−1+4—216no—
4962−1+4—13432no—
4972−1+4—13448no—
4982−1+4—13496no—
4992−1+4—13448no—
5002−1+4—13416no—
501C2×#41—6716no—
502C2×#41—671no—
503C2×#41—676no—
504C2×#41—6712no—
505C2×#41—673no—
506C2×#41—6712no—
507C2×#41—676no—
508C2×#41—6712no—
509C2×#41—6724no—
510C2×#41—673no—
511C2×#41—6712no—
512C2×#41—676no—
513C2×#41—6712no—
514C2×#41—6724no—
515C2×#41—13448no—
516C2×#41—13496no—
517C2×#41C22×D6716yes—
518C2×#41C22×D67112yes—
519C2×#41C22×D6711yescharacteristic
520C22×Q8—671no—
521C22×Q8—6712no—
522C22×Q8—676no—
523C22×Q8—6712no—
524C22×Q8—6712no—
525C22×Q8—6712no—
526C22×Q8—674no—
527C22×Q8—6712no—
528C22×Q8—676no—
529C22×Q8—6712no—
530C22×Q8—13448no—
531C22×Q8—13432no—
532C22×Q8C22×D6716yes—
533C22×Q8C22×D6714yes—
534C22×D4—673no—
535C22×D4—674no—
536C22×D4—6712no—
537C22×D4—672no—
538C23×C4—673no—
539C23×C4—676no—
540C23×C4—6712no—
541C23×C4—6712no—
542C4⋊Q8—676no—
543C4⋊Q8—6712no—
544C4⋊Q8—6724no—
545C4⋊Q8—6712no—
546C4⋊Q8—6724no—
547C4⋊Q8—6724no—
548C4⋊Q8—6724no—
549C4⋊Q8—673no—
550C4⋊Q8—676no—
551C4⋊Q8—6712no—
552C4⋊Q8C22×D6713yes—
553C4⋊Q8C22×D6716yes—
554C4⋊Q8C22×D67112yes—
555#127—672no—
556#127—674no—
557#127—671no—
558#127C22×D6711yescharacteristic
559#124—676no—
560#124—676no—
561#124—6724no—
562#124—676no—
563#124C22×D6716yes—
564#123—6724no—
565#123—6724no—
566#123—6748no—
567#123—6748no—
568#123—6724no—
569#123C22×D67124yes—
570C22⋊Q8—6724no—
571C22⋊Q8—6724no—
572C22⋊Q8—6748no—
573C22⋊Q8—6724no—
574C22⋊Q8—6748no—
575C22⋊Q8C22×D67124yes—
576#121—6712no—
577#121—6724no—
578#121—6712no—
579#121—6712no—
580#121—6724no—
581#121C22×D67112yes—
582C4×Q8—672no—
583C4×Q8—676no—
584C4×Q8—676no—
585C4×Q8C22×D6712yes—
586C4×D4—676no—
587C4×D4—6712no—
588C4×D4—6712no—
589C4×D4—6724no—
590C4×D4—676no—
591C4×D4—6712no—
592C4×D4—6712no—
593C4×D4—6724no—
594C4×D4—676no—
595C4×D4—6712no—
596C4×D4C22×D6716yes—
597C4×D4C22×D67112yes—
598#117—673no—
599#117—676no—
600#117—676no—
601#117—676no—
602#117C22×D6713yes—
603C2×C4⋊C4—6724no—
604C2×C4⋊C4—6712no—
605C2×C4⋊C4—6712no—
606C2×C4⋊C4—6724no—
607C2×C4⋊C4—6724no—
608C2×C4⋊C4—6724no—
609C2×C4⋊C4—676no—
610C2×C4⋊C4C22×D67112yes—
611C2×C22⋊C4—676no—
612C2×C22⋊C4—6724no—
613C2×C42—676no—
614C2×C42—673no—
615C2×C42—673no—
616C2×C42—676no—
617C2×C42—676no—
618C2×C42—673no—
619C2×C42—673no—
620C2×C42—671no—
621C2×C42C22×D6713yes—
622C24—673no—
623C24—674no—
624#41—248no—
625#41—224no—
626#41—678no—
627#41—6724no—
628#41—6724no—
629#41—13448no—
630#41—13496no—
631#41—13448no—
632#41—13448no—
633#41—13424no—
634#41—13424no—
635#41—13496no—
636#41—13448no—
637#41—13448no—
638#41—13424no—
639#41D4×D6718yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—678no—
643C2×Q8—673no—
644C2×Q8—6724no—
645C2×Q8—6712no—
646C2×Q8—6712no—
647C2×Q8—676no—
648C2×Q8—13448no—
649C2×Q8—13448no—
650C2×Q8—13424no—
651C2×Q8—13448no—
652C2×Q8—13448no—
653C2×Q8—13448no—
654C2×Q8—13448no—
655C2×Q8—13416no—
656C2×Q8—13424no—
657C2×Q8C23×D67112yes—
658C2×Q8C23×D6716yes—
659C2×Q8C23×D6711yescharacteristic
660C2×D4—676no—
661C2×D4—6724no—
662C2×D4—678no—
663C2×D4—6712no—
664C2×D4—6712no—
665C2×D4—674no—
666C2×D4—673no—
667C2×D4—674no—
668C2×D4—6712no—
669C2×D4—672no—
670C2×D4—1348no—
671C2×D4—13416no—
672C2×D4—13448no—
673C2×D4C23×D6714yes—
674C2×D4C23×D67112yes—
675C2×D4C23×D6712yes—
676C2×D4C23×D6713yes—
677C22×C4—673no—
678C22×C4—6724no—
679C22×C4—672no—
680C22×C4—671no—
681C22×C4—673no—
682C22×C4—673no—
683C22×C4—673no—
684C22×C4—676no—
685C22×C4—6712no—
686C22×C4—6712no—
687C22×C4—676no—
688C22×C4—676no—
689C22×C4—676no—
690C22×C4—6712no—
691C22×C4—6724no—
692C22×C4—6712no—
693C22×C4—6712no—
694C22×C4—13448no—
695C22×C4—13424no—
696C22×C4—13448no—
697C22×C4C23×D6716yes—
698C22×C4C23×D67112yes—
699C22×C4C23×D67112yes—
700C22×C4C23×D6713yes—
701C4⋊C4—6724no—
702C4⋊C4—6712no—
703C4⋊C4—6748no—
704C4⋊C4—6724no—
705C4⋊C4—6712no—
706C4⋊C4—676no—
707C4⋊C4C23×D67112yes—
708C4⋊C4C23×D67124yes—
709C4⋊C4C23×D6716yes—
710C22⋊C4—676no—
711C22⋊C4—6724no—
712C22⋊C4—6712no—
713C22⋊C4—6724no—
714C22⋊C4—6724no—
715C22⋊C4C23×D6716yes—
716C22⋊C4C23×D67124yes—
717C42—671no—
718C42—672no—
719C42—676no—
720C42—673no—
721C42—676no—
722C42—676no—
723C42—676no—
724C42C23×D6711yescharacteristic
725C42C23×D6713yes—
726C42C23×D6716yes—
727C23—671no—
728C23—6712no—
729C23—673no—
730C23—674no—
731C23—1348no—
732C23—13416no—
733C23—13412no—
734C23C24×D6714yes—
735C23C24×D6713yes—
736Q8—224no—
737Q8—212no—
738Q8—6712no—
739Q8—13424no—
740Q8—13448no—
741Q8—13424no—
742Q8—13412no—
743Q8C2×D4×D6714yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—6724no—
748D4—6712no—
749D4—13424no—
750D4—1348no—
751D4—13416no—
752D4—13424no—
753D4—13424no—
754D4—1344no—
755D4—1348no—
756D4C2×D4×D67112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—6712no—
761C2×C4—672no—
762C2×C4—671no—
763C2×C4—673no—
764C2×C4—674no—
765C2×C4—6712no—
766C2×C4—6712no—
767C2×C4—6712no—
768C2×C4—678no—
769C2×C4—676no—
770C2×C4—6712no—
771C2×C4—13424no—
772C2×C4—13412no—
773C2×C4—13424no—
774C2×C4—13448no—
775C2×C4—13412no—
776C2×C4—13424no—
777C2×C4—13412no—
778C2×C4—13424no—
779C2×C4—13424no—
780C2×C4—13412no—
781C2×C4C2×D4×D67112yes—
782C2×C4C24×D6716yes—
783C2×C4C24×D67112yes—
784C2×C4C24×D6711yescharacteristic
785C2×C4C24×D6713yes—
786C2×C4C24×D6712yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—26816no—
791C22—672no—
792C22—674no—
793C22—676no—
794C22—13424no—
795C22—1344no—
796C22—1348no—
797C22—1346no—
798C22C22×D4×D6716yes—
799C22C25×D6711yescharacteristic
800C4—212no—
801C4—26no—
802C4—672no—
803C4—676no—
804C4—674no—
805C4—13412no—
806C4—1346no—
807C4C22×D4×D6716yes—
808C4C22×D4×D6712yes—
809C42−1+4×D6714yescomplemented
810C2—26no—
811C2—44no—
812C2—2684no—
813C2—674no—
814C2—1346no—
815C2C23×D4×D6711yescharacteristic
816C2C2×2−1+4×D6712yes—
subgroupG/H
center, FrattiniC22C25×D67
commutator, socle, cosocleC22×C67C26
FittingC67×#3499C2
hypercenter#3499D67
hypocenterC67C2×#3499
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D67C2semidirect
2. #22573994C2semidirect
3. #22573993C2semidirect
4. #22573992C2semidirect
5. #22573991C2semidirect
6. #22573990C2semidirect
7. #22573989C2semidirect
8. #22573988C2semidirect
9. D4×Q8×D67C2semidirect
10. #547×D67C2semidirect
11. #536×D67C2semidirect
12. #532×D67C2semidirect
13. C2×C4⋊Q8×D67C2semidirect
14. C4×#41×D67C2semidirect
15. C67×#3499C2semidirect
16. C2×#14524091C22semidirect
17. C2×#14524091C22semidirect
18. C2×#14524090C22semidirect
19. C2×#14524090C22semidirect
20. C2×#14524090C22semidirect
27. Q8×D268C22semidirect
28. D4×Dic134C22semidirect
29. #16864061C22semidirect
30. Q8×C22⋊D67C22semidirect
31. #16864059C22semidirect
32. #16864051C22semidirect
33. #16864050C22semidirect
34. #16864049C22semidirect
35. #16864048C22semidirect
36. #16864047C22semidirect
37. #16864046C22semidirect
38. #16864045C22semidirect
39. #16864044C22semidirect
40. #16863972C22semidirect
41. #16863971C22semidirect
42. #16863970C22semidirect
43. #16863969C22semidirect
44. #16863968C22semidirect
45. #16863967C22semidirect
46. #16863966C22semidirect
47. #16863947C22semidirect
48. #16863946C22semidirect
49. #16863945C22semidirect
50. #16863944C22semidirect
51. #16863943C22semidirect
52. #16863942C22semidirect
53. #16863941C22semidirect
54. C2×#14524043C22semidirect
55. C2×#14524042C22semidirect
56. C2×#14524041C22semidirect
60. C4⋊Q8×D67C22semidirect
61. C4⋊Q8×D67C22semidirect
62. C4⋊Q8×D67C22semidirect
68. #41×Dic67C22semidirect
69. C4×#11761629C22semidirect
70. C4×#11761628C22semidirect
71. #16863864C22semidirect
72. C4×#11761627C22semidirect
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
106. #41×D67D4semidirect
217. #11761629C2×D4semidirect
222. #11761628C2×D4semidirect
227. #11761627C2×D4semidirect
296. #41×C67C2×D4semidirect
372. C4×D672−1+4semidirect
395. C4×C67C2×2−1+4semidirect
400. Dic67C2×2−1+4semidirect
408. D67#3499direct (N × H)
417. #3499D67direct (N × H)
424. C67C2×#3499semidirect
431. C2×2−1+4C2×D67semidirect
442. D4×Q8C2×D67semidirect
451. #547C2×D67semidirect
459. #536C2×D67semidirect
467. #532C2×D67semidirect
477. C2×C4⋊Q8C2×D67semidirect
488. C4×#41C2×D67semidirect
639. #41D4×D67semidirect
809. C42−1+4×D67semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D672
#225739942
#225739932
#225739922
#225739912
#225739902
#225739892
#225739882
D4×Q8×D672
#547×D672
#536×D672
#532×D672
C2×C4⋊Q8×D672
C4×#41×D672
C67×#34992
C2×#349967