Finite Group Databasebeta

← #10576501

Subgroups — #10576501

Order 512.

6625 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#61324C216yesmaximal, complemented
4#61323C216yesmaximal, complemented
5#61322C212yesmaximal, complemented
6#61321C212yesmaximal, complemented
7#61320C216yesmaximal, complemented
8#61319C212yesmaximal, complemented
9#61318C216yesmaximal, complemented
10#61317C212yesmaximal, complemented
11#61316C2112yesmaximal, complemented
12#61303C214yesmaximal, complemented
13#60618C213yesmaximal, complemented
14#60484C213yesmaximal, complemented
15#60415C213yesmaximal, complemented
16C2×Q8×M16C211yesmaximal, characteristic, complemented
17C4×#575C213yesmaximal, complemented
18C2×#575C2213yes—
19#3480—21no—
20#3480—23no—
21#3480—21no—
22#3480—23no—
23#3480C2212yes—
24#3480C2216yes—
25#3480C2212yescomplemented
26#3480C2216yescomplemented
27C2×#559C2213yescomplemented
28Q8×#41—21no—
29Q8×#41—23no—
30Q8×#41—21no—
31Q8×#41—23no—
32Q8×#41C2212yes—
33Q8×#41C2216yes—
34Q8×#41C2212yescomplemented
35Q8×#41C2216yescomplemented
36C2×Q82C2211yescharacteristic, complemented
37C2×#557C2211yescharacteristic, complemented
38C2×#557C2213yescomplemented
39C2×#556C2213yescomplemented
40C2×#554—23no—
41C2×#554C2213yescomplemented
42C2×#553—23no—
43C2×#550C2211yescharacteristic, complemented
44C2×D4×Q8—21no—
45C2×D4×Q8C2211yescharacteristic, complemented
46C2×#548—21no—
47C2×#533—23no—
48C2×#533C2213yes—
49C2×#532C2213yes—
50C2×#529—23no—
51C2×C4×#41—21no—
52C2×C4×#41C2213yes—
53C2×C4×#41C2213yes—
54C22×C4×Q8—21no—
55C22×C4×Q8C2211yescharacteristic
56#3377C22124yescomplemented
57#3376C22124yescomplemented
58#3375C22112yescomplemented
59#3374C22112yescomplemented
60#3373C22112yescomplemented
61#3372C22112yescomplemented
62#3371C22124yescomplemented
63#3370C22124yescomplemented
64#3369C22112yescomplemented
65#3368C22112yescomplemented
66#3367C22112yescomplemented
67#3366C22112yescomplemented
68#3365C22112yescomplemented
69#3364C22112yescomplemented
70#3363C2214yescomplemented
71#3362C2214yescomplemented
72#3361C22112yescomplemented
73#3360C22112yescomplemented
74#3359C2214yescomplemented
75#3358C2214yescomplemented
76#3142C22112yescomplemented
77#3141C2216yescomplemented
78#3141C2216yescomplemented
79#3140C22112yescomplemented
80#3139C2216yescomplemented
81#3138C2216yescomplemented
82#3135C22112yescomplemented
83#3131C22112yescomplemented
84#3080C22112yescomplemented
85#3079C2216yescomplemented
86#3079C2216yescomplemented
87#3078C2216yescomplemented
88#3078C2216yescomplemented
89#3077C2216yescomplemented
90#3077C2216yescomplemented
91#3076C22112yescomplemented
92#3076C22112yescomplemented
93#3040C22112yes—
94#3039C2216yes—
95#3038C2216yes—
96#3037C2216yescomplemented
97#3037C2216yescomplemented
98#3036C2216yescomplemented
99#3036C2216yescomplemented
100#3035C22112yescomplemented
101#3035C22112yescomplemented
102Q8×M16C2212yescomplemented
103Q8×M16C2216yescomplemented
104Q8×M16C2212yescomplemented
105Q8×M16C2216yescomplemented
106C2×#446C2216yescomplemented
107C2×C8×Q8C2212yescomplemented
108C4×#137C2216yes—
109C4×#137C2216yes—
110C4×#137C2216yescomplemented
111C4×#137C2216yescomplemented
112C4×AGL(1,ℤ/8)C2216yes—
113C4×AGL(1,ℤ/8)C2216yes—
114C4×AGL(1,ℤ/8)C2216yescomplemented
115C4×AGL(1,ℤ/8)C2216yescomplemented
116#2943C22112yescomplemented
117C4×#135C22112yescomplemented
118#2911C2213yes—
119C2×#423C2213yes—
120#2896C2216yes—
121#2896C2213yes—
122#2896C2211yescharacteristic
123C2×C4×M16C2213yes—
124C22×#41—21no—
125C22×#41C2313yes—
126C22×#41C2311yescharacteristic
127C23×Q8—21no—
128C23×Q8D411yescharacteristic
129#575—224no—
130C2×#137C2316yes—
131C2×#137C2316yes—
132C2×AGL(1,ℤ/8)C2316yes—
133C2×AGL(1,ℤ/8)C2316yes—
134C2×#135C23112yes—
135C22×M16C2311yescharacteristic
136C22×M16C2313yes—
137#559—23no—
138#559—26no—
139#559—23no—
140#559C2316yes—
141#559C23112yes—
142#559C2316yes—
143Q82—21no—
144Q82—23no—
145Q82C2312yes—
146Q82C2316yes—
147#557—23no—
148#557—23no—
149#557—26no—
150#557—21no—
151#557—23no—
152#557C2312yes—
153#557C2316yes—
154#557C2316yes—
155#557C2316yes—
156#557C23112yes—
157#556—23no—
158#556—26no—
159#556—23no—
160#556C2316yes—
161#556C2316yes—
162#556C23112yes—
163#554—23no—
164#554—23no—
165#554—26no—
166#554—26no—
167#554—26no—
168#554—212no—
169#554—26no—
170#554—26no—
171#554—212no—
172#554C2316yes—
173#554C2316yes—
174#554C23112yes—
175#553—26no—
176#553—212no—
177#553—26no—
178#553—26no—
179#553—26no—
180#553—212no—
181#550—21no—
182#550—23no—
183#550C2312yes—
184#550C2316yes—
185D4×Q8—22no—
186D4×Q8—26no—
187D4×Q8—22no—
188D4×Q8—26no—
189D4×Q8—21no—
190D4×Q8—23no—
191D4×Q8C2312yes—
192D4×Q8C2316yes—
193#548—22no—
194#548—26no—
195#548—22no—
196#548—26no—
197#533—26no—
198#533—212no—
199#533—26no—
200#533—26no—
201#533—26no—
202#533—212no—
203#533—23no—
204#533—23no—
205#533—23no—
206#533—23no—
207#533C2316yes—
208#533C2316yes—
209#533C2316yes—
210#533C2316yes—
211#532—23no—
212#532—23no—
213#532—23no—
214#532—23no—
215#532C2316yes—
216#532C2316yes—
217#532C2316yes—
218#532C2316yes—
219C2×C4⋊Q8—23no—
220C2×C4⋊Q8—23no—
221C2×C4⋊Q8C2313yes—
222C2×C4⋊Q8C2313yes—
223C2×C4⋊Q8C2313yes—
224C2×#127C2313yes—
225#529—26no—
226#529—212no—
227#529—26no—
228#529—26no—
229#529—26no—
230#529—212no—
231C2×#126—26no—
232C2×#125—23no—
233C2×#125—26no—
234C2×#125C2316yes—
235C2×#124—23no—
236C2×#124C2316yes—
237C2×#123—26no—
238C2×C22⋊Q8—23no—
239C2×C22⋊Q8—23no—
240C2×C22⋊Q8—23no—
241C2×C22⋊Q8—23no—
242C2×C22⋊Q8—23no—
243C2×C22⋊Q8—26no—
244C2×#121—23no—
245C2×#121—23no—
246C2×#121—23no—
247C4×#41—22no—
248C4×#41—26no—
249C4×#41—22no—
250C4×#41—26no—
251C4×#41—23no—
252C4×#41—23no—
253C4×#41—23no—
254C4×#41—23no—
255C4×#41—23no—
256C4×#41—23no—
257C4×#41—23no—
258C4×#41—23no—
259C4×#41C2316yes—
260C4×#41C2316yes—
261C4×#41C2316yes—
262C4×#41C2316yes—
263C4×#41C2316yes—
264C4×#41C2316yes—
265C4×#41C2316yes—
266C4×#41C2316yes—
267C2×C4×Q8—21no—
268C2×C4×Q8—21no—
269C2×C4×Q8—22no—
270C2×C4×Q8—26no—
271C2×C4×Q8—22no—
272C2×C4×Q8—26no—
273C2×C4×Q8—23no—
274C2×C4×Q8—23no—
275C2×C4×Q8—23no—
276C2×C4×Q8D411yescharacteristic
277C2×C4×Q8D411yescharacteristic
278C2×C4×Q8D413yes—
279C2×C4×Q8D413yes—
280C2×C4×Q8D411yescharacteristic
281C2×C4×Q8D413yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×D4—23no—
293C2×C4×D4—23no—
294C2×C4×D4—23no—
295C2×C4×D4—23no—
296C2×C4×D4—23no—
297C2×C4×D4—23no—
298C2×C4×D4—23no—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×#117—23no—
304C2×#117—23no—
305C2×#117—23no—
306C2×#117C2313yes—
307C2×#117C2311yescharacteristic
308C22×C4⋊C4—23no—
309C22×C4⋊C4D413yes—
310C22×C42—23no—
311C22×C42—23no—
312C22×C42C2313yes—
313#491C23124yes—
314#490C23124yes—
315#489C23124yes—
316#489C23124yes—
317#488C23124yes—
318#488C23124yes—
319#487C23112yes—
320#487C23112yes—
321#486C23112yes—
322#486C23112yes—
323#479C23124yes—
324#479C23124yes—
325#478C23124yes—
326#478C23124yes—
327#477C23112yes—
328#477C23112yes—
329#476C23112yes—
330#476C23112yes—
331#475C23112yes—
332#475C23112yes—
333#474C23112yes—
334#474C23112yes—
335#464C23124yes—
336#464C23124yes—
337#463C23124yes—
338#463C23124yes—
339#462C23112yes—
340#462C23112yes—
341#461C23112yes—
342#461C23112yes—
343#460C23112yes—
344#460C23112yes—
345#459C23112yes—
346#459C23112yes—
347#446C23112yes—
348#446C23112yes—
349#446C23124yes—
350C8×Q8C2314yes—
351C8×Q8C23112yes—
352#442C23112yes—
353#442C23112yes—
354#441C23112yes—
355#441C23112yes—
356#440C23112yes—
357#440C23112yes—
358#440C23112yes—
359#440C23112yes—
360C4×Q16C23112yes—
361C4×Q16C23112yes—
362C4×SD16C23112yes—
363C4×SD16C23112yes—
364C4×SD16C23112yes—
365C4×SD16C23112yes—
366C4×D8C23112yes—
367C4×D8C23112yes—
368#428C2316yes—
369#428C2316yes—
370#428C2316yes—
371#428C2316yes—
372#427C23112yes—
373#423C2316yes—
374#423C2316yes—
375#423C2316yes—
376#423C2316yes—
377C2×C4⋊C8C2316yes—
378C2×C4⋊C8C2316yes—
379#419C23112yes—
380#419C2316yes—
381#419C2312yes—
382#418C23112yes—
383#418C2316yes—
384#418C2312yes—
385#417C23112yes—
386#417C23112yes—
387#417C2316yes—
388#417C2316yes—
389#417C2312yes—
390#417C2312yes—
391#416C23124yes—
392#416C23112yes—
393#416C2314yes—
394C4×M16C2316yes—
395C4×M16C2316yes—
396C4×M16C2316yes—
397C4×M16C2316yes—
398C2×#97C2316yes—
399C2×C4×C8C2316yes—
400C2×#41—26no—
401C2×#41—22no—
402C2×#41—21no—
403C2×#41—21no—
404C2×#41—23no—
405C2×#41—23no—
406C2×#41—24no—
407C2×#41—212no—
408C2×#41—212no—
409C2×#41—48no—
410C2×#41#4118yescomplemented
411C2×#41C2416yes—
412C2×#41C2416yes—
413C2×#41C2412yes—
414C2×#41C2412yes—
415C22×Q8—26no—
416C22×Q8—22no—
417C22×Q8—23no—
418C22×Q8—23no—
419C22×Q8—44no—
420C22×Q8—48no—
421C22×Q8C2×D411yescharacteristic
422C22×Q8C2×D411yescharacteristic
423C22×Q8C2×D411yescharacteristic
424C22×Q8C2×D413yes—
425C22×Q8C2×D413yes—
426C22×Q8C2×D413yes—
427C22×Q8C2413yes—
428C22×Q8C2411yescharacteristic
429C22×D4—21no—
430C22×D4—23no—
431C22×D4—23no—
432C22×D4—23no—
433C22×D4C2413yes—
434C22×D4C2411yescharacteristic
435C23×C4—21no—
436C23×C4—23no—
437C23×C4—23no—
438C23×C4—23no—
439C23×C4—23no—
440C23×C4—23no—
441C23×C4C2×D413yes—
442C23×C4C2×D413yes—
443C23×C4C2411yescharacteristic
444#137—224no—
445#137—224no—
446AGL(1,ℤ/8)—224no—
447AGL(1,ℤ/8)—224no—
448#135—248no—
449C2×Q16C24112yes—
450C2×SD16C24112yes—
451C2×SD16C24112yes—
452C2×D8C24112yes—
453C2×M16—212no—
454C2×M16—24no—
455C2×M16C2416yes—
456C2×M16C2416yes—
457C2×M16C2412yes—
458C2×M16C2412yes—
459C22×C8C2416yes—
460C22×C8C2412yes—
461C4⋊Q8—26no—
462C4⋊Q8—26no—
463C4⋊Q8—212no—
464C4⋊Q8—26no—
465C4⋊Q8—26no—
466C4⋊Q8—212no—
467C4⋊Q8—23no—
468C4⋊Q8—23no—
469C4⋊Q8—23no—
470C4⋊Q8—23no—
471C4⋊Q8—23no—
472C4⋊Q8—23no—
473C4⋊Q8C2416yes—
474C4⋊Q8C2416yes—
475C4⋊Q8C2416yes—
476C4⋊Q8C2416yes—
477C4⋊Q8C2416yes—
478C4⋊Q8C2416yes—
479#127—23no—
480#127—23no—
481#127C2416yes—
482#127C2416yes—
483#126—212no—
484#126—212no—
485#126—212no—
486#126—212no—
487#125—26no—
488#125—212no—
489#125—26no—
490#125—212no—
491#125—212no—
492#125—212no—
493#125—212no—
494#125—26no—
495#125—26no—
496#125C24112yes—
497#125C24112yes—
498#124—26no—
499#124—26no—
500#124—212no—
501#124—26no—
502#124—26no—
503#124C24112yes—
504#124C24112yes—
505#123—212no—
506#123—212no—
507#123—212no—
508#123—212no—
509C22⋊Q8—26no—
510C22⋊Q8—26no—
511C22⋊Q8—212no—
512C22⋊Q8—26no—
513C22⋊Q8—26no—
514C22⋊Q8—212no—
515C22⋊Q8—26no—
516C22⋊Q8—26no—
517C22⋊Q8—26no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—26no—
521C22⋊Q8—26no—
522C22⋊Q8—26no—
523C22⋊Q8—26no—
524C22⋊Q8—26no—
525C22⋊Q8—212no—
526C22⋊Q8—212no—
527C22⋊Q8—212no—
528C22⋊Q8—212no—
529C22⋊Q8—212no—
530#121—26no—
531#121—26no—
532#121—26no—
533#121—26no—
534#121—26no—
535#121—26no—
536#121—26no—
537#121—26no—
538#121—26no—
539#121—212no—
540#121—26no—
541C4×Q8—26no—
542C4×Q8—22no—
543C4×Q8—26no—
544C4×Q8—22no—
545C4×Q8—26no—
546C4×Q8—26no—
547C4×Q8—212no—
548C4×Q8—26no—
549C4×Q8—26no—
550C4×Q8—26no—
551C4×Q8—26no—
552C4×Q8—26no—
553C4×Q8—26no—
554C4×Q8—26no—
555C4×Q8—26no—
556C4×Q8—23no—
557C4×Q8—23no—
558C4×Q8—23no—
559C4×Q8—23no—
560C4×Q8—23no—
561C4×Q8—23no—
562C4×Q8—23no—
563C4×Q8—23no—
564C4×Q8C2×D411yescharacteristic
565C4×Q8C2×D413yes—
566C4×Q8C2×D411yescharacteristic
567C4×Q8C2×D413yes—
568C4×Q8C2×D413yes—
569C4×Q8C2×D411yescharacteristic
570C4×Q8C2×D413yes—
571C4×Q8C2×D413yes—
572C4×Q8C2×D416yes—
573C4×Q8C2×D413yes—
574C4×Q8C2×D416yes—
575C4×Q8C2×D413yes—
576C4×Q8C2×D413yes—
577C4×Q8C2×D416yes—
578C4×Q8C2×D413yes—
579C4×Q8C2416yes—
580C4×Q8C2416yes—
581C4×Q8C2416yes—
582C4×Q8C2416yes—
583C4×Q8C2416yes—
584C4×Q8C2416yes—
585C4×Q8C2416yes—
586C4×Q8C2416yes—
587C4×Q8C2411yescharacteristic
588C4×Q8C2413yes—
589C4×Q8C2413yes—
590C4×Q8C2413yes—
591C4×Q8C2416yes—
592C4×D4—26no—
593C4×D4—26no—
594C4×D4—26no—
595C4×D4—26no—
596C4×D4—26no—
597C4×D4—26no—
598C4×D4—26no—
599C4×D4—26no—
600C4×D4—26no—
601C4×D4—26no—
602C4×D4—26no—
603C4×D4—26no—
604C4×D4—26no—
605C4×D4—26no—
606C4×D4—26no—
607C4×D4—26no—
608C4×D4—26no—
609C4×D4—212no—
610C4×D4—26no—
611C4×D4—26no—
612C4×D4—26no—
613C4×D4—26no—
614C4×D4—26no—
615C4×D4—26no—
616C4×D4—26no—
617C4×D4—26no—
618C4×D4—26no—
619C4×D4—23no—
620C4×D4—23no—
621C4×D4—23no—
622C4×D4—23no—
623C4×D4—23no—
624C4×D4—23no—
625C4×D4—23no—
626C4×D4—23no—
627C4×D4C2416yes—
628C4×D4C2416yes—
629C4×D4C2416yes—
630C4×D4C2416yes—
631C4×D4C2416yes—
632C4×D4C2416yes—
633C4×D4C2416yes—
634C4×D4C2416yes—
635#117—21no—
636#117—21no—
637#117—23no—
638#117—23no—
639#117—26no—
640#117—212no—
641#117—26no—
642#117—26no—
643#117—26no—
644#117—26no—
645#117—26no—
646#117—26no—
647#117—26no—
648#117—26no—
649#117—26no—
650#117C2412yes—
651#117C2412yes—
652#117C2416yes—
653#117C2416yes—
654C2×C4⋊C4—26no—
655C2×C4⋊C4—23no—
656C2×C4⋊C4—23no—
657C2×C4⋊C4—23no—
658C2×C4⋊C4—23no—
659C2×C4⋊C4—23no—
660C2×C4⋊C4—23no—
661C2×C4⋊C4—23no—
662C2×C4⋊C4—23no—
663C2×C4⋊C4—26no—
664C2×C4⋊C4—26no—
665C2×C4⋊C4—26no—
666C2×C4⋊C4—212no—
667C2×C4⋊C4C2×D413yes—
668C2×C4⋊C4C2×D413yes—
669C2×C4⋊C4C2×D413yes—
670C2×C4⋊C4C2×D416yes—
671C2×C4⋊C4C2×D413yes—
672C2×C4⋊C4C2×D416yes—
673C2×C4⋊C4C2×D413yes—
674C2×C4⋊C4C2×D413yes—
675C2×C4⋊C4C2×D416yes—
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—23no—
682C2×C22⋊C4—26no—
683C2×C22⋊C4—23no—
684C2×C22⋊C4—23no—
685C2×C22⋊C4—23no—
686C2×C22⋊C4—23no—
687C2×C22⋊C4—26no—
688C2×C42—21no—
689C2×C42—23no—
690C2×C42—23no—
691C2×C42—23no—
692C2×C42—23no—
693C2×C42—23no—
694C2×C42—26no—
695C2×C42—26no—
696C2×C42—26no—
697C2×C42—26no—
698C2×C42—26no—
699C2×C42—26no—
700C2×C42—26no—
701C2×C42—26no—
702C2×C42C2×D413yes—
703C2×C42C2×D413yes—
704C2×C42C2×D413yes—
705C2×C42C2×D413yes—
706C2×C42C2×D413yes—
707C2×C42C2×D413yes—
708C2×C42C2413yes—
709C2×C42C2413yes—
710C2×C42C2413yes—
711C2×C42C2413yes—
712C2×C42C2413yes—
713C2×C42C2413yes—
714#107C24112yes—
715#107C24112yes—
716#106C24112yes—
717#106C24112yes—
718C4⋊C8C24112yes—
719C4⋊C8C24112yes—
720C4⋊C8C24112yes—
721C4⋊C8C24112yes—
722#103C2414yes—
723#103C2414yes—
724#103C24112yes—
725#103C24112yes—
726#103C24124yes—
727#103C24124yes—
728#102C2414yes—
729#102C2414yes—
730#102C24112yes—
731#102C24112yes—
732#102C24124yes—
733#102C24124yes—
734#97C24112yes—
735#97C24112yes—
736C4×C8C24112yes—
737C4×C8C24112yes—
738C24—21no—
739C24—23no—
740C24C22×D411yescharacteristic
741#41—28no—
742#41—28no—
743#41—24no—
744#41—24no—
745#41—212no—
746#41—212no—
747#41—212no—
748#41—212no—
749#41—424no—
750#41—48no—
751#41—412no—
752#41—412no—
753#41C2×#4118yes—
754#41C2×#4118yescomplemented
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—24no—
758C2×Q8—21no—
759C2×Q8—26no—
760C2×Q8—26no—
761C2×Q8—23no—
762C2×Q8—26no—
763C2×Q8—26no—
764C2×Q8—22no—
765C2×Q8—26no—
766C2×Q8—26no—
767C2×Q8—46no—
768C2×Q8—46no—
769C2×Q8—46no—
770C2×Q8—412no—
771C2×Q8—424no—
772C2×Q8—48no—
773C2×Q8—86no—
774C2×Q8C22×D413yes—
775C2×Q8C22×D413yes—
776C2×Q8C22×D413yes—
777C2×Q8C22×D416yes—
778C2×Q8C22×D411yescharacteristic
779C2×Q8C2×#4114yescomplemented
780C2×Q8C2516yes—
781C2×Q8C2512yes—
782C2×D4—28no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—26no—
786C2×D4—26no—
787C2×D4—21no—
788C2×D4—26no—
789C2×D4—26no—
790C2×D4—23no—
791C2×D4—26no—
792C2×D4—26no—
793C2×D4—26no—
794C2×D4—22no—
795C2×D4—26no—
796C2×D4—412no—
797C2×D4—412no—
798C2×D4—86no—
799C2×D4C2×#4114yescomplemented
800C2×D4C2516yes—
801C2×D4C2512yes—
802C22×C4—21no—
803C22×C4—28no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—23no—
809C22×C4—23no—
810C22×C4—23no—
811C22×C4—26no—
812C22×C4—26no—
813C22×C4—26no—
814C22×C4—26no—
815C22×C4—26no—
816C22×C4—26no—
817C22×C4—26no—
818C22×C4—26no—
819C22×C4—26no—
820C22×C4—26no—
821C22×C4—46no—
822C22×C4—412no—
823C22×C4—412no—
824C22×C4—412no—
825C22×C4—83no—
826C22×C4—86no—
827C22×C4—86no—
828C22×C4C22×D413yes—
829C22×C4C22×D413yes—
830C22×C4C22×D413yes—
831C22×C4C22×D413yes—
832C22×C4C22×D413yes—
833C22×C4C22×D413yes—
834C22×C4C22×D413yes—
835C22×C4C22×D413yes—
836C22×C4C22×D413yes—
837C22×C4C22×D413yes—
838C22×C4C22×D413yes—
839C22×C4C22×D413yes—
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C2×#4114yes—
844C22×C42−1+414yes—
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848Q16—224no—
849SD16—224no—
850SD16—224no—
851D8—224no—
852M16—212no—
853M16—212no—
854M16—24no—
855M16—24no—
856C2×C8—212no—
857C2×C8—24no—
858C2×C8C2514yes—
859C2×C8C25112yes—
860C4⋊C4—212no—
861C4⋊C4—212no—
862C4⋊C4—26no—
863C4⋊C4—26no—
864C4⋊C4—26no—
865C4⋊C4—26no—
866C4⋊C4—26no—
867C4⋊C4—26no—
868C4⋊C4—26no—
869C4⋊C4—26no—
870C4⋊C4—26no—
871C4⋊C4—26no—
872C4⋊C4—26no—
873C4⋊C4—26no—
874C4⋊C4—26no—
875C4⋊C4—26no—
876C4⋊C4—26no—
877C4⋊C4—26no—
878C4⋊C4—212no—
879C4⋊C4—212no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—23no—
883C4⋊C4—23no—
884C4⋊C4C22×D413yes—
885C4⋊C4C22×D413yes—
886C4⋊C4C22×D416yes—
887C4⋊C4C22×D416yes—
888C4⋊C4C22×D413yes—
889C4⋊C4C22×D416yes—
890C4⋊C4C22×D413yes—
891C4⋊C4C22×D416yes—
892C4⋊C4C22×D416yes—
893C4⋊C4C22×D416yes—
894C4⋊C4C2516yes—
895C4⋊C4C2516yes—
896C4⋊C4C2512yes—
897C4⋊C4C2512yes—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—26no—
901C22⋊C4—26no—
902C22⋊C4—212no—
903C22⋊C4—212no—
904C22⋊C4—26no—
905C22⋊C4—26no—
906C22⋊C4—26no—
907C22⋊C4—26no—
908C22⋊C4—26no—
909C22⋊C4—26no—
910C22⋊C4—26no—
911C22⋊C4—26no—
912C22⋊C4—212no—
913C22⋊C4—212no—
914C42—22no—
915C42—26no—
916C42—26no—
917C42—26no—
918C42—26no—
919C42—26no—
920C42—26no—
921C42—26no—
922C42—26no—
923C42—26no—
924C42—22no—
925C42—26no—
926C42C22×D413yes—
927C42C22×D413yes—
928C42C22×D413yes—
929C42C22×D413yes—
930C42C22×D413yes—
931C42C22×D413yes—
932C42C22×D413yes—
933C42C22×D413yes—
934C42C22×D413yes—
935C42C22×D413yes—
936C42C22×D413yes—
937C42C22×D413yes—
938C42C2513yes—
939C42C2513yes—
940C42C2513yes—
941C42C2513yes—
942C23—22no—
943C23—24no—
944C23—26no—
945C23—41no—
946C23—41no—
947C23—42no—
948C23—42no—
949C23—46no—
950C23—46no—
951C23—46no—
952C23#54814yes—
953C23C23×D411yescharacteristic
954C23C23×D411yescharacteristic
955C23C23×D411yescharacteristic
956Q8—22no—
957Q8—24no—
958Q8—26no—
959Q8—26no—
960Q8—26no—
961Q8—26no—
962Q8—26no—
963Q8—46no—
964Q8—412no—
965Q8—46no—
966Q8—412no—
967Q8—86no—
968Q8—86no—
969Q8#57514yescomplemented
970Q8C22×#4114yes—
971D4—28no—
972D4—28no—
973D4—26no—
974D4—22no—
975D4—26no—
976D4—24no—
977D4—412no—
978D4—412no—
979D4—412no—
980D4—46no—
981D4—412no—
982D4—86no—
983D4—86no—
984D4C22×#4114yes—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—28no—
989C2×C4—26no—
990C2×C4—26no—
991C2×C4—26no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—26no—
995C2×C4—26no—
996C2×C4—26no—
997C2×C4—43no—
998C2×C4—43no—
999C2×C4—43no—
1000C2×C4—43no—
1001C2×C4—43no—
1002C2×C4—43no—
1003C2×C4—43no—
1004C2×C4—43no—
1005C2×C4—43no—
1006C2×C4—412no—
1007C2×C4—412no—
1008C2×C4—42no—
1009C2×C4—46no—
1010C2×C4—42no—
1011C2×C4—46no—
1012C2×C4—46no—
1013C2×C4—412no—
1014C2×C4—412no—
1015C2×C4—412no—
1016C2×C4—412no—
1017C2×C4—86no—
1018C2×C4—86no—
1019C2×C4—86no—
1020C2×C4—86no—
1021C2×C4#54814yes—
1022C2×C4#54814yes—
1023C2×C4#54814yes—
1024C2×C4C23×D413yes—
1025C2×C4C23×D413yes—
1026C2×C4C23×D413yes—
1027C2×C4C23×D413yes—
1028C2×C4C23×D413yes—
1029C2×C4C23×D413yes—
1030C2×C4C23×D413yes—
1031C2×C4C23×D411yescharacteristic
1032C2×C4C23×D411yescharacteristic
1033C2×C4C23×D413yes—
1034C2×C4C23×D411yescharacteristic
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C2×2−1+412yes—
1039C2×C4C2×2−1+412yes—
1040C2×C4C2×2−1+412yes—
1041C2×C4C2611yescharacteristic
1042C8—212no—
1043C8—24no—
1044C22—21no—
1045C22—21no—
1046C22—21no—
1047C22—21no—
1048C22—21no—
1049C22—21no—
1050C22—24no—
1051C22—44no—
1052C22—48no—
1053C22—42no—
1054C22—42no—
1055C22—46no—
1056C22—46no—
1057C22—46no—
1058C22—812no—
1059C22C2×#54812yes—
1060C22C2×#54812yes—
1061C22C2×#54812yes—
1062C22C24×D411yescharacteristic
1063C4—23no—
1064C4—23no—
1065C4—23no—
1066C4—23no—
1067C4—23no—
1068C4—23no—
1069C4—23no—
1070C4—24no—
1071C4—42no—
1072C4—46no—
1073C4—42no—
1074C4—46no—
1075C4—46no—
1076C4C2×#54812yes—
1077C4C2×#54812yes—
1078C4C2×#54812yes—
1079C4C2×#57516yes—
1080C4C23×#4111yescharacteristic
1081C4C22×2−1+411yescharacteristic
1082C2—22no—
1083C2—22no—
1084C2—22no—
1085C2—44no—
1086C2—86no—
1087C2C22×#54811yescharacteristic
1088C2C22×#57511yescharacteristic
1089C2#6309011yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#41C2semidirect
2. C2×#3480C2semidirect
3. #61324C2semidirect
4. #61323C2semidirect
5. #61322C2semidirect
6. #61321C2semidirect
7. #61320C2semidirect
8. #61319C2semidirect
9. #61318C2semidirect
10. #61317C2semidirect
11. #61316C2semidirect
12. #61303C2semidirect
13. #60618C2semidirect
14. #60484C2semidirect
15. #60415C2semidirect
16. C2×Q8×M16C2semidirect
17. C4×#575C2semidirect
25. #3480C22semidirect
26. #3480C22semidirect
27. C2×#559C22semidirect
34. Q8×#41C22semidirect
35. Q8×#41C22semidirect
36. C2×Q82C22semidirect
37. C2×#557C22semidirect
38. C2×#557C22semidirect
39. C2×#556C22semidirect
41. C2×#554C22semidirect
43. C2×#550C22semidirect
45. C2×D4×Q8C22semidirect
56. #3377C22semidirect
57. #3376C22semidirect
58. #3375C22semidirect
59. #3374C22semidirect
60. #3373C22semidirect
61. #3372C22semidirect
62. #3371C22semidirect
63. #3370C22semidirect
64. #3369C22semidirect
65. #3368C22semidirect
66. #3367C22semidirect
67. #3366C22semidirect
68. #3365C22semidirect
69. #3364C22semidirect
70. #3363C22semidirect
71. #3362C22semidirect
72. #3361C22semidirect
73. #3360C22semidirect
74. #3359C22semidirect
75. #3358C22semidirect
76. #3142C22semidirect
77. #3141C22semidirect
78. #3141C22semidirect
79. #3140C22semidirect
80. #3139C22semidirect
81. #3138C22semidirect
82. #3135C22semidirect
83. #3131C22semidirect
84. #3080C22semidirect
85. #3079C22semidirect
86. #3079C22semidirect
87. #3078C22semidirect
88. #3078C22semidirect
89. #3077C22semidirect
90. #3077C22semidirect
91. #3076C22semidirect
92. #3076C22semidirect
96. #3037C22semidirect
97. #3037C22semidirect
98. #3036C22semidirect
99. #3036C22semidirect
100. #3035C22semidirect
101. #3035C22semidirect
102. Q8×M16C22semidirect
103. Q8×M16C22semidirect
104. Q8×M16C22semidirect
105. Q8×M16C22semidirect
106. C2×#446C22semidirect
107. C2×C8×Q8C22semidirect
110. C4×#137C22semidirect
111. C4×#137C22semidirect
114. C4×AGL(1,ℤ/8)C22semidirect
115. C4×AGL(1,ℤ/8)C22semidirect
116. #2943C22semidirect
117. C4×#135C22semidirect
410. C2×#41#41semidirect
754. #41C2×#41semidirect
779. C2×Q8C2×#41semidirect
799. C2×D4C2×#41semidirect
969. Q8#575semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#412
C2×#34802
#613242
#613232
#613222
#613212
#613202
#613192
#613182
#613172
#613162
#613032
#606182
#604842
#604152
C2×Q8×M162
C4×#5752