Finite Group Databasebeta

← #10579497

Subgroups — #10579497

Order 512.

7392 conjugacy classes of subgroups.

The subgroup lattice has 1121 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#62151C214yesmaximal, complemented
4#62137C2112yesmaximal, complemented
5#62110C216yesmaximal, complemented
6#62109C216yesmaximal, complemented
7#62096C212yesmaximal, complemented
8#62095C212yesmaximal, complemented
9Q8×AGL(1,ℤ/8)C212yesmaximal, complemented
10#61321C212yesmaximal, complemented
11#61252C216yesmaximal, complemented
12#61155C216yesmaximal, complemented
13#60916C213yesmaximal, complemented
14#60864C213yesmaximal, complemented
15#60558C213yesmaximal, complemented
16C2×#3077C213yesmaximal, complemented
17#60263C211yesmaximal, characteristic, complemented
18C23×#41—21no—
19#3523—21no—
20#3520—23no—
21#3518C2212yescomplemented
22#3515C2216yescomplemented
23#3511C2213yescomplemented
24#3509C2213yescomplemented
25#3503C2211yescharacteristic, complemented
26#3499C2211yescharacteristic, complemented
27#3495—23no—
28#3489—21no—
29#3482—21no—
30#3482—23no—
31Q8×#41C2212yescomplemented
32#3475C2216yescomplemented
33D4×#41—21no—
34D4×#41—23no—
35D4×#41—23no—
36D4×#41—21no—
37D4×#41C2212yes—
38D4×#41C2216yes—
39D4×#41C2216yes—
40D4×#41C2212yes—
41C2×#550C2211yescharacteristic
42C2×D4×Q8C2211yescharacteristic
43C2×#548—21no—
44C2×#547C2213yes—
45C2×#546—23no—
46C2×D42C2213yes—
47#3461—23no—
48#3444C2213yescomplemented
49C2×#533C2213yescomplemented
50C2×#532C2213yes—
51C2×#525—23no—
52C4×2−1+4—21no—
53C2×C4×#41C2211yescharacteristic
54C22×C4×D4C2213yes—
55#3386C22112yescomplemented
56#3384C22112yescomplemented
57Q8×SD16C2214yescomplemented
58Q8×D8C2214yescomplemented
59#3368C22112yescomplemented
60#3366C22112yescomplemented
61#3362C2214yescomplemented
62#3358C2214yescomplemented
63#3354C22112yescomplemented
64#3353C22112yescomplemented
65#3345C22124yescomplemented
66#3343C22124yescomplemented
67#3335C22112yescomplemented
68#3334C22112yescomplemented
69#3325C22112yescomplemented
70#3324C22112yescomplemented
71#3318C22124yescomplemented
72#3310C22124yescomplemented
73#3295C22112yescomplemented
74#3294C22112yescomplemented
75#3254C2216yescomplemented
76#3253C2216yescomplemented
77#3251C22112yescomplemented
78#3247C22112yescomplemented
79#3246C2216yescomplemented
80#3245C2216yescomplemented
81#3235C22112yescomplemented
82#3234C22112yescomplemented
83#3228C22112yescomplemented
84#3227C2216yescomplemented
85#3226C2216yescomplemented
86#3165C2216yescomplemented
87#3138C2216yescomplemented
88#3114C22112yescomplemented
89#3110C2216yescomplemented
90#3109C2216yescomplemented
91#3105C22112yescomplemented
92#3101C2216yescomplemented
93#3100C2216yescomplemented
94#3094C22112yescomplemented
95#3092C2216yescomplemented
96#3079C2216yescomplemented
97#3077C2213yes—
98#3077C2216yes—
99#3077C2216yescomplemented
100#3077C2216yescomplemented
101#3077C2213yescomplemented
102#3077C22112yescomplemented
103#3077C22112yescomplemented
104C2×#478C22112yescomplemented
105C2×#476C2216yescomplemented
106C2×#474C2216yescomplemented
107#3055C22112yescomplemented
108#3038C2216yescomplemented
109#3036C2211yescharacteristic
110#3036C2213yescomplemented
111#3003C2216yes—
112#2991C2212yescomplemented
113#2990C2216yescomplemented
114#2989C2216yescomplemented
115#2988C2212yescomplemented
116Q8×M16C2212yescomplemented
117C4×AGL(1,ℤ/8)C2216yes—
118C4×AGL(1,ℤ/8)C2216yescomplemented
119D4×M16C2216yescomplemented
120#2920C2213yescomplemented
121C2×#428C2216yescomplemented
122C2×#423C2213yescomplemented
123C2×#418C2216yes—
124C2×2−1+4—21no—
125C22×#41—26no—
126C22×#41—26no—
127C22×#41—22no—
128C22×#41—22no—
129C22×#41—21no—
130C22×#41—23no—
131C22×#41—23no—
132C22×#41—416no—
133C22×#41D411yescharacteristic
134C23×Q8—21no—
135C23×D4—23no—
136C23×D4C2313yes—
137C24×C4—23no—
138C2×AGL(1,ℤ/8)C2312yes—
139C2×AGL(1,ℤ/8)C2316yes—
140C22×M16C2316yes—
141Q82C2312yescomplemented
142#557—21no—
143#557—23no—
144#557C2316yescomplemented
145#556—23no—
146#556—23no—
147#556—26no—
148#556C2316yescomplemented
149#555C2316yescomplemented
150#554—26no—
151#554C2316yescomplemented
152#554C2316yescomplemented
153#553C23112yescomplemented
154#552—26no—
155#552—212no—
156#552—26no—
157#552—26no—
158#552C23112yescomplemented
159#551—212no—
160#550—21no—
161#550—23no—
162#550C2312yes—
163#550C2316yes—
164D4×Q8—22no—
165D4×Q8—21no—
166D4×Q8—23no—
167D4×Q8—21no—
168D4×Q8—23no—
169D4×Q8C2312yes—
170D4×Q8C2316yes—
171D4×Q8C2312yescomplemented
172#548—22no—
173#548—22no—
174#548—26no—
175#548—22no—
176#548—26no—
177#548—26no—
178#547—26no—
179#547—23no—
180#547—26no—
181#547—23no—
182#547—23no—
183#547—23no—
184#547C2316yes—
185#547C23112yes—
186#547C2316yes—
187#547C2316yescomplemented
188#546—26no—
189#546—26no—
190#546—212no—
191#546—26no—
192#546—26no—
193#546—26no—
194#546—212no—
195D42—23no—
196D42—23no—
197D42—26no—
198D42C2316yes—
199D42C23112yes—
200D42C2316yes—
201#544—23no—
202#542—26no—
203#542—26no—
204#541—26no—
205#541—26no—
206#539—212no—
207#537—23no—
208#536—23no—
209#536—23no—
210#533—26no—
211#533—23no—
212#533—23no—
213#533—23no—
214#533—23no—
215#533C2313yes—
216#533C2316yes—
217#533C2313yescomplemented
218#533C2313yescomplemented
219#533C2316yescomplemented
220#533C2316yescomplemented
221#532—23no—
222#532—23no—
223#532—23no—
224#532—23no—
225#532C2311yescharacteristic
226#532C2316yes—
227#532C2316yes—
228#532C2316yes—
229#532C2316yes—
230#532C2313yescomplemented
231#532C2313yescomplemented
232C2×C4⋊Q8C2313yes—
233C2×C4⋊Q8C2313yescomplemented
234C2×C4⋊Q8C2313yescomplemented
235C2×#127C2313yes—
236#529—212no—
237#529—26no—
238#529—23no—
239#529—23no—
240#529—23no—
241#529—23no—
242#529C2316yescomplemented
243#529C2316yescomplemented
244C2×#125C2316yescomplemented
245C2×#124—23no—
246#525—23no—
247#525—23no—
248#525—26no—
249#525—26no—
250#525—212no—
251#525—26no—
252#525—212no—
253#525—26no—
254#525C2316yes—
255C2×#123—26no—
256C2×C22⋊Q8—23no—
257C2×C22⋊Q8—23no—
258C2×C22⋊Q8—23no—
259C2×C22⋊Q8—23no—
260C2×#121—23no—
261C2×#121—23no—
262C2×#121—23no—
263C2×#121C2316yes—
264C2×#120—26no—
265#520—21no—
266#520—26no—
267#520—23no—
268#519—22no—
269#519—23no—
270C4×#41—26no—
271C4×#41—23no—
272C4×#41—23no—
273C4×#41D411yescharacteristic
274C4×#41D413yes—
275C4×#41D413yes—
276C4×#41D411yescharacteristic
277C4×#41C2316yes—
278C4×#41C2311yescharacteristic
279C4×#41C2313yes—
280C4×#41C2313yes—
281C4×#41C2311yescharacteristic
282C2×C4×Q8—22no—
283C2×C4×Q8—23no—
284C2×C4×Q8—23no—
285C2×C4×Q8D411yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4—23no—
288C2×C4×D4—23no—
289C2×C4×D4—23no—
290C2×C4×D4—23no—
291C2×C4×D4—23no—
292C2×C4×D4—23no—
293C2×C4×D4—23no—
294C2×C4×D4D413yes—
295C2×C4×D4C2316yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2316yes—
300C2×C4×D4C2316yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2316yes—
303C2×C4×D4C2313yes—
304C2×#117D413yes—
305C2×#117C2316yes—
306C22×C4⋊C4C2313yes—
307C22×C22⋊C4—23no—
308C22×C42C2313yes—
309#501C23124yescomplemented
310#500C23112yescomplemented
311#498C23112yescomplemented
312#490C23124yescomplemented
313#486C23112yescomplemented
314#486C23112yescomplemented
315#484C23112yescomplemented
316#483C23112yescomplemented
317#482C23124yescomplemented
318#482C23124yescomplemented
319#481C23124yescomplemented
320#481C23112yescomplemented
321#480C23112yescomplemented
322#480C23124yescomplemented
323#478C23112yes—
324#478C23124yes—
325#478C23124yescomplemented
326#478C23124yescomplemented
327#478C23112yescomplemented
328#477C23112yescomplemented
329#476C2316yes—
330#476C23112yes—
331#476C23112yescomplemented
332#476C23112yescomplemented
333#476C2316yescomplemented
334#476C23112yescomplemented
335#475C23112yescomplemented
336#474C2316yes—
337#474C23112yes—
338#474C23112yescomplemented
339#474C23112yescomplemented
340#474C2316yescomplemented
341#474C23112yescomplemented
342#469C23124yescomplemented
343#468C23124yescomplemented
344#466C23124yescomplemented
345#465C23124yescomplemented
346#463C2314yes—
347#463C23112yescomplemented
348#461C2312yes—
349#461C2316yescomplemented
350#460C23112yescomplemented
351#460C23112yescomplemented
352#459C2312yes—
353#459C2316yescomplemented
354#459C23112yescomplemented
355#459C23112yescomplemented
356#450C23112yes—
357#450C23112yes—
358#447C23112yes—
359#447C23112yes—
360#446C23112yescomplemented
361C8×Q8C2314yescomplemented
362#442C23112yes—
363#442C23112yescomplemented
364#440C23112yes—
365#440C23112yescomplemented
366C4×SD16C23112yes—
367C4×SD16C23112yescomplemented
368C4×D8C23112yes—
369C4×D8C23112yescomplemented
370#436C23112yescomplemented
371#435C23124yescomplemented
372C8×D4C23112yescomplemented
373#432C2316yescomplemented
374#432C2316yescomplemented
375#431C2316yescomplemented
376#431C2316yescomplemented
377#428C2316yes—
378#428C23112yes—
379#428C2316yes—
380#428C23124yescomplemented
381C2×#107C23112yescomplemented
382C2×#106C23112yescomplemented
383#423C2313yes—
384#423C2316yes—
385#423C2311yescharacteristic
386#423C2316yescomplemented
387#423C2316yescomplemented
388C2×C4⋊C8C2316yescomplemented
389C2×C4⋊C8C2316yescomplemented
390#418C2316yes—
391#418C23112yes—
392#418C23124yes—
393#418C2316yes—
394#417C2316yes—
395#417C2312yes—
396C2×#102C23112yes—
397C2×#102C23112yes—
398#407C2316yes—
399C4×M16C2316yes—
400C25—23no—
4012−1+4—48no—
402C2×#41—28no—
403C2×#41—26no—
404C2×#41—22no—
405C2×#41—26no—
406C2×#41—212no—
407C2×#41—26no—
408C2×#41—26no—
409C2×#41—23no—
410C2×#41—26no—
411C2×#41—26no—
412C2×#41—26no—
413C2×#41—26no—
414C2×#41—23no—
415C2×#41—424no—
416C2×#41—424no—
417C2×#41—48no—
418C2×#41—416no—
419C2×#41—448no—
420C2×#41—448no—
421C2×#41—416no—
422C2×#41C2×D413yes—
423C2×#41C2×D413yes—
424C2×#41C2×D411yescharacteristic
425C2×#41C2×D411yescharacteristic
426C2×#41C2412yes—
427C22×Q8—22no—
428C22×Q8—26no—
429C22×Q8—22no—
430C22×Q8—23no—
431C22×Q8—23no—
432C22×Q8—23no—
433C22×Q8—48no—
434C22×Q8C2×D411yescharacteristic
435C22×D4—212no—
436C22×D4—26no—
437C22×D4—212no—
438C22×D4—26no—
439C22×D4—26no—
440C22×D4—23no—
441C22×D4—23no—
442C22×D4—23no—
443C22×D4—23no—
444C22×D4—23no—
445C22×D4—46no—
446C22×D4—424no—
447C22×D4C2×D413yes—
448C22×D4C2413yes—
449C22×D4C2416yes—
450C22×D4C2416yes—
451C22×D4C2411yescharacteristic
452C23×C4—23no—
453C23×C4—21no—
454C23×C4—23no—
455C23×C4—23no—
456C23×C4—23no—
457C23×C4—26no—
458C23×C4—26no—
459C23×C4—26no—
460C23×C4—26no—
461C23×C4—424no—
462C23×C4C2×D413yes—
463C23×C4C2×D413yes—
464C23×C4C2413yes—
465AGL(1,ℤ/8)—28no—
466AGL(1,ℤ/8)—412no—
467C2×SD16C2414yes—
468C2×SD16C24112yes—
469C2×D8C2414yes—
470C2×D8C24112yes—
471C2×M16—412no—
472C2×M16C2416yes—
473C2×M16C2412yes—
474C2×M16C24112yes—
475C22×C8C24112yes—
476C4⋊Q8—26no—
477C4⋊Q8—26no—
478C4⋊Q8—23no—
479C4⋊Q8—23no—
480C4⋊Q8—23no—
481C4⋊Q8—23no—
482C4⋊Q8—23no—
483C4⋊Q8—23no—
484C4⋊Q8C2411yescharacteristic
485C4⋊Q8C2416yes—
486C4⋊Q8C2416yes—
487C4⋊Q8C2413yes—
488C4⋊Q8C2413yes—
489C4⋊Q8C2416yes—
490C4⋊Q8C2416yes—
491#127—23no—
492#127—23no—
493#127C2416yes—
494#127C2416yes—
495#127C2411yescharacteristic
496#126—212no—
497#126—212no—
498#126—212no—
499#126—26no—
500#126—26no—
501#125—212no—
502#125—26no—
503#125—212no—
504#125—26no—
505#125—26no—
506#125—23no—
507#125—23no—
508#125C2416yes—
509#125C24112yes—
510#124—26no—
511#124—212no—
512#124—26no—
513#124—26no—
514#124—26no—
515#124—26no—
516#124—23no—
517#124—23no—
518#124C2412yes—
519#123—212no—
520#123—26no—
521#123—26no—
522#123—26no—
523#123—212no—
524#123—212no—
525#123—212no—
526#123—212no—
527#123—212no—
528#123—212no—
529C22⋊Q8—26no—
530C22⋊Q8—23no—
531C22⋊Q8—23no—
532C22⋊Q8—26no—
533C22⋊Q8—26no—
534C22⋊Q8—26no—
535C22⋊Q8—26no—
536C22⋊Q8—26no—
537C22⋊Q8—26no—
538C22⋊Q8—23no—
539C22⋊Q8—23no—
540C22⋊Q8—26no—
541C22⋊Q8—212no—
542C22⋊Q8—26no—
543C22⋊Q8—26no—
544C22⋊Q8—26no—
545C22⋊Q8—212no—
546C22⋊Q8—26no—
547C22⋊Q8—26no—
548C22⋊Q8—212no—
549C22⋊Q8—212no—
550C22⋊Q8C2416yes—
551C22⋊Q8C2416yes—
552#121—212no—
553#121—26no—
554#121—26no—
555#121—26no—
556#121—26no—
557#121—26no—
558#121—26no—
559#121—26no—
560#121—21no—
561#121—21no—
562#121—23no—
563#121—23no—
564#121—26no—
565#121—26no—
566#121—212no—
567#121—26no—
568#121—212no—
569#121—26no—
570#121C24112yes—
571#121C24112yes—
572#121C2416yes—
573#121C2416yes—
574#120—26no—
575#120—212no—
576#120—212no—
577#120—212no—
578#120—212no—
579C4×Q8—22no—
580C4×Q8—26no—
581C4×Q8—26no—
582C4×Q8—26no—
583C4×Q8—23no—
584C4×Q8—23no—
585C4×Q8—26no—
586C4×Q8—26no—
587C4×Q8—26no—
588C4×Q8—26no—
589C4×Q8—26no—
590C4×Q8—23no—
591C4×Q8—23no—
592C4×Q8C2×D411yescharacteristic
593C4×Q8C2×D411yescharacteristic
594C4×Q8C2×D413yes—
595C4×Q8C2×D411yescharacteristic
596C4×Q8C2×D413yes—
597C4×Q8C2×D413yes—
598C4×Q8C2416yes—
599C4×Q8C2416yes—
600C4×Q8C2411yescharacteristic
601C4×Q8C2413yes—
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—21no—
611C4×D4—21no—
612C4×D4—26no—
613C4×D4—26no—
614C4×D4—26no—
615C4×D4—26no—
616C4×D4—23no—
617C4×D4—23no—
618C4×D4—23no—
619C4×D4—23no—
620C4×D4—26no—
621C4×D4—26no—
622C4×D4—26no—
623C4×D4—26no—
624C4×D4—23no—
625C4×D4—23no—
626C4×D4—26no—
627C4×D4—26no—
628C4×D4—26no—
629C4×D4—26no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—23no—
633C4×D4—23no—
634C4×D4C2×D413yes—
635C4×D4C2×D416yes—
636C4×D4C2×D413yes—
637C4×D4C2×D413yes—
638C4×D4C2×D413yes—
639C4×D4C2×D416yes—
640C4×D4C2×D413yes—
641C4×D4C2×D413yes—
642C4×D4C2×D416yes—
643C4×D4C2412yes—
644C4×D4C2412yes—
645C4×D4C2416yes—
646C4×D4C2416yes—
647C4×D4C2416yes—
648C4×D4C2416yes—
649C4×D4C2416yes—
650C4×D4C2416yes—
651C4×D4C2416yes—
652C4×D4C2416yes—
653C4×D4C2413yes—
654C4×D4C2416yes—
655C4×D4C2413yes—
656#117—26no—
657#117—26no—
658#117—23no—
659#117—23no—
660#117—26no—
661#117—212no—
662#117—26no—
663#117—26no—
664#117—26no—
665#117C2×D413yes—
666#117C2×D413yes—
667#117C2×D416yes—
668#117C2×D413yes—
669#117C2×D416yes—
670#117C2×D413yes—
671#117C2416yes—
672#117C24112yes—
673C2×C4⋊C4—23no—
674C2×C4⋊C4—23no—
675C2×C4⋊C4—23no—
676C2×C4⋊C4—23no—
677C2×C4⋊C4—26no—
678C2×C4⋊C4—23no—
679C2×C4⋊C4—26no—
680C2×C4⋊C4—23no—
681C2×C4⋊C4—26no—
682C2×C4⋊C4C2×D413yes—
683C2×C4⋊C4C2×D413yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2416yes—
687C2×C4⋊C4C2416yes—
688C2×C4⋊C4C2416yes—
689C2×C4⋊C4C2416yes—
690C2×C22⋊C4—26no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—23no—
693C2×C22⋊C4—23no—
694C2×C22⋊C4—23no—
695C2×C22⋊C4—26no—
696C2×C22⋊C4—26no—
697C2×C22⋊C4—26no—
698C2×C22⋊C4—26no—
699C2×C22⋊C4—26no—
700C2×C22⋊C4C2×D416yes—
701C2×C42—26no—
702C2×C42—26no—
703C2×C42C2×D413yes—
704C2×C42C2×D413yes—
705C2×C42C2×D413yes—
706C2×C42C2×D413yes—
707C2×C42C2×D413yes—
708C2×C42C2×D413yes—
709C2×C42C2411yescharacteristic
710C2×C42C2413yes—
711C2×C42C2413yes—
712C2×C42C2413yes—
713C2×C42C2413yes—
714C2×C42C2413yes—
715#107C24112yes—
716#107C24124yes—
717#107C24112yes—
718#106C24112yes—
719#106C24124yes—
720#106C24112yes—
721C4⋊C8C2416yes—
722C4⋊C8C2416yes—
723C4⋊C8C24112yes—
724C4⋊C8C24112yes—
725C4⋊C8C2412yes—
726C4⋊C8C2412yes—
727#103C24112yes—
728#103C2414yes—
729#102C24112yes—
730#102C24112yes—
731#102C24124yes—
732#102C24124yes—
733#102C24112yes—
734#102C2414yes—
735#102C24112yes—
736#102C24112yes—
737C22⋊C8C24112yes—
738C22⋊C8C24112yes—
739#97C24112yes—
740C4×C8C24112yes—
741C24—21no—
742C24—23no—
743C24—26no—
744C24—26no—
745C24—412no—
746C24—412no—
747C24—86no—
748C24C22×D413yes—
749#41—24no—
750#41—212no—
751#41—212no—
752#41—24no—
753#41—24no—
754#41—424no—
755#41—424no—
756#41—424no—
757#41—448no—
758#41—424no—
759#41—424no—
760#41—48no—
761#41—424no—
762#41—424no—
763#41—424no—
764#41—412no—
765#41—86no—
766#41AGL(1,ℤ/8)18yescomplemented
767C2×Q8—24no—
768C2×Q8—23no—
769C2×Q8—26no—
770C2×Q8—23no—
771C2×Q8—26no—
772C2×Q8—26no—
773C2×Q8—26no—
774C2×Q8—412no—
775C2×Q8—424no—
776C2×Q8—48no—
777C2×Q8—48no—
778C2×Q8—412no—
779C2×Q8—86no—
780C2×Q8C22×D413yes—
781C2×Q8C22×D411yescharacteristic
782C2×Q8C2512yes—
783C2×D4—212no—
784C2×D4—212no—
785C2×D4—212no—
786C2×D4—22no—
787C2×D4—26no—
788C2×D4—212no—
789C2×D4—212no—
790C2×D4—26no—
791C2×D4—21no—
792C2×D4—26no—
793C2×D4—26no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—23no—
797C2×D4—26no—
798C2×D4—26no—
799C2×D4—26no—
800C2×D4—26no—
801C2×D4—26no—
802C2×D4—22no—
803C2×D4—26no—
804C2×D4—46no—
805C2×D4—46no—
806C2×D4—412no—
807C2×D4—412no—
808C2×D4—412no—
809C2×D4—412no—
810C2×D4—448no—
811C2×D4—424no—
812C2×D4—424no—
813C2×D4—424no—
814C2×D4—86no—
815C2×D4C22×D416yes—
816C2×D4C22×D413yes—
817C2×D4C22×D413yes—
818C2×D42−1+414yescomplemented
819C2×D4C2516yes—
820C2×D4C2512yes—
821C2×D4C2512yes—
822C22×C4—212no—
823C22×C4—26no—
824C22×C4—26no—
825C22×C4—26no—
826C22×C4—21no—
827C22×C4—23no—
828C22×C4—26no—
829C22×C4—26no—
830C22×C4—26no—
831C22×C4—22no—
832C22×C4—26no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—26no—
836C22×C4—26no—
837C22×C4—26no—
838C22×C4—26no—
839C22×C4—26no—
840C22×C4—26no—
841C22×C4—26no—
842C22×C4—44no—
843C22×C4—412no—
844C22×C4—424no—
845C22×C4—412no—
846C22×C4—412no—
847C22×C4—424no—
848C22×C4—424no—
849C22×C4—412no—
850C22×C4—424no—
851C22×C4—83no—
852C22×C4C22×D413yes—
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D413yes—
855C22×C4C22×D413yes—
856C22×C4C22×D413yes—
857C22×C4C22×D413yes—
858C22×C4C22×D413yes—
859C22×C4C22×D413yes—
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D413yes—
862C22×C4C22×D413yes—
863C22×C4C22×D413yes—
864C22×C4C22×D413yes—
865C22×C4C22×D413yes—
866C22×C4C22×D413yes—
867C22×C4C2513yes—
868C22×C4C2513yes—
869C22×C4C2511yescharacteristic
870SD16—28no—
871SD16—412no—
872D8—28no—
873D8—412no—
874M16—24no—
875M16—212no—
876M16—412no—
877C2×C8—412no—
878C2×C8C2514yes—
879C2×C8C25112yes—
880C4⋊C4—21no—
881C4⋊C4—23no—
882C4⋊C4—26no—
883C4⋊C4—26no—
884C4⋊C4—23no—
885C4⋊C4—26no—
886C4⋊C4—23no—
887C4⋊C4—212no—
888C4⋊C4—26no—
889C4⋊C4—26no—
890C4⋊C4—26no—
891C4⋊C4—26no—
892C4⋊C4—212no—
893C4⋊C4—26no—
894C4⋊C4—26no—
895C4⋊C4—26no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—26no—
899C4⋊C4—26no—
900C4⋊C4—26no—
901C4⋊C4—26no—
902C4⋊C4C22×D413yes—
903C4⋊C4C22×D413yes—
904C4⋊C4C22×D416yes—
905C4⋊C4C22×D413yes—
906C4⋊C4C22×D413yes—
907C4⋊C4C22×D416yes—
908C4⋊C4C2516yes—
909C4⋊C4C2516yes—
910C4⋊C4C2512yes—
911C4⋊C4C2516yes—
912C22⋊C4—26no—
913C22⋊C4—212no—
914C22⋊C4—26no—
915C22⋊C4—26no—
916C22⋊C4—22no—
917C22⋊C4—22no—
918C22⋊C4—26no—
919C22⋊C4—26no—
920C22⋊C4—26no—
921C22⋊C4—26no—
922C22⋊C4—26no—
923C22⋊C4—26no—
924C22⋊C4—212no—
925C22⋊C4—212no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—26no—
929C22⋊C4—26no—
930C22⋊C4—26no—
931C22⋊C4—26no—
932C22⋊C4C22×D416yes—
933C22⋊C4C22×D416yes—
934C22⋊C4C22×D416yes—
935C22⋊C4C22×D416yes—
936C42—26no—
937C42—26no—
938C42—212no—
939C42—26no—
940C42C22×D413yes—
941C42C22×D411yescharacteristic
942C42C22×D411yescharacteristic
943C42C22×D413yes—
944C42C22×D413yes—
945C42C22×D413yes—
946C42C22×D413yes—
947C42C22×D413yes—
948C42C22×D413yes—
949C42C22×D413yes—
950C42C22×D413yes—
951C42C22×D413yes—
952C42C2513yes—
953C42C2513yes—
954C42C2511yescharacteristic
955C42C2511yescharacteristic
956C23—22no—
957C23—26no—
958C23—24no—
959C23—26no—
960C23—22no—
961C23—26no—
962C23—43no—
963C23—412no—
964C23—412no—
965C23—42no—
966C23—42no—
967C23—46no—
968C23—412no—
969C23—46no—
970C23—46no—
971C23—412no—
972C23—86no—
973C23—86no—
974C23—848no—
975C23C23×D413yes—
976C23C23×D411yescharacteristic
977C23C23×D413yes—
978Q8—26no—
979Q8—22no—
980Q8—22no—
981Q8—412no—
982Q8—46no—
983Q8—412no—
984Q8—46no—
985Q8—412no—
986Q8—86no—
987Q8C2×AGL(1,ℤ/8)14yes—
988D4—212no—
989D4—22no—
990D4—26no—
991D4—22no—
992D4—22no—
993D4—26no—
994D4—24no—
995D4—26no—
996D4—412no—
997D4—412no—
998D4—412no—
999D4—42no—
1000D4—424no—
1001D4—44no—
1002D4—424no—
1003D4—412no—
1004D4—46no—
1005D4—412no—
1006D4—42no—
1007D4—86no—
1008D4—86no—
1009D4—86no—
1010D4C2×AGL(1,ℤ/8)112yes—
1011D4C2×2−1+414yes—
1012C2×C4—26no—
1013C2×C4—26no—
1014C2×C4—23no—
1015C2×C4—23no—
1016C2×C4—23no—
1017C2×C4—23no—
1018C2×C4—26no—
1019C2×C4—26no—
1020C2×C4—22no—
1021C2×C4—26no—
1022C2×C4—26no—
1023C2×C4—26no—
1024C2×C4—22no—
1025C2×C4—26no—
1026C2×C4—26no—
1027C2×C4—22no—
1028C2×C4—26no—
1029C2×C4—41no—
1030C2×C4—43no—
1031C2×C4—43no—
1032C2×C4—43no—
1033C2×C4—43no—
1034C2×C4—43no—
1035C2×C4—44no—
1036C2×C4—412no—
1037C2×C4—412no—
1038C2×C4—412no—
1039C2×C4—42no—
1040C2×C4—46no—
1041C2×C4—412no—
1042C2×C4—412no—
1043C2×C4—412no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—412no—
1047C2×C4—412no—
1048C2×C4—412no—
1049C2×C4—412no—
1050C2×C4—86no—
1051C2×C4—86no—
1052C2×C4C2×AGL(1,ℤ/8)112yes—
1053C2×C4C23×D413yes—
1054C2×C4C23×D413yes—
1055C2×C4C23×D411yescharacteristic
1056C2×C4C23×D411yescharacteristic
1057C2×C4C23×D411yescharacteristic
1058C2×C4C23×D413yes—
1059C2×C4C23×D413yes—
1060C2×C4C23×D413yes—
1061C2×C4C23×D411yescharacteristic
1062C2×C4C23×D413yes—
1063C2×C4C23×D411yescharacteristic
1064C2×C4C2×2−1+412yes—
1065C2×C4#58512yes—
1066C2×C4C2611yescharacteristic
1067C8—24no—
1068C8—212no—
1069C22—23no—
1070C22—21no—
1071C22—21no—
1072C22—23no—
1073C22—23no—
1074C22—24no—
1075C22—23no—
1076C22—23no—
1077C22—412no—
1078C22—48no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—46no—
1083C22—46no—
1084C22—42no—
1085C22—42no—
1086C22—46no—
1087C22—824no—
1088C22—812no—
1089C22—824no—
1090C22#348912yes—
1091C22C22×AGL(1,ℤ/8)16yes—
1092C22C24×D411yescharacteristic
1093C4—23no—
1094C4—23no—
1095C4—21no—
1096C4—23no—
1097C4—21no—
1098C4—21no—
1099C4—23no—
1100C4—23no—
1101C4—42no—
1102C4—42no—
1103C4—46no—
1104C4—46no—
1105C4—46no—
1106C4#348912yes—
1107C4C22×AGL(1,ℤ/8)12yes—
1108C4C22×AGL(1,ℤ/8)16yes—
1109C4C22×2−1+411yescharacteristic
1110C4C2×#58511yescharacteristic
1111C2—22no—
1112C2—26no—
1113C2—43no—
1114C2—44no—
1115C2—82no—
1116C2—86no—
1117C2C2×#348911yescharacteristic
1118C2C23×AGL(1,ℤ/8)11yescharacteristic
1119C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62805C2semidirect
2. C2×D4×#41C2semidirect
3. #62151C2semidirect
4. #62137C2semidirect
5. #62110C2semidirect
6. #62109C2semidirect
7. #62096C2semidirect
8. #62095C2semidirect
9. Q8×AGL(1,ℤ/8)C2semidirect
10. #61321C2semidirect
11. #61252C2semidirect
12. #61155C2semidirect
13. #60916C2semidirect
14. #60864C2semidirect
15. #60558C2semidirect
16. C2×#3077C2semidirect
17. #60263C2semidirect
21. #3518C22semidirect
22. #3515C22semidirect
23. #3511C22semidirect
24. #3509C22semidirect
25. #3503C22semidirect
26. #3499C22semidirect
31. Q8×#41C22semidirect
32. #3475C22semidirect
48. #3444C22semidirect
49. C2×#533C22semidirect
55. #3386C22semidirect
56. #3384C22semidirect
57. Q8×SD16C22semidirect
58. Q8×D8C22semidirect
59. #3368C22semidirect
60. #3366C22semidirect
61. #3362C22semidirect
62. #3358C22semidirect
63. #3354C22semidirect
64. #3353C22semidirect
65. #3345C22semidirect
66. #3343C22semidirect
67. #3335C22semidirect
68. #3334C22semidirect
69. #3325C22semidirect
70. #3324C22semidirect
71. #3318C22semidirect
72. #3310C22semidirect
73. #3295C22semidirect
74. #3294C22semidirect
75. #3254C22semidirect
76. #3253C22semidirect
77. #3251C22semidirect
78. #3247C22semidirect
79. #3246C22semidirect
80. #3245C22semidirect
81. #3235C22semidirect
82. #3234C22semidirect
83. #3228C22semidirect
84. #3227C22semidirect
85. #3226C22semidirect
86. #3165C22semidirect
87. #3138C22semidirect
88. #3114C22semidirect
89. #3110C22semidirect
90. #3109C22semidirect
91. #3105C22semidirect
92. #3101C22semidirect
93. #3100C22semidirect
94. #3094C22semidirect
95. #3092C22semidirect
96. #3079C22semidirect
99. #3077C22semidirect
100. #3077C22semidirect
101. #3077C22semidirect
102. #3077C22semidirect
103. #3077C22semidirect
104. C2×#478C22semidirect
105. C2×#476C22semidirect
106. C2×#474C22semidirect
107. #3055C22semidirect
108. #3038C22semidirect
110. #3036C22semidirect
112. #2991C22semidirect
113. #2990C22semidirect
114. #2989C22semidirect
115. #2988C22semidirect
116. Q8×M16C22semidirect
118. C4×AGL(1,ℤ/8)C22semidirect
119. D4×M16C22semidirect
120. #2920C22semidirect
121. C2×#428C22semidirect
122. C2×#423C22semidirect
141. Q82C23semidirect
144. #557C23semidirect
148. #556C23semidirect
149. #555C23semidirect
151. #554C23semidirect
152. #554C23semidirect
153. #553C23semidirect
158. #552C23semidirect
171. D4×Q8C23semidirect
187. #547C23semidirect
217. #533C23semidirect
218. #533C23semidirect
219. #533C23semidirect
220. #533C23semidirect
230. #532C23semidirect
231. #532C23semidirect
233. C2×C4⋊Q8C23semidirect
234. C2×C4⋊Q8C23semidirect
242. #529C23semidirect
243. #529C23semidirect
244. C2×#125C23semidirect
309. #501C23semidirect
310. #500C23semidirect
311. #498C23semidirect
312. #490C23semidirect
313. #486C23semidirect
314. #486C23semidirect
315. #484C23semidirect
316. #483C23semidirect
317. #482C23semidirect
318. #482C23semidirect
319. #481C23semidirect
320. #481C23semidirect
321. #480C23semidirect
322. #480C23semidirect
325. #478C23semidirect
326. #478C23semidirect
327. #478C23semidirect
328. #477C23semidirect
331. #476C23semidirect
332. #476C23semidirect
333. #476C23semidirect
334. #476C23semidirect
335. #475C23semidirect
338. #474C23semidirect
339. #474C23semidirect
340. #474C23semidirect
341. #474C23semidirect
342. #469C23semidirect
343. #468C23semidirect
344. #466C23semidirect
345. #465C23semidirect
347. #463C23semidirect
349. #461C23semidirect
350. #460C23semidirect
351. #460C23semidirect
353. #459C23semidirect
354. #459C23semidirect
355. #459C23semidirect
360. #446C23semidirect
361. C8×Q8C23semidirect
363. #442C23semidirect
365. #440C23semidirect
367. C4×SD16C23semidirect
369. C4×D8C23semidirect
370. #436C23semidirect
371. #435C23semidirect
372. C8×D4C23semidirect
373. #432C23semidirect
374. #432C23semidirect
375. #431C23semidirect
376. #431C23semidirect
380. #428C23semidirect
381. C2×#107C23semidirect
382. C2×#106C23semidirect
386. #423C23semidirect
387. #423C23semidirect
388. C2×C4⋊C8C23semidirect
389. C2×C4⋊C8C23semidirect
766. #41AGL(1,ℤ/8)semidirect
818. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
#628052
C2×D4×#412
#621512
#621372
#621102
#621092
#620962
#620952
Q8×AGL(1,ℤ/8)2
#613212
#612522
#611552
#609162
#608642
#605582
C2×#30772
#602632