Finite Group Databasebeta

← #6357456

Subgroups — #6357456

Order 512.

1865 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60972C211yesmaximal, characteristic, complemented
2#60969C211yesmaximal, characteristic, complemented
3#60965C211yesmaximal, characteristic, complemented
4#60947C211yesmaximal, characteristic, complemented
5#60862C211yesmaximal, characteristic, complemented
6#60782C211yesmaximal, characteristic, complemented
7#19744C211yesmaximal, characteristic, complemented
8#19740C211yesmaximal, characteristic, complemented
9#19738C211yesmaximal, characteristic, complemented
10#19737C211yesmaximal, characteristic, complemented
11#19737C211yesmaximal, characteristic, complemented
12#19736C211yesmaximal, characteristic, complemented
13#19735C211yesmaximal, characteristic, complemented
14#19733C211yesmaximal, characteristic, complemented
15#19730C211yesmaximal, characteristic, complemented
16#19728C211yesmaximal, characteristic, complemented
17#19726C211yesmaximal, characteristic, complemented
18#19726C211yesmaximal, characteristic, complemented
19#19722C211yesmaximal, characteristic, complemented
20#19722C211yesmaximal, characteristic, complemented
21#19718C211yesmaximal, characteristic, complemented
22#19714C211yesmaximal, characteristic, complemented
23#19696C211yesmaximal, characteristic, complemented
24#19694C211yesmaximal, characteristic, complemented
25#19691C211yesmaximal, characteristic, complemented
26#19687C211yesmaximal, characteristic, complemented
27#19649C211yesmaximal, characteristic, complemented
28#19645C211yesmaximal, characteristic, complemented
29#19643C211yesmaximal, characteristic, complemented
30#19641C211yesmaximal, characteristic, complemented
31#17324C211yesmaximal, characteristic, complemented
32#3444C2211yescharacteristic
33#3444C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#532C2211yescharacteristic
36#3256—22no—
37#3254—22no—
38#3251—22no—
39#3248—22no—
40#3240—22no—
41#3240—22no—
42#3231C2211yescharacteristic
43#3231C2211yescharacteristic
44#3231C2211yescharacteristic
45#3231C2211yescharacteristic
46#3231C2211yescharacteristic
47#3231C2211yescharacteristic, complemented
48#3231C2211yescharacteristic, complemented
49#3231C2211yescharacteristic, complemented
50#3230C2211yescharacteristic
51#3230C2211yescharacteristic
52#3229C2211yescharacteristic
53#3229C2211yescharacteristic, complemented
54#3228C2211yescharacteristic
55#3228C2211yescharacteristic
56#3228C2211yescharacteristic
57#3228C2211yescharacteristic
58#3228C2211yescharacteristic
59#3228C2211yescharacteristic, complemented
60#3228C2211yescharacteristic, complemented
61#3228C2211yescharacteristic, complemented
62#3226C2211yescharacteristic
63#3226C2211yescharacteristic
64#3226C2211yescharacteristic
65#3226C2211yescharacteristic, complemented
66#3212—22no—
67#3211—22no—
68#3210C2211yescharacteristic
69#3210C2211yescharacteristic
70#3210C2211yescharacteristic
71#3210C2211yescharacteristic
72#3210C2211yescharacteristic
73#3210C2211yescharacteristic, complemented
74#3209C2211yescharacteristic
75#3209C2211yescharacteristic, complemented
76#3208C2211yescharacteristic
77#3208C2211yescharacteristic
78#3208C2211yescharacteristic
79#3208C2211yescharacteristic
80#3207C2211yescharacteristic
81#3207C2211yescharacteristic
82#3207C2211yescharacteristic
83#3207C2211yescharacteristic
84#3207C2211yescharacteristic
85#3207C2211yescharacteristic, complemented
86#3206C2211yescharacteristic
87#3206C2211yescharacteristic
88#3206C2211yescharacteristic
89#3206C2211yescharacteristic, complemented
90#3205C2211yescharacteristic
91#3205C2211yescharacteristic
92#3197—22no—
93#3194—22no—
94#3193—22no—
95#3190—22no—
96#3185C2211yescharacteristic, complemented
97#3184C2211yescharacteristic
98#3184C2211yescharacteristic
99#3184C2211yescharacteristic, complemented
100#3182C2211yescharacteristic
101#3182C2211yescharacteristic
102#3182C2211yescharacteristic
103#3182C2211yescharacteristic
104#3182C2211yescharacteristic
105#3182C2211yescharacteristic
106#3182C2211yescharacteristic, complemented
107#3182C2211yescharacteristic, complemented
108#3170C2211yescharacteristic, complemented
109#3170C2211yescharacteristic, complemented
110#3167C2211yescharacteristic, complemented
111#3167C2211yescharacteristic, complemented
112#3165C2211yescharacteristic, complemented
113#3165C2211yescharacteristic, complemented
114#3147C2211yescharacteristic
115#3147C2211yescharacteristic
116#3141C2211yescharacteristic, complemented
117#3141C2211yescharacteristic, complemented
118#3131C2211yescharacteristic
119#3131C2211yescharacteristic
120#3115—22no—
121#3114—22no—
122#3112—22no—
123#3111—22no—
124#3111—22no—
125#3110—22no—
126#3108—22no—
127#3107—22no—
128#3093—22no—
129#3080—22no—
130#3035—22no—
131#3002—22no—
132#2920C2211yescharacteristic
133#2920C2211yescharacteristic
134C2×#431C2211yescharacteristic
135#1723C2211yescharacteristic, complemented
136#1723C2211yescharacteristic, complemented
137#1723C2211yescharacteristic, complemented
138#1723C2211yescharacteristic, complemented
139#1723C2211yescharacteristic, complemented
140#1723C2211yescharacteristic, complemented
141#1722C2211yescharacteristic, complemented
142#1722C2211yescharacteristic, complemented
143#1722C2211yescharacteristic, complemented
144#1722C2211yescharacteristic, complemented
145#1721C2211yescharacteristic, complemented
146#1721C2211yescharacteristic, complemented
147#1720C2211yescharacteristic, complemented
148#1720C2211yescharacteristic, complemented
149#1720C2211yescharacteristic, complemented
150#1720C2211yescharacteristic, complemented
151#1719C2211yescharacteristic, complemented
152#1719C2211yescharacteristic, complemented
153#1719C2211yescharacteristic, complemented
154#1719C2211yescharacteristic, complemented
155#1719C2211yescharacteristic, complemented
156#1719C2211yescharacteristic, complemented
157#1719C2211yescharacteristic, complemented
158#1719C2211yescharacteristic, complemented
159#1718C2211yescharacteristic, complemented
160#1718C2211yescharacteristic, complemented
161#1718C2211yescharacteristic, complemented
162#1718C2211yescharacteristic, complemented
163#1718C2211yescharacteristic, complemented
164#1718C2211yescharacteristic, complemented
165#1717C2211yescharacteristic, complemented
166#1717C2211yescharacteristic, complemented
167#1717C2211yescharacteristic, complemented
168#1717C2211yescharacteristic, complemented
169#1717C2211yescharacteristic, complemented
170#1717C2211yescharacteristic, complemented
171#1716C2211yescharacteristic, complemented
172#1715C2211yescharacteristic, complemented
173#1715C2211yescharacteristic, complemented
174#1715C2211yescharacteristic, complemented
175#1714C2211yescharacteristic, complemented
176#1714C2211yescharacteristic, complemented
177#1714C2211yescharacteristic, complemented
178#1714C2211yescharacteristic, complemented
179#1714C2211yescharacteristic, complemented
180#1714C2211yescharacteristic, complemented
181#1714C2211yescharacteristic, complemented
182#1714C2211yescharacteristic, complemented
183#1713C2211yescharacteristic, complemented
184#1711C2211yescharacteristic, complemented
185#1711C2211yescharacteristic, complemented
186#1710C2211yescharacteristic, complemented
187#1710C2211yescharacteristic, complemented
188#1709C2211yescharacteristic, complemented
189#1708C2211yescharacteristic, complemented
190#1708C2211yescharacteristic, complemented
191#1708C2211yescharacteristic, complemented
192#1707C2211yescharacteristic, complemented
193#1707C2211yescharacteristic, complemented
194#1706C2211yescharacteristic, complemented
195#1706C2211yescharacteristic, complemented
196#1706C2211yescharacteristic, complemented
197#1706C2211yescharacteristic, complemented
198#1705C2211yescharacteristic, complemented
199#1454C2211yescharacteristic
200#1454C2211yescharacteristic
201#1454C2211yescharacteristic
202#1454C2211yescharacteristic
203#1453C2211yescharacteristic, complemented
204#1453C2211yescharacteristic, complemented
205#1453C2211yescharacteristic, complemented
206#1453C2211yescharacteristic, complemented
207#1451C2211yescharacteristic, complemented
208#1451C2211yescharacteristic, complemented
209C8×M16C2211yescharacteristic, complemented
210C8×M16C2211yescharacteristic, complemented
211C22×#41—21no—
212C2×#135—22no—
213C2×#135—22no—
214#533—21no—
215#533—21no—
216#533—21no—
217#533—21no—
218#533—21no—
219#533—21no—
220#533C2311yescharacteristic
221#533C2311yescharacteristic
222#533C2311yescharacteristic
223#533C2311yescharacteristic
224#533C2311yescharacteristic
225#533C2311yescharacteristic
226#533C2311yescharacteristic
227#533C2311yescharacteristic
228#533C2311yescharacteristic
229#533C2311yescharacteristic
230#532—21no—
231#532—21no—
232#532—21no—
233#532—21no—
234#532—21no—
235#532—21no—
236#532C2311yescharacteristic
237#532C2311yescharacteristic
238#532C2311yescharacteristic
239#532C2311yescharacteristic
240#532C2311yescharacteristic
241#532C2311yescharacteristic
242#532C2311yescharacteristic
243#532C2311yescharacteristic
244#532C2311yescharacteristic
245#532C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2311yescharacteristic
249C2×#127C2311yescharacteristic
250#529—21no—
251#529—21no—
252#529—21no—
253#529—21no—
254#529—21no—
255#529—21no—
256#529—21no—
257#529—21no—
258#529—21no—
259#529—21no—
260#529—21no—
261#529—21no—
262C2×#125—21no—
263C2×#124—21no—
264#525—21no—
265#525—21no—
266#525—21no—
267#525—21no—
268#525—21no—
269#525—21no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—21no—
272C2×#121—21no—
273C2×#121—21no—
274C4×#41—21no—
275C4×#41—21no—
276C4×#41—21no—
277C4×#41—21no—
278C4×#41—21no—
279C4×#41—21no—
280C2×C4×Q8—21no—
281C2×C4×Q8—21no—
282C2×C4×D4—21no—
283C2×C4×D4—21no—
284C2×#117—21no—
285C22×C42C2311yescharacteristic
286#501—22no—
287#501—22no—
288#500C2311yescharacteristic
289#500C2311yescharacteristic
290#500C2311yescharacteristic
291#500C2311yescharacteristic
292#500C2311yescharacteristic
293#500C2311yescharacteristic
294#500C2311yescharacteristic
295#500C2311yescharacteristic
296#500C2311yescharacteristic
297#500C2311yescharacteristic
298#500C2311yescharacteristic
299#500C2311yescharacteristic
300#500C2311yescharacteristic
301#500C2311yescharacteristic
302#498C2311yescharacteristic
303#498C2311yescharacteristic
304#498C2311yescharacteristic
305#498C2311yescharacteristic
306#498C2311yescharacteristic
307#498C2311yescharacteristic
308#498C2311yescharacteristic
309#498C2311yescharacteristic
310#498C2311yescharacteristic
311#498C2311yescharacteristic
312#495—22no—
313#495—22no—
314#494C2311yescharacteristic
315#494C2311yescharacteristic
316#494C2311yescharacteristic
317#494C2311yescharacteristic
318#494C2311yescharacteristic
319#493C2311yescharacteristic
320#493C2311yescharacteristic
321#493C2311yescharacteristic
322#493C2311yescharacteristic
323#493C2311yescharacteristic
324#492C2311yescharacteristic
325#492C2311yescharacteristic
326#492C2311yescharacteristic
327#492C2311yescharacteristic
328#492C2311yescharacteristic
329#492C2311yescharacteristic
330#492C2311yescharacteristic
331#492C2311yescharacteristic
332#492C2311yescharacteristic
333#492C2311yescharacteristic
334#492C2311yescharacteristic
335#492C2311yescharacteristic
336#492C2311yescharacteristic
337#492C2311yescharacteristic
338#489—22no—
339#489—22no—
340#488—22no—
341#488—22no—
342#487C2311yescharacteristic
343#487C2311yescharacteristic
344#487C2311yescharacteristic
345#487C2311yescharacteristic
346#487C2311yescharacteristic
347#487C2311yescharacteristic
348#487C2311yescharacteristic
349#487C2311yescharacteristic
350#487C2311yescharacteristic
351#487C2311yescharacteristic
352#487C2311yescharacteristic
353#487C2311yescharacteristic
354#487C2311yescharacteristic
355#487C2311yescharacteristic
356#487C2311yescharacteristic
357#487C2311yescharacteristic
358#487C2311yescharacteristic
359#487C2311yescharacteristic
360#487C2311yescharacteristic
361#487C2311yescharacteristic
362#487C2311yescharacteristic
363#487C2311yescharacteristic
364#487C2311yescharacteristic
365#487C2311yescharacteristic
366#486C2311yescharacteristic
367#486C2311yescharacteristic
368#486C2311yescharacteristic
369#486C2311yescharacteristic
370#486C2311yescharacteristic
371#486C2311yescharacteristic
372#486C2311yescharacteristic
373#486C2311yescharacteristic
374#486C2311yescharacteristic
375#486C2311yescharacteristic
376#486C2311yescharacteristic
377#486C2311yescharacteristic
378#486C2311yescharacteristic
379#486C2311yescharacteristic
380#486C2311yescharacteristic
381#486C2311yescharacteristic
382#486C2311yescharacteristic
383#486C2311yescharacteristic
384#486C2311yescharacteristic
385#486C2311yescharacteristic
386#486C2311yescharacteristic
387#486C2311yescharacteristic
388#486C2311yescharacteristic
389#486C2311yescharacteristic
390#485—22no—
391#485—22no—
392#485—22no—
393#485—22no—
394#485—22no—
395#485—22no—
396#485—22no—
397#485—22no—
398#484—22no—
399#484—22no—
400#483—22no—
401#483—22no—
402#482—22no—
403#482—22no—
404#482—22no—
405#482—22no—
406#482—22no—
407#482—22no—
408#482—22no—
409#482—22no—
410#480—22no—
411#480—22no—
412#480—22no—
413#480—22no—
414#479—22no—
415#479—22no—
416#479—22no—
417#479—22no—
418#479—22no—
419#479—22no—
420#479—22no—
421#479—22no—
422#478—22no—
423#478—22no—
424#478—22no—
425#478—22no—
426#478—22no—
427#478—22no—
428#478—22no—
429#478—22no—
430#477—22no—
431#477—22no—
432#475—22no—
433#475—22no—
434#474—22no—
435#474—22no—
436#474—22no—
437#474—22no—
438#470—22no—
439#469—22no—
440#469—22no—
441#469—22no—
442#468—22no—
443#468—22no—
444#468—22no—
445#468—22no—
446#468—22no—
447#468—22no—
448#468—22no—
449#468—22no—
450#467—22no—
451#467—22no—
452#465—22no—
453#465—22no—
454#464—22no—
455#464—22no—
456#464—22no—
457#464—22no—
458#464—22no—
459#464—22no—
460#463—22no—
461#463—22no—
462#463—22no—
463#463—22no—
464#463—22no—
465#463—22no—
466#462—22no—
467#462—22no—
468#461—22no—
469#461—22no—
470#461—22no—
471#461—22no—
472#460—22no—
473#460—22no—
474#460—22no—
475#460—22no—
476#459—22no—
477#459—22no—
478#452—22no—
479#452—22no—
480#452—22no—
481#452—22no—
482#452—22no—
483#452—22no—
484#451—22no—
485#451—22no—
486#450—22no—
487#450—22no—
488#450—22no—
489#450—22no—
490#449—22no—
491#449—22no—
492#449—22no—
493#449—22no—
494#449—22no—
495#449—22no—
496#448—22no—
497#448—22no—
498#448—22no—
499#448—22no—
500#447—22no—
501#447—22no—
502#442—22no—
503#442—22no—
504#442—22no—
505#441—22no—
506#440—22no—
507#440—22no—
508#440—22no—
509#440—22no—
510#440—22no—
511#440—22no—
512#440—22no—
513#440—22no—
514C4×Q16—22no—
515C4×Q16—22no—
516C4×SD16—22no—
517C4×SD16—22no—
518#432D412yes—
519#432D412yes—
520#432D412yes—
521#432D412yes—
522#431D412yes—
523#431D412yes—
524#431C2311yescharacteristic
525#431C2311yescharacteristic
526#431C2311yescharacteristic
527#431C2311yescharacteristic
528#431C2311yescharacteristic
529#431C2311yescharacteristic
530#431C2311yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#431C2311yescharacteristic
535#431C2311yescharacteristic
536#428—22no—
537#428—22no—
538#423D412yes—
539#423D412yes—
540C2×C4⋊C8D412yes—
541#417—22no—
542#417—22no—
543#416—22no—
544#416—22no—
545#407D412yes—
546#407D412yes—
547C2×C22⋊C8D412yes—
548C4×M16C2311yescharacteristic
549C4×M16C2311yescharacteristic
550C4×M16C2311yescharacteristic
551C4×M16C2311yescharacteristic
552C2×C4×C8C2311yescharacteristic
553C2×C4×C8C2311yescharacteristic
554#322C2311yescharacteristic
555#322C2311yescharacteristic
556#322C2311yescharacteristic
557#322C2311yescharacteristic
558#322C2311yescharacteristic
559#322C2311yescharacteristic
560#322C2311yescharacteristic
561#322C2311yescharacteristic
562#322C2311yescharacteristic
563#322C2311yescharacteristic
564#322C2311yescharacteristic
565#322C2311yescharacteristic
566C82C2311yescharacteristic
567C82C2311yescharacteristic
568C82C2311yescharacteristic
569C82C2311yescharacteristic
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41—21no—
574C2×#41—21no—
575C2×#41—21no—
576C2×#41—21no—
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—41no—
581C2×#41—41no—
582C2×#41—84no—
583C22×Q8—21no—
584C22×Q8—21no—
585C22×Q8—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—41no—
590C23×C4—41no—
591C23×C4C2×D411yescharacteristic
592C23×C4C2×D411yescharacteristic
593C23×C4C2×D411yescharacteristic
594#135—84no—
595#135—84no—
596C2×Q16—22no—
597C2×Q16—22no—
598C2×Q16—22no—
599C2×Q16—22no—
600C2×Q16—22no—
601C2×SD16—22no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—22no—
605C2×SD16—22no—
606C2×SD16—22no—
607C2×SD16—22no—
608C2×SD16—22no—
609C2×SD16—22no—
610C2×SD16—22no—
611C2×SD16—22no—
612C2×SD16—22no—
613C2×SD16—22no—
614C2×SD16—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×M16C2×D412yes—
621C2×M16C2×D412yes—
622C2×M16C2×D412yes—
623C2×M16C2×D412yes—
624C22×C8C2×D412yes—
625C22×C8C2×D412yes—
626C4⋊Q8—21no—
627C4⋊Q8—21no—
628C4⋊Q8—21no—
629C4⋊Q8—21no—
630C4⋊Q8—21no—
631C4⋊Q8—21no—
632C4⋊Q8—21no—
633C4⋊Q8—21no—
634C4⋊Q8—21no—
635C4⋊Q8C2411yescharacteristic
636C4⋊Q8C2411yescharacteristic
637C4⋊Q8C2411yescharacteristic
638C4⋊Q8C2411yescharacteristic
639C4⋊Q8C2411yescharacteristic
640C4⋊Q8C2411yescharacteristic
641C4⋊Q8C2411yescharacteristic
642C4⋊Q8C2411yescharacteristic
643C4⋊Q8C2411yescharacteristic
644C4⋊Q8C2411yescharacteristic
645C4⋊Q8C2411yescharacteristic
646C4⋊Q8C2411yescharacteristic
647#127—21no—
648#127—21no—
649#127—21no—
650#127C2411yescharacteristic
651#127C2411yescharacteristic
652#127C2411yescharacteristic
653#127C2411yescharacteristic
654#126—41no—
655#126—41no—
656#126—41no—
657#126—41no—
658#125—21no—
659#125—21no—
660#125—21no—
661#125—21no—
662#125—21no—
663#125—21no—
664#125—21no—
665#125—21no—
666#125—21no—
667#125—21no—
668#125—41no—
669#125—41no—
670#124—21no—
671#124—21no—
672#124—21no—
673#124—21no—
674#124—21no—
675#124—21no—
676#124—21no—
677#124—21no—
678#124—21no—
679#124—21no—
680#124—41no—
681#124—41no—
682#123—41no—
683#123—41no—
684#123—41no—
685#123—41no—
686#123—41no—
687#123—41no—
688C22⋊Q8—21no—
689C22⋊Q8—21no—
690C22⋊Q8—21no—
691C22⋊Q8—21no—
692C22⋊Q8—21no—
693C22⋊Q8—21no—
694C22⋊Q8—21no—
695C22⋊Q8—21no—
696C22⋊Q8—21no—
697C22⋊Q8—21no—
698C22⋊Q8—21no—
699C22⋊Q8—21no—
700C22⋊Q8—21no—
701C22⋊Q8—21no—
702C22⋊Q8—21no—
703C22⋊Q8—21no—
704C22⋊Q8—21no—
705C22⋊Q8—21no—
706C22⋊Q8—21no—
707C22⋊Q8—21no—
708C22⋊Q8—41no—
709C22⋊Q8—41no—
710C22⋊Q8—41no—
711C22⋊Q8—41no—
712#121—21no—
713#121—21no—
714#121—21no—
715#121—21no—
716#121—21no—
717#121—21no—
718#121—21no—
719#121—21no—
720#121—21no—
721#121—21no—
722#121—21no—
723#121—21no—
724#121—21no—
725#121—21no—
726#121—21no—
727#121—21no—
728#121—21no—
729#121—21no—
730#121—21no—
731#121—21no—
732#121—41no—
733#121—41no—
734#121—41no—
735#121—41no—
736#120—41no—
737#120—41no—
738C4×Q8—21no—
739C4×Q8—21no—
740C4×Q8—21no—
741C4×Q8—21no—
742C4×Q8—21no—
743C4×Q8—21no—
744C4×Q8—21no—
745C4×Q8—21no—
746C4×Q8—21no—
747C4×Q8—21no—
748C4×Q8—21no—
749C4×Q8—21no—
750C4×Q8—21no—
751C4×Q8—21no—
752C4×Q8—21no—
753C4×Q8—21no—
754C4×Q8—21no—
755C4×Q8—21no—
756C4×Q8—21no—
757C4×Q8—21no—
758C4×Q8—41no—
759C4×Q8—41no—
760C4×Q8—41no—
761C4×Q8—41no—
762C4×D4—21no—
763C4×D4—21no—
764C4×D4—21no—
765C4×D4—21no—
766C4×D4—21no—
767C4×D4—21no—
768C4×D4—21no—
769C4×D4—21no—
770C4×D4—21no—
771C4×D4—21no—
772C4×D4—21no—
773C4×D4—21no—
774C4×D4—21no—
775C4×D4—21no—
776C4×D4—21no—
777C4×D4—21no—
778C4×D4—21no—
779C4×D4—21no—
780C4×D4—21no—
781C4×D4—21no—
782C4×D4—41no—
783C4×D4—41no—
784C4×D4—41no—
785C4×D4—41no—
786C4×D4—41no—
787C4×D4—41no—
788C4×D4—41no—
789C4×D4—41no—
790C4×D4—41no—
791C4×D4—41no—
792C4×D4—41no—
793C4×D4—41no—
794C4×D4—41no—
795C4×D4—41no—
796C4×D4—41no—
797C4×D4—41no—
798#117—21no—
799#117—21no—
800#117—21no—
801#117—21no—
802#117—21no—
803#117—21no—
804#117—21no—
805#117—21no—
806#117—21no—
807#117—21no—
808#117—41no—
809#117—41no—
810#117—41no—
811#117—41no—
812#117—41no—
813#117—41no—
814#117—41no—
815#117—41no—
816C2×C4⋊C4—21no—
817C2×C4⋊C4—21no—
818C2×C4⋊C4—21no—
819C2×C4⋊C4—21no—
820C2×C4⋊C4—21no—
821C2×C4⋊C4—21no—
822C2×C4⋊C4—41no—
823C2×C4⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C42—41no—
828C2×C42—41no—
829C2×C42—41no—
830C2×C42C2×D411yescharacteristic
831C2×C42C2×D411yescharacteristic
832C2×C42C2×D411yescharacteristic
833C2×C42C2×D411yescharacteristic
834C2×C42C2×D411yescharacteristic
835C2×C42C2×D411yescharacteristic
836C2×C42C2×D411yescharacteristic
837C2×C42C2×D411yescharacteristic
838C2×C42C2×D411yescharacteristic
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842#107—22no—
843#107—22no—
844#107—22no—
845#107—22no—
846#107—22no—
847#107—22no—
848#107—22no—
849#107—22no—
850#107—22no—
851#107—22no—
852#107—22no—
853#107—22no—
854#107—22no—
855#107—22no—
856#106—22no—
857#106—22no—
858#106—22no—
859#106—22no—
860#106—22no—
861#106—22no—
862#106—22no—
863#106—22no—
864#106—22no—
865#106—22no—
866C4⋊C8C2×D412yes—
867C4⋊C8C2×D412yes—
868C4⋊C8C2×D412yes—
869C4⋊C8C2×D412yes—
870C4⋊C8C2×D412yes—
871C4⋊C8C2×D412yes—
872C4⋊C8C2×D412yes—
873C4⋊C8C2×D412yes—
874C4⋊C8C2×D412yes—
875C4⋊C8C2×D412yes—
876C4⋊C8C2×D412yes—
877C4⋊C8C2×D412yes—
878#103—22no—
879#103—22no—
880#103—22no—
881#103—22no—
882#103—22no—
883#103—22no—
884#103—22no—
885#103—22no—
886#103—22no—
887#103—22no—
888#103—22no—
889#103—22no—
890#103—22no—
891#103—22no—
892#103—22no—
893#103—22no—
894#103—22no—
895#103—22no—
896#103—22no—
897#103—22no—
898#103—22no—
899#103—22no—
900#103—22no—
901#103—22no—
902#102—22no—
903#102—22no—
904#102—22no—
905#102—22no—
906#102—22no—
907#102—22no—
908#102—22no—
909#102—22no—
910#102—22no—
911#102—22no—
912#102—22no—
913#102—22no—
914#102—22no—
915#102—22no—
916#102—22no—
917#102—22no—
918#102—22no—
919#102—22no—
920#102—22no—
921#102—22no—
922#102—22no—
923#102—22no—
924#102—22no—
925#102—22no—
926C22⋊C8C2×D412yes—
927C22⋊C8C2×D412yes—
928C22⋊C8C2×D412yes—
929C22⋊C8C2×D412yes—
930C22⋊C8C2×D412yes—
931C22⋊C8C2×D412yes—
932C22⋊C8C2×D412yes—
933C22⋊C8C2×D412yes—
934C22⋊C8C2×D412yes—
935C22⋊C8C2×D412yes—
936C22⋊C8C2×D412yes—
937C22⋊C8C2×D412yes—
938#97C2×D412yes—
939#97C2×D412yes—
940#97C2×D412yes—
941#97C2×D412yes—
942C4×C8C2×D412yes—
943C4×C8C2×D412yes—
944C4×C8C2411yescharacteristic
945C4×C8C2411yescharacteristic
946C4×C8C2411yescharacteristic
947C4×C8C2411yescharacteristic
948C4×C8C2411yescharacteristic
949C4×C8C2411yescharacteristic
950C4×C8C2411yescharacteristic
951C4×C8C2411yescharacteristic
952C4×C8C2411yescharacteristic
953C4×C8C2411yescharacteristic
954C4×C8C2411yescharacteristic
955C4×C8C2411yescharacteristic
956C24—41no—
957C24#12711yescharacteristic
958#41—44no—
959#41—44no—
960#41—44no—
961#41—44no—
962#41—82no—
963#41—82no—
964#41—82no—
965#41—82no—
966#41—82no—
967#41—82no—
968#41—84no—
969#41—84no—
970C2×Q8—21no—
971C2×Q8—21no—
972C2×Q8—21no—
973C2×Q8—21no—
974C2×Q8—21no—
975C2×Q8—21no—
976C2×Q8—21no—
977C2×Q8—21no—
978C2×Q8—21no—
979C2×Q8—21no—
980C2×Q8—21no—
981C2×Q8—21no—
982C2×Q8—41no—
983C2×Q8—41no—
984C2×Q8—41no—
985C2×Q8—82no—
986C2×Q8—82no—
987C2×Q8—82no—
988C2×D4—21no—
989C2×D4—21no—
990C2×D4—21no—
991C2×D4—21no—
992C2×D4—21no—
993C2×D4—21no—
994C2×D4—21no—
995C2×D4—21no—
996C2×D4—21no—
997C2×D4—21no—
998C2×D4—21no—
999C2×D4—21no—
1000C2×D4—41no—
1001C2×D4—41no—
1002C2×D4—41no—
1003C2×D4—41no—
1004C2×D4—41no—
1005C2×D4—41no—
1006C2×D4—41no—
1007C2×D4—41no—
1008C2×D4—41no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—82no—
1014C2×D4—82no—
1015C2×D4—82no—
1016C2×D4—84no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—84no—
1034C22×C4#12711yescharacteristic
1035C22×C4#12711yescharacteristic
1036C22×C4#12711yescharacteristic
1037C22×C4#12711yescharacteristic
1038C22×C4#12711yescharacteristic
1039C22×C4#12711yescharacteristic
1040C22×C4#12711yescharacteristic
1041C22×C4#12711yescharacteristic
1042C22×C4#12711yescharacteristic
1043C22×C4C22×D411yescharacteristic
1044C22×C4C22×D411yescharacteristic
1045C22×C4C22×D411yescharacteristic
1046C22×C4C22×D411yescharacteristic
1047C22×C4C22×D411yescharacteristic
1048C22×C4C22×D411yescharacteristic
1049C22×C4C22×D411yescharacteristic
1050C22×C4C22×D411yescharacteristic
1051C22×C4C22×D411yescharacteristic
1052Q16—82no—
1053Q16—82no—
1054Q16—82no—
1055Q16—82no—
1056Q16—82no—
1057SD16—82no—
1058SD16—82no—
1059SD16—82no—
1060SD16—82no—
1061SD16—82no—
1062SD16—82no—
1063SD16—82no—
1064SD16—82no—
1065SD16—82no—
1066SD16—82no—
1067SD16—82no—
1068SD16—82no—
1069SD16—82no—
1070SD16—82no—
1071D8—82no—
1072D8—82no—
1073D8—82no—
1074D8—82no—
1075D8—82no—
1076M16—42no—
1077M16—42no—
1078M16—42no—
1079M16—42no—
1080C2×C8—42no—
1081C2×C8—42no—
1082C2×C8C22×D412yes—
1083C2×C8C22×D412yes—
1084C2×C8C22×D412yes—
1085C2×C8C22×D412yes—
1086C2×C8C22×D412yes—
1087C2×C8C22×D412yes—
1088C2×C8C22×D412yes—
1089C2×C8C22×D412yes—
1090C2×C8C22×D412yes—
1091C2×C8C22×D412yes—
1092C2×C8C22×D412yes—
1093C2×C8C22×D412yes—
1094C4⋊C4—21no—
1095C4⋊C4—21no—
1096C4⋊C4—21no—
1097C4⋊C4—21no—
1098C4⋊C4—21no—
1099C4⋊C4—21no—
1100C4⋊C4—21no—
1101C4⋊C4—21no—
1102C4⋊C4—21no—
1103C4⋊C4—21no—
1104C4⋊C4—21no—
1105C4⋊C4—21no—
1106C4⋊C4—21no—
1107C4⋊C4—21no—
1108C4⋊C4—21no—
1109C4⋊C4—21no—
1110C4⋊C4—21no—
1111C4⋊C4—21no—
1112C4⋊C4—21no—
1113C4⋊C4—21no—
1114C4⋊C4—21no—
1115C4⋊C4—21no—
1116C4⋊C4—21no—
1117C4⋊C4—21no—
1118C4⋊C4—41no—
1119C4⋊C4—41no—
1120C4⋊C4—41no—
1121C4⋊C4—41no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—41no—
1125C4⋊C4—41no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—41no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—41no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C22⋊C4—41no—
1145C22⋊C4—41no—
1146C22⋊C4—41no—
1147C22⋊C4—41no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—41no—
1151C22⋊C4—41no—
1152C22⋊C4—41no—
1153C22⋊C4—41no—
1154C22⋊C4—41no—
1155C22⋊C4—41no—
1156C22⋊C4—41no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
1165C22⋊C4—41no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—41no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—41no—
1172C22⋊C4—41no—
1173C22⋊C4—41no—
1174C42—41no—
1175C42—41no—
1176C42—41no—
1177C42—41no—
1178C42—41no—
1179C42—41no—
1180C42—41no—
1181C42—41no—
1182C42—41no—
1183C42—41no—
1184C42#12711yescharacteristic
1185C42#12711yescharacteristic
1186C42#12711yescharacteristic
1187C42#12711yescharacteristic
1188C42#12711yescharacteristic
1189C42#12711yescharacteristic
1190C42C22×D411yescharacteristic
1191C42C22×D411yescharacteristic
1192C42C22×D411yescharacteristic
1193C42C22×D411yescharacteristic
1194C42C22×D411yescharacteristic
1195C42C22×D411yescharacteristic
1196C42C22×D411yescharacteristic
1197C42C22×D411yescharacteristic
1198C42C22×D411yescharacteristic
1199C42C2511yescharacteristic
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—82no—
1208C23—82no—
1209C23—82no—
1210C23C2×#12711yescharacteristic
1211C23C2×#12711yescharacteristic
1212C23C2×#12711yescharacteristic
1213Q8—42no—
1214Q8—42no—
1215Q8—42no—
1216Q8—42no—
1217Q8—42no—
1218Q8—42no—
1219Q8—42no—
1220Q8—42no—
1221Q8—42no—
1222Q8—42no—
1223Q8—42no—
1224Q8—42no—
1225Q8—82no—
1226Q8—82no—
1227Q8—82no—
1228D4—42no—
1229D4—42no—
1230D4—42no—
1231D4—42no—
1232D4—42no—
1233D4—42no—
1234D4—42no—
1235D4—42no—
1236D4—42no—
1237D4—42no—
1238D4—42no—
1239D4—42no—
1240D4—82no—
1241D4—82no—
1242D4—82no—
1243D4—82no—
1244D4—82no—
1245D4—82no—
1246D4—82no—
1247D4—82no—
1248D4—82no—
1249D4—82no—
1250D4—82no—
1251D4—82no—
1252D4—82no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—82no—
1284C2×C4—82no—
1285C2×C4—82no—
1286C2×C4—82no—
1287C2×C4—82no—
1288C2×C4—82no—
1289C2×C4—82no—
1290C2×C4—82no—
1291C2×C4—82no—
1292C2×C4—82no—
1293C2×C4—82no—
1294C2×C4—82no—
1295C2×C4—82no—
1296C2×C4C2×#12711yescharacteristic
1297C2×C4C2×#12711yescharacteristic
1298C2×C4C2×#12711yescharacteristic
1299C2×C4C2×#12711yescharacteristic
1300C2×C4C2×#12711yescharacteristic
1301C2×C4C2×#12711yescharacteristic
1302C2×C4C2×#12711yescharacteristic
1303C2×C4C2×#12711yescharacteristic
1304C2×C4C2×#12711yescharacteristic
1305C2×C4C23×D411yescharacteristic
1306C2×C4C23×D411yescharacteristic
1307C2×C4C23×D411yescharacteristic
1308C8—22no—
1309C8—22no—
1310C8—22no—
1311C8—22no—
1312C8—22no—
1313C8—22no—
1314C8—22no—
1315C8—22no—
1316C8—22no—
1317C8—22no—
1318C8—22no—
1319C8—22no—
1320C22—21no—
1321C22—21no—
1322C22—21no—
1323C22—21no—
1324C22—21no—
1325C22—21no—
1326C22—21no—
1327C22—21no—
1328C22—21no—
1329C22—82no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—164no—
1343C22C22×#12711yescharacteristic
1344C4—21no—
1345C4—21no—
1346C4—21no—
1347C4—21no—
1348C4—21no—
1349C4—21no—
1350C4—21no—
1351C4—21no—
1352C4—21no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4#358412yes—
1366C4#358512yes—
1367C4#358612yes—
1368C2—41no—
1369C2—41no—
1370C2—41no—
1371C2—161no—
1372C2—161no—
1373C2—161no—
1374C2—161no—
1375C2#6064311yescharacteristic
1376C2#6064411yescharacteristic
1377C2#6064511yescharacteristic
subgroupG/H
center, socleC22C22×#127
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60972C2semidirect
2. #60969C2semidirect
3. #60965C2semidirect
4. #60947C2semidirect
5. #60862C2semidirect
6. #60782C2semidirect
7. #19744C2semidirect
8. #19740C2semidirect
9. #19738C2semidirect
10. #19737C2semidirect
11. #19737C2semidirect
12. #19736C2semidirect
13. #19735C2semidirect
14. #19733C2semidirect
15. #19730C2semidirect
16. #19728C2semidirect
17. #19726C2semidirect
18. #19726C2semidirect
19. #19722C2semidirect
20. #19722C2semidirect
21. #19718C2semidirect
22. #19714C2semidirect
23. #19696C2semidirect
24. #19694C2semidirect
25. #19691C2semidirect
26. #19687C2semidirect
27. #19649C2semidirect
28. #19645C2semidirect
29. #19643C2semidirect
30. #19641C2semidirect
31. #17324C2semidirect
47. #3231C22semidirect
48. #3231C22semidirect
49. #3231C22semidirect
53. #3229C22semidirect
59. #3228C22semidirect
60. #3228C22semidirect
61. #3228C22semidirect
65. #3226C22semidirect
73. #3210C22semidirect
75. #3209C22semidirect
85. #3207C22semidirect
89. #3206C22semidirect
96. #3185C22semidirect
99. #3184C22semidirect
106. #3182C22semidirect
107. #3182C22semidirect
108. #3170C22semidirect
109. #3170C22semidirect
110. #3167C22semidirect
111. #3167C22semidirect
112. #3165C22semidirect
113. #3165C22semidirect
116. #3141C22semidirect
117. #3141C22semidirect
135. #1723C22semidirect
136. #1723C22semidirect
137. #1723C22semidirect
138. #1723C22semidirect
139. #1723C22semidirect
140. #1723C22semidirect
141. #1722C22semidirect
142. #1722C22semidirect
143. #1722C22semidirect
144. #1722C22semidirect
145. #1721C22semidirect
146. #1721C22semidirect
147. #1720C22semidirect
148. #1720C22semidirect
149. #1720C22semidirect
150. #1720C22semidirect
151. #1719C22semidirect
152. #1719C22semidirect
153. #1719C22semidirect
154. #1719C22semidirect
155. #1719C22semidirect
156. #1719C22semidirect
157. #1719C22semidirect
158. #1719C22semidirect
159. #1718C22semidirect
160. #1718C22semidirect
161. #1718C22semidirect
162. #1718C22semidirect
163. #1718C22semidirect
164. #1718C22semidirect
165. #1717C22semidirect
166. #1717C22semidirect
167. #1717C22semidirect
168. #1717C22semidirect
169. #1717C22semidirect
170. #1717C22semidirect
171. #1716C22semidirect
172. #1715C22semidirect
173. #1715C22semidirect
174. #1715C22semidirect
175. #1714C22semidirect
176. #1714C22semidirect
177. #1714C22semidirect
178. #1714C22semidirect
179. #1714C22semidirect
180. #1714C22semidirect
181. #1714C22semidirect
182. #1714C22semidirect
183. #1713C22semidirect
184. #1711C22semidirect
185. #1711C22semidirect
186. #1710C22semidirect
187. #1710C22semidirect
188. #1709C22semidirect
189. #1708C22semidirect
190. #1708C22semidirect
191. #1708C22semidirect
192. #1707C22semidirect
193. #1707C22semidirect
194. #1706C22semidirect
195. #1706C22semidirect
196. #1706C22semidirect
197. #1706C22semidirect
198. #1705C22semidirect
203. #1453C22semidirect
204. #1453C22semidirect
205. #1453C22semidirect
206. #1453C22semidirect
207. #1451C22semidirect
208. #1451C22semidirect
209. C8×M16C22semidirect
210. C8×M16C22semidirect

Maximal subgroups

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

subgroupindex
#609722
#609692
#609652
#609472
#608622
#607822
#197442
#197402
#197382
#197372
#197362
#197352
#197332
#197302
#197282
#197262
#197222
#197182
#197142
#196962
#196942
#196912
#196872
#196492
#196452
#196432
#196412
#173242