Finite Group Databasebeta

← #7623775

Subgroups — #7623775

Order 512.

1509 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61289C211yesmaximal, characteristic, complemented
2#61090C211yesmaximal, characteristic, complemented
3#33894C212yesmaximal, complemented
4#33893C212yesmaximal, complemented
5#33890C212yesmaximal, complemented
6#33889C212yesmaximal, complemented
7#33868C212yesmaximal, complemented
8#33867C212yesmaximal, complemented
9#33864C212yesmaximal, complemented
10#33863C212yesmaximal, complemented
11C2×#2242C211yesmaximal, characteristic, complemented
12#33651C211yesmaximal, characteristic, complemented
13#33650C211yesmaximal, characteristic, complemented
14#33630C211yesmaximal, characteristic, complemented
15#33613C211yesmaximal, characteristic, complemented
16#33612C211yesmaximal, characteristic, complemented
17#33584C211yesmaximal, characteristic, complemented
18#33527C211yesmaximal, characteristic, complemented
19#33526C211yesmaximal, characteristic, complemented
20C4×#508C211yesmaximal, characteristic, complemented
21#33434C211yesmaximal, characteristic, complemented
22#33382C211yesmaximal, characteristic, complemented
23#33381C211yesmaximal, characteristic, complemented
24C2×#578C2211yescharacteristic
25C2×#576C2211yescharacteristic
26#3512—21no—
27#3500—21no—
28C2×#510C2211yescharacteristic, complemented
29C2×#509C2211yescharacteristic
30C2×#508C2211yescharacteristic
31C2×#504C2211yescharacteristic
32C2×#504C2211yescharacteristic, complemented
33#3351—22no—
34#3351—22no—
35#3339C2212yescomplemented
36#3339C2212yescomplemented
37#3336C2212yescomplemented
38#3336C2212yescomplemented
39#3285C2212yes—
40#3285C2212yes—
41#3280C2212yes—
42#3280C2212yes—
43#3275—22no—
44#3275—22no—
45C2×#499C2211yescharacteristic, complemented
46C2×#495C2211yescharacteristic
47#3099—21no—
48#3099—21no—
49#3080—21no—
50#3061C2211yescharacteristic
51#3061C2211yescharacteristic, complemented
52#3059C2211yescharacteristic
53#3058C2211yescharacteristic
54#3040—21no—
55#3010—21no—
56#3009—21no—
57C4×#135C2211yescharacteristic
58C4×#135C2211yescharacteristic, complemented
59#2931C2211yescharacteristic
60#2913C2211yescharacteristic
61#2913C2211yescharacteristic, complemented
62#2242C2212yescomplemented
63#2242C2212yescomplemented
64#2242C2212yescomplemented
65#2242C2212yescomplemented
66#2237C2212yescomplemented
67#2237C2212yescomplemented
68#2236C2212yescomplemented
69#2235C2212yescomplemented
70#2234C2212yescomplemented
71#2234C2212yescomplemented
72#2233C2212yescomplemented
73#2232C2212yescomplemented
74#2229C2212yescomplemented
75#2229C2212yescomplemented
76#2228C2212yescomplemented
77#2228C2212yescomplemented
78#2220C2212yescomplemented
79#2220C2212yescomplemented
80#2219C2212yescomplemented
81#2218C2212yescomplemented
82#2217C2212yescomplemented
83#2217C2212yescomplemented
84#2216C2212yescomplemented
85#2215C2212yescomplemented
86#2211C2212yescomplemented
87#2211C2212yescomplemented
88#2210C2212yescomplemented
89#2210C2212yescomplemented
90#2189C2212yes—
91#2189C2212yescomplemented
92#2188C2212yescomplemented
93#2187C2212yes—
94#2186C2212yes—
95#2186C2212yescomplemented
96#2185C2212yescomplemented
97#2184C2212yes—
98C4×Q32C2211yescharacteristic, complemented
99C4×Q32C2211yescharacteristic, complemented
100C4×SD32C2211yescharacteristic, complemented
101C4×SD32C2211yescharacteristic, complemented
102C4×SD32C2211yescharacteristic, complemented
103C4×SD32C2211yescharacteristic, complemented
104C4×D16C2211yescharacteristic, complemented
105C4×D16C2211yescharacteristic, complemented
106#2169C2212yescomplemented
107#2169C2212yescomplemented
108D4×C16C2212yescomplemented
109D4×C16C2212yescomplemented
110#2159C2211yescharacteristic, complemented
111#2159C2211yescharacteristic, complemented
112#2158C2211yescharacteristic, complemented
113#2150C2211yescharacteristic, complemented
114#2141C2211yescharacteristic, complemented
115#2141C2212yescomplemented
116#2140C2211yescharacteristic
117#2140C2212yes—
118#2139C2211yescharacteristic
119#2139C2211yescharacteristic
120#2139C2212yes—
121#2139C2212yescomplemented
122#2138C2212yes—
123#2138C2211yescharacteristic
124#2138C2212yescomplemented
125#2138C2211yescharacteristic, complemented
126C2×#358C2212yescomplemented
127C2×#358C2211yescharacteristic, complemented
128C2×#358C2211yescharacteristic, complemented
129C2×#357C2212yes—
130C2×#357C2211yescharacteristic
131C2×#357C2211yescharacteristic
132#2113C2211yescharacteristic
133#2113C2211yescharacteristic, complemented
134C2×C4×C16C2211yescharacteristic, complemented
135C2×2−1+4—21no—
136C2×H(5,𝔽2)—21no—
137#578—24no—
138#578—42no—
139#576—24no—
140#576—42no—
141C2×#137—21no—
142C2×#137—22no—
143C2×AGL(1,ℤ/8)—21no—
144C2×AGL(1,ℤ/8)—22no—
145C2×#135C2311yescharacteristic
146C2×#135C2312yes—
147C2×#135C2312yes—
148C2×#135C2311yescharacteristic
149C22×Q16C2311yescharacteristic
150C22×Q16C2312yes—
151C22×SD16—21no—
152C22×D8C2311yescharacteristic
153C22×D8C2312yes—
154C2×#131C2311yescharacteristic
155C2×#131C2311yescharacteristic
156#553—22no—
157#553—22no—
158#553—42no—
159#553—42no—
160#552—22no—
161#552—22no—
162#548—22no—
163#548—22no—
164#546—22no—
165#546—22no—
166#546—42no—
167#546—42no—
168#541—41no—
169#540—41no—
170#537—21no—
171#537—21no—
172#536—21no—
173#536—41no—
174#535—21no—
175#535—41no—
176#532—41no—
177#532D411yescharacteristic
178#529—41no—
179#529—41no—
180C2×#125—21no—
181C2×#124—21no—
182C2×#124—41no—
183#520—21no—
184#520—21no—
185C4×#41—21no—
186C4×#41—21no—
187#510—42no—
188#509—42no—
189#508—24no—
190C2×Q32C2311yescharacteristic
191C2×Q32C2312yes—
192C2×SD32C2311yescharacteristic
193C2×SD32C2311yescharacteristic
194C2×SD32C2312yes—
195C2×SD32C2312yes—
196C2×D16C2311yescharacteristic
197C2×D16C2312yes—
198#504—42no—
199#504—42no—
200C2×M32C2311yescharacteristic
201C2×M32C2311yescharacteristic
202C2×M32C2312yes—
203C2×M32C2312yes—
204C22×C16C2311yescharacteristic
205C22×C16C2311yescharacteristic
206C22×C16C2312yes—
207C22×C16C2312yes—
208#499—21no—
209#499—21no—
210#499C2312yes—
211#499C2312yes—
212#495—21no—
213#495—21no—
214#495C2312yes—
215#495C2312yes—
216#485—22no—
217#485—22no—
218#483—22no—
219#483—22no—
220#482—22no—
221#482—22no—
222#481—22no—
223#481—22no—
224#479—22no—
225#479—22no—
226#478—22no—
227#478—22no—
228#470—22no—
229#469—22no—
230#468—22no—
231#468—22no—
232#467C2312yes—
233#467C2312yes—
234#467C2312yes—
235#467C2312yes—
236#466C2312yes—
237#466C2312yes—
238#466C2312yes—
239#466C2312yes—
240#464—22no—
241#464—22no—
242#463—22no—
243#463—22no—
244#452—22no—
245#452—22no—
246#450—22no—
247#450—22no—
248#449—22no—
249#449—22no—
250#448—22no—
251#448—22no—
252C4×Q16C2311yescharacteristic
253C4×Q16C2311yescharacteristic
254C4×Q16C2311yescharacteristic
255C4×Q16C2311yescharacteristic
256C4×SD16—21no—
257C4×SD16—21no—
258C4×SD16—21no—
259C4×SD16—21no—
260C4×D8C2311yescharacteristic
261C4×D8C2311yescharacteristic
262C4×D8C2311yescharacteristic
263C4×D8C2311yescharacteristic
264#436D412yes—
265#436D412yes—
266C8×D4C2312yes—
267C8×D4C2312yes—
268#428—21no—
269#428—21no—
270#428—22no—
271#428—22no—
272#427C2312yes—
273#427C2312yes—
274#427C2311yescharacteristic
275#427C2311yescharacteristic
276C2×#107C2312yes—
277C2×#107C2312yes—
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106—21no—
281#423D411yescharacteristic
282#419—21no—
283#418—21no—
284#417—21no—
285#417—21no—
286#416—21no—
287#416—21no—
288#408D411yescharacteristic
289#408D411yescharacteristic
290C2×C4×C8C2311yescharacteristic
291#367C2311yescharacteristic
292#367C2311yescharacteristic
293#367C2312yes—
294#367C2312yes—
295#366C2311yescharacteristic
296#366C2311yescharacteristic
297#366C2312yes—
298#366C2312yes—
299C4⋊C16C2312yes—
300C4⋊C16C2312yes—
301#358C2311yescharacteristic
302#358C2312yes—
303#358C2312yes—
304#358C2312yes—
305#358C2312yes—
306#358C2312yes—
307#358C2312yes—
308#358C2311yescharacteristic
309#358C2312yes—
310#358C2312yes—
311#358C2311yescharacteristic
312#358C2311yescharacteristic
313#357C2311yescharacteristic
314#357C2312yes—
315#357C2312yes—
316#357C2312yes—
317#357C2312yes—
318#357C2312yes—
319#357C2312yes—
320#357C2311yescharacteristic
321#357C2312yes—
322#357C2312yes—
323#357C2311yescharacteristic
324#357C2311yescharacteristic
325C22⋊C16C2312yes—
326C22⋊C16C2312yes—
327C22⋊C16C2312yes—
328C22⋊C16C2312yes—
329C4×C16C2311yescharacteristic
330C4×C16C2311yescharacteristic
331C4×C16C2311yescharacteristic
332C4×C16C2311yescharacteristic
3332−1+4—44no—
3342−1+4—82no—
335H(5,𝔽2)—44no—
336H(5,𝔽2)—82no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—41no—
342C2×#41—41no—
343C2×#41—42no—
344C2×#41C2×D411yescharacteristic
345C2×#41C2×D411yescharacteristic
346C22×Q8—21no—
347C22×Q8—22no—
348C22×Q8—41no—
349C22×D4—21no—
350C22×D4—22no—
351C22×D4—41no—
352C22×D4—42no—
353#137—48no—
354#137—44no—
355AGL(1,ℤ/8)—48no—
356AGL(1,ℤ/8)—44no—
357#135—24no—
358#135—24no—
359#135—22no—
360#135—22no—
361#135—22no—
362#135—42no—
363#135—42no—
364#135#4114yes—
365C2×Q16—24no—
366C2×Q16—22no—
367C2×Q16—21no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—42no—
371C2×Q16C2412yes—
372C2×Q16C2411yescharacteristic
373C2×Q16C2411yescharacteristic
374C2×SD16—21no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—21no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—82no—
381C2×D8—24no—
382C2×D8—22no—
383C2×D8—21no—
384C2×D8—22no—
385C2×D8—22no—
386C2×D8—42no—
387C2×D8C2412yes—
388C2×D8C2411yescharacteristic
389C2×D8C2411yescharacteristic
390#131—22no—
391#131—22no—
392#131—22no—
393#131—22no—
394C2×M16C2×D411yescharacteristic
395C2×M16C2×D412yes—
396C2×M16C2×D411yescharacteristic
397C2×M16C2×D412yes—
398C22×C8C2×D411yescharacteristic
399C22×C8C2412yes—
400C22×C8C2412yes—
401C22×C8C2411yescharacteristic
402C4⋊Q8—41no—
403C4⋊Q8D811yescharacteristic
404#127—41no—
405#127D811yescharacteristic
406#126—42no—
407#126—42no—
408#126—42no—
409#126—42no—
410#125—22no—
411#125—22no—
412#125—42no—
413#125—42no—
414#125—41no—
415#125—41no—
416#124—22no—
417#124—22no—
418#124—41no—
419#124—41no—
420#124—42no—
421#124—42no—
422#124—41no—
423#124—41no—
424#124D811yescharacteristic
425#124D811yescharacteristic
426#123—42no—
427#123—42no—
428#123—42no—
429#123—42no—
430#123—42no—
431#123—42no—
432#123—42no—
433C22⋊Q8—22no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—41no—
438C22⋊Q8—41no—
439C22⋊Q8—42no—
440C22⋊Q8—42no—
441#121—22no—
442#121—22no—
443#121—22no—
444#121—22no—
445#121—41no—
446#121—41no—
447#121—42no—
448#121—42no—
449#121—42no—
450#121—42no—
451#121—42no—
452#121—42no—
453#121—42no—
454#121—42no—
455#121D812yes—
456#121D812yes—
457#120—42no—
458#120—42no—
459#120—42no—
460C4×Q8—21no—
461C4×Q8—21no—
462C4×Q8—21no—
463C4×Q8—21no—
464C4×Q8—41no—
465C4×Q8—41no—
466C4×D4—21no—
467C4×D4—21no—
468C4×D4—21no—
469C4×D4—21no—
470C4×D4—41no—
471C4×D4—41no—
472C4×D4—42no—
473C4×D4—42no—
474C4×D4—41no—
475C4×D4—41no—
476C4×D4—41no—
477C4×D4—41no—
478C4×D4—42no—
479C4×D4—42no—
480C4×D4—42no—
481C4×D4—42no—
482C4×D4C2×D412yes—
483C4×D4C2×D412yes—
484#117—21no—
485#117—21no—
486#117—22no—
487#117—22no—
488#117—42no—
489#117—42no—
490#117—41no—
491#117—41no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C42—41no—
503C2×C42—41no—
504C2×C42C2×D411yescharacteristic
505Q32—22no—
506Q32—42no—
507SD32—22no—
508SD32—22no—
509SD32—42no—
510SD32—42no—
511D16—22no—
512D16—42no—
513M32—22no—
514M32—22no—
515M32—42no—
516M32—42no—
517C2×C16—22no—
518C2×C16—22no—
519C2×C16—42no—
520C2×C16—42no—
521C2×C16C2411yescharacteristic
522C2×C16C2411yescharacteristic
523C2×C16C2411yescharacteristic
524C2×C16C2411yescharacteristic
525C2×C16C2412yes—
526C2×C16C2412yes—
527#107—21no—
528#107—21no—
529#107—22no—
530#107—22no—
531#107C2411yescharacteristic
532#107C2411yescharacteristic
533#107C2412yes—
534#107C2412yes—
535#107C2411yescharacteristic
536#107C2411yescharacteristic
537#106—22no—
538#106—22no—
539#106—21no—
540#106—22no—
541#106—22no—
542#106—21no—
543C4⋊C8C2×D412yes—
544C4⋊C8C2×D412yes—
545#103—21no—
546#103—21no—
547#103—21no—
548#103—21no—
549#103—22no—
550#103—22no—
551#103—22no—
552#103—22no—
553#102—21no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561C22⋊C8C2×D412yes—
562C22⋊C8C2×D412yes—
563C22⋊C8C2×D412yes—
564C22⋊C8C2×D412yes—
565C4×C8C2×D411yescharacteristic
566C4×C8C2×D411yescharacteristic
567C4×C8C2411yescharacteristic
568C4×C8C2411yescharacteristic
569C24—42no—
570C24—41no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—24no—
576#41—44no—
577#41—44no—
578#41—42no—
579#41—42no—
580#41—42no—
581#41—82no—
582#41—82no—
583#41—84no—
584#41—84no—
585#41—88no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—44no—
590C2×Q8—42no—
591C2×Q8—41no—
592C2×Q8—42no—
593C2×Q8—42no—
594C2×Q8—82no—
595C2×Q8—84no—
596C2×Q8C2×D811yescharacteristic
597C2×Q8C2×D811yescharacteristic
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—44no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—41no—
613C2×D4—42no—
614C2×D4—82no—
615C2×D4—84no—
616C2×D4—88no—
617C2×D4C2×D812yes—
618C2×D4C2×D812yes—
619C2×D4C2×D811yescharacteristic
620C2×D4C2×D811yescharacteristic
621C2×D4C2×D812yes—
622C2×D4C2×D812yes—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—42no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4C2×D811yescharacteristic
638C22×C4C2×D811yescharacteristic
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C22×D411yescharacteristic
642Q16—21no—
643Q16—22no—
644Q16—21no—
645Q16—21no—
646Q16—22no—
647Q16—44no—
648Q16—42no—
649Q16C2×#4112yes—
650SD16—24no—
651SD16—44no—
652SD16—44no—
653SD16—42no—
654SD16—82no—
655SD16—82no—
656D8—21no—
657D8—22no—
658D8—21no—
659D8—21no—
660D8—22no—
661D8—44no—
662D8—42no—
663D8C2×#4112yes—
664M16—22no—
665M16—22no—
666M16—24no—
667M16—24no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8C22×D411yescharacteristic
674C2×C8C22×D411yescharacteristic
675C2×C8C22×D412yes—
676C2×C8C22×D412yes—
677C2×C8C22×D411yescharacteristic
678C2×C8C2×#4112yes—
679C2×C8H(5,𝔽2)12yes—
680C2×C8C2511yescharacteristic
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—41no—
696C4⋊C4—41no—
697C4⋊C4—41no—
698C4⋊C4—41no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4C2×D812yes—
704C4⋊C4C2×D812yes—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—41no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C22⋊C4—41no—
722C22⋊C4—41no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4C2×D812yes—
726C22⋊C4C2×D812yes—
727C22⋊C4C2×D812yes—
728C22⋊C4C2×D812yes—
729C42—41no—
730C42—41no—
731C42—41no—
732C42—41no—
733C42—41no—
734C42—41no—
735C42—42no—
736C42—42no—
737C42C2×D811yescharacteristic
738C42C2×D811yescharacteristic
739C42C22×D411yescharacteristic
740C42C22×D411yescharacteristic
741C16—21no—
742C16—21no—
743C16—21no—
744C16—21no—
745C16—22no—
746C16—22no—
747C23—41no—
748C23—41no—
749C23—42no—
750C23—84no—
751C23—82no—
752C23—161no—
753C23—161no—
754C23—162no—
755C23—162no—
756C23C22×D812yes—
757C23C22×D812yes—
758C23C22×D811yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—41no—
763Q8—42no—
764Q8—41no—
765Q8—42no—
766Q8—41no—
767Q8—84no—
768Q8—82no—
769D4—24no—
770D4—24no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—42no—
775D4—42no—
776D4—44no—
777D4—42no—
778D4—41no—
779D4—41no—
780D4—42no—
781D4—41no—
782D4—84no—
783D4—84no—
784D4—84no—
785D4—82no—
786D4—82no—
787D4—162no—
788D4—162no—
789D4—162no—
790D4—162no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—161no—
813C2×C4—161no—
814C2×C4—161no—
815C2×C4—161no—
816C2×C4—162no—
817C2×C4—162no—
818C2×C4—161no—
819C2×C4—161no—
820C2×C4#54612yes—
821C2×C4C22×D811yescharacteristic
822C2×C4C22×D811yescharacteristic
823C2×C4C22×D812yes—
824C2×C4C22×D812yes—
825C2×C4C22×D811yescharacteristic
826C2×C4C22×D811yescharacteristic
827C2×C4C22×D811yescharacteristic
828C2×C4#57712yes—
829C2×C4C23×D411yescharacteristic
830C8—22no—
831C8—22no—
832C8—21no—
833C8—21no—
834C8#54612yes—
835C8C22×#4111yescharacteristic
836C8C2×H(5,𝔽2)11yescharacteristic
837C22—21no—
838C22—21no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—42no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—81no—
854C22—322no—
855C22—324no—
856C22#329412yes—
857C22C23×D811yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—22no—
863C4—22no—
864C4—42no—
865C4—81no—
866C4—81no—
867C4—82no—
868C4—82no—
869C4—81no—
870C4—81no—
871C4—82no—
872C4—81no—
873C4#329412yes—
874C4C2×#54611yescharacteristic
875C4C2×#57711yescharacteristic
876C2—22no—
877C2—42no—
878C2—42no—
879C2—82no—
880C2—161no—
881C2—162no—
882C2C2×#329411yescharacteristic
883C2#6263511yescharacteristic
884C2#6263511yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ #2931 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #61289C2semidirect
2. #61090C2semidirect
3. #33894C2semidirect
4. #33893C2semidirect
5. #33890C2semidirect
6. #33889C2semidirect
7. #33868C2semidirect
8. #33867C2semidirect
9. #33864C2semidirect
10. #33863C2semidirect
11. C2×#2242C2semidirect
12. #33651C2semidirect
13. #33650C2semidirect
14. #33630C2semidirect
15. #33613C2semidirect
16. #33612C2semidirect
17. #33584C2semidirect
18. #33527C2semidirect
19. #33526C2semidirect
20. C4×#508C2semidirect
21. #33434C2semidirect
22. #33382C2semidirect
23. #33381C2semidirect
28. C2×#510C22semidirect
32. C2×#504C22semidirect
35. #3339C22semidirect
36. #3339C22semidirect
37. #3336C22semidirect
38. #3336C22semidirect
45. C2×#499C22semidirect
51. #3061C22semidirect
58. C4×#135C22semidirect
61. #2913C22semidirect
62. #2242C22semidirect
63. #2242C22semidirect
64. #2242C22semidirect
65. #2242C22semidirect
66. #2237C22semidirect
67. #2237C22semidirect
68. #2236C22semidirect
69. #2235C22semidirect
70. #2234C22semidirect
71. #2234C22semidirect
72. #2233C22semidirect
73. #2232C22semidirect
74. #2229C22semidirect
75. #2229C22semidirect
76. #2228C22semidirect
77. #2228C22semidirect
78. #2220C22semidirect
79. #2220C22semidirect
80. #2219C22semidirect
81. #2218C22semidirect
82. #2217C22semidirect
83. #2217C22semidirect
84. #2216C22semidirect
85. #2215C22semidirect
86. #2211C22semidirect
87. #2211C22semidirect
88. #2210C22semidirect
89. #2210C22semidirect
91. #2189C22semidirect
92. #2188C22semidirect
95. #2186C22semidirect
96. #2185C22semidirect
98. C4×Q32C22semidirect
99. C4×Q32C22semidirect
100. C4×SD32C22semidirect
101. C4×SD32C22semidirect
102. C4×SD32C22semidirect
103. C4×SD32C22semidirect
104. C4×D16C22semidirect
105. C4×D16C22semidirect
106. #2169C22semidirect
107. #2169C22semidirect
108. D4×C16C22semidirect
109. D4×C16C22semidirect
110. #2159C22semidirect
111. #2159C22semidirect
112. #2158C22semidirect
113. #2150C22semidirect
114. #2141C22semidirect
115. #2141C22semidirect
121. #2139C22semidirect
124. #2138C22semidirect
125. #2138C22semidirect
126. C2×#358C22semidirect
127. C2×#358C22semidirect
128. C2×#358C22semidirect
133. #2113C22semidirect
134. C2×C4×C16C22semidirect

Maximal subgroups

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

subgroupindex
#612892
#610902
#338942
#338932
#338902
#338892
#338682
#338672
#338642
#338632
C2×#22422
#336512
#336502
#336302
#336132
#336122
#335842
#335272
#335262
C4×#5082
#334342
#333822
#333812