Finite Group Databasebeta

← #7623767

Subgroups — #7623767

Order 512.

1534 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61284C211yesmaximal, characteristic, complemented
2#61090C211yesmaximal, characteristic, complemented
3#33893C212yesmaximal, complemented
4#33889C212yesmaximal, complemented
5#33888C212yesmaximal, complemented
6#33886C212yesmaximal, complemented
7#33875C212yesmaximal, complemented
8#33873C212yesmaximal, complemented
9#33868C212yesmaximal, complemented
10#33864C212yesmaximal, complemented
11#33706C211yesmaximal, characteristic, complemented
12#33651C211yesmaximal, characteristic, complemented
13#33650C211yesmaximal, characteristic, complemented
14#33626C211yesmaximal, characteristic, complemented
15#33609C211yesmaximal, characteristic, complemented
16#33607C211yesmaximal, characteristic, complemented
17C2×#2210C211yesmaximal, characteristic, complemented
18#33524C211yesmaximal, characteristic, complemented
19#33522C211yesmaximal, characteristic, complemented
20C4×#509C211yesmaximal, characteristic, complemented
21#33438C211yesmaximal, characteristic, complemented
22#33382C211yesmaximal, characteristic, complemented
23#33381C211yesmaximal, characteristic, complemented
24C2×#578C2211yescharacteristic
25C2×#576C2211yescharacteristic
26#3506—21no—
27#3500—21no—
28C2×#509C2211yescharacteristic
29C22×SD32C2211yescharacteristic, complemented
30C22×D16C2211yescharacteristic
31C2×#504C2211yescharacteristic
32C2×#504C2211yescharacteristic, complemented
33#3355—22no—
34#3354—22no—
35#3341C2212yescomplemented
36#3339C2212yescomplemented
37#3339C2212yescomplemented
38#3334C2212yescomplemented
39#3285C2212yescomplemented
40#3285C2212yescomplemented
41#3280C2212yescomplemented
42#3280C2212yescomplemented
43#3275—22no—
44#3275—22no—
45#3160C2211yescharacteristic, complemented
46C2×#495C2211yescharacteristic
47#3096—21no—
48#3096—21no—
49#3077—21no—
50#3059C2211yescharacteristic
51#3058C2211yescharacteristic
52#3058C2211yescharacteristic
53#3058C2211yescharacteristic, complemented
54#3040—21no—
55#3010—21no—
56#3009—21no—
57C4×#135C2211yescharacteristic
58C2×C4×D8C2211yescharacteristic, complemented
59#2931C2211yescharacteristic
60#2913C2211yescharacteristic
61#2913C2211yescharacteristic, complemented
62#2243C2212yescomplemented
63#2243C2212yescomplemented
64#2242C2212yescomplemented
65#2242C2212yescomplemented
66#2237C2212yescomplemented
67#2237C2212yescomplemented
68#2236C2212yescomplemented
69#2235C2212yescomplemented
70#2234C2212yescomplemented
71#2234C2212yescomplemented
72#2233C2212yescomplemented
73#2232C2212yescomplemented
74#2229C2211yescharacteristic, complemented
75#2229C2211yescharacteristic, complemented
76#2228C2211yescharacteristic, complemented
77#2228C2211yescharacteristic, complemented
78#2227C2211yescharacteristic, complemented
79#2226C2211yescharacteristic, complemented
80#2225C2211yescharacteristic, complemented
81#2224C2211yescharacteristic, complemented
82#2220C2212yescomplemented
83#2220C2212yescomplemented
84#2218C2212yescomplemented
85#2218C2212yescomplemented
86#2217C2212yescomplemented
87#2217C2212yescomplemented
88#2215C2212yescomplemented
89#2215C2212yescomplemented
90#2210C2212yescomplemented
91#2210C2212yescomplemented
92#2210C2212yescomplemented
93#2210C2212yescomplemented
94#2186C2212yes—
95#2186C2212yes—
96#2186C2212yescomplemented
97#2186C2212yescomplemented
98#2185C2212yescomplemented
99#2185C2212yescomplemented
100#2184C2212yes—
101#2184C2212yes—
102#2177C2212yescomplemented
103#2175C2212yescomplemented
104C4×SD32C2212yescomplemented
105C4×D16C2212yescomplemented
106#2169C2212yescomplemented
107#2168C2212yescomplemented
108#2168C2212yescomplemented
109D4×C16C2212yescomplemented
110#2159C2211yescharacteristic, complemented
111#2158C2211yescharacteristic, complemented
112#2158C2211yescharacteristic, complemented
113C2×C4⋊C16C2211yescharacteristic, complemented
114#2141C2211yescharacteristic, complemented
115#2141C2212yescomplemented
116#2141C2211yescharacteristic, complemented
117#2140C2211yescharacteristic
118#2140C2211yescharacteristic
119#2140C2211yescharacteristic, complemented
120#2140C2212yescomplemented
121#2139C2211yescharacteristic
122#2139C2212yescomplemented
123#2139C2212yescomplemented
124#2138C2211yescharacteristic
125#2138C2211yescharacteristic
126#2138C2212yescomplemented
127#2138C2212yescomplemented
128C2×#358C2211yescharacteristic, complemented
129C2×#358C2212yescomplemented
130C2×#357C2211yescharacteristic
131C2×#357C2212yescomplemented
132#2113C2211yescharacteristic
133#2113C2211yescharacteristic, complemented
134C4×M32C2211yescharacteristic, 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×#135C2312yes—
146C2×#135C2312yes—
147C2×#135C2311yescharacteristic
148C22×Q16C2311yescharacteristic
149C22×Q16C2312yes—
150C22×SD16—21no—
151C22×D8C2311yescharacteristic
152C22×D8C2311yescharacteristic
153C22×D8C2312yes—
154C2×#131C2311yescharacteristic
155C2×#131C2311yescharacteristic
156#559—41no—
157#559—41no—
158#556—41no—
159#555—22no—
160#553—22no—
161#553—22no—
162#550—41no—
163#548—22no—
164#548—22no—
165#547—22no—
166#546—22no—
167#546—22no—
168#546—42no—
169#546—42no—
170#538—42no—
171#536—21no—
172#536—41no—
173#535—21no—
174#535—21no—
175#535—21no—
176#535—41no—
177#533—21no—
178#532—41no—
179#532D411yescharacteristic
180C2×#124—21no—
181C2×#124—41no—
182#525—42no—
183#520—21no—
184#520—21no—
185C4×#41—21no—
186C2×C4×D4—21no—
187#509—24no—
188C2×SD32—42no—
189C2×SD32C2312yes—
190C2×SD32C2312yes—
191C2×SD32C2312yes—
192C2×D16—42no—
193C2×D16C2312yes—
194C2×D16C2312yes—
195C2×D16C2312yes—
196#504—42no—
197#504—42no—
198C2×M32C2311yescharacteristic
199C2×M32C2311yescharacteristic
200C2×M32C2312yes—
201C2×M32C2312yes—
202C22×C16C2311yescharacteristic
203C22×C16C2311yescharacteristic
204C22×C16C2312yes—
205C22×C16C2312yes—
206#500C2311yescharacteristic
207#500C2311yescharacteristic
208#499—21no—
209#499C2311yescharacteristic
210#499C2311yescharacteristic
211#498—21no—
212#495—21no—
213#495—21no—
214#495C2312yes—
215#495C2312yes—
216#482—22no—
217#482—22no—
218#482—22no—
219#482—22no—
220#481—22no—
221#481—22no—
222#480—22no—
223#480—22no—
224#478—22no—
225#478—22no—
226#476—22no—
227#474—22no—
228#470—22no—
229#469—22no—
230#469—22no—
231#469—22no—
232#467C2312yes—
233#467C2312yes—
234#466C2312yes—
235#466C2312yes—
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×SD16—21no—
255C4×SD16—21no—
256C4×D8—21no—
257C4×D8—21no—
258C4×D8C2312yes—
259C4×D8C2312yes—
260C4×D8C2311yescharacteristic
261C4×D8C2311yescharacteristic
262#436D412yes—
263#436D412yes—
264C8×D4C2312yes—
265C8×D4C2312yes—
266#428—21no—
267#428—21no—
268#428—22no—
269#428—22no—
270#427—21no—
271#427C2312yes—
272#427C2312yes—
273#427C2311yescharacteristic
274#427C2311yescharacteristic
275#427C2311yescharacteristic
276C2×#107C2312yes—
277C2×#107C2312yes—
278C2×#107C2311yescharacteristic
279#423D411yescharacteristic
280#419—21no—
281#418—21no—
282#418—21no—
283#418—21no—
284#416—21no—
285C2×#102—21no—
286#408D411yescharacteristic
287#408D411yescharacteristic
288C2×C4×C8C2311yescharacteristic
289#367C2311yescharacteristic
290#367C2311yescharacteristic
291#367C2311yescharacteristic
292#367C2311yescharacteristic
293#367C2312yes—
294#366C2311yescharacteristic
295#366C2311yescharacteristic
296#366C2311yescharacteristic
297#366C2311yescharacteristic
298#366C2312yes—
299C4⋊C16C2311yescharacteristic
300C4⋊C16C2311yescharacteristic
301C4⋊C16C2311yescharacteristic
302C4⋊C16C2311yescharacteristic
303#358C2311yescharacteristic
304#358C2312yes—
305#358C2312yes—
306#358C2312yes—
307#358C2312yes—
308#358C2311yescharacteristic
309#358C2311yescharacteristic
310#358C2311yescharacteristic
311#358C2312yes—
312#358C2312yes—
313#358C2312yes—
314#357C2312yes—
315#357C2312yes—
316#357C2311yescharacteristic
317#357C2312yes—
318#357C2312yes—
319#357C2311yescharacteristic
320#357C2311yescharacteristic
321#357C2311yescharacteristic
322#357C2312yes—
323#357C2312yes—
324#357C2312yes—
325#357C2312yes—
326#357C2312yes—
327C22⋊C16C2312yes—
328C22⋊C16C2312yes—
329C22⋊C16C2312yes—
330C22⋊C16C2312yes—
331#346C2312yes—
332C4×C16C2312yes—
3332−1+4—44no—
3342−1+4—82no—
335H(5,𝔽2)—44no—
336H(5,𝔽2)—82no—
337C2×#41—21no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—41no—
341C2×#41—41no—
342C2×#41—42no—
343C2×#41—42no—
344C2×#41C2×D411yescharacteristic
345C2×#41C2×D411yescharacteristic
346C22×Q8—21no—
347C22×Q8—22no—
348C22×Q8—41no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—41no—
353C22×D4—42no—
354C23×C4—41no—
355#137—48no—
356#137—44no—
357AGL(1,ℤ/8)—48no—
358AGL(1,ℤ/8)—44no—
359#135—24no—
360#135—24no—
361#135—22no—
362#135—42no—
363#135—42no—
364#135#4114yescomplemented
365C2×Q16—24no—
366C2×Q16—22no—
367C2×Q16—21no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—42no—
371C2×Q16C2412yes—
372C2×Q16C2411yescharacteristic
373C2×SD16—21no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16—82no—
379C2×D8—24no—
380C2×D8—22no—
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—22no—
386C2×D8—22no—
387C2×D8—42no—
388C2×D8C2412yes—
389C2×D8C2412yes—
390C2×D8C2411yescharacteristic
391#131—22no—
392#131—22no—
393#131—22no—
394#131—22no—
395C2×M16C2×D411yescharacteristic
396C2×M16C2×D412yes—
397C2×M16C2×D411yescharacteristic
398C2×M16C2×D412yes—
399C22×C8C2×D411yescharacteristic
400C22×C8C2412yes—
401C22×C8C2412yes—
402C22×C8C2411yescharacteristic
403C4⋊Q8—21no—
404C4⋊Q8—21no—
405C4⋊Q8—41no—
406C4⋊Q8D811yescharacteristic
407#127—41no—
408#127—41no—
409#127—41no—
410#127D811yescharacteristic
411#126—42no—
412#126—42no—
413#125—21no—
414#125—21no—
415#124—22no—
416#124—22no—
417#124—41no—
418#124—41no—
419#124—41no—
420#124—41no—
421#124—42no—
422#124—42no—
423#124—42no—
424#124—42no—
425#124—41no—
426#124—41no—
427#124D811yescharacteristic
428#124D811yescharacteristic
429#123—42no—
430#123—42no—
431#123—42no—
432#123—42no—
433#123—42no—
434#123—42no—
435#123—42no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—41no—
439C22⋊Q8—41no—
440C22⋊Q8—42no—
441C22⋊Q8—42no—
442C22⋊Q8—42no—
443#121—22no—
444#121—22no—
445#121—22no—
446#121—22no—
447#121—22no—
448#121—22no—
449#121—42no—
450#121—42no—
451#121—42no—
452#121—42no—
453#121—42no—
454#121—42no—
455#121—42no—
456#121D812yes—
457#121D812yes—
458#120—42no—
459#120—42no—
460#120—42no—
461#120—42no—
462#120—42no—
463C4×Q8—21no—
464C4×Q8—21no—
465C4×Q8—41no—
466C4×Q8—41no—
467C4×Q8—41no—
468C4×Q8—41no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—42no—
474C4×D4—42no—
475C4×D4—41no—
476C4×D4—41no—
477C4×D4—41no—
478C4×D4—41no—
479C4×D4—42no—
480C4×D4—42no—
481C4×D4—42no—
482C4×D4—42no—
483C4×D4—41no—
484C4×D4—41no—
485C4×D4C2×D412yes—
486C4×D4C2×D412yes—
487#117—21no—
488#117—21no—
489#117—21no—
490#117—22no—
491#117—22no—
492#117—42no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C42—41no—
503C2×C42C2×D411yescharacteristic
504SD32—24no—
505SD32—42no—
506SD32—42no—
507D16—24no—
508D16—42no—
509D16—42no—
510M32—22no—
511M32—22no—
512M32—42no—
513M32—42no—
514C2×C16—22no—
515C2×C16—22no—
516C2×C16—42no—
517C2×C16—42no—
518C2×C16C2412yes—
519C2×C16C2412yes—
520C2×C16C2411yescharacteristic
521C2×C16C2411yescharacteristic
522C2×C16C2411yescharacteristic
523C2×C16C2411yescharacteristic
524#107—21no—
525#107—22no—
526#107—22no—
527#107—21no—
528#107—21no—
529#107C2412yes—
530#107C2411yescharacteristic
531#107C2411yescharacteristic
532#107C2411yescharacteristic
533#107C2411yescharacteristic
534#107C2411yescharacteristic
535#107C2411yescharacteristic
536#106—21no—
537#106—21no—
538#106—21no—
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—22no—
548#103—22no—
549#102—22no—
550#102—22no—
551#102—21no—
552#102—21no—
553#102—22no—
554#102—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559C22⋊C8C2×D412yes—
560C22⋊C8C2×D412yes—
561C22⋊C8C2×D412yes—
562C22⋊C8C2×D412yes—
563C4×C8C2×D411yescharacteristic
564C4×C8C2×D411yescharacteristic
565C4×C8C2411yescharacteristic
566C4×C8C2411yescharacteristic
567C24—42no—
568C24—41no—
569C24—41no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—24no—
575#41—44no—
576#41—44no—
577#41—42no—
578#41—82no—
579#41—82no—
580#41—84no—
581#41—84no—
582#41—88no—
583#41—164no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—44no—
587C2×Q8—41no—
588C2×Q8—42no—
589C2×Q8—41no—
590C2×Q8—41no—
591C2×Q8—42no—
592C2×Q8—42no—
593C2×Q8—82no—
594C2×Q8—84no—
595C2×Q8C2×D811yescharacteristic
596C2×Q8C2×D811yescharacteristic
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—44no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
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—41no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—82no—
618C2×D4—84no—
619C2×D4—88no—
620C2×D4C2×D812yes—
621C2×D4C2×D812yes—
622C2×D4C2×D811yescharacteristic
623C2×D4C2×D811yescharacteristic
624C2×D4C2×D812yes—
625C2×D4C2×D812yes—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—42no—
638C22×C4—162no—
639C22×C4C2×D811yescharacteristic
640C22×C4C2×D811yescharacteristic
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D411yescharacteristic
644Q16—22no—
645Q16—21no—
646Q16—22no—
647Q16—44no—
648Q16—42no—
649Q16C2×#4112yes—
650SD16—24no—
651SD16—44no—
652SD16—44no—
653SD16—82no—
654SD16—82no—
655D8—22no—
656D8—22no—
657D8—21no—
658D8—22no—
659D8—22no—
660D8—44no—
661D8—42no—
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—21no—
687C4⋊C4—21no—
688C4⋊C4—41no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—41no—
695C4⋊C4—41no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C4⋊C4—41no—
701C4⋊C4C2×D812yes—
702C4⋊C4C2×D812yes—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—41no—
706C22⋊C4—41no—
707C22⋊C4—41no—
708C22⋊C4—42no—
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—41no—
719C22⋊C4—41no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4C2×D812yes—
725C22⋊C4C2×D812yes—
726C22⋊C4C2×D812yes—
727C22⋊C4C2×D812yes—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—42no—
732C42—42no—
733C42—41no—
734C42—41no—
735C42C2×D811yescharacteristic
736C42C2×D811yescharacteristic
737C42C22×D411yescharacteristic
738C42C22×D411yescharacteristic
739C16—22no—
740C16—21no—
741C16—21no—
742C16—21no—
743C16—21no—
744C16—22no—
745C23—41no—
746C23—42no—
747C23—42no—
748C23—84no—
749C23—82no—
750C23—82no—
751C23—161no—
752C23—161no—
753C23—161no—
754C23—161no—
755C23—162no—
756C23—162no—
757C23C22×D812yes—
758C23C22×D812yes—
759C23C22×D811yescharacteristic
760Q8—22no—
761Q8—22no—
762Q8—22no—
763Q8—41no—
764Q8—42no—
765Q8—42no—
766Q8—84no—
767Q8—82no—
768Q8—82no—
769Q8—161no—
770D4—24no—
771D4—24no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—42no—
776D4—42no—
777D4—44no—
778D4—42no—
779D4—42no—
780D4—41no—
781D4—42no—
782D4—42no—
783D4—84no—
784D4—84no—
785D4—84no—
786D4—82no—
787D4—82no—
788D4—162no—
789D4—162no—
790D4—162no—
791D4—162no—
792D4—162no—
793D4—162no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4—82no—
815C2×C4—161no—
816C2×C4—161no—
817C2×C4—162no—
818C2×C4—161no—
819C2×C4—162no—
820C2×C4—162no—
821C2×C4#54612yes—
822C2×C4C22×D811yescharacteristic
823C2×C4C22×D811yescharacteristic
824C2×C4C22×D812yes—
825C2×C4C22×D812yes—
826C2×C4C22×D811yescharacteristic
827C2×C4C22×D811yescharacteristic
828C2×C4C22×D811yescharacteristic
829C2×C4#57712yes—
830C2×C4C23×D411yescharacteristic
831C8—22no—
832C8—22no—
833C8—21no—
834C8—21no—
835C8#54612yes—
836C8C22×#4111yescharacteristic
837C8C2×H(5,𝔽2)11yescharacteristic
838C22—21no—
839C22—21no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—42no—
847C22—81no—
848C22—81no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—164no—
856C22—322no—
857C22—324no—
858C22#329412yes—
859C22C23×D811yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—22no—
865C4—22no—
866C4—42no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—82no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—82no—
875C4#329412yes—
876C4C2×#54611yescharacteristic
877C4C2×#57711yescharacteristic
878C2—22no—
879C2—42no—
880C2—42no—
881C2—82no—
882C2—162no—
883C2—162no—
884C2C2×#329411yescharacteristic
885C2#6263511yescharacteristic
886C2#6263611yescharacteristic
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. #61284C2semidirect
2. #61090C2semidirect
3. #33893C2semidirect
4. #33889C2semidirect
5. #33888C2semidirect
6. #33886C2semidirect
7. #33875C2semidirect
8. #33873C2semidirect
9. #33868C2semidirect
10. #33864C2semidirect
11. #33706C2semidirect
12. #33651C2semidirect
13. #33650C2semidirect
14. #33626C2semidirect
15. #33609C2semidirect
16. #33607C2semidirect
17. C2×#2210C2semidirect
18. #33524C2semidirect
19. #33522C2semidirect
20. C4×#509C2semidirect
21. #33438C2semidirect
22. #33382C2semidirect
23. #33381C2semidirect
29. C22×SD32C22semidirect
32. C2×#504C22semidirect
35. #3341C22semidirect
36. #3339C22semidirect
37. #3339C22semidirect
38. #3334C22semidirect
39. #3285C22semidirect
40. #3285C22semidirect
41. #3280C22semidirect
42. #3280C22semidirect
45. #3160C22semidirect
53. #3058C22semidirect
58. C2×C4×D8C22semidirect
61. #2913C22semidirect
62. #2243C22semidirect
63. #2243C22semidirect
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. #2227C22semidirect
79. #2226C22semidirect
80. #2225C22semidirect
81. #2224C22semidirect
82. #2220C22semidirect
83. #2220C22semidirect
84. #2218C22semidirect
85. #2218C22semidirect
86. #2217C22semidirect
87. #2217C22semidirect
88. #2215C22semidirect
89. #2215C22semidirect
90. #2210C22semidirect
91. #2210C22semidirect
92. #2210C22semidirect
93. #2210C22semidirect
96. #2186C22semidirect
97. #2186C22semidirect
98. #2185C22semidirect
99. #2185C22semidirect
102. #2177C22semidirect
103. #2175C22semidirect
104. C4×SD32C22semidirect
105. C4×D16C22semidirect
106. #2169C22semidirect
107. #2168C22semidirect
108. #2168C22semidirect
109. D4×C16C22semidirect
110. #2159C22semidirect
111. #2158C22semidirect
112. #2158C22semidirect
113. C2×C4⋊C16C22semidirect
114. #2141C22semidirect
115. #2141C22semidirect
116. #2141C22semidirect
119. #2140C22semidirect
120. #2140C22semidirect
122. #2139C22semidirect
123. #2139C22semidirect
126. #2138C22semidirect
127. #2138C22semidirect
128. C2×#358C22semidirect
129. C2×#358C22semidirect
131. C2×#357C22semidirect
133. #2113C22semidirect
134. C4×M32C22semidirect
364. #135#41semidirect

Maximal subgroups

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

subgroupindex
#612842
#610902
#338932
#338892
#338882
#338862
#338752
#338732
#338682
#338642
#337062
#336512
#336502
#336262
#336092
#336072
C2×#22102
#335242
#335222
C4×#5092
#334382
#333822
#333812