Finite Group Databasebeta

← #7623781

Subgroups — #7623781

Order 512.

1523 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61287C211yesmaximal, characteristic, complemented
2#61090C211yesmaximal, characteristic, complemented
3#33888C212yesmaximal, complemented
4#33886C212yesmaximal, complemented
5#33883C212yesmaximal, complemented
6#33881C212yesmaximal, complemented
7#33880C212yesmaximal, complemented
8#33878C212yesmaximal, complemented
9#33875C212yesmaximal, complemented
10#33873C212yesmaximal, complemented
11C2×#2243C211yesmaximal, characteristic, complemented
12#33651C211yesmaximal, characteristic, complemented
13#33650C211yesmaximal, characteristic, complemented
14#33629C211yesmaximal, characteristic, complemented
15#33613C211yesmaximal, characteristic, complemented
16#33612C211yesmaximal, characteristic, complemented
17#33584C211yesmaximal, characteristic, complemented
18#33527C211yesmaximal, characteristic, complemented
19#33526C211yesmaximal, characteristic, complemented
20#33451C211yesmaximal, characteristic, complemented
21#33435C211yesmaximal, characteristic, complemented
22#33382C211yesmaximal, characteristic, complemented
23#33381C211yesmaximal, characteristic, complemented
24C2×#578C2211yescharacteristic
25C2×#576C2211yescharacteristic
26#3511—21no—
27#3500—21no—
28C2×#510C2211yescharacteristic, complemented
29C2×#509C2211yescharacteristic
30C2×#508C2211yescharacteristic
31C2×#504C2211yescharacteristic
32C2×#504C2211yescharacteristic, complemented
33#3357—22no—
34#3353—22no—
35#3342C2212yescomplemented
36#3341C2212yescomplemented
37#3338C2212yescomplemented
38#3334C2212yescomplemented
39#3285C2212yes—
40#3285C2212yes—
41#3280C2212yes—
42#3280C2212yes—
43#3275—22no—
44#3275—22no—
45C2×#500C2211yescharacteristic, complemented
46C2×#495C2211yescharacteristic
47#3098—21no—
48#3098—21no—
49#3079—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#2243C2212yescomplemented
63#2243C2212yescomplemented
64#2243C2212yescomplemented
65#2243C2212yescomplemented
66#2237C2212yescomplemented
67#2237C2212yescomplemented
68#2236C2212yescomplemented
69#2235C2212yescomplemented
70#2234C2212yescomplemented
71#2234C2212yescomplemented
72#2233C2212yescomplemented
73#2232C2212yescomplemented
74#2227C2212yescomplemented
75#2226C2212yescomplemented
76#2225C2212yescomplemented
77#2224C2212yescomplemented
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—
98#2177C2211yescharacteristic, complemented
99#2177C2211yescharacteristic, complemented
100#2176C2211yescharacteristic, complemented
101#2176C2211yescharacteristic, complemented
102#2175C2211yescharacteristic, complemented
103#2175C2211yescharacteristic, complemented
104#2175C2211yescharacteristic, complemented
105#2175C2211yescharacteristic, complemented
106#2168C2212yescomplemented
107#2168C2212yescomplemented
108#2168C2212yescomplemented
109#2168C2212yescomplemented
110#2159C2211yescharacteristic, complemented
111#2159C2211yescharacteristic, complemented
112#2158C2211yescharacteristic, complemented
113#2150C2211yescharacteristic, complemented
114#2141C2211yescharacteristic, complemented
115#2141C2212yescomplemented
116#2140C2211yescharacteristic
117#2140C2212yes—
118#2139C2212yes—
119#2139C2211yescharacteristic
120#2139C2211yescharacteristic
121#2139C2212yescomplemented
122#2138C2212yes—
123#2138C2211yescharacteristic
124#2138C2211yescharacteristic, complemented
125#2138C2212yescomplemented
126C2×#358C2211yescharacteristic, complemented
127C2×#358C2212yescomplemented
128C2×#358C2211yescharacteristic, complemented
129C2×#357C2211yescharacteristic
130C2×#357C2212yes—
131C2×#357C2211yescharacteristic
132#2113C2211yescharacteristic
133#2113C2211yescharacteristic, complemented
134C2×#346C2211yescharacteristic, 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#556—22no—
157#555—22no—
158#554—22no—
159#553—42no—
160#548—22no—
161#548—22no—
162#548—42no—
163#547—22no—
164#546—22no—
165#546—22no—
166#546—42no—
167#546—42no—
168#542—41no—
169#542—41no—
170#537—21no—
171#537—21no—
172#536—21no—
173#536—41no—
174#535—21no—
175#535—41no—
176#533—41no—
177#532—41no—
178#532—41no—
179#532D411yescharacteristic
180C2×C4⋊Q8—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#500—21no—
209#500—21no—
210#500C2312yes—
211#500C2312yes—
212#495—21no—
213#495—21no—
214#495C2312yes—
215#495C2312yes—
216#485—22no—
217#485—22no—
218#484—22no—
219#484—22no—
220#482—22no—
221#482—22no—
222#480—22no—
223#480—22no—
224#477—22no—
225#476—22no—
226#475—22no—
227#474—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×#107—21no—
277C2×#107C2312yes—
278C2×#107C2312yes—
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
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—
329#346C2311yescharacteristic
330#346C2311yescharacteristic
331#346C2311yescharacteristic
332#346C2311yescharacteristic
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×#41—42no—
345C2×#41C2×D411yescharacteristic
346C2×#41C2×D411yescharacteristic
347C22×Q8—21no—
348C22×Q8—22no—
349C22×Q8—41no—
350C22×Q8—41no—
351C22×D4—21no—
352C22×D4—22no—
353C22×D4—41no—
354C22×D4—42no—
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—22no—
363#135—22no—
364#135—42no—
365#135—42no—
366#135#4114yescomplemented
367C2×Q16—24no—
368C2×Q16—22no—
369C2×Q16—21no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—42no—
373C2×Q16C2412yes—
374C2×Q16C2411yescharacteristic
375C2×Q16C2411yescharacteristic
376C2×SD16—21no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—21no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—82no—
383C2×D8—24no—
384C2×D8—22no—
385C2×D8—21no—
386C2×D8—22no—
387C2×D8—22no—
388C2×D8—42no—
389C2×D8C2412yes—
390C2×D8C2411yescharacteristic
391C2×D8C2411yescharacteristic
392#131—22no—
393#131—22no—
394#131—22no—
395#131—22no—
396C2×M16C2×D411yescharacteristic
397C2×M16C2×D412yes—
398C2×M16C2×D411yescharacteristic
399C2×M16C2×D412yes—
400C22×C8C2×D411yescharacteristic
401C22×C8C2412yes—
402C22×C8C2412yes—
403C22×C8C2411yescharacteristic
404C4⋊Q8—22no—
405C4⋊Q8—22no—
406C4⋊Q8—41no—
407C4⋊Q8—41no—
408C4⋊Q8—41no—
409C4⋊Q8D811yescharacteristic
410#127—41no—
411#127D811yescharacteristic
412#126—42no—
413#126—42no—
414#125—42no—
415#124—22no—
416#124—22no—
417#124—41no—
418#124—41no—
419#124—42no—
420#124—42no—
421#124—42no—
422#124—42no—
423#124—42no—
424#124—41no—
425#124—41no—
426#124D811yescharacteristic
427#124D811yescharacteristic
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—
441C22⋊Q8—42no—
442C22⋊Q8—42no—
443C22⋊Q8—42no—
444#121—22no—
445#121—22no—
446#121—22no—
447#121—22no—
448#121—41no—
449#121—41no—
450#121—42no—
451#121—42no—
452#121—42no—
453#121—42no—
454#121—42no—
455#121—42no—
456#121—42no—
457#121D812yes—
458#121D812yes—
459#120—42no—
460#120—42no—
461#120—42no—
462C4×Q8—21no—
463C4×Q8—21no—
464C4×Q8—21no—
465C4×Q8—21no—
466C4×Q8—41no—
467C4×Q8—41no—
468C4×Q8—42no—
469C4×D4—21no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—41no—
474C4×D4—41no—
475C4×D4—42no—
476C4×D4—42no—
477C4×D4—42no—
478C4×D4—41no—
479C4×D4—41no—
480C4×D4—41no—
481C4×D4—41no—
482C4×D4—42no—
483C4×D4—42no—
484C4×D4C2×D412yes—
485C4×D4C2×D412yes—
486#117—21no—
487#117—21no—
488#117—22no—
489#117—22no—
490#117—42no—
491#117—41no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
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—22no—
528#107—22no—
529#107—21no—
530#107—21no—
531#107—22no—
532#107—22no—
533#107C2411yescharacteristic
534#107C2412yes—
535#107C2412yes—
536#107C2411yescharacteristic
537#107C2411yescharacteristic
538#107C2411yescharacteristic
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—
586#41—164no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—44no—
591C2×Q8—42no—
592C2×Q8—42no—
593C2×Q8—41no—
594C2×Q8—42no—
595C2×Q8—42no—
596C2×Q8—42no—
597C2×Q8—82no—
598C2×Q8—84no—
599C2×Q8—162no—
600C2×Q8C2×D811yescharacteristic
601C2×Q8C2×D811yescharacteristic
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—44no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—41no—
617C2×D4—42no—
618C2×D4—82no—
619C2×D4—84no—
620C2×D4—88no—
621C2×D4C2×D812yes—
622C2×D4C2×D812yes—
623C2×D4C2×D811yescharacteristic
624C2×D4C2×D811yescharacteristic
625C2×D4C2×D812yes—
626C2×D4C2×D812yes—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4C2×D811yescharacteristic
642C22×C4C2×D811yescharacteristic
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C22×D411yescharacteristic
646Q16—21no—
647Q16—22no—
648Q16—21no—
649Q16—21no—
650Q16—22no—
651Q16—44no—
652Q16—42no—
653Q16C2×#4112yes—
654SD16—24no—
655SD16—44no—
656SD16—44no—
657SD16—42no—
658SD16—82no—
659SD16—82no—
660D8—21no—
661D8—22no—
662D8—21no—
663D8—21no—
664D8—22no—
665D8—44no—
666D8—42no—
667D8C2×#4112yes—
668M16—22no—
669M16—22no—
670M16—24no—
671M16—24no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8C22×D411yescharacteristic
678C2×C8C22×D411yescharacteristic
679C2×C8C22×D412yes—
680C2×C8C22×D412yes—
681C2×C8C22×D411yescharacteristic
682C2×C8C2×#4112yes—
683C2×C8H(5,𝔽2)12yes—
684C2×C8C2511yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—41no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C4⋊C4—41no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C4⋊C4—42no—
705C4⋊C4C2×D812yes—
706C4⋊C4C2×D812yes—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—41no—
710C22⋊C4—41no—
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—42no—
720C22⋊C4—42no—
721C22⋊C4—41no—
722C22⋊C4—41no—
723C22⋊C4—41no—
724C22⋊C4—41no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4C2×D812yes—
728C22⋊C4C2×D812yes—
729C22⋊C4C2×D812yes—
730C22⋊C4C2×D812yes—
731C42—41no—
732C42—41no—
733C42—41no—
734C42—41no—
735C42—41no—
736C42—41no—
737C42—42no—
738C42—42no—
739C42C2×D811yescharacteristic
740C42C2×D811yescharacteristic
741C42C22×D411yescharacteristic
742C42C22×D411yescharacteristic
743C16—21no—
744C16—21no—
745C16—21no—
746C16—21no—
747C16—22no—
748C16—22no—
749C23—41no—
750C23—41no—
751C23—42no—
752C23—84no—
753C23—82no—
754C23—161no—
755C23—161no—
756C23—162no—
757C23—162no—
758C23C22×D812yes—
759C23C22×D812yes—
760C23C22×D811yescharacteristic
761Q8—22no—
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—42no—
766Q8—41no—
767Q8—42no—
768Q8—41no—
769Q8—84no—
770Q8—84no—
771Q8—82no—
772Q8—162no—
773D4—24no—
774D4—24no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—42no—
779D4—42no—
780D4—44no—
781D4—42no—
782D4—41no—
783D4—41no—
784D4—42no—
785D4—41no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—82no—
790D4—82no—
791D4—162no—
792D4—162no—
793D4—162no—
794D4—162no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—44no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—84no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—161no—
819C2×C4—161no—
820C2×C4—161no—
821C2×C4—161no—
822C2×C4—162no—
823C2×C4—162no—
824C2×C4#54612yes—
825C2×C4C22×D811yescharacteristic
826C2×C4C22×D811yescharacteristic
827C2×C4C22×D811yescharacteristic
828C2×C4C22×D811yescharacteristic
829C2×C4C22×D812yes—
830C2×C4C22×D812yes—
831C2×C4C22×D811yescharacteristic
832C2×C4#57712yes—
833C2×C4C23×D411yescharacteristic
834C8—22no—
835C8—22no—
836C8—21no—
837C8—21no—
838C8#54612yes—
839C8C22×#4111yescharacteristic
840C8C2×H(5,𝔽2)11yescharacteristic
841C22—21no—
842C22—21no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—82no—
854C22—81no—
855C22—82no—
856C22—82no—
857C22—81no—
858C22—322no—
859C22—324no—
860C22#329412yes—
861C22C23×D811yescharacteristic
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4—82no—
876C4—81no—
877C4#329412yes—
878C4C2×#54611yescharacteristic
879C4C2×#57711yescharacteristic
880C2—22no—
881C2—42no—
882C2—42no—
883C2—82no—
884C2—161no—
885C2—162no—
886C2C2×#329411yescharacteristic
887C2#6263611yescharacteristic
888C2#6263711yescharacteristic
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. #61287C2semidirect
2. #61090C2semidirect
3. #33888C2semidirect
4. #33886C2semidirect
5. #33883C2semidirect
6. #33881C2semidirect
7. #33880C2semidirect
8. #33878C2semidirect
9. #33875C2semidirect
10. #33873C2semidirect
11. C2×#2243C2semidirect
12. #33651C2semidirect
13. #33650C2semidirect
14. #33629C2semidirect
15. #33613C2semidirect
16. #33612C2semidirect
17. #33584C2semidirect
18. #33527C2semidirect
19. #33526C2semidirect
20. #33451C2semidirect
21. #33435C2semidirect
22. #33382C2semidirect
23. #33381C2semidirect
28. C2×#510C22semidirect
32. C2×#504C22semidirect
35. #3342C22semidirect
36. #3341C22semidirect
37. #3338C22semidirect
38. #3334C22semidirect
45. C2×#500C22semidirect
51. #3061C22semidirect
58. C4×#135C22semidirect
61. #2913C22semidirect
62. #2243C22semidirect
63. #2243C22semidirect
64. #2243C22semidirect
65. #2243C22semidirect
66. #2237C22semidirect
67. #2237C22semidirect
68. #2236C22semidirect
69. #2235C22semidirect
70. #2234C22semidirect
71. #2234C22semidirect
72. #2233C22semidirect
73. #2232C22semidirect
74. #2227C22semidirect
75. #2226C22semidirect
76. #2225C22semidirect
77. #2224C22semidirect
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. #2177C22semidirect
99. #2177C22semidirect
100. #2176C22semidirect
101. #2176C22semidirect
102. #2175C22semidirect
103. #2175C22semidirect
104. #2175C22semidirect
105. #2175C22semidirect
106. #2168C22semidirect
107. #2168C22semidirect
108. #2168C22semidirect
109. #2168C22semidirect
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×#346C22semidirect
366. #135#41semidirect

Maximal subgroups

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

subgroupindex
#612872
#610902
#338882
#338862
#338832
#338812
#338802
#338782
#338752
#338732
C2×#22432
#336512
#336502
#336292
#336132
#336122
#335842
#335272
#335262
#334512
#334352
#333822
#333812