Finite Group Databasebeta

← #6381474

Subgroups — #6381474

Order 512.

3087 conjugacy classes of subgroups.

The subgroup lattice has 1107 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3022C211yesmaximal, characteristic
2#60169C211yesmaximal, characteristic, complemented
3C2×#2947C211yesmaximal, characteristic, complemented
4#60089C211yesmaximal, characteristic
5#60086C211yesmaximal, characteristic
6#22896C214yesmaximal, complemented
7#22894C214yesmaximal, complemented
8#22892C214yesmaximal, complemented
9#22890C214yesmaximal, complemented
10#21205C211yesmaximal, characteristic, complemented
11#21076C211yesmaximal, characteristic, complemented
12#21075C211yesmaximal, characteristic, complemented
13#21006C211yesmaximal, characteristic, complemented
14C2×#1908C211yesmaximal, characteristic, complemented
15#20954C211yesmaximal, characteristic, complemented
16#20865C211yesmaximal, characteristic, complemented
17#20864C211yesmaximal, characteristic, complemented
18#20422C211yesmaximal, characteristic, complemented
19#20420C211yesmaximal, characteristic, complemented
20C2×#585C2211yescharacteristic
21C22×#137C2211yescharacteristic
22C22×#137C2211yescharacteristic
23C2×#568C2211yescharacteristic
24C22×#131C2211yescharacteristic
25C2×#536C2211yescharacteristic
26#3428C2211yescharacteristic
27C2×#520C2211yescharacteristic
28C2×#519C2211yescharacteristic, complemented
29#3022C4116yescomplemented
30C2×#456C2214yes—
31C2×#455C2214yes—
32#2950—22no—
33#2949—22no—
34#2947—22no—
35#2947—22no—
36#2947C2214yescomplemented
37#2947C2214yescomplemented
38#2947C2214yescomplemented
39#2947C2214yescomplemented
40C4×#137—22no—
41C4×#137—22no—
42C2×#441—21no—
43C2×#440—21no—
44C2×C4×Q16—21no—
45C2×C4×SD16—21no—
46#2911C2211yescharacteristic, complemented
47C2×#428C2211yescharacteristic, complemented
48C2×#421C2211yescharacteristic
49C2×#421C2211yescharacteristic
50#2898—22no—
51#2898—21no—
52#2898—21no—
53#2898C2212yes—
54#2898C2214yes—
55#2898C2212yes—
56#2897—22no—
57#2897—21no—
58#2897—21no—
59#2897C2212yes—
60#2897C2214yes—
61#2897C2212yes—
62#2896—22no—
63#2896—22no—
64#2896C2211yescharacteristic
65#2896C2211yescharacteristic
66#2896C2211yescharacteristic
67#2896C2211yescharacteristic
68C2×#417—22no—
69C2×#417C2211yescharacteristic
70C2×#417C2211yescharacteristic
71C2×#419C2211yescharacteristic, complemented
72C2×#416—22no—
73C2×#416C2211yescharacteristic
74C2×#416C2211yescharacteristic
75C22×#103C2211yescharacteristic, complemented
76C2×#413C2211yescharacteristic
77C22×#101C2211yescharacteristic, complemented
78#2873C2211yescharacteristic, complemented
79C2×#405C2211yescharacteristic, complemented
80C2×#405C2211yescharacteristic, complemented
81#2317C2211yescharacteristic, complemented
82#1960C2212yescomplemented
83#1959C2212yescomplemented
84#1958C2212yescomplemented
85#1956C2212yescomplemented
86#1931C2212yescomplemented
87#1931C2212yescomplemented
88#1931C2214yescomplemented
89#1930C2212yescomplemented
90#1930C2212yescomplemented
91#1930C2214yescomplemented
92#1908C2214yescomplemented
93#1908C2214yescomplemented
94#1908C2214yescomplemented
95#1908C2214yescomplemented
96#1888C2214yescomplemented
97#1886C2214yescomplemented
98#1860C2214yescomplemented
99#1860C2214yescomplemented
100#1859C2214yescomplemented
101#1859C2214yescomplemented
102#1765C2214yescomplemented
103#1765C2214yescomplemented
104#1764C2214yescomplemented
105#1764C2214yescomplemented
106#1742C2211yescharacteristic, complemented
107C2×#343C2211yescharacteristic, complemented
108#1738C2211yescharacteristic, complemented
109C2×#341C2211yescharacteristic, complemented
110#1733C2211yescharacteristic, complemented
111#1733C2211yescharacteristic, complemented
112#585—24no—
113#585—24no—
114#585—42no—
115#585C2×C418yes—
116C2×2−1+4—21no—
117C2×2−1+4—21no—
118C2×2−1+4C2312yes—
119C2×H(5,𝔽2)—21no—
120C2×H(5,𝔽2)—21no—
121C2×H(5,𝔽2)—41no—
122C2×H(5,𝔽2)C2312yes—
123C22×#41—22no—
124C22×#41—22no—
125C22×#41—41no—
126C22×#41C2311yescharacteristic
127C22×#41C2311yescharacteristic
128C22×#41C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C2×#137—22no—
131C2×#137—22no—
132C2×#137—24no—
133C2×#137—24no—
134C2×#137C2×C418yescomplemented
135C2×#137C2×C418yescomplemented
136C2×#137C2314yes—
137C2×#137C2314yes—
138C22×Q16—21no—
139C22×Q16—21no—
140C22×SD16—21no—
141C22×SD16—21no—
142#568—24no—
143#568—42no—
144C2×#131—22no—
145C2×#131—21no—
146C2×#131—21no—
147C2×#131—24no—
148C2×#131—42no—
149C2×#131C2312yes—
150C2×#131C2314yes—
151C2×#131C2312yes—
152C22×M16—22no—
153C22×M16—21no—
154C22×M16C2311yescharacteristic
155C22×M16C2311yescharacteristic
156C22×M16C2311yescharacteristic
157C22×M16C2311yescharacteristic
158C22×M16C2311yescharacteristic
159C23×C8—21no—
160C23×C8C2311yescharacteristic
161#536—42no—
162#536C2×C418yescomplemented
163C2×C4⋊Q8C2312yes—
164C2×#124C2312yes—
165C2×#123—41no—
166C2×C22⋊Q8—41no—
167#520—22no—
168#520—21no—
169#520—21no—
170#520—22no—
171#520—41no—
172#520C2312yes—
173#520C2314yes—
174#520C2312yes—
175#519—21no—
176#519—22no—
177#519—22no—
178#519—41no—
179#519C2314yes—
180#518—21no—
181#518—41no—
182C4×#41—22no—
183C4×#41—41no—
184C2×C4×Q8—21no—
185C2×C4×Q8—21no—
186C2×C4×Q8—21no—
187C2×C4×Q8—21no—
188C2×C4×Q8—21no—
189C2×C4×D4—21no—
190C2×C4×D4—41no—
191C2×#117—22no—
192C2×#117—21no—
193C2×#117—41no—
194C2×#117C2311yescharacteristic
195C2×#117C2311yescharacteristic
196C2×#117C2311yescharacteristic
197C2×#117C2311yescharacteristic
198C22×C4⋊C4—21no—
199C22×C4⋊C4C2311yescharacteristic
200#456C2×C4132yescomplemented
201#455C2×C4132yescomplemented
202#441—24no—
203#441—24no—
204#441—24no—
205#441—24no—
206#440—24no—
207#440—24no—
208#440—24no—
209#440—24no—
210C4×Q16—24no—
211C4×Q16—24no—
212C4×Q16—24no—
213C4×Q16—24no—
214C4×SD16—24no—
215C4×SD16—24no—
216C4×SD16—24no—
217C4×SD16—24no—
218#428—22no—
219#428—21no—
220#428—21no—
221#428C2312yes—
222#428C2314yes—
223#428C2312yes—
224#427—22no—
225C2×#107—21no—
226C2×#106—21no—
227#421C2×C418yescomplemented
228#421C2×C418yescomplemented
229C2×#104C2314yes—
230C2×#104C2314yes—
231#419—21no—
232#419—22no—
233#419—22no—
234#419—24no—
235#419—22no—
236#419—22no—
237#419D412yes—
238#419C2312yes—
239#419C2312yes—
240#418—21no—
241#418—24no—
242#418—22no—
243#418—22no—
244#418D412yes—
245#418C2312yes—
246#418C2312yes—
247#417—22no—
248#417—22no—
249#417—22no—
250#417—21no—
251#417—21no—
252#417—21no—
253#417—21no—
254#417—24no—
255#417—22no—
256#417—22no—
257#417—24no—
258#417—22no—
259#417—22no—
260#417D412yes—
261#417D412yes—
262#417C2312yes—
263#417C2314yes—
264#417C2312yes—
265#416—22no—
266#416—21no—
267#416—21no—
268#416—21no—
269#416—21no—
270#416—22no—
271#416—22no—
272#416—22no—
273#416—22no—
274#416—24no—
275#416—22no—
276#416—22no—
277#416—24no—
278#416D412yes—
279#416D412yes—
280#416C2312yes—
281#416C2312yes—
282#416C2314yes—
283C2×#103—21no—
284C2×#103—21no—
285C2×#103—21no—
286C2×#103—21no—
287C2×#103—21no—
288C2×#103—22no—
289C2×#103—22no—
290C2×#103—24no—
291C2×#103D411yescharacteristic
292C2×#103D411yescharacteristic
293C2×#103C2312yes—
294C2×#103C2312yes—
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2312yes—
298C2×#103C2312yes—
299C2×#103C2312yes—
300C2×#102—21no—
301C2×#102—22no—
302C2×#102—22no—
303C2×#102—24no—
304C2×#102D411yescharacteristic
305C2×#102D411yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2312yes—
309#413C2×C418yescomplemented
310C2×#101—42no—
311C2×#101C2314yes—
312C2×#101C2312yes—
313C2×#100C2312yes—
314#405—22no—
315#405—21no—
316#405—21no—
317#405—42no—
318#405C2312yes—
319#405C2312yes—
320#405C2314yes—
321C4×M16—22no—
322C2×#97—21no—
323C2×#97C2312yes—
324C2×C4×C8—21no—
325C2×C4×C8C2312yes—
326#389—41no—
327#385—41no—
328#384C2312yes—
329#382C2312yes—
330#343C2312yes—
331#343C2314yes—
332#343C2312yes—
333#341C2312yes—
334#341C2312yes—
335#341C2314yes—
336#339C2314yes—
337#339C2314yes—
3382−1+4—24no—
3392−1+4—24no—
3402−1+4—28no—
3412−1+4—28no—
3422−1+4—42no—
3432−1+4—44no—
3442−1+4—44no—
3452−1+4C22×C418yes—
346H(5,𝔽2)—24no—
347H(5,𝔽2)—24no—
348H(5,𝔽2)—28no—
349H(5,𝔽2)—28no—
350H(5,𝔽2)—48no—
351H(5,𝔽2)—48no—
352H(5,𝔽2)—42no—
353H(5,𝔽2)—44no—
354H(5,𝔽2)—44no—
355H(5,𝔽2)C22×C418yes—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—216no—
366C2×#41—216no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—42no—
378C2×#41—42no—
379C2×#41—42no—
380C2×#41—42no—
381C2×#41—48no—
382C2×#41—48no—
383C2×#41—48no—
384C2×#41—41no—
385C2×#41—41no—
386C2×#41—48no—
387C2×#41C22×C414yes—
388C2×#41C22×C414yes—
389C2×#41C22×C414yes—
390C2×#41C2×D412yes—
391C2×#41C2×D412yes—
392C2×#41#4114yes—
393C2×#41#4114yes—
394C2×#41C2412yes—
395C2×#41C2412yes—
396C22×Q8—21no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—21no—
401C22×Q8—21no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—41no—
407C22×Q8C22×C414yes—
408C22×Q8C2×D411yescharacteristic
409C22×Q8C2×D411yescharacteristic
410C22×Q8C2412yes—
411C22×Q8C2411yescharacteristic
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—21no—
417C22×D4—42no—
418C22×D4—41no—
419C22×D4—42no—
420C22×D4—42no—
421C22×D4C2×D411yescharacteristic
422C22×D4C2×D411yescharacteristic
423C22×D4C2411yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—42no—
430C23×C4—41no—
431C23×C4C2411yescharacteristic
432#137—216no—
433#137—216no—
434#137—28no—
435#137—28no—
436#137C22×C4116yes—
437#137C22×C4116yescomplemented
438C2×Q16—28no—
439C2×Q16—28no—
440C2×Q16—24no—
441C2×Q16—24no—
442C2×SD16—28no—
443C2×SD16—28no—
444C2×SD16—24no—
445C2×SD16—24no—
446#131—24no—
447#131—24no—
448#131—28no—
449#131—42no—
450#131—42no—
451#131—44no—
452#131—44no—
453#131—44no—
454#131—48no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—22no—
464C2×M16—24no—
465C2×M16—22no—
466C2×M16—22no—
467C2×M16—22no—
468C2×M16—22no—
469C2×M16—22no—
470C2×M16—44no—
471C2×M16—48no—
472C2×M16C22×C414yes—
473C2×M16C22×C414yes—
474C2×M16C2×D412yes—
475C2×M16C2×D412yes—
476C2×M16C2412yes—
477C2×M16C2412yes—
478C2×M16C2412yes—
479C2×M16C2412yes—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—22no—
487C22×C8—22no—
488C22×C8—24no—
489C22×C8—44no—
490C22×C8C2×D411yescharacteristic
491C22×C8C2×D411yescharacteristic
492C22×C8C2×D411yescharacteristic
493C22×C8C2×D411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2412yes—
497C4⋊Q8—42no—
498C4⋊Q8C22×C418yescomplemented
499#124—42no—
500#124C22×C418yescomplemented
501#123—48no—
502C22⋊Q8—48no—
503C4×Q8—24no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—24no—
507C4×Q8—24no—
508C4×Q8—24no—
509C4×Q8—24no—
510C4×Q8—42no—
511C4×Q8—42no—
512C4×Q8—42no—
513C4×Q8—42no—
514C4×Q8—42no—
515C4×Q8—41no—
516C4×Q8—41no—
517C4×D4—24no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—42no—
521C4×D4—44no—
522C4×D4—42no—
523C4×D4—42no—
524C4×D4—44no—
525C4×D4—41no—
526C4×D4—41no—
527C4×D4—42no—
528C4×D4—42no—
529#117—21no—
530#117—21no—
531#117—21no—
532#117—21no—
533#117—22no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—24no—
539#117—22no—
540#117—22no—
541#117—42no—
542#117—44no—
543#117—44no—
544#117—42no—
545#117—42no—
546#117C22×C414yes—
547#117C2×D412yes—
548#117C2×D412yes—
549#117C2412yes—
550#117C2412yes—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—42no—
561C2×C4⋊C4—42no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—42no—
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—41no—
580C2×C42—21no—
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—42no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42C2412yes—
588#107—24no—
589#107—22no—
590#107—22no—
591#106—24no—
592#106—22no—
593#106—22no—
594#104C22×C4116yes—
595#104C22×C4116yescomplemented
596#103—24no—
597#103—22no—
598#103—22no—
599#103—21no—
600#103—21no—
601#103—22no—
602#103—22no—
603#103—22no—
604#103—22no—
605#103—24no—
606#103—21no—
607#103—21no—
608#103—24no—
609#103—24no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103C2×D412yes—
615#103C2×D412yes—
616#103C2×D414yes—
617#103C2×D412yes—
618#103C2×D412yes—
619#103C2×D414yes—
620#102—24no—
621#102—22no—
622#102—22no—
623#102—21no—
624#102—21no—
625#102—24no—
626#102—21no—
627#102—21no—
628#102—22no—
629#102—22no—
630#102—22no—
631#102—22no—
632#102C2×D412yes—
633#102C2×D412yes—
634#102C2×D414yes—
635#102C2×D412yes—
636#102C2×D412yes—
637#102C2×D414yes—
638#101—44no—
639#101C22×C418yescomplemented
640#100C22×C418yescomplemented
641#97—22no—
642#97—22no—
643#97—24no—
644#97—42no—
645C4×C8—22no—
646C4×C8—22no—
647C4×C8—24no—
648C4×C8—42no—
649#95—42no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24H(5,𝔽2)11yescharacteristic
655#41—24no—
656#41—24no—
657#41—24no—
658#41—24no—
659#41—24no—
660#41—24no—
661#41—24no—
662#41—24no—
663#41—24no—
664#41—24no—
665#41—22no—
666#41—22no—
667#41—22no—
668#41—22no—
669#41—28no—
670#41—28no—
671#41—28no—
672#41—28no—
673#41—24no—
674#41—24no—
675#41—24no—
676#41—24no—
677#41—416no—
678#41—48no—
679#41—416no—
680#41—416no—
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685#41—48no—
686#41—48no—
687#41—48no—
688#41—42no—
689#41—42no—
690#41—42no—
691#41—42no—
692#41C4×D418yes—
693#41C4×D418yes—
694#41C23×C414yes—
695#41C23×C414yes—
696#41C2×#4114yes—
697#41C2×#4114yes—
698C2×Q8—24no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—22no—
702C2×Q8—22no—
703C2×Q8—22no—
704C2×Q8—21no—
705C2×Q8—28no—
706C2×Q8—28no—
707C2×Q8—24no—
708C2×Q8—24no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—22no—
714C2×Q8—22no—
715C2×Q8—22no—
716C2×Q8—22no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8—42no—
720C2×Q8—44no—
721C2×Q8—44no—
722C2×Q8—48no—
723C2×Q8—41no—
724C2×Q8—41no—
725C2×Q8—42no—
726C2×Q8—42no—
727C2×Q8—42no—
728C2×Q8—42no—
729C2×Q8—42no—
730C2×Q8C4×D414yes—
731C2×Q8C4×D414yes—
732C2×Q8C23×C412yes—
733C2×Q8C23×C414yes—
734C2×Q8C22×D412yes—
735C2×Q8C22×D412yes—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—24no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—416no—
764C2×D4—416no—
765C2×D4—42no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4C4×D414yes—
770C2×D4C4×D414yes—
771C2×D4C23×C412yes—
772C2×D4C22×D412yes—
773C2×D4C22×D412yes—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—24no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—42no—
797C22×C4—416no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—42no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—42no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—162no—
812C22×C4—161no—
813C22×C4C23×C412yes—
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C2×#4112yes—
819C22×C4C2×#4112yes—
820C22×C4H(5,𝔽2)11yescharacteristic
821C22×C4H(5,𝔽2)12yes—
822C22×C4C2511yescharacteristic
823Q16—216no—
824Q16—216no—
825SD16—216no—
826SD16—216no—
827M16—24no—
828M16—24no—
829M16—24no—
830M16—24no—
831M16—22no—
832M16—22no—
833M16—22no—
834M16—22no—
835M16—22no—
836M16—22no—
837M16—44no—
838M16—44no—
839M16—48no—
840M16—42no—
841M16—42no—
842M16C23×C414yes—
843M16C23×C414yes—
844C2×C8—24no—
845C2×C8—24no—
846C2×C8—22no—
847C2×C8—22no—
848C2×C8—22no—
849C2×C8—22no—
850C2×C8—22no—
851C2×C8—22no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—22no—
855C2×C8—21no—
856C2×C8—22no—
857C2×C8—21no—
858C2×C8—22no—
859C2×C8—22no—
860C2×C8—44no—
861C2×C8—44no—
862C2×C8—48no—
863C2×C8—42no—
864C2×C8—42no—
865C2×C8C22×D411yescharacteristic
866C2×C8C22×D411yescharacteristic
867C2×C8C22×D414yes—
868C2×C8C22×D411yescharacteristic
869C2×C8C22×D411yescharacteristic
870C4⋊C4—24no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—22no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—22no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—162no—
890C4⋊C4C22×D412yes—
891C4⋊C4C22×D412yes—
892C4⋊C4C22×D412yes—
893C4⋊C4C22×D412yes—
894C22⋊C4—24no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—41no—
904C22⋊C4—41no—
905C42—22no—
906C42—22no—
907C42—22no—
908C42—22no—
909C42—22no—
910C42—44no—
911C42—42no—
912C42—42no—
913C42—44no—
914C42—44no—
915C42—41no—
916C42—41no—
917C42C23×C414yes—
918C23—22no—
919C23—22no—
920C23—24no—
921C23—24no—
922C23—22no—
923C23—41no—
924C23—41no—
925C23—48no—
926C23—41no—
927C23—41no—
928C23—81no—
929C23—81no—
930C23—81no—
931C23—81no—
932C23—81no—
933C23—81no—
934C23—162no—
935C23—162no—
936C23#51812yes—
937C23D4211yescharacteristic
938C23D4211yescharacteristic
939C23#55112yes—
940C23C2×H(5,𝔽2)11yescharacteristic
941Q8—24no—
942Q8—24no—
943Q8—22no—
944Q8—22no—
945Q8—24no—
946Q8—24no—
947Q8—22no—
948Q8—22no—
949Q8—48no—
950Q8—44no—
951Q8—44no—
952Q8—42no—
953Q8—42no—
954Q8—41no—
955Q8—41no—
956Q8C2×C4×D414yes—
957Q8C2×C4×D414yes—
958D4—28no—
959D4—28no—
960D4—24no—
961D4—24no—
962D4—24no—
963D4—24no—
964D4—24no—
965D4—24no—
966D4—22no—
967D4—22no—
968D4—22no—
969D4—22no—
970D4—48no—
971D4—48no—
972D4—48no—
973D4—44no—
974D4—44no—
975D4—41no—
976D4—41no—
977D4C2×C4×D414yes—
978D4C2×C4×D414yes—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—28no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—48no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—42no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—42no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—42no—
1014C2×C4—81no—
1015C2×C4—81no—
1016C2×C4—82no—
1017C2×C4—81no—
1018C2×C4—82no—
1019C2×C4—81no—
1020C2×C4—162no—
1021C2×C4—162no—
1022C2×C4—164no—
1023C2×C4—161no—
1024C2×C4C2×C4×D412yes—
1025C2×C4C2×C4×D412yes—
1026C2×C4C2×C4×D412yes—
1027C2×C4C2×C4×D412yes—
1028C2×C4#51812yes—
1029C2×C4D4211yescharacteristic
1030C2×C4D4211yescharacteristic
1031C2×C4#54612yes—
1032C2×C4#54612yes—
1033C2×C4#54612yes—
1034C2×C4#54612yes—
1035C2×C4#55112yes—
1036C2×C4C24×C411yescharacteristic
1037C2×C4C23×D411yescharacteristic
1038C2×C4C23×D411yescharacteristic
1039C2×C4C22×#4111yescharacteristic
1040C2×C4C22×#4111yescharacteristic
1041C2×C4C2×H(5,𝔽2)11yescharacteristic
1042C8—24no—
1043C8—24no—
1044C8—21no—
1045C8—21no—
1046C8—21no—
1047C8—21no—
1048C8—24no—
1049C8—42no—
1050C8—42no—
1051C22—21no—
1052C22—21no—
1053C22—21no—
1054C22—21no—
1055C22—21no—
1056C22—21no—
1057C22—24no—
1058C22—24no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—84no—
1067C22—84no—
1068C22—82no—
1069C22—81no—
1070C22—81no—
1071C22—161no—
1072C22—168no—
1073C22#235812yes—
1074C22#235812yes—
1075C22C2×#51811yescharacteristic
1076C22C2×D4211yescharacteristic
1077C22C2×#55111yescharacteristic
1078C4—24no—
1079C4—24no—
1080C4—44no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—82no—
1088C4—81no—
1089C4—81no—
1090C4#235812yes—
1091C4#235812yes—
1092C4C22×C4×D411yescharacteristic
1093C4C22×C4×D411yescharacteristic
1094C4C2×#54611yescharacteristic
1095C4C2×#54611yescharacteristic
1096C2—21no—
1097C2—22no—
1098C2—22no—
1099C2—21no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2C2×#235811yescharacteristic
1104C2#6110711yescharacteristic
1105C2#6110811yescharacteristic
subgroupG/H
center, socleC22C2×D42
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#585C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60169C2semidirect
3. C2×#2947C2semidirect
6. #22896C2semidirect
7. #22894C2semidirect
8. #22892C2semidirect
9. #22890C2semidirect
10. #21205C2semidirect
11. #21076C2semidirect
12. #21075C2semidirect
13. #21006C2semidirect
14. C2×#1908C2semidirect
15. #20954C2semidirect
16. #20865C2semidirect
17. #20864C2semidirect
18. #20422C2semidirect
19. #20420C2semidirect
28. C2×#519C22semidirect
29. #3022C4semidirect
36. #2947C22semidirect
37. #2947C22semidirect
38. #2947C22semidirect
39. #2947C22semidirect
46. #2911C22semidirect
47. C2×#428C22semidirect
71. C2×#419C22semidirect
75. C22×#103C22semidirect
77. C22×#101C22semidirect
78. #2873C22semidirect
79. C2×#405C22semidirect
80. C2×#405C22semidirect
81. #2317C22semidirect
82. #1960C22semidirect
83. #1959C22semidirect
84. #1958C22semidirect
85. #1956C22semidirect
86. #1931C22semidirect
87. #1931C22semidirect
88. #1931C22semidirect
89. #1930C22semidirect
90. #1930C22semidirect
91. #1930C22semidirect
92. #1908C22semidirect
93. #1908C22semidirect
94. #1908C22semidirect
95. #1908C22semidirect
96. #1888C22semidirect
97. #1886C22semidirect
98. #1860C22semidirect
99. #1860C22semidirect
100. #1859C22semidirect
101. #1859C22semidirect
102. #1765C22semidirect
103. #1765C22semidirect
104. #1764C22semidirect
105. #1764C22semidirect
106. #1742C22semidirect
107. C2×#343C22semidirect
108. #1738C22semidirect
109. C2×#341C22semidirect
110. #1733C22semidirect
111. #1733C22semidirect
134. C2×#137C2×C4semidirect
135. C2×#137C2×C4semidirect
162. #536C2×C4semidirect
200. #456C2×C4semidirect
201. #455C2×C4semidirect
227. #421C2×C4semidirect
228. #421C2×C4semidirect
309. #413C2×C4semidirect
437. #137C22×C4semidirect
498. C4⋊Q8C22×C4semidirect
500. #124C22×C4semidirect
595. #104C22×C4semidirect
639. #101C22×C4semidirect
640. #100C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#30222
#601692
C2×#29472
#600892
#600862
#228962
#228942
#228922
#228902
#212052
#210762
#210752
#210062
C2×#19082
#209542
#208652
#208642
#204222
#204202