Finite Group Databasebeta

← #10575456

Subgroups — #10575456

Order 512.

7934 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62853C212yesmaximal, complemented
2#60772C218yesmaximal, complemented
3#60770C214yesmaximal, complemented
4#60768C214yesmaximal, complemented
5#60767C218yesmaximal, complemented
6#60766C218yesmaximal, complemented
7#60764C218yesmaximal, complemented
8#60762C218yesmaximal, complemented
9#60517C212yesmaximal, complemented
10C2×#3098C212yesmaximal, complemented
11#60456C212yesmaximal, complemented
12#60453C211yesmaximal, characteristic, complemented
13C2×#3061C211yesmaximal, characteristic, complemented
14#60371C212yesmaximal, complemented
15#60366C212yesmaximal, complemented
16#60065C211yesmaximal, characteristic, complemented
17C2×#585C2211yescharacteristic
18C2×#585C2212yescomplemented
19C2×#575C2211yescharacteristic, complemented
20C2×#575C2212yescomplemented
21C22×#135C2211yescharacteristic, complemented
22C2×#568C2211yescharacteristic, complemented
23C22×#131C2211yescharacteristic, complemented
24#3497—24no—
25#3496—28no—
26#3496—24no—
27#3489—24no—
28#3489—24no—
29#3489C2218yescomplemented
30#3489C2218yescomplemented
31#3488—24no—
32#3488—24no—
33#3488C2218yescomplemented
34#3488C2218yescomplemented
35#3449C2212yes—
36#3449C2212yescomplemented
37#3449C2218yescomplemented
38C2×#537C2212yes—
39C2×#537C2212yescomplemented
40C2×#537C2218yescomplemented
41C2×#520C2212yescomplemented
42#3203C2218yescomplemented
43#3203C22116yescomplemented
44#3203C2218yescomplemented
45#3202C2218yescomplemented
46#3201C22116yescomplemented
47#3201C22116yescomplemented
48#3200C22116yescomplemented
49#3199C2218yescomplemented
50#3198C22116yescomplemented
51#3198C22116yescomplemented
52#3197C22116yescomplemented
53#3196C22116yescomplemented
54#3194C22116yescomplemented
55#3193C22116yescomplemented
56#3191C2218yescomplemented
57#3191C2218yescomplemented
58#3190C22116yescomplemented
59#3189C2218yescomplemented
60#3188C22116yescomplemented
61#3186C2218yescomplemented
62#3099C2218yescomplemented
63#3098C2218yescomplemented
64#3098C2218yescomplemented
65#3098C2218yescomplemented
66#3098C2218yescomplemented
67#3098C2218yescomplemented
68#3097C2218yescomplemented
69#3096C2218yescomplemented
70#3093C2218yescomplemented
71#3092C2218yescomplemented
72C2×#484C2214yescomplemented
73C2×#485C2214yescomplemented
74C2×#482C2214yescomplemented
75C2×#480C2214yescomplemented
76#3063C2214yescomplemented
77#3063C2214yescomplemented
78#3063C2218yescomplemented
79#3062C2214yescomplemented
80#3062C2214yescomplemented
81#3062C2218yescomplemented
82#3061C2218yescomplemented
83#3061C2218yescomplemented
84#3061C2218yescomplemented
85#3060C2218yescomplemented
86#3056C2218yescomplemented
87#3055C2218yescomplemented
88#3054C2214yescomplemented
89C2×#468C2214yescomplemented
90#3050C2214yescomplemented
91C2×#467C2212yescomplemented
92C2×#466C2212yescomplemented
93#3013C2214yescomplemented
94#3013C2218yescomplemented
95#3013C2214yescomplemented
96#3013C2218yescomplemented
97#3012C2214yescomplemented
98#3012C2218yescomplemented
99#3012C2214yescomplemented
100#3012C2218yescomplemented
101#3011C2214yescomplemented
102#3010C2214yescomplemented
103#3009C2214yescomplemented
104#3008C2214yescomplemented
105#3007C2218yescomplemented
106#3006C2218yescomplemented
107#3002C2218yescomplemented
108#3002C2218yescomplemented
109#2911C2211yescharacteristic, complemented
110C2×#428C2212yescomplemented
111C22×#107C2211yescharacteristic, complemented
112#2896C2212yescomplemented
113C2×#417C2212yescomplemented
114C2×#417C2212yescomplemented
115C2×#416C2212yescomplemented
116#2880C2218yescomplemented
117#2880C2218yescomplemented
118#2879C2214yescomplemented
119#2879C2212yescomplemented
120C2×#408C2214yescomplemented
121C2×#408C2212yescomplemented
122#585—44no—
123#585—44no—
124#585—48no—
125#585—48no—
126C2×2−1+4—22no—
127C2×2−1+4D412yes—
128C2×2−1+4D414yes—
129C2×2−1+4C2314yes—
130C2×2−1+4C2314yes—
131C2×H(5,𝔽2)—24no—
132C2×H(5,𝔽2)—22no—
133C2×H(5,𝔽2)D412yes—
134C2×H(5,𝔽2)D414yes—
135C2×H(5,𝔽2)D414yes—
136C2×H(5,𝔽2)C2314yes—
137C2×H(5,𝔽2)C2314yes—
138C22×#41—24no—
139C22×#41—24no—
140C22×#41C2312yes—
141C22×#41C2312yes—
142C22×#41C2318yes—
143C22×#41C2312yes—
144C22×#41C2311yescharacteristic
145C22×#41C2314yes—
146C22×#41C2318yes—
147#575—44no—
148#575—48no—
149C2×#137C2314yes—
150C2×#137C2314yes—
151C2×#137C2314yes—
152C2×AGL(1,ℤ/8)C2314yes—
153C2×AGL(1,ℤ/8)C2314yes—
154C2×AGL(1,ℤ/8)C2314yes—
155C2×#135—44no—
156C2×#135C2318yes—
157C2×#135C2314yes—
158C2×#135C2314yes—
159C2×#135C2314yes—
160C22×Q16C2311yescharacteristic
161C22×SD16C2312yes—
162C22×D8C2311yescharacteristic
163#568—44no—
164C2×#131—44no—
165C2×#131C2314yes—
166C2×#131C2314yes—
167C2×#131C2318yes—
168C22×M16C2312yes—
169C22×M16C2311yescharacteristic
170C22×M16C2314yes—
171C22×M16C2312yes—
172C23×C8C2311yescharacteristic
173C23×C8C2312yes—
174#550—28no—
175#550—28no—
176D4×Q8—28no—
177D4×Q8—28no—
178#548—28no—
179#548—28no—
180#548—28no—
181#548—28no—
182#547—28no—
183#547—216no—
184#547—216no—
185#547—28no—
186#546—28no—
187#546—216no—
188#546—216no—
189#546—28no—
190#546—216no—
191#546—28no—
192#546—216no—
193#546—28no—
194D42—216no—
195D42—28no—
196D42—216no—
197D42—28no—
198#537—24no—
199#537—24no—
200#537—24no—
201#537—28no—
202#537—28no—
203#537—24no—
204#537—216no—
205#537C2318yes—
206#537C2318yes—
207#537C2314yes—
208#537C2314yes—
209#537C2318yes—
210#537C2314yes—
211#537C23116yes—
212#537C23116yes—
213#537C2318yes—
214#537C2314yes—
215#536—22no—
216#536—22no—
217#536—28no—
218#536C2314yes—
219#536C23116yes—
220#536C2314yes—
221#535—22no—
222#535—22no—
223#535—28no—
224#535C2314yes—
225#535C23116yes—
226#535C2314yes—
227#534—24no—
228#534—24no—
229#534—216no—
230#532—24no—
231#532—24no—
232#532—216no—
233#525—24no—
234#525—24no—
235#525—28no—
236#525—28no—
237#525C2318yes—
238#525C23116yes—
239#525C23116yes—
240#525C2318yes—
241C2×C22⋊Q8—22no—
242C2×C22⋊Q8—22no—
243C2×C22⋊Q8—28no—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C23116yes—
246C2×C22⋊Q8C2314yes—
247C2×#121—22no—
248C2×#121—24no—
249C2×#121—22no—
250C2×#121—28no—
251C2×#121—24no—
252C2×#121—216no—
253C2×#121C2314yes—
254C2×#121C23116yes—
255C2×#121C2314yes—
256#520—24no—
257#520—24no—
258#520C2318yes—
259#520C2318yes—
260C2×C4×Q8—22no—
261C2×C4×D4—24no—
262C2×C4×D4—22no—
263C2×#117C2314yes—
264C2×#117C2312yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2312yes—
267#485C23116yes—
268#485C23116yes—
269#485C23116yes—
270#485C23116yes—
271#484C23116yes—
272#484C23116yes—
273#484C23116yes—
274#483C23116yes—
275#482C23116yes—
276#482C23116yes—
277#482C23116yes—
278#482C23116yes—
279#481C23116yes—
280#480C23116yes—
281#480C23116yes—
282#480C23116yes—
283#470C2318yes—
284#470C23116yes—
285#469C2318yes—
286#469C23116yes—
287#468C2318yes—
288#468C23116yes—
289#468C23116yes—
290#468C23116yes—
291#468C23116yes—
292#468C2318yes—
293#467C2314yes—
294#467C23116yes—
295#467C2318yes—
296#467C2318yes—
297#467C2314yes—
298#466C2314yes—
299#466C23116yes—
300#466C2318yes—
301#466C2318yes—
302#466C2314yes—
303#465C2318yes—
304#465C23116yes—
305#465C2318yes—
306#465C23116yes—
307#452C2318yes—
308#452C23116yes—
309#452C2318yes—
310#452C23116yes—
311#452C2318yes—
312#452C2318yes—
313#451C2318yes—
314#451C23116yes—
315#451C2318yes—
316#450C23116yes—
317#450C2318yes—
318#450C2318yes—
319#449C2318yes—
320#449C23116yes—
321#449C2318yes—
322#449C23116yes—
323#449C2318yes—
324#449C2318yes—
325#448C23116yes—
326#448C2318yes—
327#448C2318yes—
328#447C2318yes—
329#447C23116yes—
330#447C2318yes—
331#428C2314yes—
332#428C2318yes—
333#428C2314yes—
334#428C2318yes—
335#427C2314yes—
336C2×#107C2314yes—
337C2×#107C2314yes—
338C2×#107C2314yes—
339C2×#107C2312yes—
340C2×#107C2312yes—
341C2×#106C2314yes—
342#419C2314yes—
343#418C2314yes—
344#417C2314yes—
345#417C2318yes—
346#417C2314yes—
347#417C2318yes—
348#417C2318yes—
349#417C2318yes—
350#416C2314yes—
351#416C2314yes—
352#416C2314yes—
353#416C2314yes—
354#416C2318yes—
355C2×#103C2312yes—
356C2×#103C2314yes—
357C2×#103C2312yes—
358C2×#103C2314yes—
359C2×#102C2312yes—
360C2×#102C2314yes—
361C2×#102C2312yes—
362C2×#102C2314yes—
363#408C2318yes—
364#408C2314yes—
365#408C2314yes—
366#408C2314yes—
367#408C2314yes—
368#408C2318yes—
369#408C2318yes—
370#408C2318yes—
371#408C23116yes—
372#407C2318yes—
373#407C23116yes—
374C2×C22⋊C8C2314yes—
375C2×C22⋊C8C2314yes—
376C2×C22⋊C8C2318yes—
377C2×C22⋊C8C2318yes—
3782−1+4—48no—
3792−1+4—416no—
3802−1+4—48no—
3812−1+4—48no—
3822−1+4—48no—
3832−1+4—48no—
3842−1+4—416no—
385H(5,𝔽2)—416no—
386H(5,𝔽2)—48no—
387H(5,𝔽2)—416no—
388H(5,𝔽2)—48no—
389H(5,𝔽2)—48no—
390H(5,𝔽2)—48no—
391H(5,𝔽2)—48no—
392H(5,𝔽2)—432no—
393H(5,𝔽2)—416no—
394C2×#41—24no—
395C2×#41—24no—
396C2×#41—28no—
397C2×#41—24no—
398C2×#41—28no—
399C2×#41—24no—
400C2×#41—28no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—28no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—24no—
407C2×#41—24no—
408C2×#41—28no—
409C2×#41—28no—
410C2×#41—28no—
411C2×#41—28no—
412C2×#41—28no—
413C2×#41—28no—
414C2×#41—48no—
415C2×#41—48no—
416C2×#41—416no—
417C2×#41—416no—
418C2×#41—416no—
419C2×#41—416no—
420C2×#41—432no—
421C2×#41—432no—
422C2×#41C2×D414yes—
423C2×#41C2×D414yes—
424C2×#41C2×D414yes—
425C2×#41C2×D418yes—
426C2×#41C2×D418yes—
427C2×#41C2×D4116yes—
428C2×#41C2×D418yes—
429C2×#41C2×D418yes—
430C2×#41C2414yes—
431C2×#41C2414yes—
432C2×#41C2414yes—
433C2×#41C2414yes—
434C2×#41C2418yes—
435C2×#41C2418yes—
436C2×#41C2414yes—
437C2×#41C2414yes—
438C2×#41C2414yes—
439C2×#41C2418yes—
440C22×Q8—24no—
441C22×Q8—24no—
442C22×Q8C2×D412yes—
443C22×Q8C2×D411yescharacteristic
444C22×Q8C2×D418yes—
445C22×Q8C2×D414yes—
446C22×Q8C2412yes—
447C22×Q8C2412yes—
448C22×Q8C2418yes—
449C22×D4—28no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—216no—
455C22×D4—28no—
456C22×D4—28no—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4C2×D414yes—
460C22×D4C2×D412yes—
461C22×D4C2×D412yes—
462C22×D4C2×D411yescharacteristic
463C22×D4C2×D4116yes—
464C22×D4C2×D418yes—
465C22×D4C2×D414yes—
466C22×D4C2×D418yes—
467C22×D4C2412yes—
468C22×D4C2412yes—
469C22×D4C2418yes—
470C23×C4—24no—
471C23×C4—22no—
472C23×C4—28no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4C2414yes—
476C23×C4C2412yes—
477C23×C4C2418yes—
478C23×C4C2411yescharacteristic
479#137—48no—
480#137—48no—
481#137—48no—
482AGL(1,ℤ/8)—48no—
483AGL(1,ℤ/8)—48no—
484AGL(1,ℤ/8)—48no—
485#135—48no—
486#135—48no—
487#135—48no—
488#135—416no—
489C2×Q16—42no—
490C2×Q16C2412yes—
491C2×Q16C2412yes—
492C2×Q16C2418yes—
493C2×Q16C2414yes—
494C2×SD16—44no—
495C2×SD16C2414yes—
496C2×SD16C2414yes—
497C2×SD16C2418yes—
498C2×SD16C2418yes—
499C2×SD16C2418yes—
500C2×D8—42no—
501C2×D8C2412yes—
502C2×D8C2412yes—
503C2×D8C2418yes—
504C2×D8C2414yes—
505#131—48no—
506#131—48no—
507#131—416no—
508C2×M16—24no—
509C2×M16—28no—
510C2×M16—44no—
511C2×M16—48no—
512C2×M16C2414yes—
513C2×M16C2414yes—
514C2×M16C2414yes—
515C2×M16C2418yes—
516C2×M16C2418yes—
517C22×C8—24no—
518C22×C8—44no—
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2412yes—
522C22×C8C2412yes—
523C22×C8C2412yes—
524C22×C8C2414yes—
525C22×C8C2414yes—
526C22×C8C2414yes—
527C22×C8C2418yes—
528C4⋊Q8—24no—
529C4⋊Q8—24no—
530C4⋊Q8—216no—
531#127—24no—
532#127—24no—
533#127—216no—
534#124—24no—
535#124—24no—
536#124—216no—
537#124—24no—
538#124—24no—
539#124—216no—
540#123—28no—
541#123—28no—
542#123—216no—
543#123—216no—
544#123—28no—
545#123—28no—
546#123—216no—
547#123—216no—
548C22⋊Q8—28no—
549C22⋊Q8—24no—
550C22⋊Q8—28no—
551C22⋊Q8—24no—
552C22⋊Q8—28no—
553C22⋊Q8—28no—
554C22⋊Q8—216no—
555C22⋊Q8—216no—
556C22⋊Q8—24no—
557C22⋊Q8—24no—
558C22⋊Q8—28no—
559C22⋊Q8—28no—
560C22⋊Q8—216no—
561C22⋊Q8—216no—
562C22⋊Q8C24116yes—
563C22⋊Q8C2418yes—
564C22⋊Q8C2418yes—
565C22⋊Q8C24116yes—
566C22⋊Q8C2418yes—
567C22⋊Q8C2418yes—
568#121—28no—
569#121—24no—
570#121—28no—
571#121—24no—
572#121—216no—
573#121—28no—
574#121—216no—
575#121—28no—
576#121—216no—
577#121—216no—
578#121—216no—
579#121—216no—
580#121—216no—
581#121—216no—
582#121—28no—
583#121—28no—
584#121—216no—
585#121—216no—
586#121—24no—
587#121—24no—
588#121—28no—
589#121—28no—
590#121—28no—
591#121—28no—
592#121—216no—
593#121—216no—
594#121C24116yes—
595#121C2418yes—
596#121C2418yes—
597#121C24116yes—
598#121C2418yes—
599#121C2418yes—
600#120—28no—
601#120—28no—
602#120—216no—
603#120—216no—
604#120—28no—
605#120—28no—
606#120—216no—
607#120—216no—
608C4×Q8—28no—
609C4×Q8—28no—
610C4×D4—216no—
611C4×D4—216no—
612C4×D4—28no—
613C4×D4—28no—
614C4×D4—28no—
615C4×D4—28no—
616C4×D4—216no—
617C4×D4—216no—
618C4×D4—28no—
619C4×D4—28no—
620C4×D4—216no—
621C4×D4—216no—
622#117—28no—
623#117—22no—
624#117—22no—
625#117C2414yes—
626#117C2414yes—
627#117C24116yes—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—216no—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C24116yes—
641C2×C4⋊C4C2412yes—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—216no—
647C2×C22⋊C4—24no—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—216no—
650C2×C42—24no—
651C2×C42—22no—
652#107C2414yes—
653#107C2414yes—
654#107C2418yes—
655#107C24116yes—
656#107C2414yes—
657#107C2414yes—
658#106C24116yes—
659#106C2418yes—
660#103C2414yes—
661#103C2414yes—
662#103C2414yes—
663#103C2414yes—
664#103C24116yes—
665#103C24116yes—
666#103C2418yes—
667#103C2418yes—
668#102C2414yes—
669#102C2414yes—
670#102C2414yes—
671#102C2414yes—
672#102C24116yes—
673#102C24116yes—
674#102C2418yes—
675#102C2418yes—
676C22⋊C8C2418yes—
677C22⋊C8C2418yes—
678C22⋊C8C24116yes—
679C22⋊C8C2418yes—
680C22⋊C8C2418yes—
681C22⋊C8C24116yes—
682C24—28no—
683C24—22no—
684C24—22no—
685C24C22×D412yes—
686C24C22×D414yes—
687C24C22×D418yes—
688C24C22×D411yescharacteristic
689#41—216no—
690#41—216no—
691#41—216no—
692#41—28no—
693#41—28no—
694#41—28no—
695#41—28no—
696#41—28no—
697#41—28no—
698#41—28no—
699#41—28no—
700#41—28no—
701#41—28no—
702#41—28no—
703#41—28no—
704#41—28no—
705#41—28no—
706#41—48no—
707#41—48no—
708#41—416no—
709#41—432no—
710#41—416no—
711#41—416no—
712#41—416no—
713#41—48no—
714#41—48no—
715#41—48no—
716#41—48no—
717#41—432no—
718#41—432no—
719#41—432no—
720#41—432no—
721#41—416no—
722#41—416no—
723#41—416no—
724#41—416no—
725#41—48no—
726#41—48no—
727#41—48no—
728#41—48no—
729C2×Q8—24no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—416no—
739C2×Q8—48no—
740C2×Q8—48no—
741C2×Q8—48no—
742C2×Q8—416no—
743C2×Q8—416no—
744C2×Q8C22×D414yes—
745C2×Q8C22×D414yes—
746C2×Q8C22×D414yes—
747C2×Q8C22×D418yes—
748C2×Q8C2514yes—
749C2×Q8C2514yes—
750C2×D4—28no—
751C2×D4—216no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—216no—
762C2×D4—28no—
763C2×D4—216no—
764C2×D4—24no—
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—416no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—416no—
778C2×D4—432no—
779C2×D4—432no—
780C2×D4—432no—
781C2×D4—416no—
782C2×D4—416no—
783C2×D4—432no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—164no—
787C2×D4—164no—
788C2×D4—1616no—
789C2×D4C22×D418yes—
790C2×D4C22×D418yes—
791C2×D4C22×D414yes—
792C2×D4C22×D414yes—
793C2×D4C22×D418yes—
794C2×D4C22×D414yes—
795C2×D4C22×D418yes—
796C2×D4C22×D4116yes—
797C2×D4C2514yes—
798C2×D4C2514yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—24no—
808C22×C4—22no—
809C22×C4—216no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—432no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—162no—
824C22×C4—164no—
825C22×C4C22×D414yes—
826C22×C4C22×D412yes—
827C22×C4C22×D418yes—
828C22×C4C22×D414yes—
829C22×C4C22×D4116yes—
830C22×C4C22×D418yes—
831C22×C4C22×D412yes—
832C22×C4C22×D411yescharacteristic
833C22×C4H(5,𝔽2)14yes—
834C22×C4H(5,𝔽2)14yes—
835C22×C4C2518yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2511yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—44no—
842Q16—48no—
843SD16—44no—
844SD16—44no—
845SD16—48no—
846SD16—48no—
847SD16—48no—
848D8—42no—
849D8—42no—
850D8—44no—
851D8—48no—
852M16—28no—
853M16—28no—
854M16—28no—
855M16—48no—
856M16—48no—
857C2×C8—22no—
858C2×C8—22no—
859C2×C8—24no—
860C2×C8—24no—
861C2×C8—24no—
862C2×C8—28no—
863C2×C8—44no—
864C2×C8—44no—
865C2×C8—48no—
866C2×C8C2518yes—
867C2×C8C2514yes—
868C2×C8C2511yescharacteristic
869C2×C8C2511yescharacteristic
870C2×C8C2512yes—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—216no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—216no—
877C4⋊C4—28no—
878C4⋊C4—216no—
879C4⋊C4—28no—
880C4⋊C4—22no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4C2514yes—
884C4⋊C4C2514yes—
885C4⋊C4C2518yes—
886C22⋊C4—216no—
887C22⋊C4—28no—
888C22⋊C4—216no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—216no—
896C22⋊C4—28no—
897C22⋊C4—216no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C42—216no—
902C42—24no—
903C42—24no—
904C23—28no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—41no—
909C23—41no—
910C23—44no—
911C23—42no—
912C23—44no—
913C23—42no—
914C23—48no—
915C23—48no—
916C23—48no—
917C23—416no—
918C23—44no—
919C23—44no—
920C23—82no—
921C23—82no—
922C23—88no—
923C23—82no—
924C23—82no—
925C23—88no—
926C23#53414yes—
927C23C23×D414yes—
928C23C23×D418yes—
929C23C23×D411yescharacteristic
930C23C23×D412yes—
931Q8—28no—
932Q8—28no—
933Q8—28no—
934Q8—24no—
935Q8—24no—
936Q8—24no—
937Q8—24no—
938Q8—48no—
939Q8—416no—
940Q8—44no—
941Q8—44no—
942D4—216no—
943D4—216no—
944D4—216no—
945D4—24no—
946D4—24no—
947D4—24no—
948D4—24no—
949D4—28no—
950D4—28no—
951D4—28no—
952D4—416no—
953D4—48no—
954D4—416no—
955D4—416no—
956D4—416no—
957D4—48no—
958D4—48no—
959D4—48no—
960D4—48no—
961D4—44no—
962D4—44no—
963D4—88no—
964D4—88no—
965D4—816no—
966D4—88no—
967D4—816no—
968D4—88no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—216no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—28no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—48no—
983C2×C4—416no—
984C2×C4—416no—
985C2×C4—416no—
986C2×C4—416no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—82no—
994C2×C4—84no—
995C2×C4—82no—
996C2×C4—84no—
997C2×C4—84no—
998C2×C4—816no—
999C2×C4#53414yes—
1000C2×C4#53418yes—
1001C2×C4C23×D418yes—
1002C2×C4C23×D414yes—
1003C2×C4C23×D411yescharacteristic
1004C2×C4C23×D412yes—
1005C2×C4C2×H(5,𝔽2)12yes—
1006C2×C4C2×H(5,𝔽2)14yes—
1007C2×C4C2×H(5,𝔽2)14yes—
1008C2×C4C2×H(5,𝔽2)12yes—
1009C2×C4C2611yescharacteristic
1010C8—21no—
1011C8—21no—
1012C8—22no—
1013C8—24no—
1014C8—28no—
1015C22—22no—
1016C22—21no—
1017C22—22no—
1018C22—21no—
1019C22—28no—
1020C22—24no—
1021C22—24no—
1022C22—28no—
1023C22—28no—
1024C22—24no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22—84no—
1033C22—88no—
1034C22—164no—
1035C22—164no—
1036C22—168no—
1037C22—1616no—
1038C22C2×#53412yes—
1039C22C2×#53414yes—
1040C22C24×D411yescharacteristic
1041C4—28no—
1042C4—24no—
1043C4—48no—
1044C4—44no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4C2×#53414yes—
1049C4C2×#53412yes—
1050C4C22×H(5,𝔽2)11yescharacteristic
1051C4C22×H(5,𝔽2)11yescharacteristic
1052C2—22no—
1053C2—24no—
1054C2—44no—
1055C2—48no—
1056C2—84no—
1057C2—84no—
1058C2C22×#53411yescharacteristic
1059C2#6309111yescharacteristic
1060C2#6309311yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#585 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62853C2semidirect
2. #60772C2semidirect
3. #60770C2semidirect
4. #60768C2semidirect
5. #60767C2semidirect
6. #60766C2semidirect
7. #60764C2semidirect
8. #60762C2semidirect
9. #60517C2semidirect
10. C2×#3098C2semidirect
11. #60456C2semidirect
12. #60453C2semidirect
13. C2×#3061C2semidirect
14. #60371C2semidirect
15. #60366C2semidirect
16. #60065C2semidirect
18. C2×#585C22semidirect
19. C2×#575C22semidirect
20. C2×#575C22semidirect
21. C22×#135C22semidirect
22. C2×#568C22semidirect
23. C22×#131C22semidirect
29. #3489C22semidirect
30. #3489C22semidirect
33. #3488C22semidirect
34. #3488C22semidirect
36. #3449C22semidirect
37. #3449C22semidirect
39. C2×#537C22semidirect
40. C2×#537C22semidirect
41. C2×#520C22semidirect
42. #3203C22semidirect
43. #3203C22semidirect
44. #3203C22semidirect
45. #3202C22semidirect
46. #3201C22semidirect
47. #3201C22semidirect
48. #3200C22semidirect
49. #3199C22semidirect
50. #3198C22semidirect
51. #3198C22semidirect
52. #3197C22semidirect
53. #3196C22semidirect
54. #3194C22semidirect
55. #3193C22semidirect
56. #3191C22semidirect
57. #3191C22semidirect
58. #3190C22semidirect
59. #3189C22semidirect
60. #3188C22semidirect
61. #3186C22semidirect
62. #3099C22semidirect
63. #3098C22semidirect
64. #3098C22semidirect
65. #3098C22semidirect
66. #3098C22semidirect
67. #3098C22semidirect
68. #3097C22semidirect
69. #3096C22semidirect
70. #3093C22semidirect
71. #3092C22semidirect
72. C2×#484C22semidirect
73. C2×#485C22semidirect
74. C2×#482C22semidirect
75. C2×#480C22semidirect
76. #3063C22semidirect
77. #3063C22semidirect
78. #3063C22semidirect
79. #3062C22semidirect
80. #3062C22semidirect
81. #3062C22semidirect
82. #3061C22semidirect
83. #3061C22semidirect
84. #3061C22semidirect
85. #3060C22semidirect
86. #3056C22semidirect
87. #3055C22semidirect
88. #3054C22semidirect
89. C2×#468C22semidirect
90. #3050C22semidirect
91. C2×#467C22semidirect
92. C2×#466C22semidirect
93. #3013C22semidirect
94. #3013C22semidirect
95. #3013C22semidirect
96. #3013C22semidirect
97. #3012C22semidirect
98. #3012C22semidirect
99. #3012C22semidirect
100. #3012C22semidirect
101. #3011C22semidirect
102. #3010C22semidirect
103. #3009C22semidirect
104. #3008C22semidirect
105. #3007C22semidirect
106. #3006C22semidirect
107. #3002C22semidirect
108. #3002C22semidirect
109. #2911C22semidirect
110. C2×#428C22semidirect
111. C22×#107C22semidirect
112. #2896C22semidirect
113. C2×#417C22semidirect
114. C2×#417C22semidirect
115. C2×#416C22semidirect
116. #2880C22semidirect
117. #2880C22semidirect
118. #2879C22semidirect
119. #2879C22semidirect
120. C2×#408C22semidirect
121. C2×#408C22semidirect

Maximal subgroups

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

subgroupindex
#628532
#607722
#607702
#607682
#607672
#607662
#607642
#607622
#605172
C2×#30982
#604562
#604532
C2×#30612
#603712
#603662
#600652