Finite Group Databasebeta

← #6529792

Subgroups — #6529792

Order 512.

1885 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3240C211yesmaximal, characteristic, complemented
2C2×#3077C211yesmaximal, characteristic, complemented
3#35233C211yesmaximal, characteristic
4#34394C211yesmaximal, characteristic, complemented
5#28293C212yesmaximal, complemented
6#28292C212yesmaximal, complemented
7#28215C212yesmaximal, complemented
8#28214C212yesmaximal, complemented
9#25462C212yesmaximal, complemented
10#25461C212yesmaximal, complemented
11#25285C212yesmaximal, complemented
12#25284C212yesmaximal, complemented
13#24595C211yesmaximal, characteristic, complemented
14#24594C211yesmaximal, characteristic, complemented
15#24593C211yesmaximal, characteristic, complemented
16#24592C211yesmaximal, characteristic, complemented
17#24495C211yesmaximal, characteristic, complemented
18#24494C211yesmaximal, characteristic
19#24493C211yesmaximal, characteristic, complemented
20#24492C211yesmaximal, characteristic
21#21979C211yesmaximal, characteristic, complemented
22#21890C211yesmaximal, characteristic, complemented
23#20738C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#529C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27#3240—28no—
28C2×#501C2211yescharacteristic, complemented
29C2×#501C2211yescharacteristic, complemented
30C2×#489C2211yescharacteristic, complemented
31C2×#489C2211yescharacteristic, complemented
32C2×#485C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36#3077—28no—
37C2×#479C2211yescharacteristic, complemented
38C2×#479C2211yescharacteristic, complemented
39C2×#478C2212yes—
40C2×#478C2212yes—
41C2×#478C2211yescharacteristic, complemented
42C2×#478C2211yescharacteristic, complemented
43C2×#476C2212yes—
44C2×#474C2212yes—
45C2×#432C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#423C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×#418C2211yescharacteristic
51#2849—22no—
52#2636—21no—
53#2636—21no—
54#2598—21no—
55#2598—21no—
56#2566C2212yes—
57#2544C2212yes—
58#2534—22no—
59#2503C2211yescharacteristic
60#2501C2211yescharacteristic
61#2435C2211yescharacteristic
62#2433C2211yescharacteristic
63#2378—22no—
64#2369C2212yescomplemented
65#2365C2212yescomplemented
66#2356—21no—
67#2351—21no—
68#2347C2211yescharacteristic
69#2347C2211yescharacteristic
70#2346C2211yescharacteristic
71#2346C2211yescharacteristic
72#2330C2212yescomplemented
73#2330C2212yescomplemented
74#2328C2212yes—
75#2326C2212yes—
76#2323—22no—
77#2320—21no—
78#2320—21no—
79#2285C2211yescharacteristic
80#2283C2211yescharacteristic
81#2085C2212yescomplemented
82#2085C2212yescomplemented
83#2084C2212yescomplemented
84#2083C2212yescomplemented
85#2068C2212yescomplemented
86#2067C2212yes—
87#2067C2212yes—
88#2067C2212yescomplemented
89#2066C2212yescomplemented
90#2065C2212yes—
91#2065C2212yes—
92#2065C2212yescomplemented
93#2042C2212yes—
94#2042C2212yes—
95#2041C2212yes—
96#2041C2212yes—
97#1989C2212yescomplemented
98#1983C2212yes—
99#1983C2212yes—
100#1983C2212yescomplemented
101#1982C2212yes—
102#1982C2212yes—
103#1949C2212yescomplemented
104#1949C2212yescomplemented
105#1948C2212yescomplemented
106#1947C2212yescomplemented
107#1940C2212yescomplemented
108#1940C2212yescomplemented
109#1928C2212yescomplemented
110#1927C2212yescomplemented
111#1926C2212yes—
112#1926C2212yes—
113#1926C2212yescomplemented
114#1925C2212yes—
115#1925C2212yes—
116#1925C2212yescomplemented
117#1895C2211yescharacteristic
118#1895C2211yescharacteristic
119#1894C2211yescharacteristic
120#1894C2211yescharacteristic
121#1851C2211yescharacteristic
122#1851C2211yescharacteristic
123#1851C2211yescharacteristic
124#1851C2211yescharacteristic
125#1843C2212yescomplemented
126#1832C2212yescomplemented
127#1824C2211yescharacteristic
128#1824C2211yescharacteristic
129#1803C2212yescomplemented
130#1802C2212yes—
131#1802C2212yes—
132#1802C2212yescomplemented
133#1786C2211yescharacteristic
134#1786C2211yescharacteristic
135#1762C2212yes—
136#1762C2212yes—
137C23×D4C2311yescharacteristic
138C24×C4—21no—
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141#533—24no—
142#533D418yescomplemented
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×#127C2312yes—
146#529—24no—
147#529—24no—
148C2×#126—21no—
149C2×#125C2311yescharacteristic
150C2×#125C2311yescharacteristic
151C2×#125C2311yescharacteristic
152C2×#124C2311yescharacteristic
153C2×#124C2312yes—
154C2×#123—21no—
155C2×#123—22no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8C2311yescharacteristic
159C2×#121C2311yescharacteristic
160C2×#120—22no—
161C2×C4×Q8—22no—
162C2×C4×Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×Q8C2311yescharacteristic
165C2×C4×D4—21no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4C2312yes—
171C2×C4×D4C2311yescharacteristic
172C2×C4×D4C2312yes—
173C2×#117—21no—
174C2×#117—21no—
175C2×#117C2311yescharacteristic
176C2×#117C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C22⋊C4—21no—
179C22×C42C2311yescharacteristic
180#501—24no—
181#501—24no—
182#489—24no—
183#489—24no—
184#485—24no—
185#485—24no—
186#482—24no—
187#482—24no—
188#479—24no—
189#479—24no—
190#478—28no—
191#478—28no—
192#478—24no—
193#478—24no—
194#476—28no—
195#474—28no—
196#432—24no—
197#428—24no—
198#428—24no—
199C2×#107C2312yes—
200C2×#107C2312yes—
201C2×#107C2311yescharacteristic
202C2×#107C2311yescharacteristic
203C2×#107C2311yescharacteristic
204C2×#107C2311yescharacteristic
205C2×#106C2312yes—
206C2×#106C2312yes—
207C2×#106C2311yescharacteristic
208C2×#106C2311yescharacteristic
209C2×#106C2311yescharacteristic
210C2×#106C2311yescharacteristic
211#423—24no—
212C2×C4⋊C8C2312yes—
213C2×C4⋊C8C2311yescharacteristic
214C2×C4⋊C8C2311yescharacteristic
215C2×C4⋊C8C2312yes—
216C2×C4⋊C8C2312yes—
217C2×C4⋊C8C2312yes—
218C2×C4⋊C8C2312yes—
219C2×C4⋊C8C2312yes—
220#418—24no—
221#418—24no—
222C2×#103C2311yescharacteristic
223C2×#103C2311yescharacteristic
224C2×#103C2311yescharacteristic
225C2×#103C2311yescharacteristic
226C2×#103C2312yes—
227C2×#103C2312yes—
228C2×#102C2312yes—
229C2×#102C2312yes—
230C2×#102C2312yes—
231C2×#102C2312yes—
232C2×#102C2311yescharacteristic
233C2×#102C2311yescharacteristic
234C2×#102C2311yescharacteristic
235C2×#102C2311yescharacteristic
236C2×#102C2312yes—
237C2×#102C2312yes—
238C2×#102C2312yes—
239C2×#102C2312yes—
240C2×#102C2312yes—
241C2×#102C2312yes—
242C2×C22⋊C8C2311yescharacteristic
243C2×C22⋊C8C2311yescharacteristic
244C2×#97C2311yescharacteristic
245C2×#97C2311yescharacteristic
246#400—21no—
247#400—21no—
248#399—21no—
249#399—21no—
250#396—22no—
251#396—22no—
252#394—22no—
253#394—22no—
254#394—21no—
255#394—21no—
256#392—21no—
257#392—21no—
258#391—22no—
259#391—22no—
260#391—22no—
261#391C2312yes—
262#390C2312yes—
263#390C2312yes—
264#390C2312yes—
265#389—22no—
266#389—22no—
267#389—22no—
268#389—22no—
269#389—22no—
270#389C2312yes—
271#389C2312yes—
272#389C2312yes—
273#389C2312yes—
274#388—22no—
275#388—22no—
276#388—22no—
277#388—22no—
278#388—22no—
279#388—22no—
280#387—22no—
281#387—22no—
282#387—22no—
283#387—22no—
284#387—22no—
285#387—22no—
286#386—22no—
287#386—22no—
288#386—22no—
289#386—22no—
290#386—22no—
291#386—22no—
292#385—22no—
293#385—22no—
294#385—22no—
295#385—22no—
296#384C2312yes—
297#384C2312yes—
298#383—21no—
299#383—21no—
300#383D411yescharacteristic
301#383D411yescharacteristic
302#382—21no—
303#382—21no—
304#382—21no—
305#382D411yescharacteristic
306#382D411yescharacteristic
307#382C2312yes—
308#381—22no—
309#381D412yes—
310#380—21no—
311#380D412yes—
312#380C2311yescharacteristic
313#380C2311yescharacteristic
314#379—22no—
315C4×C4⋊C4—22no—
316C4×C4⋊C4—21no—
317C4×C4⋊C4—21no—
318C4×C4⋊C4—21no—
319C4×C4⋊C4C2312yes—
320C4×C4⋊C4C2312yes—
321C4×C4⋊C4C2312yes—
322C4×C4⋊C4C2312yes—
323C4×C4⋊C4C2312yes—
324C4×C4⋊C4C2312yes—
325C4×C22⋊C4C2311yescharacteristic
326C4×C22⋊C4C2311yescharacteristic
327#376—21no—
328#376—21no—
329#376C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#336C2312yes—
339#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342C25—21no—
343C22×Q8—21no—
344C22×Q8—21no—
345C22×Q8C2411yescharacteristic
346C22×D4—24no—
347C22×D4—21no—
348C22×D4—22no—
349C22×D4—21no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—42no—
354C22×D4C2411yescharacteristic
355C22×D4C2412yes—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—44no—
361C23×C4—84no—
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2411yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—42no—
368C2×M16—42no—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2411yescharacteristic
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8C2×D414yes—
378C4⋊Q8C2×D414yes—
379#127—24no—
380#127—42no—
381#126—44no—
382#125—22no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125C2×D414yes—
387#125C2×D414yes—
388#124—24no—
389#124—22no—
390#124—22no—
391#124—42no—
392#123—44no—
393#123—84no—
394C22⋊Q8—28no—
395C22⋊Q8—28no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398#121—22no—
399#121—22no—
400#120—84no—
401C4×Q8—28no—
402C4×Q8—28no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—84no—
406C4×D4—24no—
407C4×D4—24no—
408C4×D4—22no—
409C4×D4—24no—
410C4×D4—24no—
411C4×D4—22no—
412C4×D4—44no—
413C4×D4—44no—
414C4×D4—44no—
415#117—22no—
416#117—22no—
417#117—44no—
418#117—82no—
419#117C2×D414yes—
420#117C2×D414yes—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—44no—
473C2×C22⋊C4C2×D412yes—
474C2×C22⋊C4C2×D412yes—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D414yes—
486C2×C42#4114yes—
487C2×C42C2412yes—
488C2×C42C2412yes—
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491#107—24no—
492#107—24no—
493#107—22no—
494#107—22no—
495#107—22no—
496#107—22no—
497#106—24no—
498#106—24no—
499#106—22no—
500#106—22no—
501#106—22no—
502#106—22no—
503C4⋊C8—24no—
504C4⋊C8—24no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—42no—
508C4⋊C8—42no—
509C4⋊C8—42no—
510C4⋊C8—42no—
511#103—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—42no—
516#103—42no—
517#102—24no—
518#102—24no—
519#102—24no—
520#102—24no—
521#102—24no—
522#102—24no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—42no—
528#102—42no—
529#102—42no—
530#102—42no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533#97—22no—
534#97—22no—
535#95—21no—
536#95—22no—
537#95—22no—
538#95—21no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D412yes—
553#95C2×D412yes—
554#95C2×D412yes—
555#95C2×D412yes—
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D412yes—
559#95C2×D412yes—
560C24—22no—
561C24—21no—
562C24—44no—
563C24—44no—
564C24—42no—
565C24—81no—
566C24—81no—
567C24C22×D411yescharacteristic
568C2×Q8—24no—
569C2×Q8—24no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8—82no—
577C2×D4—28no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—48no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—82no—
596C2×D4—82no—
597C2×D4—82no—
598C2×D4—82no—
599C2×D42−1+414yes—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—41no—
615C22×C4—44no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—82no—
623C22×C4—82no—
624C22×C4—82no—
625C22×C4—82no—
626C22×C4—816no—
627C22×C4#12114yes—
628C22×C4#12114yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D412yes—
639C22×C4C2×#4112yes—
640C22×C4C2511yescharacteristic
641M16—44no—
642M16—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4C22×D412yes—
693C4⋊C4C22×D412yes—
694C4⋊C4C22×D412yes—
695C4⋊C4C22×D412yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—42no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C22⋊C4—82no—
712C22⋊C4—82no—
713C22⋊C4—82no—
714C22⋊C4—82no—
715C22⋊C4—81no—
716C22⋊C4—81no—
717C42—24no—
718C42—24no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—44no—
724C42—42no—
725C42—82no—
726C42—82no—
727C42—82no—
728C42—82no—
729C42#12114yes—
730C42#12114yes—
731C42C22×D412yes—
732C42C22×D412yes—
733C42C2×#4112yes—
734C42C2×#4112yes—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—24no—
740C23—48no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—42no—
752C23—84no—
753C23—84no—
754C23—88no—
755C23—88no—
756C23C2×#12112yes—
757C23C23×D411yescharacteristic
758Q8—48no—
759Q8—41no—
760Q8—41no—
761Q8—42no—
762Q8—84no—
763D4—24no—
764D4—24no—
765D4—48no—
766D4—41no—
767D4—42no—
768D4—41no—
769D4—42no—
770D4—42no—
771D4—84no—
772D4—164no—
773D4—164no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—84no—
825C2×C4—88no—
826C2×C4—88no—
827C2×C4—84no—
828C2×C4C2×#12112yes—
829C2×C4C2×#12112yes—
830C2×C4C2×#12112yes—
831C2×C4C2×#12112yes—
832C2×C4C2×#12112yes—
833C2×C4C23×D411yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C2×2−1+412yes—
836C2×C4#58512yes—
837C8—41no—
838C8—41no—
839C8—41no—
840C8—41no—
841C8—42no—
842C8—42no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—42no—
847C22—42no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—816no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—81no—
857C22—81no—
858C22—82no—
859C22—82no—
860C22—81no—
861C22C22×#12111yescharacteristic
862C22#348912yes—
863C22#358511yescharacteristic
864C22#358512yes—
865C22#358611yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—81no—
880C4—82no—
881C4—81no—
882C4—82no—
883C4—82no—
884C4—81no—
885C4#348611yescharacteristic
886C4#348711yescharacteristic
887C4#349512yes—
888C2—42no—
889C2—84no—
890C2—161no—
891C2#3566111yescharacteristic
892C2#6042511yescharacteristic
893C2#6042611yescharacteristic
894C2#6223112yes—
895C2#6223212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3240C2semidirect
2. C2×#3077C2semidirect
4. #34394C2semidirect
5. #28293C2semidirect
6. #28292C2semidirect
7. #28215C2semidirect
8. #28214C2semidirect
9. #25462C2semidirect
10. #25461C2semidirect
11. #25285C2semidirect
12. #25284C2semidirect
13. #24595C2semidirect
14. #24594C2semidirect
15. #24593C2semidirect
16. #24592C2semidirect
17. #24495C2semidirect
19. #24493C2semidirect
21. #21979C2semidirect
22. #21890C2semidirect
23. #20738C2semidirect
28. C2×#501C22semidirect
29. C2×#501C22semidirect
30. C2×#489C22semidirect
31. C2×#489C22semidirect
37. C2×#479C22semidirect
38. C2×#479C22semidirect
41. C2×#478C22semidirect
42. C2×#478C22semidirect
64. #2369C22semidirect
65. #2365C22semidirect
72. #2330C22semidirect
73. #2330C22semidirect
81. #2085C22semidirect
82. #2085C22semidirect
83. #2084C22semidirect
84. #2083C22semidirect
85. #2068C22semidirect
88. #2067C22semidirect
89. #2066C22semidirect
92. #2065C22semidirect
97. #1989C22semidirect
100. #1983C22semidirect
103. #1949C22semidirect
104. #1949C22semidirect
105. #1948C22semidirect
106. #1947C22semidirect
107. #1940C22semidirect
108. #1940C22semidirect
109. #1928C22semidirect
110. #1927C22semidirect
113. #1926C22semidirect
116. #1925C22semidirect
125. #1843C22semidirect
126. #1832C22semidirect
129. #1803C22semidirect
132. #1802C22semidirect
142. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32402
C2×#30772
#352332
#343942
#282932
#282922
#282152
#282142
#254622
#254612
#252852
#252842
#245952
#245942
#245932
#245922
#244952
#244942
#244932
#244922
#219792
#218902
#207382