Finite Group Databasebeta

← #6473299

Subgroups — #6473299

Order 512.

2872 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3188C212yesmaximal, complemented
2C2×#3055C212yesmaximal, complemented
3#35032C211yesmaximal, characteristic, complemented
4#35001C211yesmaximal, characteristic, complemented
5#33183C212yesmaximal, complemented
6#33171C211yesmaximal, characteristic, complemented
7#33170C211yesmaximal, characteristic, complemented
8#30243C212yesmaximal, complemented
9#30240C211yesmaximal, characteristic, complemented
10#30239C211yesmaximal, characteristic, complemented
11#28365C212yesmaximal, complemented
12#28364C212yesmaximal, complemented
13#28358C212yesmaximal, complemented
14#28353C212yesmaximal, complemented
15#27944C212yesmaximal, complemented
16#27941C212yesmaximal, complemented
17#25794C212yesmaximal, complemented
18#25791C212yesmaximal, complemented
19C2×#1753C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2212yescomplemented
21C23×M16C2211yescharacteristic
22C2×#534—22no—
23C2×#525C2212yes—
24C22×#121C2212yes—
25#3188—216no—
26C2×#496C2212yescomplemented
27C2×#493C2211yescharacteristic, complemented
28C2×#492C2211yescharacteristic, complemented
29C2×#484C2212yescomplemented
30C2×#481C2212yescomplemented
31C2×#482C2212yes—
32C2×#482C2212yes—
33#3055—216no—
34C2×#469C2212yes—
35C2×#469C2212yes—
36C2×#468C2212yes—
37C2×#468C2212yes—
38C2×#466C2212yescomplemented
39C2×#466C2212yescomplemented
40C2×#466C2212yescomplemented
41C2×#466C2212yescomplemented
42C2×#465C2212yescomplemented
43C2×#465C2212yescomplemented
44C2×#465C2212yescomplemented
45C2×#465C2212yescomplemented
46C2×#449C2212yes—
47C2×#449C2212yes—
48C2×#450C2212yescomplemented
49C2×#447C2212yescomplemented
50C2×#428C2212yescomplemented
51C2×#417C2212yescomplemented
52C2×#418C2212yescomplemented
53C22×C22⋊C8C2211yescharacteristic
54C22×#97C2211yescharacteristic, complemented
55C22×C4×C8C2211yescharacteristic, complemented
56#2857C2211yescharacteristic, complemented
57#2856C2211yescharacteristic
58#2856C2211yescharacteristic
59#2856C2212yes—
60#2856C2211yescharacteristic, complemented
61#2850C2212yescomplemented
62#2656—22no—
63#2617—22no—
64#2602—24no—
65#2539—24no—
66#2501C2212yes—
67#2501C2212yes—
68#2500C2212yescomplemented
69#2499C2212yescomplemented
70#2433C2212yes—
71#2433C2212yes—
72#2432C2212yescomplemented
73#2431C2212yescomplemented
74#2325—22no—
75C2×C4×C22⋊C4C2211yescharacteristic
76#2096C2212yescomplemented
77#2095C2212yescomplemented
78#2094C2212yescomplemented
79#2094C2212yescomplemented
80#2093C2212yescomplemented
81#2093C2212yescomplemented
82#2092C2212yescomplemented
83#2092C2212yescomplemented
84#2014C2212yescomplemented
85#2014C2212yescomplemented
86#2013C2212yescomplemented
87#2012C2212yescomplemented
88#2012C2212yescomplemented
89#2011C2212yescomplemented
90#2011C2212yescomplemented
91#2011C2212yescomplemented
92#1973C2212yescomplemented
93#1973C2212yescomplemented
94#1972C2212yescomplemented
95#1972C2212yescomplemented
96#1970C2212yescomplemented
97#1970C2212yescomplemented
98#1968C2212yescomplemented
99#1968C2212yescomplemented
100#1961C2212yescomplemented
101#1959C2212yescomplemented
102#1957C2211yescharacteristic, complemented
103#1957C2211yescharacteristic, complemented
104#1957C2211yescharacteristic, complemented
105#1956C2211yescharacteristic, complemented
106#1847C2212yescomplemented
107#1845C2211yescharacteristic, complemented
108#1844C2211yescharacteristic, complemented
109#1753C2212yescomplemented
110#1753C2212yescomplemented
111#1753C2212yescomplemented
112#1753C2212yescomplemented
113C2×#336C2211yescharacteristic, complemented
114C2×#336C2211yescharacteristic, complemented
115C22×#41C2312yes—
116C23×D4—22no—
117C23×D4C2312yes—
118C24×C4C2311yescharacteristic
119C2×AGL(1,ℤ/8)—28no—
120C2×AGL(1,ℤ/8)—44no—
121C2×AGL(1,ℤ/8)—44no—
122C22×SD16C2312yes—
123C22×SD16C2312yes—
124C22×SD16C2312yes—
125C22×SD16C2312yes—
126C22×D8C2312yes—
127C22×D8C2312yes—
128C22×D8C2312yes—
129C22×D8C2312yes—
130C22×M16—42no—
131C22×M16—42no—
132C22×M16D418yescomplemented
133C22×M16C2312yes—
134C22×M16C2312yes—
135C23×C8C2311yescharacteristic
136C23×C8C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139#534—416no—
140C2×C4⋊Q8C2311yescharacteristic
141C2×#127C2311yescharacteristic
142C2×#127C2311yescharacteristic
143C2×#127C2312yes—
144C2×#127C2311yescharacteristic
145C2×#124C2312yes—
146#525—28no—
147#525—28no—
148C2×#123—22no—
149C2×#123—24no—
150C2×#123—24no—
151C2×C22⋊Q8C2312yes—
152C2×C22⋊Q8C2312yes—
153C2×#121—22no—
154C2×#121—24no—
155C2×#121—22no—
156C2×#121—22no—
157C2×#121—22no—
158C2×#121—22no—
159C2×#121—28no—
160C2×#121—28no—
161C2×#121C2312yes—
162C2×#121C2312yes—
163C2×#121C2312yes—
164C2×#121C2312yes—
165C2×#121C2312yes—
166C2×#121C2312yes—
167C2×#120—22no—
168C2×#120—24no—
169C2×#120—24no—
170C2×C4×D4—22no—
171C2×C4×D4—22no—
172C2×#117C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4—22no—
175C22×C22⋊C4D412yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#496—44no—
179#493—42no—
180#492—42no—
181#484—28no—
182#482—28no—
183#482—28no—
184#481—28no—
185#469—28no—
186#469—28no—
187#468—28no—
188#468—28no—
189#466—28no—
190#466—28no—
191#466—28no—
192#466—28no—
193#465—28no—
194#465—28no—
195#465—28no—
196#465—28no—
197#450—28no—
198#449—28no—
199#449—28no—
200#447—28no—
201#428—28no—
202C2×#107C2312yes—
203C2×#107C2312yes—
204C2×#107C2312yes—
205C2×#107C2312yes—
206C2×#106C2312yes—
207C2×#106C2312yes—
208C2×#106C2312yes—
209C2×#106C2312yes—
210#418—28no—
211#417—28no—
212C2×#103C2312yes—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#102C2312yes—
217C2×#102C2312yes—
218C2×#102C2312yes—
219C2×#102C2312yes—
220C2×#102C2312yes—
221C2×#102C2312yes—
222C2×#102C2312yes—
223C2×#102C2312yes—
224C2×#102C2312yes—
225C2×#102C2312yes—
226C2×#102C2312yes—
227C2×#102C2312yes—
228C2×C22⋊C8D418yescomplemented
229C2×C22⋊C8C2312yes—
230C2×C22⋊C8C2312yes—
231C2×#97—42no—
232C2×#97C2312yes—
233C2×#97C2312yes—
234C2×C4×C8—42no—
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2311yescharacteristic
239#399—24no—
240#399—24no—
241#397—24no—
242#394—24no—
243#394—24no—
244#392—24no—
245#392—24no—
246#392—24no—
247#391C2312yes—
248#391C2312yes—
249#390—24no—
250#390—22no—
251#390—22no—
252#390—22no—
253#390C2312yes—
254#390C2312yes—
255#390C2312yes—
256#390C2312yes—
257#390C2312yes—
258#390C2312yes—
259#389—22no—
260#388—24no—
261#388—24no—
262#387—24no—
263#386—24no—
264#386—24no—
265#385—24no—
266#384C2311yescharacteristic
267#384C2312yes—
268#384C2311yescharacteristic
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#382C2312yes—
272#380—22no—
273C4×C22⋊C4D414yes—
274C4×C22⋊C4C2312yes—
275C4×C22⋊C4C2312yes—
276C2×#95D412yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281C25—22no—
282C25C2×D411yescharacteristic
283C2×#41—24no—
284C2×#41—24no—
285C2×#41—42no—
286C2×#41—42no—
287C2×#41—42no—
288C2×#41—42no—
289C22×Q8C2412yes—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—24no—
298C22×D4—24no—
299C22×D4—24no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—42no—
305C22×D4—42no—
306C22×D4—42no—
307C22×D4—42no—
308C22×D4—416no—
309C22×D4—48no—
310C22×D4C2412yes—
311C22×D4C2412yes—
312C22×D4C2412yes—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—41no—
316C23×C4—41no—
317C23×C4—41no—
318C23×C4—41no—
319C23×C4C2×D412yes—
320C23×C4C2×D412yes—
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D414yes—
323C23×C4C2×D414yes—
324C23×C4C2×D412yes—
325C23×C4C2412yes—
326C23×C4C2411yescharacteristic
327AGL(1,ℤ/8)—432no—
328C2×SD16—24no—
329C2×SD16—24no—
330C2×SD16—24no—
331C2×SD16—24no—
332C2×SD16—24no—
333C2×SD16—24no—
334C2×SD16—42no—
335C2×SD16—42no—
336C2×SD16—42no—
337C2×SD16—42no—
338C2×SD16—42no—
339C2×SD16—42no—
340C2×D8—24no—
341C2×D8—24no—
342C2×D8—24no—
343C2×D8—24no—
344C2×D8—24no—
345C2×D8—24no—
346C2×D8—42no—
347C2×D8—42no—
348C2×D8—42no—
349C2×D8—42no—
350C2×D8—42no—
351C2×D8—42no—
352C2×M16—24no—
353C2×M16—24no—
354C2×M16—42no—
355C2×M16—42no—
356C2×M16—416no—
357C2×M16C2×D418yes—
358C2×M16C2×D418yes—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—41no—
362C22×C8—41no—
363C22×C8—41no—
364C22×C8—41no—
365C22×C8—41no—
366C22×C8—41no—
367C22×C8C2×D414yes—
368C22×C8C2×D414yes—
369C22×C8C2×D414yes—
370C22×C8C2×D414yes—
371C22×C8C2412yes—
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2412yes—
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C4⋊Q8—41no—
378C4⋊Q8—41no—
379#127—42no—
380#127—41no—
381#127—41no—
382#127—41no—
383#127—41no—
384#127—41no—
385#127—41no—
386#127—42no—
387#124—42no—
388#124—42no—
389#123—416no—
390#123—416no—
391#123—48no—
392C22⋊Q8—24no—
393C22⋊Q8—24no—
394C22⋊Q8—24no—
395C22⋊Q8—24no—
396#121—24no—
397#121—24no—
398#121—24no—
399#121—24no—
400#121—24no—
401#121—24no—
402#121—24no—
403#121—24no—
404#121—24no—
405#121—24no—
406#121—24no—
407#121—24no—
408#121—416no—
409#121—48no—
410#121—48no—
411#121—48no—
412#121—48no—
413#121—48no—
414#120—416no—
415#120—416no—
416#120—48no—
417C4×D4—48no—
418C4×D4—48no—
419#117—24no—
420#117—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—48no—
454C2×C22⋊C4C2×D414yes—
455C2×C22⋊C4C2×D414yes—
456C2×C42—22no—
457C2×C42—41no—
458C2×C42—41no—
459C2×C42—41no—
460C2×C42—41no—
461C2×C42C2×D412yes—
462C2×C42C2×D412yes—
463C2×C42C2412yes—
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466#107—24no—
467#107—24no—
468#107—24no—
469#107—24no—
470#106—24no—
471#106—24no—
472#106—24no—
473#106—24no—
474#103—24no—
475#103—24no—
476#103—24no—
477#103—24no—
478#102—24no—
479#102—24no—
480#102—24no—
481#102—24no—
482#102—24no—
483#102—24no—
484#102—24no—
485#102—24no—
486#102—24no—
487#102—24no—
488#102—24no—
489#102—24no—
490C22⋊C8C2×D418yes—
491C22⋊C8C2×D418yes—
492#97—24no—
493#97—42no—
494C4×C8—22no—
495C4×C8—22no—
496C4×C8—41no—
497C4×C8—41no—
498#95—24no—
499#95—24no—
500#95—24no—
501#95C2×D414yes—
502#95C2×D414yes—
503C24—24no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—41no—
508C24—41no—
509C24—42no—
510C24—48no—
511C24—44no—
512C24—82no—
513C24—82no—
514C24—84no—
515C24#12714yes—
516C24C22×D412yes—
517C24C22×D411yescharacteristic
518#41—48no—
519#41—48no—
520#41—84no—
521#41—84no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—84no—
566C2×D4—84no—
567C2×D4—82no—
568C2×D4—82no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—82no—
572C2×D4—84no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4—84no—
577C2×D4—84no—
578C2×D4—82no—
579C2×D4—82no—
580C2×D4—832no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4#12718yes—
613C22×C4#12714yes—
614C22×C4AGL(1,ℤ/8)18yescomplemented
615C22×C4C22×D414yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C2511yescharacteristic
625SD16—48no—
626SD16—48no—
627SD16—84no—
628SD16—84no—
629D8—48no—
630D8—48no—
631D8—84no—
632D8—84no—
633M16—216no—
634M16—48no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—28no—
646C2×C8—44no—
647C2×C8—44no—
648C2×C8—44no—
649C2×C8C22×D412yes—
650C2×C8C22×D414yes—
651C2×C8C22×D412yes—
652C2×C8C22×D412yes—
653C2×C8C22×D414yes—
654C2×C8C22×D412yes—
655C2×C8H(5,𝔽2)12yes—
656C2×C8H(5,𝔽2)12yes—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—48no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—84no—
691C22⋊C4—84no—
692C42—21no—
693C42—21no—
694C42—22no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—42no—
699C42—42no—
700C42—44no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—28no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—84no—
727C23—84no—
728C23—88no—
729C23—88no—
730C23—88no—
731C23—168no—
732C23—168no—
733C23C2×#12714yes—
734C23C2×#12712yes—
735C23C2×AGL(1,ℤ/8)14yes—
736C23C23×D411yescharacteristic
737Q8—42no—
738Q8—42no—
739Q8—42no—
740Q8—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—88no—
754D4—88no—
755D4—88no—
756D4—88no—
757D4—88no—
758D4—88no—
759D4—88no—
760D4—88no—
761D4—164no—
762D4—164no—
763D4—164no—
764D4—168no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—88no—
799C2×C4—84no—
800C2×C4—88no—
801C2×C4C2×#12714yes—
802C2×C4C2×#12712yes—
803C2×C4C2×AGL(1,ℤ/8)14yes—
804C2×C4C2×AGL(1,ℤ/8)14yes—
805C2×C4C23×D411yescharacteristic
806C2×C4C23×D411yescharacteristic
807C2×C4C2×H(5,𝔽2)11yescharacteristic
808C2×C4C2×H(5,𝔽2)11yescharacteristic
809C2×C4#58511yescharacteristic
810C2×C4#58511yescharacteristic
811C8—22no—
812C8—24no—
813C8—22no—
814C8—24no—
815C8—22no—
816C8#53414yescomplemented
817C22—24no—
818C22—24no—
819C22—22no—
820C22—22no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—44no—
825C22—44no—
826C22—88no—
827C22—84no—
828C22—84no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—84no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—1616no—
843C22#315114yes—
844C22C22×#12711yescharacteristic
845C22#349611yescharacteristic
846C22#349611yescharacteristic
847C22C22×AGL(1,ℤ/8)12yes—
848C22#358412yes—
849C4—24no—
850C4—24no—
851C4—24no—
852C4—22no—
853C4—44no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4C2×#53411yescharacteristic
860C4#344911yescharacteristic
861C4#349611yescharacteristic
862C4#349611yescharacteristic
863C2—24no—
864C2—44no—
865C2—162no—
866C2—162no—
867C2—162no—
868C2#3500111yescharacteristic
869C2C2×#315111yescharacteristic
870C2#6064311yescharacteristic
871C2#6225312yes—
872C2#6225912yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3188C2semidirect
2. C2×#3055C2semidirect
3. #35032C2semidirect
4. #35001C2semidirect
5. #33183C2semidirect
6. #33171C2semidirect
7. #33170C2semidirect
8. #30243C2semidirect
9. #30240C2semidirect
10. #30239C2semidirect
11. #28365C2semidirect
12. #28364C2semidirect
13. #28358C2semidirect
14. #28353C2semidirect
15. #27944C2semidirect
16. #27941C2semidirect
17. #25794C2semidirect
18. #25791C2semidirect
19. C2×#1753C2semidirect
20. C22×AGL(1,ℤ/8)C22semidirect
26. C2×#496C22semidirect
27. C2×#493C22semidirect
28. C2×#492C22semidirect
29. C2×#484C22semidirect
30. C2×#481C22semidirect
38. C2×#466C22semidirect
39. C2×#466C22semidirect
40. C2×#466C22semidirect
41. C2×#466C22semidirect
42. C2×#465C22semidirect
43. C2×#465C22semidirect
44. C2×#465C22semidirect
45. C2×#465C22semidirect
48. C2×#450C22semidirect
49. C2×#447C22semidirect
50. C2×#428C22semidirect
51. C2×#417C22semidirect
52. C2×#418C22semidirect
54. C22×#97C22semidirect
55. C22×C4×C8C22semidirect
56. #2857C22semidirect
60. #2856C22semidirect
61. #2850C22semidirect
68. #2500C22semidirect
69. #2499C22semidirect
72. #2432C22semidirect
73. #2431C22semidirect
76. #2096C22semidirect
77. #2095C22semidirect
78. #2094C22semidirect
79. #2094C22semidirect
80. #2093C22semidirect
81. #2093C22semidirect
82. #2092C22semidirect
83. #2092C22semidirect
84. #2014C22semidirect
85. #2014C22semidirect
86. #2013C22semidirect
87. #2012C22semidirect
88. #2012C22semidirect
89. #2011C22semidirect
90. #2011C22semidirect
91. #2011C22semidirect
92. #1973C22semidirect
93. #1973C22semidirect
94. #1972C22semidirect
95. #1972C22semidirect
96. #1970C22semidirect
97. #1970C22semidirect
98. #1968C22semidirect
99. #1968C22semidirect
100. #1961C22semidirect
101. #1959C22semidirect
102. #1957C22semidirect
103. #1957C22semidirect
104. #1957C22semidirect
105. #1956C22semidirect
106. #1847C22semidirect
107. #1845C22semidirect
108. #1844C22semidirect
109. #1753C22semidirect
110. #1753C22semidirect
111. #1753C22semidirect
112. #1753C22semidirect
113. C2×#336C22semidirect
114. C2×#336C22semidirect
132. C22×M16D4semidirect
228. C2×C22⋊C8D4semidirect
614. C22×C4AGL(1,ℤ/8)semidirect
816. C8#534semidirect

Maximal subgroups

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

subgroupindex
C2×#31882
C2×#30552
#350322
#350012
#331832
#331712
#331702
#302432
#302402
#302392
#283652
#283642
#283582
#283532
#279442
#279412
#257942
#257912
C2×#17532