Finite Group Databasebeta

← #6558048

Subgroups — #6558048

Order 512.

2853 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3319C212yesmaximal, complemented
2C2×#3264C212yesmaximal, complemented
3#39355C211yesmaximal, characteristic, complemented
4#38953C211yesmaximal, characteristic, complemented
5#30268C211yesmaximal, characteristic, complemented
6#30251C212yesmaximal, complemented
7#28475C212yesmaximal, complemented
8#28443C211yesmaximal, characteristic, complemented
9#28422C212yesmaximal, complemented
10#28369C211yesmaximal, characteristic, complemented
11#28353C212yesmaximal, complemented
12#28339C212yesmaximal, complemented
13#28321C212yesmaximal, complemented
14#25791C212yesmaximal, complemented
15#25779C212yesmaximal, complemented
16#25734C212yesmaximal, complemented
17#23802C211yesmaximal, characteristic, complemented
18#23422C212yesmaximal, complemented
19#20566C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2212yes—
21C23×D8C2212yescomplemented
22C2×#555C2211yescharacteristic
23C2×#546C2212yes—
24C2×D42C2211yescharacteristic
25C2×#535C2212yescomplemented
26#3319—216no—
27#3264—216no—
28C2×#496C2212yescomplemented
29C2×#496C2212yescomplemented
30C2×#493C2211yescharacteristic
31C2×#493C2212yescomplemented
32C2×#492C2211yescharacteristic, complemented
33C2×#489C2212yescomplemented
34C2×#485C2212yescomplemented
35C2×#482C2212yescomplemented
36C2×#474C2212yescomplemented
37C2×#469C2212yes—
38C2×#468C2212yescomplemented
39C2×#466C2212yescomplemented
40C2×#465C2212yescomplemented
41C2×#463C2212yescomplemented
42C2×#463C2212yescomplemented
43C2×#459C2212yescomplemented
44C2×#449C2212yes—
45C2×#449C2212yescomplemented
46C2×#450C2212yescomplemented
47C2×#447C2212yes—
48C2×#447C2212yescomplemented
49C2×#447C2212yescomplemented
50C2×#442C2212yescomplemented
51C2×#442C2212yescomplemented
52C2×#435C2212yes—
53C2×#418C2212yescomplemented
54C2×#416C2212yescomplemented
55#2858C2211yescharacteristic, complemented
56#2858C2211yescharacteristic, complemented
57#2682—22no—
58#2679—22no—
59#2670—24no—
60#2620C2212yescomplemented
61#2619C2212yescomplemented
62#2563C2211yescharacteristic, complemented
63#2544C2212yescomplemented
64#2541C2211yescharacteristic, complemented
65#2500C2212yescomplemented
66#2433C2212yescomplemented
67#2433C2212yescomplemented
68#2432C2212yescomplemented
69#2424—24no—
70#2414—22no—
71#2408—22no—
72#2309C2212yescomplemented
73C4×#127C2211yescharacteristic, complemented
74C4×#127C2211yescharacteristic, complemented
75#2293C2211yescharacteristic
76#2097C2212yescomplemented
77#2094C2211yescharacteristic, complemented
78#2094C2211yescharacteristic, complemented
79#2094C2212yescomplemented
80#2093C2212yescomplemented
81#2092C2212yescomplemented
82#2014C2212yescomplemented
83#2013C2212yescomplemented
84#2012C2212yescomplemented
85#2012C2212yescomplemented
86#2012C2212yescomplemented
87#2012C2212yescomplemented
88#2012C2212yescomplemented
89#2012C2212yescomplemented
90#2011C2212yes—
91#2011C2211yescharacteristic
92#2011C2212yescomplemented
93#2011C2212yescomplemented
94#2011C2212yescomplemented
95#2011C2212yescomplemented
96#2011C2211yescharacteristic, complemented
97#2011C2212yescomplemented
98#1973C2212yescomplemented
99#1972C2212yescomplemented
100#1970C2212yescomplemented
101#1970C2212yescomplemented
102#1970C2212yescomplemented
103#1968C2212yescomplemented
104#1961C2212yescomplemented
105#1958C2212yescomplemented
106#1957C2211yescharacteristic, complemented
107#1956C2211yescharacteristic, complemented
108#1771C2212yescomplemented
109C4×C4⋊C8C2211yescharacteristic, complemented
110#1753C2212yescomplemented
111C8×C22⋊C4C2212yescomplemented
112#1750C2212yescomplemented
113#1745C2211yescharacteristic, complemented
114#1729C2212yescomplemented
115C22×#41C2312yes—
116C23×D4—21no—
117C23×D4C2312yes—
118C23×D4C2312yes—
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×D8—28no—
127C22×D8—44no—
128C22×D8—44no—
129C22×D8C2312yes—
130C22×D8C2312yes—
131C22×D8C2312yes—
132C22×D8C2312yes—
133C22×D8C2312yes—
134C22×D8C2312yes—
135C22×D8C2312yes—
136C22×D8C2312yes—
137C22×M16C2312yes—
138C23×C8C2312yes—
139#555—28no—
140#546—28no—
141#546—28no—
142D42—28no—
143#535—44no—
144#535—44no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×#127C2311yescharacteristic
148C2×#127C2311yescharacteristic
149C2×#127C2311yescharacteristic
150C2×#127C2312yes—
151C2×#127C2311yescharacteristic
152C2×#127C2312yes—
153C2×#124—22no—
154C2×#124—22no—
155C2×#124C2312yes—
156C2×#124C2312yes—
157C2×#124C2312yes—
158C2×#123—22no—
159C2×C22⋊Q8C2312yes—
160C2×#121—21no—
161C2×#121—21no—
162C2×#121—24no—
163C2×#121—22no—
164C2×#121—22no—
165C2×#121C2312yes—
166C2×#121C2312yes—
167C2×#121C2312yes—
168C2×#120—22no—
169C2×#120—22no—
170C2×#120—24no—
171C2×#120—24no—
172C2×#120—24no—
173C2×C4×D4—22no—
174C2×C4×D4—22no—
175C2×C4×D4C2311yescharacteristic
176C2×C4×D4C2312yes—
177C2×C4×D4C2311yescharacteristic
178C2×C4×D4C2311yescharacteristic
179C2×#117—21no—
180C2×#117C2312yes—
181C2×#117C2312yes—
182C22×C22⋊C4—22no—
183#496—28no—
184#496—44no—
185#493—42no—
186#493—44no—
187#492—42no—
188#489—28no—
189#485—28no—
190#482—28no—
191#474—28no—
192#469—28no—
193#468—28no—
194#466—28no—
195#465—28no—
196#463—28no—
197#463—28no—
198#459—28no—
199#450—28no—
200#449—28no—
201#449—28no—
202#447—28no—
203#447—28no—
204#447—28no—
205#442—28no—
206#442—28no—
207#435D4116yescomplemented
208C2×#107C2312yes—
209C2×#107C2312yes—
210C2×#106C2312yes—
211C2×#106C2312yes—
212C2×C4⋊C8C2312yes—
213#418—28no—
214#416—28no—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#102C2312yes—
220C2×#102C2312yes—
221C2×#102C2312yes—
222C2×#102C2312yes—
223C2×#102C2312yes—
224C2×#102C2312yes—
225C2×#102C2312yes—
226C2×#102C2312yes—
227C2×#102C2312yes—
228C2×#102C2312yes—
229C2×#102C2312yes—
230C2×#102C2312yes—
231C2×C22⋊C8C2312yes—
232C2×C22⋊C8C2312yes—
233C2×#97C2312yes—
234C2×#97C2312yes—
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2312yes—
238#396—24no—
239#394—24no—
240#394—24no—
241#394—24no—
242#394—24no—
243#394—24no—
244#393—22no—
245#392—24no—
246#392—24no—
247#392—22no—
248#392—24no—
249#391C2312yes—
250#390—24no—
251#390—22no—
252#390—22no—
253#390—22no—
254#390—22no—
255#390—22no—
256#390D412yes—
257#390C2311yescharacteristic
258#390C2311yescharacteristic
259#390C2312yes—
260#390C2312yes—
261#390C2312yes—
262#390C2312yes—
263#390C2312yes—
264#390C2312yes—
265#389D412yes—
266#388—24no—
267#388D414yes—
268#386—24no—
269#385—24no—
270#384C2311yescharacteristic
271#384C2311yescharacteristic
272#382C2312yes—
273#380—22no—
274#379—24no—
275C4×C4⋊C4C2311yescharacteristic
276C4×C22⋊C4C2312yes—
277C43C2311yescharacteristic
278#336C2312yes—
279#336C2312yes—
280#336C2311yescharacteristic
281#336C2311yescharacteristic
282#336C2312yes—
283#336C2312yes—
284C25—22no—
285C25—22no—
286C2×#41—24no—
287C2×#41—24no—
288C2×#41—24no—
289C2×#41—42no—
290C2×#41—42no—
291C2×#41—42no—
292C22×Q8—21no—
293C22×Q8C2412yes—
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—21no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—24no—
310C22×D4—21no—
311C22×D4—22no—
312C22×D4—24no—
313C22×D4—42no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4—42no—
319C22×D4—44no—
320C22×D4—84no—
321C22×D4C2×D411yescharacteristic
322C22×D4C2411yescharacteristic
323C22×D4C2412yes—
324C22×D4C2412yes—
325C22×D4C2412yes—
326C22×D4C2411yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4C2412yes—
332AGL(1,ℤ/8)—432no—
333C2×SD16—24no—
334C2×SD16—24no—
335C2×SD16—24no—
336C2×SD16—24no—
337C2×SD16—24no—
338C2×SD16—42no—
339C2×SD16—42no—
340C2×SD16—42no—
341C2×SD16—42no—
342C2×SD16—42no—
343C2×SD16—42no—
344C2×SD16—42no—
345C2×D8—24no—
346C2×D8—24no—
347C2×D8—24no—
348C2×D8—24no—
349C2×D8—24no—
350C2×D8—24no—
351C2×D8—24no—
352C2×D8—24no—
353C2×D8—24no—
354C2×D8—24no—
355C2×D8—24no—
356C2×D8—24no—
357C2×D8—24no—
358C2×D8—24no—
359C2×D8—42no—
360C2×D8—42no—
361C2×D8—42no—
362C2×D8—42no—
363C2×D8—42no—
364C2×D8—42no—
365C2×D8—42no—
366C2×D8—42no—
367C2×D8—42no—
368C2×D8—42no—
369C2×D8—432no—
370C2×M16—42no—
371C2×M16—42no—
372C2×M16C2×D418yes—
373C22×C8—42no—
374C22×C8—42no—
375C22×C8C2×D418yes—
376C22×C8C2412yes—
377C22×C8C2412yes—
378C22×C8C2412yes—
379C22×C8C2412yes—
380C4⋊Q8—24no—
381C4⋊Q8—41no—
382C4⋊Q8—41no—
383#127—24no—
384#127—24no—
385#127—22no—
386#127—24no—
387#127—41no—
388#127—42no—
389#127—41no—
390#127—41no—
391#127—42no—
392#127—42no—
393#124—24no—
394#124—24no—
395#124—24no—
396#124—42no—
397#124—42no—
398#124—42no—
399#124—48no—
400#124—84no—
401#123—48no—
402C22⋊Q8—24no—
403C22⋊Q8—24no—
404#121—24no—
405#121—24no—
406#121—24no—
407#121—24no—
408#121—24no—
409#121—24no—
410#121—416no—
411#121—44no—
412#121—44no—
413#121—48no—
414#121—84no—
415#120—416no—
416#120—48no—
417#120—48no—
418#120—88no—
419#120—88no—
420C4×D4—24no—
421C4×D4—24no—
422C4×D4—24no—
423C4×D4—24no—
424C4×D4—84no—
425C4×D4—84no—
426C4×D4C2×D418yes—
427#117—24no—
428#117—24no—
429#117—42no—
430#117—42no—
431#117—44no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4C2×D414yes—
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2412yes—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—48no—
465C2×C22⋊C4C2×D414yes—
466C2×C22⋊C4C2×D414yes—
467C2×C22⋊C4C2×D412yes—
468C2×C42—22no—
469C2×C42C2×D412yes—
470C2×C42C2×D412yes—
471C2×C42C2411yescharacteristic
472C2×C42C2412yes—
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475#107—24no—
476#107—24no—
477#106—24no—
478#106—24no—
479C4⋊C8C2×D418yes—
480#103—24no—
481#103—24no—
482#103—24no—
483#103—24no—
484#102—24no—
485#102—24no—
486#102—24no—
487#102—24no—
488#102—24no—
489#102—24no—
490#102—24no—
491#102—24no—
492#102—24no—
493#102—24no—
494#102—24no—
495#102—24no—
496C22⋊C8C2×D418yes—
497C22⋊C8C2×D418yes—
498#97—42no—
499#97C2×D418yes—
500C4×C8—41no—
501C4×C8—41no—
502C4×C8—42no—
503#95—24no—
504#95—24no—
505#95C2×D414yes—
506#95C2×D412yes—
507C24—21no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—21no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—82no—
517C24—82no—
518C24—84no—
519C24—84no—
520C24—84no—
521C24—84no—
522C24C22×D412yes—
523#41—48no—
524#41—48no—
525#41—84no—
526#41—84no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—42no—
534C2×Q8—82no—
535C2×D4—28no—
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—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—48no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—84no—
582C2×D4—84no—
583C2×D4—84no—
584C2×D4—84no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4—82no—
589C2×D4—82no—
590C2×D4—84no—
591C2×D4—84no—
592C2×D4—84no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—84no—
596C2×D4—82no—
597C2×D4—84no—
598C2×D4—84no—
599C2×D4—82no—
600C2×D4—84no—
601C2×D4—84no—
602C2×D4—816no—
603C2×D4#12714yes—
604C2×D4H(5,𝔽2)14yes—
605C2×D4H(5,𝔽2)12yes—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—44no—
622C22×C4—82no—
623C22×C4—84no—
624C22×C4C22×D414yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D414yes—
630C22×C4C22×D414yes—
631C22×C4C22×D412yes—
632C22×C4C2511yescharacteristic
633SD16—48no—
634SD16—48no—
635SD16—84no—
636SD16—84no—
637D8—216no—
638D8—48no—
639D8—48no—
640D8—48no—
641D8—48no—
642D8—48no—
643D8—84no—
644D8—84no—
645M16—48no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—48no—
655C2×C8C22×D414yes—
656C2×C8C22×D414yes—
657C2×C8C22×D414yes—
658C2×C8C22×D414yes—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4#12714yes—
673C22⋊C4—28no—
674C22⋊C4—44no—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—44no—
684C22⋊C4—42no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—84no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C22⋊C4#12718yes—
696C42—24no—
697C42—21no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—21no—
702C42—42no—
703C42—44no—
704C42C22×D414yes—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—22no—
711C23—42no—
712C23—44no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—44no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—44no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—44no—
732C23—44no—
733C23—42no—
734C23—88no—
735C23—88no—
736C23—88no—
737C23—88no—
738C23—164no—
739C23—164no—
740C23—168no—
741C23—168no—
742C23—168no—
743C23—168no—
744C23C2×#12714yes—
745C23C23×D411yescharacteristic
746Q8—42no—
747Q8—42no—
748Q8—42no—
749Q8—42no—
750Q8—162no—
751D4—24no—
752D4—24no—
753D4—24no—
754D4—44no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—88no—
769D4—88no—
770D4—88no—
771D4—84no—
772D4—88no—
773D4—88no—
774D4—88no—
775D4—164no—
776D4—162no—
777D4—168no—
778D4—168no—
779D4—164no—
780D4—164no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—88no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—164no—
812C2×C4C2×#12714yes—
813C2×C4C2×#12712yes—
814C2×C4C2×#12712yes—
815C2×C4#57614yes—
816C2×C4C23×D412yes—
817C2×C4C2×H(5,𝔽2)11yescharacteristic
818C2×C4C2×H(5,𝔽2)12yes—
819C2×C4#58511yescharacteristic
820C8—24no—
821C8—24no—
822C8—24no—
823C8—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—42no—
832C22—48no—
833C22—84no—
834C22—81no—
835C22—82no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—84no—
841C22—84no—
842C22—82no—
843C22—82no—
844C22—81no—
845C22—81no—
846C22—82no—
847C22—82no—
848C22—81no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—84no—
853C22—84no—
854C22—1616no—
855C22—1616no—
856C22C22×#12711yescharacteristic
857C22#348411yescharacteristic
858C22#348811yescharacteristic
859C22C2×#57612yes—
860C22#358512yes—
861C4—24no—
862C4—24no—
863C4—22no—
864C4—22no—
865C4—42no—
866C4—44no—
867C4—82no—
868C4—81no—
869C4—81no—
870C4—82no—
871C4—82no—
872C4#348412yes—
873C4#348812yes—
874C2—44no—
875C2—84no—
876C2—82no—
877C2—161no—
878C2—162no—
879C2—162no—
880C2#3592111yescharacteristic
881C2#6064411yescharacteristic
882C2#6064711yescharacteristic
883C2#6167912yes—
884C2#6201512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3319C2semidirect
2. C2×#3264C2semidirect
3. #39355C2semidirect
4. #38953C2semidirect
5. #30268C2semidirect
6. #30251C2semidirect
7. #28475C2semidirect
8. #28443C2semidirect
9. #28422C2semidirect
10. #28369C2semidirect
11. #28353C2semidirect
12. #28339C2semidirect
13. #28321C2semidirect
14. #25791C2semidirect
15. #25779C2semidirect
16. #25734C2semidirect
17. #23802C2semidirect
18. #23422C2semidirect
19. #20566C2semidirect
21. C23×D8C22semidirect
25. C2×#535C22semidirect
28. C2×#496C22semidirect
29. C2×#496C22semidirect
31. C2×#493C22semidirect
32. C2×#492C22semidirect
33. C2×#489C22semidirect
34. C2×#485C22semidirect
35. C2×#482C22semidirect
36. C2×#474C22semidirect
38. C2×#468C22semidirect
39. C2×#466C22semidirect
40. C2×#465C22semidirect
41. C2×#463C22semidirect
42. C2×#463C22semidirect
43. C2×#459C22semidirect
45. C2×#449C22semidirect
46. C2×#450C22semidirect
48. C2×#447C22semidirect
49. C2×#447C22semidirect
50. C2×#442C22semidirect
51. C2×#442C22semidirect
53. C2×#418C22semidirect
54. C2×#416C22semidirect
55. #2858C22semidirect
56. #2858C22semidirect
60. #2620C22semidirect
61. #2619C22semidirect
62. #2563C22semidirect
63. #2544C22semidirect
64. #2541C22semidirect
65. #2500C22semidirect
66. #2433C22semidirect
67. #2433C22semidirect
68. #2432C22semidirect
72. #2309C22semidirect
73. C4×#127C22semidirect
74. C4×#127C22semidirect
76. #2097C22semidirect
77. #2094C22semidirect
78. #2094C22semidirect
79. #2094C22semidirect
80. #2093C22semidirect
81. #2092C22semidirect
82. #2014C22semidirect
83. #2013C22semidirect
84. #2012C22semidirect
85. #2012C22semidirect
86. #2012C22semidirect
87. #2012C22semidirect
88. #2012C22semidirect
89. #2012C22semidirect
92. #2011C22semidirect
93. #2011C22semidirect
94. #2011C22semidirect
95. #2011C22semidirect
96. #2011C22semidirect
97. #2011C22semidirect
98. #1973C22semidirect
99. #1972C22semidirect
100. #1970C22semidirect
101. #1970C22semidirect
102. #1970C22semidirect
103. #1968C22semidirect
104. #1961C22semidirect
105. #1958C22semidirect
106. #1957C22semidirect
107. #1956C22semidirect
108. #1771C22semidirect
109. C4×C4⋊C8C22semidirect
110. #1753C22semidirect
111. C8×C22⋊C4C22semidirect
112. #1750C22semidirect
113. #1745C22semidirect
114. #1729C22semidirect
207. #435D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33192
C2×#32642
#393552
#389532
#302682
#302512
#284752
#284432
#284222
#283692
#283532
#283392
#283212
#257912
#257792
#257342
#238022
#234222
#205662