Finite Group Databasebeta

← #6496459

Subgroups — #6496459

Order 512.

2210 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3234C211yesmaximal, characteristic, complemented
2C22×#432C211yesmaximal, characteristic, complemented
3#36624C211yesmaximal, characteristic
4C2×#2851C211yesmaximal, characteristic, complemented
5#33217C212yesmaximal, complemented
6#33052C212yesmaximal, complemented
7#29883C212yesmaximal, complemented
8#29851C212yesmaximal, complemented
9#24839C214yesmaximal, complemented
10#24706C214yesmaximal, complemented
11#24608C212yesmaximal, complemented
12#24607C212yesmaximal, complemented
13#24553C212yesmaximal, complemented
14#24550C212yesmaximal, complemented
15#21986C211yesmaximal, characteristic, complemented
16#21865C211yesmaximal, characteristic, complemented
17#21838C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C22×#125C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22#3234—28no—
23C2×#501C2212yescomplemented
24C2×#490C2212yescomplemented
25C2×#481C2212yes—
26C2×#480C2212yes—
27C2×#478C2214yescomplemented
28C2×#432—28no—
29C2×#432C2212yes—
30C2×#432C2211yescharacteristic
31C2×#432C2212yes—
32C2×#432C2212yes—
33C2×#432C2211yescharacteristic
34C22×C4⋊C8C2212yes—
35C22×C22⋊C8C2212yes—
36C22×#97C2212yes—
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2856C2211yescharacteristic
40#2856C2211yescharacteristic
41#2854—21no—
42#2854C2212yes—
43#2851—21no—
44#2851—21no—
45#2851—21no—
46#2851—21no—
47#2851C2212yes—
48#2851C2212yes—
49#2851C2212yes—
50#2851C2212yes—
51#2850—21no—
52#2850—21no—
53#2847—21no—
54#2847C2212yes—
55C4×#121—21no—
56C4×#121—21no—
57C4×#121C2212yes—
58C4×#121C2212yes—
59#2297—21no—
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#387—21no—
63C2×#387—21no—
64C2×#385—21no—
65C2×#385—21no—
66#2285C2211yescharacteristic
67C2×#382C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70#2088C2214yescomplemented
71#2087C2214yescomplemented
72#2077C2214yes—
73#2075C2214yes—
74#2067C2214yescomplemented
75#2065C2214yescomplemented
76#2034C2214yes—
77#2033C2214yes—
78#1993C2212yescomplemented
79#1992C2212yescomplemented
80#1992C2212yescomplemented
81#1989C2214yescomplemented
82#1961C2212yescomplemented
83#1949C2214yescomplemented
84#1944C2214yescomplemented
85#1943C2214yescomplemented
86#1936C2214yescomplemented
87#1936C2214yescomplemented
88#1893C2214yes—
89#1893C2214yes—
90#1874C2212yes—
91#1874C2212yes—
92#1853C2212yes—
93#1852C2212yes—
94#1847C2212yescomplemented
95#1836C2212yescomplemented
96#1824C2212yes—
97#1823C2212yes—
98#1808C2214yes—
99#1807C2214yes—
100#1804C2214yescomplemented
101C22×#41—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C23×C8C2314yes—
106#532—24no—
107#532—24no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#125—21no—
111C2×#125—21no—
112C2×#125—24no—
113C2×#125—24no—
114C2×#125C2312yes—
115C2×#125C2312yes—
116C2×#124—21no—
117#525—48no—
118C2×#123—22no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#120—22no—
130C2×C4×D4—22no—
131C2×C4×D4—22no—
132C2×C4×D4—21no—
133C2×C4×D4C2312yes—
134C2×#117—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#501—28no—
160#490—28no—
161#481—28no—
162#480—28no—
163#478—216no—
164#432—24no—
165#432—28no—
166#432—28no—
167#432—28no—
168#432D418yescomplemented
169C2×#107C2314yes—
170C2×#107C2314yes—
171C2×#106C2314yes—
172C2×#106C2314yes—
173C2×C4⋊C8—28no—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2314yes—
176C2×C4⋊C8C2312yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×C22⋊C8—28no—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×#97—28no—
186C2×#97C2314yes—
187C2×#97C2312yes—
188C2×#97C2312yes—
189#391—21no—
190#391—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390C2312yes—
196#390C2312yes—
197#389—21no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389C2312yes—
204#389C2312yes—
205#389C2312yes—
206#389C2312yes—
207#389C2312yes—
208#389C2312yes—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#387—22no—
214#387—22no—
215#387—22no—
216#387—22no—
217#387—22no—
218#387—22no—
219#387—22no—
220#387—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#385—22no—
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#382—21no—
238#382—21no—
239#382—21no—
240#382C2312yes—
241#382C2312yes—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380C2312yes—
250#380C2312yes—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4C2312yes—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C2×#95—21no—
261C2×#95—21no—
262C2×#95—21no—
263C2×#95—21no—
264C2×#95—21no—
265C2×#95—21no—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274C25C2×D411yescharacteristic
275C2×#41—44no—
276C2×#41—44no—
277C2×#41—44no—
278C22×Q8—21no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4C2412yes—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—22no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C22×C8—28no—
319C22×C8—28no—
320C22×C8—44no—
321C22×C8C2414yes—
322C22×C8C2414yes—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325#127—22no—
326#127—22no—
327#125—24no—
328#125—24no—
329#125—24no—
330#125—24no—
331#125—44no—
332#125—44no—
333#124—44no—
334#123—48no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337#121—24no—
338#121—24no—
339#121—28no—
340#121—44no—
341#121—44no—
342#121—44no—
343#121—44no—
344#121—44no—
345#121—44no—
346#120—48no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—48no—
350C4×D4—48no—
351C4×D4—44no—
352#117—44no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D414yes—
436C2×C42#4114yes—
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—28no—
442#107—44no—
443#106—28no—
444#106—44no—
445C4⋊C8—28no—
446C4⋊C8—24no—
447C4⋊C8C2×D418yes—
448#102—28no—
449#102—28no—
450#102—44no—
451#102—44no—
452C22⋊C8—24no—
453C22⋊C8—28no—
454C22⋊C8C2×D418yes—
455#97—28no—
456#97—24no—
457#97C2×D418yes—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—41no—
482C24—41no—
483C24AGL(1,ℤ/8)14yes—
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487#41—816no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—42no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—416no—
572C22×C4—416no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—44no—
588C22×C4#12114yes—
589C22×C4#12114yes—
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C2×#4112yes—
603C22×C42−1+414yes—
604C22×C4C2511yescharacteristic
605C2×C8—24no—
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—24no—
610C2×C8—416no—
611C2×C8C22×D418yes—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—44no—
671C42#12114yes—
672C42#12114yes—
673C42C22×D412yes—
674C42C22×D412yes—
675C42C2×#4112yes—
676C42C2×#4112yes—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—28no—
689C23—28no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23C2×#12112yes—
706C23#53612yes—
707C23C2×AGL(1,ℤ/8)12yes—
708C23C2×AGL(1,ℤ/8)12yes—
709C23C2×AGL(1,ℤ/8)12yes—
710C23#57512yes—
711C23#57512yes—
712C23C23×D411yescharacteristic
713Q8—84no—
714D4—44no—
715D4—44no—
716D4—84no—
717D4—84no—
718D4—88no—
719D4—88no—
720D4—88no—
721C2×C4—28no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—28no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—88no—
790C2×C4—84no—
791C2×C4—84no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4C2×#12112yes—
795C2×C4C2×#12112yes—
796C2×C4C2×#12112yes—
797C2×C4C2×#12112yes—
798C2×C4C2×#12112yes—
799C2×C4#53612yes—
800C2×C4#57512yes—
801C2×C4C23×D411yescharacteristic
802C2×C4C22×#4111yescharacteristic
803C2×C4C2×2−1+412yes—
804C2×C4#58512yes—
805C8—28no—
806C8—44no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—416no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22#305514yes—
835C22#323414yescomplemented
836C22C22×#12111yescharacteristic
837C22C2×#53611yescharacteristic
838C22#344911yescharacteristic
839C22C22×AGL(1,ℤ/8)11yescharacteristic
840C22C2×#57511yescharacteristic
841C22C2×#57511yescharacteristic
842C22C2×#57511yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4#348912yes—
862C4#349512yes—
863C2—24no—
864C2—24no—
865C2—42no—
866C2—162no—
867C2#3530611yescharacteristic
868C2C2×#305511yescharacteristic
869C2#6044411yescharacteristic
870C2C2×#323411yescharacteristic
871C2#6085411yescharacteristic
872C2#6095811yescharacteristic
873C2#6095911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3234C2semidirect
2. C22×#432C2semidirect
4. C2×#2851C2semidirect
5. #33217C2semidirect
6. #33052C2semidirect
7. #29883C2semidirect
8. #29851C2semidirect
9. #24839C2semidirect
10. #24706C2semidirect
11. #24608C2semidirect
12. #24607C2semidirect
13. #24553C2semidirect
14. #24550C2semidirect
15. #21986C2semidirect
16. #21865C2semidirect
17. #21838C2semidirect
23. C2×#501C22semidirect
24. C2×#490C22semidirect
27. C2×#478C22semidirect
70. #2088C22semidirect
71. #2087C22semidirect
74. #2067C22semidirect
75. #2065C22semidirect
78. #1993C22semidirect
79. #1992C22semidirect
80. #1992C22semidirect
81. #1989C22semidirect
82. #1961C22semidirect
83. #1949C22semidirect
84. #1944C22semidirect
85. #1943C22semidirect
86. #1936C22semidirect
87. #1936C22semidirect
94. #1847C22semidirect
95. #1836C22semidirect
100. #1804C22semidirect
168. #432D4semidirect
835. C22#3234semidirect

Maximal subgroups

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

subgroupindex
C2×#32342
C22×#4322
#366242
C2×#28512
#332172
#330522
#298832
#298512
#248392
#247062
#246082
#246072
#245532
#245502
#219862
#218652
#218382