Finite Group Databasebeta

← #6452015

Subgroups — #6452015

Order 512.

2980 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3006C211yesmaximal, characteristic
2C2×#2924C211yesmaximal, characteristic, complemented
3#35262C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic, complemented
5#24519C214yesmaximal, complemented
6#24513C214yesmaximal, complemented
7#24509C212yesmaximal, complemented
8#24506C212yesmaximal, complemented
9#24503C212yesmaximal, complemented
10#24500C212yesmaximal, complemented
11#23616C212yesmaximal, complemented
12#23544C212yesmaximal, complemented
13#21235C212yesmaximal, complemented
14#21087C212yesmaximal, complemented
15C2×#1874C211yesmaximal, characteristic, complemented
16#20844C211yesmaximal, characteristic, complemented
17#20597C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C22×AGL(1,ℤ/8)C2212yes—
20C22×#121C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23#3006—28no—
24C2×#449C2214yes—
25C2×#448C2212yes—
26C2×#447C2212yes—
27#2924—28no—
28C2×#433C2214yescomplemented
29C2×#432C2212yescomplemented
30C2×#431C2212yescomplemented
31C2×#428C2212yescomplemented
32C2×#424C2212yescomplemented
33C2×#417C2212yes—
34C2×#416C2212yes—
35C2×#416C2212yes—
36C22×#102C2212yescomplemented
37C2×#407C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C2×#405C2212yescomplemented
40#2854C2212yes—
41#2854C2212yes—
42#2624C2212yescomplemented
43#2624C2212yescomplemented
44#2504—21no—
45#2501—21no—
46#2500—21no—
47#2500—21no—
48#2482—22no—
49#2405—22no—
50#2317C2211yescharacteristic, complemented
51#2317C2211yescharacteristic, complemented
52#2311—22no—
53#2311—21no—
54#2311—21no—
55#2311C2212yes—
56#2311C2212yes—
57#2311C2214yescomplemented
58#2309C2211yescharacteristic, complemented
59#2309C2211yescharacteristic, complemented
60C2×#391C2212yescomplemented
61C2×#390C2212yescomplemented
62C2×#386—22no—
63#2280C2211yescharacteristic
64C2×#380—21no—
65C2×#380—21no—
66#2068C2214yescomplemented
67#2067C2214yescomplemented
68#2066C2214yescomplemented
69#2065C2214yescomplemented
70#2055C2214yescomplemented
71#2055C2214yescomplemented
72#2054C2214yescomplemented
73#2054C2214yescomplemented
74#1973C2214yescomplemented
75#1972C2214yescomplemented
76#1970C2214yescomplemented
77#1968C2214yescomplemented
78#1936C2214yescomplemented
79#1935C2214yescomplemented
80#1934C2214yescomplemented
81#1933C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1874C2214yescomplemented
85#1853C2212yescomplemented
86#1853C2212yescomplemented
87#1852C2212yescomplemented
88#1852C2212yescomplemented
89#1788C2212yescomplemented
90#1788C2212yescomplemented
91#1787C2211yescharacteristic, complemented
92#1787C2211yescharacteristic, complemented
93#1786C2211yescharacteristic, complemented
94#1786C2211yescharacteristic, complemented
95#1736C2212yescomplemented
96C2×#340C2212yescomplemented
97C22×#41—28no—
98C22×#41—21no—
99C22×#41—21no—
100C22×#41—24no—
101C22×#41—24no—
102C22×#41—44no—
103C22×#41C2312yes—
104C22×#41C2312yes—
105C23×Q8C2311yescharacteristic
106C23×D4—21no—
107C23×D4—21no—
108C23×D4C2311yescharacteristic
109C23×D4C2311yescharacteristic
110C24×C4—21no—
111C24×C4—21no—
112C24×C4C2311yescharacteristic
113C2×AGL(1,ℤ/8)—28no—
114C2×AGL(1,ℤ/8)—28no—
115C2×AGL(1,ℤ/8)—44no—
116C22×SD16C2314yes—
117C22×D8C2314yes—
118C22×M16C2312yes—
119C23×C8C2312yes—
120C2×#123—22no—
121C2×#123—22no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—24no—
125C2×#121—24no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#117—24no—
129C2×#117—24no—
130C2×#117D412yes—
131C2×#117D411yescharacteristic
132C2×#117D411yescharacteristic
133C2×#117C2311yescharacteristic
134C2×#117C2311yescharacteristic
135C2×#117C2311yescharacteristic
136C2×#117C2311yescharacteristic
137C2×#117C2312yes—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—44no—
142C22×C4⋊C4D411yescharacteristic
143C22×C4⋊C4D411yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—22no—
150C22×C22⋊C4—22no—
151C22×C22⋊C4D412yes—
152C22×C42C2312yes—
153#449—216no—
154#448—28no—
155#447—28no—
156#433—216no—
157#432—28no—
158#431—28no—
159#428—44no—
160C2×#107C2314yes—
161C2×#106C2314yes—
162#424—28no—
163C2×C4⋊C8C2314yes—
164C2×C4⋊C8C2314yes—
165#417—28no—
166#416—28no—
167#416—44no—
168C2×#103C2312yes—
169C2×#103C2312yes—
170C2×#103C2314yes—
171C2×#103C2312yes—
172C2×#103C2312yes—
173C2×#102—44no—
174C2×#102C2312yes—
175C2×#102C2312yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181#407D418yes—
182C2×C22⋊C8—24no—
183C2×C22⋊C8C2311yescharacteristic
184C2×C22⋊C8C2311yescharacteristic
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188#405—28no—
189C2×#97C2314yes—
190C2×C4×C8C2314yes—
191#399—22no—
192#399—22no—
193#397—22no—
194#397—22no—
195#394—22no—
196#394—22no—
197#394—22no—
198#394—22no—
199#391—22no—
200#391—22no—
201#391C2314yes—
202#391C2314yes—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—22no—
208#390—22no—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#390C2312yes—
213#390C2314yes—
214#390C2314yes—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#386—22no—
224#386—22no—
225#386—24no—
226#386—24no—
227#386—24no—
228#386—24no—
229#385—22no—
230#385—22no—
231#384—21no—
232#384—21no—
233#382—21no—
234#382—21no—
235#381—21no—
236#380—22no—
237#380—22no—
238#380—22no—
239#380—22no—
240#380—24no—
241#380—24no—
242#380C2311yescharacteristic
243#380C2311yescharacteristic
244#380C2311yescharacteristic
245#380C2311yescharacteristic
246#379—21no—
247#379—22no—
248#379—22no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251C2×#95—22no—
252C2×#95—22no—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257C25—21no—
258C25—21no—
259C25C2×D411yescharacteristic
260C2×#41—28no—
261C2×#41—28no—
262C2×#41—24no—
263C2×#41—24no—
264C2×#41—24no—
265C2×#41—24no—
266C2×#41—24no—
267C2×#41—24no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—24no—
271C2×#41—42no—
272C2×#41—42no—
273C2×#41—432no—
274C2×#41—432no—
275C2×#41—44no—
276C2×#41—44no—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41#4118yes—
280C22×Q8—24no—
281C22×Q8—21no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—42no—
285C22×Q8C2412yes—
286C22×D4—28no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—24no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—24no—
298C22×D4—22no—
299C22×D4—24no—
300C22×D4—42no—
301C22×D4—44no—
302C22×D4—44no—
303C22×D4—44no—
304C22×D4—82no—
305C22×D4—82no—
306C22×D4C2412yes—
307C22×D4C2412yes—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—28no—
311C23×C4—21no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—21no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—44no—
319C23×C4—44no—
320C23×C4—44no—
321C23×C4—82no—
322C23×C4—82no—
323C23×C4C2×D412yes—
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D414yes—
328C23×C4C2×D412yes—
329C23×C4#4114yes—
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333AGL(1,ℤ/8)—432no—
334C2×SD16—28no—
335C2×SD16—28no—
336C2×SD16—44no—
337C2×D8—28no—
338C2×D8—28no—
339C2×D8—44no—
340C2×M16—24no—
341C2×M16—24no—
342C2×M16C2×D418yes—
343C22×C8—24no—
344C22×C8—24no—
345C22×C8—24no—
346C22×C8C2412yes—
347C22×C8C2412yes—
348C22×C8C2414yes—
349#123—84no—
350#123—84no—
351#121—24no—
352#121—24no—
353#121—24no—
354#121—24no—
355#121—44no—
356#121—44no—
357#117—28no—
358#117—24no—
359#117—24no—
360#117—22no—
361#117—22no—
362#117—24no—
363#117—24no—
364#117—22no—
365#117—22no—
366#117—24no—
367#117—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D412yes—
392C2×C4⋊C4C2×D412yes—
393C2×C4⋊C4C2414yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2411yescharacteristic
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C22⋊C4—28no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—84no—
422C2×C22⋊C4—84no—
423C2×C22⋊C4C2×D412yes—
424C2×C22⋊C4C2×D412yes—
425C2×C22⋊C4C2×D412yes—
426C2×C22⋊C4C2×D412yes—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42C2×D412yes—
432C2×C42C2×D412yes—
433C2×C42C2412yes—
434C2×C42C2412yes—
435#107—44no—
436#106—44no—
437C4⋊C8—28no—
438C4⋊C8—28no—
439#103—24no—
440#103—24no—
441#103—28no—
442#103—42no—
443#103—42no—
444#102—24no—
445#102—24no—
446#102—28no—
447#102—44no—
448#102—44no—
449#102—42no—
450#102—42no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453C22⋊C8—24no—
454C22⋊C8C2×D418yes—
455C22⋊C8C2×D418yes—
456#97—28no—
457C4×C8—28no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—24no—
475C24—22no—
476C24—22no—
477C24—41no—
478C24—41no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—42no—
483C24—42no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24—81no—
489C24—81no—
490C24—81no—
491C24—81no—
492C24#12114yes—
493C24C22×D411yescharacteristic
494C24C22×D411yescharacteristic
495C24C22×D411yescharacteristic
496#41—216no—
497#41—216no—
498#41—48no—
499#41—48no—
500#41—48no—
501#41—48no—
502#41—432no—
503#41—432no—
504#41—48no—
505#41—48no—
506C2×Q8—24no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—48no—
513C2×Q8—48no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8C2×#4114yes—
517C2×D4—24no—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—42no—
532C2×D4—432no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—82no—
548C2×D4—82no—
549C2×D4—816no—
550C2×D4C2×#4114yes—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—216no—
558C22×C4—216no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—28no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—432no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4—816no—
599C22×C4#12114yes—
600C22×C4#12114yes—
601C22×C4#12114yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D412yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4114yes—
616C22×C4H(5,𝔽2)14yes—
617C22×C4C2511yescharacteristic
618SD16—416no—
619D8—416no—
620M16—216no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—48no—
630C2×C8C22×D418yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—24no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—82no—
650C4⋊C4—82no—
651C4⋊C4—82no—
652C4⋊C4—82no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—84no—
668C22⋊C4—84no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—24no—
678C42—24no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—42no—
684C42—42no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—28no—
696C23—21no—
697C23—21no—
698C23—28no—
699C23—21no—
700C23—21no—
701C23—24no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—48no—
708C23—48no—
709C23—48no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—162no—
731C23—162no—
732C23—162no—
733C23—162no—
734C23C2×#12112yes—
735C23C2×#12112yes—
736C23C2×#12112yes—
737C23#52512yes—
738C23#53512yes—
739C23#57612yes—
740C23#57712yes—
741C23C23×D411yescharacteristic
742Q8—24no—
743Q8—24no—
744Q8—48no—
745Q8—42no—
746Q8—42no—
747D4—24no—
748D4—24no—
749D4—48no—
750D4—416no—
751D4—416no—
752D4—42no—
753D4—44no—
754D4—42no—
755D4—44no—
756D4—88no—
757D4—88no—
758D4—84no—
759C2×C4—28no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—416no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—48no—
788C2×C4—416no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—84no—
808C2×C4—88no—
809C2×C4—88no—
810C2×C4—84no—
811C2×C4—88no—
812C2×C4C2×#12112yes—
813C2×C4C2×#12112yes—
814C2×C4C2×#12112yes—
815C2×C4#52512yes—
816C2×C4#53512yes—
817C2×C4#54618yes—
818C2×C4#55118yes—
819C2×C4C23×D411yescharacteristic
820C2×C4C22×#4112yes—
821C2×C4C22×#4111yescharacteristic
822C2×C4C2×H(5,𝔽2)12yes—
823C8—28no—
824C8—42no—
825C8—42no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—416no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—816no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—168no—
862C22#241114yes—
863C22#306214yes—
864C22C22×#12111yescharacteristic
865C22C2×#52511yescharacteristic
866C22C2×#53511yescharacteristic
867C22C2×#57611yescharacteristic
868C22C2×#57711yescharacteristic
869C22#358511yescharacteristic
870C22#358611yescharacteristic
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—44no—
878C4—82no—
879C4—81no—
880C4—84no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4#241114yes—
885C4C2×#54612yes—
886C4C2×#55112yes—
887C2—24no—
888C2—24no—
889C2—42no—
890C2—84no—
891C2—162no—
892C2C2×#241111yescharacteristic
893C2C2×#306211yescharacteristic
894C2#6045611yescharacteristic
895C2#6058411yescharacteristic
896C2#6058811yescharacteristic
897C2#6081111yescharacteristic
898C2#6081311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2924C2semidirect
3. #35262C2semidirect
4. C2×#2311C2semidirect
5. #24519C2semidirect
6. #24513C2semidirect
7. #24509C2semidirect
8. #24506C2semidirect
9. #24503C2semidirect
10. #24500C2semidirect
11. #23616C2semidirect
12. #23544C2semidirect
13. #21235C2semidirect
14. #21087C2semidirect
15. C2×#1874C2semidirect
16. #20844C2semidirect
17. #20597C2semidirect
28. C2×#433C22semidirect
29. C2×#432C22semidirect
30. C2×#431C22semidirect
31. C2×#428C22semidirect
32. C2×#424C22semidirect
36. C22×#102C22semidirect
39. C2×#405C22semidirect
42. #2624C22semidirect
43. #2624C22semidirect
50. #2317C22semidirect
51. #2317C22semidirect
57. #2311C22semidirect
58. #2309C22semidirect
59. #2309C22semidirect
60. C2×#391C22semidirect
61. C2×#390C22semidirect
66. #2068C22semidirect
67. #2067C22semidirect
68. #2066C22semidirect
69. #2065C22semidirect
70. #2055C22semidirect
71. #2055C22semidirect
72. #2054C22semidirect
73. #2054C22semidirect
74. #1973C22semidirect
75. #1972C22semidirect
76. #1970C22semidirect
77. #1968C22semidirect
78. #1936C22semidirect
79. #1935C22semidirect
80. #1934C22semidirect
81. #1933C22semidirect
84. #1874C22semidirect
85. #1853C22semidirect
86. #1853C22semidirect
87. #1852C22semidirect
88. #1852C22semidirect
89. #1788C22semidirect
90. #1788C22semidirect
91. #1787C22semidirect
92. #1787C22semidirect
93. #1786C22semidirect
94. #1786C22semidirect
95. #1736C22semidirect
96. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30062
C2×#29242
#352622
C2×#23112
#245192
#245132
#245092
#245062
#245032
#245002
#236162
#235442
#212352
#210872
C2×#18742
#208442
#205972