Finite Group Databasebeta

← #6508615

Subgroups — #6508615

Order 512.

3246 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#3091C212yesmaximal, complemented
3C2×#2485C211yesmaximal, characteristic, complemented
4#24099C214yesmaximal, complemented
5#24090C214yesmaximal, complemented
6#24067C212yesmaximal, complemented
7#24066C212yesmaximal, complemented
8#24040C214yesmaximal, complemented
9#24037C214yesmaximal, complemented
10#24006C211yesmaximal, characteristic, complemented
11#24005C211yesmaximal, characteristic, complemented
12#24003C211yesmaximal, characteristic, complemented
13#24002C211yesmaximal, characteristic, complemented
14#21763C212yesmaximal, complemented
15#21738C211yesmaximal, characteristic, complemented
16#3505—216no—
17C2×#553—22no—
18C2×#553C2212yes—
19C2×#552C2212yes—
20C2×#551—22no—
21C2×#548C2212yes—
22C2×#546C2212yes—
23C2×#539—21no—
24C2×#538—21no—
25C2×#534—21no—
26C2×#529C2212yes—
27C2×#525C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C2×#518—21no—
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic, complemented
33#3091—216no—
34C2×#484C2212yescomplemented
35C2×#481C2212yes—
36C2×#485C2214yescomplemented
37C2×#482C2214yescomplemented
38C2×#483C2212yescomplemented
39C2×#480C2212yes—
40C2×#427C2214yescomplemented
41C2×#416C2214yescomplemented
42C22×C22⋊C8C2212yescomplemented
43#2485—22no—
44#2485—22no—
45#2485C2214yes—
46#2485C2214yescomplemented
47C2×#397—21no—
48C2×#394—21no—
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#388—21no—
52C2×#387—21no—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic, complemented
56#2059C2214yescomplemented
57#2059C2214yescomplemented
58#2042C2214yescomplemented
59#2042C2214yescomplemented
60#2036C2214yescomplemented
61#2035C2214yescomplemented
62#2034C2214yescomplemented
63#2033C2214yescomplemented
64#1893C2214yescomplemented
65#1892C2214yescomplemented
66#1874C2212yes—
67#1874C2212yes—
68#1872C2212yescomplemented
69#1872C2212yescomplemented
70#1869C2214yes—
71#1869C2214yescomplemented
72#1865C2214yescomplemented
73#1864C2214yescomplemented
74#1863C2214yescomplemented
75#1862C2214yescomplemented
76#1853C2212yescomplemented
77#1853C2212yescomplemented
78#1852C2212yescomplemented
79#1852C2212yescomplemented
80#1825C2214yescomplemented
81#1817C2212yescomplemented
82#1788C2214yescomplemented
83#1787C2212yescomplemented
84#1787C2212yescomplemented
85#1786C2212yescomplemented
86#1786C2212yescomplemented
87#1779C2211yescharacteristic
88#1779C2211yescharacteristic
89C22×#41C2312yes—
90C23×Q8C2311yescharacteristic
91C23×D4—21no—
92C23×D4D411yescharacteristic
93C23×D4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C23×C8C2314yes—
97#553—232no—
98#553—28no—
99#553—28no—
100#552—28no—
101#552—28no—
102#551—232no—
103#548—28no—
104#548—28no—
105#546—28no—
106#546—28no—
107#539—216no—
108#538—216no—
109#534—216no—
110#529—28no—
111#529—28no—
112C2×#126—22no—
113C2×#126—22no—
114C2×#126—22no—
115C2×#125—22no—
116C2×#125C2312yes—
117C2×#124—22no—
118C2×#124C2312yes—
119#525—28no—
120#525D4116yes—
121C2×#123—22no—
122C2×#123—22no—
123C2×#123—22no—
124C2×#123—22no—
125C2×#123—22no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—28no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×#121—22no—
134C2×#121—22no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—28no—
138C2×#121—22no—
139C2×#121C2312yes—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#120—22no—
143C2×#120—22no—
144#518—216no—
145C2×C4×Q8C2312yes—
146C2×C4×D4—28no—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4—22no—
151C2×C4×D4—22no—
152C2×C4×D4D412yes—
153C2×C4×D4D412yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C2×#117—22no—
158C2×#117—22no—
159C2×#117—22no—
160C2×#117—28no—
161C2×#117C2314yes—
162C2×#117C2312yes—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4D411yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4—22no—
176C22×C22⋊C4—21no—
177C22×C22⋊C4—21no—
178C22×C22⋊C4—21no—
179C22×C22⋊C4—21no—
180C22×C22⋊C4D411yescharacteristic
181C22×C22⋊C4D411yescharacteristic
182C22×C42—21no—
183C22×C42C2311yescharacteristic
184#485—216no—
185#484—28no—
186#483—28no—
187#482—216no—
188#481—28no—
189#480—28no—
190#427—216no—
191C2×#107C2314yes—
192C2×#107C2314yes—
193C2×#106C2314yes—
194C2×#106C2314yes—
195#416—216no—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#103C2314yes—
200C2×#102C2314yes—
201C2×#102C2314yes—
202C2×#102C2314yes—
203C2×#102C2314yes—
204C2×C22⋊C8—28no—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2314yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212#397—24no—
213#397—24no—
214#394—24no—
215#394—24no—
216#389—22no—
217#389—22no—
218#389C2314yes—
219#389C2314yes—
220#388—24no—
221#388—24no—
222#387—24no—
223#387—24no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—22no—
229#380C2314yes—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234C2×#95—21no—
235C2×#95—21no—
236C2×#95—21no—
237C2×#95—21no—
238C2×#95—21no—
239#340C2314yes—
240#340C2314yes—
241#340C2314yes—
242#340C2314yes—
243#336C2314yes—
244#336C2314yes—
245C25—21no—
246C25C2×D411yescharacteristic
247C25C2×D411yescharacteristic
248C2×#41—24no—
249C2×#41—44no—
250C2×#41—44no—
251C2×#41C2×D418yes—
252C22×Q8—24no—
253C22×Q8—21no—
254C22×Q8—42no—
255C22×Q8—42no—
256C22×Q8C2412yes—
257C22×D4—28no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—24no—
265C22×D4—21no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4C2×D412yes—
272C22×D4C2×D412yes—
273C22×D4C2412yes—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D412yes—
295C23×C4C2×D418yes—
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C22×C8—28no—
301C22×C8—44no—
302C22×C8—44no—
303C22×C8C2414yes—
304C22×C8C2414yes—
305#126—216no—
306#126—216no—
307#126—216no—
308#125—216no—
309#125—24no—
310#125—24no—
311#124—216no—
312#124—24no—
313#124—24no—
314#123—216no—
315#123—216no—
316#123—216no—
317#123—216no—
318#123—216no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—216no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8C2×D418yes—
327C22⋊Q8C2×D418yes—
328#121—28no—
329#121—28no—
330#121—216no—
331#121—216no—
332#121—216no—
333#121—24no—
334#121—24no—
335#121—24no—
336#121—24no—
337#121C2×D418yes—
338#121C2×D418yes—
339#120—216no—
340#120—216no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×D4—216no—
344C4×D4—216no—
345C4×D4—216no—
346C4×D4—24no—
347C4×D4—28no—
348C4×D4—28no—
349C4×D4—216no—
350C4×D4—216no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4—24no—
355C4×D4—24no—
356#117—216no—
357#117—216no—
358#117—24no—
359#117—28no—
360#117—28no—
361#117—48no—
362#117C2×D418yes—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—82no—
387C2×C4⋊C4C2×D412yes—
388C2×C4⋊C4C2×D412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—216no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—82no—
419C2×C22⋊C4—82no—
420C2×C22⋊C4C2×D412yes—
421C2×C22⋊C4C2×D412yes—
422C2×C22⋊C4C2×D412yes—
423C2×C22⋊C4C2×D412yes—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—44no—
429C2×C42C2×D412yes—
430C2×C42C2412yes—
431#107—28no—
432#107—28no—
433#106—28no—
434#106—28no—
435#103—28no—
436#103—28no—
437#103—44no—
438#103—44no—
439#102—28no—
440#102—28no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445C22⋊C8—28no—
446C22⋊C8—42no—
447C22⋊C8—42no—
448C22⋊C8—42no—
449C22⋊C8—42no—
450#95—24no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—24no—
456#95—24no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—24no—
462C24—22no—
463C24—41no—
464C24—41no—
465C24—41no—
466C24—41no—
467C24—41no—
468C24—41no—
469C24—41no—
470C24—41no—
471C24—42no—
472C24—42no—
473C24—81no—
474C24—81no—
475C24—81no—
476C24—81no—
477C24#12014yes—
478C24#13514yes—
479C24C22×D412yes—
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482C24C22×D411yescharacteristic
483#41—416no—
484#41—88no—
485C2×Q8—24no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—81no—
490C2×Q8—81no—
491C2×Q8—88no—
492C2×Q8C22×D414yes—
493C2×D4—28no—
494C2×D4—24no—
495C2×D4—28no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—416no—
508C2×D4—432no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4—88no—
516C2×D4—82no—
517C2×D4—82no—
518C2×D4—82no—
519C2×D4—82no—
520C2×D4C22×D414yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—28no—
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—28no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—416no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4—41no—
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—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—88no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4#12014yes—
587C22×C4#12018yes—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C2511yescharacteristic
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—24no—
601C2×C8—24no—
602C2×C8—24no—
603C2×C8—24no—
604C2×C8—416no—
605C4⋊C4—24no—
606C4⋊C4—28no—
607C4⋊C4—24no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—28no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—48no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—84no—
627C4⋊C4C22×D414yes—
628C4⋊C4C22×D414yes—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—24no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—24no—
643C22⋊C4—48no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—82no—
647C22⋊C4—84no—
648C22⋊C4—82no—
649C42—28no—
650C42—24no—
651C42—28no—
652C42—22no—
653C42—22no—
654C42—48no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—28no—
678C23—28no—
679C23—24no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—48no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—82no—
692C23—82no—
693C23—82no—
694C23—82no—
695C23—82no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23—84no—
700C23—84no—
701C23—162no—
702C23—162no—
703C23—162no—
704C23—162no—
705C23C2×#12014yes—
706C23C2×#12012yes—
707C23C2×#13512yes—
708C23C2×#13512yes—
709C23C2×#13512yes—
710C23#57512yes—
711C23C23×D411yescharacteristic
712Q8—28no—
713Q8—44no—
714Q8—84no—
715D4—28no—
716D4—48no—
717D4—48no—
718D4—416no—
719D4—416no—
720D4—44no—
721D4—88no—
722D4—88no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—82no—
771C2×C4—82no—
772C2×C4—88no—
773C2×C4—82no—
774C2×C4—82no—
775C2×C4—88no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4C2×#12014yes—
783C2×C4C2×#12012yes—
784C2×C4C23×D412yes—
785C2×C4#58512yes—
786C2×C4#58512yes—
787C8—44no—
788C8—44no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—24no—
800C22—22no—
801C22—22no—
802C22—24no—
803C22—24no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—88no—
820C22—88no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—168no—
826C22#300214yes—
827C22C22×#12011yescharacteristic
828C22#348511yescharacteristic
829C22#348511yescharacteristic
830C22C22×#13511yescharacteristic
831C22C2×#57511yescharacteristic
832C22#358511yescharacteristic
833C22#358611yescharacteristic
834C4—22no—
835C4—24no—
836C4—41no—
837C4—41no—
838C4—44no—
839C4—42no—
840C4—44no—
841C4—42no—
842C4—44no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4#348514yes—
848C2—24no—
849C2—42no—
850C2—44no—
851C2—42no—
852C2—84no—
853C2#3544611yescharacteristic
854C2C2×#300211yescharacteristic
855C2#6037111yescharacteristic
856C2#6169611yescharacteristic
857C2#6169911yescharacteristic
858C2#6171011yescharacteristic
859C2#6171211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3091C2semidirect
3. C2×#2485C2semidirect
4. #24099C2semidirect
5. #24090C2semidirect
6. #24067C2semidirect
7. #24066C2semidirect
8. #24040C2semidirect
9. #24037C2semidirect
10. #24006C2semidirect
11. #24005C2semidirect
12. #24003C2semidirect
13. #24002C2semidirect
14. #21763C2semidirect
15. #21738C2semidirect
32. C22×#117C22semidirect
34. C2×#484C22semidirect
36. C2×#485C22semidirect
37. C2×#482C22semidirect
38. C2×#483C22semidirect
40. C2×#427C22semidirect
41. C2×#416C22semidirect
42. C22×C22⋊C8C22semidirect
46. #2485C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
55. C2×#380C22semidirect
56. #2059C22semidirect
57. #2059C22semidirect
58. #2042C22semidirect
59. #2042C22semidirect
60. #2036C22semidirect
61. #2035C22semidirect
62. #2034C22semidirect
63. #2033C22semidirect
64. #1893C22semidirect
65. #1892C22semidirect
68. #1872C22semidirect
69. #1872C22semidirect
71. #1869C22semidirect
72. #1865C22semidirect
73. #1864C22semidirect
74. #1863C22semidirect
75. #1862C22semidirect
76. #1853C22semidirect
77. #1853C22semidirect
78. #1852C22semidirect
79. #1852C22semidirect
80. #1825C22semidirect
81. #1817C22semidirect
82. #1788C22semidirect
83. #1787C22semidirect
84. #1787C22semidirect
85. #1786C22semidirect
86. #1786C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#30912
C2×#24852
#240992
#240902
#240672
#240662
#240402
#240372
#240062
#240052
#240032
#240022
#217632
#217382