Finite Group Databasebeta

← #6766315

Subgroups — #6766315

Order 512.

1765 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36187C211yesmaximal, characteristic, complemented
2#36150C211yesmaximal, characteristic, complemented
3#33042C211yesmaximal, characteristic, complemented
4#32119C214yesmaximal, complemented
5#31391C214yesmaximal, complemented
6#30203C211yesmaximal, characteristic, complemented
7#29806C211yesmaximal, characteristic, complemented
8#29218C211yesmaximal, characteristic, complemented
9#28615C211yesmaximal, characteristic, complemented
10#27890C211yesmaximal, characteristic, complemented
11#27875C211yesmaximal, characteristic, complemented
12#27427C214yesmaximal, complemented
13#26729C214yesmaximal, complemented
14#25905C211yesmaximal, characteristic, complemented
15#25599C211yesmaximal, characteristic, complemented
16#22219C211yesmaximal, characteristic, complemented
17#21835C211yesmaximal, characteristic, complemented
18#21401C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#555—21no—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#493C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28#2868C2211yescharacteristic
29#2858C2211yescharacteristic
30#2857C2211yescharacteristic
31#2856C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2563—21no—
35#2540—21no—
36#2537—21no—
37#2537C2212yes—
38#2500—21no—
39#2500—21no—
40#2491—21no—
41#2491—21no—
42#2491C2212yes—
43#2491C2212yes—
44#2490C2212yes—
45#2454C2212yes—
46#2448—21no—
47#2427—21no—
48#2426—21no—
49#2426—21no—
50#2414C2212yes—
51#2407—21no—
52#2367—21no—
53#2363C2212yes—
54#2354—21no—
55#2354C2212yes—
56#2341—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2100C2214yes—
63#2077C2214yes—
64#2071C2214yes—
65#2054C2214yes—
66#2054C2214yes—
67#2034C2214yes—
68#2025C2214yes—
69#2023C2214yes—
70#1999C2214yes—
71#1999C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1989C2214yes—
79#1987C2214yes—
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1934C2214yes—
85#1926C2214yes—
86#1926C2214yes—
87#1923C2212yes—
88#1920C2214yes—
89#1916C2212yes—
90#1893C2214yes—
91#1893C2214yes—
92#1879C2214yes—
93#1879C2214yes—
94#1875C2214yes—
95#1869C2212yes—
96#1864C2214yes—
97#1850C2212yes—
98#1844C2211yescharacteristic
99#1834C2211yescharacteristic
100#1834C2211yescharacteristic
101#1825C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×#102C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×#41—21no—
108C22×D8C2314yes—
109C23×C8C2312yes—
110#555—48no—
111#533—24no—
112#533—42no—
113#532—24no—
114#532—42no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2312yes—
120C2×#127C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#125C2312yes—
123C2×#124—22no—
124C2×#124—22no—
125C2×#124—21no—
126C2×#124—21no—
127C2×#124—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×#121—22no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121C2312yes—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4D411yescharacteristic
150C2×C4×D4D411yescharacteristic
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2311yescharacteristic
154C2×#117—21no—
155C2×#117—21no—
156C2×#117—22no—
157C2×#117C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#493—42no—
161#486—24no—
162#486—42no—
163#431—42no—
164C2×#106C2314yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C4×C8—42no—
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182#399—22no—
183#397—22no—
184#396—22no—
185#394—22no—
186#394—22no—
187#394—22no—
188#394—22no—
189#394—22no—
190#394—22no—
191#393—22no—
192#393—22no—
193#392—22no—
194#391—21no—
195#391—21no—
196#390—22no—
197#390—22no—
198#390—22no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#390C2312yes—
213#390C2312yes—
214#390C2312yes—
215#389—21no—
216#389—21no—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#386—22no—
227#385—22no—
228#384—21no—
229#384—21no—
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#384C2312yes—
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#382—21no—
236#382—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—22no—
241#380—22no—
242#380—22no—
243#380C2312yes—
244#380C2312yes—
245#380C2312yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4D411yescharacteristic
250C4×C4⋊C4D411yescharacteristic
251C4×C4⋊C4C2312yes—
252C4×C4⋊C4C2312yes—
253C4×C4⋊C4C2312yes—
254C4×C4⋊C4C2311yescharacteristic
255C4×C22⋊C4—22no—
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4C2311yescharacteristic
261C4×C22⋊C4C2311yescharacteristic
262C43C2311yescharacteristic
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C2×#41—44no—
277C2×#41—44no—
278C2×#41—82no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C2×D411yescharacteristic
291C22×D4C2412yes—
292C22×D4C2412yes—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C2×D8—44no—
302C2×D8—44no—
303C2×D8—44no—
304C22×C8—42no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—44no—
315C4⋊Q8—44no—
316C4⋊Q8—82no—
317C4⋊Q8#4114yes—
318#127—22no—
319#127—22no—
320#127—22no—
321#127—22no—
322#125—24no—
323#125—42no—
324#124—44no—
325#124—48no—
326#124—48no—
327#124—44no—
328#124—82no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—82no—
332#121—24no—
333#121—44no—
334#121—42no—
335#121—44no—
336#121—44no—
337#121—48no—
338#121—44no—
339#121—44no—
340#121—44no—
341#121—82no—
342#121—82no—
343#121—82no—
344#121—82no—
345C4×Q8—44no—
346C4×Q8—44no—
347C4×Q8—82no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—44no—
352C4×D4—42no—
353C4×D4—44no—
354C4×D4—42no—
355C4×D4—44no—
356C4×D4—44no—
357#117—24no—
358#117—42no—
359#117—48no—
360#117—44no—
361#117—44no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C22⋊C4—22no—
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—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
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×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437#106—44no—
438C4⋊C8—42no—
439C4⋊C8—42no—
440#102—28no—
441#102—44no—
442#102—44no—
443#102—44no—
444#102—44no—
445#102—44no—
446C22⋊C8—42no—
447C22⋊C8—42no—
448C22⋊C8—42no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8—42no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468C24—22no—
469C24—22no—
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472#41—816no—
473C2×Q8—24no—
474C2×Q8—44no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—82no—
481C2×Q8—82no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—41no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—82no—
511C2×D4—82no—
512C2×D4—82no—
513C2×D4—82no—
514C2×D4—82no—
515C2×D4—82no—
516C2×D4—82no—
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—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
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—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—82no—
548C22×C4AGL(1,ℤ/8)14yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C2511yescharacteristic
562D8—88no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—48no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—41no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4C2×#4114yes—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—22no—
644C42—22no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42—82no—
649C42#13514yes—
650C42C2×#4112yes—
651C42H(5,𝔽2)12yes—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23C2×AGL(1,ℤ/8)12yes—
680C23C23×D411yescharacteristic
681Q8—48no—
682Q8—84no—
683Q8—164no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—44no—
689D4—88no—
690D4—84no—
691D4—84no—
692D4—84no—
693D4—84no—
694D4—164no—
695D4—164no—
696D4—164no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—28no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—24no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—88no—
751C2×C4—88no—
752C2×C4#54612yes—
753C2×C4#54612yes—
754C2×C4C2×#13512yes—
755C2×C4C2×#13512yes—
756C2×C4C2×#13512yes—
757C2×C4C2×AGL(1,ℤ/8)12yes—
758C2×C4C2×AGL(1,ℤ/8)12yes—
759C2×C4#57612yes—
760C2×C4#57712yes—
761C2×C4C22×#4111yescharacteristic
762C2×C4C2×H(5,𝔽2)11yescharacteristic
763C2×C4#58512yes—
764C2×C4#58512yes—
765C8—42no—
766C8—42no—
767C8—42no—
768C8—42no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22#344911yescharacteristic
798C22C2×#54611yescharacteristic
799C22#350011yescharacteristic
800C22C22×#13511yescharacteristic
801C22C22×AGL(1,ℤ/8)11yescharacteristic
802C22C2×#57611yescharacteristic
803C22C2×#57711yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—44no—
813C4—41no—
814C4—41no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4#330514yes—
821C4#330614yes—
822C4#352412yes—
823C4#354012yes—
824C2—42no—
825C2—81no—
826C2—162no—
827C2—162no—
828C2#3809511yescharacteristic
829C2#6094611yescharacteristic
830C2#6100611yescharacteristic
831C2C2×#330511yescharacteristic
832C2C2×#330611yescharacteristic
833C2#6253211yescharacteristic
834C2#6253511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36187C2semidirect
2. #36150C2semidirect
3. #33042C2semidirect
4. #32119C2semidirect
5. #31391C2semidirect
6. #30203C2semidirect
7. #29806C2semidirect
8. #29218C2semidirect
9. #28615C2semidirect
10. #27890C2semidirect
11. #27875C2semidirect
12. #27427C2semidirect
13. #26729C2semidirect
14. #25905C2semidirect
15. #25599C2semidirect
16. #22219C2semidirect
17. #21835C2semidirect
18. #21401C2semidirect
19. #21101C2semidirect

Maximal subgroups

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

subgroupindex
#361872
#361502
#330422
#321192
#313912
#302032
#298062
#292182
#286152
#278902
#278752
#274272
#267292
#259052
#255992
#222192
#218352
#214012
#211012