Finite Group Databasebeta

← #6614906

Subgroups — #6614906

Order 512.

1786 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36211C211yesmaximal, characteristic, complemented
2#36150C211yesmaximal, characteristic, complemented
3#33277C211yesmaximal, characteristic, complemented
4#33171C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#29179C211yesmaximal, characteristic, complemented
7#29072C214yesmaximal, complemented
8#28976C214yesmaximal, complemented
9#28615C211yesmaximal, characteristic, complemented
10#28552C214yesmaximal, complemented
11#27974C211yesmaximal, characteristic, complemented
12#27878C211yesmaximal, characteristic, complemented
13#25905C211yesmaximal, characteristic, complemented
14#25599C211yesmaximal, characteristic, complemented
15#23130C214yesmaximal, complemented
16C4×#486C211yesmaximal, characteristic, complemented
17#21401C211yesmaximal, characteristic, complemented
18#21318C211yesmaximal, characteristic, complemented
19C4×C8×D4C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#493C2211yescharacteristic
23C2×#486C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#466C2214yes—
26C2×C8×D4C2212yes—
27C22×C4×C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29#2859C2211yescharacteristic
30#2858C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2540—21no—
36#2535—21no—
37#2513—21no—
38#2513C2212yes—
39#2490—21no—
40#2490—21no—
41#2490C2212yes—
42#2454C2212yes—
43#2448—21no—
44#2427—21no—
45#2426—21no—
46#2426—21no—
47#2420—21no—
48#2420C2212yes—
49#2414—21no—
50#2414C2212yes—
51#2414C2212yes—
52#2407—21no—
53#2367—21no—
54#2363—21no—
55#2363C2212yes—
56#2363C2212yes—
57#2357—21no—
58#2341—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62#2285C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2087C2214yes—
65#2076C2214yes—
66#2073C2214yes—
67#2054C2214yes—
68#2025C2214yes—
69#1999C2214yes—
70#1991C2214yes—
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1970C2214yes—
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1934C2214yes—
83#1934C2214yes—
84#1934C2214yes—
85#1934C2214yes—
86#1921C2214yes—
87#1921C2214yes—
88#1893C2214yes—
89#1893C2214yes—
90#1879C2214yes—
91#1879C2214yes—
92#1875C2214yes—
93#1875C2214yes—
94#1845C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97C8×C4⋊C4C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99C4×#102C2214yes—
100C4×#102C2214yes—
101C8×C22⋊C4C2212yes—
102C8×C22⋊C4C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105#1735C2214yes—
106C42×C8C2211yescharacteristic
107C22×#41—21no—
108C22×D8C2314yes—
109C23×C8C2312yes—
110C23×C8C2312yes—
111#533—24no—
112#533—42no—
113#532—24no—
114#532—42no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×#127C2311yescharacteristic
118C2×#127C2311yescharacteristic
119C2×#125—21no—
120C2×#125C2312yes—
121C2×#124—21no—
122C2×#124—21no—
123C2×#124—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121C2312yes—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×#121C2312yes—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4D411yescharacteristic
145C2×C4×D4D411yescharacteristic
146C2×C4×D4C2312yes—
147C2×C4×D4C2312yes—
148C2×C4×D4C2311yescharacteristic
149C2×#117—21no—
150C2×#117C2312yes—
151C2×#117C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#493—42no—
155#486—24no—
156#486—42no—
157#466—216no—
158C8×D4—28no—
159C2×#107C2314yes—
160C2×C4⋊C8C2312yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×C4×C8—42no—
170C2×C4×C8—42no—
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2312yes—
176C2×C4×C8C2312yes—
177C2×C4×C8C2312yes—
178C2×C4×C8C2312yes—
179#399—22no—
180#397—22no—
181#397—22no—
182#397—22no—
183#397—22no—
184#396—22no—
185#394—22no—
186#394—22no—
187#394—22no—
188#394—22no—
189#392—22no—
190#392—22no—
191#391—21no—
192#391—21no—
193#390—22no—
194#390—22no—
195#390—22no—
196#390—22no—
197#390—22no—
198#390—21no—
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#390C2312yes—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#390C2312yes—
213#390C2312yes—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#385—22no—
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#382—21no—
238#382—21no—
239#382C2312yes—
240#381—22no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—22no—
246#380C2312yes—
247#380C2312yes—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2311yescharacteristic
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4C2311yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265C43C2311yescharacteristic
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—82no—
280C22×Q8—21no—
281C22×Q8—21no—
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—28no—
302C2×D8—44no—
303C2×D8—44no—
304C22×C8—24no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8—42no—
308C22×C8—42no—
309C22×C8#4118yescomplemented
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8#4114yes—
318#127—22no—
319#127—22no—
320#127—22no—
321#127—22no—
322#125—24no—
323#125—42no—
324#125—82no—
325#124—44no—
326#124—44no—
327#124—82no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C22⋊Q8—82no—
331#121—28no—
332#121—28no—
333#121—24no—
334#121—42no—
335#121—44no—
336#121—44no—
337#121—44no—
338#121—82no—
339#121—82no—
340#121—82no—
341#121—82no—
342#121—82no—
343C4×Q8—44no—
344C4×Q8—44no—
345C4×Q8—82no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—42no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—82no—
355#117—24no—
356#117—42no—
357#117—44no—
358#117—82no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433#107—28no—
434C4⋊C8—24no—
435#102—28no—
436#102—28no—
437#102—28no—
438#102—44no—
439#102—44no—
440#102—44no—
441C22⋊C8—24no—
442C22⋊C8—24no—
443C4×C8—24no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—22no—
448C4×C8—42no—
449C4×C8—42no—
450C4×C8—42no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467C24—22no—
468C24—22no—
469C24C22×D411yescharacteristic
470C24C22×D411yescharacteristic
471#41—816no—
472C2×Q8—24no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
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—82no—
507C2×D4—82no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4—82no—
511C2×D4—82no—
512C2×D4—82no—
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—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4#13514yes—
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C2×#4114yes—
557C22×C4C2511yescharacteristic
558D8—88no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—48no—
570C2×C8—48no—
571C2×C8C2×#4114yes—
572C2×C8C2×#4114yes—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4C2×#4114yes—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C22⋊C4—82no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—22no—
641C42—44no—
642C42—82no—
643C42—82no—
644C42—82no—
645C42#13514yes—
646C42C2×#4112yes—
647C42H(5,𝔽2)12yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23#53212yes—
675C23C2×#13512yes—
676C23C23×D411yescharacteristic
677Q8—48no—
678Q8—84no—
679D4—28no—
680D4—44no—
681D4—44no—
682D4—44no—
683D4—44no—
684D4—88no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689D4—164no—
690D4—164no—
691D4—164no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—24no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
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—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
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—88no—
745C2×C4—164no—
746C2×C4#53212yes—
747C2×C4#54612yes—
748C2×C4#54612yes—
749C2×C4C2×#13512yes—
750C2×C4C2×#13512yes—
751C2×C4C2×#13512yes—
752C2×C4C2×#13512yes—
753C2×C4C2×#13512yes—
754C2×C4#57612yes—
755C2×C4#57612yes—
756C2×C4C22×#4111yescharacteristic
757C2×C4C22×#4112yes—
758C2×C4C2×H(5,𝔽2)11yescharacteristic
759C2×C4#58512yes—
760C8—24no—
761C8—24no—
762C8—42no—
763C8—42no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22C2×#53211yescharacteristic
793C22C2×#54611yescharacteristic
794C22#350011yescharacteristic
795C22C22×#13511yescharacteristic
796C22C22×#13511yescharacteristic
797C22C2×#57611yescharacteristic
798C22C2×#57611yescharacteristic
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—44no—
808C4—41no—
809C4—41no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4#329714yes—
816C4#330514yes—
817C4#348012yes—
818C4#350512yes—
819C2—42no—
820C2—42no—
821C2—162no—
822C2—162no—
823C2#3639611yescharacteristic
824C2#6067311yescharacteristic
825C2#6071411yescharacteristic
826C2C2×#329711yescharacteristic
827C2C2×#330511yescharacteristic
828C2#6252711yescharacteristic
829C2#6252711yescharacteristic
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. #36211C2semidirect
2. #36150C2semidirect
3. #33277C2semidirect
4. #33171C2semidirect
5. #33042C2semidirect
6. #29179C2semidirect
7. #29072C2semidirect
8. #28976C2semidirect
9. #28615C2semidirect
10. #28552C2semidirect
11. #27974C2semidirect
12. #27878C2semidirect
13. #25905C2semidirect
14. #25599C2semidirect
15. #23130C2semidirect
16. C4×#486C2semidirect
17. #21401C2semidirect
18. #21318C2semidirect
19. C4×C8×D4C2semidirect
309. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
#362112
#361502
#332772
#331712
#330422
#291792
#290722
#289762
#286152
#285522
#279742
#278782
#259052
#255992
#231302
C4×#4862
#214012
#213182
C4×C8×D42