Finite Group Databasebeta

← #6765804

Subgroups — #6765804

Order 512.

1916 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic, complemented
2#36127C211yesmaximal, characteristic, complemented
3#33042C211yesmaximal, characteristic, complemented
4#31550C214yesmaximal, complemented
5#31382C214yesmaximal, complemented
6#30228C211yesmaximal, characteristic, complemented
7#29842C211yesmaximal, characteristic, complemented
8#29192C211yesmaximal, characteristic, complemented
9#28716C211yesmaximal, characteristic, complemented
10#27960C211yesmaximal, characteristic, complemented
11#27877C211yesmaximal, characteristic, complemented
12#27550C214yesmaximal, complemented
13#26656C214yesmaximal, complemented
14#25599C211yesmaximal, characteristic, complemented
15#25599C211yesmaximal, characteristic, complemented
16#22269C211yesmaximal, characteristic, complemented
17#21859C211yesmaximal, characteristic, complemented
18#21401C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#553—21no—
21C2×#547—21no—
22C2×#532C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C2×#493C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#431C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29#2868C2211yescharacteristic
30#2859C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2566—21no—
36#2547—21no—
37#2537—21no—
38#2537C2212yes—
39#2512—21no—
40#2512C2212yes—
41#2504—21no—
42#2500—21no—
43#2432—21no—
44#2432—21no—
45#2422—21no—
46#2422—21no—
47#2422—21no—
48#2422C2212yes—
49#2422C2212yes—
50#2422C2212yes—
51#2416—21no—
52#2416C2212yes—
53#2361—21no—
54#2361C2212yes—
55D4×C4⋊C4—21no—
56D4×C4⋊C4C2212yes—
57C4×#127C2211yescharacteristic
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2099C2214yes—
63#2099C2214yes—
64#2099C2214yes—
65#2075C2214yes—
66#2071C2214yes—
67#2067C2214yes—
68#2067C2214yes—
69#2033C2214yes—
70#1999C2214yes—
71#1999C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1934C2214yes—
83#1923C2212yes—
84#1918C2214yes—
85#1916C2212yes—
86#1893C2214yes—
87#1893C2214yes—
88#1879C2214yes—
89#1879C2214yes—
90#1879C2214yes—
91#1879C2214yes—
92#1874C2214yes—
93#1869C2212yes—
94#1862C2214yes—
95#1850C2212yes—
96#1845C2211yescharacteristic
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1823C2214yes—
100#1802C2214yes—
101#1802C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×#102C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×#41—21no—
108C22×#41—21no—
109C22×D8C2314yes—
110C23×C8C2312yes—
111#553—48no—
112#547—48no—
113#532—24no—
114#532—24no—
115#532—42no—
116#532—42no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#127C2311yescharacteristic
123C2×#126—22no—
124C2×#125—21no—
125C2×#124—21no—
126C2×#124—21no—
127C2×#123—22no—
128C2×#123—22no—
129C2×#123—22no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×#121—22no—
133C2×#121—22no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×C4×D4—22no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4D411yescharacteristic
152C2×C4×D4D411yescharacteristic
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×#117—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—22no—
162C22×C4⋊C4C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#493—24no—
166#486—42no—
167#486—42no—
168#431—42no—
169C2×#107C2314yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C4×C8—42no—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2312yes—
187#397—22no—
188#397—22no—
189#397—22no—
190#397—22no—
191#396—22no—
192#396—22no—
193#394—22no—
194#394—22no—
195#394—22no—
196#394—22no—
197#394—22no—
198#394—22no—
199#391—21no—
200#391—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#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#388—22no—
222#388—22no—
223#386—22no—
224#386—22no—
225#385—22no—
226#385—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#384—21no—
232#384—21no—
233#384—21no—
234#384—21no—
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#384C2312yes—
238#384C2312yes—
239#384C2312yes—
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#382—21no—
243#382—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—22no—
248#380—22no—
249#380C2312yes—
250#380C2312yes—
251#380C2312yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4D411yescharacteristic
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2311yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4C2311yescharacteristic
262C4×C22⋊C4C2311yescharacteristic
263C43C2311yescharacteristic
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—44no—
280C2×#41—44no—
281C2×#41—82no—
282C2×#41—82no—
283C22×Q8—21no—
284C22×Q8—21no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2×D411yescharacteristic
294C22×D4C2412yes—
295C22×D4C2412yes—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C2×D8—28no—
308C2×D8—44no—
309C2×D8—44no—
310C22×C8—42no—
311C22×C8—42no—
312C22×C8—42no—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—44no—
322C4⋊Q8—82no—
323#127—22no—
324#127—22no—
325#127—22no—
326#127#4114yes—
327#126—48no—
328#125—44no—
329#124—44no—
330#124—44no—
331#123—48no—
332#123—48no—
333#123—48no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336#121—24no—
337#121—24no—
338#121—44no—
339#121—42no—
340#121—42no—
341#121—44no—
342#121—44no—
343#121—44no—
344#121—48no—
345#121—48no—
346#121—44no—
347#121—44no—
348#121—44no—
349#121—82no—
350C4×D4—24no—
351C4×D4—24no—
352C4×D4—44no—
353C4×D4—42no—
354C4×D4—42no—
355C4×D4—42no—
356C4×D4—42no—
357C4×D4—44no—
358C4×D4—44no—
359C4×D4—44no—
360C4×D4—44no—
361C4×D4—48no—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—82no—
365C4×D4D818yescomplemented
366#117—44no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—48no—
391C2×C4⋊C4—82no—
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
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⋊C4—22no—
411C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444#107—44no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447#102—44no—
448#102—44no—
449#102—44no—
450#102—44no—
451#102—44no—
452#102—44no—
453C22⋊C8—42no—
454C22⋊C8—42no—
455C22⋊C8—42no—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—22no—
459C4×C8—22no—
460C4×C8—42no—
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#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473#95C2×D411yescharacteristic
474#95C2×D411yescharacteristic
475C24—22no—
476C24—22no—
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479#41—816no—
480#41—816no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—82no—
517C2×D4—82no—
518C2×D4—82no—
519C2×D4—82no—
520C2×D4C2×D814yes—
521C2×D4C2×#4114yes—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
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—22no—
545C22×C4—22no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4C2×D814yes—
562C22×C4C2×D814yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C2511yescharacteristic
576D8—88no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—48no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C4⋊C4—82no—
621C4⋊C4C2×D814yes—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C22⋊C4C2×D814yes—
646C22⋊C4C2×D814yes—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—22no—
659C42—22no—
660C42—44no—
661C42C2×D814yes—
662C42C2×#4112yes—
663C42H(5,𝔽2)12yes—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—24no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23C22×D812yes—
691C23C22×D812yes—
692C23C23×D411yescharacteristic
693Q8—84no—
694Q8—84no—
695D4—28no—
696D4—44no—
697D4—44no—
698D4—44no—
699D4—44no—
700D4—48no—
701D4—48no—
702D4—88no—
703D4—88no—
704D4—88no—
705D4—84no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—28no—
717C2×C4—28no—
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—21no—
727C2×C4—21no—
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—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
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—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—88no—
761C2×C4—88no—
762C2×C4—88no—
763C2×C4—164no—
764C2×C4—164no—
765C2×C4#54612yes—
766C2×C4#54612yes—
767C2×C4C22×D812yes—
768C2×C4C22×D812yes—
769C2×C4C22×D812yes—
770C2×C4C22×D812yes—
771C2×C4C22×D812yes—
772C2×C4#57512yes—
773C2×C4#57712yes—
774C2×C4#57712yes—
775C2×C4C22×#4111yescharacteristic
776C2×C4C2×H(5,𝔽2)11yescharacteristic
777C2×C4#58512yes—
778C2×C4#58512yes—
779C8—42no—
780C8—42no—
781C8—42no—
782C8—42no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22#344911yescharacteristic
812C22C2×#54611yescharacteristic
813C22#350011yescharacteristic
814C22C23×D811yescharacteristic
815C22C2×#57511yescharacteristic
816C22C2×#57711yescharacteristic
817C22C2×#57711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4#329414yes—
835C4#330714yes—
836C4#352112yes—
837C4#353912yes—
838C2—42no—
839C2—42no—
840C2—84no—
841C2—162no—
842C2#3809211yescharacteristic
843C2#6094011yescharacteristic
844C2#6101511yescharacteristic
845C2C2×#329411yescharacteristic
846C2C2×#330711yescharacteristic
847C2#6252911yescharacteristic
848C2#6254311yescharacteristic
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. #36182C2semidirect
2. #36127C2semidirect
3. #33042C2semidirect
4. #31550C2semidirect
5. #31382C2semidirect
6. #30228C2semidirect
7. #29842C2semidirect
8. #29192C2semidirect
9. #28716C2semidirect
10. #27960C2semidirect
11. #27877C2semidirect
12. #27550C2semidirect
13. #26656C2semidirect
14. #25599C2semidirect
15. #25599C2semidirect
16. #22269C2semidirect
17. #21859C2semidirect
18. #21401C2semidirect
19. #21101C2semidirect
365. C4×D4D8semidirect

Maximal subgroups

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

subgroupindex
#361822
#361272
#330422
#315502
#313822
#302282
#298422
#291922
#287162
#279602
#278772
#275502
#266562
#255992
#222692
#218592
#214012
#211012