Finite Group Databasebeta

← #6798119

Subgroups — #6798119

Order 512.

1770 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36180C211yesmaximal, characteristic, complemented
2#36150C211yesmaximal, characteristic
3#33230C211yesmaximal, characteristic, complemented
4#30657C214yesmaximal, complemented
5#30655C214yesmaximal, complemented
6#29845C211yesmaximal, characteristic, complemented
7#29843C211yesmaximal, characteristic, complemented
8#29206C211yesmaximal, characteristic, complemented
9#28750C211yesmaximal, characteristic, complemented
10#27906C211yesmaximal, characteristic, complemented
11#27905C211yesmaximal, characteristic, complemented
12#26544C214yesmaximal, complemented
13#26242C214yesmaximal, complemented
14#25674C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#21860C211yesmaximal, characteristic, complemented
17#21859C211yesmaximal, characteristic, complemented
18#21726C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#554—21no—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#500C2211yescharacteristic
24C2×#489C2214yes—
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#481C2214yes—
28C2×#483C2214yes—
29C2×#431C2211yescharacteristic
30C2×#431C2211yescharacteristic
31#2868C2211yescharacteristic
32#2858C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2856C2211yescharacteristic
37#2567—21no—
38#2552—21no—
39#2552C2212yes—
40#2540C2212yes—
41#2502—21no—
42#2502—21no—
43#2490—21no—
44#2454—21no—
45#2448—21no—
46#2440—21no—
47#2440—21no—
48#2440C2212yes—
49#2440C2212yes—
50#2427C2212yes—
51#2426—21no—
52#2426C2212yes—
53#2414—21no—
54#2407—21no—
55#2367C2212yes—
56#2363—21no—
57D4×C4⋊C4—21no—
58D4×C4⋊C4C2212yes—
59#2341—21no—
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C42×D4C2211yescharacteristic
65#2096C2214yes—
66#2094C2214yes—
67#2066C2214yes—
68#2065C2214yes—
69#2058C2214yes—
70#2042C2214yes—
71#2036C2214yes—
72#2035C2214yes—
73#2034C2214yes—
74#2033C2214yes—
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1983C2214yes—
80#1959C2214yes—
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1956C2211yescharacteristic
87#1955C2212yes—
88#1948C2214yes—
89#1943C2214yes—
90#1940C2212yes—
91#1924C2212yes—
92#1924C2212yes—
93#1874C2214yes—
94#1872C2214yes—
95#1863C2214yes—
96#1862C2214yes—
97#1844C2211yescharacteristic
98#1844C2211yescharacteristic
99#1844C2211yescharacteristic
100#1803C2214yes—
101#1802C2214yes—
102#1776C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41—21no—
108#554—48no—
109#533—24no—
110#533—42no—
111#532—24no—
112#532—42no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2312yes—
119C2×#127C2311yescharacteristic
120C2×#125—22no—
121C2×#125—21no—
122C2×#124—21no—
123C2×#124C2312yes—
124C2×#124C2312yes—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8C2312yes—
141C2×C4×D4—22no—
142C2×C4×D4—21no—
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4C2312yes—
146C2×C4×D4C2311yescharacteristic
147C2×#117—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#500—24no—
157#489—48no—
158#487—42no—
159#486—42no—
160#483—48no—
161#481—48no—
162#431—42no—
163#431—42no—
164C2×#107C2314yes—
165C2×#106C2314yes—
166C2×#106C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×#97C2312yes—
184C2×#97C2312yes—
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2311yescharacteristic
189#399—22no—
190#398—22no—
191#398—22no—
192#398—22no—
193#398—22no—
194#397—22no—
195#396—22no—
196#395—22no—
197#395—22no—
198#394—22no—
199#394—22no—
200#392—22no—
201#391—21no—
202#391—21no—
203#391—21no—
204#391—21no—
205#391C2312yes—
206#390—22no—
207#390—22no—
208#390—22no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#389—22no—
217#389—22no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389C2312yes—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#388—22no—
229#388—22no—
230#388—22no—
231#386—22no—
232#385—22no—
233#385—22no—
234#385—22no—
235#385—22no—
236#385—22no—
237#384—21no—
238#384—21no—
239#384—21no—
240#384—21no—
241#384—21no—
242#384—21no—
243#384C2311yescharacteristic
244#384C2311yescharacteristic
245#384C2312yes—
246#384C2312yes—
247#384C2311yescharacteristic
248#384C2311yescharacteristic
249#384C2312yes—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380—22no—
255#380C2312yes—
256#380C2312yes—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2311yescharacteristic
264C4×C22⋊C4—22no—
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4C2311yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271C43C2311yescharacteristic
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279C2×#41—44no—
280C2×#41—44no—
281C2×#41—82no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8—22no—
285C22×Q8C2412yes—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C2×D411yescharacteristic
291C22×D4C2412yes—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8—44no—
311C4⋊Q8—44no—
312C4⋊Q8—82no—
313C4⋊Q8#4114yes—
314#127—22no—
315#127—22no—
316#125—44no—
317#125—48no—
318#124—28no—
319#124—44no—
320#124—44no—
321C22⋊Q8—24no—
322C22⋊Q8—48no—
323C22⋊Q8—48no—
324C22⋊Q8—42no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329#121—24no—
330#121—42no—
331#121—44no—
332#121—44no—
333#121—44no—
334#121—82no—
335C4×Q8—24no—
336C4×Q8—42no—
337C4×Q8—44no—
338C4×Q8—44no—
339C4×Q8—82no—
340C4×D4—24no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—42no—
345C4×D4—44no—
346C4×D4—48no—
347#117—44no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—82no—
381C2×C4⋊C4—82no—
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—28no—
431#106—28no—
432#106—44no—
433#106—44no—
434C4⋊C8—24no—
435C4⋊C8—42no—
436C4⋊C8—42no—
437#103—28no—
438#103—44no—
439#103—44no—
440#103—44no—
441#102—28no—
442#102—44no—
443#102—44no—
444#102—44no—
445C22⋊C8—24no—
446C22⋊C8—24no—
447C22⋊C8—42no—
448C22⋊C8—42no—
449#97—24no—
450#97—24no—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8—22no—
454C4×C8—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471C24—22no—
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474#41—816no—
475C2×Q8—24no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—44no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—82no—
487C2×Q8—82no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—22no—
494C2×D4—24no—
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—82no—
505C2×D4—82no—
506C2×D4—82no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
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—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4—82no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4AGL(1,ℤ/8)14yes—
542C22×C4#13714yes—
543C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
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×C8H(5,𝔽2)14yes—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4—82no—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C4⋊C4C2×#4114yes—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
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—82no—
622C22⋊C4—82no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—44no—
640C42—44no—
641C42—82no—
642C42C2×#4112yes—
643C42H(5,𝔽2)12yes—
644C422−1+414yes—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23C2×AGL(1,ℤ/8)12yes—
665C23C2×#13712yes—
666C23C23×D411yescharacteristic
667Q8—48no—
668Q8—44no—
669Q8—44no—
670Q8—84no—
671Q8—164no—
672D4—28no—
673D4—44no—
674D4—44no—
675D4—88no—
676D4—84no—
677D4—84no—
678D4—164no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—24no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—88no—
735C2×C4—164no—
736C2×C4—164no—
737C2×C4#53612yes—
738C2×C4#53612yes—
739C2×C4#54612yes—
740C2×C4#54612yes—
741C2×C4C2×AGL(1,ℤ/8)12yes—
742C2×C4C2×AGL(1,ℤ/8)12yes—
743C2×C4C2×#13712yes—
744C2×C4C2×#13712yes—
745C2×C4#57712yes—
746C2×C4#57712yes—
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×H(5,𝔽2)12yes—
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×2−1+412yes—
751C8—24no—
752C8—42no—
753C8—42no—
754C8—42no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22C2×#53611yescharacteristic
777C22C2×#54611yescharacteristic
778C22#349811yescharacteristic
779C22C22×AGL(1,ℤ/8)11yescharacteristic
780C22C22×#13711yescharacteristic
781C22C2×#57711yescharacteristic
782C22C2×#57711yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—44no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#330614yes—
801C4#331614yes—
802C4#352212yes—
803C4#354812yes—
804C2—42no—
805C2—42no—
806C2—162no—
807C2#3895211yescharacteristic
808C2#6086011yescharacteristic
809C2#6088111yescharacteristic
810C2C2×#330611yescharacteristic
811C2C2×#331611yescharacteristic
812C2#6242111yescharacteristic
813C2#6242211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36150C2
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. #36180C2semidirect
3. #33230C2semidirect
4. #30657C2semidirect
5. #30655C2semidirect
6. #29845C2semidirect
7. #29843C2semidirect
8. #29206C2semidirect
9. #28750C2semidirect
10. #27906C2semidirect
11. #27905C2semidirect
12. #26544C2semidirect
13. #26242C2semidirect
14. #25674C2semidirect
15. #25673C2semidirect
16. #21860C2semidirect
17. #21859C2semidirect
18. #21726C2semidirect
19. #21265C2semidirect

Maximal subgroups

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

subgroupindex
#361802
#361502
#332302
#306572
#306552
#298452
#298432
#292062
#287502
#279062
#279052
#265442
#262422
#256742
#256732
#218602
#218592
#217262
#212652