Finite Group Databasebeta

← #6798567

Subgroups — #6798567

Order 512.

1774 conjugacy classes of subgroups.

The subgroup lattice has 819 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#31860C214yesmaximal, complemented
5#31858C214yesmaximal, complemented
6#29808C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29219C211yesmaximal, characteristic, complemented
9#28444C211yesmaximal, characteristic, complemented
10#27973C211yesmaximal, characteristic, complemented
11#27972C211yesmaximal, characteristic, complemented
12#25600C211yesmaximal, characteristic, complemented
13#25597C211yesmaximal, characteristic, complemented
14#25579C214yesmaximal, complemented
15#25336C214yesmaximal, complemented
16#21860C211yesmaximal, characteristic, complemented
17#21859C211yesmaximal, characteristic, complemented
18#21647C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#554C2212yes—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#494C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#489C2214yes—
26C2×#487C2211yescharacteristic
27C2×#464C2214yes—
28C2×#431C2211yescharacteristic
29C2×#431C2211yescharacteristic
30#2868C2211yescharacteristic
31#2858C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2567C2212yes—
37#2552—21no—
38#2552—21no—
39#2540C2212yes—
40#2502C2212yes—
41#2502C2212yes—
42#2490—21no—
43#2454—21no—
44#2448—21no—
45#2440—21no—
46#2440—21no—
47#2440—21no—
48#2440—21no—
49#2427C2212yes—
50#2426—21no—
51#2426C2212yes—
52#2414—21no—
53#2407—21no—
54#2367C2212yes—
55#2363—21no—
56D4×C4⋊C4—21no—
57D4×C4⋊C4—21no—
58#2341—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2099C2214yes—
65#2072C2214yes—
66#2071C2214yes—
67#2056C2214yes—
68#2055C2214yes—
69#2015C2214yes—
70#2001C2214yes—
71#2001C2214yes—
72#2000C2214yes—
73#2000C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1988C2214yes—
78#1959C2214yes—
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1955C2212yes—
87#1940C2212yes—
88#1935C2214yes—
89#1924C2212yes—
90#1924C2212yes—
91#1878C2214yes—
92#1877C2214yes—
93#1874C2214yes—
94#1874C2214yes—
95#1872C2214yes—
96#1872C2214yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1803C2214yes—
101#1802C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103#1763C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41—21no—
108C22×Q16C2314yes—
109C22×SD16C2314yes—
110#554—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×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#125—22no—
123C2×#125—21no—
124C2×#124—21no—
125C2×#124C2312yes—
126C2×#124C2312yes—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8C2312yes—
142C2×C4×Q8C2312yes—
143C2×C4×D4—22no—
144C2×C4×D4—21no—
145C2×C4×D4D411yescharacteristic
146C2×C4×D4D411yescharacteristic
147C2×C4×D4C2312yes—
148C2×C4×D4C2311yescharacteristic
149C2×#117—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#494—42no—
159#492—42no—
160#489—48no—
161#487—24no—
162#464—48no—
163#431—42no—
164#431—42no—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×#97C2312yes—
181C2×#97C2312yes—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186#399—22no—
187#398—22no—
188#398—22no—
189#398—22no—
190#398—22no—
191#397—22no—
192#396—22no—
193#395—22no—
194#395—22no—
195#394—22no—
196#394—22no—
197#392—22no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#390—22no—
204#390—22no—
205#390—22no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390C2312yes—
213#389—22no—
214#389—22no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389C2312yes—
225#388—22no—
226#388—22no—
227#388—22no—
228#386—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#384—21no—
235#384—21no—
236#384—21no—
237#384—21no—
238#384—21no—
239#384—21no—
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#384C2312yes—
243#384C2312yes—
244#384C2311yescharacteristic
245#384C2311yescharacteristic
246#384C2312yes—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—22no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4D411yescharacteristic
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2311yescharacteristic
261C4×C22⋊C4—22no—
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4C2311yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C43C2311yescharacteristic
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C2×#41—44no—
279C2×#41—44no—
280C2×#41—82no—
281C22×Q8—21no—
282C22×Q8—22no—
283C22×Q8C2412yes—
284C22×Q8C2412yes—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C2×D411yescharacteristic
290C22×D4C2412yes—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×Q16—44no—
301C2×Q16—44no—
302C2×Q16—44no—
303C2×SD16—44no—
304C2×SD16—44no—
305C2×SD16—44no—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—28no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—82no—
317C4⋊Q8—82no—
318C4⋊Q8#4114yes—
319#127—22no—
320#127—22no—
321#125—44no—
322#125—48no—
323#124—28no—
324#124—44no—
325#124—44no—
326C22⋊Q8—24no—
327C22⋊Q8—48no—
328C22⋊Q8—48no—
329C22⋊Q8—42no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334#121—24no—
335#121—42no—
336#121—44no—
337#121—44no—
338#121—44no—
339#121—82no—
340C4×Q8—24no—
341C4×Q8—28no—
342C4×Q8—42no—
343C4×Q8—44no—
344C4×Q8—82no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—42no—
350C4×D4—44no—
351C4×D4—48no—
352#117—44no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—82no—
385C2×C4⋊C4—82no—
386C2×C4⋊C4—82no—
387C2×C4⋊C4—82no—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C4⋊C8—24no—
436C4⋊C8—42no—
437C4⋊C8—42no—
438#103—28no—
439#103—44no—
440#103—44no—
441#103—44no—
442#103—44no—
443#102—44no—
444#102—44no—
445#102—44no—
446C22⋊C8—42no—
447C22⋊C8—42no—
448C22⋊C8—42no—
449C22⋊C8—42no—
450#97—24no—
451#97—42no—
452C4×C8—22no—
453C4×C8—22no—
454C4×C8—22no—
455C4×C8—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#95—22no—
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472C24—22no—
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475#41—816no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—24no—
484C2×Q8—24no—
485C2×Q8—44no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—82no—
489C2×Q8—82no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—24no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
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—
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—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
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—22no—
533C22×C4—22no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—82no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4#13714yes—
544C22×C4#13714yes—
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×C4C22×D411yescharacteristic
557C22×C4C2511yescharacteristic
558Q16—88no—
559SD16—88no—
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—22no—
570C2×C8—22no—
571C2×C8—22no—
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—42no—
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—42no—
600C4⋊C4—42no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4—82no—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C4⋊C4C2×#4114yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—22no—
642C42—44no—
643C42—44no—
644C42—82no—
645C42C2×#4112yes—
646C42H(5,𝔽2)14yes—
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—
667C23C2×#13712yes—
668C23C2×#13712yes—
669C23C23×D411yescharacteristic
670Q8—48no—
671Q8—44no—
672Q8—44no—
673Q8—44no—
674Q8—44no—
675Q8—164no—
676D4—28no—
677D4—44no—
678D4—44no—
679D4—88no—
680D4—84no—
681D4—84no—
682D4—164no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—24no—
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—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
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—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—88no—
739C2×C4—164no—
740C2×C4—164no—
741C2×C4#53512yes—
742C2×C4#53512yes—
743C2×C4#54612yes—
744C2×C4#54612yes—
745C2×C4C2×#13712yes—
746C2×C4C2×#13712yes—
747C2×C4C2×#13712yes—
748C2×C4C2×#13712yes—
749C2×C4#57612yes—
750C2×C4#57712yes—
751C2×C4C22×#4111yescharacteristic
752C2×C4C2×H(5,𝔽2)12yes—
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C2×C4#58512yes—
755C8—42no—
756C8—42no—
757C8—42no—
758C8—42no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22C2×#53511yescharacteristic
781C22C2×#54611yescharacteristic
782C22#350011yescharacteristic
783C22C22×#13711yescharacteristic
784C22C22×#13711yescharacteristic
785C22C2×#57611yescharacteristic
786C22C2×#57711yescharacteristic
787C4—22no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—44no—
797C4—41no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4#331414yes—
805C4#331614yes—
806C4#351712yes—
807C4#354612yes—
808C2—42no—
809C2—42no—
810C2—162no—
811C2#3895611yescharacteristic
812C2#6080011yescharacteristic
813C2#6082211yescharacteristic
814C2C2×#331411yescharacteristic
815C2C2×#331611yescharacteristic
816C2#6253711yescharacteristic
817C2#6254211yescharacteristic
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. #31860C2semidirect
5. #31858C2semidirect
6. #29808C2semidirect
7. #29807C2semidirect
8. #29219C2semidirect
9. #28444C2semidirect
10. #27973C2semidirect
11. #27972C2semidirect
12. #25600C2semidirect
13. #25597C2semidirect
14. #25579C2semidirect
15. #25336C2semidirect
16. #21860C2semidirect
17. #21859C2semidirect
18. #21647C2semidirect
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
#318602
#318582
#298082
#298072
#292192
#284442
#279732
#279722
#256002
#255972
#255792
#253362
#218602
#218592
#216472
#212652