Finite Group Databasebeta

← #6797228

Subgroups — #6797228

Order 512.

1882 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic, complemented
3#33286C211yesmaximal, characteristic, complemented
4#31818C214yesmaximal, complemented
5#31736C214yesmaximal, complemented
6#29842C211yesmaximal, characteristic, complemented
7#29806C211yesmaximal, characteristic, complemented
8#29179C211yesmaximal, characteristic, complemented
9#28615C211yesmaximal, characteristic, complemented
10#27961C211yesmaximal, characteristic, complemented
11#27891C211yesmaximal, characteristic, complemented
12#26737C214yesmaximal, complemented
13#26673C214yesmaximal, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25599C211yesmaximal, characteristic, complemented
16#21859C211yesmaximal, characteristic, complemented
17#21834C211yesmaximal, characteristic, complemented
18#21646C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#553—21no—
21C2×#548—21no—
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#493C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#431C2211yescharacteristic
28C2×#431C2211yescharacteristic
29#2859C2211yescharacteristic
30#2858C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2566—21no—
36#2545—21no—
37#2512—21no—
38#2512C2212yes—
39#2504—21no—
40#2500—21no—
41#2491—21no—
42#2491C2212yes—
43#2452—21no—
44#2452C2212yes—
45#2436—21no—
46#2432—21no—
47#2422—21no—
48#2422C2212yes—
49#2416—21no—
50#2416—21no—
51#2416C2212yes—
52#2416C2212yes—
53#2361—21no—
54#2361—21no—
55#2361C2212yes—
56#2361C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2100C2214yes—
63#2087C2214yes—
64#2067C2214yes—
65#2054C2214yes—
66#2054C2214yes—
67#2033C2214yes—
68#2033C2214yes—
69#2023C2214yes—
70#1999C2214yes—
71#1999C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1987C2214yes—
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1955C2212yes—
84#1940C2212yes—
85#1936C2214yes—
86#1936C2214yes—
87#1936C2214yes—
88#1925C2214yes—
89#1924C2212yes—
90#1924C2212yes—
91#1921C2214yes—
92#1879C2214yes—
93#1879C2214yes—
94#1874C2214yes—
95#1874C2214yes—
96#1845C2211yescharacteristic
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1824C2214yes—
100#1824C2214yes—
101#1802C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103#1762C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41—21no—
108C23×Q8—21no—
109C22×D8C2314yes—
110#553—48no—
111#548—48no—
112#532—24no—
113#532—42no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2312yes—
120C2×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#127C2311yescharacteristic
123C2×#126—22no—
124C2×#125—21no—
125C2×#124—22no—
126C2×#124—21no—
127C2×#124—21no—
128C2×#124—21no—
129C2×#123—22no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—22no—
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×#121—21no—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×#121C2312yes—
145C2×C4×Q8—21no—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
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×D4C2311yescharacteristic
156C2×#117—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#493—42no—
165#486—24no—
166#486—42no—
167#431—42no—
168#431—42no—
169C2×#107C2314yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
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#397—22no—
190#397—22no—
191#396—22no—
192#396—22no—
193#396—22no—
194#396—22no—
195#394—22no—
196#394—22no—
197#394—22no—
198#394—22no—
199#393—22no—
200#393—22no—
201#391—21no—
202#391—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390C2312yes—
214#390C2312yes—
215#390C2312yes—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#389C2312yes—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#385—22no—
236#385—22no—
237#385—22no—
238#385—22no—
239#384—21no—
240#384—21no—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#384C2312yes—
244#384C2311yescharacteristic
245#384C2311yescharacteristic
246#382—21no—
247#382—21no—
248#380—21no—
249#380—21no—
250#380C2312yes—
251#380C2312yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4D411yescharacteristic
255C4×C4⋊C4D411yescharacteristic
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2311yescharacteristic
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×Q8—22no—
283C22×Q8—44no—
284C22×Q8—44no—
285C22×Q8—82no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C2×D411yescharacteristic
295C22×D4C2412yes—
296C22×D4C2412yes—
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—44no—
308C2×D8—44no—
309C2×D8—44no—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C4⋊Q8—24no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—42no—
319C4⋊Q8—44no—
320C4⋊Q8—44no—
321C4⋊Q8#4114yes—
322#127—22no—
323#127—22no—
324#127—22no—
325#127—22no—
326#126—48no—
327#125—44no—
328#124—44no—
329#124—44no—
330#124—48no—
331#124—82no—
332#123—48no—
333C22⋊Q8—48no—
334C22⋊Q8—44no—
335#121—24no—
336#121—44no—
337#121—44no—
338#121—42no—
339#121—44no—
340#121—44no—
341#121—44no—
342#121—48no—
343#121—48no—
344#121—44no—
345#121—44no—
346#121—44no—
347#121—44no—
348#121—82no—
349C4×Q8—44no—
350C4×D4—24no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—42no—
354C4×D4—44no—
355C4×D4—42no—
356C4×D4—44no—
357C4×D4—44no—
358C4×D4—48no—
359C4×D4—48no—
360C4×D4—82no—
361#117—44no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—82no—
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2412yes—
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⋊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⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—44no—
442C4⋊C8—42no—
443C4⋊C8—42no—
444C4⋊C8—42no—
445#102—28no—
446#102—44no—
447#102—44no—
448#102—44no—
449#102—44no—
450#102—44no—
451C22⋊C8—42no—
452C22⋊C8—42no—
453C22⋊C8—42no—
454C22⋊C8—42no—
455#97—42no—
456#97—42no—
457C4×C8—22no—
458C4×C8—22no—
459C4×C8—22no—
460C4×C8—22no—
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—
480C2×Q8—24no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—82no—
489C2×Q8—816no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—41no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—82no—
523C2×D4—82no—
524C2×D4—82no—
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—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
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×C4AGL(1,ℤ/8)14yes—
562C22×C4AGL(1,ℤ/8)14yes—
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—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—41no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C4⋊C4C2×#4114yes—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—44no—
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—82no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—22no—
658C42—22no—
659C42—44no—
660C42—44no—
661C42C2×#4112yes—
662C42H(5,𝔽2)12yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23C2×AGL(1,ℤ/8)12yes—
690C23C2×AGL(1,ℤ/8)12yes—
691C23C23×D411yescharacteristic
692Q8—48no—
693Q8—88no—
694Q8—84no—
695D4—44no—
696D4—44no—
697D4—44no—
698D4—44no—
699D4—44no—
700D4—88no—
701D4—88no—
702D4—88no—
703D4—84no—
704D4—84no—
705D4—84no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—28no—
713C2×C4—28no—
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—24no—
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—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—44no—
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—42no—
761C2×C4—42no—
762C2×C4—88no—
763C2×C4—88no—
764C2×C4—164no—
765C2×C4—164no—
766C2×C4#54612yes—
767C2×C4#54612yes—
768C2×C4C2×AGL(1,ℤ/8)12yes—
769C2×C4C2×AGL(1,ℤ/8)12yes—
770C2×C4C2×AGL(1,ℤ/8)12yes—
771C2×C4C2×AGL(1,ℤ/8)12yes—
772C2×C4#57612yes—
773C2×C4#57812yes—
774C2×C4C22×#4111yescharacteristic
775C2×C4C2×H(5,𝔽2)11yescharacteristic
776C2×C4#58512yes—
777C2×C4#58512yes—
778C8—42no—
779C8—42no—
780C8—42no—
781C8—42no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22#344911yescharacteristic
811C22C2×#54611yescharacteristic
812C22#350011yescharacteristic
813C22C22×AGL(1,ℤ/8)11yescharacteristic
814C22C22×AGL(1,ℤ/8)11yescharacteristic
815C22C2×#57611yescharacteristic
816C22C2×#57811yescharacteristic
817C4—22no—
818C4—22no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—44no—
827C4—41no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4#330814yes—
834C4#331814yes—
835C4#352412yes—
836C4#355112yes—
837C2—42no—
838C2—42no—
839C2—162no—
840C2—162no—
841C2#3894811yescharacteristic
842C2#6096811yescharacteristic
843C2#6101411yescharacteristic
844C2C2×#331811yescharacteristic
845C2C2×#330811yescharacteristic
846C2#6253511yescharacteristic
847C2#6253811yescharacteristic
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. #36122C2semidirect
3. #33286C2semidirect
4. #31818C2semidirect
5. #31736C2semidirect
6. #29842C2semidirect
7. #29806C2semidirect
8. #29179C2semidirect
9. #28615C2semidirect
10. #27961C2semidirect
11. #27891C2semidirect
12. #26737C2semidirect
13. #26673C2semidirect
14. #25903C2semidirect
15. #25599C2semidirect
16. #21859C2semidirect
17. #21834C2semidirect
18. #21646C2semidirect
19. #21265C2semidirect

Maximal subgroups

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

subgroupindex
#361822
#361222
#332862
#318182
#317362
#298422
#298062
#291792
#286152
#279612
#278912
#267372
#266732
#259032
#255992
#218592
#218342
#216462
#212652