Finite Group Databasebeta

← #6493830

Subgroups — #6493830

Order 512.

2110 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35294C211yesmaximal, characteristic, complemented
2#35274C211yesmaximal, characteristic
3#33286C211yesmaximal, characteristic, complemented
4#33277C211yesmaximal, characteristic, complemented
5#33231C211yesmaximal, characteristic, complemented
6#33224C211yesmaximal, characteristic, complemented
7#30218C211yesmaximal, characteristic, complemented
8#30218C211yesmaximal, characteristic, complemented
9#30204C211yesmaximal, characteristic, complemented
10#30203C211yesmaximal, characteristic, complemented
11#27780C214yesmaximal, complemented
12#27760C214yesmaximal, complemented
13#27279C214yesmaximal, complemented
14#27273C214yesmaximal, complemented
15#21863C211yesmaximal, characteristic, complemented
16#21803C211yesmaximal, characteristic, complemented
17#21410C211yesmaximal, characteristic, complemented
18#21203C211yesmaximal, characteristic, complemented
19#20472C211yesmaximal, characteristic, complemented
20C2×#535—21no—
21C2×#535—21no—
22C2×#532C2211yescharacteristic
23C22×#127C2211yescharacteristic
24C2×#490C2214yescomplemented
25C2×#486C2214yescomplemented
26C2×#431C2211yescharacteristic
27C2×#418C2214yes—
28C2×C4×M16C2211yescharacteristic
29#2868C2211yescharacteristic, complemented
30#2867C2211yescharacteristic
31#2867C2211yescharacteristic
32#2859C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2859C2211yescharacteristic, complemented
35#2858C2211yescharacteristic
36#2858C2211yescharacteristic
37#2657—21no—
38#2657—21no—
39#2629—21no—
40#2628—21no—
41#2570—21no—
42#2570C2212yescomplemented
43#2550—21no—
44#2550C2212yescomplemented
45#2541—21no—
46#2541—21no—
47#2541C2212yes—
48#2541C2212yes—
49#2441—21no—
50#2441C2212yes—
51#2439—21no—
52#2439C2212yes—
53#2433—21no—
54#2433—21no—
55#2433C2212yes—
56#2433C2212yes—
57#2331—21no—
58#2330—21no—
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic
61C4×#117C2211yescharacteristic
62#2073C2214yescomplemented
63#2071C2214yescomplemented
64#2041C2214yescomplemented
65#2041C2214yescomplemented
66#2041C2214yescomplemented
67#2041C2214yescomplemented
68#2025C2214yescomplemented
69#2023C2214yescomplemented
70#1990C2211yescharacteristic, complemented
71#1990C2211yescharacteristic, complemented
72#1990C2211yescharacteristic, complemented
73#1990C2211yescharacteristic, complemented
74#1982C2214yes—
75#1961C2214yes—
76#1961C2214yescomplemented
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1957C2211yescharacteristic
85#1957C2211yescharacteristic, complemented
86#1957C2211yescharacteristic, complemented
87#1957C2211yescharacteristic, complemented
88#1957C2214yescomplemented
89#1957C2211yescharacteristic, complemented
90#1936C2214yescomplemented
91#1936C2214yescomplemented
92#1934C2214yescomplemented
93#1934C2214yescomplemented
94#1895C2214yes—
95#1875C2214yes—
96#1804C2214yescomplemented
97#1786C2214yes—
98#1771C2212yescomplemented
99#1771C2212yescomplemented
100#1762C2214yescomplemented
101#1753C2212yes—
102#1753C2212yes—
103#1744C2211yescharacteristic, complemented
104#1744C2211yescharacteristic, complemented
105C4×#97C2211yescharacteristic, complemented
106C42×C8C2211yescharacteristic, complemented
107C22×#41—21no—
108C23×D4—21no—
109C23×D4—21no—
110C23×D4C2312yes—
111C22×M16C2312yes—
112#535—48no—
113#535—48no—
114#532—24no—
115#532—24no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2312yes—
120C2×#127—21no—
121C2×#127—21no—
122C2×#127—21no—
123C2×#127—21no—
124C2×#127—21no—
125C2×#127—21no—
126C2×#127—21no—
127C2×#127—21no—
128C2×#127—21no—
129C2×#127—21no—
130C2×#127—24no—
131C2×#127—24no—
132C2×#127C2311yescharacteristic
133C2×#127C2311yescharacteristic
134C2×#127C2311yescharacteristic
135C2×#127C2312yes—
136C2×#127C2312yes—
137C2×#127C2312yes—
138C2×#127C2312yes—
139C2×#127C2312yes—
140C2×#125—21no—
141C2×#125—21no—
142C2×#125C2312yes—
143C2×#124—21no—
144C2×#124—21no—
145C2×#124—21no—
146C2×#124—21no—
147C2×#124—21no—
148C2×#121—21no—
149C2×#121—22no—
150C2×#121—22no—
151C2×#121—22no—
152C2×#121—22no—
153C2×#121C2312yes—
154C2×#120—22no—
155C2×#120—22no—
156C2×#120—22no—
157C2×#120—22no—
158C2×C4×D4—21no—
159C2×C4×D4C2312yes—
160C2×#117—21no—
161C2×#117D411yescharacteristic
162C2×#117D411yescharacteristic
163C2×#117C2312yes—
164C22×C42C2311yescharacteristic
165#490—48no—
166#486—48no—
167#431—24no—
168C2×C4⋊C8C2312yes—
169#418—48no—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×C22⋊C8C2312yes—
183C4×M16—24no—
184C2×#97C2312yes—
185C2×#97C2312yes—
186C2×#97C2312yes—
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2311yescharacteristic
189C2×C4×C8C2312yes—
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2312yes—
193#400—22no—
194#399—22no—
195#398—22no—
196#398—22no—
197#396—22no—
198#396—22no—
199#395—22no—
200#393—22no—
201#392—22no—
202#392—22no—
203#392—22no—
204#392—22no—
205#392—22no—
206#392—22no—
207#392—22no—
208#392—22no—
209#391—22no—
210#391—22no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—22no—
228#389—22no—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#384—21no—
238#384—21no—
239#384C2312yes—
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#384C2311yescharacteristic
244#382—21no—
245#382—21no—
246#382—21no—
247#382C2312yes—
248#382C2312yes—
249#380—21no—
250#380—21no—
251#380—21no—
252#380C2312yes—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2311yescharacteristic
260C4×C4⋊C4C2311yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4C2311yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265#376D411yescharacteristic
266#376D411yescharacteristic
267C43C2311yescharacteristic
268C43C2311yescharacteristic
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277C25—22no—
278C2×#41—44no—
279C2×#41—44no—
280C2×#41—44no—
281C22×Q8—21no—
282C22×Q8—22no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—44no—
304C22×D4—44no—
305C22×D4—44no—
306C22×D4—44no—
307C22×D4—44no—
308C22×D4—44no—
309C22×D4—82no—
310C22×D4—82no—
311C22×D4C2412yes—
312C22×D4C2412yes—
313C22×D4C2412yes—
314C23×C4—22no—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—42no—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—44no—
328C4⋊Q8—44no—
329C4⋊Q8—82no—
330#127—22no—
331#127—22no—
332#127—22no—
333#127—22no—
334#127—24no—
335#127—24no—
336#127—22no—
337#127—22no—
338#127—44no—
339#127—44no—
340#127—44no—
341#127—44no—
342#127—44no—
343#127—44no—
344#127—44no—
345#127—44no—
346#127—44no—
347#127—44no—
348#127—82no—
349#127—82no—
350#127—82no—
351#127—82no—
352#125—44no—
353#125—44no—
354#125—82no—
355#124—44no—
356#124—44no—
357#124—44no—
358#124—44no—
359#124—44no—
360#121—24no—
361#121—24no—
362#121—48no—
363#121—48no—
364#121—48no—
365#121—48no—
366#121—44no—
367#120—48no—
368#120—48no—
369#120—48no—
370#120—48no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—44no—
374#117—24no—
375#117—24no—
376#117—44no—
377#117—82no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2×D411yescharacteristic
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C42—22no—
422C2×C42—22no—
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42#4114yes—
434C2×C42#4114yes—
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C4⋊C8—24no—
442#102—28no—
443#102—28no—
444#102—28no—
445#102—44no—
446#102—44no—
447#102—44no—
448#102—44no—
449#102—44no—
450#102—44no—
451#102—44no—
452#102—44no—
453#102—44no—
454C22⋊C8—24no—
455#97—24no—
456#97—24no—
457#97—42no—
458C4×C8—24no—
459C4×C8—22no—
460C4×C8—22no—
461C4×C8—22no—
462C4×C8—22no—
463C4×C8—42no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95C2×D411yescharacteristic
475#95C2×D411yescharacteristic
476#95C2×D411yescharacteristic
477#95C2×D411yescharacteristic
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482C24—22no—
483C24—22no—
484C24—22no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—82no—
489C24—82no—
490C24—82no—
491C24—82no—
492C24C22×D411yescharacteristic
493#41—816no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—44no—
498C2×Q8—82no—
499C2×Q8—82no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—416no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—44no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—88no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—816no—
553C2×D4—816no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—82no—
568C2×D4—82no—
569C2×D4—82no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4#12414yes—
585C22×C4#12414yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C2×#4112yes—
600C22×C4C2×#4112yes—
601C22×C4C2511yescharacteristic
602M16—48no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8H(5,𝔽2)14yes—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4—82no—
640C4⋊C4—82no—
641C4⋊C4—82no—
642C4⋊C4—82no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—82no—
670C42—82no—
671C42#12414yes—
672C42#12414yes—
673C42AGL(1,ℤ/8)14yes—
674C42AGL(1,ℤ/8)14yes—
675C42C2×#4112yes—
676C42C2×#4112yes—
677C42C2×#4112yes—
678C42C2×#4112yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—88no—
707C23—88no—
708C23—88no—
709C23—164no—
710C23—164no—
711C23—164no—
712C23—164no—
713C23C2×#12412yes—
714C23C23×D411yescharacteristic
715Q8—84no—
716Q8—164no—
717D4—44no—
718D4—44no—
719D4—44no—
720D4—44no—
721D4—44no—
722D4—44no—
723D4—88no—
724D4—88no—
725D4—88no—
726D4—88no—
727D4—84no—
728D4—84no—
729D4—84no—
730D4—84no—
731D4—84no—
732D4—84no—
733D4—164no—
734D4—164no—
735D4—164no—
736D4—164no—
737D4—164no—
738D4—164no—
739D4—164no—
740D4—164no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—88no—
787C2×C4C2×#12412yes—
788C2×C4C2×#12412yes—
789C2×C4C2×#12412yes—
790C2×C4C2×#12412yes—
791C2×C4C2×#12412yes—
792C2×C4C2×AGL(1,ℤ/8)12yes—
793C2×C4C2×AGL(1,ℤ/8)12yes—
794C2×C4C2×AGL(1,ℤ/8)12yes—
795C2×C4C2×AGL(1,ℤ/8)12yes—
796C2×C4C2×AGL(1,ℤ/8)12yes—
797C2×C4C2×AGL(1,ℤ/8)12yes—
798C2×C4#57612yes—
799C2×C4#57712yes—
800C2×C4C22×#4111yescharacteristic
801C2×C4C22×#4111yescharacteristic
802C2×C4C2×H(5,𝔽2)12yes—
803C2×C4#58512yes—
804C8—24no—
805C8—42no—
806C8—42no—
807C8—42no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—1616no—
837C22C22×#12411yescharacteristic
838C22#349811yescharacteristic
839C22#350011yescharacteristic
840C22C22×AGL(1,ℤ/8)11yescharacteristic
841C22C22×AGL(1,ℤ/8)11yescharacteristic
842C22C2×#57611yescharacteristic
843C22C2×#57711yescharacteristic
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4#313614yes—
861C4#313814yes—
862C4#346012yes—
863C4#349412yes—
864C2—42no—
865C2—162no—
866C2—162no—
867C2—162no—
868C2#3526411yescharacteristic
869C2C2×#313611yescharacteristic
870C2C2×#313811yescharacteristic
871C2#6242111yescharacteristic
872C2#6242311yescharacteristic
873C2#6253511yescharacteristic
874C2#6253911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35274C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #35294C2semidirect
3. #33286C2semidirect
4. #33277C2semidirect
5. #33231C2semidirect
6. #33224C2semidirect
7. #30218C2semidirect
8. #30218C2semidirect
9. #30204C2semidirect
10. #30203C2semidirect
11. #27780C2semidirect
12. #27760C2semidirect
13. #27279C2semidirect
14. #27273C2semidirect
15. #21863C2semidirect
16. #21803C2semidirect
17. #21410C2semidirect
18. #21203C2semidirect
19. #20472C2semidirect
24. C2×#490C22semidirect
25. C2×#486C22semidirect
29. #2868C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
42. #2570C22semidirect
44. #2550C22semidirect
62. #2073C22semidirect
63. #2071C22semidirect
64. #2041C22semidirect
65. #2041C22semidirect
66. #2041C22semidirect
67. #2041C22semidirect
68. #2025C22semidirect
69. #2023C22semidirect
70. #1990C22semidirect
71. #1990C22semidirect
72. #1990C22semidirect
73. #1990C22semidirect
76. #1961C22semidirect
85. #1957C22semidirect
86. #1957C22semidirect
87. #1957C22semidirect
88. #1957C22semidirect
89. #1957C22semidirect
90. #1936C22semidirect
91. #1936C22semidirect
92. #1934C22semidirect
93. #1934C22semidirect
96. #1804C22semidirect
98. #1771C22semidirect
99. #1771C22semidirect
100. #1762C22semidirect
103. #1744C22semidirect
104. #1744C22semidirect
105. C4×#97C22semidirect
106. C42×C8C22semidirect

Maximal subgroups

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

subgroupindex
#352942
#352742
#332862
#332772
#332312
#332242
#302182
#302042
#302032
#277802
#277602
#272792
#272732
#218632
#218032
#214102
#212032
#204722