Finite Group Databasebeta

← #6462439

Subgroups — #6462439

Order 512.

1532 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35315C211yesmaximal, characteristic
2C2×#2320C211yesmaximal, characteristic
3#29585C212yesmaximal, complemented
4#29565C212yesmaximal, complemented
5#29439C212yesmaximal, complemented
6#29438C212yesmaximal, complemented
7#29335C211yesmaximal, characteristic
8#29298C211yesmaximal, characteristic
9#29112C211yesmaximal, characteristic
10#28304C211yesmaximal, characteristic
11#24606C211yesmaximal, characteristic
12#24602C211yesmaximal, characteristic
13#24508C211yesmaximal, characteristic
14#24502C211yesmaximal, characteristic
15#23792C212yesmaximal, complemented
16#23691C212yesmaximal, complemented
17#21581C211yesmaximal, characteristic
18C4×#484C211yesmaximal, characteristic
19#21455C211yesmaximal, characteristic
20C4×#451C211yesmaximal, characteristic
21#21289C212yesmaximal, complemented
22#21281C212yesmaximal, complemented
23#20469C211yesmaximal, characteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#484C2211yescharacteristic
26C2×#484C2211yescharacteristic
27C2×#451C2211yescharacteristic
28C2×#451C2211yescharacteristic
29C2×#441C2212yes—
30C2×C4×Q16C2212yes—
31C2×#432C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2857C2211yescharacteristic
34#2855C2211yescharacteristic
35#2855C2211yescharacteristic
36#2851C2211yescharacteristic
37#2647C2211yescharacteristic
38#2645C2211yescharacteristic
39#2645C2211yescharacteristic
40#2642C2211yescharacteristic
41#2533—21no—
42#2533—21no—
43#2528—21no—
44#2528—21no—
45#2505—21no—
46#2505—21no—
47#2493—21no—
48#2493—21no—
49#2330C2211yescharacteristic
50#2327C2211yescharacteristic
51#2320—21no—
52#2320—21no—
53#2320—21no—
54#2320—21no—
55#2320C2212yes—
56#2320C2212yes—
57#2320C2212yes—
58#2320C2212yes—
59#2320C2211yescharacteristic
60#2320C2211yescharacteristic
61C4×C22⋊Q8C2211yescharacteristic
62C4×C22⋊Q8C2211yescharacteristic
63C2×#391C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#389C2211yescharacteristic
66C2×#389C2211yescharacteristic
67C2×#387—21no—
68C2×#387—21no—
69C2×#383—21no—
70C2×#382—21no—
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×#376C2211yescharacteristic
73#2099C2212yes—
74#2095C2212yes—
75#2087C2212yes—
76#2086C2212yes—
77#2085C2212yes—
78#2074C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2066C2212yes—
82#2066C2212yes—
83#2059C2212yes—
84#2056C2212yes—
85#2056C2212yes—
86#2043C2212yes—
87#2026C2212yes—
88#2016C2212yes—
89#1971C2212yes—
90#1969C2212yes—
91#1969C2212yes—
92#1969C2212yes—
93#1944C2212yes—
94#1942C2212yes—
95#1942C2212yes—
96#1941C2212yes—
97#1935C2212yes—
98#1935C2212yes—
99#1935C2212yes—
100#1935C2212yes—
101#1935C2212yes—
102#1935C2212yes—
103#1933C2212yes—
104#1933C2212yes—
105#1928C2212yes—
106#1927C2212yes—
107#1921C2212yes—
108#1918C2212yes—
109#1878C2212yes—
110#1878C2212yes—
111#1872C2211yescharacteristic
112#1872C2211yescharacteristic
113#1872C2211yescharacteristic
114#1872C2211yescharacteristic
115#1865C2212yes—
116#1863C2212yes—
117#1853C2211yescharacteristic
118#1853C2211yescharacteristic
119#1852C2211yescharacteristic
120#1852C2211yescharacteristic
121#1824C2211yescharacteristic
122#1824C2211yescharacteristic
123#1787C2211yescharacteristic
124#1787C2211yescharacteristic
125#1776C2212yes—
126C4×#107C2212yes—
127#1768C2212yes—
128#1768C2212yes—
129#1763C2212yes—
130#1763C2212yes—
131C4×#103C2212yes—
132C4×#103C2212yes—
133#1749C2211yescharacteristic
134#1749C2211yescharacteristic
135C4×C22⋊C8C2211yescharacteristic
136C4×C22⋊C8C2211yescharacteristic
137#1746C2212yes—
138#1726C2212yes—
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C22×Q16C2312yes—
142C2×C4⋊Q8C2311yescharacteristic
143C2×#125C2311yescharacteristic
144C2×C22⋊Q8C2311yescharacteristic
145C2×C22⋊Q8C2311yescharacteristic
146C2×C4×Q8—28no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8C2312yes—
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2312yes—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C42—21no—
160C22×C42—21no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#484—24no—
165#484—24no—
166#451—24no—
167#451—24no—
168#441—28no—
169C4×Q16—28no—
170#432—24no—
171#431—24no—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2311yescharacteristic
196C2×#97C2312yes—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×C4×C8C2312yes—
200C2×C4×C8C2312yes—
201C2×C4×C8C2312yes—
202#401—21no—
203#401—21no—
204#400—21no—
205#400—21no—
206#400—21no—
207#400—21no—
208#400—21no—
209#400—21no—
210#400—21no—
211#400—21no—
212#400—21no—
213#400—21no—
214#400—21no—
215#400—21no—
216#398—21no—
217#398—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391C2312yes—
223#391C2311yescharacteristic
224#391C2311yescharacteristic
225#391C2312yes—
226#391C2312yes—
227#391C2312yes—
228#391C2311yescharacteristic
229#391C2311yescharacteristic
230#391C2311yescharacteristic
231#391C2311yescharacteristic
232#391C2311yescharacteristic
233#391C2311yescharacteristic
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#389C2311yescharacteristic
250#389C2311yescharacteristic
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#387—22no—
268#387—22no—
269#387—22no—
270#387—21no—
271#387—21no—
272#387—21no—
273#387—21no—
274#387—21no—
275#387—21no—
276#387—21no—
277#387—21no—
278#387—21no—
279#387—21no—
280#385—21no—
281#385—21no—
282#385—21no—
283#385—21no—
284#385—21no—
285#385—21no—
286#384C2311yescharacteristic
287#383—22no—
288#383—22no—
289#383—22no—
290#383—22no—
291#383—21no—
292#383—21no—
293#382—22no—
294#382—22no—
295#382—22no—
296#382—22no—
297#382—21no—
298#382—21no—
299#382C2311yescharacteristic
300#381—21no—
301#381—21no—
302#380—21no—
303#380—21no—
304#380C2311yescharacteristic
305#380C2311yescharacteristic
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316#376D411yescharacteristic
317#376D411yescharacteristic
318#376D411yescharacteristic
319#376D411yescharacteristic
320#376C2311yescharacteristic
321#376C2311yescharacteristic
322#376C2311yescharacteristic
323#376C2311yescharacteristic
324C2×#95—21no—
325C2×#95—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—21no—
331C2×#95D411yescharacteristic
332C2×#95D411yescharacteristic
333C2×#95D411yescharacteristic
334C2×#95D411yescharacteristic
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—24no—
352C22×Q8—21no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—42no—
356C22×Q8C2411yescharacteristic
357C22×Q8C2411yescharacteristic
358C22×Q8C2412yes—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2411yescharacteristic
370C2×Q16—24no—
371C2×Q16—24no—
372C2×Q16—24no—
373C2×Q16—24no—
374C2×Q16—42no—
375C2×Q16—42no—
376C22×C8C2412yes—
377C22×C8C2412yes—
378C22×C8C2412yes—
379C22×C8C2412yes—
380C4⋊Q8—42no—
381#125—42no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C4×Q8—28no—
387C4×Q8—28no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×Q8—24no—
391C4×Q8—24no—
392C4×Q8—24no—
393C4×Q8#4118yes—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—82no—
427C2×C4⋊C4—82no—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C42—28no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—24no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—42no—
454C2×C42—82no—
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467#107—24no—
468#107—24no—
469#107—24no—
470#107—42no—
471#106—24no—
472#106—42no—
473C4⋊C8—24no—
474C4⋊C8—24no—
475#103—24no—
476#103—24no—
477#103—24no—
478#103—24no—
479#103—24no—
480#103—24no—
481#103—24no—
482#103—24no—
483#103—42no—
484#103—42no—
485#103—42no—
486#103—42no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8#4114yes—
490C22⋊C8#4114yes—
491#97—24no—
492#97—24no—
493#97—42no—
494C4×C8—24no—
495C4×C8—24no—
496C4×C8—42no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95C2×D411yescharacteristic
542#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557C24C22×D411yescharacteristic
558C2×Q8—24no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—48no—
573C2×Q8—48no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8C2×#4114yes—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2511yescharacteristic
637Q16—48no—
638Q16—48no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8C2×#4114yes—
650C2×C8C2×#4114yes—
651C4⋊C4—24no—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4C2×#4114yes—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C42—28no—
697C42—28no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—41no—
710C42—41no—
711C42—42no—
712C42—42no—
713C42—81no—
714C42—81no—
715C42—82no—
716C42—82no—
717C42C2×#4114yes—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23#53212yes—
723C23#57812yes—
724C23#57812yes—
725C23C23×D411yescharacteristic
726Q8—24no—
727Q8—24no—
728Q8—48no—
729Q8—42no—
730Q8—42no—
731Q8—42no—
732Q8—42no—
733Q8—42no—
734Q8—42no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—24no—
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—24no—
756C2×C4—24no—
757C2×C4—21no—
758C2×C4—21no—
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—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—48no—
778C2×C4—48no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4#52512yes—
820C2×C4#52512yes—
821C2×C4#53212yes—
822C2×C4C22×#4112yes—
823C2×C4C22×#4111yescharacteristic
824C2×C4C22×#4111yescharacteristic
825C2×C4#58512yes—
826C8—24no—
827C8—24no—
828C8—42no—
829C8—42no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22#317714yes—
837C22C2×#52511yescharacteristic
838C22C2×#53211yescharacteristic
839C22#344911yescharacteristic
840C22C2×#57811yescharacteristic
841C22C2×#57811yescharacteristic
842C22#358511yescharacteristic
843C22#358611yescharacteristic
844C4—22no—
845C4—22no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—44no—
856C4—41no—
857C4—41no—
858C4—44no—
859C4—81no—
860C4—81no—
861C4—82no—
862C4—81no—
863C4—82no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4—81no—
869C4#347512yes—
870C4#347512yes—
871C2—24no—
872C2#3487711yescharacteristic
873C2#6058311yescharacteristic
874C2#6058911yescharacteristic
875C2C2×#317711yescharacteristic
876C2#6070311yescharacteristic
877C2#6098111yescharacteristic
878C2#6098311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29585C2semidirect
4. #29565C2semidirect
5. #29439C2semidirect
6. #29438C2semidirect
15. #23792C2semidirect
16. #23691C2semidirect
21. #21289C2semidirect
22. #21281C2semidirect

Maximal subgroups

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

subgroupindex
#353152
C2×#23202
#295852
#295652
#294392
#294382
#293352
#292982
#291122
#283042
#246062
#246022
#245082
#245022
#237922
#236912
#215812
C4×#4842
#214552
C4×#4512
#212892
#212812
#204692