Finite Group Databasebeta

← #6481194

Subgroups — #6481194

Order 512.

1426 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35315C211yesmaximal, characteristic, complemented
2C2×#2644C211yesmaximal, characteristic
3#33274C212yesmaximal, complemented
4#33271C212yesmaximal, complemented
5#30395C212yesmaximal, complemented
6#30355C212yesmaximal, complemented
7#29529C212yesmaximal, complemented
8#29508C212yesmaximal, complemented
9#29443C212yesmaximal, complemented
10#29442C212yesmaximal, complemented
11#29335C211yesmaximal, characteristic, complemented
12#29298C211yesmaximal, characteristic, complemented
13#29110C211yesmaximal, characteristic
14#28302C211yesmaximal, characteristic
15#24609C211yesmaximal, characteristic, complemented
16#24601C211yesmaximal, characteristic, complemented
17#24507C211yesmaximal, characteristic
18#24501C211yesmaximal, characteristic
19#22084C211yesmaximal, characteristic, complemented
20#22078C211yesmaximal, characteristic, complemented
21#22049C211yesmaximal, characteristic
22#22043C211yesmaximal, characteristic
23#20469C211yesmaximal, characteristic, complemented
24C2×#483C2211yescharacteristic
25C2×#483C2211yescharacteristic
26C2×#450C2211yescharacteristic
27C2×#450C2211yescharacteristic
28C2×#432C2211yescharacteristic
29C2×#431C2211yescharacteristic
30#2857C2211yescharacteristic
31#2855C2211yescharacteristic
32#2855C2211yescharacteristic
33#2851C2211yescharacteristic
34#2647C2211yescharacteristic, complemented
35#2645C2211yescharacteristic, complemented
36#2645C2211yescharacteristic, complemented
37#2644—21no—
38#2644—21no—
39#2644—21no—
40#2644—21no—
41#2644C2212yes—
42#2644C2212yes—
43#2644C2212yes—
44#2644C2212yes—
45#2642C2211yescharacteristic, complemented
46#2533—21no—
47#2533—21no—
48#2528—21no—
49#2528—21no—
50#2505—21no—
51#2505—21no—
52#2493—21no—
53#2493—21no—
54C2×#397—21no—
55C2×#397—21no—
56C2×#397—21no—
57C2×#396—21no—
58#2330C2211yescharacteristic, complemented
59#2327C2211yescharacteristic, complemented
60#2320C2211yescharacteristic, complemented
61#2320C2211yescharacteristic, complemented
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C2×#390C2211yescharacteristic
66C2×#390C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#389C2211yescharacteristic
69C2×#389C2211yescharacteristic
70C2×#376C2211yescharacteristic
71#2099C2212yescomplemented
72#2094C2212yes—
73#2088C2212yescomplemented
74#2088C2212yescomplemented
75#2085C2212yescomplemented
76#2073C2212yes—
77#2068C2212yescomplemented
78#2067C2212yes—
79#2066C2212yescomplemented
80#2065C2212yes—
81#2059C2212yescomplemented
82#2055C2212yes—
83#2055C2212yes—
84#2043C2212yescomplemented
85#2025C2212yes—
86#2013C2212yes—
87#1973C2212yes—
88#1973C2212yes—
89#1968C2212yes—
90#1968C2212yes—
91#1968C2212yes—
92#1968C2212yes—
93#1944C2212yescomplemented
94#1943C2212yescomplemented
95#1942C2212yescomplemented
96#1941C2212yescomplemented
97#1941C2212yescomplemented
98#1941C2212yescomplemented
99#1936C2212yes—
100#1936C2212yes—
101#1936C2212yes—
102#1936C2212yes—
103#1935C2212yescomplemented
104#1935C2212yescomplemented
105#1935C2212yescomplemented
106#1935C2212yescomplemented
107#1934C2212yes—
108#1934C2212yes—
109#1933C2212yescomplemented
110#1933C2212yescomplemented
111#1926C2212yes—
112#1925C2212yes—
113#1920C2212yescomplemented
114#1919C2212yescomplemented
115#1880C2212yes—
116#1880C2212yes—
117#1872C2211yescharacteristic
118#1872C2211yescharacteristic
119#1872C2211yescharacteristic
120#1872C2211yescharacteristic
121#1865C2212yescomplemented
122#1863C2212yescomplemented
123#1853C2211yescharacteristic
124#1853C2211yescharacteristic
125#1852C2211yescharacteristic
126#1852C2211yescharacteristic
127#1823C2211yescharacteristic
128#1823C2211yescharacteristic
129#1786C2211yescharacteristic
130#1786C2211yescharacteristic
131#1768C2212yescomplemented
132#1768C2212yescomplemented
133#1749C2211yescharacteristic
134#1749C2211yescharacteristic
135C4×C22⋊C8C2211yescharacteristic
136C4×C22⋊C8C2211yescharacteristic
137#1746C2212yescomplemented
138#1726C2212yescomplemented
139C23×D4C2311yescharacteristic
140C22×SD16C2312yes—
141C22×SD16C2312yes—
142C2×C4⋊Q8C2311yescharacteristic
143C2×#125C2311yescharacteristic
144C2×C22⋊Q8C2311yescharacteristic
145C2×C22⋊Q8C2311yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147C2×C4×Q8C2311yescharacteristic
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#483—24no—
164#483—24no—
165#450—24no—
166#450—24no—
167#432—24no—
168#431—24no—
169C2×#107C2312yes—
170C2×#107C2312yes—
171C2×#106C2312yes—
172C2×#106C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×#103C2312yes—
178C2×#103C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×C22⋊C8C2311yescharacteristic
190C2×C22⋊C8C2311yescharacteristic
191C2×C22⋊C8C2311yescharacteristic
192C2×C22⋊C8C2311yescharacteristic
193C2×#97C2312yes—
194C2×#97C2312yes—
195C2×#97C2312yes—
196C2×C4×C8C2312yes—
197C2×C4×C8C2312yes—
198C2×C4×C8C2312yes—
199#401—21no—
200#401—21no—
201#400—21no—
202#400—21no—
203#400—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#398—21no—
214#398—21no—
215#397—22no—
216#397—22no—
217#397—22no—
218#397—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#397—22no—
223#397—22no—
224#397—22no—
225#397—22no—
226#397—22no—
227#396—22no—
228#396—22no—
229#396—22no—
230#396—22no—
231#391C2311yescharacteristic
232#391C2311yescharacteristic
233#391C2311yescharacteristic
234#391C2311yescharacteristic
235#391C2311yescharacteristic
236#391C2311yescharacteristic
237#391C2311yescharacteristic
238#391C2311yescharacteristic
239#390—21no—
240#390—21no—
241#390—21no—
242#390—21no—
243#390—21no—
244#390—21no—
245#390C2312yes—
246#390C2312yes—
247#390C2312yes—
248#390C2312yes—
249#390C2312yes—
250#390C2312yes—
251#389—21no—
252#389—21no—
253#389—21no—
254#389—21no—
255#389—21no—
256#389—21no—
257#389—21no—
258#389—21no—
259#389—21no—
260#389—21no—
261#389C2312yes—
262#389C2311yescharacteristic
263#389C2311yescharacteristic
264#389C2311yescharacteristic
265#389C2311yescharacteristic
266#389C2312yes—
267#389C2311yescharacteristic
268#389C2311yescharacteristic
269#389C2312yes—
270#389C2312yes—
271#389C2312yes—
272#389C2312yes—
273#389C2311yescharacteristic
274#389C2311yescharacteristic
275#387—21no—
276#387—21no—
277#387—21no—
278#387—21no—
279#387—21no—
280#387—21no—
281#387—21no—
282#387—21no—
283#387—21no—
284#387—21no—
285#387—21no—
286#387—21no—
287#387—21no—
288#387—21no—
289#387—21no—
290#387—21no—
291#387—21no—
292#387—21no—
293#385—21no—
294#385—21no—
295#385—21no—
296#385—21no—
297#385—21no—
298#385—21no—
299#384C2311yescharacteristic
300#383—21no—
301#383—21no—
302#382—21no—
303#382—21no—
304#382C2311yescharacteristic
305#381—21no—
306#381—21no—
307#380—21no—
308#380—21no—
309#380C2311yescharacteristic
310#380C2311yescharacteristic
311C4×C4⋊C4—21no—
312C4×C4⋊C4—21no—
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C22⋊C4—21no—
316C4×C22⋊C4—21no—
317#376D411yescharacteristic
318#376D411yescharacteristic
319#376D411yescharacteristic
320#376D411yescharacteristic
321#376C2311yescharacteristic
322#376C2311yescharacteristic
323#376C2311yescharacteristic
324#376C2311yescharacteristic
325C2×#95—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95D411yescharacteristic
329C2×#95D411yescharacteristic
330C2×#95D411yescharacteristic
331C2×#95D411yescharacteristic
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C25—21no—
349C22×Q8C2411yescharacteristic
350C22×Q8C2411yescharacteristic
351C22×D4—21no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4C2412yes—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2411yescharacteristic
367C2×SD16—24no—
368C2×SD16—24no—
369C2×SD16—42no—
370C2×SD16—42no—
371C2×SD16—42no—
372C2×SD16—42no—
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C22×C8C2412yes—
377C4⋊Q8—42no—
378#125—42no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C4×Q8—42no—
384C4×Q8—42no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
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—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—82no—
417C2×C4⋊C4—82no—
418C2×C4⋊C4—82no—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2411yescharacteristic
425C2×C4⋊C4C2411yescharacteristic
426C2×C4⋊C4C2411yescharacteristic
427C2×C4⋊C4C2411yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—82no—
445C2×C22⋊C4—82no—
446C2×C22⋊C4—82no—
447C2×C22⋊C4—82no—
448C2×C22⋊C4—82no—
449C2×C22⋊C4—82no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—42no—
457C2×C42—42no—
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470#107—42no—
471#107—42no—
472#106—24no—
473#106—24no—
474#106—42no—
475#106—42no—
476C4⋊C8—24no—
477C4⋊C8—24no—
478#103—24no—
479#103—24no—
480#103—42no—
481#103—42no—
482#103—42no—
483#103—42no—
484#102—24no—
485#102—24no—
486#102—42no—
487#102—42no—
488#102—42no—
489#102—42no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8#4114yes—
493C22⋊C8#4114yes—
494#97—24no—
495#97—42no—
496#97—42no—
497C4×C8—24no—
498C4×C8—42no—
499C4×C8—42no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
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#95C2×D411yescharacteristic
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D411yescharacteristic
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
552C24—22no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—42no—
560C24C22×D411yescharacteristic
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—84no—
579C2×D4—84no—
580C22×C4—22no—
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—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—41no—
602C22×C4—41no—
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×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2511yescharacteristic
636SD16—84no—
637SD16—84no—
638C2×C8—22no—
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×C8C2×#4114yes—
649C2×C8C2×#4114yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
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—81no—
676C4⋊C4—81no—
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—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C42—22no—
708C42—22no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—41no—
718C42—41no—
719C42—41no—
720C42—41no—
721C42—42no—
722C42—42no—
723C42—81no—
724C42—81no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23#53212yes—
744C23#57712yes—
745C23#57712yes—
746C23C23×D411yescharacteristic
747Q8—42no—
748Q8—42no—
749Q8—42no—
750Q8—42no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—24no—
759C2×C4—24no—
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—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—44no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—82no—
835C2×C4—84no—
836C2×C4—84no—
837C2×C4—84no—
838C2×C4#53212yes—
839C2×C4C22×#4111yescharacteristic
840C2×C4C22×#4111yescharacteristic
841C2×C4#58512yes—
842C2×C4#58512yes—
843C8—24no—
844C8—24no—
845C8—42no—
846C8—42no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—168no—
861C22#317414yes—
862C22C2×#53211yescharacteristic
863C22#344911yescharacteristic
864C22#344911yescharacteristic
865C22C2×#57711yescharacteristic
866C22C2×#57711yescharacteristic
867C22#358511yescharacteristic
868C22#358611yescharacteristic
869C4—22no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—82no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4#352112yes—
894C4#352112yes—
895C2—24no—
896C2—162no—
897C2#3514511yescharacteristic
898C2C2×#317411yescharacteristic
899C2#6070311yescharacteristic
900C2#6097711yescharacteristic
901C2#6097711yescharacteristic
902C2#6097911yescharacteristic
903C2#6097911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
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
1. #35315C2semidirect
3. #33274C2semidirect
4. #33271C2semidirect
5. #30395C2semidirect
6. #30355C2semidirect
7. #29529C2semidirect
8. #29508C2semidirect
9. #29443C2semidirect
10. #29442C2semidirect
11. #29335C2semidirect
12. #29298C2semidirect
15. #24609C2semidirect
16. #24601C2semidirect
19. #22084C2semidirect
20. #22078C2semidirect
23. #20469C2semidirect
34. #2647C22semidirect
35. #2645C22semidirect
36. #2645C22semidirect
45. #2642C22semidirect
58. #2330C22semidirect
59. #2327C22semidirect
60. #2320C22semidirect
61. #2320C22semidirect
71. #2099C22semidirect
73. #2088C22semidirect
74. #2088C22semidirect
75. #2085C22semidirect
77. #2068C22semidirect
79. #2066C22semidirect
81. #2059C22semidirect
84. #2043C22semidirect
93. #1944C22semidirect
94. #1943C22semidirect
95. #1942C22semidirect
96. #1941C22semidirect
97. #1941C22semidirect
98. #1941C22semidirect
103. #1935C22semidirect
104. #1935C22semidirect
105. #1935C22semidirect
106. #1935C22semidirect
109. #1933C22semidirect
110. #1933C22semidirect
113. #1920C22semidirect
114. #1919C22semidirect
121. #1865C22semidirect
122. #1863C22semidirect
131. #1768C22semidirect
132. #1768C22semidirect
137. #1746C22semidirect
138. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#353152
C2×#26442
#332742
#332712
#303952
#303552
#295292
#295082
#294432
#294422
#293352
#292982
#291102
#283022
#246092
#246012
#245072
#245012
#220842
#220782
#220492
#220432
#204692