Finite Group Databasebeta

← #7594055

Subgroups — #7594055

Order 512.

1788 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59313C211yesmaximal, characteristic
2#59305C211yesmaximal, characteristic, complemented
3#31934C212yesmaximal, complemented
4#31690C212yesmaximal, complemented
5#28845C212yesmaximal, complemented
6#28791C211yesmaximal, characteristic, complemented
7#28141C211yesmaximal, characteristic, complemented
8#27697C212yesmaximal, complemented
9#27678C211yesmaximal, characteristic, complemented
10#27647C211yesmaximal, characteristic, complemented
11#26110C211yesmaximal, characteristic, complemented
12#26022C211yesmaximal, characteristic, complemented
13#25531C212yesmaximal, complemented
14#25236C212yesmaximal, complemented
15#24969C211yesmaximal, characteristic, complemented
16#24967C211yesmaximal, characteristic, complemented
17#24937C212yesmaximal, complemented
18#22770C211yesmaximal, characteristic, complemented
19#22703C211yesmaximal, characteristic, complemented
20#22485C212yesmaximal, complemented
21C4×#465C211yesmaximal, characteristic, complemented
22C8×#121C211yesmaximal, characteristic, complemented
23C2×#1834C211yesmaximal, characteristic, complemented
24C2×#547—21no—
25C2×#547C2212yes—
26C2×#483C2212yes—
27C2×#465C2211yescharacteristic
28C2×C4×SD16C2211yescharacteristic
29C2×C8×D4C2211yescharacteristic
30C2×C8×D4C2212yes—
31C22×C4×C8C2211yescharacteristic
32#2790—22no—
33#2680—22no—
34#2579—22no—
35#2566—21no—
36#2552C2211yescharacteristic
37#2551C2211yescharacteristic
38#2538C2211yescharacteristic
39#2537C2211yescharacteristic
40#2507—21no—
41#2502C2212yes—
42#2497C2212yes—
43#2486—21no—
44#2486C2212yes—
45#2442—21no—
46#2440—21no—
47#2440C2212yes—
48#2422—21no—
49#2422C2212yes—
50#2417C2212yes—
51#2406—22no—
52#2361—21no—
53#2355C2211yescharacteristic
54D4×C4⋊C4C2211yescharacteristic
55D4×C4⋊C4C2212yes—
56D4×C4⋊C4C2211yescharacteristic
57D4×C4⋊C4C2211yescharacteristic
58C4×C22⋊Q8C2211yescharacteristic
59C4×#121C2211yescharacteristic
60C4×#121C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63#2100C2212yes—
64#2100C2212yes—
65#2094C2212yes—
66#2088C2212yes—
67#2084C2212yes—
68#2084C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2077C2212yes—
72#2072C2212yes—
73#2066C2212yes—
74#2058C2212yes—
75#2035C2212yes—
76#2034C2212yes—
77#2024C2212yes—
78#2000C2212yes—
79#1990C2212yes—
80#1988C2212yes—
81#1968C2211yescharacteristic
82#1954C2211yescharacteristic
83#1948C2211yescharacteristic
84#1948C2211yescharacteristic
85#1948C2211yescharacteristic
86#1948C2211yescharacteristic
87#1941C2211yescharacteristic
88#1941C2212yes—
89#1939C2211yescharacteristic
90#1934C2211yescharacteristic
91#1933C2211yescharacteristic
92#1933C2212yes—
93#1923C2212yes—
94#1919C2212yes—
95#1919C2212yes—
96#1893C2211yescharacteristic
97#1893C2212yes—
98#1892C2211yescharacteristic
99#1892C2212yes—
100#1877C2212yes—
101#1874C2212yes—
102#1874C2212yes—
103#1872C2212yes—
104#1869C2212yes—
105#1864C2212yes—
106#1853C2212yes—
107#1853C2212yes—
108#1853C2212yes—
109#1834C2212yes—
110#1834C2211yescharacteristic
111#1834C2211yescharacteristic
112#1834C2211yescharacteristic
113#1834C2211yescharacteristic
114#1834C2212yes—
115#1824C2212yes—
116#1823C2212yes—
117#1823C2212yes—
118#1807C2211yescharacteristic
119#1807C2212yes—
120#1803C2211yescharacteristic
121#1803C2211yescharacteristic
122#1802C2211yescharacteristic
123#1802C2211yescharacteristic
124#1802C2212yes—
125#1797C2211yescharacteristic
126C4×#106C2211yescharacteristic
127C8×C4⋊C4C2211yescharacteristic
128C4×#103C2211yescharacteristic
129C4×#102C2211yescharacteristic
130C4×#102C2212yes—
131C8×C22⋊C4C2212yes—
132C2×#340C2212yes—
133C2×#340C2212yes—
134C2×#340C2212yes—
135C22×#41—22no—
136C22×SD16C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2312yes—
140#547—28no—
141#547—44no—
142#547—48no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2312yes—
145C2×#125—21no—
146C2×#123—22no—
147C2×#123—22no—
148C2×#123—22no—
149C2×#123—22no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8C2311yescharacteristic
153C2×C22⋊Q8C2312yes—
154C2×#121—21no—
155C2×#121D411yescharacteristic
156C2×#121C2312yes—
157C2×#121C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4—22no—
163C2×C4×D4C2311yescharacteristic
164C2×C4×D4C2312yes—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2312yes—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C42C2311yescharacteristic
177#483—44no—
178#465—24no—
179C4×SD16—24no—
180C8×D4—24no—
181C8×D4—44no—
182C2×#106C2311yescharacteristic
183C2×#106C2311yescharacteristic
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2311yescharacteristic
188C2×#106C2312yes—
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2312yes—
192C2×#103C2311yescharacteristic
193C2×#103C2311yescharacteristic
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2311yescharacteristic
197C2×#102C2311yescharacteristic
198C2×#102C2311yescharacteristic
199C2×#102C2312yes—
200C2×#102C2311yescharacteristic
201C2×#102C2312yes—
202C2×C22⋊C8C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C4×C8—24no—
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2312yes—
211C2×C4×C8C2311yescharacteristic
212#400—22no—
213#398—22no—
214#398—22no—
215#398—22no—
216#398—22no—
217#398—22no—
218#398—22no—
219#397—22no—
220#397—22no—
221#396—22no—
222#396—22no—
223#396—22no—
224#395—22no—
225#395—22no—
226#394—22no—
227#394—22no—
228#391C2312yes—
229#391C2311yescharacteristic
230#390—21no—
231#390D411yescharacteristic
232#390C2311yescharacteristic
233#389—21no—
234#389—21no—
235#389—22no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389D411yescharacteristic
240#389C2312yes—
241#389C2312yes—
242#389C2311yescharacteristic
243#389C2312yes—
244#389C2311yescharacteristic
245#388—22no—
246#388—21no—
247#388D412yes—
248#387—21no—
249#387—22no—
250#387—22no—
251#386—22no—
252#386—21no—
253#386D412yes—
254#385—21no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#385—22no—
263#385—22no—
264#384—21no—
265#384—21no—
266#384—21no—
267#384—21no—
268#384C2312yes—
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#384C2311yescharacteristic
272#384C2311yescharacteristic
273#384C2312yes—
274#384C2312yes—
275#382—21no—
276#381—22no—
277#380—21no—
278#380—21no—
279#380—22no—
280#380D411yescharacteristic
281#380C2312yes—
282#380C2312yes—
283#380C2311yescharacteristic
284#380C2311yescharacteristic
285#380C2312yes—
286#380C2312yes—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C22⋊C4—21no—
294C4×C22⋊C4—21no—
295C4×C22⋊C4C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321C2×#41—48no—
322C2×#41—48no—
323C2×#41—84no—
324C22×Q8—22no—
325C22×Q8C2411yescharacteristic
326C22×D4—21no—
327C22×D4—22no—
328C22×D4C2×D411yescharacteristic
329C22×D4C2×D412yes—
330C22×D4C2411yescharacteristic
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—21no—
336C23×C4—22no—
337C23×C4C2×D411yescharacteristic
338C23×C4C2×D411yescharacteristic
339C23×C4C2412yes—
340C23×C4C2411yescharacteristic
341C2×SD16—22no—
342C2×SD16—22no—
343C2×SD16—41no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—24no—
349C22×C8—41no—
350C22×C8—41no—
351C22×C8—42no—
352C22×C8—42no—
353C22×C8C2411yescharacteristic
354C22×C8C2412yes—
355C22×C8C2411yescharacteristic
356C22×C8C2412yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C4⋊Q8—24no—
360C4⋊Q8—42no—
361C4⋊Q8—44no—
362#125—82no—
363#123—48no—
364#123—48no—
365#123—48no—
366#123—48no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—48no—
370C22⋊Q8—48no—
371C22⋊Q8—42no—
372C22⋊Q8—42no—
373#121—22no—
374#121—24no—
375#121—42no—
376#121—44no—
377#121SD1618yescomplemented
378#121#4114yes—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—24no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—42no—
389C4×D4—44no—
390C4×D4—44no—
391C4×D4—82no—
392C4×D4—84no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—44no—
429C2×C4⋊C4—44no—
430C2×C4⋊C4—82no—
431C2×C4⋊C4—82no—
432C2×C4⋊C4—82no—
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C22⋊C4C2×D412yes—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2412yes—
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477#106—22no—
478#106—22no—
479#106—42no—
480#106—41no—
481#106—42no—
482#106—42no—
483#106—42no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—42no—
487#103—22no—
488#103—22no—
489#103—41no—
490#103—42no—
491#103—42no—
492#102—22no—
493#102—22no—
494#102—42no—
495#102—41no—
496#102—42no—
497C22⋊C8—24no—
498C22⋊C8—24no—
499C22⋊C8—42no—
500C22⋊C8—42no—
501C4×C8—22no—
502C4×C8—22no—
503C4×C8—22no—
504C4×C8—42no—
505C4×C8#4114yescomplemented
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—21no—
515#95—21no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95C2×D412yes—
525#95C2×D412yes—
526#95C2×D412yes—
527C24—21no—
528C24C22×D412yes—
529C24C22×D411yescharacteristic
530#41—832no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—82no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—82no—
555C2×D4C2×SD1614yes—
556C2×D4C2×SD1618yes—
557C2×D4C2×#4112yes—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4C2×SD1614yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C2×#4112yes—
612C22×C4H(5,𝔽2)12yes—
613C22×C4C2511yescharacteristic
614SD16—44no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—22no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—22no—
631C2×C8—44no—
632C2×C8—44no—
633C2×C8—84no—
634C2×C8C2×#4112yes—
635C2×C8C2×#4112yes—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C4⋊C4—81no—
677C4⋊C4—81no—
678C4⋊C4—82no—
679C4⋊C4—81no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4C2×SD1614yes—
686C4⋊C4C2×#4112yes—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4C2×SD1618yes—
706C42—22no—
707C42—22no—
708C42—21no—
709C42—22no—
710C42—22no—
711C42—21no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—82no—
716C42C2×#4112yes—
717C422−1+412yes—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23#54612yes—
736C23C22×SD1614yes—
737C23C22×SD1612yes—
738C23#57612yes—
739C23C23×D411yescharacteristic
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—88no—
745D4—216no—
746D4—28no—
747D4—22no—
748D4—22no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—88no—
753C2×C4—28no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—88no—
813C2×C4—88no—
814C2×C4—88no—
815C2×C4—84no—
816C2×C4—164no—
817C2×C4—164no—
818C2×C4#54612yes—
819C2×C4#54712yes—
820C2×C4#54712yes—
821C2×C4C22×SD1612yes—
822C2×C4C22×SD1614yes—
823C2×C4C22×SD1612yes—
824C2×C4#57712yes—
825C2×C4#57812yes—
826C2×C4C22×#4111yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C2×H(5,𝔽2)11yescharacteristic
829C2×C4C2×2−1+411yescharacteristic
830C2×C4#58511yescharacteristic
831C2×C4#58511yescharacteristic
832C8—22no—
833C8—22no—
834C8—41no—
835C8—41no—
836C8—42no—
837C8—42no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22#329514yes—
859C22C2×#54611yescharacteristic
860C22C2×#54711yescharacteristic
861C22#350011yescharacteristic
862C22C23×SD1611yescharacteristic
863C22C2×#57611yescharacteristic
864C22C2×#57711yescharacteristic
865C22C2×#57811yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—24no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—81no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—82no—
879C4—82no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—82no—
884C4#333514yes—
885C4#347511yescharacteristic
886C4#349411yescharacteristic
887C4#351511yescharacteristic
888C4#355911yescharacteristic
889C2—24no—
890C2—44no—
891C2—82no—
892C2#5931811yescharacteristic
893C2C2×#329511yescharacteristic
894C2#6121711yescharacteristic
895C2C2×#333511yescharacteristic
896C2#6125811yescharacteristic
897C2#6252611yescharacteristic
898C2#6255211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59313C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59305C2semidirect
3. #31934C2semidirect
4. #31690C2semidirect
5. #28845C2semidirect
6. #28791C2semidirect
7. #28141C2semidirect
8. #27697C2semidirect
9. #27678C2semidirect
10. #27647C2semidirect
11. #26110C2semidirect
12. #26022C2semidirect
13. #25531C2semidirect
14. #25236C2semidirect
15. #24969C2semidirect
16. #24967C2semidirect
17. #24937C2semidirect
18. #22770C2semidirect
19. #22703C2semidirect
20. #22485C2semidirect
21. C4×#465C2semidirect
22. C8×#121C2semidirect
23. C2×#1834C2semidirect
377. #121SD16semidirect
505. C4×C8#41semidirect

Maximal subgroups

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

subgroupindex
#593132
#593052
#319342
#316902
#288452
#287912
#281412
#276972
#276782
#276472
#261102
#260222
#255312
#252362
#249692
#249672
#249372
#227702
#227032
#224852
C4×#4652
C8×#1212
C2×#18342