Finite Group Databasebeta

← #7610869

Subgroups — #7610869

Order 512.

1731 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59302C211yesmaximal, characteristic, complemented
2#59125C211yesmaximal, characteristic
3#32053C212yesmaximal, complemented
4#31424C212yesmaximal, complemented
5#28565C212yesmaximal, complemented
6#28092C212yesmaximal, complemented
7#27736C211yesmaximal, characteristic, complemented
8#27722C212yesmaximal, complemented
9#27677C211yesmaximal, characteristic, complemented
10#26509C211yesmaximal, characteristic, complemented
11#26301C211yesmaximal, characteristic, complemented
12#26212C212yesmaximal, complemented
13#26204C212yesmaximal, complemented
14#25348C211yesmaximal, characteristic, complemented
15#24678C211yesmaximal, characteristic, complemented
16#24301C211yesmaximal, characteristic, complemented
17#24120C211yesmaximal, characteristic, complemented
18#23068C211yesmaximal, characteristic, complemented
19#22711C212yesmaximal, complemented
20#22500C211yesmaximal, characteristic, complemented
21C4×#465C211yesmaximal, characteristic, complemented
22#21487C211yesmaximal, characteristic, complemented
23C2×#1990C211yesmaximal, characteristic, complemented
24C2×#548—21no—
25C2×#547C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#475C2211yescharacteristic
28C2×#475C2211yescharacteristic
29C2×#465C2211yescharacteristic
30C2×C4×SD16C2211yescharacteristic
31C2×#436C2211yescharacteristic
32C2×#435C2212yes—
33C22×C4×C8C2211yescharacteristic
34#2793—22no—
35#2674—22no—
36#2571C2211yescharacteristic
37#2570—21no—
38#2547C2211yescharacteristic
39#2542C2211yescharacteristic
40#2538C2211yescharacteristic
41#2512—21no—
42#2504—21no—
43#2499C2212yes—
44#2496C2212yes—
45#2491C2212yes—
46#2481—22no—
47#2443—22no—
48#2440C2212yes—
49#2432—21no—
50#2429—21no—
51#2417C2212yes—
52#2416C2212yes—
53#2409—21no—
54#2365C2211yescharacteristic
55#2355C2211yescharacteristic
56#2354C2211yescharacteristic
57#2352C2212yes—
58D4×C4⋊C4C2212yes—
59#2345—21no—
60C4×C22⋊Q8C2211yescharacteristic
61C4×#121C2211yescharacteristic
62C4×#121C2211yescharacteristic
63C2×#384C2211yescharacteristic
64#2101C2212yes—
65#2100C2212yes—
66#2099C2212yes—
67#2093C2212yes—
68#2088C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2076C2212yes—
72#2073C2212yes—
73#2072C2212yes—
74#2058C2212yes—
75#2055C2212yes—
76#2036C2212yes—
77#2034C2212yes—
78#2024C2212yes—
79#2000C2212yes—
80#1990C2211yescharacteristic
81#1990C2211yescharacteristic
82#1990C2212yes—
83#1990C2211yescharacteristic
84#1990C2212yes—
85#1990C2211yescharacteristic
86#1988C2211yescharacteristic
87#1988C2211yescharacteristic
88#1968C2211yescharacteristic
89#1954C2211yescharacteristic
90#1949C2212yes—
91#1948C2212yes—
92#1947C2211yescharacteristic
93#1947C2211yescharacteristic
94#1941C2211yescharacteristic
95#1939C2211yescharacteristic
96#1936C2212yes—
97#1935C2212yes—
98#1934C2211yescharacteristic
99#1933C2211yescharacteristic
100#1928C2212yes—
101#1926C2212yes—
102#1923C2212yes—
103#1921C2212yes—
104#1920C2212yes—
105#1895C2212yes—
106#1894C2212yes—
107#1893C2211yescharacteristic
108#1892C2211yescharacteristic
109#1875C2212yes—
110#1874C2212yes—
111#1872C2212yes—
112#1872C2212yes—
113#1869C2212yes—
114#1854C2212yes—
115#1853C2212yes—
116#1853C2212yes—
117#1852C2212yes—
118#1836C2212yes—
119#1825C2212yes—
120#1824C2212yes—
121#1809C2212yes—
122#1807C2211yescharacteristic
123#1802C2211yescharacteristic
124#1802C2211yescharacteristic
125#1797C2211yescharacteristic
126#1776C2212yes—
127C4×#106C2211yescharacteristic
128#1770C2211yescharacteristic
129C4×#103C2211yescharacteristic
130C4×#102C2211yescharacteristic
131#1753C2212yes—
132#1736C2212yes—
133C2×#340C2212yes—
134C2×#340C2212yes—
135C22×#41—21no—
136C23×Q8—21no—
137C22×SD16C2311yescharacteristic
138C22×M16C2312yes—
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#548—48no—
142#547—24no—
143#547—42no—
144C2×C4⋊Q8—24no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—42no—
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2312yes—
150C2×C4⋊Q8C2311yescharacteristic
151C2×#126—22no—
152C2×#124—21no—
153C2×#124—22no—
154C2×#123—22no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8C2311yescharacteristic
160C2×C22⋊Q8C2312yes—
161C2×#121—22no—
162C2×#121D411yescharacteristic
163C2×#121C2311yescharacteristic
164C2×#121C2312yes—
165C2×C4×Q8—21no—
166C2×C4×Q8C2311yescharacteristic
167C2×C4×D4—22no—
168C2×C4×D4—21no—
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2312yes—
171C2×C4×D4C2311yescharacteristic
172C2×#117C2312yes—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C42C2311yescharacteristic
180#475—24no—
181#475—42no—
182#465—24no—
183C4×SD16—42no—
184#436—42no—
185#435—28no—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#106C2312yes—
189C2×#106C2311yescharacteristic
190C2×#106C2312yes—
191C2×#106C2311yescharacteristic
192C2×#106C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2312yes—
196C2×#103C2312yes—
197C2×#103C2311yescharacteristic
198C2×#103C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#102C2311yescharacteristic
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2311yescharacteristic
205C2×#102C2311yescharacteristic
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×#97C2312yes—
211C2×C4×C8—42no—
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216#400—22no—
217#400—22no—
218#399—22no—
219#398—22no—
220#398—22no—
221#397—22no—
222#397—22no—
223#397—22no—
224#397—22no—
225#396—22no—
226#396—22no—
227#396—22no—
228#395—22no—
229#394—22no—
230#394—22no—
231#393—22no—
232#391—21no—
233#391—21no—
234#391C2312yes—
235#391C2311yescharacteristic
236#390—21no—
237#390—21no—
238#390D411yescharacteristic
239#390C2312yes—
240#390C2311yescharacteristic
241#389—21no—
242#389—21no—
243#389—22no—
244#389D411yescharacteristic
245#389C2311yescharacteristic
246#389C2312yes—
247#389C2312yes—
248#389C2311yescharacteristic
249#388—22no—
250#388—22no—
251#388—21no—
252#388—22no—
253#388D412yes—
254#387—22no—
255#387—21no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#386—22no—
262#386—22no—
263#386—21no—
264#386—22no—
265#386D412yes—
266#385—21no—
267#385—22no—
268#385—22no—
269#385—22no—
270#384—21no—
271#384—21no—
272#384C2311yescharacteristic
273#384C2311yescharacteristic
274#384C2312yes—
275#384C2312yes—
276#382—21no—
277#382—21no—
278#382C2312yes—
279#380—22no—
280#380D411yescharacteristic
281#380C2311yescharacteristic
282#380C2311yescharacteristic
283#380C2312yes—
284#380C2312yes—
285#380C2312yes—
286#380C2312yes—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C22⋊C4—21no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—21no—
298C4×C22⋊C4C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324C2×#41—44no—
325C2×#41—44no—
326C2×#41—82no—
327C22×Q8—21no—
328C22×Q8—21no—
329C22×Q8—22no—
330C22×Q8—44no—
331C22×Q8—44no—
332C22×Q8—82no—
333C22×Q8C2411yescharacteristic
334C22×D4—21no—
335C22×D4—22no—
336C22×D4C2×D412yes—
337C22×D4C2×D411yescharacteristic
338C22×D4C2411yescharacteristic
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—21no—
343C23×C4C2×D411yescharacteristic
344C23×C4C2×D411yescharacteristic
345C23×C4C2412yes—
346C23×C4C2411yescharacteristic
347C2×SD16—22no—
348C2×SD16—41no—
349C2×SD16—41no—
350C2×M16—24no—
351C2×M16—42no—
352C2×M16—42no—
353C22×C8—22no—
354C22×C8—41no—
355C22×C8—41no—
356C22×C8—41no—
357C22×C8—41no—
358C22×C8#4114yescomplemented
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C4⋊Q8—24no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—42no—
370C4⋊Q8—44no—
371C4⋊Q8—44no—
372C4⋊Q8#4114yes—
373#126—84no—
374#124—48no—
375#124—44no—
376#123—48no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—48no—
380C22⋊Q8—44no—
381C22⋊Q8—44no—
382C22⋊Q8—42no—
383C22⋊Q8—42no—
384C22⋊Q8—82no—
385#121—24no—
386#121—22no—
387#121—22no—
388#121—24no—
389#121—42no—
390#121—48no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—44no—
394C4×D4—24no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—48no—
401C4×D4—44no—
402#117—42no—
403#117—42no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
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—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—82no—
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2412yes—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C22⋊C4C2×D412yes—
468C2×C22⋊C4C2×D412yes—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—42no—
483#107—42no—
484#106—22no—
485#106—24no—
486#106—41no—
487#106—41no—
488#106—42no—
489C4⋊C8—24no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492#103—22no—
493#103—24no—
494#103—41no—
495#103—41no—
496#103—42no—
497#102—22no—
498#102—42no—
499#102—42no—
500#102—41no—
501#102—41no—
502C22⋊C8—24no—
503C22⋊C8—24no—
504C22⋊C8—42no—
505C22⋊C8—42no—
506#97—24no—
507C4×C8—22no—
508C4×C8—22no—
509C4×C8—41no—
510C4×C8—41no—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—21no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534C24—21no—
535C24C22×D412yes—
536C24C22×D411yescharacteristic
537#41—816no—
538C2×Q8—24no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—44no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8—44no—
549C2×Q8—42no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—82no—
553C2×Q8—816no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—82no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4AGL(1,ℤ/8)14yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4112yes—
620C22×C42−1+412yes—
621C22×C4C2511yescharacteristic
622SD16—44no—
623M16—84no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—44no—
641C2×C8—44no—
642C2×C8C2×#4112yes—
643C2×C8C2×#4112yes—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—44no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—82no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4C2×#4114yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—21no—
714C42—21no—
715C42—22no—
716C42—44no—
717C42—42no—
718C42—42no—
719C42—42no—
720C42—82no—
721C42—82no—
722C42C2×#4112yes—
723C42H(5,𝔽2)12yes—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#54712yes—
743C23C2×AGL(1,ℤ/8)12yes—
744C23#57812yes—
745C23C23×D411yescharacteristic
746Q8—48no—
747Q8—41no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751Q8—88no—
752Q8—84no—
753D4—48no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—44no—
759D4—88no—
760D4—84no—
761C2×C4—28no—
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—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
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—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—88no—
822C2×C4—88no—
823C2×C4—84no—
824C2×C4—164no—
825C2×C4#54612yes—
826C2×C4#54612yes—
827C2×C4#54712yes—
828C2×C4C2×AGL(1,ℤ/8)12yes—
829C2×C4C2×AGL(1,ℤ/8)12yes—
830C2×C4#57712yes—
831C2×C4#57712yes—
832C2×C4C22×#4111yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4C2×H(5,𝔽2)11yescharacteristic
835C2×C4C2×2−1+411yescharacteristic
836C2×C4#58511yescharacteristic
837C2×C4#58511yescharacteristic
838C8—22no—
839C8—22no—
840C8—42no—
841C8—42no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22#335314yes—
865C22C2×#54611yescharacteristic
866C22C2×#54711yescharacteristic
867C22#350011yescharacteristic
868C22C22×AGL(1,ℤ/8)11yescharacteristic
869C22C2×#57711yescharacteristic
870C22C2×#57711yescharacteristic
871C22C2×#57811yescharacteristic
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—82no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—82no—
889C4—81no—
890C4#331014yes—
891C4#348011yescharacteristic
892C4#350511yescharacteristic
893C4#351611yescharacteristic
894C4#354111yescharacteristic
895C2—24no—
896C2—82no—
897C2—161no—
898C2#5980611yescharacteristic
899C2C2×#331011yescharacteristic
900C2#6116811yescharacteristic
901C2C2×#335311yescharacteristic
902C2#6128811yescharacteristic
903C2#6254111yescharacteristic
904C2#6255311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59125C2
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
1. #59302C2semidirect
3. #32053C2semidirect
4. #31424C2semidirect
5. #28565C2semidirect
6. #28092C2semidirect
7. #27736C2semidirect
8. #27722C2semidirect
9. #27677C2semidirect
10. #26509C2semidirect
11. #26301C2semidirect
12. #26212C2semidirect
13. #26204C2semidirect
14. #25348C2semidirect
15. #24678C2semidirect
16. #24301C2semidirect
17. #24120C2semidirect
18. #23068C2semidirect
19. #22711C2semidirect
20. #22500C2semidirect
21. C4×#465C2semidirect
22. #21487C2semidirect
23. C2×#1990C2semidirect
358. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
#593022
#591252
#320532
#314242
#285652
#280922
#277362
#277222
#276772
#265092
#263012
#262122
#262042
#253482
#246782
#243012
#241202
#230682
#227112
#225002
C4×#4652
#214872
C2×#19902