Finite Group Databasebeta

← #7201228

Subgroups — #7201228

Order 512.

1852 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45645C211yesmaximal, characteristic, complemented
2#36103C211yesmaximal, characteristic, complemented
3#32979C212yesmaximal, complemented
4#32707C212yesmaximal, complemented
5#32259C211yesmaximal, characteristic, complemented
6#32072C212yesmaximal, complemented
7#31756C212yesmaximal, complemented
8#31666C211yesmaximal, characteristic, complemented
9#31332C212yesmaximal, complemented
10#31032C212yesmaximal, complemented
11#30775C212yesmaximal, complemented
12#27344C212yesmaximal, complemented
13#26801C212yesmaximal, complemented
14#26723C212yesmaximal, complemented
15#26310C212yesmaximal, complemented
16#25699C211yesmaximal, characteristic, complemented
17#24865C212yesmaximal, complemented
18#23960C211yesmaximal, characteristic, complemented
19#23307C211yesmaximal, characteristic, complemented
20C2×#547C2211yescharacteristic
21C2×#525—21no—
22C23×C4⋊C4C2211yescharacteristic, complemented
23C2×#498C2211yescharacteristic, complemented
24C2×#481C2212yes—
25C2×#481C2212yes—
26C2×#476C2211yescharacteristic, complemented
27C2×#447C2211yescharacteristic, complemented
28C22×#102C2211yescharacteristic, complemented
29#2849—21no—
30#2847C2212yes—
31#2847C2211yescharacteristic, complemented
32#2824—21no—
33#2753—22no—
34#2684—22no—
35#2679—21no—
36#2670—21no—
37#2563C2211yescharacteristic
38#2562C2212yes—
39#2501C2211yescharacteristic, complemented
40#2491C2212yes—
41#2490C2212yes—
42#2490C2212yes—
43#2486C2211yescharacteristic
44#2449—22no—
45#2443—22no—
46#2440C2212yescomplemented
47#2416C2212yes—
48#2413—21no—
49#2408C2212yes—
50#2408C2211yescharacteristic
51#2406—21no—
52#2375—21no—
53#2361C2212yescomplemented
54D4×C4⋊C4C2212yes—
55#2344C2211yescharacteristic, complemented
56C4×#120C2211yescharacteristic
57#2094C2212yescomplemented
58#2077C2212yescomplemented
59#2077C2212yescomplemented
60#2077C2212yescomplemented
61#2076C2212yescomplemented
62#2075C2212yescomplemented
63#2071C2212yescomplemented
64#2067C2212yescomplemented
65#2065C2212yescomplemented
66#2059C2212yescomplemented
67#2058C2212yescomplemented
68#2054C2212yescomplemented
69#2034C2212yes—
70#2034C2212yes—
71#2034C2212yescomplemented
72#2034C2212yescomplemented
73#2034C2212yescomplemented
74#2033C2212yes—
75#2033C2212yescomplemented
76#2025C2212yescomplemented
77#2023C2212yescomplemented
78#1999C2212yes—
79#1999C2212yes—
80#1999C2212yes—
81#1992C2212yescomplemented
82#1989C2212yescomplemented
83#1988C2211yescharacteristic, complemented
84#1972C2212yescomplemented
85#1955C2212yes—
86#1954C2211yescharacteristic
87#1948C2212yescomplemented
88#1936C2212yescomplemented
89#1934C2212yescomplemented
90#1926C2212yescomplemented
91#1926C2212yescomplemented
92#1926C2212yescomplemented
93#1924C2212yescomplemented
94#1924C2212yescomplemented
95#1923C2212yescomplemented
96#1920C2212yescomplemented
97#1919C2212yescomplemented
98#1893C2211yescharacteristic, complemented
99#1879C2212yescomplemented
100#1874C2212yes—
101#1874C2212yes—
102#1874C2212yes—
103#1874C2212yes—
104#1869C2211yescharacteristic
105#1869C2212yes—
106#1853C2212yescomplemented
107#1853C2212yescomplemented
108#1853C2212yescomplemented
109#1853C2212yescomplemented
110#1853C2212yescomplemented
111#1824C2212yescomplemented
112#1824C2212yescomplemented
113#1823C2211yescharacteristic, complemented
114#1807C2212yescomplemented
115#1786C2212yescomplemented
116#1779C2212yescomplemented
117#1776C2212yescomplemented
118C4×#102C2211yescharacteristic, complemented
119C22×#41—21no—
120C23×D4C2311yescharacteristic
121C24×C4—21no—
122C24×C4C2311yescharacteristic
123C22×D8C2312yes—
124C23×C8C2311yescharacteristic
125#547—42no—
126#547—42no—
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×#125C2312yes—
130C2×#124—22no—
131#525—48no—
132C2×#123—21no—
133C2×#123—21no—
134C2×#123—21no—
135C2×#123—21no—
136C2×#123—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—22no—
139C2×#121—22no—
140C2×#121C2311yescharacteristic
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×#121C2312yes—
145C2×#121C2311yescharacteristic
146C2×#120—21no—
147C2×#120—21no—
148C2×#120—22no—
149C2×#120—22no—
150C2×#120D411yescharacteristic
151C2×C4×D4—22no—
152C2×C4×D4—22no—
153C2×C4×D4C2311yescharacteristic
154C2×C4×D4C2312yes—
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—22no—
159C22×C4⋊C4—42no—
160C22×C4⋊C4—42no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166#498—42no—
167#481—44no—
168#481—44no—
169#476—42no—
170#447—42no—
171C2×#107C2312yes—
172C2×#106C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2311yescharacteristic
180C2×#102—42no—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2311yescharacteristic
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×#97C2312yes—
200C2×C4×C8C2311yescharacteristic
201#400—22no—
202#399—22no—
203#398—21no—
204#398—22no—
205#397—21no—
206#397—22no—
207#397—22no—
208#396—22no—
209#395—22no—
210#394—22no—
211#394—22no—
212#394—21no—
213#394—22no—
214#394—22no—
215#394—22no—
216#394—22no—
217#393—21no—
218#393—21no—
219#393—22no—
220#392—21no—
221#392—22no—
222#390—21no—
223#390—22no—
224#390—22no—
225#390C2312yes—
226#390C2312yes—
227#390C2312yes—
228#390C2312yes—
229#389—22no—
230#389C2312yes—
231#389C2312yes—
232#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#387—22no—
239#386—22no—
240#386—22no—
241#386—22no—
242#386—21no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386D411yescharacteristic
247#386D412yes—
248#385—22no—
249#385—22no—
250#385—22no—
251#385—22no—
252#385D411yescharacteristic
253#385D412yes—
254#384C2312yes—
255#382—21no—
256#381—21no—
257#381—21no—
258#380C2311yescharacteristic
259#380C2312yes—
260#380C2312yes—
261#380C2312yes—
262#380C2312yes—
263#380C2312yes—
264#380C2312yes—
265#380C2311yescharacteristic
266#379—22no—
267#379—21no—
268#379D411yescharacteristic
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2311yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C22⋊C4C2311yescharacteristic
273C4×C22⋊C4C2312yes—
274#340C2312yes—
275#340C2312yes—
276#340C2312yes—
277#340C2312yes—
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C25—21no—
292C25C2×D411yescharacteristic
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—82no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×D4—22no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—42no—
306C22×D4—41no—
307C22×D4—42no—
308C22×D4—41no—
309C22×D4C2×D412yes—
310C22×D4C2×D411yescharacteristic
311C22×D4C2411yescharacteristic
312C22×D4C2412yes—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—41no—
320C23×C4—41no—
321C23×C4—42no—
322C23×C4—42no—
323C23×C4—44no—
324C23×C4—44no—
325C23×C4—82no—
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D412yes—
328C23×C4C2412yes—
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C2×D8—42no—
332C2×D8—42no—
333C2×D8—42no—
334C22×C8—42no—
335C22×C8—41no—
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C4⋊Q8—22no—
341C4⋊Q8—41no—
342C4⋊Q8—41no—
343C4⋊Q8—41no—
344#125—42no—
345#125—42no—
346#124—84no—
347#123—44no—
348#123—44no—
349#123—44no—
350#123—44no—
351#123—82no—
352C22⋊Q8—48no—
353C22⋊Q8—44no—
354#121—22no—
355#121—42no—
356#121—42no—
357#121—41no—
358#121—41no—
359#121—41no—
360#121—48no—
361#121—42no—
362#121—42no—
363#121—42no—
364#121—42no—
365#121—42no—
366#121—42no—
367#120—24no—
368#120—44no—
369#120—44no—
370#120—84no—
371#120—84no—
372C4×D4—22no—
373C4×D4—41no—
374C4×D4—42no—
375C4×D4—42no—
376C4×D4—41no—
377C4×D4—41no—
378C4×D4—48no—
379C4×D4—48no—
380#117—44no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4—48no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2411yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C22⋊C4C2×D411yescharacteristic
444C2×C22⋊C4C2×D412yes—
445C2×C22⋊C4C2×D412yes—
446C2×C22⋊C4C2×D411yescharacteristic
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—21no—
450C2×C42C2411yescharacteristic
451C2×C42C2412yes—
452#107—42no—
453#106—24no—
454#106—24no—
455#106—42no—
456#106—42no—
457#106—42no—
458#106—42no—
459C4⋊C8—42no—
460C4⋊C8—41no—
461#102—24no—
462#102—24no—
463#102—42no—
464#102—42no—
465#102—42no—
466#102—42no—
467#102—42no—
468#102—42no—
469#102—42no—
470#102—42no—
471C22⋊C8—42no—
472C22⋊C8—42no—
473C22⋊C8—42no—
474C22⋊C8—42no—
475C22⋊C8—42no—
476C22⋊C8—41no—
477C22⋊C8—42no—
478C22⋊C8—42no—
479#97—42no—
480C4×C8—41no—
481#95—22no—
482#95—21no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—21no—
489#95—22no—
490#95—22no—
491#95—21no—
492#95—22no—
493#95—22no—
494#95C2×D412yes—
495#95C2×D412yes—
496#95C2×D412yes—
497C24—22no—
498C24—24no—
499C24—21no—
500C24—22no—
501C24—41no—
502C24—42no—
503C24—41no—
504C24—42no—
505C24—81no—
506C24—82no—
507C24—82no—
508C24—81no—
509C24C22×D411yescharacteristic
510C24C22×D411yescharacteristic
511C24C22×D412yes—
512#41—816no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—81no—
516C2×Q8—82no—
517C2×Q8—81no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—42no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—42no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—44no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—81no—
546C2×D4—82no—
547C2×D4—82no—
548C2×D4—84no—
549C2×D4—81no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4AGL(1,ℤ/8)14yes—
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
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—21no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—81no—
605C22×C4—816no—
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C2511yescharacteristic
614D8—84no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—82no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—42no—
644C4⋊C4—41no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—81no—
657C4⋊C4H(5,𝔽2)12yes—
658C4⋊C4H(5,𝔽2)12yes—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—42no—
672C22⋊C4—44no—
673C22⋊C4—42no—
674C22⋊C4—44no—
675C22⋊C4—42no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C42—21no—
691C42—21no—
692C42—22no—
693C42—22no—
694C42—44no—
695C42—81no—
696C42—82no—
697C23—21no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—48no—
712C23—44no—
713C23—44no—
714C23—48no—
715C23—44no—
716C23—41no—
717C23—42no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—84no—
729C23—164no—
730C23—162no—
731C23—164no—
732C23—162no—
733C23C2×AGL(1,ℤ/8)12yes—
734C23C2×AGL(1,ℤ/8)12yes—
735C23#57714yes—
736C23C23×D411yescharacteristic
737Q8—84no—
738Q8—162no—
739D4—44no—
740D4—48no—
741D4—41no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—41no—
746D4—42no—
747D4—42no—
748D4—84no—
749D4—84no—
750D4—88no—
751D4—84no—
752D4—164no—
753D4—164no—
754D4—164no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
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—48no—
775C2×C4—48no—
776C2×C4—44no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—88no—
812C2×C4—88no—
813C2×C4—84no—
814C2×C4C2×AGL(1,ℤ/8)12yes—
815C2×C4C2×H(5,𝔽2)11yescharacteristic
816C2×C4C2×H(5,𝔽2)11yescharacteristic
817C2×C4#58512yes—
818C2×C4#58512yes—
819C8—42no—
820C8—42no—
821C8—42no—
822C8—42no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—22no—
828C22—22no—
829C22—24no—
830C22—416no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—81no—
849C22—81no—
850C22—82no—
851C22—82no—
852C22—81no—
853C22—168no—
854C22#348411yescharacteristic
855C22#348512yes—
856C22C22×AGL(1,ℤ/8)11yescharacteristic
857C22C2×#57712yes—
858C22#358511yescharacteristic
859C4—22no—
860C4—42no—
861C4—42no—
862C4—41no—
863C4—42no—
864C4—41no—
865C4—42no—
866C4—42no—
867C4—41no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4—82no—
874C4#352911yescharacteristic
875C4#354012yes—
876C4#354011yescharacteristic
877C2—44no—
878C2—42no—
879C2—42no—
880C2—161no—
881C2—162no—
882C2#4544211yescharacteristic
883C2#6157111yescharacteristic
884C2#6163311yescharacteristic
885C2#6172812yes—
886C2#6174612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45645C2semidirect
2. #36103C2semidirect
3. #32979C2semidirect
4. #32707C2semidirect
5. #32259C2semidirect
6. #32072C2semidirect
7. #31756C2semidirect
8. #31666C2semidirect
9. #31332C2semidirect
10. #31032C2semidirect
11. #30775C2semidirect
12. #27344C2semidirect
13. #26801C2semidirect
14. #26723C2semidirect
15. #26310C2semidirect
16. #25699C2semidirect
17. #24865C2semidirect
18. #23960C2semidirect
19. #23307C2semidirect
22. C23×C4⋊C4C22semidirect
23. C2×#498C22semidirect
26. C2×#476C22semidirect
27. C2×#447C22semidirect
28. C22×#102C22semidirect
31. #2847C22semidirect
39. #2501C22semidirect
46. #2440C22semidirect
53. #2361C22semidirect
55. #2344C22semidirect
57. #2094C22semidirect
58. #2077C22semidirect
59. #2077C22semidirect
60. #2077C22semidirect
61. #2076C22semidirect
62. #2075C22semidirect
63. #2071C22semidirect
64. #2067C22semidirect
65. #2065C22semidirect
66. #2059C22semidirect
67. #2058C22semidirect
68. #2054C22semidirect
71. #2034C22semidirect
72. #2034C22semidirect
73. #2034C22semidirect
75. #2033C22semidirect
76. #2025C22semidirect
77. #2023C22semidirect
81. #1992C22semidirect
82. #1989C22semidirect
83. #1988C22semidirect
84. #1972C22semidirect
87. #1948C22semidirect
88. #1936C22semidirect
89. #1934C22semidirect
90. #1926C22semidirect
91. #1926C22semidirect
92. #1926C22semidirect
93. #1924C22semidirect
94. #1924C22semidirect
95. #1923C22semidirect
96. #1920C22semidirect
97. #1919C22semidirect
98. #1893C22semidirect
99. #1879C22semidirect
106. #1853C22semidirect
107. #1853C22semidirect
108. #1853C22semidirect
109. #1853C22semidirect
110. #1853C22semidirect
111. #1824C22semidirect
112. #1824C22semidirect
113. #1823C22semidirect
114. #1807C22semidirect
115. #1786C22semidirect
116. #1779C22semidirect
117. #1776C22semidirect
118. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#456452
#361032
#329792
#327072
#322592
#320722
#317562
#316662
#313322
#310322
#307752
#273442
#268012
#267232
#263102
#256992
#248652
#239602
#233072