Finite Group Databasebeta

← #6627447

Subgroups — #6627447

Order 512.

1412 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36600C211yesmaximal, characteristic
2C4×#557C211yesmaximal, characteristic
3#33200C212yesmaximal
4#33200C211yesmaximal, characteristic
5#29291C212yesmaximal
6#29288C211yesmaximal, characteristic
7#29221C212yesmaximal
8#29220C211yesmaximal, characteristic
9#26517C212yesmaximal
10#26515C212yesmaximal
11#26510C211yesmaximal, characteristic
12#26506C211yesmaximal, characteristic
13#26116C212yesmaximal
14#26114C212yesmaximal
15#26112C211yesmaximal, characteristic
16#26108C211yesmaximal, characteristic
17#22741C211yesmaximal, characteristic
18#22739C211yesmaximal, characteristic
19Q8×C4⋊C8C211yesmaximal, characteristic
20#22521C211yesmaximal, characteristic
21#22521C211yesmaximal, characteristic
22C4×#479C211yesmaximal, characteristic
23C4×#479C212yesmaximal
24C2×#557C2211yescharacteristic
25C2×#479C2211yescharacteristic
26C2×#479C2212yes—
27C2×C8×Q8C2211yescharacteristic
28C2×C8×Q8C2211yescharacteristic
29#2859C2211yescharacteristic
30#2859C2212yes—
31#2585—22no—
32#2585—22no—
33#2570C2212yes—
34#2570C2212yes—
35#2552C2211yescharacteristic
36#2552C2211yescharacteristic
37#2453—21no—
38#2453—21no—
39#2370—22no—
40#2370—21no—
41#2370—21no—
42#2370C2212yes—
43#2365—21no—
44#2365C2211yescharacteristic
45#2355—21no—
46#2355C2211yescharacteristic
47#2355C2211yescharacteristic
48#2355C2211yescharacteristic
49#2351C2212yes—
50Q8×C4⋊C4C2211yescharacteristic
51C4×C4⋊Q8—21no—
52C4×C4⋊Q8C2211yescharacteristic
53C4×#125—22no—
54C4×#125C2212yes—
55C4×#125C2211yescharacteristic
56C4×#125C2212yes—
57C42×Q8—21no—
58C42×Q8C2212yes—
59C42×Q8C2211yescharacteristic
60C42×Q8C2211yescharacteristic
61#2101C2212yes—
62#2101C2212yes—
63#2100C2212yes—
64#2100C2212yes—
65#2099C2212yes—
66#2099C2212yes—
67#2088C2212yes—
68#2088C2212yes—
69#2088C2212yes—
70#2087C2212yes—
71#2087C2212yes—
72#2086C2212yes—
73#1991C2212yes—
74#1991C2212yes—
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1989C2212yes—
78#1989C2212yes—
79#1989C2211yescharacteristic
80#1989C2212yes—
81#1989C2212yes—
82#1989C2212yes—
83#1989C2212yes—
84#1988C2211yescharacteristic
85#1988C2211yescharacteristic
86#1949C2212yes—
87#1949C2212yes—
88#1949C2212yes—
89#1949C2211yescharacteristic
90#1949C2212yes—
91#1949C2212yes—
92#1949C2212yes—
93#1948C2211yescharacteristic
94#1948C2212yes—
95#1948C2211yescharacteristic
96#1947C2211yescharacteristic
97#1947C2212yes—
98#1947C2211yescharacteristic
99#1939C2211yescharacteristic
100#1939C2212yes—
101#1939C2212yes—
102#1939C2211yescharacteristic
103#1920C2212yes—
104#1920C2211yescharacteristic
105#1918C2212yes—
106#1918C2211yescharacteristic
107#1865C2211yescharacteristic
108#1865C2212yes—
109#1863C2212yes—
110#1863C2211yescharacteristic
111#1842C2211yescharacteristic
112#1842C2212yes—
113#1835C2212yes—
114#1835C2212yes—
115#1834C2211yescharacteristic
116#1834C2211yescharacteristic
117#1805C2212yes—
118#1805C2212yes—
119#1805C2212yes—
120#1805C2211yescharacteristic
121#1803C2212yes—
122#1803C2211yescharacteristic
123#1803C2212yes—
124#1803C2211yescharacteristic
125C4×#107C2211yescharacteristic
126C4×#107C2212yes—
127C4×#106C2211yescharacteristic
128C4×#106C2212yes—
129C4×C4⋊C8C2211yescharacteristic
130C4×C4⋊C8C2212yes—
131C4×#103C2211yescharacteristic
132C4×#103C2212yes—
133C4×#103C2212yes—
134C4×#103C2211yescharacteristic
135#557—24no—
136#557Q818yes—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8C2311yescharacteristic
139C2×#125—22no—
140C2×#125—21no—
141C2×#125—21no—
142C2×#125C2311yescharacteristic
143C2×#125C2312yes—
144C2×#125C2312yes—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8D411yescharacteristic
149C2×C4×Q8D411yescharacteristic
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2312yes—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156#479—24no—
157#479—28no—
158C8×Q8—24no—
159C8×Q8—24no—
160C2×#107C2312yes—
161C2×#107C2311yescharacteristic
162C2×#107C2311yescharacteristic
163C2×#107C2312yes—
164C2×#106C2312yes—
165C2×#106C2311yescharacteristic
166C2×#106C2312yes—
167C2×#106C2311yescharacteristic
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×#103C2311yescharacteristic
179C2×#103C2312yes—
180C2×#103C2311yescharacteristic
181C2×#103C2312yes—
182C2×#103C2311yescharacteristic
183C2×#103C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2312yes—
187C2×C4×C8C2312yes—
188#400—22no—
189#400—22no—
190#398—22no—
191#398—22no—
192#398—22no—
193#398—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391—21no—
199#389—22no—
200#389—22no—
201#389—22no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—22no—
208#389—22no—
209#389—22no—
210#389—22no—
211#389—21no—
212#389—21no—
213#389—22no—
214#389C2311yescharacteristic
215#389C2311yescharacteristic
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#387—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#387—21no—
226#387—21no—
227#387—22no—
228#387—22no—
229#387—22no—
230#387—22no—
231#387—22no—
232#387—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#384—21no—
238#384C2311yescharacteristic
239#384C2312yes—
240#384C2312yes—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#382—22no—
244#382C2311yescharacteristic
245#382C2312yes—
246#382C2312yes—
247#382C2312yes—
248#382C2312yes—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—22no—
257C4×C4⋊C4—22no—
258C4×C4⋊C4—22no—
259C4×C4⋊C4—22no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—22no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—22no—
268C4×C4⋊C4D412yes—
269C4×C4⋊C4D412yes—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2311yescharacteristic
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2311yescharacteristic
284C43—22no—
285C43—21no—
286C43C2312yes—
287C43C2311yescharacteristic
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2311yescharacteristic
301#340C2311yescharacteristic
302#340C2312yes—
303#340C2311yescharacteristic
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#336C2312yes—
315#336C2312yes—
316#336C2311yescharacteristic
317#336C2311yescharacteristic
318C22×Q8—21no—
319C22×Q8C2×D411yescharacteristic
320C22×Q8C2411yescharacteristic
321C22×C8C2411yescharacteristic
322C22×C8C2411yescharacteristic
323C22×C8C2412yes—
324C22×C8C2411yescharacteristic
325C22×C8C2412yes—
326C22×C8C2411yescharacteristic
327C4⋊Q8—28no—
328C4⋊Q8—22no—
329C4⋊Q8C2×Q814yes—
330#125—216no—
331#125—24no—
332#125—22no—
333#125—24no—
334#125—22no—
335#125—24no—
336#125—44no—
337#125—44no—
338#125C2×Q818yes—
339C4×Q8—28no—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—24no—
345C4×Q8—22no—
346C4×Q8—42no—
347C4×Q8—42no—
348C4×Q8—41no—
349C4×Q8—44no—
350C4×Q8—44no—
351C4×Q8C2×Q818yes—
352C4×Q8C2×Q814yes—
353C4×Q8C2×Q814yes—
354C4×Q8#4114yes—
355C4×Q8#4114yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2×D412yes—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D412yes—
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2411yescharacteristic
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2411yescharacteristic
402C2×C42—22no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—22no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—22no—
414C2×C42—21no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D412yes—
420C2×C42C2×D412yes—
421C2×C42C2×D412yes—
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D412yes—
424C2×C42C2×D411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2412yes—
427C2×C42C2412yes—
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—24no—
431#107—22no—
432#107—41no—
433#107—42no—
434#106—24no—
435#106—22no—
436#106—42no—
437#106—41no—
438C4⋊C8—24no—
439C4⋊C8—24no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—24no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448#103—22no—
449#103—24no—
450#103—22no—
451#103—24no—
452#103—22no—
453#103—22no—
454C4×C8—24no—
455C4×C8—24no—
456C4×C8—22no—
457C4×C8—22no—
458#95—22no—
459#95—21no—
460#95—21no—
461#95—22no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—21no—
474#95—21no—
475#95—22no—
476#95—22no—
477#95—21no—
478#95—21no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95C2×D412yes—
486#95C2×D412yes—
487#95C2×D412yes—
488C2×Q8—24no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8C22⋊Q814yes—
497C2×Q8C22×Q812yes—
498C2×Q8C2×#4112yes—
499C2×Q82−1+412yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D412yes—
521C22×C4C22×D411yescharacteristic
522C22×C4C2511yescharacteristic
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—22no—
526C2×C8—21no—
527C2×C8—22no—
528C2×C8—21no—
529C2×C8—22no—
530C2×C8—21no—
531C2×C8—22no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—21no—
541C4⋊C4—28no—
542C4⋊C4—24no—
543C4⋊C4—28no—
544C4⋊C4—24no—
545C4⋊C4—28no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—22no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4—81no—
587C4⋊C4—82no—
588C4⋊C4—81no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—81no—
592C4⋊C4C22⋊Q814yes—
593C4⋊C4C22⋊Q818yes—
594C4⋊C4#13514yes—
595C4⋊C4C22×Q812yes—
596C4⋊C4C22×Q814yes—
597C4⋊C4C2×#4112yes—
598C42—28no—
599C42—24no—
600C42—24no—
601C42—24no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—21no—
606C42—22no—
607C42—21no—
608C42—42no—
609C42—41no—
610C42—42no—
611C42—41no—
612C42—42no—
613C42—44no—
614C42—42no—
615C42—42no—
616C42—44no—
617C42—44no—
618C42—42no—
619C42—42no—
620C42—42no—
621C42—82no—
622C42—82no—
623C42—82no—
624C42—81no—
625C42C22×Q814yes—
626C42C22×Q812yes—
627C42C2×#4114yes—
628C42C2×#4112yes—
629C42C2×#4112yes—
630C422−1+412yes—
631C23C23×D411yescharacteristic
632Q8—28no—
633Q8—22no—
634Q8—22no—
635Q8—22no—
636Q8—48no—
637Q8#55714yes—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4C2×C22⋊Q814yes—
696C2×C4C2×C22⋊Q812yes—
697C2×C4C2×C22⋊Q814yes—
698C2×C4C2×C22⋊Q812yes—
699C2×C4#54812yes—
700C2×C4#54812yes—
701C2×C4C2×#13514yes—
702C2×C4C2×#13512yes—
703C2×C4#57512yes—
704C2×C4C23×Q811yescharacteristic
705C2×C4C22×#4111yescharacteristic
706C2×C4C22×#4111yescharacteristic
707C2×C4C2×2−1+411yescharacteristic
708C2×C4C2×2−1+411yescharacteristic
709C2×C4#58511yescharacteristic
710C8—42no—
711C8—41no—
712C8—42no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22C22×C22⋊Q811yescharacteristic
717C22C2×#54811yescharacteristic
718C22#348911yescharacteristic
719C22C22×#13511yescharacteristic
720C22C2×#57511yescharacteristic
721C22#358411yescharacteristic
722C22#358611yescharacteristic
723C4—24no—
724C4—24no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—24no—
729C4—24no—
730C4—44no—
731C4—42no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—82no—
737C4—81no—
738C4—82no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—82no—
744C4#307614yes—
745C4C2×#55711yescharacteristic
746C4#348011yescharacteristic
747C4#350211yescharacteristic
748C4#352311yescharacteristic
749C2#3657711yescharacteristic
750C2C2×#307611yescharacteristic
751C2#6049911yescharacteristic
752C2#6130311yescharacteristic
753C2#6132011yescharacteristic
754C2#6210411yescharacteristic
755C2#6215411yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#366002
C4×#5572
#332002
#292912
#292882
#292212
#292202
#265172
#265152
#265102
#265062
#261162
#261142
#261122
#261082
#227412
#227392
Q8×C4⋊C82
#225212
C4×#4792