Finite Group Databasebeta

← #6679142

Subgroups — #6679142

Order 512.

1576 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39480C211yesmaximal, characteristic, complemented
2#36154C211yesmaximal, characteristic
3#32956C211yesmaximal, characteristic
4#31874C212yesmaximal, complemented
5#31694C212yesmaximal, complemented
6#31462C212yesmaximal, complemented
7#31430C212yesmaximal, complemented
8#29938C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#27728C211yesmaximal, characteristic, complemented
11#27525C212yesmaximal
12#27523C212yesmaximal
13#27307C212yesmaximal, complemented
14#26115C212yesmaximal, complemented
15#26107C211yesmaximal, characteristic, complemented
16#25839C211yesmaximal, characteristic, complemented
17#25470C211yesmaximal, characteristic, complemented
18#25450C211yesmaximal, characteristic, complemented
19#24991C211yesmaximal, characteristic, complemented
20#22963C211yesmaximal, characteristic, complemented
21#22519C211yesmaximal, characteristic, complemented
22#22098C211yesmaximal, characteristic, complemented
23#20732C211yesmaximal, characteristic
24C2×#554C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C2×#500C2211yescharacteristic, complemented
27C2×#476C2211yescharacteristic
28C2×#476C2211yescharacteristic
29C2×C8×Q8C2211yescharacteristic, complemented
30C2×#431C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2848—21no—
34#2762—22no—
35#2690—22no—
36#2625—21no—
37#2571C2211yescharacteristic, complemented
38#2570C2212yescomplemented
39#2567C2211yescharacteristic, complemented
40#2563C2211yescharacteristic
41#2538C2211yescharacteristic
42#2514—21no—
43#2506—21no—
44#2506C2212yescomplemented
45#2495C2212yes—
46#2494C2212yes—
47#2487—21no—
48#2454C2212yes—
49#2450—22no—
50#2442C2212yes—
51#2437—22no—
52#2417—21no—
53#2369C2211yescharacteristic, complemented
54#2355C2211yescharacteristic, complemented
55#2349C2212yes—
56D4×C4⋊C4C2211yescharacteristic
57D4×C22⋊C4C2212yes—
58#2314—21no—
59C4×C22⋊Q8C2211yescharacteristic
60#2285C2211yescharacteristic
61C2×#380—21no—
62#2101C2212yescomplemented
63#2101C2212yescomplemented
64#2101C2212yescomplemented
65#2099C2212yescomplemented
66#2088C2212yescomplemented
67#2088C2212yescomplemented
68#2087C2212yescomplemented
69#2087C2212yescomplemented
70#2085C2212yescomplemented
71#2084C2212yescomplemented
72#2077C2212yes—
73#2077C2212yes—
74#2076C2212yes—
75#2076C2212yes—
76#2073C2212yes—
77#2073C2212yes—
78#2067C2212yes—
79#2065C2212yes—
80#2059C2212yescomplemented
81#2059C2212yescomplemented
82#1991C2212yescomplemented
83#1990C2211yescharacteristic, complemented
84#1990C2211yescharacteristic, complemented
85#1989C2212yescomplemented
86#1987C2211yescharacteristic, complemented
87#1987C2211yescharacteristic, complemented
88#1984C2211yescharacteristic, complemented
89#1949C2212yescomplemented
90#1948C2211yescharacteristic, complemented
91#1948C2211yescharacteristic, complemented
92#1941C2212yescomplemented
93#1941C2212yescomplemented
94#1939C2212yescomplemented
95#1939C2211yescharacteristic, complemented
96#1934C2212yes—
97#1934C2212yes—
98#1926C2212yes—
99#1925C2212yes—
100#1923C2212yes—
101#1923C2212yes—
102#1920C2212yescomplemented
103#1919C2212yescomplemented
104#1916C2212yescomplemented
105#1864C2212yes—
106#1864C2212yes—
107#1864C2212yes—
108#1864C2212yes—
109#1862C2212yes—
110#1862C2212yes—
111#1853C2212yes—
112#1835C2212yescomplemented
113#1834C2211yescharacteristic, complemented
114#1823C2211yescharacteristic
115#1823C2211yescharacteristic
116#1804C2212yes—
117#1804C2212yes—
118#1802C2211yescharacteristic
119#1802C2211yescharacteristic
120#1802C2211yescharacteristic
121#1802C2211yescharacteristic
122#1802C2211yescharacteristic
123#1802C2211yescharacteristic
124#1797C2211yescharacteristic
125#1786C2211yescharacteristic
126#1786C2212yes—
127#1786C2211yescharacteristic
128C8×C4⋊C4C2211yescharacteristic, complemented
129C4×#102C2212yes—
130C4×#102C2211yescharacteristic
131C4×#102C2211yescharacteristic
132C4×#102C2212yes—
133C4×#102C2211yescharacteristic
134C4×#102C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C24×C4—21no—
137#554—24no—
138#554—42no—
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×#125—22no—
142C2×#125C2312yes—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—22no—
148C2×C22⋊Q8D411yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×D4—24no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4—42no—
154C2×C4×D4C2311yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×C4×D4C2311yescharacteristic
160C2×#117—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C22⋊C4—21no—
165C22×C22⋊C4—22no—
166C22×C42C2311yescharacteristic
167#500—42no—
168#476—24no—
169#476—42no—
170C8×Q8—42no—
171#431—42no—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×#102C2311yescharacteristic
185C2×#102C2312yes—
186C2×#102C2311yescharacteristic
187C2×#102C2312yes—
188C2×#102C2311yescharacteristic
189C2×#102C2311yescharacteristic
190C2×#102C2311yescharacteristic
191C2×#102C2311yescharacteristic
192C2×#102C2312yes—
193C2×#102C2311yescharacteristic
194C2×#102C2311yescharacteristic
195C2×#102C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2311yescharacteristic
198C2×C22⋊C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203#401—22no—
204#400—22no—
205#400—22no—
206#400—22no—
207#400—22no—
208#400—22no—
209#399—22no—
210#398—22no—
211#398—22no—
212#398—22no—
213#397—22no—
214#397—22no—
215#396—22no—
216#396—22no—
217#395—22no—
218#393—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—22no—
224#391D411yescharacteristic
225#390C2312yes—
226#390C2312yes—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389D411yescharacteristic
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387D412yes—
248#386—22no—
249#386—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#385D412yes—
256#384—21no—
257#384C2311yescharacteristic
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#383—22no—
262#382—21no—
263#382—21no—
264#382C2312yes—
265#382C2312yes—
266#382C2312yes—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—21no—
271#380—21no—
272#380—21no—
273#380—21no—
274#380—22no—
275#380—22no—
276#380—22no—
277#380D411yescharacteristic
278#380C2312yes—
279#380C2312yes—
280#380C2311yescharacteristic
281#380C2311yescharacteristic
282#379—22no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2312yes—
292C4×C22⋊C4C2312yes—
293C2×#95—22no—
294#340C2311yescharacteristic
295#340C2311yescharacteristic
296#340C2311yescharacteristic
297#340C2311yescharacteristic
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2311yescharacteristic
301#340C2311yescharacteristic
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321C25—21no—
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8C2×D411yescharacteristic
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4C2411yescharacteristic
333C22×D4C2411yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—44no—
342C23×C4—44no—
343C23×C4—82no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2411yescharacteristic
347C22×C8C2412yes—
348C22×C8C2411yescharacteristic
349C22×C8C2411yescharacteristic
350C22×C8C2412yes—
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353C4⋊Q8—22no—
354C4⋊Q8—22no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357#125—24no—
358#125—42no—
359#125—84no—
360C22⋊Q8—24no—
361C22⋊Q8—48no—
362C22⋊Q8—44no—
363C22⋊Q8—82no—
364C22⋊Q8—82no—
365C22⋊Q8—82no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×D4—22no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—44no—
376C4×D4—41no—
377C4×D4—41no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—44no—
381C4×D4#4114yes—
382#117—44no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—82no—
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D412yes—
413C2×C4⋊C4C2×D412yes—
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2411yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
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—44no—
439C2×C22⋊C4—84no—
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2412yes—
452C2×C42C2412yes—
453C2×C42C2411yescharacteristic
454#107—42no—
455#107—42no—
456#106—24no—
457#106—42no—
458#106—42no—
459#106—42no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462C4⋊C8—42no—
463C4⋊C8—41no—
464C4⋊C8—41no—
465C4⋊C8—42no—
466#102—24no—
467#102—24no—
468#102—22no—
469#102—22no—
470#102—22no—
471#102—24no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102—41no—
476#102—41no—
477#102—42no—
478C22⋊C8—42no—
479C22⋊C8—41no—
480C22⋊C8—41no—
481C4×C8—22no—
482C4×C8—22no—
483C4×C8—42no—
484C4×C8—42no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—21no—
489#95—21no—
490#95—22no—
491#95—22no—
492#95—21no—
493#95—21no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95C2×D412yes—
508#95C2×D412yes—
509#95C2×D412yes—
510#95C2×D412yes—
511#95C2×D412yes—
512C24—21no—
513C24—24no—
514C24—21no—
515C24—42no—
516C24—42no—
517C24—42no—
518C24—42no—
519C24—81no—
520C24—81no—
521C24C22×D411yescharacteristic
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—81no—
528C2×Q8—81no—
529C2×Q8—81no—
530C2×Q8—81no—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4C2×#4112yes—
547C2×D42−1+412yes—
548C2×D42−1+412yes—
549C2×D42−1+412yes—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—816no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—81no—
593C22×C4#13514yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C2511yescharacteristic
604C2×C8—22no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—21no—
622C4⋊C4—22no—
623C4⋊C4—24no—
624C4⋊C4—22no—
625C4⋊C4—24no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—82no—
659C4⋊C4—81no—
660C4⋊C4—82no—
661C4⋊C4—81no—
662C4⋊C4—81no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4C2×#4112yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C42—22no—
686C42—22no—
687C42—21no—
688C42—22no—
689C42—22no—
690C42—21no—
691C42—22no—
692C42—22no—
693C42—42no—
694C42—42no—
695C42—82no—
696C42—82no—
697C42C2×#4112yes—
698C42H(5,𝔽2)12yes—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—48no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23C2×#13512yes—
727C23C23×D411yescharacteristic
728Q8—44no—
729Q8—162no—
730Q8—162no—
731D4—22no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—48no—
737D4—41no—
738D4—41no—
739D4#54114yes—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—48no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—82no—
799C2×C4—84no—
800C2×C4—84no—
801C2×C4—84no—
802C2×C4—84no—
803C2×C4—164no—
804C2×C4—164no—
805C2×C4#54612yes—
806C2×C4#54612yes—
807C2×C4C2×#13512yes—
808C2×C4C2×#13512yes—
809C2×C4#57712yes—
810C2×C4C22×#4111yescharacteristic
811C2×C4C2×H(5,𝔽2)11yescharacteristic
812C2×C4C2×2−1+411yescharacteristic
813C2×C4C2×2−1+411yescharacteristic
814C2×C4C2×2−1+411yescharacteristic
815C2×C4#58511yescharacteristic
816C8—42no—
817C8—41no—
818C8—41no—
819C8—41no—
820C8—41no—
821C8—42no—
822C22—24no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22C2×#54611yescharacteristic
845C22#348611yescharacteristic
846C22#348911yescharacteristic
847C22C22×#13511yescharacteristic
848C22C2×#57711yescharacteristic
849C22#358511yescharacteristic
850C22#358511yescharacteristic
851C4—22no—
852C4—22no—
853C4—41no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—41no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—82no—
865C4—81no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4#329614yes—
870C4C2×#54111yescharacteristic
871C4#349511yescharacteristic
872C4#353811yescharacteristic
873C4#354111yescharacteristic
874C2—42no—
875C2—44no—
876C2—82no—
877C2#3766311yescharacteristic
878C2C2×#329611yescharacteristic
879C2#6117911yescharacteristic
880C2#6181911yescharacteristic
881C2#6185011yescharacteristic
882C2#6209811yescharacteristic
883C2#6218811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39480C2semidirect
4. #31874C2semidirect
5. #31694C2semidirect
6. #31462C2semidirect
7. #31430C2semidirect
8. #29938C2semidirect
9. #29878C2semidirect
10. #27728C2semidirect
13. #27307C2semidirect
14. #26115C2semidirect
15. #26107C2semidirect
16. #25839C2semidirect
17. #25470C2semidirect
18. #25450C2semidirect
19. #24991C2semidirect
20. #22963C2semidirect
21. #22519C2semidirect
22. #22098C2semidirect
26. C2×#500C22semidirect
29. C2×C8×Q8C22semidirect
37. #2571C22semidirect
38. #2570C22semidirect
39. #2567C22semidirect
44. #2506C22semidirect
53. #2369C22semidirect
54. #2355C22semidirect
62. #2101C22semidirect
63. #2101C22semidirect
64. #2101C22semidirect
65. #2099C22semidirect
66. #2088C22semidirect
67. #2088C22semidirect
68. #2087C22semidirect
69. #2087C22semidirect
70. #2085C22semidirect
71. #2084C22semidirect
80. #2059C22semidirect
81. #2059C22semidirect
82. #1991C22semidirect
83. #1990C22semidirect
84. #1990C22semidirect
85. #1989C22semidirect
86. #1987C22semidirect
87. #1987C22semidirect
88. #1984C22semidirect
89. #1949C22semidirect
90. #1948C22semidirect
91. #1948C22semidirect
92. #1941C22semidirect
93. #1941C22semidirect
94. #1939C22semidirect
95. #1939C22semidirect
102. #1920C22semidirect
103. #1919C22semidirect
104. #1916C22semidirect
112. #1835C22semidirect
113. #1834C22semidirect
128. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#394802
#361542
#329562
#318742
#316942
#314622
#314302
#299382
#298782
#277282
#275252
#275232
#273072
#261152
#261072
#258392
#254702
#254502
#249912
#229632
#225192
#220982
#207322