Finite Group Databasebeta

← #6672012

Subgroups — #6672012

Order 512.

1924 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3381C211yesmaximal, characteristic, complemented
2C2×#3105C211yesmaximal, characteristic
3#39859C211yesmaximal, characteristic, complemented
4#36215C211yesmaximal, characteristic, complemented
5#32959C211yesmaximal, characteristic, complemented
6#31155C211yesmaximal, characteristic, complemented
7#31153C211yesmaximal, characteristic, complemented
8#31081C211yesmaximal, characteristic, complemented
9#31079C211yesmaximal, characteristic, complemented
10#30951C211yesmaximal, characteristic, complemented
11#30947C211yesmaximal, characteristic, complemented
12#30783C211yesmaximal, characteristic, complemented
13#30775C211yesmaximal, characteristic, complemented
14#29879C211yesmaximal, characteristic, complemented
15#29693C211yesmaximal, characteristic, complemented
16#28534C211yesmaximal, characteristic, complemented
17#28188C211yesmaximal, characteristic, complemented
18#27229C211yesmaximal, characteristic
19#27222C211yesmaximal, characteristic
20#26172C211yesmaximal, characteristic, complemented
21#26168C211yesmaximal, characteristic, complemented
22#26049C211yesmaximal, characteristic, complemented
23#26041C211yesmaximal, characteristic, complemented
24#24905C211yesmaximal, characteristic, complemented
25#24901C211yesmaximal, characteristic, complemented
26#24820C211yesmaximal, characteristic, complemented
27#24685C211yesmaximal, characteristic, complemented
28#24335C211yesmaximal, characteristic, complemented
29#24334C211yesmaximal, characteristic, complemented
30#22768C211yesmaximal, characteristic, complemented
31#22098C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#554C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#3381—28no—
37C2×#499C2211yescharacteristic, complemented
38C2×#499C2211yescharacteristic, complemented
39C2×#498C2211yescharacteristic, complemented
40#3105—28no—
41C2×#484C2211yescharacteristic
42C2×#481C2211yescharacteristic
43C2×#479C2211yescharacteristic, complemented
44C2×#479C2211yescharacteristic, complemented
45C2×#477C2211yescharacteristic, complemented
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic, complemented
52C2×#474C2211yescharacteristic
53C2×#463C2211yescharacteristic
54C2×#463C2211yescharacteristic
55C2×#450C2211yescharacteristic
56C2×#447C2211yescharacteristic
57C2×C8×Q8C2211yescharacteristic, complemented
58C2×C4×SD16C2211yescharacteristic
59C2×C4×SD16C2211yescharacteristic
60C2×C4×SD16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×C4×D8C2211yescharacteristic
63C2×C4×D8C2211yescharacteristic
64C2×#431C2211yescharacteristic
65#2851C2211yescharacteristic
66#2851C2211yescharacteristic
67#2848—21no—
68#2721—21no—
69#2716—21no—
70#2694—21no—
71#2674—21no—
72#2633—21no—
73#2611—21no—
74#2599—21no—
75#2580C2211yescharacteristic
76#2580C2211yescharacteristic, complemented
77#2579—21no—
78#2566C2211yescharacteristic
79#2566C2211yescharacteristic, complemented
80#2564—21no—
81#2552C2211yescharacteristic, complemented
82#2550C2211yescharacteristic, complemented
83#2491C2211yescharacteristic
84#2490C2211yescharacteristic
85#2454C2211yescharacteristic
86#2452C2211yescharacteristic
87#2450—21no—
88#2449—21no—
89#2448C2211yescharacteristic, complemented
90#2448C2211yescharacteristic, complemented
91#2442C2211yescharacteristic
92#2440C2211yescharacteristic
93#2437—21no—
94#2437—21no—
95#2423C2211yescharacteristic
96#2421C2211yescharacteristic
97#2356C2211yescharacteristic, complemented
98#2349C2211yescharacteristic
99#2349C2211yescharacteristic
100D4×C4⋊C4C2211yescharacteristic
101D4×C22⋊C4C2211yescharacteristic
102D4×C22⋊C4C2211yescharacteristic
103#2326—21no—
104C4×C22⋊Q8C2211yescharacteristic
105C2×#385—21no—
106#2094C2211yescharacteristic
107#2094C2211yescharacteristic, complemented
108#2092C2211yescharacteristic
109#2092C2211yescharacteristic, complemented
110#2088C2211yescharacteristic, complemented
111#2088C2211yescharacteristic, complemented
112#2087C2211yescharacteristic, complemented
113#2087C2211yescharacteristic, complemented
114#2087C2211yescharacteristic, complemented
115#2086C2211yescharacteristic, complemented
116#2085C2211yescharacteristic, complemented
117#2083C2211yescharacteristic, complemented
118#2077C2211yescharacteristic
119#2077C2211yescharacteristic
120#2076C2211yescharacteristic
121#2075C2211yescharacteristic
122#2074C2211yescharacteristic, complemented
123#2072C2211yescharacteristic, complemented
124#2067C2211yescharacteristic, complemented
125#2065C2211yescharacteristic, complemented
126#2059C2211yescharacteristic, complemented
127#2059C2211yescharacteristic, complemented
128#2059C2211yescharacteristic, complemented
129#2059C2211yescharacteristic, complemented
130#2058C2211yescharacteristic, complemented
131#2057C2211yescharacteristic, complemented
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2054C2211yescharacteristic
135#2054C2211yescharacteristic
136#2042C2211yescharacteristic, complemented
137#2042C2211yescharacteristic, complemented
138#2036C2211yescharacteristic
139#2035C2211yescharacteristic
140#2034C2211yescharacteristic
141#2033C2211yescharacteristic
142#2025C2211yescharacteristic
143#2025C2211yescharacteristic, complemented
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic, complemented
146#1991C2211yescharacteristic, complemented
147#1991C2211yescharacteristic, complemented
148#1984C2211yescharacteristic, complemented
149#1970C2211yescharacteristic
150#1970C2211yescharacteristic
151#1949C2211yescharacteristic, complemented
152#1948C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1939C2211yescharacteristic, complemented
155#1939C2211yescharacteristic, complemented
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic, complemented
159#1934C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1920C2211yescharacteristic, complemented
169#1920C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1853C2211yescharacteristic
189#1852C2211yescharacteristic
190#1846C2211yescharacteristic, complemented
191#1845C2211yescharacteristic, complemented
192#1835C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1804C2211yescharacteristic
196#1804C2211yescharacteristic
197#1804C2211yescharacteristic, complemented
198#1802C2211yescharacteristic
199#1797C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202C8×C4⋊C4C2211yescharacteristic, complemented
203C4×#102C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4—21no—
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211#557—24no—
212#557—42no—
213#554—24no—
214#554—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218#529—24no—
219#529—42no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8D411yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—24no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—42no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C22×C4⋊C4—21no—
260C22×C4⋊C4—21no—
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C22×C42C2311yescharacteristic
266#499—24no—
267#499—24no—
268#498—24no—
269#484—24no—
270#481—24no—
271#479—24no—
272#479—24no—
273#478—24no—
274#478—24no—
275#478—24no—
276#478—24no—
277#478—42no—
278#478—42no—
279#477—24no—
280#474—24no—
281#463—24no—
282#463—24no—
283#450—24no—
284#447—24no—
285C8×Q8—24no—
286C4×SD16—24no—
287C4×SD16—24no—
288C4×SD16—24no—
289C4×SD16D418yes—
290C4×D8—24no—
291C4×D8—24no—
292#431—24no—
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351#400—21no—
352#400—21no—
353#399—21no—
354#399—21no—
355#399—21no—
356#399—21no—
357#399—21no—
358#399—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#397—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#395—21no—
376#395—21no—
377#394—21no—
378#394—21no—
379#393—21no—
380#393—21no—
381#393—21no—
382#393—21no—
383#391—21no—
384#391D411yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#390—21no—
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389—21no—
398#389D411yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387D411yescharacteristic
426#387D411yescharacteristic
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385D411yescharacteristic
454#385D411yescharacteristic
455#384—21no—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#383—21no—
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#380—21no—
464#380—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380D411yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#379—21no—
474#379—21no—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376—21no—
483C2×#95—21no—
484C2×#95—21no—
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—44no—
542C23×C4—82no—
543C23×C4—82no—
544C23×C4C2×D411yescharacteristic
545C23×C4C2×D411yescharacteristic
546C23×C4C2411yescharacteristic
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16C2×D414yes—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—41no—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—44no—
572#126—44no—
573#125—22no—
574#125—22no—
575#125—22no—
576#125—22no—
577#125—22no—
578#125—22no—
579#125—22no—
580#125—41no—
581#125—41no—
582#125—41no—
583#125—44no—
584#125—44no—
585#124—22no—
586#124—41no—
587#124—44no—
588#123—44no—
589C22⋊Q8—24no—
590C22⋊Q8—22no—
591C22⋊Q8—44no—
592C22⋊Q8—44no—
593C22⋊Q8—41no—
594C22⋊Q8—44no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597#121—22no—
598#121—41no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—44no—
607C4×Q8C2×D414yes—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—44no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—44no—
627C4×D4—44no—
628C4×D4C2×D414yes—
629#117—44no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—44no—
664C2×C4⋊C4—82no—
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—44no—
720C2×C22⋊C4—44no—
721C2×C22⋊C4—82no—
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C42—21no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741#107—22no—
742#107—22no—
743#107—22no—
744#107—22no—
745#107—22no—
746#107—22no—
747#107—41no—
748#107—41no—
749#106—22no—
750#106—22no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—41no—
755#106—41no—
756#106C2×D414yes—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—41no—
769#103—41no—
770#103C2×D414yes—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102C2×D414yes—
789C22⋊C8—22no—
790C22⋊C8—22no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C4×C8—22no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—41no—
797C4×C8—41no—
798C4×C8C2×D414yes—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—24no—
839C24—21no—
840C24—21no—
841C24—42no—
842C24—42no—
843C24—42no—
844C24—42no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848C2×Q8—22no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—41no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—42no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8C22×D412yes—
863C2×D4—24no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—42no—
886C2×D4—81no—
887C2×D4C22×D412yes—
888C2×D42−1+412yes—
889C2×D42−1+412yes—
890C2×D42−1+412yes—
891C22×C4—22no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—816no—
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C2511yescharacteristic
961SD16—28no—
962SD16—44no—
963D8—44no—
964D8—44no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8C22×D412yes—
988C2×C8C22×D412yes—
989C4⋊C4—24no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4C22×D412yes—
1052C4⋊C4C22×D412yes—
1053C22⋊C4—22no—
1054C22⋊C4—24no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4#13514yes—
1090C42—22no—
1091C42—22no—
1092C42—24no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—81no—
1107C42C22×D412yes—
1108C42H(5,𝔽2)12yes—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—21no—
1114C23—21no—
1115C23—22no—
1116C23—22no—
1117C23—21no—
1118C23—22no—
1119C23—48no—
1120C23—48no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—84no—
1139C23—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23C2×#13512yes—
1144C23C23×D411yescharacteristic
1145Q8—22no—
1146Q8—22no—
1147Q8—44no—
1148Q8—41no—
1149Q8—41no—
1150Q8—84no—
1151Q8—162no—
1152D4—22no—
1153D4—22no—
1154D4—22no—
1155D4—22no—
1156D4—22no—
1157D4—48no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—84no—
1165D4#53614yes—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4D4212yes—
1257C2×C4D4212yes—
1258C2×C4C2×#13512yes—
1259C2×C4C2×#13512yes—
1260C2×C4C23×D411yescharacteristic
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4C2×2−1+411yescharacteristic
1263C2×C4C2×2−1+411yescharacteristic
1264C2×C4C2×2−1+411yescharacteristic
1265C2×C4#58511yescharacteristic
1266C8—22no—
1267C8—22no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C22—24no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—41no—
1282C22—42no—
1283C22—42no—
1284C22—41no—
1285C22—42no—
1286C22—42no—
1287C22—41no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—816no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22C2×D4211yescharacteristic
1304C22#348611yescharacteristic
1305C22#348911yescharacteristic
1306C22C22×#13511yescharacteristic
1307C22#358411yescharacteristic
1308C22#358511yescharacteristic
1309C22#358511yescharacteristic
1310C4—22no—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—41no—
1315C4—42no—
1316C4—41no—
1317C4—41no—
1318C4—42no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—42no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4C2×#53611yescharacteristic
1337C4#348911yescharacteristic
1338C4#353811yescharacteristic
1339C4#354111yescharacteristic
1340C2—42no—
1341C2—44no—
1342C2—82no—
1343C2—161no—
1344C2#3765111yescharacteristic
1345C2D4×#13511yescharacteristic
1346C2#6105911yescharacteristic
1347C2#6181911yescharacteristic
1348C2#6185511yescharacteristic
1349C2#6210311yescharacteristic
1350C2#6217511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
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. C2×#3381C2semidirect
3. #39859C2semidirect
4. #36215C2semidirect
5. #32959C2semidirect
6. #31155C2semidirect
7. #31153C2semidirect
8. #31081C2semidirect
9. #31079C2semidirect
10. #30951C2semidirect
11. #30947C2semidirect
12. #30783C2semidirect
13. #30775C2semidirect
14. #29879C2semidirect
15. #29693C2semidirect
16. #28534C2semidirect
17. #28188C2semidirect
20. #26172C2semidirect
21. #26168C2semidirect
22. #26049C2semidirect
23. #26041C2semidirect
24. #24905C2semidirect
25. #24901C2semidirect
26. #24820C2semidirect
27. #24685C2semidirect
28. #24335C2semidirect
29. #24334C2semidirect
30. #22768C2semidirect
31. #22098C2semidirect
32. C2×#557C22semidirect
37. C2×#499C22semidirect
38. C2×#499C22semidirect
39. C2×#498C22semidirect
43. C2×#479C22semidirect
44. C2×#479C22semidirect
45. C2×#477C22semidirect
51. C2×#478C22semidirect
57. C2×C8×Q8C22semidirect
76. #2580C22semidirect
79. #2566C22semidirect
81. #2552C22semidirect
82. #2550C22semidirect
89. #2448C22semidirect
90. #2448C22semidirect
97. #2356C22semidirect
107. #2094C22semidirect
109. #2092C22semidirect
110. #2088C22semidirect
111. #2088C22semidirect
112. #2087C22semidirect
113. #2087C22semidirect
114. #2087C22semidirect
115. #2086C22semidirect
116. #2085C22semidirect
117. #2083C22semidirect
122. #2074C22semidirect
123. #2072C22semidirect
124. #2067C22semidirect
125. #2065C22semidirect
126. #2059C22semidirect
127. #2059C22semidirect
128. #2059C22semidirect
129. #2059C22semidirect
130. #2058C22semidirect
131. #2057C22semidirect
136. #2042C22semidirect
137. #2042C22semidirect
143. #2025C22semidirect
145. #2023C22semidirect
146. #1991C22semidirect
147. #1991C22semidirect
148. #1984C22semidirect
151. #1949C22semidirect
152. #1948C22semidirect
153. #1939C22semidirect
154. #1939C22semidirect
155. #1939C22semidirect
158. #1934C22semidirect
159. #1934C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
168. #1920C22semidirect
169. #1920C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
180. #1865C22semidirect
184. #1863C22semidirect
190. #1846C22semidirect
191. #1845C22semidirect
192. #1835C22semidirect
193. #1805C22semidirect
197. #1804C22semidirect
202. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33812
C2×#31052
#398592
#362152
#329592
#311552
#311532
#310812
#310792
#309512
#309472
#307832
#307752
#298792
#296932
#285342
#281882
#272292
#272222
#261722
#261682
#260492
#260412
#249052
#249012
#248202
#246852
#243352
#243342
#227682
#220982