Finite Group Databasebeta

← #6673908

Subgroups — #6673908

Order 512.

1869 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3241C211yesmaximal, characteristic, complemented
2C2×#3118C211yesmaximal, characteristic, complemented
3#39346C211yesmaximal, characteristic, complemented
4#35529C211yesmaximal, characteristic, complemented
5#33014C211yesmaximal, characteristic, complemented
6#31250C211yesmaximal, characteristic, complemented
7#31247C211yesmaximal, characteristic, complemented
8#31170C211yesmaximal, characteristic, complemented
9#31168C211yesmaximal, characteristic, complemented
10#30974C211yesmaximal, characteristic, complemented
11#30950C211yesmaximal, characteristic, complemented
12#30891C211yesmaximal, characteristic, complemented
13#30875C211yesmaximal, characteristic, complemented
14#29762C211yesmaximal, characteristic, complemented
15#29648C211yesmaximal, characteristic, complemented
16#28312C211yesmaximal, characteristic, complemented
17#28117C211yesmaximal, characteristic, complemented
18#26917C211yesmaximal, characteristic, complemented
19#26901C211yesmaximal, characteristic, complemented
20#26834C211yesmaximal, characteristic, complemented
21#26827C211yesmaximal, characteristic, complemented
22#26494C211yesmaximal, characteristic, complemented
23#26486C211yesmaximal, characteristic, complemented
24#26388C211yesmaximal, characteristic, complemented
25#26370C211yesmaximal, characteristic, complemented
26#24612C211yesmaximal, characteristic, complemented
27#24516C211yesmaximal, characteristic, complemented
28#24074C211yesmaximal, characteristic, complemented
29#23939C211yesmaximal, characteristic
30#22602C211yesmaximal, characteristic, complemented
31#22086C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#518C2211yescharacteristic
36#3241—28no—
37C2×#501C2211yescharacteristic, complemented
38C2×#499C2211yescharacteristic, complemented
39C2×#490C2211yescharacteristic, complemented
40C2×#486C2211yescharacteristic, complemented
41#3118—28no—
42C2×#481C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#482C2211yescharacteristic
45C2×#482C2211yescharacteristic
46C2×#483C2211yescharacteristic
47C2×#480C2211yescharacteristic
48C2×#478C2211yescharacteristic, complemented
49C2×#478C2211yescharacteristic, complemented
50C2×#476C2211yescharacteristic
51C2×#476C2211yescharacteristic, complemented
52C2×#474C2211yescharacteristic
53C2×#474C2211yescharacteristic, complemented
54C2×#463C2211yescharacteristic
55C2×#463C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×#447C2211yescharacteristic
58C2×#447C2211yescharacteristic
59C2×#442C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×C4×D8C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×#433C2211yescharacteristic
65#2850C2211yescharacteristic
66#2718—21no—
67#2708—21no—
68#2686—21no—
69#2680—21no—
70#2625C2211yescharacteristic
71#2624C2211yescharacteristic
72#2566—21no—
73#2566—21no—
74#2563—21no—
75#2553—21no—
76#2550C2211yescharacteristic, complemented
77#2544C2211yescharacteristic, complemented
78#2542—21no—
79#2488—21no—
80#2454C2211yescharacteristic
81#2454C2211yescharacteristic
82#2454C2211yescharacteristic
83#2454C2211yescharacteristic
84#2453C2211yescharacteristic, complemented
85#2452C2211yescharacteristic
86#2452C2211yescharacteristic
87#2452C2211yescharacteristic
88#2452C2211yescharacteristic
89#2452C2211yescharacteristic, complemented
90#2447C2211yescharacteristic, complemented
91#2445C2211yescharacteristic, complemented
92#2437—21no—
93#2437—21no—
94#2437—21no—
95#2437—21no—
96#2427—21no—
97#2425—21no—
98#2367C2211yescharacteristic, complemented
99#2349C2211yescharacteristic, complemented
100#2317C2211yescharacteristic
101#2309C2211yescharacteristic
102C4×#121C2211yescharacteristic
103#2296C2211yescharacteristic
104C2×#390C2211yescharacteristic
105#2285C2211yescharacteristic
106#2092C2211yescharacteristic
107#2092C2211yescharacteristic
108#2087C2211yescharacteristic, complemented
109#2086C2211yescharacteristic, complemented
110#2085C2211yescharacteristic, complemented
111#2085C2211yescharacteristic, complemented
112#2068C2211yescharacteristic, complemented
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic, complemented
115#2067C2211yescharacteristic, complemented
116#2066C2211yescharacteristic, complemented
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic, complemented
121#2065C2211yescharacteristic, complemented
122#2059C2211yescharacteristic, complemented
123#2059C2211yescharacteristic, complemented
124#2058C2211yescharacteristic, complemented
125#2058C2211yescharacteristic, complemented
126#2058C2211yescharacteristic, complemented
127#2058C2211yescharacteristic, complemented
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2054C2211yescharacteristic
131#2054C2211yescharacteristic
132#2042C2211yescharacteristic, complemented
133#2042C2211yescharacteristic, complemented
134#2042C2211yescharacteristic, complemented
135#2042C2211yescharacteristic, complemented
136#2026C2211yescharacteristic, complemented
137#2026C2211yescharacteristic, complemented
138#2025C2211yescharacteristic
139#2025C2211yescharacteristic
140#2024C2211yescharacteristic, complemented
141#2024C2211yescharacteristic, complemented
142#2012C2211yescharacteristic
143#2012C2211yescharacteristic
144#2011C2211yescharacteristic
145#2011C2211yescharacteristic
146#1973C2211yescharacteristic
147#1973C2211yescharacteristic
148#1973C2211yescharacteristic
149#1972C2211yescharacteristic
150#1972C2211yescharacteristic
151#1968C2211yescharacteristic
152#1944C2211yescharacteristic, complemented
153#1944C2211yescharacteristic, complemented
154#1943C2211yescharacteristic, complemented
155#1942C2211yescharacteristic, complemented
156#1940C2211yescharacteristic, complemented
157#1940C2211yescharacteristic, complemented
158#1936C2211yescharacteristic
159#1936C2211yescharacteristic, complemented
160#1936C2211yescharacteristic, complemented
161#1936C2211yescharacteristic, complemented
162#1934C2211yescharacteristic
163#1934C2211yescharacteristic, complemented
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1920C2211yescharacteristic, complemented
167#1918C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1875C2211yescharacteristic
183#1875C2211yescharacteristic
184#1873C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1865C2211yescharacteristic, complemented
187#1864C2211yescharacteristic
188#1864C2211yescharacteristic
189#1864C2211yescharacteristic, complemented
190#1864C2211yescharacteristic, complemented
191#1864C2211yescharacteristic, complemented
192#1862C2211yescharacteristic
193#1862C2211yescharacteristic
194#1862C2211yescharacteristic, complemented
195#1854C2211yescharacteristic
196#1825C2211yescharacteristic
197#1824C2211yescharacteristic
198#1818C2211yescharacteristic
199#1818C2211yescharacteristic
200#1797C2211yescharacteristic
201#1786C2211yescharacteristic
202#1771C2211yescharacteristic, complemented
203#1771C2211yescharacteristic, complemented
204#1749C2211yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212#544—24no—
213#544—42no—
214#542—24no—
215#542—42no—
216#540—24no—
217#540—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#126—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121—21no—
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248#518—24no—
249#518—42no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4—21no—
268C22×C22⋊C4—21no—
269C22×C22⋊C4—21no—
270C22×C22⋊C4—21no—
271C22×C42C2311yescharacteristic
272#501—24no—
273#499—24no—
274#490—24no—
275#486—24no—
276#485—24no—
277#483—42no—
278#482—24no—
279#482D418yes—
280#481—24no—
281#480—24no—
282#478—24no—
283#478—24no—
284#476—24no—
285#476—24no—
286#474—24no—
287#474—24no—
288#463—24no—
289#463—24no—
290#450—24no—
291#447—24no—
292#447—42no—
293#442—24no—
294#440—24no—
295C4×SD16—24no—
296C4×D8—24no—
297#433—24no—
298#433—24no—
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356C2×C4×C8C2311yescharacteristic
357#400—21no—
358#400—21no—
359#399—21no—
360#399—21no—
361#399—21no—
362#399—21no—
363#399—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#395—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#393—21no—
389#393—21no—
390#393—21no—
391#393—21no—
392#393—21no—
393#391—21no—
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#390—21no—
398#390—21no—
399#390—21no—
400#390—21no—
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#389—21no—
414#389—21no—
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#387—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—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#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#384—21no—
458#384D411yescharacteristic
459#384D411yescharacteristic
460#382—21no—
461#382D411yescharacteristic
462#382D411yescharacteristic
463#382C2311yescharacteristic
464#381—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380—21no—
469#380—21no—
470#380D411yescharacteristic
471#380D411yescharacteristic
472#380D411yescharacteristic
473#380D411yescharacteristic
474#380C2311yescharacteristic
475#379—21no—
476#379—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C2×#95—21no—
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#336C2311yescharacteristic
504#336C2311yescharacteristic
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×Q8—21no—
519C22×Q8C2411yescharacteristic
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C2×D411yescharacteristic
545C23×C4C2×D411yescharacteristic
546C23×C4C2411yescharacteristic
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—44no—
580#127—22no—
581#127—41no—
582#126—44no—
583#125—22no—
584#125—22no—
585#125—22no—
586#125—41no—
587#125—41no—
588#125—41no—
589#125—44no—
590#124—22no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—44no—
595#123—44no—
596#123—44no—
597#123—44no—
598#123—82no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604C22⋊Q8—82no—
605C22⋊Q8—82no—
606C22⋊Q8—82no—
607C22⋊Q8—82no—
608C22⋊Q8—82no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—44no—
613#121—44no—
614#121C2×D414yes—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—44no—
634C4×D4—44no—
635C4×D4—82no—
636#117—22no—
637#117—22no—
638#117—22no—
639#117—22no—
640#117—22no—
641#117—41no—
642#117—41no—
643#117C2×D414yes—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
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—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
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—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—44no—
737C2×C22⋊C4—44no—
738C2×C22⋊C4—82no—
739C2×C22⋊C4—82no—
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—41no—
749C2×C42—41no—
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758#107—22no—
759#107—22no—
760#107—22no—
761#107—22no—
762#107—41no—
763#107C2×D414yes—
764#106—22no—
765#106—22no—
766#106—22no—
767#106—22no—
768#106—41no—
769#106—41no—
770#106—41no—
771#106C2×D414yes—
772C4⋊C8—22no—
773C4⋊C8—22no—
774C4⋊C8—22no—
775C4⋊C8—22no—
776C4⋊C8—41no—
777C4⋊C8—41no—
778#103—22no—
779#103—22no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802#102—41no—
803#102—41no—
804#102C2×D414yes—
805#102C2×D414yes—
806C22⋊C8—22no—
807C22⋊C8—22no—
808C22⋊C8—22no—
809C22⋊C8C2×D414yes—
810#97—22no—
811#97—22no—
812#97—41no—
813#97—41no—
814C4×C8—22no—
815C4×C8—22no—
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#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847C24—24no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—42no—
853C24—42no—
854C24—81no—
855C24—81no—
856C24—81no—
857C24—81no—
858C24C22×D411yescharacteristic
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4C22×D412yes—
915C2×D42−1+412yes—
916C2×D42−1+412yes—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D412yes—
980C22×C4H(5,𝔽2)12yes—
981C22×C4C2511yescharacteristic
982SD16—44no—
983SD16—44no—
984D8—44no—
985D8—44no—
986D8—82no—
987D8—82no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8C22×D412yes—
1011C2×C8C22×D412yes—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4C22×D412yes—
1069C4⋊C4C22×D412yes—
1070C4⋊C4C22×D412yes—
1071C22⋊C4—24no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—24no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C42—24no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—41no—
1131C42—41no—
1132C42—42no—
1133C42—42no—
1134C42—81no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—48no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—84no—
1171C23—84no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23D4212yes—
1177C23C23×D411yescharacteristic
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—162no—
1183Q8—162no—
1184Q8—162no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—22no—
1191D4—48no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—84no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—82no—
1285C2×C4—82no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4D4212yes—
1296C2×C4C23×D411yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C2×C4C2×2−1+411yescharacteristic
1299C2×C4C2×2−1+411yescharacteristic
1300C2×C4#58511yescharacteristic
1301C2×C4#58511yescharacteristic
1302C8—22no—
1303C8—22no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—168no—
1346C22#344911yescharacteristic
1347C22C2×D4211yescharacteristic
1348C22#348611yescharacteristic
1349C22#358411yescharacteristic
1350C22#358511yescharacteristic
1351C22#358511yescharacteristic
1352C22#358511yescharacteristic
1353C4—22no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—42no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4#348911yescharacteristic
1379C4#348911yescharacteristic
1380C4#353511yescharacteristic
1381C4#353511yescharacteristic
1382C2—42no—
1383C2—82no—
1384C2—82no—
1385C2—82no—
1386C2—161no—
1387C2#3765311yescharacteristic
1388C2#6098611yescharacteristic
1389C2#6100311yescharacteristic
1390C2#6108211yescharacteristic
1391C2#6109211yescharacteristic
1392C2#6185511yescharacteristic
1393C2#6187211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23939C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3241C2semidirect
2. C2×#3118C2semidirect
3. #39346C2semidirect
4. #35529C2semidirect
5. #33014C2semidirect
6. #31250C2semidirect
7. #31247C2semidirect
8. #31170C2semidirect
9. #31168C2semidirect
10. #30974C2semidirect
11. #30950C2semidirect
12. #30891C2semidirect
13. #30875C2semidirect
14. #29762C2semidirect
15. #29648C2semidirect
16. #28312C2semidirect
17. #28117C2semidirect
18. #26917C2semidirect
19. #26901C2semidirect
20. #26834C2semidirect
21. #26827C2semidirect
22. #26494C2semidirect
23. #26486C2semidirect
24. #26388C2semidirect
25. #26370C2semidirect
26. #24612C2semidirect
27. #24516C2semidirect
28. #24074C2semidirect
30. #22602C2semidirect
31. #22086C2semidirect
37. C2×#501C22semidirect
38. C2×#499C22semidirect
39. C2×#490C22semidirect
40. C2×#486C22semidirect
48. C2×#478C22semidirect
49. C2×#478C22semidirect
51. C2×#476C22semidirect
53. C2×#474C22semidirect
76. #2550C22semidirect
77. #2544C22semidirect
84. #2453C22semidirect
89. #2452C22semidirect
90. #2447C22semidirect
91. #2445C22semidirect
98. #2367C22semidirect
99. #2349C22semidirect
108. #2087C22semidirect
109. #2086C22semidirect
110. #2085C22semidirect
111. #2085C22semidirect
112. #2068C22semidirect
114. #2067C22semidirect
115. #2067C22semidirect
116. #2066C22semidirect
120. #2065C22semidirect
121. #2065C22semidirect
122. #2059C22semidirect
123. #2059C22semidirect
124. #2058C22semidirect
125. #2058C22semidirect
126. #2058C22semidirect
127. #2058C22semidirect
132. #2042C22semidirect
133. #2042C22semidirect
134. #2042C22semidirect
135. #2042C22semidirect
136. #2026C22semidirect
137. #2026C22semidirect
140. #2024C22semidirect
141. #2024C22semidirect
152. #1944C22semidirect
153. #1944C22semidirect
154. #1943C22semidirect
155. #1942C22semidirect
156. #1940C22semidirect
157. #1940C22semidirect
159. #1936C22semidirect
160. #1936C22semidirect
161. #1936C22semidirect
163. #1934C22semidirect
166. #1920C22semidirect
167. #1918C22semidirect
168. #1917C22semidirect
169. #1917C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
185. #1865C22semidirect
186. #1865C22semidirect
189. #1864C22semidirect
190. #1864C22semidirect
191. #1864C22semidirect
194. #1862C22semidirect
202. #1771C22semidirect
203. #1771C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32412
C2×#31182
#393462
#355292
#330142
#312502
#312472
#311702
#311682
#309742
#309502
#308912
#308752
#297622
#296482
#283122
#281172
#269172
#269012
#268342
#268272
#264942
#264862
#263882
#263702
#246122
#245162
#240742
#239392
#226022
#220862