Finite Group Databasebeta

← #6574767

Subgroups — #6574767

Order 512.

2056 conjugacy classes of subgroups.

The subgroup lattice has 1383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3081C211yesmaximal, characteristic, complemented
2C2×#3080C211yesmaximal, characteristic, complemented
3#37687C211yesmaximal, characteristic, complemented
4#34292C211yesmaximal, characteristic
5#33203C211yesmaximal, characteristic, complemented
6#32966C211yesmaximal, characteristic, complemented
7#32955C211yesmaximal, characteristic, complemented
8#28524C211yesmaximal, characteristic, complemented
9#28293C211yesmaximal, characteristic, complemented
10#26477C211yesmaximal, characteristic, complemented
11#26471C211yesmaximal, characteristic, complemented
12#26365C211yesmaximal, characteristic, complemented
13#26361C211yesmaximal, characteristic, complemented
14#26357C211yesmaximal, characteristic, complemented
15#26351C211yesmaximal, characteristic, complemented
16#26053C211yesmaximal, characteristic, complemented
17#26045C211yesmaximal, characteristic, complemented
18#25980C211yesmaximal, characteristic, complemented
19#25978C211yesmaximal, characteristic, complemented
20#25976C211yesmaximal, characteristic, complemented
21#25952C211yesmaximal, characteristic, complemented
22#24850C211yesmaximal, characteristic, complemented
23#24843C211yesmaximal, characteristic, complemented
24#24310C211yesmaximal, characteristic, complemented
25#24305C211yesmaximal, characteristic, complemented
26#22663C211yesmaximal, characteristic, complemented
27#22660C211yesmaximal, characteristic, complemented
28#22649C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic
30#22419C211yesmaximal, characteristic
31#21620C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C22×#125C2211yescharacteristic, complemented
35C2×#518C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#3081—28no—
38#3080—28no—
39C2×#479C2211yescharacteristic, complemented
40C2×#479C2211yescharacteristic, complemented
41C2×#479C2211yescharacteristic, complemented
42C2×#479C2211yescharacteristic, complemented
43C2×#475C2211yescharacteristic, complemented
44C2×#478C2211yescharacteristic
45C2×#478C2211yescharacteristic
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#476C2211yescharacteristic
53C2×#476C2211yescharacteristic
54C2×#474C2211yescharacteristic
55C2×#474C2211yescharacteristic
56C2×#436C2211yescharacteristic
57C2×#435C2211yescharacteristic
58C2×#428C2211yescharacteristic
59C2×#428C2211yescharacteristic, complemented
60C2×#428C2211yescharacteristic, complemented
61C2×#427C2211yescharacteristic
62C2×#424C2211yescharacteristic
63C2×#423C2211yescharacteristic, complemented
64C2×#417C2211yescharacteristic
65C2×#417C2211yescharacteristic
66C2×#418C2211yescharacteristic
67C22×#102C2211yescharacteristic
68#2857C2211yescharacteristic, complemented
69#2726—21no—
70#2720—21no—
71#2713—21no—
72#2704—21no—
73#2660C2211yescharacteristic, complemented
74#2629C2211yescharacteristic
75#2552C2211yescharacteristic, complemented
76#2550C2211yescharacteristic, complemented
77#2473—21no—
78#2449—21no—
79#2442C2211yescharacteristic
80#2442C2211yescharacteristic, complemented
81#2441C2211yescharacteristic
82#2440—21no—
83#2440C2211yescharacteristic, complemented
84#2417—21no—
85#2367C2211yescharacteristic
86#2363C2211yescharacteristic
87#2362C2211yescharacteristic
88#2361—21no—
89#2359—21no—
90#2358—21no—
91#2354C2211yescharacteristic
92#2352C2211yescharacteristic
93D4×C4⋊C4C2211yescharacteristic
94D4×C4⋊C4C2211yescharacteristic
95#2342—21no—
96#2339C2211yescharacteristic
97D4×C22⋊C4C2211yescharacteristic
98#2330C2211yescharacteristic, complemented
99#2326C2211yescharacteristic
100#2325—21no—
101#2323C2211yescharacteristic
102#2321—21no—
103C4×#123—21no—
104C4×#121C2211yescharacteristic
105#2290C2211yescharacteristic
106C2×#388—21no—
107#2275C2211yescharacteristic
108#2097C2211yescharacteristic, complemented
109#2096C2211yescharacteristic, complemented
110#2094C2211yescharacteristic
111#2092C2211yescharacteristic
112#2088C2211yescharacteristic, complemented
113#2088C2211yescharacteristic, complemented
114#2088C2211yescharacteristic, complemented
115#2086C2211yescharacteristic, complemented
116#2068C2211yescharacteristic, complemented
117#2068C2211yescharacteristic, complemented
118#2068C2211yescharacteristic, complemented
119#2067C2211yescharacteristic
120#2067C2211yescharacteristic
121#2067C2211yescharacteristic
122#2066C2211yescharacteristic, complemented
123#2065C2211yescharacteristic
124#2059C2211yescharacteristic, complemented
125#2059C2211yescharacteristic, complemented
126#2059C2211yescharacteristic, complemented
127#2058C2211yescharacteristic, complemented
128#2026C2211yescharacteristic, complemented
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2024C2211yescharacteristic, complemented
132#1989C2211yescharacteristic, complemented
133#1989C2211yescharacteristic, complemented
134#1987C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1959C2211yescharacteristic
138#1958C2211yescharacteristic
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1947C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1947C2211yescharacteristic, complemented
146#1940C2211yescharacteristic, complemented
147#1939C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1894C2211yescharacteristic
153#1892C2211yescharacteristic
154#1874C2211yescharacteristic
155#1874C2211yescharacteristic
156#1873C2211yescharacteristic
157#1872C2211yescharacteristic
158#1864C2211yescharacteristic
159#1864C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1863C2211yescharacteristic, complemented
163#1863C2211yescharacteristic, complemented
164#1862C2211yescharacteristic
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic, complemented
172#1854C2211yescharacteristic, complemented
173#1853C2211yescharacteristic
174#1853C2211yescharacteristic, complemented
175#1852C2211yescharacteristic, complemented
176#1851C2211yescharacteristic
177#1851C2211yescharacteristic, complemented
178#1851C2211yescharacteristic, complemented
179#1850C2211yescharacteristic
180#1847C2211yescharacteristic, complemented
181#1844C2211yescharacteristic, complemented
182#1843C2211yescharacteristic, complemented
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic, complemented
185#1809C2211yescharacteristic, complemented
186#1808C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1803C2211yescharacteristic, complemented
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic, complemented
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200#1776C2211yescharacteristic, complemented
201C4×#107C2211yescharacteristic, complemented
202#1768C2211yescharacteristic, complemented
203#1762C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#546—24no—
212#546Q818yescomplemented
213#544—24no—
214#544—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125—21no—
219C2×#125—24no—
220C2×#125—21no—
221C2×#125—21no—
222C2×#125—42no—
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238#518—24no—
239#518—42no—
240C4×#41—24no—
241C4×#41—42no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
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—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C4⋊C4—21no—
264C22×C4⋊C4—21no—
265C22×C4⋊C4—21no—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C22⋊C4—21no—
270C22×C22⋊C4—21no—
271C22×C22⋊C4—21no—
272C22×C22⋊C4—21no—
273C22×C42—21no—
274C22×C42C2311yescharacteristic
275#479—24no—
276#479—24no—
277#479—24no—
278#479—24no—
279#478—24no—
280#478—24no—
281#478—24no—
282#478—24no—
283#478—24no—
284#478—24no—
285#478—42no—
286#478D418yescomplemented
287#476—24no—
288#476—24no—
289#475—42no—
290#474—24no—
291#474—24no—
292#436—24no—
293#435—24no—
294#428—24no—
295#428—24no—
296#428—24no—
297#427—24no—
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×#106C2311yescharacteristic
318#424—24no—
319#423—24no—
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
328C2×C4⋊C8C2311yescharacteristic
329C2×C4⋊C8C2311yescharacteristic
330C2×C4⋊C8C2311yescharacteristic
331C2×C4⋊C8C2311yescharacteristic
332#418—24no—
333#417—24no—
334#417—24no—
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#102—24no—
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×C22⋊C8C2311yescharacteristic
361C2×C22⋊C8C2311yescharacteristic
362C2×C22⋊C8C2311yescharacteristic
363C2×C22⋊C8C2311yescharacteristic
364C2×#97C2311yescharacteristic
365C2×C4×C8C2311yescharacteristic
366#400—21no—
367#400—21no—
368#399—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#398—21no—
375#398—21no—
376#398—21no—
377#398—21no—
378#398—21no—
379#396—21no—
380#396—21no—
381#396—21no—
382#395—21no—
383#395—21no—
384#395—21no—
385#395—21no—
386#391—21no—
387#391—21no—
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#390—21no—
391#390—21no—
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388D411yescharacteristic
424#388D411yescharacteristic
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387D411yescharacteristic
432#387D411yescharacteristic
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386D411yescharacteristic
441#386D411yescharacteristic
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#385D411yescharacteristic
453#385D411yescharacteristic
454#384—21no—
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#381—21no—
462#380—21no—
463#380—21no—
464#380—21no—
465#380—21no—
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#379—21no—
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4—21no—
487C4×C22⋊C4—21no—
488C4×C22⋊C4C2311yescharacteristic
489C4×C22⋊C4C2311yescharacteristic
490#376C2311yescharacteristic
491C2×#95—21no—
492C2×#95—21no—
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#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519C25—21no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41C2×Q814yes—
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8C2411yescharacteristic
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—22no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4C2×D411yescharacteristic
538C22×D4C2×Q814yes—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4C2×D411yescharacteristic
553C23×C4C2×D411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C2×M16—22no—
557C2×M16—22no—
558C2×M16—22no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—41no—
565C22×C8—22no—
566C22×C8—22no—
567C22×C8—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—41no—
580C4⋊Q8—44no—
581#125—22no—
582#125—22no—
583#125—22no—
584#125—22no—
585#125—22no—
586#125—22no—
587#125—41no—
588#125—41no—
589#125—41no—
590#125—44no—
591#125—44no—
592#125—44no—
593#125C2×D414yes—
594#124—22no—
595#124C2×Q814yes—
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600C22⋊Q8—82no—
601C22⋊Q8—82no—
602C22⋊Q8C2×Q814yes—
603#121—22no—
604#121—28no—
605#121C2×Q814yes—
606#120—28no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—41no—
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—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—44no—
624C4×D4—44no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4—82no—
628C4×D4—82no—
629C4×D4C2×D414yes—
630C4×D4C2×Q814yes—
631C4×D4C2×Q814yes—
632C4×D4#4114yes—
633#117—22no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—22no—
638#117—44no—
639#117—41no—
640#117—41no—
641#117—41no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
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⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—41no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4—41no—
682C2×C4⋊C4—44no—
683C2×C4⋊C4—44no—
684C2×C4⋊C4—82no—
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
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—28no—
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—44no—
729C2×C22⋊C4—44no—
730C2×C22⋊C4—82no—
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C42—22no—
740C2×C42—22no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—44no—
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759#107—22no—
760#107—22no—
761#107—22no—
762#107—22no—
763#107—22no—
764#107—22no—
765#107—41no—
766#107—41no—
767#107—41no—
768#107C2×D414yes—
769#106—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—41no—
776#106—41no—
777#106—41no—
778#106C2×D414yes—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—22no—
784C4⋊C8—22no—
785C4⋊C8—22no—
786C4⋊C8—22no—
787C4⋊C8—22no—
788C4⋊C8—41no—
789C4⋊C8—41no—
790C4⋊C8C2×D414yes—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—41no—
810#102—41no—
811#102—41no—
812#102—41no—
813#102C2×D414yes—
814#102C2×D414yes—
815C22⋊C8—22no—
816C22⋊C8—22no—
817C22⋊C8—22no—
818C22⋊C8—22no—
819#97—22no—
820C4×C8—22no—
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#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858C24—21no—
859C24—21no—
860C24—24no—
861C24—42no—
862C24—42no—
863C24—81no—
864C24—81no—
865C24—81no—
866C24—81no—
867C24C22×D411yescharacteristic
868C24C22×D411yescharacteristic
869#41—28no—
870#41—44no—
871#41—44no—
872#41—44no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×Q8C22×Q812yes—
885C2×D4—28no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—24no—
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—41no—
901C2×D4—41no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4C22⋊Q814yes—
909C2×D4C22×D412yes—
910C2×D4C22×Q812yes—
911C2×D4C22×Q812yes—
912C2×D42−1+412yes—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
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—24no—
927C22×C4—24no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—24no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
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×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×Q812yes—
987C22×C4C22×Q812yes—
988C22×C4C2×#4112yes—
989C22×C4C2×#4112yes—
990C22×C4C2511yescharacteristic
991M16—44no—
992M16—44no—
993M16—44no—
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×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—44no—
1017C2×C8C22×D412yes—
1018C2×C8C22×D412yes—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
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—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
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—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4C22⋊Q814yes—
1080C4⋊C4C22×D412yes—
1081C4⋊C4C22×D412yes—
1082C4⋊C4C22×D412yes—
1083C4⋊C4C22×Q812yes—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—24no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4C22⋊Q814yes—
1115C22⋊C4C22⋊Q814yes—
1116C42—22no—
1117C42—22no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—81no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C42—81no—
1134C42C22×D412yes—
1135C42C22×Q812yes—
1136C42C2×#4112yes—
1137C42H(5,𝔽2)12yes—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—22no—
1147C23—21no—
1148C23—22no—
1149C23—21no—
1150C23—22no—
1151C23—21no—
1152C23—21no—
1153C23—22no—
1154C23—48no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—84no—
1166C23—84no—
1167C23—162no—
1168C23—162no—
1169C23—162no—
1170C23—162no—
1171C23C2×C22⋊Q812yes—
1172C23C2×C22⋊Q812yes—
1173C23C23×D411yescharacteristic
1174Q8—22no—
1175Q8—22no—
1176Q8—41no—
1177Q8—41no—
1178Q8—162no—
1179Q8—162no—
1180D4—22no—
1181D4—22no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—44no—
1186D4—48no—
1187D4—48no—
1188D4—41no—
1189D4—41no—
1190D4—84no—
1191D4D4×Q814yes—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
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—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
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—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—48no—
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—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
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—82no—
1274C2×C4—82no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4C2×C22⋊Q812yes—
1286C2×C4C2×C22⋊Q812yes—
1287C2×C4C2×C22⋊Q812yes—
1288C2×C4C2×C22⋊Q812yes—
1289C2×C4D4212yes—
1290C2×C4D4212yes—
1291C2×C4C23×D411yescharacteristic
1292C2×C4C23×Q811yescharacteristic
1293C2×C4C22×#4111yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×2−1+411yescharacteristic
1296C2×C4#58511yescharacteristic
1297C8—22no—
1298C8—22no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—24no—
1312C22—42no—
1313C22—41no—
1314C22—41no—
1315C22—42no—
1316C22—42no—
1317C22—41no—
1318C22—42no—
1319C22—41no—
1320C22—41no—
1321C22—42no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—168no—
1334C22C22×C22⋊Q811yescharacteristic
1335C22C2×D4211yescharacteristic
1336C22#348911yescharacteristic
1337C22#358411yescharacteristic
1338C22#358511yescharacteristic
1339C22#358511yescharacteristic
1340C22#358611yescharacteristic
1341C4—22no—
1342C4—22no—
1343C4—22no—
1344C4—22no—
1345C4—22no—
1346C4—22no—
1347C4—41no—
1348C4—42no—
1349C4—41no—
1350C4—41no—
1351C4—42no—
1352C4—41no—
1353C4—41no—
1354C4—42no—
1355C4—42no—
1356C4—41no—
1357C4—42no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4C2×D4×Q811yescharacteristic
1368C4D4×#4111yescharacteristic
1369C4#350111yescharacteristic
1370C4#352011yescharacteristic
1371C2—42no—
1372C2—42no—
1373C2—44no—
1374C2—82no—
1375C2D4×C22⋊Q811yescharacteristic
1376C2#6049311yescharacteristic
1377C2#6049611yescharacteristic
1378C2#6106211yescharacteristic
1379C2#6107411yescharacteristic
1380C2#6219611yescharacteristic
1381C2#6223511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3081C2semidirect
2. C2×#3080C2semidirect
3. #37687C2semidirect
5. #33203C2semidirect
6. #32966C2semidirect
7. #32955C2semidirect
8. #28524C2semidirect
9. #28293C2semidirect
10. #26477C2semidirect
11. #26471C2semidirect
12. #26365C2semidirect
13. #26361C2semidirect
14. #26357C2semidirect
15. #26351C2semidirect
16. #26053C2semidirect
17. #26045C2semidirect
18. #25980C2semidirect
19. #25978C2semidirect
20. #25976C2semidirect
21. #25952C2semidirect
22. #24850C2semidirect
23. #24843C2semidirect
24. #24310C2semidirect
25. #24305C2semidirect
26. #22663C2semidirect
27. #22660C2semidirect
28. #22649C2semidirect
31. #21620C2semidirect
34. C22×#125C22semidirect
39. C2×#479C22semidirect
40. C2×#479C22semidirect
41. C2×#479C22semidirect
42. C2×#479C22semidirect
43. C2×#475C22semidirect
59. C2×#428C22semidirect
60. C2×#428C22semidirect
63. C2×#423C22semidirect
68. #2857C22semidirect
73. #2660C22semidirect
75. #2552C22semidirect
76. #2550C22semidirect
80. #2442C22semidirect
83. #2440C22semidirect
98. #2330C22semidirect
108. #2097C22semidirect
109. #2096C22semidirect
112. #2088C22semidirect
113. #2088C22semidirect
114. #2088C22semidirect
115. #2086C22semidirect
116. #2068C22semidirect
117. #2068C22semidirect
118. #2068C22semidirect
122. #2066C22semidirect
124. #2059C22semidirect
125. #2059C22semidirect
126. #2059C22semidirect
127. #2058C22semidirect
128. #2026C22semidirect
131. #2024C22semidirect
132. #1989C22semidirect
133. #1989C22semidirect
134. #1987C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1948C22semidirect
142. #1947C22semidirect
143. #1947C22semidirect
144. #1947C22semidirect
145. #1947C22semidirect
146. #1940C22semidirect
147. #1939C22semidirect
148. #1921C22semidirect
149. #1920C22semidirect
162. #1863C22semidirect
163. #1863C22semidirect
171. #1854C22semidirect
172. #1854C22semidirect
174. #1853C22semidirect
175. #1852C22semidirect
177. #1851C22semidirect
178. #1851C22semidirect
180. #1847C22semidirect
181. #1844C22semidirect
182. #1843C22semidirect
184. #1809C22semidirect
185. #1809C22semidirect
189. #1803C22semidirect
195. #1797C22semidirect
200. #1776C22semidirect
201. C4×#107C22semidirect
202. #1768C22semidirect
212. #546Q8semidirect
286. #478D4semidirect

Maximal subgroups

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

subgroupindex
C2×#30812
C2×#30802
#376872
#342922
#332032
#329662
#329552
#285242
#282932
#264772
#264712
#263652
#263612
#263572
#263512
#260532
#260452
#259802
#259782
#259762
#259522
#248502
#248432
#243102
#243052
#226632
#226602
#226492
#224272
#224192
#216202