Finite Group Databasebeta

← #6548168

Subgroups — #6548168

Order 512.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39057C211yesmaximal, characteristic, complemented
2#34476C211yesmaximal, characteristic, complemented
3#30141C211yesmaximal, characteristic, complemented
4#30020C211yesmaximal, characteristic, complemented
5#29729C211yesmaximal, characteristic, complemented
6#29547C211yesmaximal, characteristic, complemented
7#29452C211yesmaximal, characteristic, complemented
8#29249C211yesmaximal, characteristic, complemented
9#28114C211yesmaximal, characteristic, complemented
10#27520C211yesmaximal, characteristic, complemented
11#27358C211yesmaximal, characteristic, complemented
12#27195C211yesmaximal, characteristic, complemented
13#27053C211yesmaximal, characteristic, complemented
14#26765C211yesmaximal, characteristic, complemented
15#26620C211yesmaximal, characteristic, complemented
16#26596C211yesmaximal, characteristic, complemented
17#26200C211yesmaximal, characteristic, complemented
18#26142C211yesmaximal, characteristic, complemented
19#25164C211yesmaximal, characteristic, complemented
20#24763C211yesmaximal, characteristic, complemented
21#24501C211yesmaximal, characteristic, complemented
22#24452C211yesmaximal, characteristic, complemented
23#24428C211yesmaximal, characteristic
24#23701C211yesmaximal, characteristic, complemented
25#23695C211yesmaximal, characteristic, complemented
26#23616C211yesmaximal, characteristic, complemented
27#23127C211yesmaximal, characteristic, complemented
28#23040C211yesmaximal, characteristic, complemented
29#22883C211yesmaximal, characteristic, complemented
30#22873C211yesmaximal, characteristic, complemented
31#22752C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#466C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#452C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×C4×Q16C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×#431C2211yescharacteristic
45C2×#428C2211yescharacteristic, complemented
46C2×#424C2211yescharacteristic, complemented
47C2×#417C2211yescharacteristic
48C2×#416C2211yescharacteristic
49#2855C2211yescharacteristic
50#2793—21no—
51#2781—21no—
52#2761—21no—
53#2749—21no—
54#2644C2211yescharacteristic, complemented
55#2620C2211yescharacteristic, complemented
56#2600—21no—
57#2566—21no—
58#2515—21no—
59#2506C2211yescharacteristic, complemented
60#2497C2211yescharacteristic
61#2460—21no—
62#2447C2211yescharacteristic, complemented
63#2426C2211yescharacteristic
64#2417C2211yescharacteristic
65#2414C2211yescharacteristic
66#2377—21no—
67#2376—21no—
68#2367C2211yescharacteristic
69#2362C2211yescharacteristic, complemented
70#2361C2211yescharacteristic
71#2361C2211yescharacteristic, complemented
72#2360C2211yescharacteristic
73#2358—21no—
74#2354C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76#2342—21no—
77#2341C2211yescharacteristic
78D4×C22⋊C4C2211yescharacteristic
79#2335—21no—
80#2326C2211yescharacteristic
81#2324—21no—
82#2324C2211yescharacteristic
83#2321—21no—
84#2320C2211yescharacteristic, complemented
85#2319C2211yescharacteristic
86#2317C2211yescharacteristic, complemented
87#2315—21no—
88#2311C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C4×#121C2211yescharacteristic
91C2×#390C2211yescharacteristic
92#2290C2211yescharacteristic
93#2099C2211yescharacteristic, complemented
94#2094C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2066C2211yescharacteristic, complemented
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2056C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic, complemented
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2036C2211yescharacteristic
124#2036C2211yescharacteristic
125#2035C2211yescharacteristic
126#2033C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic, complemented
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2001C2211yescharacteristic
132#2000C2211yescharacteristic
133#1983C2211yescharacteristic, complemented
134#1972C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1947C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic, complemented
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1923C2211yescharacteristic
151#1921C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1895C2211yescharacteristic, complemented
160#1892C2211yescharacteristic, complemented
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic, complemented
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1878C2211yescharacteristic, complemented
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic, complemented
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic, complemented
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1865C2211yescharacteristic, complemented
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1854C2211yescharacteristic, complemented
185#1853C2211yescharacteristic
186#1853C2211yescharacteristic, complemented
187#1832C2211yescharacteristic, complemented
188#1823C2211yescharacteristic
189#1802C2211yescharacteristic
190#1798C2211yescharacteristic, complemented
191#1797C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194C4×#107C2211yescharacteristic, complemented
195#1768C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#546—24no—
214#546—24no—
215C2×#125—21no—
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250#480—42no—
251#468—24no—
252#466—24no—
253#463—42no—
254#452—24no—
255#450—42no—
256#449—24no—
257#447—42no—
258#440—42no—
259C4×Q16—42no—
260C4×SD16—42no—
261#431—42no—
262#428—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273#424—42no—
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#417—42no—
281#416—42no—
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#400—21no—
321#400—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#392—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#390—21no—
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388D411yescharacteristic
391#388D411yescharacteristic
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387D411yescharacteristic
402#387D411yescharacteristic
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386D411yescharacteristic
413#386D411yescharacteristic
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385D411yescharacteristic
429#385D411yescharacteristic
430#384—21no—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#383—21no—
434#382—21no—
435#382—21no—
436#381—21no—
437#381—21no—
438#381—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#379—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41#4114yes—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×Q16—22no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—41no—
553C22×C8—22no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564#125—82no—
565#124—22no—
566#124—22no—
567#124—41no—
568#124—41no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576#121—28no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121#4114yes—
583#120—28no—
584C4×Q8—22no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—82no—
601C4×D4—82no—
602C4×D4—82no—
603C4×D4—82no—
604#117—22no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—82no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C22⋊C4—28no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
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—82no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#107—22no—
722#107—22no—
723#107—22no—
724#107—22no—
725#107—22no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8—22no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771#97—41no—
772C4×C8—22no—
773C4×C8—41no—
774C4×C8—41no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—24no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826#41—44no—
827#41—44no—
828#41—82no—
829#41—82no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8C2×#4112yes—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—41no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4C2×#4112yes—
881C2×D4C2×#4112yes—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—22no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—24no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—24no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C2×#4112yes—
948C22×C4C2×#4112yes—
949C22×C4C2511yescharacteristic
950Q16—44no—
951SD16—44no—
952SD16—44no—
953SD16—82no—
954D8—82no—
955D8—82no—
956M16—44no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
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—82no—
981C2×C8H(5,𝔽2)12yes—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
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—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4C2×#4112yes—
1031C4⋊C4H(5,𝔽2)12yes—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—24no—
1040C22⋊C4—22no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—41no—
1088C42—41no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—48no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—84no—
1133C23—84no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23—162no—
1138C23#52512yes—
1139C23#57712yes—
1140C23C23×D411yescharacteristic
1141Q8—22no—
1142Q8—22no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149D4—22no—
1150D4—22no—
1151D4—22no—
1152D4—22no—
1153D4—44no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—84no—
1163D4—84no—
1164D4—84no—
1165D4—84no—
1166D4—84no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
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—22no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—22no—
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—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—44no—
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—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—82no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—162no—
1253C2×C4—162no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4#52512yes—
1259C2×C4#57612yes—
1260C2×C4C22×#4111yescharacteristic
1261C2×C4C22×#4111yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C8—22no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—168no—
1310C22C2×#52511yescharacteristic
1311C22#348811yescharacteristic
1312C22#349611yescharacteristic
1313C22C2×#57611yescharacteristic
1314C22C2×#57711yescharacteristic
1315C22#358411yescharacteristic
1316C22#358611yescharacteristic
1317C4—22no—
1318C4—22no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—42no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—42no—
1329C4—41no—
1330C4—41no—
1331C4—42no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4#350511yescharacteristic
1343C4#350511yescharacteristic
1344C4#351911yescharacteristic
1345C4#352111yescharacteristic
1346C2—42no—
1347C2—42no—
1348C2—82no—
1349C2—82no—
1350C2—161no—
1351C2#3577711yescharacteristic
1352C2#6057011yescharacteristic
1353C2#6058511yescharacteristic
1354C2#6205011yescharacteristic
1355C2#6205311yescharacteristic
1356C2#6227711yescharacteristic
1357C2#6231111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24428C2
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. #39057C2semidirect
2. #34476C2semidirect
3. #30141C2semidirect
4. #30020C2semidirect
5. #29729C2semidirect
6. #29547C2semidirect
7. #29452C2semidirect
8. #29249C2semidirect
9. #28114C2semidirect
10. #27520C2semidirect
11. #27358C2semidirect
12. #27195C2semidirect
13. #27053C2semidirect
14. #26765C2semidirect
15. #26620C2semidirect
16. #26596C2semidirect
17. #26200C2semidirect
18. #26142C2semidirect
19. #25164C2semidirect
20. #24763C2semidirect
21. #24501C2semidirect
22. #24452C2semidirect
24. #23701C2semidirect
25. #23695C2semidirect
26. #23616C2semidirect
27. #23127C2semidirect
28. #23040C2semidirect
29. #22883C2semidirect
30. #22873C2semidirect
31. #22752C2semidirect
42. C2×C4×Q16C22semidirect
43. C2×C4×SD16C22semidirect
45. C2×#428C22semidirect
46. C2×#424C22semidirect
54. #2644C22semidirect
55. #2620C22semidirect
59. #2506C22semidirect
62. #2447C22semidirect
69. #2362C22semidirect
71. #2361C22semidirect
84. #2320C22semidirect
86. #2317C22semidirect
93. #2099C22semidirect
94. #2094C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2083C22semidirect
100. #2072C22semidirect
101. #2072C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
109. #2067C22semidirect
110. #2066C22semidirect
111. #2066C22semidirect
115. #2056C22semidirect
118. #2055C22semidirect
128. #2015C22semidirect
133. #1983C22semidirect
137. #1947C22semidirect
138. #1943C22semidirect
142. #1934C22semidirect
143. #1927C22semidirect
144. #1927C22semidirect
146. #1926C22semidirect
151. #1921C22semidirect
152. #1920C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1918C22semidirect
157. #1916C22semidirect
158. #1916C22semidirect
159. #1895C22semidirect
160. #1892C22semidirect
162. #1880C22semidirect
167. #1878C22semidirect
171. #1874C22semidirect
173. #1872C22semidirect
176. #1865C22semidirect
177. #1865C22semidirect
181. #1863C22semidirect
184. #1854C22semidirect
186. #1853C22semidirect
187. #1832C22semidirect
190. #1798C22semidirect
194. C4×#107C22semidirect
195. #1768C22semidirect
196. #1763C22semidirect
197. C4×#103C22semidirect
199. C4×#102C22semidirect
200. #1753C22semidirect
201. C8×C22⋊C4C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#390572
#344762
#301412
#300202
#297292
#295472
#294522
#292492
#281142
#275202
#273582
#271952
#270532
#267652
#266202
#265962
#262002
#261422
#251642
#247632
#245012
#244522
#244282
#237012
#236952
#236162
#231272
#230402
#228832
#228732
#227522