Finite Group Databasebeta

← #6627685

Subgroups — #6627685

Order 512.

1513 conjugacy classes of subgroups.

The subgroup lattice has 1177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36590C211yesmaximal, characteristic, complemented
2C4×#554C211yesmaximal, characteristic, complemented
3#33199C211yesmaximal, characteristic, complemented
4#33028C211yesmaximal, characteristic
5#33028C211yesmaximal, characteristic
6#29353C211yesmaximal, characteristic, complemented
7#29350C211yesmaximal, characteristic, complemented
8#29280C211yesmaximal, characteristic, complemented
9#29279C211yesmaximal, characteristic, complemented
10#29227C211yesmaximal, characteristic, complemented
11#28285C211yesmaximal, characteristic, complemented
12#27568C211yesmaximal, characteristic
13#27566C211yesmaximal, characteristic, complemented
14#27560C211yesmaximal, characteristic
15#27558C211yesmaximal, characteristic, complemented
16#27148C211yesmaximal, characteristic, complemented
17#27146C211yesmaximal, characteristic, complemented
18#27136C211yesmaximal, characteristic, complemented
19#27134C211yesmaximal, characteristic, complemented
20#25008C211yesmaximal, characteristic, complemented
21#25006C211yesmaximal, characteristic, complemented
22#24349C211yesmaximal, characteristic, complemented
23#24347C211yesmaximal, characteristic
24#23078C211yesmaximal, characteristic, complemented
25#23076C211yesmaximal, characteristic, complemented
26#22823C211yesmaximal, characteristic, complemented
27#22780C211yesmaximal, characteristic
28#22776C211yesmaximal, characteristic, complemented
29#21617C211yesmaximal, characteristic, complemented
30C4×#478C211yesmaximal, characteristic, complemented
31#21507C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#442C2211yescharacteristic
39C2×#440C2211yescharacteristic
40#2861C2211yescharacteristic
41#2861C2211yescharacteristic
42#2859C2211yescharacteristic
43#2594—21no—
44#2594—21no—
45#2582C2211yescharacteristic
46#2538C2211yescharacteristic
47#2525—21no—
48#2525—21no—
49#2514C2211yescharacteristic
50#2514C2211yescharacteristic
51#2513C2211yescharacteristic
52#2513C2211yescharacteristic
53#2494—21no—
54#2421—21no—
55#2370C2211yescharacteristic
56#2370C2211yescharacteristic
57#2369C2211yescharacteristic
58#2368—21no—
59#2368—21no—
60#2362—21no—
61#2360—21no—
62#2355C2211yescharacteristic
63#2355C2211yescharacteristic
64#2354C2211yescharacteristic
65#2349C2211yescharacteristic
66#2349C2211yescharacteristic
67D4×C4⋊C4C2211yescharacteristic
68#2347—21no—
69#2345—21no—
70C4×C4⋊Q8C2211yescharacteristic
71C4×#125C2211yescharacteristic
72C4×#125C2211yescharacteristic
73C4×#125C2211yescharacteristic
74C4×#125C2211yescharacteristic
75C4×#124C2211yescharacteristic
76C4×C22⋊Q8—21no—
77C4×C22⋊Q8—21no—
78C4×C22⋊Q8—21no—
79C42×Q8C2211yescharacteristic
80C42×D4C2211yescharacteristic
81C42×D4C2211yescharacteristic
82C42×D4C2211yescharacteristic
83C2×C4×C4⋊C4—21no—
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2074C2211yescharacteristic
93#2073C2211yescharacteristic
94#2072C2211yescharacteristic
95#2071C2211yescharacteristic
96#2068C2211yescharacteristic
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2058C2211yescharacteristic
103#2057C2211yescharacteristic
104#2026C2211yescharacteristic
105#2025C2211yescharacteristic
106#2024C2211yescharacteristic
107#2023C2211yescharacteristic
108#1992C2211yescharacteristic
109#1992C2211yescharacteristic
110#1989C2211yescharacteristic
111#1989C2211yescharacteristic
112#1989C2211yescharacteristic
113#1989C2211yescharacteristic
114#1989C2211yescharacteristic
115#1989C2211yescharacteristic
116#1985C2211yescharacteristic
117#1985C2211yescharacteristic
118#1983C2211yescharacteristic
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1948C2211yescharacteristic
127#1947C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1933C2211yescharacteristic
135#1933C2211yescharacteristic
136#1928C2211yescharacteristic
137#1928C2211yescharacteristic
138#1927C2211yescharacteristic
139#1927C2211yescharacteristic
140#1927C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1842C2211yescharacteristic
177#1836C2211yescharacteristic
178#1836C2211yescharacteristic
179#1831C2211yescharacteristic
180#1831C2211yescharacteristic
181#1805C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1767C2211yescharacteristic
195#1767C2211yescharacteristic
196C4×C4⋊C8C2211yescharacteristic
197#1763C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205#554—24no—
206#554—24no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C4×Q8—21no—
218C2×C4×Q8D411yescharacteristic
219C2×C4×Q8D411yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C22×C4⋊C4—21no—
232C22×C4⋊C4—21no—
233C22×C42—21no—
234C22×C42—21no—
235C22×C42—21no—
236#479—24no—
237#478—24no—
238#478—24no—
239#478—24no—
240#463—24no—
241#442—24no—
242#440—24no—
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#401—21no—
288#401—21no—
289#400—21no—
290#400—21no—
291#398—21no—
292#398—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#396—21no—
298#396—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#390C2311yescharacteristic
310#390C2311yescharacteristic
311#390C2311yescharacteristic
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#385—21no—
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#383—21no—
377#383—21no—
378#382—21no—
379#382C2311yescharacteristic
380#382C2311yescharacteristic
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#380—21no—
385#380—21no—
386#380—21no—
387#380—21no—
388#380—21no—
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4—21no—
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4D411yescharacteristic
404C4×C4⋊C4D411yescharacteristic
405C4×C4⋊C4D411yescharacteristic
406C4×C4⋊C4D411yescharacteristic
407C4×C4⋊C4D411yescharacteristic
408C4×C4⋊C4D411yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C2×#95—21no—
437C2×#95—21no—
438C43C2311yescharacteristic
439C43C2311yescharacteristic
440C43C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C22×D4C2411yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—22no—
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516#125—22no—
517#125—22no—
518#125—22no—
519#125—22no—
520#125—22no—
521#125—22no—
522#125—22no—
523#125#4114yes—
524#124—22no—
525#124—22no—
526C22⋊Q8—28no—
527C22⋊Q8—28no—
528C22⋊Q8—28no—
529C22⋊Q8—44no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—42no—
535C4×Q8—42no—
536C4×Q8—82no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4#4114yes—
552C4×D4#4114yes—
553#117—44no—
554C2×C4⋊C4—28no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—44no—
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—44no—
639C2×C42—82no—
640C2×C42—82no—
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—22no—
662#107—22no—
663#107—22no—
664#107—22no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103—41no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—41no—
696#102—41no—
697#102—41no—
698#97—22no—
699#97—22no—
700#97—41no—
701#97—41no—
702C4×C8—41no—
703C4×C8—41no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753C24—21no—
754C24—21no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—22no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—41no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4C2×#4112yes—
777C2×D4C2×#4112yes—
778C2×D42−1+412yes—
779C22×C4—24no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C2511yescharacteristic
832SD16—44no—
833D8—44no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4C2×#4112yes—
916C4⋊C4C2×#4112yes—
917C4⋊C4C2×#4112yes—
918C4⋊C4C2×#4112yes—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C42—22no—
940C42—22no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—41no—
952C42—41no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—41no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42C2×#4112yes—
976C42C2×#4112yes—
977C42C2×#4112yes—
978C422−1+412yes—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23C23×D411yescharacteristic
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—84no—
1000D4—22no—
1001D4—22no—
1002D4—22no—
1003D4—41no—
1004D4—41no—
1005D4—41no—
1006D4—41no—
1007D4#55614yes—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—84no—
1089C2×C4—84no—
1090C2×C4—84no—
1091C2×C4—84no—
1092C2×C4—84no—
1093C2×C4—84no—
1094C2×C4#52512yes—
1095C2×C4#52512yes—
1096C2×C4#54812yes—
1097C2×C4#54812yes—
1098C2×C4#57512yes—
1099C2×C4#57512yes—
1100C2×C4C22×#4111yescharacteristic
1101C2×C4C22×#4111yescharacteristic
1102C2×C4C22×#4111yescharacteristic
1103C2×C4C2×2−1+411yescharacteristic
1104C2×C4C2×2−1+411yescharacteristic
1105C2×C4#58511yescharacteristic
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C8—41no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C22—24no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22C2×#52511yescharacteristic
1129C22C2×#54811yescharacteristic
1130C22#348911yescharacteristic
1131C22C2×#57511yescharacteristic
1132C22C2×#57511yescharacteristic
1133C22#358411yescharacteristic
1134C22#358511yescharacteristic
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—22no—
1141C4—42no—
1142C4—41no—
1143C4—42no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—42no—
1150C4—42no—
1151C4—41no—
1152C4—41no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4C2×#55611yescharacteristic
1164C4#348011yescharacteristic
1165C4#350711yescharacteristic
1166C4#352311yescharacteristic
1167C2—44no—
1168C2—161no—
1169C2#3657911yescharacteristic
1170C2#6056311yescharacteristic
1171C2#6060111yescharacteristic
1172C2#6131611yescharacteristic
1173C2#6131811yescharacteristic
1174C2#6212211yescharacteristic
1175C2#6213811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36590C2semidirect
2. C4×#554C2semidirect
3. #33199C2semidirect
6. #29353C2semidirect
7. #29350C2semidirect
8. #29280C2semidirect
9. #29279C2semidirect
10. #29227C2semidirect
11. #28285C2semidirect
13. #27566C2semidirect
15. #27558C2semidirect
16. #27148C2semidirect
17. #27146C2semidirect
18. #27136C2semidirect
19. #27134C2semidirect
20. #25008C2semidirect
21. #25006C2semidirect
22. #24349C2semidirect
24. #23078C2semidirect
25. #23076C2semidirect
26. #22823C2semidirect
28. #22776C2semidirect
29. #21617C2semidirect
30. C4×#478C2semidirect

Maximal subgroups

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

subgroupindex
#365902
C4×#5542
#331992
#330282
#293532
#293502
#292802
#292792
#292272
#282852
#275682
#275662
#275602
#275582
#271482
#271462
#271362
#271342
#250082
#250062
#243492
#243472
#230782
#230762
#228232
#227802
#227762
#216172
C4×#4782
#215072