Finite Group Databasebeta

← #221739

Subgroups — #221739

Order 512.

1485 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36123C211yesmaximal, characteristic
2#22554C211yesmaximal, characteristic, complemented
3C2×#1514C211yesmaximal, characteristic, complemented
4C22×#327C211yesmaximal, characteristic, complemented
5#13901C211yesmaximal, characteristic, complemented
6#9715C211yesmaximal, characteristic, complemented
7#9684C211yesmaximal, characteristic, complemented
8#9157C211yesmaximal, characteristic, complemented
9#9147C211yesmaximal, characteristic, complemented
10#9118C211yesmaximal, characteristic, complemented
11#9113C211yesmaximal, characteristic, complemented
12#8573C211yesmaximal, characteristic, complemented
13#8332C211yesmaximal, characteristic, complemented
14#8328C211yesmaximal, characteristic, complemented
15#8216C211yesmaximal, characteristic, complemented
16C2×#546—21no—
17C2×#532C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C2×#432C2211yescharacteristic, complemented
20C22×C22⋊C8C2211yescharacteristic
21#2856C2211yescharacteristic
22#2854C2211yescharacteristic
23#2847C2211yescharacteristic
24#2555—21no—
25#2543—21no—
26#2491C411yescharacteristic, complemented
27#2472—21no—
28#2464—21no—
29#2440C411yescharacteristic, complemented
30#2433C411yescharacteristic, complemented
31#2430—21no—
32#2428C411yescharacteristic, complemented
33#2428C411yescharacteristic, complemented
34#2422C411yescharacteristic, complemented
35#2410—21no—
36#2361C411yescharacteristic, complemented
37#2358—21no—
38D4×C22⋊C4C411yescharacteristic, complemented
39C4×#121C2211yescharacteristic
40C2×#383C2211yescharacteristic, complemented
41C2×C4×C22⋊C4C2211yescharacteristic
42C22×#95C2211yescharacteristic
43#1924—21no—
44#1924—21no—
45#1850—21no—
46#1817C2211yescharacteristic, complemented
47#1797C2211yescharacteristic, complemented
48#1779C2211yescharacteristic
49#1752—21no—
50#1749C2211yescharacteristic, complemented
51#1514—24no—
52C2×#327—24no—
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic, complemented
62C2×#327C2211yescharacteristic, complemented
63C2×#327C2211yescharacteristic, complemented
64C2×#327C2211yescharacteristic, complemented
65#1443—21no—
66#1443—21no—
67#1434C2211yescharacteristic, complemented
68#1434C2211yescharacteristic, complemented
69#1434C2211yescharacteristic, complemented
70C22⋊#95—21no—
71C22⋊#95—21no—
72C22⋊#95C2211yescharacteristic
73#1294C2211yescharacteristic, complemented
74#1294C2211yescharacteristic, complemented
75#1294C2211yescharacteristic, complemented
76#1294C2211yescharacteristic, complemented
77C22×#41—21no—
78C23×D4—21no—
79C23×D4C2×C411yescharacteristic
80C24×C4—21no—
81C24×C4C2311yescharacteristic
82C23×C8—21no—
83#546—44no—
84#546—44no—
85#532—22no—
86#532—22no—
87#532—41no—
88#532—41no—
89C2×C4⋊Q8C2×C411yescharacteristic, complemented
90C2×#127C2×C411yescharacteristic, complemented
91C2×#127C2×C411yescharacteristic, complemented
92C2×#124—21no—
93C2×#124—21no—
94C2×#123—21no—
95C2×#123—21no—
96C2×C22⋊Q8—21no—
97C2×#121—21no—
98C2×#121—21no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—21no—
102C2×#121—21no—
103C2×#121—21no—
104C2×#121—22no—
105C2×#121—22no—
106C2×#121—41no—
107C2×#121—41no—
108C2×#121C2×C411yescharacteristic
109C2×#121C2×C411yescharacteristic
110C2×#121C2×C411yescharacteristic
111C2×#121C2×C411yescharacteristic
112C2×#121C2311yescharacteristic
113C2×#121C2311yescharacteristic
114C2×#121C2311yescharacteristic
115C2×#120—21no—
116C2×#120—21no—
117C2×#120—21no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4C2×C411yescharacteristic, complemented
122C2×C4×D4C2×C411yescharacteristic, complemented
123C2×C4×D4C2×C411yescharacteristic, complemented
124C22×C4⋊C4C2×C411yescharacteristic
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4D411yescharacteristic
129C22×C22⋊C4D411yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132#432—22no—
133#432—41no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—21no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—41no—
141C2×C22⋊C8C2311yescharacteristic
142C2×C22⋊C8C2311yescharacteristic
143C2×C22⋊C8C2311yescharacteristic
144C2×C22⋊C8C2311yescharacteristic
145C2×#97—21no—
146C2×#97—21no—
147#398—21no—
148#397—21no—
149#395—21no—
150#394—21no—
151#394—21no—
152#394—21no—
153#394—21no—
154#393—21no—
155#392—21no—
156#392—21no—
157#392—21no—
158#392—21no—
159#390—21no—
160#390—21no—
161#390C2×C411yescharacteristic, complemented
162#390C2×C411yescharacteristic, complemented
163#390C2×C411yescharacteristic, complemented
164#390C2×C411yescharacteristic, complemented
165#390C2×C411yescharacteristic, complemented
166#389C2×C411yescharacteristic, complemented
167#389C2×C411yescharacteristic, complemented
168#389C2×C411yescharacteristic, complemented
169#388—21no—
170#388—21no—
171#388—21no—
172#388—21no—
173#388—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#386—21no—
180#386—21no—
181#386—21no—
182#386—21no—
183#386—21no—
184#385—21no—
185#385—21no—
186#385—21no—
187#384C2×C411yescharacteristic, complemented
188#383—22no—
189#383—41no—
190#380C2×C411yescharacteristic
191#380C2×C411yescharacteristic
192#380C2311yescharacteristic
193#379—21no—
194C4×C4⋊C4C2×C411yescharacteristic, complemented
195C4×C22⋊C4—21no—
196C4×C22⋊C4C2×C411yescharacteristic
197C4×C22⋊C4C2×C411yescharacteristic
198C4×C22⋊C4C2×C411yescharacteristic
199C4×C22⋊C4C2×C411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202C4×C22⋊C4D411yescharacteristic
203C4×C22⋊C4D411yescharacteristic
204C2×#95—22no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—41no—
216C2×#95D411yescharacteristic
217C2×#95D411yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226#327—22no—
227#327—22no—
228#327—22no—
229#327—22no—
230#327—22no—
231#327—22no—
232#327—22no—
233#327—41no—
234#327—41no—
235#327—41no—
236#327—41no—
237#327D414yescomplemented
238C25—21no—
239C25C2×D411yescharacteristic
240C2×#41—42no—
241C2×#41—42no—
242C2×#41—42no—
243C2×#41—42no—
244C2×#41—81no—
245C2×#41—81no—
246C22×Q8—21no—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—41no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—81no—
267C22×D4—81no—
268C22×D4—81no—
269C22×D4C22×C411yescharacteristic
270C22×D4C22×C411yescharacteristic
271C22×D4C22×C411yescharacteristic
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—81no—
291C23×C4—81no—
292C23×C4—81no—
293C23×C4C22×C411yescharacteristic
294C23×C4C22×C411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—42no—
308C22×C8—42no—
309C22×C8—81no—
310C4⋊Q8—22no—
311C4⋊Q8—41no—
312#127—22no—
313#127—41no—
314#127—81no—
315#124—42no—
316#124—42no—
317#124—44no—
318#123—44no—
319#123—42no—
320#123—42no—
321C22⋊Q8—44no—
322#121—21no—
323#121—21no—
324#121—22no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—22no—
334#121—42no—
335#121—42no—
336#121—44no—
337#121—44no—
338#121—41no—
339#121—41no—
340#121—42no—
341#121—42no—
342#121—42no—
343#121—42no—
344#121—42no—
345#121—42no—
346#121—42no—
347#121—81no—
348#121—81no—
349#121—81no—
350#121C2×D412yes—
351#121#4112yes—
352#120—44no—
353#120—44no—
354#120—42no—
355#120—42no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—42no—
359C4×D4—42no—
360C4×D4—41no—
361C4×D4—41no—
362C4×D4—44no—
363C4×D4—42no—
364C4×D4—42no—
365C4×D4—81no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C4⋊C4C22×C411yescharacteristic
377C2×C4⋊C4C22×C411yescharacteristic
378C2×C4⋊C4C22×C411yescharacteristic
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4C22⋊C411yescharacteristic
413C2×C22⋊C4C22⋊C411yescharacteristic
414C2×C22⋊C4C22⋊C411yescharacteristic
415C2×C22⋊C4C22⋊C411yescharacteristic
416C2×C22⋊C4C22⋊C411yescharacteristic
417C2×C22⋊C4C22⋊C411yescharacteristic
418C2×C22⋊C4C22⋊C411yescharacteristic
419C2×C22⋊C4C22⋊C411yescharacteristic
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—81no—
426C2×C42C22×C411yescharacteristic
427C2×C42C22×C411yescharacteristic
428C2×C42C22×C411yescharacteristic
429C2×C42C22×C411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C4⋊C8—42no—
435C4⋊C8—81no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—42no—
444C22⋊C8—42no—
445C22⋊C8—81no—
446C22⋊C8C2×D412yes—
447#97—42no—
448#97—81no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95—81no—
469#95—81no—
470#95—81no—
471#95—81no—
472#95—81no—
473#95C22⋊C411yescharacteristic
474#95C22⋊C411yescharacteristic
475#95C22⋊C411yescharacteristic
476#95C22⋊C411yescharacteristic
477#95C22⋊C411yescharacteristic
478#95C22⋊C411yescharacteristic
479#95C22⋊C411yescharacteristic
480#95C22⋊C411yescharacteristic
481#95C2×D412yes—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—41no—
492C24—41no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24—81no—
498C24—81no—
499C24—81no—
500C24C2×C22⋊C411yescharacteristic
501C24C2×C22⋊C411yescharacteristic
502C24AGL(1,ℤ/8)12yes—
503C24AGL(1,ℤ/8)12yes—
504C24C22×D411yescharacteristic
505#41—84no—
506#41—84no—
507#41—84no—
508#41—84no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—81no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—42no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—84no—
565C2×D4—84no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—84no—
571C2×D4—84no—
572C2×D4—84no—
573C2×D4—84no—
574C2×D4C4×D412yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—48no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—42no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—81no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—82no—
661C22×C4—82no—
662C22×C4—82no—
663C22×C4—82no—
664C22×C4—81no—
665C22×C4—84no—
666C22×C4—84no—
667C22×C4—84no—
668C22×C4—84no—
669C22×C4—84no—
670C22×C4—84no—
671C22×C4C2×C22⋊C411yescharacteristic
672C22×C4C2×C22⋊C411yescharacteristic
673C22×C4C2×C22⋊C411yescharacteristic
674C22×C4C2×C22⋊C411yescharacteristic
675C22×C4C2×C22⋊C411yescharacteristic
676C22×C4C2×C22⋊C411yescharacteristic
677C22×C4C2×C22⋊C411yescharacteristic
678C22×C4C2×C22⋊C411yescharacteristic
679C22×C4C2×C22⋊C411yescharacteristic
680C22×C4C2×C22⋊C411yescharacteristic
681C22×C4C23×C411yescharacteristic
682C22×C4C22×D411yescharacteristic
683C22×C4C22×D411yescharacteristic
684C22×C4C2×#4111yescharacteristic
685C22×C4H(5,𝔽2)11yescharacteristic
686C22×C4H(5,𝔽2)11yescharacteristic
687C2×C8—22no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C2×C8—84no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4—41no—
708C4⋊C4—41no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—42no—
713C4⋊C4—81no—
714C4⋊C4C4×D412yes—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—41no—
724C22⋊C4—41no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—41no—
738C22⋊C4—41no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—41no—
742C22⋊C4—41no—
743C22⋊C4—41no—
744C22⋊C4—41no—
745C22⋊C4—81no—
746C22⋊C4—81no—
747C22⋊C4—81no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—84no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—41no—
760C42—41no—
761C42—41no—
762C42—41no—
763C42—42no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—24no—
781C23—24no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—162no—
820C23—162no—
821C23—162no—
822C23#41012yes—
823C23#41812yes—
824C23#41812yes—
825C23#42112yes—
826C23C22×C22⋊C411yescharacteristic
827C23D4211yescharacteristic
828C23#54611yescharacteristic
829C23C2×AGL(1,ℤ/8)11yescharacteristic
830C23C2×AGL(1,ℤ/8)11yescharacteristic
831C23#57611yescharacteristic
832C23#57711yescharacteristic
833Q8—84no—
834D4—42no—
835D4—42no—
836D4—42no—
837D4—42no—
838D4—42no—
839D4—42no—
840D4—81no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—84no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4—84no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853D4—84no—
854D4—81no—
855D4—81no—
856D4—81no—
857D4—81no—
858D4—162no—
859D4—162no—
860D4—162no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—81no—
940C2×C4—84no—
941C2×C4—84no—
942C2×C4—84no—
943C2×C4—81no—
944C2×C4—81no—
945C2×C4—81no—
946C2×C4—81no—
947C2×C4—81no—
948C2×C4—81no—
949C2×C4—81no—
950C2×C4—816no—
951C2×C4—81no—
952C2×C4—81no—
953C2×C4—81no—
954C2×C4—81no—
955C2×C4—81no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—81no—
962C2×C4—81no—
963C2×C4—81no—
964C2×C4—81no—
965C2×C4—81no—
966C2×C4—162no—
967C2×C4C2×C4×D411yescharacteristic
968C2×C4#51811yescharacteristic
969C2×C4D4211yescharacteristic
970C2×C4#54611yescharacteristic
971C8—42no—
972C8—81no—
973C8—81no—
974C8—81no—
975C22—21no—
976C22—22no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—22no—
981C22—21no—
982C22—21no—
983C22—22no—
984C22—21no—
985C22—21no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—22no—
990C22—21no—
991C22—21no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22—81no—
1008C22—81no—
1009C22—81no—
1010C22—81no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—81no—
1015C22—81no—
1016C22—81no—
1017C22—81no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22—81no—
1025C22—168no—
1026C22#151414yescomplemented
1027C22D4×C22⋊C411yescharacteristic
1028C22C2×#41011yescharacteristic
1029C22#288311yescharacteristic
1030C22C2×#41811yescharacteristic
1031C22#289711yescharacteristic
1032C22C2×#42111yescharacteristic
1033C22#290111yescharacteristic
1034C22#326411yescharacteristic
1035C22#326511yescharacteristic
1036C22#331011yescharacteristic
1037C22#331811yescharacteristic
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—21no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—42no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—41no—
1051C4—41no—
1052C4—41no—
1053C4—82no—
1054C4—82no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4—81no—
1059C4—161no—
1060C4—161no—
1061C2—21no—
1062C2—21no—
1063C2—21no—
1064C2—24no—
1065C2—21no—
1066C2—42no—
1067C2—82no—
1068C2—161no—
1069C2—161no—
1070C2C2×#151411yescharacteristic
1071C2#1759711yescharacteristic
1072C2#1760411yescharacteristic
1073C2#1762011yescharacteristic
1074C2#2240511yescharacteristic
1075C2#2242311yescharacteristic
1076C2#2243411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36123C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22554C2semidirect
3. C2×#1514C2semidirect
4. C22×#327C2semidirect
5. #13901C2semidirect
6. #9715C2semidirect
7. #9684C2semidirect
8. #9157C2semidirect
9. #9147C2semidirect
10. #9118C2semidirect
11. #9113C2semidirect
12. #8573C2semidirect
13. #8332C2semidirect
14. #8328C2semidirect
15. #8216C2semidirect
19. C2×#432C22semidirect
26. #2491C4semidirect
29. #2440C4semidirect
30. #2433C4semidirect
32. #2428C4semidirect
33. #2428C4semidirect
34. #2422C4semidirect
36. #2361C4semidirect
38. D4×C22⋊C4C4semidirect
40. C2×#383C22semidirect
46. #1817C22semidirect
47. #1797C22semidirect
50. #1749C22semidirect
61. C2×#327C22semidirect
62. C2×#327C22semidirect
63. C2×#327C22semidirect
64. C2×#327C22semidirect
67. #1434C22semidirect
68. #1434C22semidirect
69. #1434C22semidirect
73. #1294C22semidirect
74. #1294C22semidirect
75. #1294C22semidirect
76. #1294C22semidirect
89. C2×C4⋊Q8C2×C4semidirect
90. C2×#127C2×C4semidirect
91. C2×#127C2×C4semidirect
121. C2×C4×D4C2×C4semidirect
122. C2×C4×D4C2×C4semidirect
123. C2×C4×D4C2×C4semidirect
161. #390C2×C4semidirect
162. #390C2×C4semidirect
163. #390C2×C4semidirect
164. #390C2×C4semidirect
165. #390C2×C4semidirect
166. #389C2×C4semidirect
167. #389C2×C4semidirect
168. #389C2×C4semidirect
187. #384C2×C4semidirect
194. C4×C4⋊C4C2×C4semidirect
237. #327D4semidirect
1026. C22#1514semidirect

Maximal subgroups

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

subgroupindex
#361232
#225542
C2×#15142
C22×#3272
#139012
#97152
#96842
#91572
#91472
#91182
#91132
#85732
#83322
#83282
#82162