Finite Group Databasebeta

← #223616

Subgroups — #223616

Order 512.

1551 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36153C211yesmaximal, characteristic
2#22399C211yesmaximal, characteristic, complemented
3#13813C211yesmaximal, characteristic, complemented
4#9908C211yesmaximal, characteristic, complemented
5#9888C211yesmaximal, characteristic, complemented
6#9150C211yesmaximal, characteristic, complemented
7#9147C211yesmaximal, characteristic, complemented
8#9117C211yesmaximal, characteristic, complemented
9#9113C211yesmaximal, characteristic, complemented
10#8713C211yesmaximal, characteristic, complemented
11#8712C211yesmaximal, characteristic, complemented
12#8573C211yesmaximal, characteristic, complemented
13#8218C211yesmaximal, characteristic, complemented
14#8019C211yesmaximal, characteristic, complemented
15C2×#1294C211yesmaximal, characteristic, complemented
16C2×#547C411yescharacteristic, complemented
17C2×#546—21no—
18C22×C4×D4C2211yescharacteristic
19C2×#435—21no—
20C2×#407C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22#2857C2211yescharacteristic
23#2847C2211yescharacteristic
24#2847C2211yescharacteristic
25#2547C411yescharacteristic, complemented
26#2537C411yescharacteristic, complemented
27#2486C411yescharacteristic, complemented
28#2486C411yescharacteristic, complemented
29#2427—21no—
30#2425—21no—
31#2425—21no—
32#2417—21no—
33#2416C411yescharacteristic, complemented
34#2416C411yescharacteristic, complemented
35#2412—21no—
36#2412—21no—
37D4×C4⋊C4C411yescharacteristic, complemented
38#2339—21no—
39C4×#121C2211yescharacteristic
40C2×#386—21no—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C22⋊C4—21no—
44C2×C4×C22⋊C4C2211yescharacteristic
45C22×#95C2211yescharacteristic
46#1955—21no—
47#1870—21no—
48#1869—21no—
49#1797C2211yescharacteristic
50#1779C2211yescharacteristic
51#1779C2211yescharacteristic
52#1749C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57#1437—21no—
58#1436—21no—
59#1434C2211yescharacteristic
60C22⋊#95C2211yescharacteristic
61C22⋊#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C22×#41—21no—
76C23×D4D411yescharacteristic
77C24×C4—21no—
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C22×M16—21no—
81C23×C8—21no—
82#547—44no—
83#546—44no—
84#546—44no—
85C2×C4⋊Q8C2×C411yescharacteristic, complemented
86C2×#124—21no—
87C2×#123—21no—
88C2×#123—21no—
89C2×#123—21no—
90C2×#123—21no—
91C2×C22⋊Q8—21no—
92C2×C22⋊Q8—21no—
93C2×#121—21no—
94C2×#121—21no—
95C2×#121—21no—
96C2×#121C2×C411yescharacteristic
97C2×#121C2×C411yescharacteristic
98C2×#121C2×C411yescharacteristic, complemented
99C2×#121C2×C411yescharacteristic, complemented
100C2×#121C2311yescharacteristic
101C2×#120—21no—
102C2×#120—21no—
103C2×C4×D4—21no—
104C2×C4×D4—21no—
105C2×C4×D4—44no—
106C2×C4×D4C2×C411yescharacteristic
107C2×C4×D4C2×C411yescharacteristic
108C2×C4×D4C2×C411yescharacteristic
109C2×C4×D4C2×C411yescharacteristic
110C2×C4×D4C2×C411yescharacteristic, complemented
111C2×C4×D4D411yescharacteristic
112C2×C4×D4D411yescharacteristic
113C2×C4×D4D411yescharacteristic
114C2×C4×D4D411yescharacteristic
115C22×C4⋊C4C2×C411yescharacteristic
116C22×C4⋊C4C2×C411yescharacteristic
117C22×C4⋊C4C2×C411yescharacteristic, complemented
118C22×C4⋊C4C2×C411yescharacteristic, complemented
119C22×C4⋊C4D411yescharacteristic
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4D411yescharacteristic
126C22×C22⋊C4D411yescharacteristic
127C22×C42—21no—
128C22×C42—21no—
129C22×C42C2311yescharacteristic
130#435—44no—
131C2×C4⋊C8—21no—
132#407—22no—
133#407—41no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—21no—
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—41no—
142C2×C22⋊C8C2311yescharacteristic
143C2×C22⋊C8C2311yescharacteristic
144C2×C22⋊C8C2311yescharacteristic
145C2×C22⋊C8C2311yescharacteristic
146C2×#97—21no—
147#398—21no—
148#398—21no—
149#397—21no—
150#397—21no—
151#397—21no—
152#397—21no—
153#396—21no—
154#396—21no—
155#394—21no—
156#394—21no—
157#394—21no—
158#394—21no—
159#391—21no—
160#391—21no—
161#390C2×C411yescharacteristic, complemented
162#389—21no—
163#389—21no—
164#389C2×C411yescharacteristic, complemented
165#389C2×C411yescharacteristic, complemented
166#389C2×C411yescharacteristic, complemented
167#388—21no—
168#386—28no—
169#386—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#386—21no—
178#385—21no—
179#385—21no—
180#384C2×C411yescharacteristic, complemented
181#381—21no—
182#381—21no—
183#380—21no—
184#380—21no—
185#380—21no—
186#380—21no—
187#380—21no—
188#380—21no—
189#380C2×C411yescharacteristic
190#380C2×C411yescharacteristic
191#380C2×C411yescharacteristic
192#380C2×C411yescharacteristic
193#380C2×C411yescharacteristic, complemented
194#380C2×C411yescharacteristic, complemented
195#380C2×C411yescharacteristic, complemented
196#380C2×C411yescharacteristic, complemented
197#380C2311yescharacteristic
198#380C2311yescharacteristic
199#380C2311yescharacteristic
200C4×C4⋊C4C2×C411yescharacteristic, complemented
201C4×C22⋊C4—21no—
202C4×C22⋊C4—22no—
203C4×C22⋊C4—41no—
204C4×C22⋊C4—44no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—22no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—41no—
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219#336—21no—
220#336—21no—
221#327—22no—
222#327—22no—
223#327—41no—
224#327—41no—
225C25C2×D411yescharacteristic
226C25C2×D411yescharacteristic
227C2×#41—44no—
228C2×#41—44no—
229C2×#41—44no—
230C22×Q8—21no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—42no—
240C22×D4C22⋊C411yescharacteristic
241C22×D4C22⋊C411yescharacteristic
242C22×D4C22⋊C411yescharacteristic
243C22×D4C22⋊C411yescharacteristic
244C22×D4C22×C411yescharacteristic
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—24no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—81no—
270C23×C4—81no—
271C23×C4—81no—
272C23×C4—81no—
273C23×C4C22×C411yescharacteristic
274C23×C4C22×C411yescharacteristic
275C23×C4C22×C411yescharacteristic
276C23×C4C22×C411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2411yescharacteristic
286C2×M16—42no—
287C2×M16—42no—
288C2×M16—81no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—42no—
294C22×C8—42no—
295C22×C8—81no—
296C4⋊Q8—42no—
297#124—44no—
298#123—44no—
299#123—44no—
300#123—44no—
301#123—44no—
302C22⋊Q8—44no—
303C22⋊Q8—42no—
304C22⋊Q8—42no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121—42no—
310#121—44no—
311#121—44no—
312#121—44no—
313#121—42no—
314#121—81no—
315#121—81no—
316#120—42no—
317#120—42no—
318#120—42no—
319#120—42no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—42no—
323C4×D4—42no—
324C4×D4—42no—
325C4×D4—42no—
326C4×D4—42no—
327C4×D4—42no—
328C4×D4—42no—
329C4×D4—42no—
330C4×D4—42no—
331C4×D4—44no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—81no—
346C2×C4⋊C4—81no—
347C2×C4⋊C4C22⋊C411yescharacteristic
348C2×C4⋊C4C22⋊C411yescharacteristic
349C2×C4⋊C4C22⋊C411yescharacteristic
350C2×C4⋊C4C22⋊C411yescharacteristic
351C2×C4⋊C4C22×C411yescharacteristic
352C2×C4⋊C4C22×C411yescharacteristic
353C2×C4⋊C4C22×C411yescharacteristic
354C2×C4⋊C4C22×C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—81no—
391C2×C22⋊C4—81no—
392C2×C22⋊C4C22⋊C411yescharacteristic
393C2×C22⋊C4C22⋊C411yescharacteristic
394C2×C22⋊C4C22⋊C411yescharacteristic
395C2×C22⋊C4C22⋊C411yescharacteristic
396C2×C22⋊C4C22⋊C411yescharacteristic
397C2×C22⋊C4C22⋊C411yescharacteristic
398C2×C22⋊C4C22⋊C411yescharacteristic
399C2×C22⋊C4C22⋊C411yescharacteristic
400C2×C42—21no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—81no—
407C2×C42—81no—
408C2×C42C22×C411yescharacteristic
409C2×C42C22×C411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C4⋊C8—42no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—42no—
421C22⋊C8—42no—
422C22⋊C8—42no—
423C22⋊C8—42no—
424C22⋊C8—81no—
425C22⋊C8—81no—
426C22⋊C8#4112yescomplemented
427#97—42no—
428#95—24no—
429#95—24no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—81no—
456#95#4112yescomplemented
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—41no—
472C24—41no—
473C24—41no—
474C24—41no—
475C24—41no—
476C24C2×C22⋊C411yescharacteristic
477C24C2×C22⋊C411yescharacteristic
478C24C2×C22⋊C411yescharacteristic
479C24C2×C22⋊C411yescharacteristic
480C24AGL(1,ℤ/8)12yes—
481C24AGL(1,ℤ/8)12yes—
482C24C22×D411yescharacteristic
483#41—816no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—22no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4—81no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4#10414yes—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—48no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—48no—
604C22×C4—41no—
605C22×C4—41no—
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—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—82no—
622C22×C4—82no—
623C22×C4—82no—
624C22×C4—82no—
625C22×C4—82no—
626C22×C4—82no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4—84no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4—84no—
638C22×C4C2×C22⋊C411yescharacteristic
639C22×C4C2×C22⋊C411yescharacteristic
640C22×C4C2×C22⋊C411yescharacteristic
641C22×C4C2×C22⋊C411yescharacteristic
642C22×C4C2×C22⋊C411yescharacteristic
643C22×C4C2×C22⋊C411yescharacteristic
644C22×C4C2×C22⋊C411yescharacteristic
645C22×C4C2×C22⋊C411yescharacteristic
646C22×C4C23×C411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C2×#4111yescharacteristic
649C22×C4C2×#4111yescharacteristic
650C22×C4H(5,𝔽2)11yescharacteristic
651C22×C42−1+411yescharacteristic
652M16—84no—
653C2×C8—22no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—84no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—48no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—48no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—41no—
704C22⋊C4—41no—
705C22⋊C4—41no—
706C22⋊C4—41no—
707C22⋊C4—41no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—41no—
714C22⋊C4—41no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4—81no—
720C22⋊C4—84no—
721C22⋊C4#9914yes—
722C42—22no—
723C42—22no—
724C42—41no—
725C42—41no—
726C42—42no—
727C42—84no—
728C42—84no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—24no—
752C23—24no—
753C23—22no—
754C23—22no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—81no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23C2×#9912yes—
796C23#41812yes—
797C23#41812yes—
798C23C2×#10412yes—
799C23C2×#10412yes—
800C23C22×C22⋊C411yescharacteristic
801C23#54611yescharacteristic
802C23#54711yescharacteristic
803C23C2×AGL(1,ℤ/8)11yescharacteristic
804C23C2×AGL(1,ℤ/8)11yescharacteristic
805C23#57711yescharacteristic
806C23#57811yescharacteristic
807Q8—84no—
808D4—28no—
809D4—44no—
810D4—44no—
811D4—44no—
812D4—81no—
813D4—81no—
814D4—84no—
815D4—81no—
816D4—81no—
817D4—84no—
818D4—81no—
819D4—81no—
820D4—162no—
821D4—162no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—24no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—84no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—816no—
914C2×C4—81no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—84no—
924C2×C4—81no—
925C2×C4—84no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—162no—
929C2×C4—162no—
930C2×C4C2×#9912yes—
931C2×C4C2×#9912yes—
932C2×C4C2×#10412yes—
933C2×C4C4×#4111yescharacteristic
934C2×C4#52011yescharacteristic
935C2×C4#54611yescharacteristic
936C2×C4#54711yescharacteristic
937C8—42no—
938C8—81no—
939C8—81no—
940C8—81no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—22no—
946C22—21no—
947C22—21no—
948C22—22no—
949C22—21no—
950C22—21no—
951C22—22no—
952C22—21no—
953C22—21no—
954C22—22no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—41no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22#150714yes—
996C22#233911yescharacteristic
997C22C22×#9911yescharacteristic
998C22#288311yescharacteristic
999C22C2×#41811yescharacteristic
1000C22#289811yescharacteristic
1001C22C22×#10411yescharacteristic
1002C22#290111yescharacteristic
1003C22#330611yescharacteristic
1004C22#330811yescharacteristic
1005C22#334311yescharacteristic
1006C22#334511yescharacteristic
1007C4—22no—
1008C4—22no—
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—21no—
1013C4—22no—
1014C4—44no—
1015C4—41no—
1016C4—41no—
1017C4—41no—
1018C4—41no—
1019C4—41no—
1020C4—82no—
1021C4—82no—
1022C4—82no—
1023C4—81no—
1024C4—81no—
1025C4—81no—
1026C4—81no—
1027C4—81no—
1028C4—81no—
1029C4—81no—
1030C2—21no—
1031C2—21no—
1032C2—21no—
1033C2—21no—
1034C2—24no—
1035C2—42no—
1036C2—42no—
1037C2—81no—
1038C2—161no—
1039C2C2×#150711yescharacteristic
1040C2#1754811yescharacteristic
1041C2#1760811yescharacteristic
1042C2#1762011yescharacteristic
1043C2#2247611yescharacteristic
1044C2#2249511yescharacteristic
1045C2#2250511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36153C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22399C2semidirect
3. #13813C2semidirect
4. #9908C2semidirect
5. #9888C2semidirect
6. #9150C2semidirect
7. #9147C2semidirect
8. #9117C2semidirect
9. #9113C2semidirect
10. #8713C2semidirect
11. #8712C2semidirect
12. #8573C2semidirect
13. #8218C2semidirect
14. #8019C2semidirect
15. C2×#1294C2semidirect
16. C2×#547C4semidirect
25. #2547C4semidirect
26. #2537C4semidirect
27. #2486C4semidirect
28. #2486C4semidirect
33. #2416C4semidirect
34. #2416C4semidirect
37. D4×C4⋊C4C4semidirect
85. C2×C4⋊Q8C2×C4semidirect
98. C2×#121C2×C4semidirect
99. C2×#121C2×C4semidirect
110. C2×C4×D4C2×C4semidirect
117. C22×C4⋊C4C2×C4semidirect
118. C22×C4⋊C4C2×C4semidirect
161. #390C2×C4semidirect
164. #389C2×C4semidirect
165. #389C2×C4semidirect
166. #389C2×C4semidirect
180. #384C2×C4semidirect
193. #380C2×C4semidirect
194. #380C2×C4semidirect
195. #380C2×C4semidirect
196. #380C2×C4semidirect
200. C4×C4⋊C4C2×C4semidirect
426. C22⋊C8#41semidirect
456. #95#41semidirect

Maximal subgroups

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

subgroupindex
#361532
#223992
#138132
#99082
#98882
#91502
#91472
#91172
#91132
#87132
#87122
#85732
#82182
#80192
C2×#12942