Finite Group Databasebeta

← #221704

Subgroups — #221704

Order 512.

1854 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36096C211yesmaximal, characteristic
2#22399C211yesmaximal, characteristic, complemented
3C2×#1504C211yesmaximal, characteristic, complemented
4C22×#327C211yesmaximal, characteristic, complemented
5D4×#95C211yesmaximal, characteristic, complemented
6#9713C211yesmaximal, characteristic, complemented
7#9682C211yesmaximal, characteristic, complemented
8#9147C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9117C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic, complemented
12#8577C211yesmaximal, characteristic, complemented
13#8331C211yesmaximal, characteristic, complemented
14#8328C211yesmaximal, characteristic, complemented
15#8218C211yesmaximal, characteristic, complemented
16C2×#546C411yescharacteristic, complemented
17C2×#525C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C2×#435—21no—
22C2×#407C2211yescharacteristic, complemented
23C22×C22⋊C8C2211yescharacteristic
24#2850C2211yescharacteristic
25#2848C2211yescharacteristic
26#2847C2211yescharacteristic
27#2540C411yescharacteristic, complemented
28#2535C411yescharacteristic, complemented
29#2464—21no—
30#2456—21no—
31#2443—21no—
32#2424—21no—
33#2418—21no—
34#2417C411yescharacteristic, complemented
35#2414C411yescharacteristic, complemented
36#2408C411yescharacteristic, complemented
37#2407C411yescharacteristic, complemented
38#2403—21no—
39#2358—21no—
40#2352C411yescharacteristic, complemented
41D4×C22⋊C4—21no—
42C4×#121C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic, complemented
45#1955—21no—
46#1870—21no—
47#1869—21no—
48#1797C2211yescharacteristic, complemented
49#1779C2211yescharacteristic
50#1779C2211yescharacteristic, complemented
51#1749C2211yescharacteristic, complemented
52#1504—24no—
53C2×#328C2211yescharacteristic, complemented
54C2×#328C2211yescharacteristic, complemented
55C2×#328C2211yescharacteristic, complemented
56C2×#328C2211yescharacteristic, complemented
57C2×#327—24no—
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62C2×#327C2211yescharacteristic
63C2×#327C2211yescharacteristic
64C2×#327C2211yescharacteristic
65C2×#327C2211yescharacteristic
66C4⋊#95—21no—
67C4⋊#95C2211yescharacteristic, complemented
68C22⋊#95—21no—
69C22⋊#95—21no—
70C22⋊#95C2211yescharacteristic
71C22⋊#95C2211yescharacteristic, complemented
72C4×#95C2211yescharacteristic, complemented
73#1294C2211yescharacteristic, complemented
74#1294C2211yescharacteristic, complemented
75#1294C2211yescharacteristic, complemented
76#1294C2211yescharacteristic, complemented
77C22×#41C2×C411yescharacteristic, complemented
78C23×D4—21no—
79C23×D4C2×C411yescharacteristic, complemented
80C23×D4D411yescharacteristic
81C24×C4—21no—
82C24×C4—21no—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×M16—21no—
86C23×C8—21no—
87#546—44no—
88C2×#124C2×C411yescharacteristic, complemented
89#525—22no—
90#525—22no—
91#525—41no—
92#525—41no—
93C2×#123—21no—
94C2×#123—21no—
95C2×C22⋊Q8C2×C411yescharacteristic, complemented
96C2×C22⋊Q8C2×C411yescharacteristic, complemented
97C2×C22⋊Q8C2×C411yescharacteristic, complemented
98C2×C22⋊Q8C2311yescharacteristic
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—21no—
102C2×#121—22no—
103C2×#121—22no—
104C2×#121—41no—
105C2×#121—41no—
106C2×#121C2×C411yescharacteristic, complemented
107C2×#121C2×C411yescharacteristic, complemented
108C2×#121C2×C411yescharacteristic, complemented
109C2×#121C2×C411yescharacteristic, complemented
110C2×#121C2×C411yescharacteristic, complemented
111C2×#121C2311yescharacteristic
112C2×#121C2311yescharacteristic
113C2×#120—21no—
114C2×#120—21no—
115C2×#120—21no—
116C2×#120—21no—
117C2×C4×D4—28no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—44no—
122C2×C4×D4—44no—
123C2×C4×D4—44no—
124C2×C4×D4C2×C411yescharacteristic
125C2×C4×D4C2×C411yescharacteristic
126C2×C4×D4C2×C411yescharacteristic
127C2×C4×D4C2×C411yescharacteristic
128C2×C4×D4C2×C411yescharacteristic, complemented
129C2×C4×D4D411yescharacteristic
130C2×C4×D4D411yescharacteristic
131C2×C4×D4D411yescharacteristic
132C2×C4×D4D411yescharacteristic
133C2×#117C2×C411yescharacteristic, complemented
134C22×C4⋊C4—21no—
135C22×C4⋊C4C2×C411yescharacteristic, complemented
136C22×C4⋊C4D411yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4D411yescharacteristic
142C22×C22⋊C4D411yescharacteristic
143C22×C42—21no—
144C22×C42C2311yescharacteristic
145#435—44no—
146C2×C4⋊C8—21no—
147#407—22no—
148#407—41no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—41no—
157C2×C22⋊C8C2311yescharacteristic
158C2×C22⋊C8C2311yescharacteristic
159C2×C22⋊C8C2311yescharacteristic
160C2×C22⋊C8C2311yescharacteristic
161C2×#97—21no—
162#399—21no—
163#398—21no—
164#397—21no—
165#396—21no—
166#394—21no—
167#394—21no—
168#394—21no—
169#392—21no—
170#392—21no—
171#392—21no—
172#392—21no—
173#392—21no—
174#391C2×C411yescharacteristic, complemented
175#390—21no—
176#390—21no—
177#390—21no—
178#390C2×C411yescharacteristic, complemented
179#390C2×C411yescharacteristic, complemented
180#389C2×C411yescharacteristic, complemented
181#388—21no—
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#387—21no—
187#386—21no—
188#386—21no—
189#386—21no—
190#386—21no—
191#386—21no—
192#386—21no—
193#386—21no—
194#386—21no—
195#386—21no—
196#386—21no—
197#386—21no—
198#385—21no—
199#385—21no—
200#385—21no—
201#385—21no—
202#382C2×C411yescharacteristic, complemented
203#380—21no—
204#380C2×C411yescharacteristic, complemented
205#380C2×C411yescharacteristic, complemented
206#380C2×C411yescharacteristic, complemented
207#380C2×C411yescharacteristic, complemented
208#380C2311yescharacteristic
209#379—21no—
210#379—21no—
211C4×C4⋊C4C2×C411yescharacteristic, complemented
212C4×C22⋊C4—21no—
213C4×C22⋊C4—21no—
214C2×#95—22no—
215C2×#95—22no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—41no—
223C2×#95—41no—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228#336—21no—
229#336—21no—
230#328—22no—
231#328—22no—
232#328—41no—
233#328—41no—
234#327—22no—
235#327—22no—
236#327—22no—
237#327—22no—
238#327—22no—
239#327—41no—
240#327—41no—
241#327D414yescomplemented
242C25—21no—
243C25C2×D411yescharacteristic
244C25C2×D411yescharacteristic
245C2×#41—22no—
246C2×#41—41no—
247C2×#41—42no—
248C2×#41—81no—
249C22×Q8C22×C411yescharacteristic
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—21no—
255C22×D4—22no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—41no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4—81no—
271C22×D4—81no—
272C22×D4—81no—
273C22×D4C22⋊C411yescharacteristic
274C22×D4C22⋊C411yescharacteristic
275C22×D4C22⋊C411yescharacteristic
276C22×D4C22⋊C411yescharacteristic
277C22×D4C22×C411yescharacteristic
278C22×D4C22×C411yescharacteristic
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—81no—
307C23×C4—81no—
308C23×C4—81no—
309C23×C4—81no—
310C23×C4—81no—
311C23×C4—81no—
312C23×C4C22×C411yescharacteristic
313C23×C4C22×C411yescharacteristic
314C23×C4C22×C411yescharacteristic
315C23×C4C22×C411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2411yescharacteristic
325C2×M16—42no—
326C2×M16—42no—
327C2×M16—81no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—42no—
333C22×C8—42no—
334C22×C8—81no—
335#124—42no—
336#123—42no—
337#123—42no—
338#123—44no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—22no—
344C22⋊Q8—41no—
345C22⋊Q8—42no—
346C22⋊Q8—81no—
347#121—21no—
348#121—21no—
349#121—22no—
350#121—22no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—22no—
356#121—42no—
357#121—42no—
358#121—44no—
359#121—41no—
360#121—41no—
361#121—41no—
362#121—42no—
363#121—42no—
364#121—42no—
365#121—81no—
366#121C2×D412yes—
367#121#4112yes—
368#120—42no—
369#120—42no—
370#120—44no—
371#120—44no—
372#120—81no—
373#120—81no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—42no—
377C4×D4—42no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—42no—
381C4×D4—42no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—42no—
386C4×D4—42no—
387C4×D4—432no—
388C4×D4—81no—
389C4×D4—81no—
390#117—22no—
391#117—41no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4C22⋊C411yescharacteristic
405C2×C4⋊C4C22⋊C411yescharacteristic
406C2×C4⋊C4C22⋊C411yescharacteristic
407C2×C4⋊C4C22⋊C411yescharacteristic
408C2×C4⋊C4C22×C411yescharacteristic
409C2×C4⋊C4C22×C411yescharacteristic
410C2×C4⋊C4C22×C411yescharacteristic
411C2×C4⋊C4C22×C411yescharacteristic
412C2×C4⋊C4C22×C411yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4C22⋊C411yescharacteristic
449C2×C22⋊C4C22⋊C411yescharacteristic
450C2×C22⋊C4C22⋊C411yescharacteristic
451C2×C22⋊C4C22⋊C411yescharacteristic
452C2×C22⋊C4C22⋊C411yescharacteristic
453C2×C22⋊C4C22⋊C411yescharacteristic
454C2×C22⋊C4C22⋊C411yescharacteristic
455C2×C22⋊C4C22⋊C411yescharacteristic
456C2×C42—24no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—42no—
460C2×C42—42no—
461C2×C42—42no—
462C2×C42C22×C411yescharacteristic
463C2×C42C22×C411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C4⋊C8—42no—
467C22⋊C8—21no—
468C22⋊C8—21no—
469C22⋊C8—21no—
470C22⋊C8—21no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—42no—
475C22⋊C8—42no—
476C22⋊C8—42no—
477C22⋊C8—42no—
478C22⋊C8—81no—
479C22⋊C8—81no—
480C22⋊C8C2×D412yes—
481#97—42no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—42no—
501#95—42no—
502#95—42no—
503#95—81no—
504#95—81no—
505#95—81no—
506#95C2×D412yes—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—41no—
524C24—41no—
525C24—41no—
526C24—41no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24—81no—
534C24C2×C22⋊C411yescharacteristic
535C24C2×C22⋊C411yescharacteristic
536C24C2×C22⋊C411yescharacteristic
537C24C2×C22⋊C411yescharacteristic
538C24AGL(1,ℤ/8)12yes—
539C24#13712yes—
540C24C22×D411yescharacteristic
541#41—84no—
542#41—84no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×D4—216no—
548C2×D4—216no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—42no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—84no—
592C2×D4—84no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—84no—
602C2×D4—84no—
603C2×D4—84no—
604C2×D4—84no—
605C2×D4#9914yes—
606C2×D4#10414yes—
607C2×D4C4×D412yescomplemented
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—48no—
674C22×C4—48no—
675C22×C4—42no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—42no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4—82no—
705C22×C4—82no—
706C22×C4—82no—
707C22×C4—82no—
708C22×C4—82no—
709C22×C4—82no—
710C22×C4—82no—
711C22×C4—82no—
712C22×C4—81no—
713C22×C4—84no—
714C22×C4—84no—
715C22×C4—84no—
716C22×C4—84no—
717C22×C4—84no—
718C22×C4—84no—
719C22×C4—84no—
720C22×C4—84no—
721C22×C4—84no—
722C22×C4—84no—
723C22×C4C2×C22⋊C411yescharacteristic
724C22×C4C2×C22⋊C411yescharacteristic
725C22×C4C2×C22⋊C411yescharacteristic
726C22×C4C2×C22⋊C411yescharacteristic
727C22×C4C2×C22⋊C411yescharacteristic
728C22×C4C2×C22⋊C411yescharacteristic
729C22×C4C2×C22⋊C411yescharacteristic
730C22×C4C2×C22⋊C411yescharacteristic
731C22×C4C23×C411yescharacteristic
732C22×C4C22×D411yescharacteristic
733C22×C4C22×D411yescharacteristic
734C22×C4C2×#4111yescharacteristic
735C22×C4H(5,𝔽2)11yescharacteristic
736C22×C4H(5,𝔽2)11yescharacteristic
737M16—84no—
738C2×C8—22no—
739C2×C8—41no—
740C2×C8—41no—
741C2×C8—41no—
742C2×C8—41no—
743C2×C8—41no—
744C2×C8—41no—
745C2×C8—41no—
746C2×C8—41no—
747C2×C8—41no—
748C2×C8—41no—
749C2×C8—41no—
750C2×C8—84no—
751C4⋊C4—21no—
752C4⋊C4—22no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—41no—
759C4⋊C4—41no—
760C4⋊C4—42no—
761C4⋊C4—42no—
762C4⋊C4—41no—
763C4⋊C4—41no—
764C4⋊C4—48no—
765C4⋊C4—42no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—81no—
769C4⋊C4—81no—
770C4⋊C4C4×D412yescomplemented
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C22⋊C4—41no—
780C22⋊C4—41no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—41no—
791C22⋊C4—41no—
792C22⋊C4—41no—
793C22⋊C4—41no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—41no—
797C22⋊C4—41no—
798C22⋊C4—42no—
799C22⋊C4—42no—
800C22⋊C4—42no—
801C22⋊C4—42no—
802C22⋊C4—81no—
803C22⋊C4—81no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—22no—
810C42—22no—
811C42—41no—
812C42—41no—
813C42—42no—
814C42—48no—
815C42—81no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—24no—
825C23—24no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—22no—
845C23—22no—
846C23—24no—
847C23—24no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—84no—
889C23—84no—
890C23—84no—
891C23—84no—
892C23—162no—
893C23—162no—
894C23—162no—
895C23C2×#9912yes—
896C23C2×#9912yes—
897C23#41712yes—
898C23#41712yes—
899C23C2×#10412yes—
900C23C2×#10412yes—
901C23C22×C22⋊C411yescharacteristic
902C23D4211yescharacteristic
903C23#54611yescharacteristic
904C23C2×AGL(1,ℤ/8)11yescharacteristic
905C23C2×#13711yescharacteristic
906C23#57611yescharacteristic
907C23#57711yescharacteristic
908Q8—81no—
909Q8—81no—
910D4—28no—
911D4—28no—
912D4—28no—
913D4—28no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—42no—
920D4—81no—
921D4—81no—
922D4—84no—
923D4—84no—
924D4—84no—
925D4—84no—
926D4—84no—
927D4—81no—
928D4—81no—
929D4—81no—
930D4—81no—
931D4—162no—
932D4—162no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—24no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—81no—
1008C2×C4—81no—
1009C2×C4—81no—
1010C2×C4—81no—
1011C2×C4—81no—
1012C2×C4—81no—
1013C2×C4—81no—
1014C2×C4—81no—
1015C2×C4—81no—
1016C2×C4—81no—
1017C2×C4—81no—
1018C2×C4—81no—
1019C2×C4—81no—
1020C2×C4—81no—
1021C2×C4—84no—
1022C2×C4—816no—
1023C2×C4—816no—
1024C2×C4—84no—
1025C2×C4—81no—
1026C2×C4—81no—
1027C2×C4—81no—
1028C2×C4—81no—
1029C2×C4—81no—
1030C2×C4—81no—
1031C2×C4—81no—
1032C2×C4—81no—
1033C2×C4—81no—
1034C2×C4—81no—
1035C2×C4—81no—
1036C2×C4—81no—
1037C2×C4—162no—
1038C2×C4C2×#9912yes—
1039C2×C4C2×#10412yes—
1040C2×C4C2×C4×D411yescharacteristic
1041C2×C4#51811yescharacteristic
1042C2×C4D4211yescharacteristic
1043C2×C4#54611yescharacteristic
1044C8—42no—
1045C8—81no—
1046C8—81no—
1047C8—81no—
1048C22—21no—
1049C22—21no—
1050C22—21no—
1051C22—22no—
1052C22—21no—
1053C22—21no—
1054C22—21no—
1055C22—22no—
1056C22—22no—
1057C22—21no—
1058C22—21no—
1059C22—22no—
1060C22—21no—
1061C22—21no—
1062C22—22no—
1063C22—21no—
1064C22—21no—
1065C22—22no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—168no—
1110C22#150414yescomplemented
1111C22D4×C22⋊C411yescharacteristic
1112C22C22×#9911yescharacteristic
1113C22#288311yescharacteristic
1114C22C2×#41711yescharacteristic
1115C22#289711yescharacteristic
1116C22C22×#10411yescharacteristic
1117C22#290111yescharacteristic
1118C22#326411yescharacteristic
1119C22#326611yescharacteristic
1120C22#330611yescharacteristic
1121C22#331411yescharacteristic
1122C4—22no—
1123C4—22no—
1124C4—21no—
1125C4—21no—
1126C4—21no—
1127C4—21no—
1128C4—44no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—42no—
1134C4—41no—
1135C4—41no—
1136C4—82no—
1137C4—82no—
1138C4—82no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C2—21no—
1145C2—21no—
1146C2—21no—
1147C2—21no—
1148C2—24no—
1149C2—42no—
1150C2—42no—
1151C2—42no—
1152C2—82no—
1153C2—161no—
1154C2C2×#150411yescharacteristic
1155C2#1754711yescharacteristic
1156C2#1760311yescharacteristic
1157C2#1762211yescharacteristic
1158C2D4×#9911yescharacteristic
1159C2#2241911yescharacteristic
1160C2D4×#10411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36096C2
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. C2×#1504C2semidirect
4. C22×#327C2semidirect
5. D4×#95C2semidirect
6. #9713C2semidirect
7. #9682C2semidirect
8. #9147C2semidirect
9. #9143C2semidirect
10. #9117C2semidirect
11. #9111C2semidirect
12. #8577C2semidirect
13. #8331C2semidirect
14. #8328C2semidirect
15. #8218C2semidirect
16. C2×#546C4semidirect
22. C2×#407C22semidirect
27. #2540C4semidirect
28. #2535C4semidirect
34. #2417C4semidirect
35. #2414C4semidirect
36. #2408C4semidirect
37. #2407C4semidirect
40. #2352C4semidirect
44. C22×#95C22semidirect
48. #1797C22semidirect
50. #1779C22semidirect
51. #1749C22semidirect
53. C2×#328C22semidirect
54. C2×#328C22semidirect
55. C2×#328C22semidirect
56. C2×#328C22semidirect
67. C4⋊#95C22semidirect
71. C22⋊#95C22semidirect
72. C4×#95C22semidirect
73. #1294C22semidirect
74. #1294C22semidirect
75. #1294C22semidirect
76. #1294C22semidirect
77. C22×#41C2×C4semidirect
79. C23×D4C2×C4semidirect
88. C2×#124C2×C4semidirect
95. C2×C22⋊Q8C2×C4semidirect
96. C2×C22⋊Q8C2×C4semidirect
97. C2×C22⋊Q8C2×C4semidirect
106. C2×#121C2×C4semidirect
107. C2×#121C2×C4semidirect
108. C2×#121C2×C4semidirect
109. C2×#121C2×C4semidirect
110. C2×#121C2×C4semidirect
128. C2×C4×D4C2×C4semidirect
133. C2×#117C2×C4semidirect
135. C22×C4⋊C4C2×C4semidirect
174. #391C2×C4semidirect
178. #390C2×C4semidirect
179. #390C2×C4semidirect
180. #389C2×C4semidirect
202. #382C2×C4semidirect
204. #380C2×C4semidirect
205. #380C2×C4semidirect
206. #380C2×C4semidirect
207. #380C2×C4semidirect
211. C4×C4⋊C4C2×C4semidirect
241. #327D4semidirect
607. C2×D4C4×D4semidirect
770. C4⋊C4C4×D4semidirect
1110. C22#1504semidirect

Maximal subgroups

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

subgroupindex
#360962
#223992
C2×#15042
C22×#3272
D4×#952
#97132
#96822
#91472
#91432
#91172
#91112
#85772
#83312
#83282
#82182