Finite Group Databasebeta

← #219905

Subgroups — #219905

Order 512.

1477 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36123C211yesmaximal, characteristic
2#22552C211yesmaximal, characteristic, complemented
3C2×#1517C211yesmaximal, characteristic, complemented
4C2×#1519C211yesmaximal, characteristic, complemented
5#13915C211yesmaximal, characteristic, complemented
6#9712C211yesmaximal, characteristic, complemented
7#9680C211yesmaximal, characteristic, complemented
8#9156C211yesmaximal, characteristic, complemented
9#9155C211yesmaximal, characteristic, complemented
10#9114C211yesmaximal, characteristic, complemented
11#9113C211yesmaximal, characteristic, complemented
12#8577C211yesmaximal, characteristic, complemented
13#8332C211yesmaximal, characteristic, complemented
14#8328C211yesmaximal, characteristic, complemented
15C4×#327C211yesmaximal, characteristic, complemented
16C2×#546—21no—
17C2×#532C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C2×#431C2211yescharacteristic, 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×#388—21no—
41C2×#382C2211yescharacteristic, complemented
42C2×#380C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44#1923—21no—
45#1923—21no—
46#1850—21no—
47#1817C2211yescharacteristic, complemented
48#1797C2211yescharacteristic, complemented
49#1779C2211yescharacteristic
50C8×C22⋊C4—21no—
51C4×C22⋊C8C2211yescharacteristic, complemented
52#1519—24no—
53#1517—24no—
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62C2×#327C2211yescharacteristic, complemented
63C2×#327C2211yescharacteristic, complemented
64C2×#327C2211yescharacteristic, complemented
65C2×#327C2211yescharacteristic, complemented
66#1444—21no—
67#1439—21no—
68#1436—21no—
69C4⋊#95C2211yescharacteristic, complemented
70#1434C2211yescharacteristic, complemented
71C22⋊#95C2211yescharacteristic
72C4×#95C2211yescharacteristic, complemented
73#1294C2211yescharacteristic, complemented
74#1294C2211yescharacteristic, complemented
75#1294C2211yescharacteristic, complemented
76#1294C2211yescharacteristic, complemented
77C22×#41—21no—
78C23×D4—21no—
79C23×D4C2×C411yescharacteristic
80C24×C4C2311yescharacteristic
81C23×C8—21no—
82#546—44no—
83#546—44no—
84#532—22no—
85#532—22no—
86#532—41no—
87#532—41no—
88C2×C4⋊Q8C2×C411yescharacteristic
89C2×#127C2×C411yescharacteristic
90C2×#127C2×C411yescharacteristic
91C2×#124—21no—
92C2×#124—21no—
93C2×#123—21no—
94C2×#123—21no—
95C2×C22⋊Q8—21no—
96C2×#121—21no—
97C2×#121—21no—
98C2×#121—21no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—21no—
102C2×#121—21no—
103C2×#121—22no—
104C2×#121—22no—
105C2×#121—41no—
106C2×#121—41no—
107C2×#121C2×C411yescharacteristic
108C2×#121C2×C411yescharacteristic
109C2×#121C2×C411yescharacteristic
110C2×#121C2×C411yescharacteristic
111C2×#121C2311yescharacteristic
112C2×#121C2311yescharacteristic
113C2×#121C2311yescharacteristic
114C2×#120—21no—
115C2×#120—21no—
116C2×#120—21no—
117C2×C4×D4—21no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4C2×C411yescharacteristic
121C2×C4×D4C2×C411yescharacteristic
122C2×C4×D4C2×C411yescharacteristic
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4C2×C411yescharacteristic
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4D411yescharacteristic
132C22×C22⋊C4D411yescharacteristic
133C22×C42—21no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136#431—22no—
137#431—41no—
138C2×C4⋊C8—21no—
139C2×C4⋊C8—21no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—41no—
145C2×C22⋊C8C2311yescharacteristic
146C2×C22⋊C8C2311yescharacteristic
147C2×C22⋊C8C2311yescharacteristic
148C2×C22⋊C8C2311yescharacteristic
149C2×C4×C8—21no—
150C2×C4×C8—21no—
151#398—21no—
152#397—21no—
153#395—21no—
154#394—21no—
155#394—21no—
156#394—21no—
157#394—21no—
158#393—21no—
159#392—21no—
160#392—21no—
161#392—21no—
162#392—21no—
163#390—21no—
164#390—21no—
165#390C2×C411yescharacteristic
166#390C2×C411yescharacteristic
167#390C2×C411yescharacteristic
168#390C2×C411yescharacteristic
169#390C2×C411yescharacteristic
170#389C2×C411yescharacteristic
171#389C2×C411yescharacteristic
172#389C2×C411yescharacteristic
173#388—21no—
174#388—21no—
175#388—21no—
176#388—21no—
177#388—21no—
178#388—44no—
179#386—21no—
180#386—21no—
181#386—21no—
182#386—21no—
183#386—21no—
184#386—21no—
185#386—21no—
186#386—21no—
187#386—21no—
188#386—21no—
189#385—21no—
190#385—21no—
191#385—21no—
192#384C2×C411yescharacteristic
193#382—22no—
194#382—41no—
195#380—22no—
196#380—41no—
197#380C2×C411yescharacteristic
198#380C2×C411yescharacteristic
199#380C2311yescharacteristic
200#379—21no—
201C4×C4⋊C4C2×C411yescharacteristic
202C4×C22⋊C4—21no—
203C4×C22⋊C4C2×C411yescharacteristic
204C4×C22⋊C4C2×C411yescharacteristic
205C4×C22⋊C4C2×C411yescharacteristic
206C4×C22⋊C4C2×C411yescharacteristic
207C4×C22⋊C4D411yescharacteristic
208C4×C22⋊C4D411yescharacteristic
209C4×C22⋊C4D411yescharacteristic
210C4×C22⋊C4D411yescharacteristic
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95D411yescharacteristic
218C2×#95D411yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223#336—21no—
224#336—21no—
225#336—21no—
226#336—21no—
227#327—22no—
228#327—22no—
229#327—22no—
230#327—22no—
231#327—22no—
232#327—22no—
233#327—22no—
234#327—41no—
235#327—41no—
236#327—41no—
237#327—41no—
238#327D414yescomplemented
239C25—21no—
240C25C2×D411yescharacteristic
241C2×#41—42no—
242C2×#41—42no—
243C2×#41—42no—
244C2×#41—42no—
245C2×#41—81no—
246C2×#41—81no—
247C22×Q8—21no—
248C22×D4—21no—
249C22×D4—22no—
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—21no—
261C22×D4—41no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—81no—
268C22×D4—81no—
269C22×D4—81no—
270C22×D4C22×C411yescharacteristic
271C22×D4C22×C411yescharacteristic
272C22×D4C22×C411yescharacteristic
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—21no—
285C23×C4—42no—
286C23×C4—81no—
287C23×C4C22×C411yescharacteristic
288C23×C4C22×C411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—42no—
302C22×C8—42no—
303C22×C8—81no—
304C4⋊Q8—22no—
305C4⋊Q8—41no—
306#127—22no—
307#127—41no—
308#127—81no—
309#124—42no—
310#124—42no—
311#124—44no—
312#123—42no—
313#123—42no—
314#123—44no—
315C22⋊Q8—44no—
316#121—21no—
317#121—21no—
318#121—22no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—22no—
328#121—42no—
329#121—42no—
330#121—41no—
331#121—41no—
332#121—42no—
333#121—42no—
334#121—42no—
335#121—42no—
336#121—42no—
337#121—42no—
338#121—44no—
339#121—44no—
340#121—42no—
341#121—81no—
342#121—81no—
343#121—81no—
344#121C2×D412yes—
345#121#4112yes—
346#120—44no—
347#120—42no—
348#120—42no—
349#120—44no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—42no—
353C4×D4—42no—
354C4×D4—41no—
355C4×D4—41no—
356C4×D4—42no—
357C4×D4—42no—
358C4×D4—44no—
359C4×D4—81no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—81no—
375C2×C4⋊C4—81no—
376C2×C4⋊C4—81no—
377C2×C4⋊C4—81no—
378C2×C4⋊C4C22×C411yescharacteristic
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C411yescharacteristic
381C2×C4⋊C4C22×C411yescharacteristic
382C2×C4⋊C4C22×C411yescharacteristic
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—21no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—81no—
415C2×C22⋊C4—81no—
416C2×C22⋊C4C22⋊C411yescharacteristic
417C2×C22⋊C4C22⋊C411yescharacteristic
418C2×C22⋊C4C22⋊C411yescharacteristic
419C2×C22⋊C4C22⋊C411yescharacteristic
420C2×C22⋊C4C22⋊C411yescharacteristic
421C2×C22⋊C4C22⋊C411yescharacteristic
422C2×C22⋊C4C22⋊C411yescharacteristic
423C2×C22⋊C4C22⋊C411yescharacteristic
424C2×C22⋊C4D814yes—
425C2×C22⋊C4SD1614yes—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—81no—
434C2×C42—81no—
435C2×C42C22×C411yescharacteristic
436C2×C42C22×C411yescharacteristic
437C2×C42C22×C411yescharacteristic
438C2×C42C22×C411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C4⋊C8—42no—
444C4⋊C8—81no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—42no—
453C22⋊C8—42no—
454C22⋊C8—81no—
455C22⋊C8C2×D412yes—
456C4×C8—42no—
457C4×C8—81no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95—42no—
477#95—42no—
478#95C22⋊C411yescharacteristic
479#95C22⋊C411yescharacteristic
480#95C22⋊C411yescharacteristic
481#95C22⋊C411yescharacteristic
482#95C22⋊C411yescharacteristic
483#95C22⋊C411yescharacteristic
484#95C22⋊C411yescharacteristic
485#95C22⋊C411yescharacteristic
486#95C2×D412yes—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—41no—
495C24—41no—
496C24—41no—
497C24—41no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—81no—
503C24—81no—
504C24—81no—
505C24C2×C22⋊C411yescharacteristic
506C24C2×C22⋊C411yescharacteristic
507C24C2×D812yes—
508C24C2×SD1612yes—
509C24C22×D411yescharacteristic
510#41—84no—
511#41—84no—
512#41—84no—
513#41—84no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—81no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—42no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
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—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—84no—
570C2×D4—84no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—84no—
576C2×D4—84no—
577C2×D4—84no—
578C2×D4—84no—
579C2×D4C4×D412yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
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—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
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—41no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
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×C4C2×C22⋊C411yescharacteristic
666C22×C4C2×C22⋊C411yescharacteristic
667C22×C4C2×C22⋊C411yescharacteristic
668C22×C4C2×C22⋊C411yescharacteristic
669C22×C4C2×C22⋊C411yescharacteristic
670C22×C4C2×C22⋊C411yescharacteristic
671C22×C4C2×C22⋊C411yescharacteristic
672C22×C4C2×C22⋊C411yescharacteristic
673C22×C4C2×C22⋊C411yescharacteristic
674C22×C4C2×C22⋊C411yescharacteristic
675C22×C4C2×D812yes—
676C22×C4C2×D812yes—
677C22×C4C2×SD1612yes—
678C22×C4C2×SD1612yes—
679C22×C4C23×C411yescharacteristic
680C22×C4C22×D411yescharacteristic
681C22×C4C22×D411yescharacteristic
682C22×C4C2×#4111yescharacteristic
683C22×C4H(5,𝔽2)11yescharacteristic
684C22×C4H(5,𝔽2)11yescharacteristic
685C2×C8—22no—
686C2×C8—41no—
687C2×C8—41no—
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—84no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—42no—
704C4⋊C4—42no—
705C4⋊C4—41no—
706C4⋊C4—41no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—81no—
712C4⋊C4—84no—
713C4⋊C4—84no—
714C4⋊C4—84no—
715C4⋊C4C4×D412yes—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—41no—
721C22⋊C4—41no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—41no—
732C22⋊C4—41no—
733C22⋊C4—41no—
734C22⋊C4—41no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C22⋊C4—81no—
746C22⋊C4—81no—
747C22⋊C4—84no—
748C22⋊C4—84no—
749C22⋊C4#10214yes—
750C22⋊C4#10214yes—
751C22⋊C4#10214yes—
752C22⋊C4#10214yes—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—41no—
762C42—41no—
763C42—41no—
764C42—41no—
765C42—42no—
766C42—84no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
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—81no—
813C23—81no—
814C23—81no—
815C23—81no—
816C23—81no—
817C23—81no—
818C23—81no—
819C23—81no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—162no—
825C23—162no—
826C23—162no—
827C23C2×#10212yes—
828C23C2×#10212yes—
829C23C22×C22⋊C411yescharacteristic
830C23D4211yescharacteristic
831C23#54611yescharacteristic
832C23C22×D811yescharacteristic
833C23C22×SD1611yescharacteristic
834C23#57611yescharacteristic
835C23#57711yescharacteristic
836Q8—84no—
837D4—42no—
838D4—42no—
839D4—42no—
840D4—42no—
841D4—42no—
842D4—42no—
843D4—84no—
844D4—84no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—84no—
850D4—84no—
851D4—84no—
852D4—84no—
853D4—81no—
854D4—81no—
855D4—81no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—162no—
862D4—162no—
863D4—162no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
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—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
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—21no—
897C2×C4—42no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
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—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—84no—
936C2×C4—84no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—84no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—81no—
945C2×C4—81no—
946C2×C4—81no—
947C2×C4—81no—
948C2×C4—81no—
949C2×C4—81no—
950C2×C4—81no—
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—162no—
963C2×C4#41012yes—
964C2×C4C2×#10212yes—
965C2×C4C2×#10212yes—
966C2×C4C2×#10212yes—
967C2×C4C2×#10212yes—
968C2×C4#42112yes—
969C2×C4C2×C4×D411yescharacteristic
970C2×C4#51811yescharacteristic
971C2×C4D4211yescharacteristic
972C2×C4#54611yescharacteristic
973C8—42no—
974C8—81no—
975C8—81no—
976C8—81no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
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—81no—
1026C22—81no—
1027C22—81no—
1028C22—168no—
1029C22D4×C22⋊C411yescharacteristic
1030C22C2×#41011yescharacteristic
1031C22#288311yescharacteristic
1032C22C22×#10211yescharacteristic
1033C22#289711yescharacteristic
1034C22C2×#42111yescharacteristic
1035C22#290111yescharacteristic
1036C22D4×D811yescharacteristic
1037C22D4×SD1611yescharacteristic
1038C22#329411yescharacteristic
1039C22#329511yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—21no—
1044C4—21no—
1045C4—22no—
1046C4—22no—
1047C4—22no—
1048C4—22no—
1049C4—22no—
1050C4—41no—
1051C4—42no—
1052C4—41no—
1053C4—41no—
1054C4—41no—
1055C4—82no—
1056C4—82no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4—81no—
1061C4—161no—
1062C4—161no—
1063C2—21no—
1064C2—21no—
1065C2—21no—
1066C2—21no—
1067C2—42no—
1068C2—42no—
1069C2—82no—
1070C2—161no—
1071C2—161no—
1072C2#1757411yescharacteristic
1073C2#1759711yescharacteristic
1074C2#1761011yescharacteristic
1075C2#1761311yescharacteristic
1076C2#2240511yescharacteristic
1077C2D4×#10211yescharacteristic
1078C2#2243511yescharacteristic
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. #22552C2semidirect
3. C2×#1517C2semidirect
4. C2×#1519C2semidirect
5. #13915C2semidirect
6. #9712C2semidirect
7. #9680C2semidirect
8. #9156C2semidirect
9. #9155C2semidirect
10. #9114C2semidirect
11. #9113C2semidirect
12. #8577C2semidirect
13. #8332C2semidirect
14. #8328C2semidirect
15. C4×#327C2semidirect
19. C2×#431C22semidirect
26. #2491C4semidirect
29. #2440C4semidirect
30. #2433C4semidirect
32. #2428C4semidirect
33. #2428C4semidirect
34. #2422C4semidirect
36. #2361C4semidirect
38. D4×C22⋊C4C4semidirect
41. C2×#382C22semidirect
47. #1817C22semidirect
48. #1797C22semidirect
51. C4×C22⋊C8C22semidirect
62. C2×#327C22semidirect
63. C2×#327C22semidirect
64. C2×#327C22semidirect
65. C2×#327C22semidirect
69. C4⋊#95C22semidirect
70. #1434C22semidirect
72. C4×#95C22semidirect
73. #1294C22semidirect
74. #1294C22semidirect
75. #1294C22semidirect
76. #1294C22semidirect
238. #327D4semidirect

Maximal subgroups

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

subgroupindex
#361232
#225522
C2×#15172
C2×#15192
#139152
#97122
#96802
#91562
#91552
#91142
#91132
#85772
#83322
#83282
C4×#3272