Finite Group Databasebeta

← #221802

Subgroups — #221802

Order 512.

1621 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36096C211yesmaximal, characteristic
2D4×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#1516C211yesmaximal, characteristic, complemented
4C22×#327C211yesmaximal, characteristic, complemented
5#13894C211yesmaximal, characteristic, complemented
6#9716C211yesmaximal, characteristic, complemented
7#9681C211yesmaximal, characteristic, complemented
8#9158C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9113C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic, complemented
12#8573C211yesmaximal, characteristic, complemented
13#8331C211yesmaximal, characteristic, complemented
14#8328C211yesmaximal, characteristic, complemented
15#8220C211yesmaximal, characteristic, complemented
16C2×#546C411yescharacteristic, complemented
17C2×#525C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C2×C8×D4—21no—
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic, complemented
23#2850C2211yescharacteristic
24#2848C2211yescharacteristic
25#2847C2211yescharacteristic
26#2540C411yescharacteristic, complemented
27#2535C411yescharacteristic, complemented
28#2464—21no—
29#2456—21no—
30#2443—21no—
31#2424—21no—
32#2418—21no—
33#2417C411yescharacteristic, complemented
34#2414C411yescharacteristic, complemented
35#2408C411yescharacteristic, complemented
36#2407C411yescharacteristic, complemented
37#2403—21no—
38#2358—21no—
39#2352C411yescharacteristic, complemented
40D4×C22⋊C4—21no—
41C4×#121C2211yescharacteristic
42C2×#386—21no—
43C2×#381C2211yescharacteristic, complemented
44C22×#95C2211yescharacteristic
45#1954—21no—
46#1869—21no—
47#1869—21no—
48#1797C2211yescharacteristic, complemented
49#1779C2211yescharacteristic
50#1779C2211yescharacteristic, complemented
51C4×C22⋊C8C2211yescharacteristic, complemented
52#1516—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
66#1445—21no—
67#1440—21no—
68#1434C2211yescharacteristic, complemented
69#1434C2211yescharacteristic, complemented
70C22⋊#95—21no—
71C22⋊#95C2211yescharacteristic
72C22⋊#95C2211yescharacteristic, complemented
73#1294C2211yescharacteristic, complemented
74#1294C2211yescharacteristic, complemented
75#1294C2211yescharacteristic, complemented
76#1294C2211yescharacteristic, complemented
77C22×#41C2×C411yescharacteristic, complemented
78C23×D4—21no—
79C23×D4C2×C411yescharacteristic
80C23×D4D411yescharacteristic
81C24×C4—21no—
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C23×C8—21no—
85C23×C8—21no—
86#546—44no—
87C2×#124C2×C411yescharacteristic, complemented
88#525—22no—
89#525—22no—
90#525—41no—
91#525—41no—
92C2×#123—21no—
93C2×#123—21no—
94C2×C22⋊Q8C2×C411yescharacteristic
95C2×C22⋊Q8C2×C411yescharacteristic
96C2×C22⋊Q8C2×C411yescharacteristic, complemented
97C2×C22⋊Q8C2311yescharacteristic
98C2×#121—21no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—22no—
102C2×#121—22no—
103C2×#121—41no—
104C2×#121—41no—
105C2×#121C2×C411yescharacteristic
106C2×#121C2×C411yescharacteristic
107C2×#121C2×C411yescharacteristic, complemented
108C2×#121C2×C411yescharacteristic, complemented
109C2×#121C2×C411yescharacteristic, complemented
110C2×#121C2311yescharacteristic
111C2×#121C2311yescharacteristic
112C2×#120—21no—
113C2×#120—21no—
114C2×#120—21no—
115C2×#120—21no—
116C2×C4×D4—21no—
117C2×C4×D4—21no—
118C2×C4×D4—21no—
119C2×C4×D4—44no—
120C2×C4×D4C2×C411yescharacteristic
121C2×C4×D4C2×C411yescharacteristic
122C2×C4×D4C2×C411yescharacteristic
123C2×C4×D4C2×C411yescharacteristic
124C2×C4×D4C2×C411yescharacteristic, complemented
125C2×C4×D4D411yescharacteristic
126C2×C4×D4D411yescharacteristic
127C2×C4×D4D411yescharacteristic
128C2×C4×D4D411yescharacteristic
129C2×#117C2×C411yescharacteristic, complemented
130C22×C4⋊C4C2×C411yescharacteristic
131C22×C4⋊C4D411yescharacteristic
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4D411yescharacteristic
138C22×C22⋊C4D411yescharacteristic
139C22×C42C2311yescharacteristic
140C8×D4—44no—
141C2×C4⋊C8—21no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—21no—
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—21no—
149C2×C22⋊C8—21no—
150C2×C22⋊C8—41no—
151C2×C22⋊C8—41no—
152C2×C22⋊C8C2311yescharacteristic
153C2×C22⋊C8C2311yescharacteristic
154C2×C22⋊C8C2311yescharacteristic
155C2×C22⋊C8C2311yescharacteristic
156C2×C4×C8—21no—
157#399—21no—
158#398—21no—
159#397—21no—
160#396—21no—
161#394—21no—
162#394—21no—
163#394—21no—
164#392—21no—
165#392—21no—
166#392—21no—
167#392—21no—
168#392—21no—
169#391C2×C411yescharacteristic, complemented
170#390—21no—
171#390—21no—
172#390—21no—
173#390C2×C411yescharacteristic, complemented
174#390C2×C411yescharacteristic, complemented
175#389C2×C411yescharacteristic, complemented
176#388—21no—
177#388—21no—
178#388—21no—
179#388—21no—
180#388—21no—
181#387—21no—
182#386—21no—
183#386—21no—
184#386—21no—
185#386—21no—
186#386—21no—
187#386—21no—
188#386—21no—
189#386—21no—
190#386—21no—
191#386—21no—
192#386—21no—
193#386—44no—
194#385—21no—
195#385—21no—
196#385—21no—
197#385—21no—
198#382C2×C411yescharacteristic, complemented
199#381—22no—
200#381—41no—
201#380—21no—
202#380C2×C411yescharacteristic
203#380C2×C411yescharacteristic
204#380C2×C411yescharacteristic, complemented
205#380C2×C411yescharacteristic, complemented
206#380C2311yescharacteristic
207#379—21no—
208#379—21no—
209C4×C4⋊C4C2×C411yescharacteristic, complemented
210C4×C22⋊C4—21no—
211C4×C22⋊C4—21no—
212C2×#95—22no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—41no—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226#336—21no—
227#336—21no—
228#328—22no—
229#328—22no—
230#328—41no—
231#328—41no—
232#327—22no—
233#327—22no—
234#327—22no—
235#327—22no—
236#327—22no—
237#327—41no—
238#327—41no—
239#327D414yescomplemented
240C25—21no—
241C25C2×D411yescharacteristic
242C25C2×D411yescharacteristic
243C2×#41—22no—
244C2×#41—41no—
245C2×#41—42no—
246C2×#41—81no—
247C22×Q8C22×C411yescharacteristic
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—24no—
252C22×D4—22no—
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—42no—
268C22×D4—81no—
269C22×D4—81no—
270C22×D4—81no—
271C22×D4C22⋊C411yescharacteristic
272C22×D4C22⋊C411yescharacteristic
273C22×D4C22⋊C411yescharacteristic
274C22×D4C22⋊C411yescharacteristic
275C22×D4C22×C411yescharacteristic
276C22×D4C22×C411yescharacteristic
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—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—81no—
300C23×C4—81no—
301C23×C4—81no—
302C23×C4—81no—
303C23×C4C22×C411yescharacteristic
304C23×C4C22×C411yescharacteristic
305C23×C4C22×C411yescharacteristic
306C23×C4C22×C411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—42no—
321C22×C8—42no—
322C22×C8—42no—
323C22×C8—42no—
324C22×C8—81no—
325C22×C8—81no—
326#124—42no—
327#123—42no—
328#123—42no—
329#123—44no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—22no—
335C22⋊Q8—41no—
336C22⋊Q8—42no—
337C22⋊Q8—81no—
338#121—21no—
339#121—21no—
340#121—22no—
341#121—22no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—22no—
347#121—42no—
348#121—42no—
349#121—44no—
350#121—41no—
351#121—41no—
352#121—41no—
353#121—42no—
354#121—42no—
355#121—42no—
356#121—81no—
357#121C2×D412yes—
358#121#4112yes—
359#120—42no—
360#120—42no—
361#120—44no—
362#120—44no—
363#120—81no—
364#120—81no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—42no—
370C4×D4—42no—
371C4×D4—42no—
372C4×D4—42no—
373C4×D4—42no—
374C4×D4—42no—
375C4×D4—42no—
376C4×D4—42no—
377C4×D4—42no—
378C4×D4—81no—
379C4×D4—81no—
380#117—22no—
381#117—41no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4C22⋊C411yescharacteristic
392C2×C4⋊C4C22⋊C411yescharacteristic
393C2×C4⋊C4C22⋊C411yescharacteristic
394C2×C4⋊C4C22⋊C411yescharacteristic
395C2×C4⋊C4C22×C411yescharacteristic
396C2×C4⋊C4C22×C411yescharacteristic
397C2×C4⋊C4C22×C411yescharacteristic
398C2×C4⋊C4C22×C411yescharacteristic
399C2×C4⋊C4C22×C411yescharacteristic
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—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
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—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—81no—
437C2×C22⋊C4—81no—
438C2×C22⋊C4C22⋊C411yescharacteristic
439C2×C22⋊C4C22⋊C411yescharacteristic
440C2×C22⋊C4C22⋊C411yescharacteristic
441C2×C22⋊C4C22⋊C411yescharacteristic
442C2×C22⋊C4C22⋊C411yescharacteristic
443C2×C22⋊C4C22⋊C411yescharacteristic
444C2×C22⋊C4C22⋊C411yescharacteristic
445C2×C22⋊C4C22⋊C411yescharacteristic
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—42no—
449C2×C42C22×C411yescharacteristic
450C2×C42C22×C411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C4⋊C8—42no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461C22⋊C8—42no—
462C22⋊C8—42no—
463C22⋊C8—42no—
464C22⋊C8—42no—
465C22⋊C8—81no—
466C22⋊C8—81no—
467C22⋊C8C2×D412yes—
468C4×C8—42no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—42no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95—42no—
492#95—81no—
493#95—81no—
494#95—81no—
495#95C2×D412yes—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—41no—
512C24—41no—
513C24—41no—
514C24—41no—
515C24—41no—
516C24—42no—
517C24—42no—
518C24—42no—
519C24—42no—
520C24—81no—
521C24—81no—
522C24—81no—
523C24C2×C22⋊C411yescharacteristic
524C24C2×C22⋊C411yescharacteristic
525C24C2×C22⋊C411yescharacteristic
526C24C2×C22⋊C411yescharacteristic
527C24#13512yes—
528C24#13512yes—
529C24C22×D411yescharacteristic
530#41—84no—
531#41—84no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—42no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—84no—
582C2×D4—84no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—84no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4#9914yes—
596C2×D4C4×D412yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
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—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—48no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—42no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
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—81no—
688C22×C4—81no—
689C22×C4—81no—
690C22×C4—82no—
691C22×C4—82no—
692C22×C4—82no—
693C22×C4—82no—
694C22×C4—82no—
695C22×C4—82no—
696C22×C4—82no—
697C22×C4—82no—
698C22×C4—81no—
699C22×C4—84no—
700C22×C4—84no—
701C22×C4—84no—
702C22×C4—84no—
703C22×C4—84no—
704C22×C4—84no—
705C22×C4C2×C22⋊C411yescharacteristic
706C22×C4C2×C22⋊C411yescharacteristic
707C22×C4C2×C22⋊C411yescharacteristic
708C22×C4C2×C22⋊C411yescharacteristic
709C22×C4C2×C22⋊C411yescharacteristic
710C22×C4C2×C22⋊C411yescharacteristic
711C22×C4C2×C22⋊C411yescharacteristic
712C22×C4C2×C22⋊C411yescharacteristic
713C22×C4C23×C411yescharacteristic
714C22×C4C22×D411yescharacteristic
715C22×C4C22×D411yescharacteristic
716C22×C4C2×#4111yescharacteristic
717C22×C4H(5,𝔽2)11yescharacteristic
718C22×C4H(5,𝔽2)11yescharacteristic
719C2×C8—22no—
720C2×C8—41no—
721C2×C8—41no—
722C2×C8—41no—
723C2×C8—41no—
724C2×C8—41no—
725C2×C8—41no—
726C2×C8—41no—
727C2×C8—41no—
728C2×C8—41no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—84no—
732C2×C8—84no—
733C4⋊C4—21no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—41no—
741C4⋊C4—41no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—41no—
745C4⋊C4—41no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—41no—
749C4⋊C4—81no—
750C4⋊C4—81no—
751C4⋊C4C4×D412yes—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—41no—
760C22⋊C4—41no—
761C22⋊C4—41no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—81no—
782C22⋊C4—81no—
783C22⋊C4—81no—
784C22⋊C4—81no—
785C22⋊C4—81no—
786C22⋊C4—81no—
787C22⋊C4—81no—
788C22⋊C4—84no—
789C22⋊C4—84no—
790C22⋊C4—84no—
791C42—22no—
792C42—22no—
793C42—41no—
794C42—41no—
795C42—42no—
796C42—81no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—24no—
822C23—24no—
823C23—22no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23—81no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—162no—
875C23—162no—
876C23—162no—
877C23C2×#9912yes—
878C23C2×#9912yes—
879C23#41612yes—
880C23#41612yes—
881C23#42112yes—
882C23C22×C22⋊C411yescharacteristic
883C23D4211yescharacteristic
884C23#54611yescharacteristic
885C23C2×#13511yescharacteristic
886C23C2×#13511yescharacteristic
887C23#57611yescharacteristic
888C23#57711yescharacteristic
889Q8—81no—
890Q8—81no—
891D4—28no—
892D4—44no—
893D4—42no—
894D4—42no—
895D4—44no—
896D4—42no—
897D4—42no—
898D4—42no—
899D4—42no—
900D4—44no—
901D4—81no—
902D4—81no—
903D4—84no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4—84no—
908D4—81no—
909D4—81no—
910D4—81no—
911D4—81no—
912D4—162no—
913D4—162no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—42no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—81no—
982C2×C4—81no—
983C2×C4—81no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—81no—
992C2×C4—81no—
993C2×C4—84no—
994C2×C4—84no—
995C2×C4—81no—
996C2×C4—81no—
997C2×C4—81no—
998C2×C4—81no—
999C2×C4—81no—
1000C2×C4—81no—
1001C2×C4—81no—
1002C2×C4—816no—
1003C2×C4—81no—
1004C2×C4—81no—
1005C2×C4—81no—
1006C2×C4—81no—
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—162no—
1019C2×C4C2×#9912yes—
1020C2×C4C2×C4×D411yescharacteristic
1021C2×C4#51811yescharacteristic
1022C2×C4D4211yescharacteristic
1023C2×C4#54611yescharacteristic
1024C8—42no—
1025C8—81no—
1026C8—81no—
1027C8—81no—
1028C22—21no—
1029C22—22no—
1030C22—21no—
1031C22—22no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—22no—
1037C22—21no—
1038C22—21no—
1039C22—22no—
1040C22—21no—
1041C22—21no—
1042C22—22no—
1043C22—21no—
1044C22—21no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—41no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—41no—
1064C22—41no—
1065C22—42no—
1066C22—42no—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—42no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—82no—
1075C22—82no—
1076C22—82no—
1077C22—82no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—168no—
1090C22#151614yescomplemented
1091C22D4×C22⋊C411yescharacteristic
1092C22C22×#9911yescharacteristic
1093C22#288311yescharacteristic
1094C22C2×#41611yescharacteristic
1095C22#289711yescharacteristic
1096C22C2×#42111yescharacteristic
1097C22#290111yescharacteristic
1098C22#328011yescharacteristic
1099C22#328211yescharacteristic
1100C22#329611yescharacteristic
1101C22#329711yescharacteristic
1102C4—21no—
1103C4—21no—
1104C4—21no—
1105C4—21no—
1106C4—22no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—82no—
1116C4—82no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—161no—
1123C4—161no—
1124C2—21no—
1125C2—21no—
1126C2—21no—
1127C2—21no—
1128C2—24no—
1129C2—42no—
1130C2—42no—
1131C2—81no—
1132C2—82no—
1133C2—161no—
1134C2C2×#151611yescharacteristic
1135C2#1759711yescharacteristic
1136C2#1760311yescharacteristic
1137C2#1761511yescharacteristic
1138C2D4×#9911yescharacteristic
1139C2#2241411yescharacteristic
1140C2#2243411yescharacteristic
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. D4×C22⋊C8C2semidirect
3. C2×#1516C2semidirect
4. C22×#327C2semidirect
5. #13894C2semidirect
6. #9716C2semidirect
7. #9681C2semidirect
8. #9158C2semidirect
9. #9143C2semidirect
10. #9113C2semidirect
11. #9111C2semidirect
12. #8573C2semidirect
13. #8331C2semidirect
14. #8328C2semidirect
15. #8220C2semidirect
16. C2×#546C4semidirect
22. C22×C22⋊C8C22semidirect
26. #2540C4semidirect
27. #2535C4semidirect
33. #2417C4semidirect
34. #2414C4semidirect
35. #2408C4semidirect
36. #2407C4semidirect
39. #2352C4semidirect
43. C2×#381C22semidirect
48. #1797C22semidirect
50. #1779C22semidirect
51. C4×C22⋊C8C22semidirect
53. C2×#328C22semidirect
54. C2×#328C22semidirect
55. C2×#328C22semidirect
56. C2×#328C22semidirect
68. #1434C22semidirect
69. #1434C22semidirect
72. C22⋊#95C22semidirect
73. #1294C22semidirect
74. #1294C22semidirect
75. #1294C22semidirect
76. #1294C22semidirect
77. C22×#41C2×C4semidirect
87. C2×#124C2×C4semidirect
96. C2×C22⋊Q8C2×C4semidirect
107. C2×#121C2×C4semidirect
108. C2×#121C2×C4semidirect
109. C2×#121C2×C4semidirect
124. C2×C4×D4C2×C4semidirect
129. C2×#117C2×C4semidirect
169. #391C2×C4semidirect
173. #390C2×C4semidirect
174. #390C2×C4semidirect
175. #389C2×C4semidirect
198. #382C2×C4semidirect
204. #380C2×C4semidirect
205. #380C2×C4semidirect
209. C4×C4⋊C4C2×C4semidirect
239. #327D4semidirect
1090. C22#1516semidirect

Maximal subgroups

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

subgroupindex
#360962
D4×C22⋊C82
C2×#15162
C22×#3272
#138942
#97162
#96812
#91582
#91432
#91132
#91112
#85732
#83312
#83282
#82202