Finite Group Databasebeta

← #221806

Subgroups — #221806

Order 512.

1527 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36097C211yesmaximal, characteristic
2D4×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#1516C211yesmaximal, characteristic, complemented
4C22×#328C211yesmaximal, characteristic, complemented
5#13894C211yesmaximal, characteristic, complemented
6#9716C211yesmaximal, characteristic, complemented
7#9681C211yesmaximal, characteristic, complemented
8#9154C211yesmaximal, characteristic, complemented
9#9147C211yesmaximal, characteristic, complemented
10#9113C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic, complemented
12#8574C211yesmaximal, characteristic, complemented
13#8331C211yesmaximal, characteristic, complemented
14#8329C211yesmaximal, characteristic, complemented
15#8221C211yesmaximal, characteristic, complemented
16C2×#548C411yescharacteristic, complemented
17C2×#525C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C2×C8×D4—21no—
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23#2850C2211yescharacteristic
24#2848C2211yescharacteristic
25#2847C2211yescharacteristic
26#2540C411yescharacteristic, complemented
27#2536C411yescharacteristic, complemented
28#2472—21no—
29#2463—21no—
30#2461—21no—
31#2449—21no—
32#2443—21no—
33#2416C411yescharacteristic, complemented
34#2415C411yescharacteristic, complemented
35#2410—21no—
36#2409C411yescharacteristic, complemented
37#2407C411yescharacteristic, complemented
38#2361—21no—
39#2358—21no—
40#2352C411yescharacteristic, complemented
41C4×C22⋊Q8C2211yescharacteristic
42C2×#386—21no—
43C2×#381C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1954—21no—
46#1869—21no—
47#1869—21no—
48#1797C2211yescharacteristic
49#1779C2211yescharacteristic
50#1779C2211yescharacteristic
51C4×C22⋊C8C2211yescharacteristic
52#1516—24no—
53C2×#328—24no—
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#328C2211yescharacteristic
59C2×#328C2211yescharacteristic
60C2×#328C2211yescharacteristic
61C2×#328C2211yescharacteristic
62C2×#327C2211yescharacteristic
63C2×#327C2211yescharacteristic
64C2×#327C2211yescharacteristic
65C2×#327C2211yescharacteristic
66#1445—21no—
67#1440—21no—
68#1434C2211yescharacteristic
69#1434C2211yescharacteristic
70C22⋊#95—21no—
71C22⋊#95C2211yescharacteristic
72C22⋊#95C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77C22×#41C2×C411yescharacteristic, complemented
78C23×Q8C2×C411yescharacteristic
79C23×D4D411yescharacteristic
80C24×C4—21no—
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C23×C8—21no—
84C23×C8—21no—
85#548—44no—
86C2×#124—21no—
87C2×#124C2×C411yescharacteristic, complemented
88#525—22no—
89#525—22no—
90#525—41no—
91#525—41no—
92C2×#123—21no—
93C2×C22⋊Q8—21no—
94C2×C22⋊Q8—21no—
95C2×C22⋊Q8—21no—
96C2×C22⋊Q8—22no—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—41no—
99C2×C22⋊Q8—41no—
100C2×C22⋊Q8C2×C411yescharacteristic
101C2×C22⋊Q8C2×C411yescharacteristic
102C2×C22⋊Q8C2×C411yescharacteristic, complemented
103C2×C22⋊Q8C2×C411yescharacteristic, complemented
104C2×C22⋊Q8C2×C411yescharacteristic, complemented
105C2×C22⋊Q8C2311yescharacteristic
106C2×C22⋊Q8C2311yescharacteristic
107C2×#121—21no—
108C2×#121—21no—
109C2×#121C2×C411yescharacteristic
110C2×#121C2×C411yescharacteristic
111C2×#121C2×C411yescharacteristic, complemented
112C2×#121C2311yescharacteristic
113C2×#120—21no—
114C2×#120—21no—
115C2×C4×Q8C2×C411yescharacteristic, complemented
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×D4D411yescharacteristic
125C2×C4×D4D411yescharacteristic
126C2×C4×D4D411yescharacteristic
127C2×C4×D4D411yescharacteristic
128C2×#117C2×C411yescharacteristic, complemented
129C22×C4⋊C4—21no—
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⋊C4D411yescharacteristic
137C22×C22⋊C4D411yescharacteristic
138C22×C42C2311yescharacteristic
139C8×D4—44no—
140C2×C4⋊C8—21no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—21no—
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—21no—
149C2×C22⋊C8—41no—
150C2×C22⋊C8—41no—
151C2×C22⋊C8C2311yescharacteristic
152C2×C22⋊C8C2311yescharacteristic
153C2×C22⋊C8C2311yescharacteristic
154C2×C22⋊C8C2311yescharacteristic
155C2×C4×C8—21no—
156#399—21no—
157#398—21no—
158#397—21no—
159#396—21no—
160#395—21no—
161#394—21no—
162#394—21no—
163#394—21no—
164#394—21no—
165#393—21no—
166#392—21no—
167#392—21no—
168#391C2×C411yescharacteristic, complemented
169#391C2×C411yescharacteristic, complemented
170#390—21no—
171#390—21no—
172#390C2×C411yescharacteristic, complemented
173#389—21no—
174#389C2×C411yescharacteristic, complemented
175#388—21no—
176#388—21no—
177#388—21no—
178#388—21no—
179#388—21no—
180#388—21no—
181#387—21no—
182#387—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—44no—
193#385—21no—
194#385—21no—
195#385—21no—
196#385—21no—
197#385—21no—
198#385—21no—
199#382C2×C411yescharacteristic, complemented
200#381—22no—
201#381—41no—
202#380C2×C411yescharacteristic
203#380C2×C411yescharacteristic
204#380C2×C411yescharacteristic, complemented
205#380C2×C411yescharacteristic, complemented
206#380C2311yescharacteristic
207#379—21no—
208C4×C4⋊C4—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—22no—
231#328—22no—
232#328—22no—
233#328—41no—
234#328—41no—
235#328D414yescomplemented
236#327—22no—
237#327—22no—
238#327—41no—
239#327—41no—
240C25C2×D411yescharacteristic
241C25C2×D411yescharacteristic
242C2×#41—22no—
243C2×#41—41no—
244C2×#41—42no—
245C2×#41—81no—
246C22×Q8—21no—
247C22×Q8—22no—
248C22×Q8—41no—
249C22×Q8—42no—
250C22×Q8—81no—
251C22×Q8C22×C411yescharacteristic
252C22×Q8C22×C411yescharacteristic
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—24no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—42no—
262C22×D4C22⋊C411yescharacteristic
263C22×D4C22⋊C411yescharacteristic
264C22×D4C22⋊C411yescharacteristic
265C22×D4C22⋊C411yescharacteristic
266C22×D4C22×C411yescharacteristic
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—81no—
290C23×C4—81no—
291C23×C4—81no—
292C23×C4—81no—
293C23×C4C22×C411yescharacteristic
294C23×C4C22×C411yescharacteristic
295C23×C4C22×C411yescharacteristic
296C23×C4C22×C411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2411yescharacteristic
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—42no—
311C22×C8—42no—
312C22×C8—42no—
313C22×C8—42no—
314C22×C8—81no—
315C22×C8—81no—
316#124—42no—
317#124—44no—
318#123—42no—
319#123—42no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—22no—
329C22⋊Q8—42no—
330C22⋊Q8—42no—
331C22⋊Q8—41no—
332C22⋊Q8—41no—
333C22⋊Q8—41no—
334C22⋊Q8—42no—
335C22⋊Q8—42no—
336C22⋊Q8—44no—
337C22⋊Q8—42no—
338C22⋊Q8—81no—
339C22⋊Q8C2×D412yes—
340C22⋊Q8#4112yes—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—22no—
346#121—41no—
347#121—42no—
348#121—44no—
349#121—44no—
350#121—81no—
351#120—42no—
352#120—42no—
353#120—42no—
354#120—42no—
355C4×Q8—42no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—42no—
359C4×D4—42no—
360C4×D4—42no—
361C4×D4—42no—
362C4×D4—42no—
363C4×D4—42no—
364C4×D4—42no—
365C4×D4—42no—
366C4×D4—44no—
367C4×D4—42no—
368C4×D4—42no—
369#117—22no—
370#117—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4C22⋊C411yescharacteristic
387C2×C4⋊C4C22⋊C411yescharacteristic
388C2×C4⋊C4C22⋊C411yescharacteristic
389C2×C4⋊C4C22⋊C411yescharacteristic
390C2×C4⋊C4C22×C411yescharacteristic
391C2×C4⋊C4C22×C411yescharacteristic
392C2×C4⋊C4C22×C411yescharacteristic
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C4⋊C4C22×C411yescharacteristic
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—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—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—81no—
428C2×C22⋊C4—81no—
429C2×C22⋊C4C22⋊C411yescharacteristic
430C2×C22⋊C4C22⋊C411yescharacteristic
431C2×C22⋊C4C22⋊C411yescharacteristic
432C2×C22⋊C4C22⋊C411yescharacteristic
433C2×C22⋊C4C22⋊C411yescharacteristic
434C2×C22⋊C4C22⋊C411yescharacteristic
435C2×C22⋊C4C22⋊C411yescharacteristic
436C2×C22⋊C4C22⋊C411yescharacteristic
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—42no—
441C2×C42C22×C411yescharacteristic
442C2×C42C22×C411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C4⋊C8—42no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—42no—
454C22⋊C8—42no—
455C22⋊C8—42no—
456C22⋊C8—42no—
457C22⋊C8—81no—
458C22⋊C8—81no—
459C22⋊C8C2×D412yes—
460C4×C8—42no—
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—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—42no—
482#95—42no—
483#95—42no—
484#95—42no—
485#95—42no—
486#95—81no—
487#95—81no—
488#95—81no—
489#95C2×D412yes—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—41no—
505C24—41no—
506C24—41no—
507C24—41no—
508C24—41no—
509C24C2×C22⋊C411yescharacteristic
510C24C2×C22⋊C411yescharacteristic
511C24C2×C22⋊C411yescharacteristic
512C24C2×C22⋊C411yescharacteristic
513C24#13512yes—
514C24#13512yes—
515C24C22×D411yescharacteristic
516#41—84no—
517#41—84no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—41no—
524C2×Q8—41no—
525C2×Q8—41no—
526C2×Q8—41no—
527C2×Q8—81no—
528C2×Q8—84no—
529C2×Q8—84no—
530C2×Q8C4×D412yes—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—42no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
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#9914yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
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—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
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—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—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—48no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—42no—
644C22×C4—42no—
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—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—81no—
660C22×C4—82no—
661C22×C4—82no—
662C22×C4—82no—
663C22×C4—82no—
664C22×C4—82no—
665C22×C4—82no—
666C22×C4—82no—
667C22×C4—82no—
668C22×C4—81no—
669C22×C4—81no—
670C22×C4—84no—
671C22×C4—84no—
672C22×C4—84no—
673C22×C4—84no—
674C22×C4—84no—
675C22×C4—84no—
676C22×C4C2×C22⋊C411yescharacteristic
677C22×C4C2×C22⋊C411yescharacteristic
678C22×C4C2×C22⋊C411yescharacteristic
679C22×C4C2×C22⋊C411yescharacteristic
680C22×C4C2×C22⋊C411yescharacteristic
681C22×C4C2×C22⋊C411yescharacteristic
682C22×C4C2×C22⋊C411yescharacteristic
683C22×C4C2×C22⋊C411yescharacteristic
684C22×C4C23×C411yescharacteristic
685C22×C4C22×D411yescharacteristic
686C22×C4C22×D411yescharacteristic
687C22×C4C2×#4111yescharacteristic
688C22×C4H(5,𝔽2)11yescharacteristic
689C22×C4H(5,𝔽2)11yescharacteristic
690C2×C8—22no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C2×C8—41no—
700C2×C8—41no—
701C2×C8—41no—
702C2×C8—84no—
703C2×C8—84no—
704C4⋊C4—21no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—41no—
714C4⋊C4—41no—
715C4⋊C4—42no—
716C4⋊C4—42no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—41no—
720C4⋊C4—41no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—41no—
724C4⋊C4—41no—
725C4⋊C4—42no—
726C4⋊C4—81no—
727C4⋊C4C4×D412yes—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—41no—
735C22⋊C4—41no—
736C22⋊C4—41no—
737C22⋊C4—41no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—41no—
748C22⋊C4—41no—
749C22⋊C4—41no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—41no—
755C22⋊C4—41no—
756C22⋊C4—42no—
757C22⋊C4—81no—
758C22⋊C4—81no—
759C22⋊C4—81no—
760C22⋊C4—81no—
761C22⋊C4—84no—
762C22⋊C4—84no—
763C22⋊C4—84no—
764C42—22no—
765C42—22no—
766C42—41no—
767C42—41no—
768C42—42no—
769C42—42no—
770C42—81no—
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—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—24no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23C2×#9912yes—
838C23C2×#9912yes—
839C23#41612yes—
840C23#41612yes—
841C23#42112yes—
842C23C22×C22⋊C411yescharacteristic
843C23D4211yescharacteristic
844C23#54611yescharacteristic
845C23C2×#13511yescharacteristic
846C23C2×#13511yescharacteristic
847C23#57711yescharacteristic
848C23#57811yescharacteristic
849Q8—42no—
850Q8—42no—
851Q8—81no—
852Q8—81no—
853Q8—84no—
854D4—28no—
855D4—44no—
856D4—44no—
857D4—44no—
858D4—81no—
859D4—81no—
860D4—84no—
861D4—84no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—84no—
867D4—162no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—42no—
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—41no—
914C2×C4—41no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
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—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—81no—
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—84no—
951C2×C4—84no—
952C2×C4—84no—
953C2×C4—81no—
954C2×C4—81no—
955C2×C4—81no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—816no—
961C2×C4—81no—
962C2×C4—81no—
963C2×C4—81no—
964C2×C4—81no—
965C2×C4—81no—
966C2×C4—81no—
967C2×C4—81no—
968C2×C4—81no—
969C2×C4—81no—
970C2×C4—81no—
971C2×C4—81no—
972C2×C4—81no—
973C2×C4—81no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4C2×#9912yes—
977C2×C4C2×C4×D411yescharacteristic
978C2×C4#51811yescharacteristic
979C2×C4D4211yescharacteristic
980C2×C4#54611yescharacteristic
981C8—42no—
982C8—81no—
983C8—81no—
984C8—81no—
985C22—21no—
986C22—22no—
987C22—21no—
988C22—22no—
989C22—21no—
990C22—21no—
991C22—21no—
992C22—22no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—22no—
997C22—21no—
998C22—21no—
999C22—22no—
1000C22—21no—
1001C22—21no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—82no—
1029C22—82no—
1030C22—82no—
1031C22—82no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22#151614yescomplemented
1040C22D4×C22⋊C411yescharacteristic
1041C22C22×#9911yescharacteristic
1042C22#288311yescharacteristic
1043C22C2×#41611yescharacteristic
1044C22#289811yescharacteristic
1045C22C2×#42111yescharacteristic
1046C22#290111yescharacteristic
1047C22#328211yescharacteristic
1048C22#328511yescharacteristic
1049C22#330011yescharacteristic
1050C22#330111yescharacteristic
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—22no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—41no—
1060C4—42no—
1061C4—41no—
1062C4—42no—
1063C4—41no—
1064C4—41no—
1065C4—82no—
1066C4—82no—
1067C4—81no—
1068C4—81no—
1069C4—81no—
1070C4—81no—
1071C4—81no—
1072C4—161no—
1073C4—161no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—24no—
1079C2—42no—
1080C2—42no—
1081C2—81no—
1082C2—161no—
1083C2C2×#151611yescharacteristic
1084C2#1759811yescharacteristic
1085C2#1760811yescharacteristic
1086C2#1761511yescharacteristic
1087C2D4×#9911yescharacteristic
1088C2#2241611yescharacteristic
1089C2#2243411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36097C2
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×#328C2semidirect
5. #13894C2semidirect
6. #9716C2semidirect
7. #9681C2semidirect
8. #9154C2semidirect
9. #9147C2semidirect
10. #9113C2semidirect
11. #9111C2semidirect
12. #8574C2semidirect
13. #8331C2semidirect
14. #8329C2semidirect
15. #8221C2semidirect
16. C2×#548C4semidirect
26. #2540C4semidirect
27. #2536C4semidirect
33. #2416C4semidirect
34. #2415C4semidirect
36. #2409C4semidirect
37. #2407C4semidirect
40. #2352C4semidirect
77. C22×#41C2×C4semidirect
87. C2×#124C2×C4semidirect
102. C2×C22⋊Q8C2×C4semidirect
103. C2×C22⋊Q8C2×C4semidirect
104. C2×C22⋊Q8C2×C4semidirect
111. C2×#121C2×C4semidirect
115. C2×C4×Q8C2×C4semidirect
128. C2×#117C2×C4semidirect
168. #391C2×C4semidirect
169. #391C2×C4semidirect
172. #390C2×C4semidirect
174. #389C2×C4semidirect
199. #382C2×C4semidirect
204. #380C2×C4semidirect
205. #380C2×C4semidirect
209. C4×C4⋊C4C2×C4semidirect
235. #328D4semidirect
1039. C22#1516semidirect

Maximal subgroups

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

subgroupindex
#360972
D4×C22⋊C82
C2×#15162
C22×#3282
#138942
#97162
#96812
#91542
#91472
#91132
#91112
#85742
#83312
#83292
#82212