Finite Group Databasebeta

← #383682

Subgroups — #383682

Order 512.

1808 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2417C211yesmaximal, characteristic
2C2×#1955C211yesmaximal, characteristic
3C2×#1872C211yesmaximal, characteristic, complemented
4C2×#1823C211yesmaximal, characteristic, complemented
5#13872C211yesmaximal, characteristic
6#11227C211yesmaximal, characteristic, complemented
7#11200C211yesmaximal, characteristic, complemented
8#11077C211yesmaximal, characteristic, complemented
9#10970C211yesmaximal, characteristic, complemented
10#10970C211yesmaximal, characteristic, complemented
11#10970C211yesmaximal, characteristic, complemented
12#10928C211yesmaximal, characteristic, complemented
13#10881C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31#2417—24no—
32#2417C418yescomplemented
33C2×#398—21no—
34C2×#396—21no—
35C2×#391C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#386—21no—
38C2×#386—21no—
39C2×#380—21no—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44#1955—24no—
45#1872—24no—
46#1823—24no—
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59#1441—21no—
60#1439—21no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C22⋊#95—21no—
64C23×Q8C2311yescharacteristic
65C23×D4D411yescharacteristic
66C24×C4—21no—
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×C22⋊Q8—22no—
75C2×C22⋊Q8—22no—
76C2×C22⋊Q8—22no—
77C2×C22⋊Q8—22no—
78C2×C22⋊Q8—41no—
79C2×C22⋊Q8—41no—
80C2×C22⋊Q8—41no—
81C2×C22⋊Q8—41no—
82C2×C22⋊Q8—41no—
83C2×C22⋊Q8—41no—
84C2×C22⋊Q8C2×C414yes—
85C2×C22⋊Q8C2×C414yescomplemented
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C2×C4×D4C2×C414yes—
91C2×C4×D4D414yes—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—41no—
103C22×C4⋊C4—41no—
104C22×C4⋊C4—41no—
105C22×C4⋊C4—41no—
106C22×C4⋊C4—41no—
107C22×C4⋊C4—41no—
108C22×C4⋊C4C2×C414yescomplemented
109C22×C4⋊C4D411yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4D411yescharacteristic
124C22×C22⋊C4D411yescharacteristic
125C22×C42C2311yescharacteristic
126C2×C4⋊C8—22no—
127C2×C4⋊C8—41no—
128C2×C4⋊C8—41no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—41no—
134C2×#103—41no—
135C2×#103—41no—
136C2×#103—41no—
137C2×#103—41no—
138C2×#103—41no—
139C2×#103—41no—
140C2×#103—41no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8—22no—
146C2×C22⋊C8—22no—
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—41no—
150C2×C22⋊C8—41no—
151C2×C22⋊C8—41no—
152C2×C22⋊C8—41no—
153C2×#97—22no—
154C2×#97—41no—
155C2×#97—41no—
156#398—28no—
157#396—28no—
158#391—22no—
159#391C2×C414yescomplemented
160#389—22no—
161#389C2×C414yescomplemented
162#386—28no—
163#386—44no—
164#380—22no—
165#380—28no—
166#380—22no—
167#380—22no—
168#380—41no—
169#380—41no—
170#380—41no—
171#380—41no—
172#380C2×C414yes—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—22no—
189#340—41no—
190#340—41no—
191#340—41no—
192#340—41no—
193#340—41no—
194#340—41no—
195#340D414yescomplemented
196C25C2×D411yescharacteristic
197C25C2×D411yescharacteristic
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8C22×C412yes—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—41no—
217C22×D4—41no—
218C22×D4C22⋊C414yes—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—24no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—81no—
262C23×C4—81no—
263C23×C4—81no—
264C23×C4—81no—
265C23×C4C22×C412yes—
266C23×C4C22×C412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D412yes—
272C23×C4C2×D412yes—
273C23×C4C2411yescharacteristic
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8C2×D412yes—
301C22×C8#4112yes—
302C22⋊Q8—28no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306C22⋊Q8—44no—
307C22⋊Q8—44no—
308C22⋊Q8—44no—
309C22⋊Q8—44no—
310C4×D4—44no—
311C4×D4—44no—
312C4×D4—44no—
313C4×D4—44no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—81no—
373C2×C4⋊C4—81no—
374C2×C4⋊C4C22⋊C414yes—
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C412yes—
378C2×C4⋊C4C2×D412yes—
379C2×C4⋊C4C2×D412yes—
380C2×C4⋊C4#4112yes—
381C2×C4⋊C4#4112yes—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—81no—
401C2×C22⋊C4—81no—
402C2×C22⋊C4—81no—
403C2×C22⋊C4—81no—
404C2×C22⋊C4C22⋊C414yes—
405C2×C22⋊C4C22⋊C414yes—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42C22×C412yes—
411C2×C42C2×D412yes—
412C4⋊C8—44no—
413#103—44no—
414#103—44no—
415#103—44no—
416#103—44no—
417C22⋊C8—44no—
418C22⋊C8—44no—
419C22⋊C8—44no—
420C22⋊C8—44no—
421#97—44no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—81no—
432#95—81no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24C2×C22⋊C412yes—
458C24C2×C22⋊C412yes—
459C24AGL(1,ℤ/8)12yes—
460C24#13712yes—
461C24#13712yes—
462C24#13712yes—
463C24C22×D411yescharacteristic
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—41no—
473C2×Q8—41no—
474C2×Q8—41no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—48no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—48no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—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—48no—
624C22×C4—41no—
625C22×C4—41no—
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—84no—
639C22×C4—84no—
640C22×C4—84no—
641C22×C4—84no—
642C22×C4—84no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—84no—
646C22×C4—84no—
647C22×C4—84no—
648C22×C4—84no—
649C22×C4C2×C22⋊C412yes—
650C22×C4C2×C22⋊C412yes—
651C22×C4C2×C22⋊C412yes—
652C22×C4C2×C22⋊C412yes—
653C22×C4C23×C411yescharacteristic
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C2×#4111yescharacteristic
657C22×C4C2×#4111yescharacteristic
658C22×C4C2×#4111yescharacteristic
659C22×C4H(5,𝔽2)11yescharacteristic
660C22×C4H(5,𝔽2)11yescharacteristic
661C22×C4H(5,𝔽2)11yescharacteristic
662C22×C4H(5,𝔽2)11yescharacteristic
663C22×C4H(5,𝔽2)11yescharacteristic
664C22×C4H(5,𝔽2)11yescharacteristic
665C22×C4H(5,𝔽2)11yescharacteristic
666C22×C42−1+411yescharacteristic
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—41no—
674C2×C8—41no—
675C2×C8—41no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—41no—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8—41no—
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—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—44no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4—48no—
711C4⋊C4—41no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—41no—
715C4⋊C4—41no—
716C4⋊C4—41no—
717C4⋊C4—41no—
718C4⋊C4—41no—
719C4⋊C4—41no—
720C4⋊C4—41no—
721C4⋊C4—41no—
722C4⋊C4—41no—
723C4⋊C4—41no—
724C4⋊C4—41no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—84no—
728C4⋊C4C4×D414yes—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—84no—
734C22⋊C4—84no—
735C22⋊C4—84no—
736C22⋊C4—84no—
737C42—22no—
738C42—22no—
739C42—22no—
740C42—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
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#41714yes—
810C23#41914yes—
811C23C22×C22⋊C411yescharacteristic
812C23#53411yescharacteristic
813C23#53411yescharacteristic
814C23D4211yescharacteristic
815C23#54611yescharacteristic
816C23#54611yescharacteristic
817C23#54711yescharacteristic
818C23C2×AGL(1,ℤ/8)11yescharacteristic
819C23C2×#13711yescharacteristic
820C23C2×#13711yescharacteristic
821C23C2×#13711yescharacteristic
822C23#57611yescharacteristic
823C23#57711yescharacteristic
824C23#57711yescharacteristic
825C23#57811yescharacteristic
826Q8—42no—
827Q8—42no—
828Q8—42no—
829Q8—42no—
830Q8—81no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—416no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—816no—
902C2×C4—816no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—81no—
914C2×C4—81no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4C2×C4×D411yescharacteristic
938C2×C4C4×#4111yescharacteristic
939C2×C4#51811yescharacteristic
940C2×C4#51811yescharacteristic
941C2×C4#51811yescharacteristic
942C2×C4#52011yescharacteristic
943C2×C4#53411yescharacteristic
944C2×C4#53411yescharacteristic
945C2×C4#53511yescharacteristic
946C2×C4#53711yescharacteristic
947C2×C4#53811yescharacteristic
948C2×C4#53811yescharacteristic
949C2×C4#54011yescharacteristic
950C2×C4#54011yescharacteristic
951C2×C4#54011yescharacteristic
952C2×C4#54211yescharacteristic
953C2×C4D4211yescharacteristic
954C2×C4#54611yescharacteristic
955C2×C4#54611yescharacteristic
956C2×C4#54611yescharacteristic
957C2×C4#54711yescharacteristic
958C2×C4#55011yescharacteristic
959C2×C4#55311yescharacteristic
960C2×C4#55511yescharacteristic
961C2×C4#56011yescharacteristic
962C2×C4#56011yescharacteristic
963C2×C4#56211yescharacteristic
964C2×C4#56211yescharacteristic
965C8—42no—
966C8—42no—
967C8—81no—
968C8—81no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22#230811yescharacteristic
1000C22D4×C22⋊C411yescharacteristic
1001C22#233911yescharacteristic
1002C22#267811yescharacteristic
1003C22#268211yescharacteristic
1004C22#269911yescharacteristic
1005C22#270111yescharacteristic
1006C22C2×#41911yescharacteristic
1007C22C2×#41711yescharacteristic
1008C22#289711yescharacteristic
1009C22#289811yescharacteristic
1010C22#319311yescharacteristic
1011C22#319311yescharacteristic
1012C22#319511yescharacteristic
1013C22#319511yescharacteristic
1014C22#319811yescharacteristic
1015C22#320111yescharacteristic
1016C22#320311yescharacteristic
1017C22#320411yescharacteristic
1018C22#326411yescharacteristic
1019C22#326611yescharacteristic
1020C22#326611yescharacteristic
1021C22#327011yescharacteristic
1022C22#330611yescharacteristic
1023C22#331011yescharacteristic
1024C22#331211yescharacteristic
1025C22#331211yescharacteristic
1026C22#331411yescharacteristic
1027C22#331411yescharacteristic
1028C22#331611yescharacteristic
1029C22#332011yescharacteristic
1030C22#334311yescharacteristic
1031C22#334411yescharacteristic
1032C22#334411yescharacteristic
1033C22#334611yescharacteristic
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—42no—
1038C4—44no—
1039C4—82no—
1040C4—82no—
1041C4—82no—
1042C4—82no—
1043C4—82no—
1044C4—161no—
1045C4—161no—
1046C4#232411yescharacteristic
1047C4#233311yescharacteristic
1048C4#236311yescharacteristic
1049C4#237711yescharacteristic
1050C4#267111yescharacteristic
1051C4#267311yescharacteristic
1052C4#268611yescharacteristic
1053C4#268811yescharacteristic
1054C2—44no—
1055C2—44no—
1056C2#1436311yescharacteristic
1057C2#2176511yescharacteristic
1058C2#2177211yescharacteristic
1059C2#2241911yescharacteristic
1060C2#2242511yescharacteristic
1061C2#2249111yescharacteristic
1062C2#2249711yescharacteristic
1063C2#3103511yescharacteristic
1064C2#3104011yescharacteristic
1065C2#3120211yescharacteristic
1066C2#3120311yescharacteristic
1067C2#3173211yescharacteristic
1068C2#3173411yescharacteristic
1069C2#3179411yescharacteristic
1070C2#3179811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1872C2semidirect
4. C2×#1823C2semidirect
6. #11227C2semidirect
7. #11200C2semidirect
8. #11077C2semidirect
9. #10970C2semidirect
10. #10970C2semidirect
11. #10970C2semidirect
12. #10928C2semidirect
13. #10881C2semidirect
14. #10730C2semidirect
15. #10730C2semidirect
32. #2417C4semidirect
85. C2×C22⋊Q8C2×C4semidirect
108. C22×C4⋊C4C2×C4semidirect
159. #391C2×C4semidirect
161. #389C2×C4semidirect
195. #340D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24172
C2×#19552
C2×#18722
C2×#18232
#138722
#112272
#112002
#110772
#109702
#109282
#108812
#107302