Finite Group Databasebeta

← #361494

Subgroups — #361494

Order 512.

1920 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2360C211yesmaximal, characteristic
2C2×#1892C211yesmaximal, characteristic
3C2×#1872C211yesmaximal, characteristic
4C2×#1850C211yesmaximal, characteristic
5C2×#1803C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic
7#13880C211yesmaximal, characteristic
8#11228C211yesmaximal, characteristic, complemented
9#11207C211yesmaximal, characteristic, complemented
10#11077C211yesmaximal, characteristic, complemented
11#11050C211yesmaximal, characteristic, complemented
12#10849C211yesmaximal, characteristic, complemented
13#10807C211yesmaximal, characteristic, complemented
14#10789C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28#2360—24no—
29#2360C418yescomplemented
30C2×#391C2211yescharacteristic
31C2×#389—21no—
32C2×#389C2211yescharacteristic
33C2×#387—21no—
34C2×#385—21no—
35C2×#385—21no—
36C2×#385—21no—
37C2×#384C2211yescharacteristic
38C2×#384C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4—21no—
42C2×C4×C22⋊C4C2211yescharacteristic
43#1892—24no—
44#1872—24no—
45#1850—24no—
46#1803—24no—
47C2×#340—24no—
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62#1444—21no—
63#1444—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8—22no—
84C2×C22⋊Q8C2×C414yes—
85C2×C22⋊Q8D414yes—
86C2×C22⋊Q8Q814yes—
87C2×C4×Q8—22no—
88C2×C4×Q8—22no—
89C2×C4×Q8—22no—
90C2×C4×Q8—41no—
91C2×C4×Q8—41no—
92C2×C4×Q8C2×C414yescomplemented
93C22×C4⋊C4—21no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—41no—
110C22×C4⋊C4—41no—
111C22×C4⋊C4—41no—
112C22×C4⋊C4—41no—
113C22×C4⋊C4C2×C414yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4D411yescharacteristic
124C22×C22⋊C4D411yescharacteristic
125C22×C42—21no—
126C22×C42—21no—
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C2×C4⋊C8—22no—
130C2×C4⋊C8—22no—
131C2×C4⋊C8—22no—
132C2×C4⋊C8—22no—
133C2×C4⋊C8—41no—
134C2×C4⋊C8—41no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—41no—
144C2×#103—41no—
145C2×#103—41no—
146C2×#103—41no—
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—22no—
150#391—22no—
151#391C2×C414yescomplemented
152#389—22no—
153#389—28no—
154#389C2×C414yescomplemented
155#387—28no—
156#385—28no—
157#385—44no—
158#385—44no—
159#384—22no—
160#384—22no—
161#384—41no—
162#384—41no—
163#380—22no—
164#380—22no—
165C4×C4⋊C4—22no—
166C4×C4⋊C4C2×C414yescomplemented
167C4×C22⋊C4—28no—
168C4×C22⋊C4C2×C414yes—
169C4×C22⋊C4D414yes—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95D411yescharacteristic
180C2×#95D411yescharacteristic
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—22no—
189#340—22no—
190#340—41no—
191#340—41no—
192#340D414yes—
193#336—22no—
194#336—22no—
195C25C2×D411yescharacteristic
196C22×Q8—21no—
197C22×Q8—21no—
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×Q8C22×C412yes—
208C22×Q8C2×D412yes—
209C22×Q8C2×Q812yes—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—24no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—81no—
237C23×C4—81no—
238C23×C4—81no—
239C23×C4—81no—
240C23×C4C22×C412yes—
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D412yes—
247C23×C4C2×D412yes—
248C23×C4C2×Q812yes—
249C23×C4#4112yes—
250C23×C4#4112yes—
251C23×C4C2411yescharacteristic
252C22×C8—28no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—44no—
280C22×C8—44no—
281C22×C8—44no—
282C22×C8—44no—
283C22×C8—44no—
284C22×C8—44no—
285C22×C8C2×D412yes—
286C22×C8#4112yes—
287C22⋊Q8—28no—
288C22⋊Q8—28no—
289C22⋊Q8—28no—
290C22⋊Q8C4⋊C4116yescomplemented
291C4×Q8—28no—
292C4×Q8—44no—
293C4×Q8—44no—
294C4×Q8—44no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
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—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—81no—
358C2×C4⋊C4—81no—
359C2×C4⋊C4—81no—
360C2×C4⋊C4—81no—
361C2×C4⋊C4—81no—
362C2×C4⋊C4—81no—
363C2×C4⋊C4C22×C412yes—
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C412yes—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4C2×D412yes—
368C2×C4⋊C4C2×D412yes—
369C2×C4⋊C4C2×Q812yes—
370C2×C4⋊C4#4112yes—
371C2×C4⋊C4#4112yes—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4C22⋊C414yes—
381C2×C22⋊C4C22⋊C414yes—
382C2×C22⋊C4SD1614yes—
383C2×C22⋊C4Q1614yes—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—81no—
397C2×C42—81no—
398C2×C42C22×C412yes—
399C2×C42C22×C412yes—
400C2×C42C2×D412yes—
401C2×C42C2×D412yes—
402C4⋊C8—44no—
403C4⋊C8—44no—
404#103—44no—
405#103—44no—
406#103—44no—
407#103—44no—
408C22⋊C8—44no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95C22⋊C414yes—
419#95C22⋊C414yes—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24C2×C22⋊C412yes—
429C24#12112yes—
430C24C22⋊Q812yes—
431C24C2×SD1612yes—
432C24C2×Q1612yes—
433C24AGL(1,ℤ/8)12yes—
434C24#13712yes—
435C24C22×D411yescharacteristic
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8C2×C4⋊C414yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
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—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—48no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—48no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—48no—
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—84no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4C2×C22⋊C412yes—
583C22×C4C2×C22⋊C412yes—
584C22×C4C2×C22⋊C412yes—
585C22×C4C2×C22⋊C412yes—
586C22×C4C2×C22⋊C412yes—
587C22×C4C2×C4⋊C414yes—
588C22×C4#11714yes—
589C22×C4#12114yes—
590C22×C4#12112yes—
591C22×C4C22⋊Q814yes—
592C22×C4C22⋊Q812yes—
593C22×C4C2×SD1612yes—
594C22×C4C2×SD1612yes—
595C22×C4C2×Q1612yes—
596C22×C4C2×Q1612yes—
597C22×C4C23×C411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×Q811yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4C2×#4111yescharacteristic
604C22×C4C2×#4111yescharacteristic
605C22×C4C2×#4111yescharacteristic
606C22×C4C2×#4111yescharacteristic
607C22×C4H(5,𝔽2)11yescharacteristic
608C22×C4H(5,𝔽2)11yescharacteristic
609C22×C4H(5,𝔽2)11yescharacteristic
610C22×C42−1+411yescharacteristic
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—416no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—216no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—84no—
671C4⋊C4—84no—
672C4⋊C4—84no—
673C4⋊C4—84no—
674C4⋊C4—84no—
675C4⋊C4C2×C4⋊C414yes—
676C4⋊C4C4×D414yes—
677C22⋊C4—216no—
678C22⋊C4—28no—
679C22⋊C4—84no—
680C22⋊C4#103116yescomplemented
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—48no—
690C42—84no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23#38014yes—
720C23C2×#10314yes—
721C23#41714yes—
722C23#46014yes—
723C23#46214yes—
724C23#47514yes—
725C23#47714yes—
726C23C22×C22⋊C411yescharacteristic
727C23C2×#12111yescharacteristic
728C23C2×C22⋊Q811yescharacteristic
729C23D4211yescharacteristic
730C23#54611yescharacteristic
731C23#54611yescharacteristic
732C23#54711yescharacteristic
733C23C22×SD1611yescharacteristic
734C23C22×Q1611yescharacteristic
735C23C2×AGL(1,ℤ/8)11yescharacteristic
736C23C2×#13711yescharacteristic
737C23#57611yescharacteristic
738C23#57711yescharacteristic
739C23#57711yescharacteristic
740C23#57811yescharacteristic
741Q8—24no—
742Q8—24no—
743Q8—42no—
744Q8—42no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—816no—
820C2×C4—816no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4#38014yes—
848C2×C4C2×#10314yes—
849C2×C4C2×#10314yes—
850C2×C4C22×C4⋊C411yescharacteristic
851C2×C4C2×#11711yescharacteristic
852C2×C4C2×C4×D411yescharacteristic
853C2×C4C4×#4111yescharacteristic
854C2×C4#51811yescharacteristic
855C2×C4#52011yescharacteristic
856C2×C4C2×#12111yescharacteristic
857C2×C4C2×C22⋊Q811yescharacteristic
858C2×C4#52511yescharacteristic
859C2×C4#52511yescharacteristic
860C2×C4#52911yescharacteristic
861C2×C4#52911yescharacteristic
862C2×C4#53811yescharacteristic
863C2×C4#53811yescharacteristic
864C2×C4#53911yescharacteristic
865C2×C4#53911yescharacteristic
866C2×C4D4211yescharacteristic
867C2×C4D4211yescharacteristic
868C2×C4#54611yescharacteristic
869C2×C4#54611yescharacteristic
870C2×C4#54611yescharacteristic
871C2×C4#54611yescharacteristic
872C2×C4#54711yescharacteristic
873C2×C4#54711yescharacteristic
874C2×C4D4×Q811yescharacteristic
875C2×C4#55411yescharacteristic
876C2×C4#55411yescharacteristic
877C2×C4#55411yescharacteristic
878C8—42no—
879C8—42no—
880C8—81no—
881C8—81no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22#180318yescomplemented
897C22C2×#38011yescharacteristic
898C22D4×C22⋊C411yescharacteristic
899C22#233911yescharacteristic
900C22#242411yescharacteristic
901C22#242511yescharacteristic
902C22#244911yescharacteristic
903C22#245011yescharacteristic
904C22C22×#10311yescharacteristic
905C22C2×#41711yescharacteristic
906C22#289711yescharacteristic
907C22#289811yescharacteristic
908C22C2×#46011yescharacteristic
909C22C2×#46211yescharacteristic
910C22#304511yescharacteristic
911C22#304611yescharacteristic
912C22C2×#47511yescharacteristic
913C22C2×#47711yescharacteristic
914C22#308311yescharacteristic
915C22#308411yescharacteristic
916C22#326411yescharacteristic
917C22#326611yescharacteristic
918C22D4×SD1611yescharacteristic
919C22D4×Q1611yescharacteristic
920C22#329511yescharacteristic
921C22#329811yescharacteristic
922C22#329911yescharacteristic
923C22#329911yescharacteristic
924C22#330611yescharacteristic
925C22#331011yescharacteristic
926C22#331211yescharacteristic
927C22#331411yescharacteristic
928C22#333511yescharacteristic
929C22#333811yescharacteristic
930C22#334311yescharacteristic
931C22#334411yescharacteristic
932C4—24no—
933C4—24no—
934C4—24no—
935C4—44no—
936C4—42no—
937C4—44no—
938C4—44no—
939C4—42no—
940C4—82no—
941C4—82no—
942C4—82no—
943C4—161no—
944C4—161no—
945C4#229011yescharacteristic
946C4#231811yescharacteristic
947C4D4×C4⋊C411yescharacteristic
948C4#234911yescharacteristic
949C4#242411yescharacteristic
950C4#242511yescharacteristic
951C4#244911yescharacteristic
952C4#245011yescharacteristic
953C2—28no—
954C2#1389911yescharacteristic
955C2C2×#180311yescharacteristic
956C2#2065211yescharacteristic
957C2D4×#10311yescharacteristic
958C2#2241911yescharacteristic
959C2#2248711yescharacteristic
960C2#2249111yescharacteristic
961C2#2508011yescharacteristic
962C2#2508211yescharacteristic
963C2#2520411yescharacteristic
964C2#2520611yescharacteristic
965C2#2634011yescharacteristic
966C2#2634211yescharacteristic
967C2#2641211yescharacteristic
968C2#2641411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. C2×#1803C2semidirect
8. #11228C2semidirect
9. #11207C2semidirect
10. #11077C2semidirect
11. #11050C2semidirect
12. #10849C2semidirect
13. #10807C2semidirect
14. #10789C2semidirect
29. #2360C4semidirect
92. C2×C4×Q8C2×C4semidirect
151. #391C2×C4semidirect
154. #389C2×C4semidirect
166. C4×C4⋊C4C2×C4semidirect
290. C22⋊Q8C4⋊C4semidirect
680. C22⋊C4#103semidirect
896. C22#1803semidirect

Maximal subgroups

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

subgroupindex
C2×#23602
C2×#18922
C2×#18722
C2×#18502
C2×#18032
C22×#3402
#138802
#112282
#112072
#110772
#110502
#108492
#108072
#107892
#107302