Finite Group Databasebeta

← #357012

Subgroups — #357012

Order 512.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2366C211yesmaximal, characteristic
2C2×#1982C211yesmaximal, characteristic
3C2×#1961C211yesmaximal, characteristic
4C2×#1771C211yesmaximal, characteristic, complemented
5C2×#1762C211yesmaximal, characteristic, complemented
6C2×C4×#102C211yesmaximal, characteristic, complemented
7#13804C211yesmaximal, characteristic, complemented
8#10931C211yesmaximal, characteristic, complemented
9#10931C211yesmaximal, characteristic, complemented
10#10927C211yesmaximal, characteristic, complemented
11#10925C211yesmaximal, characteristic, complemented
12#10850C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic, complemented
15#10703C211yesmaximal, characteristic, complemented
16C22×#127C2211yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2366—24no—
33#2366C418yescomplemented
34C2×#390—21no—
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#386—21no—
38C2×#386—21no—
39C2×#382C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45#1982C418yescomplemented
46#1961C418yescomplemented
47#1771—24no—
48#1762—24no—
49C4×#102—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64#1434—21no—
65C4×#95—21no—
66C23×D4—21no—
67C23×D4—21no—
68C23×D4C2311yescharacteristic
69C23×D4C2311yescharacteristic
70C24×C4—21no—
71C24×C4—21no—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×#127—22no—
77C2×#127—22no—
78C2×#127—22no—
79C2×#127C2×C414yes—
80C2×#127C2×C414yes—
81C2×#127C2×C414yes—
82C2×C4×D4—28no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4—41no—
90C2×C4×D4—41no—
91C2×C4×D4—41no—
92C2×C4×D4—41no—
93C2×C4×D4—44no—
94C2×C4×D4—44no—
95C2×C4×D4C2×C414yes—
96C2×C4×D4C2×C414yes—
97C22×C4⋊C4D411yescharacteristic
98C22×C4⋊C4D411yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C42—21no—
112C22×C42—21no—
113C22×C42—21no—
114C22×C42—21no—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8C2×C414yescomplemented
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—41no—
130C2×#102—41no—
131C2×#102—41no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102—41no—
135C2×#102—41no—
136C2×#102—41no—
137C2×#102C2×C414yescomplemented
138C2×#102C2×C414yescomplemented
139C2×#102C2×C414yescomplemented
140C2×#102C2×C414yescomplemented
141C2×#102C2×C414yescomplemented
142C2×#102C2×C414yescomplemented
143C2×#102C2×C414yescomplemented
144C2×#102C2×C414yescomplemented
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—41no—
150C2×#97C2×C414yescomplemented
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153C2×C4×C8—41no—
154#390—28no—
155#390—22no—
156#390—22no—
157#390C2×C414yes—
158#390C2×C414yes—
159#386—28no—
160#386—28no—
161#382—22no—
162#382C2×C414yescomplemented
163C4×C4⋊C4—22no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C4×C4⋊C4—22no—
167C4×C4⋊C4—41no—
168C4×C4⋊C4—41no—
169C4×C4⋊C4C2×C414yes—
170C4×C4⋊C4C2×C414yes—
171C4×C4⋊C4C2×C414yescomplemented
172C4×C4⋊C4D414yes—
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×#95D411yescharacteristic
184C2×#95D411yescharacteristic
185#340—22no—
186#340—22no—
187#340—22no—
188#340—22no—
189#340—22no—
190#340—41no—
191#340—41no—
192#340D414yescomplemented
193#336—22no—
194#336—22no—
195C25—21no—
196C25—21no—
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—24no—
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—81no—
230C22×D4—81no—
231C22×D4—81no—
232C22×D4—81no—
233C22×D4C22×C412yes—
234C22×D4C22×C412yes—
235C22×D4C22×C412yes—
236C22×D4C22×C412yes—
237C22×D4C22×C412yes—
238C22×D4C22×C412yes—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—81no—
256C23×C4—81no—
257C23×C4—81no—
258C23×C4—81no—
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2411yescharacteristic
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—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×C8C22×C412yes—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C22×C412yes—
292C22×C8C2×D412yes—
293C22×C8#4112yes—
294#127—28no—
295#127—28no—
296#127—28no—
297#127C42116yescomplemented
298C4×D4—28no—
299C4×D4—28no—
300C4×D4—44no—
301C4×D4—44no—
302C4×D4—44no—
303C4×D4—44no—
304C4×D4—44no—
305C4×D4—44no—
306C4×D4—432no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
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—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—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4C22⋊C414yes—
338C2×C4⋊C4C22⋊C414yes—
339C2×C4⋊C4C22×C412yes—
340C2×C4⋊C4C22×C412yes—
341C2×C4⋊C4C22×C412yes—
342C2×C4⋊C4C22×C412yes—
343C2×C4⋊C4C22×C412yes—
344C2×C4⋊C4C22×C412yes—
345C2×C4⋊C4C2×D412yes—
346C2×C4⋊C4C2×D412yes—
347C2×C4⋊C4#4112yes—
348C2×C4⋊C4#4112yes—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—81no—
364C2×C22⋊C4—81no—
365C2×C22⋊C4—81no—
366C2×C22⋊C4—81no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—81no—
384C2×C42—81no—
385C2×C42—81no—
386C2×C42—81no—
387C2×C42C22×C412yes—
388C2×C42C22×C412yes—
389C2×C42C22×C412yes—
390C2×C42C22×C412yes—
391C2×C42C22×C412yes—
392C2×C42C2×D412yes—
393C2×C42C2×D412yes—
394C2×C42C2×D412yes—
395C2×C42#4112yes—
396C2×C42#4112yes—
397C4⋊C8—28no—
398#102—28no—
399#102—28no—
400#102—28no—
401#102—28no—
402#102—44no—
403#102—44no—
404#102—44no—
405#102—44no—
406#97—28no—
407#97—44no—
408C4×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—81no—
418#95—81no—
419#95C22⋊C414yes—
420#95C22⋊C414yes—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24—41no—
439C24—41no—
440C24—41no—
441C24—41no—
442C24—41no—
443C24—41no—
444C24—41no—
445C24—41no—
446C24—41no—
447C24—41no—
448C24—41no—
449C24—41no—
450C24—41no—
451C24C22×D411yescharacteristic
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—216no—
483C2×D4—216no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—84no—
515C2×D4—84no—
516C2×D4—84no—
517C2×D4—84no—
518C2×D4—84no—
519C2×D4—84no—
520C2×D4C2×C4214yes—
521C2×D4C2×C4214yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
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—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—48no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4C2×C22⋊C412yes—
609C22×C4C2×C22⋊C412yes—
610C22×C4C2×C22⋊C412yes—
611C22×C4C2×C22⋊C412yes—
612C22×C4C2×C22⋊C412yes—
613C22×C4C2×C22⋊C412yes—
614C22×C4C4×D412yes—
615C22×C4C4×D412yes—
616C22×C4C4×D412yes—
617C22×C4C4×D412yes—
618C22×C4AGL(1,ℤ/8)12yes—
619C22×C4AGL(1,ℤ/8)12yes—
620C22×C4C23×C411yescharacteristic
621C22×C4C23×C411yescharacteristic
622C22×C4C23×C411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C2×#4111yescharacteristic
626C22×C4C2×#4111yescharacteristic
627C22×C4C2×#4111yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4H(5,𝔽2)11yescharacteristic
631C22×C4H(5,𝔽2)11yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C22×C42−1+411yescharacteristic
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8C4×D414yescomplemented
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—28no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—44no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4C4×D414yes—
687C4⋊C4C4×D414yescomplemented
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—48no—
703C42—84no—
704C42—84no—
705C42—84no—
706C42C2×C4214yes—
707C42#11714yes—
708C42C4×D414yes—
709C42C4×D414yes—
710C23—24no—
711C23—24no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—81no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23—81no—
762C23—81no—
763C23—81no—
764C23—81no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23—81no—
774C23—81no—
775C23—81no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23C22×C22⋊C411yescharacteristic
781C23C2×C4×D411yescharacteristic
782C23C2×C4×D411yescharacteristic
783C23D4211yescharacteristic
784C23#54611yescharacteristic
785C23#54811yescharacteristic
786C23#55011yescharacteristic
787C23C2×AGL(1,ℤ/8)11yescharacteristic
788C23C2×AGL(1,ℤ/8)11yescharacteristic
789C23#57511yescharacteristic
790C23#57511yescharacteristic
791C23#57611yescharacteristic
792C23#57611yescharacteristic
793C23#57711yescharacteristic
794C23#57711yescharacteristic
795D4—24no—
796D4—24no—
797D4—24no—
798D4—24no—
799D4—432no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—42no—
804D4—42no—
805D4—42no—
806D4—42no—
807D4—42no—
808D4—42no—
809D4—42no—
810D4—42no—
811D4—42no—
812D4—816no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
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—816no—
879C2×C4—816no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4C4×C22⋊C414yes—
897C2×C4C4×C22⋊C414yes—
898C2×C4#41814yes—
899C2×C4C22×C4211yescharacteristic
900C2×C4C2×#11711yescharacteristic
901C2×C4C2×C4×D411yescharacteristic
902C2×C4C2×C4×D411yescharacteristic
903C2×C4C2×C4×D411yescharacteristic
904C2×C4C2×C4×D411yescharacteristic
905C2×C4C2×C4×D411yescharacteristic
906C2×C4C4×#4111yescharacteristic
907C2×C4C4×#4111yescharacteristic
908C2×C4C4×#4111yescharacteristic
909C2×C4#51811yescharacteristic
910C2×C4#51811yescharacteristic
911C2×C4#51811yescharacteristic
912C2×C4#52011yescharacteristic
913C2×C4#52011yescharacteristic
914C2×C4#52011yescharacteristic
915C2×C4D4211yescharacteristic
916C2×C4#54611yescharacteristic
917C2×C4#54711yescharacteristic
918C2×C4#54811yescharacteristic
919C2×C4#55011yescharacteristic
920C2×C4#55011yescharacteristic
921C2×C4#55311yescharacteristic
922C2×C4#55311yescharacteristic
923C2×C4#55511yescharacteristic
924C2×C4#55611yescharacteristic
925C2×C4#55911yescharacteristic
926C2×C4#55911yescharacteristic
927C8—24no—
928C8—42no—
929C8—42no—
930C8—42no—
931C22—44no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22—82no—
941C22—82no—
942C22—82no—
943C22—82no—
944C22—82no—
945C22—82no—
946C22—82no—
947C22—82no—
948C22—82no—
949C22—82no—
950C22—82no—
951C22—82no—
952C22—82no—
953C22—82no—
954C22—82no—
955C22—82no—
956C22—82no—
957C22—82no—
958C22—82no—
959C22—82no—
960C22—82no—
961C22C2×C4×C22⋊C411yescharacteristic
962C22D4×C22⋊C411yescharacteristic
963C22#234111yescharacteristic
964C22#236111yescharacteristic
965C22#236311yescharacteristic
966C22#236611yescharacteristic
967C22#236711yescharacteristic
968C22C2×#41811yescharacteristic
969C22#289611yescharacteristic
970C22#289711yescharacteristic
971C22#289711yescharacteristic
972C22C4×AGL(1,ℤ/8)11yescharacteristic
973C22C4×AGL(1,ℤ/8)11yescharacteristic
974C22C4×AGL(1,ℤ/8)11yescharacteristic
975C22C4×AGL(1,ℤ/8)11yescharacteristic
976C22#294611yescharacteristic
977C22#294611yescharacteristic
978C22#294811yescharacteristic
979C22#294911yescharacteristic
980C22#326411yescharacteristic
981C22#326511yescharacteristic
982C22#326811yescharacteristic
983C22#327111yescharacteristic
984C22#330911yescharacteristic
985C22#331011yescharacteristic
986C22#331711yescharacteristic
987C22#331811yescharacteristic
988C22#336611yescharacteristic
989C22#336811yescharacteristic
990C22#337011yescharacteristic
991C22#337111yescharacteristic
992C22#339711yescharacteristic
993C22#339911yescharacteristic
994C22#340111yescharacteristic
995C22#340311yescharacteristic
996C4—24no—
997C4—24no—
998C4—24no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—44no—
1003C4—44no—
1004C4—82no—
1005C4—82no—
1006C4—82no—
1007C4—82no—
1008C4C42×D411yescharacteristic
1009C4#227511yescharacteristic
1010C4#235411yescharacteristic
1011C4#235711yescharacteristic
1012C4#236111yescharacteristic
1013C4#236311yescharacteristic
1014C4#236611yescharacteristic
1015C4#236711yescharacteristic
1016C2—84no—
1017C2—84no—
1018C2#1382011yescharacteristic
1019C2C4×#41811yescharacteristic
1020C2#2041611yescharacteristic
1021C2#2242211yescharacteristic
1022C2#2242311yescharacteristic
1023C2#2254511yescharacteristic
1024C2#2254911yescharacteristic
1025C2#2300811yescharacteristic
1026C2#2301011yescharacteristic
1027C2#2310611yescharacteristic
1028C2#2310811yescharacteristic
1029C2#2319311yescharacteristic
1030C2#2319511yescharacteristic
1031C2#2322911yescharacteristic
1032C2#2323111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC22×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1771C2semidirect
5. C2×#1762C2semidirect
6. C2×C4×#102C2semidirect
7. #13804C2semidirect
8. #10931C2semidirect
9. #10931C2semidirect
10. #10927C2semidirect
11. #10925C2semidirect
12. #10850C2semidirect
13. #10788C2semidirect
14. #10788C2semidirect
15. #10703C2semidirect
33. #2366C4semidirect
45. #1982C4semidirect
46. #1961C4semidirect
120. C2×C4⋊C8C2×C4semidirect
137. C2×#102C2×C4semidirect
138. C2×#102C2×C4semidirect
139. C2×#102C2×C4semidirect
140. C2×#102C2×C4semidirect
141. C2×#102C2×C4semidirect
142. C2×#102C2×C4semidirect
143. C2×#102C2×C4semidirect
144. C2×#102C2×C4semidirect
150. C2×#97C2×C4semidirect
162. #382C2×C4semidirect
171. C4×C4⋊C4C2×C4semidirect
192. #340D4semidirect
297. #127C42semidirect
661. C2×C8C4×D4semidirect
687. C4⋊C4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23662
C2×#19822
C2×#19612
C2×#17712
C2×#17622
C2×C4×#1022
#138042
#109312
#109272
#109252
#108502
#107882
#107032