Finite Group Databasebeta

← #365407

Subgroups — #365407

Order 512.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2352C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1854C211yesmaximal, characteristic, complemented
4C2×#1852C211yesmaximal, characteristic, complemented
5C2×#1807C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic, complemented
7#13872C211yesmaximal, characteristic
8#11325C211yesmaximal, characteristic, complemented
9#11268C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic, complemented
11#11095C211yesmaximal, characteristic, complemented
12#10908C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28#2352—24no—
29#2352—24no—
30C2×#388—21no—
31C2×#387—21no—
32C2×#386—21no—
33C2×#386—21no—
34C2×#382C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4—21no—
42#1869C418yescomplemented
43#1854—24no—
44#1852—24no—
45#1807—24no—
46C2×#340—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
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1441—21no—
62#1439—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C22⋊#95—21no—
66C23×D4D411yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8C2×C414yes—
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4C2×C414yes—
87C2×C4×D4Q814yes—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—41no—
93C2×#117—41no—
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—22no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—41no—
104C22×C4⋊C4—41no—
105C22×C4⋊C4—41no—
106C22×C4⋊C4—41no—
107C22×C4⋊C4D411yescharacteristic
108C22×C4⋊C4D414yes—
109C22×C4⋊C4C2311yescharacteristic
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×C42—21no—
126C22×C42—21no—
127C22×C42C2311yescharacteristic
128C2×#107—22no—
129C2×#107—22no—
130C2×#107—22no—
131C2×#107—22no—
132C2×#107—41no—
133C2×#107—41no—
134C2×#106—22no—
135C2×#106—22no—
136C2×#106—22no—
137C2×#106—22no—
138C2×#106—41no—
139C2×#106—41no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—41no—
145C2×C22⋊C8—41no—
146C2×C22⋊C8C2×C414yes—
147C2×C22⋊C8C2×C414yescomplemented
148C2×C22⋊C8C2×C414yescomplemented
149#388—28no—
150#387—28no—
151#386—28no—
152#386—44no—
153#382—22no—
154#382—22no—
155#380—22no—
156#380—22no—
157#380—22no—
158#380—22no—
159#380—22no—
160#380—22no—
161#380—22no—
162#380—41no—
163#380—41no—
164#380D414yes—
165C4×C4⋊C4—22no—
166C4×C4⋊C4—22no—
167C4×C22⋊C4—28no—
168C2×#95—21no—
169C2×#95—21no—
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×#95—21no—
180#340—22no—
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—41no—
190#340—41no—
191#340D414yescomplemented
192#336C2×C414yescomplemented
193#336C2×C414yescomplemented
194C25C2×D411yescharacteristic
195C25C2×D411yescharacteristic
196C22×D4—22no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4C4⋊C414yes—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
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—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—24no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4—81no—
244C23×C4—81no—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D412yes—
252C23×C4C2×D412yes—
253C23×C4C2×Q812yes—
254C23×C4C2×Q812yes—
255C23×C4#4112yes—
256C23×C4#4112yes—
257C23×C4C2411yescharacteristic
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—28no—
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—21no—
280C22×C8—21no—
281C22×C8—28no—
282C22×C8—44no—
283C22×C8—44no—
284C22×C8—44no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8C22×C412yes—
288C22×C8C22×C412yes—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C2×D412yes—
292C22×C8#4112yes—
293C4×D4—28no—
294C4×D4—28no—
295C4×D4—28no—
296C4×D4—28no—
297#117—44no—
298#117—44no—
299#117—44no—
300#117—44no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—28no—
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—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—28no—
328C2×C4⋊C4—24no—
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—21no—
336C2×C4⋊C4—21no—
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—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4C4⋊C414yes—
358C2×C4⋊C4C2×D412yes—
359C2×C4⋊C4C2×D412yes—
360C2×C4⋊C4C2×D412yes—
361C2×C4⋊C4C2×D412yes—
362C2×C4⋊C4C2×D412yes—
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4#4112yes—
365C2×C4⋊C4#4112yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—81no—
385C2×C22⋊C4—81no—
386C2×C22⋊C4—81no—
387C2×C22⋊C4—81no—
388C2×C22⋊C4C4⋊C414yes—
389C2×C22⋊C4C4⋊C414yes—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—81no—
399C2×C42—81no—
400C2×C42C22×C412yes—
401C2×C42C2×Q812yes—
402#107—44no—
403#107—44no—
404#106—44no—
405#106—44no—
406C22⋊C8—28no—
407C22⋊C8—28no—
408C22⋊C8—44no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—81no—
420#95—81no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24C2×C4⋊C412yes—
444C24C2×C4⋊C412yes—
445C24#12012yes—
446C24#12312yes—
447C24#13512yes—
448C24#13512yes—
449C24AGL(1,ℤ/8)12yes—
450C24#13712yes—
451C24C22×D411yescharacteristic
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
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—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
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—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—48no—
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—41no—
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—48no—
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—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—48no—
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—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4C2×C4⋊C412yes—
604C22×C4C2×C4⋊C412yes—
605C22×C4C2×C4⋊C412yes—
606C22×C4C2×C4⋊C412yes—
607C22×C4C4×D414yes—
608C22×C4C4×D414yes—
609C22×C4#12012yes—
610C22×C4C22⋊Q814yes—
611C22×C4C22⋊Q814yes—
612C22×C4#12312yes—
613C22×C4C23×C411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×Q811yescharacteristic
618C22×C4C2×#4111yescharacteristic
619C22×C4C2×#4111yescharacteristic
620C22×C4C2×#4111yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4H(5,𝔽2)11yescharacteristic
624C22×C4H(5,𝔽2)11yescharacteristic
625C22×C4H(5,𝔽2)11yescharacteristic
626C22×C42−1+411yescharacteristic
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
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—416no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8C4×D414yes—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—28no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
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⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C4⋊C4#12114yes—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—84no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C22⋊C4—84no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—48no—
704C42—84no—
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—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23#38514yes—
769C23#42714yes—
770C23#42814yes—
771C23#44914yes—
772C23#45214yes—
773C23#48214yes—
774C23#48514yes—
775C23C22×C4⋊C411yescharacteristic
776C23C2×#12011yescharacteristic
777C23C2×#12311yescharacteristic
778C23D4211yescharacteristic
779C23#54611yescharacteristic
780C23#54611yescharacteristic
781C23#54711yescharacteristic
782C23C2×#13511yescharacteristic
783C23C2×#13511yescharacteristic
784C23C2×AGL(1,ℤ/8)11yescharacteristic
785C23C2×#13711yescharacteristic
786C23#57611yescharacteristic
787C23#57711yescharacteristic
788C23#57711yescharacteristic
789C23#57811yescharacteristic
790D4—416no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—816no—
857C2×C4—816no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
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#38514yes—
893C2×C4C2×C4×D411yescharacteristic
894C2×C4C2×C4×D411yescharacteristic
895C2×C4C2×C4×D411yescharacteristic
896C2×C4C4×#4111yescharacteristic
897C2×C4#51811yescharacteristic
898C2×C4#52011yescharacteristic
899C2×C4C2×#12111yescharacteristic
900C2×C4C2×C22⋊Q811yescharacteristic
901C2×C4C2×C22⋊Q811yescharacteristic
902C2×C4#52511yescharacteristic
903C2×C4#52911yescharacteristic
904C2×C4#53211yescharacteristic
905C2×C4#53411yescharacteristic
906C2×C4#53711yescharacteristic
907C2×C4#53811yescharacteristic
908C2×C4#53911yescharacteristic
909C2×C4D4211yescharacteristic
910C2×C4#54611yescharacteristic
911C2×C4#54611yescharacteristic
912C2×C4#54611yescharacteristic
913C2×C4#54711yescharacteristic
914C2×C4D4×Q811yescharacteristic
915C2×C4#55111yescharacteristic
916C2×C4#55111yescharacteristic
917C2×C4#55211yescharacteristic
918C2×C4#55411yescharacteristic
919C2×C4#55411yescharacteristic
920C2×C4#55411yescharacteristic
921C8—24no—
922C8—42no—
923C8—42no—
924C8—42no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22#185418yescomplemented
955C22C2×#38511yescharacteristic
956C22D4×C4⋊C411yescharacteristic
957C22#234911yescharacteristic
958C22#241011yescharacteristic
959C22#241811yescharacteristic
960C22#241911yescharacteristic
961C22#243011yescharacteristic
962C22C2×#42711yescharacteristic
963C22C2×#42811yescharacteristic
964C22#291211yescharacteristic
965C22#291311yescharacteristic
966C22C2×#44911yescharacteristic
967C22C2×#45211yescharacteristic
968C22#301211yescharacteristic
969C22#301311yescharacteristic
970C22C2×#48211yescharacteristic
971C22C2×#48511yescharacteristic
972C22#309611yescharacteristic
973C22#309711yescharacteristic
974C22#326411yescharacteristic
975C22#327011yescharacteristic
976C22#328211yescharacteristic
977C22#328211yescharacteristic
978C22#329711yescharacteristic
979C22#329711yescharacteristic
980C22#330011yescharacteristic
981C22#330011yescharacteristic
982C22#330611yescharacteristic
983C22#331011yescharacteristic
984C22#331611yescharacteristic
985C22#332011yescharacteristic
986C22#333711yescharacteristic
987C22#333711yescharacteristic
988C22#334311yescharacteristic
989C22#334611yescharacteristic
990C4—24no—
991C4—42no—
992C4—42no—
993C4—44no—
994C4—42no—
995C4—82no—
996C4—82no—
997C4—82no—
998C4—82no—
999C4—82no—
1000C4—161no—
1001C4—161no—
1002C4C4×#12111yescharacteristic
1003C4#232511yescharacteristic
1004C4#235811yescharacteristic
1005C4#235911yescharacteristic
1006C4#241711yescharacteristic
1007C4#244911yescharacteristic
1008C4#245011yescharacteristic
1009C4#256411yescharacteristic
1010C2—28no—
1011C2—82no—
1012C2#1397511yescharacteristic
1013C2C2×#185411yescharacteristic
1014C2#2084911yescharacteristic
1015C2#2265411yescharacteristic
1016C2#2266111yescharacteristic
1017C2#2270411yescharacteristic
1018C2#2271111yescharacteristic
1019C2#2443111yescharacteristic
1020C2#2443411yescharacteristic
1021C2#2487111yescharacteristic
1022C2#2487311yescharacteristic
1023C2#2494311yescharacteristic
1024C2#2494511yescharacteristic
1025C2#2553511yescharacteristic
1026C2#2553911yescharacteristic
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×#1854C2semidirect
4. C2×#1852C2semidirect
5. C2×#1807C2semidirect
6. C22×#340C2semidirect
8. #11325C2semidirect
9. #11268C2semidirect
10. #11096C2semidirect
11. #11095C2semidirect
12. #10908C2semidirect
13. #10907C2semidirect
14. #10731C2semidirect
15. #10730C2semidirect
42. #1869C4semidirect
147. C2×C22⋊C8C2×C4semidirect
148. C2×C22⋊C8C2×C4semidirect
191. #340D4semidirect
192. #336C2×C4semidirect
193. #336C2×C4semidirect
954. C22#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#23522
C2×#18692
C2×#18542
C2×#18522
C2×#18072
C22×#3402
#138722
#113252
#112682
#110962
#110952
#109082
#109072
#107312
#107302