Finite Group Databasebeta

← #390394

Subgroups — #390394

Order 512.

1512 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2034C211yesmaximal, characteristic
2C2×#1925C211yesmaximal, characteristic, complemented
3C2×#1895C211yesmaximal, characteristic
4#13974C211yesmaximal, characteristic, complemented
5#13970C211yesmaximal, characteristic
6#11378C211yesmaximal, characteristic, complemented
7#11293C211yesmaximal, characteristic, complemented
8#11256C211yesmaximal, characteristic, complemented
9#11096C211yesmaximal, characteristic, complemented
10#11066C211yesmaximal, characteristic, complemented
11#10908C211yesmaximal, characteristic, complemented
12#10788C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10722C211yesmaximal, characteristic, complemented
15#10715C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#388—21no—
29C2×#386—21no—
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35#2034C418yescomplemented
36#1925—24no—
37#1895—24no—
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1443—21no—
53#1440—21no—
54#1440—21no—
55#1438—21no—
56#1436—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C22⋊#95—21no—
62C23×D4—21no—
63C23×D4C2311yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—41no—
70C22×M16—41no—
71C22×M16—41no—
72C22×M16—41no—
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C2×#121—22no—
78C2×#121—22no—
79C2×#121—22no—
80C2×#121—41no—
81C2×#121—41no—
82C2×#121C2×C414yes—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4D411yescharacteristic
105C22×C22⋊C4D411yescharacteristic
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C2×#107—22no—
110C2×#107—41no—
111C2×#107—41no—
112C2×#106—41no—
113C2×#106—41no—
114C2×#106C2×C414yescomplemented
115C2×#102—22no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—41no—
120C2×#102—41no—
121C2×#102—41no—
122C2×#102—41no—
123C2×#102—41no—
124C2×#102C2×C414yes—
125C2×#102C2×C414yes—
126C2×#102D414yes—
127C2×C22⋊C8—41no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8C2×C414yescomplemented
130#390—22no—
131#390—41no—
132#389—41no—
133#389—41no—
134#388—44no—
135#386—44no—
136#380—22no—
137#380—22no—
138#380—22no—
139#380—41no—
140#380—41no—
141#380C2×C414yescomplemented
142C4×C4⋊C4—22no—
143C4×C4⋊C4—41no—
144C4×C22⋊C4—41no—
145C4×C22⋊C4—41no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95D411yescharacteristic
160C2×#95D411yescharacteristic
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—41no—
166#340—41no—
167#340—41no—
168#340—41no—
169#340—41no—
170#340C2×C414yescomplemented
171#336—22no—
172#336—22no—
173#336—41no—
174#336—41no—
175C25—21no—
176C25C2×D411yescharacteristic
177C22×D4—24no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—42no—
190C22×D4—42no—
191C22×D4—42no—
192C22×D4—42no—
193C22×D4—81no—
194C22×D4—81no—
195C22×D4C22×C412yes—
196C22×D4C2×D412yes—
197C22×D4#4112yes—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
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—42no—
218C23×C4—42no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—42no—
222C23×C4—81no—
223C23×C4—81no—
224C23×C4C22×C412yes—
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4#4112yes—
231C23×C4C2411yescharacteristic
232C2×M16—44no—
233C2×M16—44no—
234C2×M16—44no—
235C2×M16—44no—
236C2×M16—44no—
237C2×M16—44no—
238C2×M16—44no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
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×C8C22×C412yes—
264C22×C8C22×C412yes—
265C22×C8C2×D412yes—
266C22×C8#4112yes—
267#121—28no—
268#121—44no—
269#121—44no—
270#121—44no—
271C4×D4—44no—
272C4×D4—44no—
273C4×D4—44no—
274C4×D4—44no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
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—21no—
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—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4C22×C412yes—
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C22×C412yes—
318C2×C4⋊C4C2×D412yes—
319C2×C4⋊C4#4112yes—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—81no—
344C2×C22⋊C4—81no—
345C2×C22⋊C4—81no—
346C2×C22⋊C4—81no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42—81no—
362#107—44no—
363#106—44no—
364#102—28no—
365#102—44no—
366#102—44no—
367#102—44no—
368C22⋊C8—44no—
369#95—24no—
370#95—41no—
371#95—41no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—81no—
382#95—81no—
383#95—81no—
384C24—22no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24C4×D412yes—
414C24C22×D411yescharacteristic
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—48no—
431C2×D4—48no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—84no—
445C2×D4—84no—
446C2×D4—84no—
447C2×D4—84no—
448C2×D4—84no—
449C2×D4C4×D414yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
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—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—48no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
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—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—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—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—84no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4C4×D412yes—
567C22×C4AGL(1,ℤ/8)12yes—
568C22×C4AGL(1,ℤ/8)12yes—
569C22×C4C23×C411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4C2×#4111yescharacteristic
574C22×C4C2×#4111yescharacteristic
575C22×C4H(5,𝔽2)11yescharacteristic
576C22×C4H(5,𝔽2)11yescharacteristic
577C22×C4H(5,𝔽2)11yescharacteristic
578C22×C4H(5,𝔽2)11yescharacteristic
579C22×C4H(5,𝔽2)11yescharacteristic
580C22×C4H(5,𝔽2)11yescharacteristic
581C22×C42−1+411yescharacteristic
582C22×C42−1+411yescharacteristic
583M16—416no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—84no—
641C22⋊C4—48no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—84no—
647C22⋊C4—84no—
648C22⋊C4—84no—
649C22⋊C4—84no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—84no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—42no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23C2×C4×D411yescharacteristic
730C23#53411yescharacteristic
731C23#53711yescharacteristic
732C23D4211yescharacteristic
733C23#54611yescharacteristic
734C23#54611yescharacteristic
735C23#54711yescharacteristic
736C23C2×AGL(1,ℤ/8)11yescharacteristic
737C23C2×AGL(1,ℤ/8)11yescharacteristic
738C23#57511yescharacteristic
739C23#57511yescharacteristic
740C23#57611yescharacteristic
741C23#57711yescharacteristic
742C23#57711yescharacteristic
743C23#57811yescharacteristic
744D4—24no—
745D4—24no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—816no—
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—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—816no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
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×C4C2×C4×D411yescharacteristic
847C2×C4C4×#4111yescharacteristic
848C2×C4#51811yescharacteristic
849C2×C4#51811yescharacteristic
850C2×C4#52011yescharacteristic
851C2×C4#52011yescharacteristic
852C2×C4#53411yescharacteristic
853C2×C4#53711yescharacteristic
854C2×C4#53811yescharacteristic
855C2×C4#53811yescharacteristic
856C2×C4#53811yescharacteristic
857C2×C4#53811yescharacteristic
858C2×C4#53911yescharacteristic
859C2×C4#53911yescharacteristic
860C2×C4#54011yescharacteristic
861C2×C4#54011yescharacteristic
862C2×C4#54611yescharacteristic
863C2×C4#54611yescharacteristic
864C2×C4#54711yescharacteristic
865C2×C4#55111yescharacteristic
866C2×C4#55111yescharacteristic
867C2×C4#55111yescharacteristic
868C2×C4#55211yescharacteristic
869C2×C4#55211yescharacteristic
870C2×C4H(3,𝔽4)11yescharacteristic
871C2×C4#56211yescharacteristic
872C2×C4#56211yescharacteristic
873C2×C4#56311yescharacteristic
874C8—42no—
875C8—42no—
876C8—42no—
877C8—42no—
878C22—42no—
879C22—44no—
880C22—42no—
881C22—44no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—44no—
888C22—82no—
889C22—81no—
890C22—81no—
891C22—82no—
892C22—81no—
893C22—82no—
894C22—81no—
895C22—82no—
896C22—81no—
897C22—82no—
898C22—82no—
899C22—81no—
900C22—82no—
901C22—81no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22#232511yescharacteristic
909C22#235811yescharacteristic
910C22#235911yescharacteristic
911C22#267111yescharacteristic
912C22#267111yescharacteristic
913C22#268411yescharacteristic
914C22#269511yescharacteristic
915C22C4×AGL(1,ℤ/8)11yescharacteristic
916C22C4×AGL(1,ℤ/8)11yescharacteristic
917C22#294911yescharacteristic
918C22#295111yescharacteristic
919C22#319411yescharacteristic
920C22#319411yescharacteristic
921C22#319811yescharacteristic
922C22#320111yescharacteristic
923C22#325311yescharacteristic
924C22#325611yescharacteristic
925C22#325711yescharacteristic
926C22#325811yescharacteristic
927C22#326411yescharacteristic
928C22#326911yescharacteristic
929C22#327211yescharacteristic
930C22#327511yescharacteristic
931C22#331011yescharacteristic
932C22#331111yescharacteristic
933C22#331311yescharacteristic
934C22#331811yescharacteristic
935C22#332211yescharacteristic
936C22#332311yescharacteristic
937C22#333011yescharacteristic
938C22#333211yescharacteristic
939C22#334511yescharacteristic
940C22#334811yescharacteristic
941C22#335311yescharacteristic
942C22#335511yescharacteristic
943C4—42no—
944C4—42no—
945C4—42no—
946C4—82no—
947C4—81no—
948C4—82no—
949C4—82no—
950C4—81no—
951C4—82no—
952C4—82no—
953C4—161no—
954C4—161no—
955C4#232511yescharacteristic
956C4#233311yescharacteristic
957C4#235911yescharacteristic
958C4#237911yescharacteristic
959C4#268411yescharacteristic
960C4#269511yescharacteristic
961C4#274311yescharacteristic
962C4#274311yescharacteristic
963C2—82no—
964C2—84no—
965C2#1457111yescharacteristic
966C2#2219011yescharacteristic
967C2#2219411yescharacteristic
968C2#2286411yescharacteristic
969C2#2287811yescharacteristic
970C2#2292611yescharacteristic
971C2#2294311yescharacteristic
972C2#3058111yescharacteristic
973C2#3058211yescharacteristic
974C2#3060911yescharacteristic
975C2#3061011yescharacteristic
976C2#3127611yescharacteristic
977C2#3127811yescharacteristic
978C2#3162911yescharacteristic
979C2#3163011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
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
2. C2×#1925C2semidirect
4. #13974C2semidirect
6. #11378C2semidirect
7. #11293C2semidirect
8. #11256C2semidirect
9. #11096C2semidirect
10. #11066C2semidirect
11. #10908C2semidirect
12. #10788C2semidirect
13. #10788C2semidirect
14. #10722C2semidirect
15. #10715C2semidirect
35. #2034C4semidirect
114. C2×#106C2×C4semidirect
129. C2×C22⋊C8C2×C4semidirect
141. #380C2×C4semidirect
170. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20342
C2×#19252
C2×#18952
#139742
#139702
#113782
#112932
#112562
#110962
#110662
#109082
#107882
#107222
#107152