Finite Group Databasebeta

← #455928

Subgroups — #455928

Order 512.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2076C211yesmaximal, characteristic, complemented
2C2×#2036C211yesmaximal, characteristic, complemented
3C2×#1872C211yesmaximal, characteristic, complemented
4C2×#1852C211yesmaximal, characteristic, complemented
5#15177C211yesmaximal, characteristic
6#13872C211yesmaximal, characteristic
7#11316C211yesmaximal, characteristic, complemented
8#11256C211yesmaximal, characteristic, complemented
9#11124C211yesmaximal, characteristic, complemented
10#11124C211yesmaximal, characteristic, complemented
11#11096C211yesmaximal, characteristic, complemented
12#11096C211yesmaximal, characteristic, complemented
13#10970C211yesmaximal, characteristic, complemented
14#10970C211yesmaximal, characteristic, complemented
15#10964C211yesmaximal, characteristic
16C22×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#386—21no—
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38#2076—24no—
39#2036—24no—
40#1872—24no—
41#1852—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1444—21no—
54#1441—21no—
55#1439—21no—
56#1439—21no—
57#1439—21no—
58#1438—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—21no—
63C23×Q8C2311yescharacteristic
64C23×D4D411yescharacteristic
65C24×C4—21no—
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×C22⋊Q8—22no—
73C2×C22⋊Q8—22no—
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×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—41no—
96C22×C4⋊C4—41no—
97C22×C4⋊C4—41no—
98C22×C4⋊C4—41no—
99C22×C4⋊C4D411yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4D411yescharacteristic
115C22×C22⋊C4D411yescharacteristic
116C22×C42C2311yescharacteristic
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—22no—
120C2×#107—22no—
121C2×#107—41no—
122C2×#107—41no—
123C2×#107—41no—
124C2×#107—41no—
125C2×#107—41no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—41no—
133C2×#103—41no—
134C2×#103—41no—
135C2×#103—41no—
136C2×#103—41no—
137C2×#103—41no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8—22no—
146C2×C22⋊C8—41no—
147C2×C22⋊C8—41no—
148C2×C22⋊C8—41no—
149C2×C22⋊C8—41no—
150#391—41no—
151#391—41no—
152#386—44no—
153#380—22no—
154#380—22no—
155#380—22no—
156#380—22no—
157#380—41no—
158#380—41no—
159#380—41no—
160#380—41no—
161#380—41no—
162#380—41no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—41no—
181#340—41no—
182#340—41no—
183#340D414yescomplemented
184#340D414yescomplemented
185#336—41no—
186#336—41no—
187C25C2×D411yescharacteristic
188C25C2×D411yescharacteristic
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8#4112yes—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—41no—
206C22×D4—41no—
207C22×D4—41no—
208C22×D4—41no—
209C22×D4Q1614yes—
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—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—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—81no—
250C23×C4—81no—
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4#4112yes—
256C23×C4#4112yes—
257C23×C4C2411yescharacteristic
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—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8C2×D412yes—
284C22×C8C2×D412yes—
285C22×C8#4112yes—
286C22⋊Q8—28no—
287C22⋊Q8—44no—
288C22⋊Q8—44no—
289C22⋊Q8—44no—
290C22⋊Q8—44no—
291C22⋊Q8—44no—
292C22⋊Q8—44no—
293C22⋊Q8—44no—
294C4×D4—44no—
295C4×D4—44no—
296C4×D4—44no—
297C4×D4—44no—
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—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
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—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4C2×D412yes—
353C2×C4⋊C4C2×D412yes—
354C2×C4⋊C4C2×D412yes—
355C2×C4⋊C4C2×D412yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
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—81no—
380C2×C22⋊C4—81no—
381C2×C22⋊C4—81no—
382C2×C22⋊C4—81no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389#107—44no—
390#107—44no—
391#107—44no—
392#103—44no—
393#103—44no—
394#103—44no—
395#103—44no—
396C22⋊C8—28no—
397C22⋊C8—44no—
398C22⋊C8—44no—
399C22⋊C8—44no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—81no—
411#95—81no—
412#95—81no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
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#12312yes—
440C24C2×Q1612yes—
441C24C2×Q1612yes—
442C24AGL(1,ℤ/8)12yes—
443C24C22×D411yescharacteristic
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—41no—
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×Q8—41no—
464C2×Q8—41no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×D4—28no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
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—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
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—48no—
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—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—41no—
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—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4#12312yes—
625C22×C4C2×Q1612yes—
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4C2×#4111yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C22×C4H(5,𝔽2)11yescharacteristic
634C22×C4H(5,𝔽2)11yescharacteristic
635C22×C4H(5,𝔽2)11yescharacteristic
636C22×C4H(5,𝔽2)11yescharacteristic
637C22×C4H(5,𝔽2)11yescharacteristic
638C22×C4H(5,𝔽2)11yescharacteristic
639C22×C42−1+411yescharacteristic
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×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—44no—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C4⋊C4—48no—
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—41no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—41no—
695C4⋊C4—41no—
696C4⋊C4—41no—
697C4⋊C4—41no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—48no—
703C22⋊C4—48no—
704C22⋊C4—84no—
705C22⋊C4—84no—
706C22⋊C4—84no—
707C22⋊C4—84no—
708C22⋊C4—84no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—41no—
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—41no—
739C23—41no—
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—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#48414yes—
783C23C2×#12311yescharacteristic
784C23#53411yescharacteristic
785C23#53411yescharacteristic
786C23D4211yescharacteristic
787C23D4211yescharacteristic
788C23#54611yescharacteristic
789C23#54711yescharacteristic
790C23C22×Q1611yescharacteristic
791C23C2×AGL(1,ℤ/8)11yescharacteristic
792C23#57511yescharacteristic
793C23#57511yescharacteristic
794C23#57611yescharacteristic
795C23#57711yescharacteristic
796C23#57811yescharacteristic
797C23#57811yescharacteristic
798Q8—42no—
799Q8—42no—
800Q8—42no—
801Q8—42no—
802Q8—81no—
803Q8—81no—
804Q8—81no—
805Q8—81no—
806D4—416no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—816no—
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—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4#52511yescharacteristic
909C2×C4#52511yescharacteristic
910C2×C4#53511yescharacteristic
911C2×C4#53511yescharacteristic
912C2×C4#53511yescharacteristic
913C2×C4#53711yescharacteristic
914C2×C4#53811yescharacteristic
915C2×C4#53811yescharacteristic
916C2×C4#53811yescharacteristic
917C2×C4#53811yescharacteristic
918C2×C4#53811yescharacteristic
919C2×C4#53811yescharacteristic
920C2×C4#53811yescharacteristic
921C2×C4#53811yescharacteristic
922C2×C4#53911yescharacteristic
923C2×C4#53911yescharacteristic
924C2×C4D4211yescharacteristic
925C2×C4#54611yescharacteristic
926C2×C4#54611yescharacteristic
927C2×C4#54811yescharacteristic
928C2×C4#55011yescharacteristic
929C2×C4#55111yescharacteristic
930C2×C4#55311yescharacteristic
931C2×C4#55311yescharacteristic
932C2×C4#56011yescharacteristic
933C2×C4#56011yescharacteristic
934C2×C4#56211yescharacteristic
935C2×C4#56211yescharacteristic
936C8—42no—
937C8—42no—
938C8—42no—
939C8—81no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22#241811yescharacteristic
971C22#244311yescharacteristic
972C22#262211yescharacteristic
973C22#266911yescharacteristic
974C22#267811yescharacteristic
975C22#268211yescharacteristic
976C22#270811yescharacteristic
977C22C2×#48411yescharacteristic
978C22#309311yescharacteristic
979C22#309711yescharacteristic
980C22#309811yescharacteristic
981C22#318911yescharacteristic
982C22#318911yescharacteristic
983C22#319411yescharacteristic
984C22#319411yescharacteristic
985C22#319811yescharacteristic
986C22#320111yescharacteristic
987C22#320211yescharacteristic
988C22#320311yescharacteristic
989C22#326411yescharacteristic
990C22#326511yescharacteristic
991C22#326911yescharacteristic
992C22#326911yescharacteristic
993C22#327311yescharacteristic
994C22#327511yescharacteristic
995C22D4×Q1611yescharacteristic
996C22D4×Q1611yescharacteristic
997C22#329911yescharacteristic
998C22#330811yescharacteristic
999C22#330911yescharacteristic
1000C22#332711yescharacteristic
1001C22#333811yescharacteristic
1002C22#334311yescharacteristic
1003C22#335011yescharacteristic
1004C22#335211yescharacteristic
1005C4—42no—
1006C4—42no—
1007C4—82no—
1008C4—82no—
1009C4—82no—
1010C4—82no—
1011C4—81no—
1012C4—82no—
1013C4—81no—
1014C4—161no—
1015C4—161no—
1016C4—161no—
1017C4#245611yescharacteristic
1018C4#263111yescharacteristic
1019C4#263611yescharacteristic
1020C4#267611yescharacteristic
1021C4#269611yescharacteristic
1022C4#271411yescharacteristic
1023C4#277811yescharacteristic
1024C4#282611yescharacteristic
1025C2—44no—
1026C2—82no—
1027C2#1627211yescharacteristic
1028C2#2486711yescharacteristic
1029C2#2488911yescharacteristic
1030C2#2613211yescharacteristic
1031C2#2615411yescharacteristic
1032C2#2989511yescharacteristic
1033C2#2990111yescharacteristic
1034C2#3050711yescharacteristic
1035C2#3051111yescharacteristic
1036C2#3101911yescharacteristic
1037C2#3104211yescharacteristic
1038C2#3119011yescharacteristic
1039C2#3119911yescharacteristic
1040C2#3200011yescharacteristic
1041C2#3202411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C23×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
1. C2×#2076C2semidirect
2. C2×#2036C2semidirect
3. C2×#1872C2semidirect
4. C2×#1852C2semidirect
7. #11316C2semidirect
8. #11256C2semidirect
9. #11124C2semidirect
10. #11124C2semidirect
11. #11096C2semidirect
12. #11096C2semidirect
13. #10970C2semidirect
14. #10970C2semidirect
183. #340D4semidirect
184. #340D4semidirect

Maximal subgroups

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

subgroupindex
C2×#20762
C2×#20362
C2×#18722
C2×#18522
#151772
#138722
#113162
#112562
#111242
#110962
#109702
#109642