Finite Group Databasebeta

← #367035

Subgroups — #367035

Order 512.

2386 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2541C211yesmaximal, characteristic
2C2×#1982C211yesmaximal, characteristic, complemented
3C2×#1982C212yesmaximal, complemented
4C2×#1957C211yesmaximal, characteristic, complemented
5C2×#1939C211yesmaximal, characteristic, complemented
6C2×#1802C211yesmaximal, characteristic, complemented
7C2×C4×#102C211yesmaximal, characteristic, complemented
8C4⋊C42C211yesmaximal, characteristic, complemented
9#11076C212yesmaximal, complemented
10#11008C212yesmaximal, complemented
11#10931C212yesmaximal, complemented
12C22×#127C2211yescharacteristic
13C22×#127C2212yes—
14C22×#121—21no—
15C22×#121—21no—
16C22×C4×D4C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2212yes—
19C22×#102C2211yescharacteristic
20C22×#102C2212yes—
21C22×#102C2212yes—
22C22×#102C2212yes—
23C22×#102C2212yes—
24C22×#102C2211yescharacteristic
25C22×#102C2212yes—
26C22×C4×C8C2211yescharacteristic
27#2541—24no—
28#2541C418yescomplemented
29C2×#392—22no—
30C2×#390C2212yes—
31C2×#384C2211yescharacteristic
32C2×C4×C4⋊C4—21no—
33C2×C4×C4⋊C4C2212yes—
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36#1982—28no—
37#1982—24no—
38#1957—24no—
39#1939—24no—
40#1802—24no—
41C4×#102—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2212yes—
44C2×#340C2211yescharacteristic
45C2×#336C2212yes—
46#1436—22no—
47C4⋊#95—21no—
48C4⋊#95C2212yes—
49C23×D4—21no—
50C23×D4—22no—
51C23×D4—22no—
52C23×D4—21no—
53C23×D4C2312yes—
54C23×D4C2311yescharacteristic
55C24×C4—21no—
56C23×C8C2312yes—
57C23×C8C2311yescharacteristic
58C23×C8C2311yescharacteristic
59C2×#127—24no—
60C2×#127—24no—
61C2×#127—22no—
62C2×#127—22no—
63C2×#127—24no—
64C2×#127—22no—
65C2×#127—22no—
66C2×#127—22no—
67C2×#127—42no—
68C2×#127—42no—
69C2×#127C2×C414yes—
70C2×#127C2×C418yes—
71C2×#121—28no—
72C2×#121—28no—
73C2×#121—44no—
74C2×#121—44no—
75C2×#121—44no—
76C2×#121—44no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4C2×C414yes—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4D411yescharacteristic
86C22×C4⋊C4D411yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2312yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C22⋊C4—21no—
92C22×C22⋊C4—22no—
93C22×C22⋊C4—22no—
94C22×C42—21no—
95C22×C42—22no—
96C22×C42C2312yes—
97C22×C42C2311yescharacteristic
98C2×C4⋊C8—24no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—24no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—42no—
104C2×#102—22no—
105C2×#102—22no—
106C2×#102—22no—
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—24no—
110C2×#102—24no—
111C2×#102—24no—
112C2×#102—24no—
113C2×#102—24no—
114C2×#102—24no—
115C2×#102—24no—
116C2×#102—24no—
117C2×#102—24no—
118C2×#102—24no—
119C2×#102—42no—
120C2×#102—42no—
121C2×#102—42no—
122C2×#102—42no—
123C2×#102—42no—
124C2×#102D414yescomplemented
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127C2×C4×C8—22no—
128#392—216no—
129#390—24no—
130#390C2×C418yes—
131#384—22no—
132#384D414yescomplemented
133C4×C4⋊C4—22no—
134C4×C4⋊C4—24no—
135C4×C4⋊C4—42no—
136C4×C4⋊C4—44no—
137C4×C4⋊C4C2×C414yes—
138C4×C4⋊C4D414yes—
139C4×C4⋊C4D414yescomplemented
140C2×#95—21no—
141C2×#95—22no—
142C2×#95—22no—
143C2×#95—22no—
144C2×#95D412yes—
145#340—24no—
146#340—22no—
147#340—22no—
148#336—24no—
149C25—21no—
150C25—22no—
151C22×D4—24no—
152C22×D4—28no—
153C22×D4—28no—
154C22×D4—24no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4—21no—
158C22×D4—22no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4—22no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—22no—
167C22×D4—22no—
168C22×D4—22no—
169C22×D4—22no—
170C22×D4—22no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C22×D4—22no—
175C22×D4—22no—
176C22×D4—22no—
177C22×D4—21no—
178C22×D4—22no—
179C22×D4—44no—
180C22×D4—44no—
181C22×D4—44no—
182C22×D4—44no—
183C22×D4—44no—
184C22×D4—44no—
185C22×D4—42no—
186C22×D4—42no—
187C22×D4—42no—
188C22×D4—42no—
189C22×D4—44no—
190C22×D4—42no—
191C22×D4—44no—
192C22×D4—42no—
193C22×D4—42no—
194C22×D4—42no—
195C22×D4—82no—
196C22×D4—81no—
197C22×D4—81no—
198C22×D4—82no—
199C22×D4—81no—
200C22×D4—81no—
201C22×D4—82no—
202C22×D4—82no—
203C22×D4C22×C414yes—
204C22×D4C22×C412yes—
205C22×D4C2×D412yes—
206C22×D4#4112yes—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—22no—
210C23×C4—21no—
211C23×C4—24no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4C2×D412yes—
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D412yes—
221C23×C4C2×D411yescharacteristic
222C23×C4C2411yescharacteristic
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8—22no—
238C22×C8—22no—
239C22×C8—22no—
240C22×C8—22no—
241C22×C8—22no—
242C22×C8C2×D412yes—
243C22×C8#4112yes—
244#127—216no—
245#127—28no—
246#127—28no—
247#127—48no—
248#127—48no—
249#127—48no—
250#127—44no—
251#127—44no—
252#121—432no—
253#121—432no—
254C4×D4—28no—
255C4×D4—28no—
256C4×D4—44no—
257C4×D4—44no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4C22⋊C414yes—
285C2×C4⋊C4C22⋊C414yes—
286C2×C4⋊C4D814yes—
287C2×C4⋊C4SD1614yes—
288C2×C4⋊C4C22×C412yes—
289C2×C4⋊C4C2×D412yes—
290C2×C4⋊C4C2×D414yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4C2×D412yes—
293C2×C4⋊C4#4112yes—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—28no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—44no—
298C2×C22⋊C4—44no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—44no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—24no—
308C2×C42—42no—
309C2×C42—42no—
310C2×C42—44no—
311C2×C42—44no—
312C2×C42—82no—
313C2×C42C22×C414yes—
314C2×C42C22×C412yes—
315C2×C42C2×D414yes—
316C2×C42C2×D412yes—
317C2×C42C2×D412yes—
318C2×C42C2×D412yes—
319C2×C42#4112yes—
320C2×C42#4112yes—
321C4⋊C8—48no—
322C4⋊C8—44no—
323#102—28no—
324#102—28no—
325#102—48no—
326#102—48no—
327#102—48no—
328#102—48no—
329#102—48no—
330C4×C8—44no—
331#95—24no—
332#95—44no—
333#95—44no—
334#95—82no—
335#95C22⋊C418yes—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—24no—
340C24—41no—
341C24—41no—
342C24—41no—
343C24—41no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—41no—
350C24—41no—
351C24—41no—
352C24—42no—
353C24—42no—
354C24—42no—
355C24—42no—
356C24—42no—
357C24—42no—
358C24—42no—
359C24—42no—
360C24—42no—
361C24—42no—
362C24—42no—
363C24—42no—
364C24—42no—
365C24—42no—
366C24C22×D411yescharacteristic
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—24no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—416no—
389C2×D4—416no—
390C2×D4—416no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4—42no—
405C2×D4—41no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—41no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—416no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—88no—
431C2×D4—84no—
432C2×D4—84no—
433C2×D4—88no—
434C2×D4—88no—
435C2×D4—88no—
436C2×D4—88no—
437C2×D4—88no—
438C2×D4—84no—
439C2×D4—84no—
440C2×D4—84no—
441C2×D4—84no—
442C2×D4—88no—
443C2×D4—88no—
444C2×D4—88no—
445C2×D4—88no—
446C2×D4—84no—
447C2×D4—84no—
448C2×D4—84no—
449C2×D4—84no—
450C2×D4C4×D414yes—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—42no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—41no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—84no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4—84no—
500C22×C4C2×C22⋊C414yes—
501C22×C4C2×C22⋊C412yes—
502C22×C4C2×C22⋊C414yes—
503C22×C4C2×C22⋊C412yes—
504C22×C4#12112yes—
505C22×C4#12112yes—
506C22×C4#12112yes—
507C22×C4#12112yes—
508C22×C4C2×D814yes—
509C22×C4C2×D812yes—
510C22×C4C2×SD1614yes—
511C22×C4C2×SD1612yes—
512C22×C4AGL(1,ℤ/8)12yes—
513C22×C4AGL(1,ℤ/8)12yes—
514C22×C4C23×C411yescharacteristic
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4H(5,𝔽2)11yescharacteristic
525C22×C4H(5,𝔽2)11yescharacteristic
526C22×C4H(5,𝔽2)11yescharacteristic
527C22×C42−1+411yescharacteristic
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—42no—
545C2×C8—42no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—42no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—28no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—48no—
566C4⋊C4—84no—
567C4⋊C4#102116yescomplemented
568C4⋊C4#12114yescomplemented
569C22⋊C4—416no—
570C22⋊C4—48no—
571C22⋊C4—416no—
572C42—24no—
573C42—24no—
574C42—24no—
575C42—24no—
576C42—48no—
577C42—88no—
578C42C4×D414yes—
579C42C4×D414yes—
580C42#12414yes—
581C42#12714yes—
582C23—24no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—82no—
629C23—82no—
630C23—82no—
631C23—82no—
632C23—82no—
633C23—82no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—82no—
639C23—82no—
640C23—82no—
641C23—82no—
642C23—82no—
643C23—82no—
644C23—82no—
645C23—82no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23—82no—
650C23—82no—
651C23—82no—
652C23C22×C22⋊C411yescharacteristic
653C23C2×#12111yescharacteristic
654C23C2×#12111yescharacteristic
655C23D4211yescharacteristic
656C23#54611yescharacteristic
657C23#54811yescharacteristic
658C23#55011yescharacteristic
659C23C22×D811yescharacteristic
660C23C22×SD1611yescharacteristic
661C23C2×AGL(1,ℤ/8)11yescharacteristic
662C23C2×AGL(1,ℤ/8)11yescharacteristic
663C23#57611yescharacteristic
664C23#57611yescharacteristic
665C23#57711yescharacteristic
666C23#57711yescharacteristic
667D4—24no—
668D4—24no—
669D4—42no—
670D4—44no—
671D4—44no—
672D4—42no—
673D4—44no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—44no—
679D4—832no—
680D4—816no—
681D4—832no—
682D4—82no—
683D4—82no—
684D4—816no—
685D4—82no—
686D4—82no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—82no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—816no—
735C2×C4#39014yes—
736C2×C4#39014yes—
737C2×C4C2×#10218yes—
738C2×C4C2×#10214yes—
739C2×C4#41814yes—
740C2×C4#45914yes—
741C2×C4#45914yes—
742C2×C4#46014yes—
743C2×C4#46014yes—
744C2×C4C2×C4×D411yescharacteristic
745C2×C4C2×C4×D411yescharacteristic
746C2×C4C2×C4×D411yescharacteristic
747C2×C4C4×#4111yescharacteristic
748C2×C4#51811yescharacteristic
749C2×C4#52011yescharacteristic
750C2×C4C2×#12111yescharacteristic
751C2×C4#52511yescharacteristic
752C2×C4C2×#12411yescharacteristic
753C2×C4#52911yescharacteristic
754C2×C4C2×#12711yescharacteristic
755C2×C4#53211yescharacteristic
756C2×C4#53511yescharacteristic
757C2×C4#53711yescharacteristic
758C2×C4#54011yescharacteristic
759C2×C4#54211yescharacteristic
760C2×C4D4211yescharacteristic
761C2×C4D4211yescharacteristic
762C2×C4#54611yescharacteristic
763C2×C4#54611yescharacteristic
764C2×C4#54711yescharacteristic
765C2×C4#54811yescharacteristic
766C2×C4#54811yescharacteristic
767C2×C4#55011yescharacteristic
768C2×C4#55011yescharacteristic
769C2×C4#55311yescharacteristic
770C2×C4#55311yescharacteristic
771C2×C4#55511yescharacteristic
772C8—42no—
773C8—42no—
774C8—82no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—84no—
791C22—84no—
792C22—84no—
793C22—84no—
794C22—84no—
795C22—84no—
796C22—84no—
797C22—162no—
798C22—162no—
799C22—162no—
800C22—162no—
801C22—162no—
802C22—162no—
803C22—162no—
804C22—162no—
805C22C2×#39011yescharacteristic
806C22D4×C22⋊C411yescharacteristic
807C22#234111yescharacteristic
808C22#241411yescharacteristic
809C22#241611yescharacteristic
810C22#242611yescharacteristic
811C22#242811yescharacteristic
812C22C22×#10211yescharacteristic
813C22C2×#41811yescharacteristic
814C22#289711yescharacteristic
815C22#289711yescharacteristic
816C22C2×#45911yescharacteristic
817C22C2×#45911yescharacteristic
818C22C2×#46011yescharacteristic
819C22C2×#46011yescharacteristic
820C22#304111yescharacteristic
821C22#304311yescharacteristic
822C22#304511yescharacteristic
823C22#304511yescharacteristic
824C22#327211yescharacteristic
825C22#327411yescharacteristic
826C22D4×D811yescharacteristic
827C22D4×SD1611yescharacteristic
828C22#329411yescharacteristic
829C22#329511yescharacteristic
830C22#332411yescharacteristic
831C22#332511yescharacteristic
832C22#335811yescharacteristic
833C22#336211yescharacteristic
834C22#336611yescharacteristic
835C22#336811yescharacteristic
836C22#339111yescharacteristic
837C22#339211yescharacteristic
838C22#339711yescharacteristic
839C22#339911yescharacteristic
840C4—24no—
841C4—28no—
842C4—44no—
843C4—44no—
844C4—82no—
845C4—84no—
846C4—82no—
847C4#198218yescomplemented
848C4C4×#12111yescharacteristic
849C4#232411yescharacteristic
850C4#236111yescharacteristic
851C4#236311yescharacteristic
852C4#249011yescharacteristic
853C4#249111yescharacteristic
854C4#254011yescharacteristic
855C4#254111yescharacteristic
856C2—84no—
857C2—164no—
858C2#1399811yescharacteristic
859C2C2×#198211yescharacteristic
860C2#2126311yescharacteristic
861C2D4×#10211yescharacteristic
862C2#2242811yescharacteristic
863C2#2254011yescharacteristic
864C2#2254511yescharacteristic
865C2#2462611yescharacteristic
866C2#2462811yescharacteristic
867C2#2472611yescharacteristic
868C2#2472811yescharacteristic
869C2#2527211yescharacteristic
870C2#2527411yescharacteristic
871C2#2536411yescharacteristic
872C2#2536611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#2541C2
LCSG ▷ C22×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
2. C2×#1982C2semidirect
3. C2×#1982C2semidirect
4. C2×#1957C2semidirect
5. C2×#1939C2semidirect
6. C2×#1802C2semidirect
7. C2×C4×#102C2semidirect
8. C4⋊C42C2semidirect
9. #11076C2semidirect
10. #11008C2semidirect
11. #10931C2semidirect
28. #2541C4semidirect
124. C2×#102D4semidirect
132. #384D4semidirect
139. C4×C4⋊C4D4semidirect
567. C4⋊C4#102semidirect
568. C4⋊C4#121semidirect
847. C4#1982semidirect

Maximal subgroups

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

subgroupindex
C2×#25412
C2×#19822
C2×#19572
C2×#19392
C2×#18022
C2×C4×#1022
C4⋊C422
#110762
#110082
#109312