Finite Group Databasebeta

← #360574

Subgroups — #360574

Order 512.

2596 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#104C211yesmaximal, characteristic
2C22⋊C4×#41C211yesmaximal, characteristic
3#20837C211yesmaximal, characteristic, complemented
4C2×#1806C212yesmaximal, complemented
5C2×#1789C211yesmaximal, characteristic
6C4×#385C211yesmaximal, characteristic, complemented
7#11075C212yesmaximal, complemented
8#11053C212yesmaximal, complemented
9#10790C212yesmaximal, complemented
10#10732C211yesmaximal, characteristic, complemented
11#10719C211yesmaximal, characteristic, complemented
12C23×#41C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C2×C4×#41C2212yes—
15C23×C42C2211yescharacteristic
16C2×#423C2212yescomplemented
17C22×#104—28no—
18C22×#104—24no—
19C22×#104C2211yescharacteristic
20C22×#104C2212yes—
21C22×#104C2211yescharacteristic
22C22×#104C2212yes—
23C22×#104C2211yescharacteristic
24C22×#104C2211yescharacteristic
25C2×#407C2211yescharacteristic
26#2341C412yescomplemented
27Q8×C22⋊C4C411yescharacteristic, complemented
28Q8×C22⋊C4C411yescharacteristic, complemented
29#2339—22no—
30#2339C412yescomplemented
31D4×C22⋊C4—21no—
32D4×C22⋊C4—21no—
33D4×C22⋊C4C411yescharacteristic, complemented
34D4×C22⋊C4C411yescharacteristic, complemented
35#2297—22no—
36#2297C2212yes—
37C2×#385—21no—
38#2280—21no—
39#2280C2211yescharacteristic
40C2×C4×C4⋊C4C2212yescomplemented
41C2×C4×C22⋊C4—21no—
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44#1851—22no—
45#1850—21no—
46#1850—21no—
47#1806—28no—
48#1789—24no—
49C2×#339C2212yescomplemented
50C2×#339C2212yescomplemented
51C2×#339C2212yescomplemented
52C2×#339C2212yescomplemented
53#1728C2212yescomplemented
54#1436—22no—
55C22⋊#95—21no—
56C4×#95C2212yescomplemented
57C22×#41—21no—
58C22×#41—21no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41—24no—
62C22×#41—24no—
63C22×#41—42no—
64C22×#41—42no—
65C22×#41C2×C411yescharacteristic
66C22×#41C2×C411yescharacteristic
67C22×#41D414yes—
68C22×#41Q814yes—
69C22×#41C2311yescharacteristic
70C22×#41C2311yescharacteristic
71C23×Q8C2×C411yescharacteristic
72C23×D4—21no—
73C23×D4C2×C411yescharacteristic
74C24×C4—21no—
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C22×M16—21no—
78C22×M16—22no—
79C22×M16—24no—
80C22×M16—22no—
81C22×M16—42no—
82C22×M16C2311yescharacteristic
83C22×M16C2311yescharacteristic
84C22×M16C2312yes—
85C23×C8—21no—
86C4×#41—24no—
87C4×#41—24no—
88C4×#41—42no—
89C4×#41—42no—
90C2×C4×Q8C2×C412yescomplemented
91C2×C4×Q8C2×C412yescomplemented
92C2×C4×D4—22no—
93C2×C4×D4—22no—
94C2×C4×D4C2×C412yescomplemented
95C2×C4×D4C2×C412yescomplemented
96C2×#117—22no—
97C2×#117C2312yes—
98C22×C4⋊C4—22no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4D411yescharacteristic
103C22×C22⋊C4D411yescharacteristic
104C22×C42—22no—
105C22×C42—24no—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—21no—
109C22×C42—42no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2312yes—
113C22×C42C2312yes—
114#423—24no—
115#423—42no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×#104—232no—
119C2×#104—24no—
120C2×#104—24no—
121C2×#104—24no—
122C2×#104—24no—
123C2×#104—24no—
124C2×#104—24no—
125C2×#104—22no—
126C2×#104—22no—
127C2×#104—22no—
128C2×#104—22no—
129C2×#104—24no—
130C2×#104—42no—
131C2×#104—42no—
132C2×#104D418yes—
133#407—22no—
134#407—22no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—21no—
137#391—22no—
138#391—22no—
139#391C2×C412yescomplemented
140#391C2×C412yescomplemented
141#390—22no—
142#390—22no—
143#390C2×C412yescomplemented
144#390C2×C412yescomplemented
145#386—22no—
146#386—22no—
147#386—22no—
148#386—22no—
149#386—22no—
150#386—22no—
151#385—28no—
152#381—21no—
153#381—22no—
154#380—21no—
155#380—21no—
156#380—22no—
157#380C2×C411yescharacteristic
158#380C2×C411yescharacteristic
159#380C2×C412yes—
160#379—21no—
161#379—21no—
162#379—21no—
163C4×C4⋊C4—24no—
164C4×C4⋊C4—42no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4—21no—
167C4×C22⋊C4—21no—
168C4×C22⋊C4—21no—
169C4×C22⋊C4—22no—
170C4×C22⋊C4—22no—
171C4×C22⋊C4—22no—
172C4×C22⋊C4—22no—
173C4×C22⋊C4—22no—
174C4×C22⋊C4C2×C411yescharacteristic
175C4×C22⋊C4C2×C411yescharacteristic
176C4×C22⋊C4C2×C412yes—
177C4×C22⋊C4D411yescharacteristic
178C4×C22⋊C4D411yescharacteristic
179C4×C22⋊C4D412yes—
180C2×#95—22no—
181C2×#95—22no—
182C2×#95—22no—
183C2×#95—22no—
184C2×#95—21no—
185C2×#95D412yes—
186#339—24no—
187#339—24no—
188#339—42no—
189#339—42no—
190#336—22no—
191#336—22no—
192C25—21no—
193C25C2×D411yescharacteristic
194C2×#41—22no—
195C2×#41—22no—
196C2×#41—24no—
197C2×#41—24no—
198C2×#41—24no—
199C2×#41—24no—
200C2×#41—21no—
201C2×#41—21no—
202C2×#41—21no—
203C2×#41—21no—
204C2×#41—22no—
205C2×#41—22no—
206C2×#41—28no—
207C2×#41—216no—
208C2×#41—28no—
209C2×#41—24no—
210C2×#41—24no—
211C2×#41—22no—
212C2×#41—22no—
213C2×#41—22no—
214C2×#41—22no—
215C2×#41—44no—
216C2×#41—44no—
217C2×#41—42no—
218C2×#41—42no—
219C2×#41—44no—
220C2×#41—44no—
221C2×#41—44no—
222C2×#41—44no—
223C2×#41—48no—
224C2×#41—48no—
225C2×#41—48no—
226C2×#41—48no—
227C2×#41—48no—
228C2×#41C4⋊C414yescomplemented
229C2×#41C4⋊C414yescomplemented
230C2×#41C2×D412yes—
231C2×#41C2×D412yes—
232C2×#41C2×D414yes—
233C2×#41C2×Q812yes—
234C2×#41C2×Q812yes—
235C2×#41#4114yes—
236C22×Q8—21no—
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—42no—
240C22×Q8C4⋊C414yescomplemented
241C22×Q8C22×C411yescharacteristic
242C22×Q8C22×C411yescharacteristic
243C22×D4—21no—
244C22×D4—24no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—22no—
252C22×D4—42no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4C4⋊C414yescomplemented
256C22×D4C22×C411yescharacteristic
257C22×D4C22×C411yescharacteristic
258C23×C4—22no—
259C23×C4—21no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—21no—
264C23×C4—22no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C22×C411yescharacteristic
282C23×C4C22×C411yescharacteristic
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×Q812yes—
290C23×C4#4112yes—
291C23×C4#4112yes—
292C23×C4C2411yescharacteristic
293C2×M16—22no—
294C2×M16—28no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16—21no—
303C2×M16—21no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—44no—
308C2×M16—48no—
309C2×M16—44no—
310C2×M16—42no—
311C2×M16C2×D414yes—
312C22×C8—22no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—44no—
316C22×C8—42no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8—42no—
320C4×Q8—42no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—42no—
324C4×D4—42no—
325C4×D4—44no—
326C4×D4—44no—
327C4×D4—44no—
328C4×D4—44no—
329#117—22no—
330#117—22no—
331#117—22no—
332#117—22no—
333#117—44no—
334#117—44no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4C22×C412yes—
341C2×C4⋊C4C22×C412yes—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C22⋊C4C22⋊C411yescharacteristic
361C2×C22⋊C4C22⋊C411yescharacteristic
362C2×C22⋊C4C22⋊C412yes—
363C2×C22⋊C4C22⋊C412yes—
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—28no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—44no—
387C2×C42—44no—
388C2×C42—48no—
389C2×C42—44no—
390C2×C42—44no—
391C2×C42—42no—
392C2×C42C22×C412yes—
393C2×C42C22×C412yes—
394C2×C42C2×D414yes—
395C2×C42C2×D412yes—
396C2×C42C2×D412yes—
397C4⋊C8—44no—
398C4⋊C8—44no—
399#104—216no—
400#104—216no—
401#104—44no—
402#104—44no—
403#104—44no—
404#104—44no—
405C22⋊C8—42no—
406C22⋊C8—42no—
407#95—28no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—21no—
414#95—21no—
415#95—44no—
416#95—44no—
417#95—42no—
418#95C22⋊C412yes—
419#95C22⋊C412yes—
420#95C22⋊C412yes—
421#95C22⋊C412yes—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—24no—
429C24—42no—
430C24—44no—
431C24—42no—
432C24—42no—
433C24—82no—
434C24C2×C22⋊C411yescharacteristic
435C24C2×C22⋊C411yescharacteristic
436C24#12112yes—
437C24C22⋊Q812yes—
438C24C22×D411yescharacteristic
439#41—22no—
440#41—22no—
441#41—24no—
442#41—24no—
443#41—24no—
444#41—24no—
445#41—24no—
446#41—28no—
447#41—28no—
448#41—22no—
449#41—24no—
450#41—22no—
451#41—22no—
452#41—22no—
453#41—24no—
454#41—48no—
455#41—48no—
456#41—416no—
457#41—44no—
458#41—44no—
459#41—48no—
460#41—48no—
461#41—416no—
462#41—48no—
463#41—48no—
464#41—42no—
465#41—42no—
466#41—42no—
467#41—42no—
468#41#12014yes—
469#41C22⋊Q818yes—
470#41#12314yes—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—22no—
474C2×Q8—24no—
475C2×Q8—28no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—48no—
481C2×Q8C2×C4⋊C412yes—
482C2×Q8C2×C4⋊C412yes—
483C2×Q8C4×D414yes—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—28no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—24no—
499C2×D4—44no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—416no—
506C2×D4—44no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×C4⋊C412yes—
510C2×D4C2×C4⋊C412yes—
511C2×D4C4×D414yes—
512C22×C4—21no—
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—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—416no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—416no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—48no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—416no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—42no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4C2×C22⋊C412yes—
590C22×C4C2×C22⋊C412yes—
591C22×C4C2×C22⋊C412yes—
592C22×C4C2×C22⋊C411yescharacteristic
593C22×C4C2×C22⋊C411yescharacteristic
594C22×C4C2×C22⋊C412yes—
595C22×C4C2×C4⋊C412yes—
596C22×C4C2×C4⋊C412yes—
597C22×C4#11712yes—
598C22×C4#11712yes—
599C22×C4#12112yes—
600C22×C4#12112yes—
601C22×C4#12112yes—
602C22×C4C22⋊Q812yes—
603C22×C4C22⋊Q812yes—
604C22×C4C22⋊Q812yes—
605C22×C4C23×C411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×Q811yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4112yes—
613C22×C4H(5,𝔽2)12yes—
614C22×C4H(5,𝔽2)12yes—
615M16—24no—
616M16—24no—
617M16—48no—
618M16—42no—
619M16—42no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—24no—
627C2×C8—48no—
628C2×C8—42no—
629C2×C8—42no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—42no—
633C2×C8—42no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—416no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—24no—
645C22⋊C4—42no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—48no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—44no—
655C22⋊C4—82no—
656C22⋊C4—82no—
657C22⋊C4—82no—
658C22⋊C4#10414yescomplemented
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—24no—
668C42—24no—
669C42—44no—
670C42—44no—
671C42—48no—
672C42—42no—
673C42—42no—
674C42—42no—
675C42—42no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—42no—
681C42—42no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—22no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—48no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—84no—
715C23—88no—
716C23—88no—
717C23#38012yes—
718C23#38012yes—
719C23C2×#10412yes—
720C23#42112yes—
721C23C22×C22⋊C411yescharacteristic
722C23C2×#12111yescharacteristic
723C23C2×C22⋊Q811yescharacteristic
724C23D4212yes—
725C23#54612yes—
726Q8—22no—
727Q8—24no—
728Q8—22no—
729Q8—22no—
730Q8—48no—
731Q8—42no—
732Q8#38514yescomplemented
733D4—24no—
734D4—24no—
735D4—28no—
736D4—22no—
737D4—22no—
738D4—24no—
739D4—22no—
740D4—48no—
741D4—48no—
742D4—48no—
743D4—42no—
744D4—42no—
745D4—44no—
746D4—42no—
747D4#38514yescomplemented
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—28no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—48no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—48no—
787C2×C4—48no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—432no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—88no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—88no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4#38012yes—
820C2×C4#38012yes—
821C2×C4C2×#10414yescomplemented
822C2×C4C22×C4⋊C411yescharacteristic
823C2×C4C2×#11711yescharacteristic
824C2×C4C2×C4×D412yes—
825C2×C4#51812yes—
826C2×C4C2×#12011yescharacteristic
827C2×C4C2×#12111yescharacteristic
828C2×C4C2×C22⋊Q811yescharacteristic
829C2×C4C2×C22⋊Q812yes—
830C2×C4C2×#12311yescharacteristic
831C2×C4#53411yescharacteristic
832C2×C4#53411yescharacteristic
833C2×C4#54312yes—
834C2×C4D4212yes—
835C2×C4#54612yes—
836C2×C4#54612yes—
837C2×C4#54612yes—
838C2×C4#55112yes—
839C2×C4#55112yes—
840C8—44no—
841C8—81no—
842C8—81no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—24no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—21no—
855C22—22no—
856C22—24no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—44no—
861C22—48no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—816no—
872C22—82no—
873C22—82no—
874C22#180614yescomplemented
875C22C2×#38011yescharacteristic
876C22D4×C22⋊C412yes—
877C22#241011yescharacteristic
878C22#241211yescharacteristic
879C22#243712yes—
880C22C22×#10411yescharacteristic
881C22C2×#42111yescharacteristic
882C22#290112yes—
883C4—22no—
884C4—22no—
885C4—24no—
886C4—24no—
887C4—48no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4C2×#38511yescharacteristic
897C4#231511yescharacteristic
898C4#234212yes—
899C4#241011yescharacteristic
900C4#241211yescharacteristic
901C4#243712yes—
902C2—21no—
903C2—21no—
904C2—24no—
905C2—22no—
906C2—42no—
907C2—44no—
908C2—82no—
909C2#1387711yescharacteristic
910C2C2×#180611yescharacteristic
911C2#2065511yescharacteristic
912C2D4×#10412yes—
913C2#2243412yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #20837C2semidirect
4. C2×#1806C2semidirect
6. C4×#385C2semidirect
7. #11075C2semidirect
8. #11053C2semidirect
9. #10790C2semidirect
10. #10732C2semidirect
11. #10719C2semidirect
16. C2×#423C22semidirect
26. #2341C4semidirect
27. Q8×C22⋊C4C4semidirect
28. Q8×C22⋊C4C4semidirect
30. #2339C4semidirect
33. D4×C22⋊C4C4semidirect
34. D4×C22⋊C4C4semidirect
40. C2×C4×C4⋊C4C22semidirect
49. C2×#339C22semidirect
50. C2×#339C22semidirect
51. C2×#339C22semidirect
52. C2×#339C22semidirect
53. #1728C22semidirect
56. C4×#95C22semidirect
90. C2×C4×Q8C2×C4semidirect
91. C2×C4×Q8C2×C4semidirect
94. C2×C4×D4C2×C4semidirect
95. C2×C4×D4C2×C4semidirect
139. #391C2×C4semidirect
140. #391C2×C4semidirect
143. #390C2×C4semidirect
144. #390C2×C4semidirect
228. C2×#41C4⋊C4semidirect
229. C2×#41C4⋊C4semidirect
240. C22×Q8C4⋊C4semidirect
255. C22×D4C4⋊C4semidirect
658. C22⋊C4#104semidirect
732. Q8#385semidirect
747. D4#385semidirect
821. C2×C4C2×#104semidirect
874. C22#1806semidirect

Maximal subgroups

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

subgroupindex
C23×#1042
C22⋊C4×#412
#208372
C2×#18062
C2×#17892
C4×#3852
#110752
#110532
#107902
#107322
#107192