Finite Group Databasebeta

← #530263

Subgroups — #530263

Order 512.

5586 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C2×#2329C212yesmaximal, complemented
3#14680C211yesmaximal, characteristic
4#14449C212yesmaximal, complemented
5#14448C212yesmaximal, complemented
6#14362C214yesmaximal, complemented
7#14281C212yesmaximal, complemented
8#14052C214yesmaximal, complemented
9#13922C212yesmaximal, complemented
10#13907C212yesmaximal, complemented
11#13882C212yesmaximal, complemented
12#13882C212yesmaximal, complemented
13#13877C212yesmaximal
14C22⋊C42C212yesmaximal
15C2×C22⋊#95C211yesmaximal, characteristic
16C24×Q8C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×C22⋊Q8—216no—
19C22×C22⋊Q8C4116yescomplemented
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2212yes—
28C23×C22⋊C4C2212yes—
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31#2329—216no—
32C2×#391C2214yescomplemented
33C2×#391C2214yescomplemented
34C2×#389C2214yescomplemented
35C2×#387C2214yescomplemented
36C2×#387C2214yescomplemented
37C2×#385C2214yes—
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×#380C2212yes—
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#379C2212yes—
45C2×C4×C22⋊C4C2214yes—
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C22×#95C2212yes—
49C22×#95C2212yes—
50#1446C2214yescomplemented
51#1446C2214yescomplemented
52#1445C2214yescomplemented
53#1445C2214yescomplemented
54#1441C2214yescomplemented
55#1441C2214yescomplemented
56#1441C2214yescomplemented
57#1441C2214yescomplemented
58#1439C2214yes—
59#1439C2214yes—
60#1437C2214yes—
61#1437C2214yes—
62#1436C2214yescomplemented
63#1436C2214yescomplemented
64C4⋊#95C2214yescomplemented
65C22⋊#95C2212yes—
66C22⋊#95C2212yes—
67C22⋊#95C2212yes—
68C22⋊#95C2214yes—
69C22⋊#95C2212yes—
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2214yes—
78C26C2311yescharacteristic
79C23×Q8—28no—
80C23×Q8—42no—
81C23×Q8—42no—
82C23×Q8—44no—
83C23×Q8C2×C418yescomplemented
84C23×Q8C2312yes—
85C23×Q8C2311yescharacteristic
86C23×Q8C2311yescharacteristic
87C24×C4—28no—
88C24×C4—44no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4C2×C418yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—2128no—
105C2×C22⋊Q8—28no—
106C2×C22⋊Q8—216no—
107C2×C22⋊Q8—216no—
108C2×C22⋊Q8C2×C418yes—
109C2×C22⋊Q8C2×C4116yes—
110C2×C22⋊Q8C2×C418yes—
111C2×C22⋊Q8C2×C418yescomplemented
112C2×C22⋊Q8C2×C4116yescomplemented
113C2×C22⋊Q8C2×C418yescomplemented
114C2×C22⋊Q8D4116yes—
115C22×C4⋊C4—28no—
116C22×C4⋊C4—216no—
117C22×C4⋊C4C2×C418yescomplemented
118C22×C4⋊C4C2×C4116yescomplemented
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4—216no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4C2×C4116yes—
137C22×C22⋊C4Q818yescomplemented
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C42C2314yes—
151C22×C42C2314yes—
152#391—216no—
153#391—48no—
154#389—216no—
155#387—216no—
156#387—216no—
157#385—216no—
158#380—28no—
159#380—44no—
160#380—44no—
161#380—44no—
162#380—42no—
163#380—42no—
164#379—28no—
165C4×C22⋊C4—216no—
166C4×C22⋊C4—44no—
167C4×C22⋊C4—44no—
168C2×#95—28no—
169C2×#95—44no—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C25—24no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—24no—
195C25—22no—
196C25—42no—
197C25—42no—
198C25C22×C414yes—
199C25C2×Q814yes—
200C25#4114yes—
201C25C2411yescharacteristic
202C25C2411yescharacteristic
203C25C2411yescharacteristic
204C22×Q8—232no—
205C22×Q8—28no—
206C22×Q8—24no—
207C22×Q8—28no—
208C22×Q8—416no—
209C22×Q8—41no—
210C22×Q8—42no—
211C22×Q8—42no—
212C22×Q8—41no—
213C22×Q8—42no—
214C22×Q8—41no—
215C22×Q8—41no—
216C22×Q8—42no—
217C22×Q8—416no—
218C22×Q8—432no—
219C22×Q8—432no—
220C22×Q8C22×C418yes—
221C22×Q8C22×C414yes—
222C22×Q8C22×C414yes—
223C22×Q8C2×D418yes—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—232no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—416no—
249C23×C4—416no—
250C23×C4—42no—
251C23×C4—41no—
252C23×C4—41no—
253C23×C4—41no—
254C23×C4—41no—
255C23×C4—42no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4—42no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—432no—
272C23×C4—432no—
273C23×C4C22×C414yes—
274C23×C4C22×C418yes—
275C23×C4C22×C418yes—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C22×C414yes—
280C23×C4C22×C414yes—
281C23×C4C2×D418yes—
282C23×C4C2×Q818yescomplemented
283C23×C4C2414yes—
284C23×C4C2414yes—
285C23×C4C2414yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2414yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C22⋊Q8—232no—
296C22⋊Q8—232no—
297C22⋊Q8—264no—
298C22⋊Q8—232no—
299C22⋊Q8—264no—
300C22⋊Q8C22⋊C4164yescomplemented
301C2×C4⋊C4—28no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—232no—
307C2×C4⋊C4—264no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4C22×C414yes—
321C2×C4⋊C4C22×C418yes—
322C2×C4⋊C4C22×C418yes—
323C2×C4⋊C4C22×C418yes—
324C2×C4⋊C4C22×C418yes—
325C2×C4⋊C4C22×C414yes—
326C2×C4⋊C4C22×C418yes—
327C2×C4⋊C4C2×D418yes—
328C2×C4⋊C4C2×D4116yes—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—264no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—416no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—416no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C22×C418yes—
358C2×C22⋊C4C22×C418yes—
359C2×C22⋊C4C22×C418yes—
360C2×C22⋊C4C22×C418yes—
361C2×C22⋊C4C2×D4116yes—
362C2×C22⋊C4C2×Q818yes—
363C2×C22⋊C4C2×Q818yescomplemented
364C2×C42—28no—
365C2×C42—28no—
366C2×C42—44no—
367C2×C42—44no—
368C2×C42—44no—
369C2×C42—44no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—42no—
386#95—42no—
387#95—44no—
388#95—44no—
389#95—44no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24—28no—
401C24—28no—
402C24—28no—
403C24—28no—
404C24—28no—
405C24—28no—
406C24—28no—
407C24—28no—
408C24—216no—
409C24—216no—
410C24—22no—
411C24—21no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—21no—
417C24—22no—
418C24—44no—
419C24—44no—
420C24—48no—
421C24—48no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24—48no—
426C24—48no—
427C24—48no—
428C24—48no—
429C24—48no—
430C24C4×Q8116yes—
431C24C23×C412yes—
432C24C23×C412yes—
433C24C23×C412yes—
434C24C22×D414yes—
435C24C22×Q812yes—
436C24C22×Q812yes—
437C24C22×Q812yes—
438C24C2×#4112yes—
439C24C2×#4112yes—
440C24C2×#4112yes—
441C24H(5,𝔽2)12yes—
442C24H(5,𝔽2)12yes—
443C24H(5,𝔽2)12yes—
444C242−1+414yes—
445C242−1+412yes—
446C24C2511yescharacteristic
447C2×Q8—216no—
448C2×Q8—28no—
449C2×Q8—216no—
450C2×Q8—44no—
451C2×Q8—48no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—48no—
456C2×Q8—48no—
457C2×Q8—416no—
458C2×Q8—416no—
459C2×Q8—4128no—
460C2×Q8—48no—
461C2×Q8—48no—
462C2×Q8C2×C22⋊C4116yescomplemented
463C22×C4—216no—
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—216no—
486C22×C4—216no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—216no—
506C22×C4—216no—
507C22×C4—216no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—416no—
550C22×C4—416no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—416no—
556C22×C4—416no—
557C22×C4—4128no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—84no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4C2×C22⋊C4116yes—
572C22×C4C23×C414yes—
573C22×C4C23×C414yes—
574C22×C4C23×C412yes—
575C22×C4C23×C414yes—
576C22×C4C23×C414yes—
577C22×C4C23×C412yes—
578C22×C4C23×C412yes—
579C22×C4C23×C412yes—
580C22×C4C22×D414yes—
581C22×C4C22×D418yes—
582C22×C4C22×D418yes—
583C22×C4C22×D414yes—
584C22×C4C22×Q818yes—
585C22×C4H(5,𝔽2)14yes—
586C4⋊C4—216no—
587C4⋊C4—28no—
588C4⋊C4—216no—
589C4⋊C4—216no—
590C4⋊C4—216no—
591C4⋊C4—84no—
592C4⋊C4—84no—
593C4⋊C4—88no—
594C4⋊C4—88no—
595C4⋊C4C2×C22⋊C4116yescomplemented
596C4⋊C4C2×C22⋊C4132yescomplemented
597C22⋊C4—216no—
598C22⋊C4—216no—
599C22⋊C4—216no—
600C22⋊C4—216no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—416no—
607C22⋊C4—88no—
608C22⋊C4C2×C22⋊C4132yes—
609C42—88no—
610C42—88no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—232no—
646C23—232no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—416no—
662C23—416no—
663C23—432no—
664C23—432no—
665C23—416no—
666C23—432no—
667C23—432no—
668C23—416no—
669C23—416no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23C22×C22⋊C414yes—
679C23C2×C4×Q814yes—
680C23C2×C4×Q814yes—
681C23C2×C4×Q814yes—
682C23#51814yes—
683C23#51914yes—
684C23#52014yes—
685C23#53814yes—
686C23#53914yes—
687C23#54314yes—
688C23#54414yes—
689C23#54818yes—
690C23D4×Q818yes—
691C23C24×C411yescharacteristic
692C23C23×D412yes—
693C23C23×Q811yescharacteristic
694C23C22×#4111yescharacteristic
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×H(5,𝔽2)12yes—
698C23C2×H(5,𝔽2)11yescharacteristic
699C23C2×2−1+412yes—
700C23C2×2−1+411yescharacteristic
701C23#58512yes—
702Q8—416no—
703Q8—432no—
704Q8—416no—
705C2×C4—232no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—416no—
739C2×C4—416no—
740C2×C4—432no—
741C2×C4—416no—
742C2×C4—416no—
743C2×C4—432no—
744C2×C4—416no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—816no—
777C2×C4—816no—
778C2×C4C22×C22⋊C418yes—
779C2×C4C22×C22⋊C418yes—
780C2×C4C22×C22⋊C414yes—
781C2×C4C22×C22⋊C414yes—
782C2×C4#51814yes—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—28no—
788C22—28no—
789C22—24no—
790C22—24no—
791C22—28no—
792C22—28no—
793C22—28no—
794C22—28no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—464no—
807C22—44no—
808C22—44no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22#232918yescomplemented
816C22Q8×C22⋊C418yes—
817C22C23×C22⋊C411yescharacteristic
818C22C22×C4×Q811yescharacteristic
819C22C2×#51811yescharacteristic
820C22C2×#51811yescharacteristic
821C22C2×#51911yescharacteristic
822C22C2×#52011yescharacteristic
823C22#342811yescharacteristic
824C22C2×#53811yescharacteristic
825C22C2×#53911yescharacteristic
826C22C2×#54311yescharacteristic
827C22C2×#54411yescharacteristic
828C22C2×#54812yes—
829C22C2×D4×Q812yes—
830C22#348412yes—
831C22#348412yes—
832C22#348812yes—
833C22#348912yes—
834C22#350112yes—
835C22#350512yes—
836C22#353512yes—
837C22#353512yes—
838C22#353612yes—
839C22#353812yes—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—28no—
844C4—28no—
845C4—48no—
846C4—42no—
847C4—44no—
848C4—44no—
849C4—84no—
850C4—84no—
851C4—84no—
852C2—28no—
853C2—28no—
854C2—44no—
855C2C2×#232911yescharacteristic
856C2C2×Q8×C22⋊C411yescharacteristic
857C2#3417111yescharacteristic
858C2#3417511yescharacteristic
859C2#3421211yescharacteristic
860C2#3435911yescharacteristic
861C2#3438011yescharacteristic
862C2#3768412yes—
863C2#3768512yes—
864C2#3770212yes—
865C2#3770312yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2329C2semidirect
4. #14449C2semidirect
5. #14448C2semidirect
6. #14362C2semidirect
7. #14281C2semidirect
8. #14052C2semidirect
9. #13922C2semidirect
10. #13907C2semidirect
11. #13882C2semidirect
12. #13882C2semidirect
19. C22×C22⋊Q8C4semidirect
32. C2×#391C22semidirect
33. C2×#391C22semidirect
34. C2×#389C22semidirect
35. C2×#387C22semidirect
36. C2×#387C22semidirect
50. #1446C22semidirect
51. #1446C22semidirect
52. #1445C22semidirect
53. #1445C22semidirect
54. #1441C22semidirect
55. #1441C22semidirect
56. #1441C22semidirect
57. #1441C22semidirect
62. #1436C22semidirect
63. #1436C22semidirect
64. C4⋊#95C22semidirect
83. C23×Q8C2×C4semidirect
111. C2×C22⋊Q8C2×C4semidirect
112. C2×C22⋊Q8C2×C4semidirect
113. C2×C22⋊Q8C2×C4semidirect
117. C22×C4⋊C4C2×C4semidirect
118. C22×C4⋊C4C2×C4semidirect
137. C22×C22⋊C4Q8semidirect
282. C23×C4C2×Q8semidirect
300. C22⋊Q8C22⋊C4semidirect
363. C2×C22⋊C4C2×Q8semidirect
462. C2×Q8C2×C22⋊C4semidirect
595. C4⋊C4C2×C22⋊C4semidirect
596. C4⋊C4C2×C22⋊C4semidirect
815. C22#2329semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C2×#23292
#146802
#144492
#144482
#143622
#142812
#140522
#139222
#139072
#138822
#138772
C22⋊C422
C2×C22⋊#952