Finite Group Databasebeta

← #845305

Subgroups — #845305

Order 512.

4862 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C212yesmaximal, complemented
2C2×#2409C212yesmaximal, complemented
3C2×#2409C211yesmaximal, characteristic, complemented
4C2×C4×#120C211yesmaximal, characteristic
5#16318C212yesmaximal, complemented
6#16297C212yesmaximal, complemented
7#15961C214yesmaximal, complemented
8#15622C214yesmaximal, complemented
9#15182C212yesmaximal, complemented
10#15181C212yesmaximal, complemented
11#15179C212yesmaximal, complemented
12#14440C212yesmaximal, complemented
13#14357C212yesmaximal
14#13997C212yesmaximal, complemented
15#13906C211yesmaximal, characteristic, complemented
16C24×Q8C2211yescharacteristic, complemented
17C25×C4C2211yescharacteristic
18C22×C22⋊Q8C2212yes—
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×#120C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24#2848—216no—
25#2409—216no—
26#2409—28no—
27C2×#395C2212yescomplemented
28C2×#395C2214yescomplemented
29C2×#393C2214yes—
30C2×#393C2212yes—
31C4×#120—28no—
32C2×#391C2212yescomplemented
33C2×#391C2212yescomplemented
34C2×#391C2212yescomplemented
35C2×#390C2212yes—
36C2×#389C2212yescomplemented
37C2×#386C2214yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2211yescharacteristic
41C2×#385C2214yes—
42C2×#385C2214yes—
43C2×#385C2214yes—
44C2×#385C2212yes—
45C2×#385C2211yescharacteristic
46C2×#385C2212yescomplemented
47C2×#385C2214yescomplemented
48C2×#384C2211yescharacteristic, complemented
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic, complemented
53C2×#380C2212yescomplemented
54C2×#379C2214yes—
55C2×#379C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic, complemented
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59#1445C2214yescomplemented
60#1442C2214yescomplemented
61#1442C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1440C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yescomplemented
73#1439C2212yescomplemented
74#1438C2214yes—
75#1437C2214yes—
76C4⋊#95C2212yescomplemented
77C4⋊#95C2214yescomplemented
78C4⋊#95C2212yescomplemented
79C26C2311yescharacteristic
80C23×Q8—28no—
81C23×Q8—24no—
82C23×Q8—44no—
83C23×Q8—42no—
84C23×Q8—42no—
85C23×Q8C2312yes—
86C23×Q8C2312yes—
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C24×C4—28no—
90C24×C4—24no—
91C24×C4—42no—
92C24×C4—44no—
93C24×C4—42no—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×C22⋊Q8—44no—
108C2×C22⋊Q8D4116yescomplemented
109C2×#120—24no—
110C2×#120—24no—
111C2×#120Q818yescomplemented
112C2×C4×D4—28no—
113C2×C4×D4—28no—
114C2×C4×D4—42no—
115C2×C4×D4—42no—
116C2×C4×D4—44no—
117C2×C4×D4D418yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2311yescharacteristic
147C22×C42C2312yes—
148#395—216no—
149#395—28no—
150#393—216no—
151#393—28no—
152#391—28no—
153#391—28no—
154#391—28no—
155#390—28no—
156#389—44no—
157#386—28no—
158#386—24no—
159#386—216no—
160#386—28no—
161#385—216no—
162#385—216no—
163#385—216no—
164#385—28no—
165#385—216no—
166#385—28no—
167#385—24no—
168#384—42no—
169#380—28no—
170#380—24no—
171#380—28no—
172#380—28no—
173#380—28no—
174#379—216no—
175#379—24no—
176C4×C4⋊C4—42no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—28no—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C25—22no—
198C25—24no—
199C25—22no—
200C25—24no—
201C25—42no—
202C25—41no—
203C25—41no—
204C25—42no—
205C25—41no—
206C25—41no—
207C25C2×Q814yescomplemented
208C25C2411yescharacteristic
209C25C2411yescharacteristic
210C25C2412yes—
211C22×Q8—24no—
212C22×Q8—24no—
213C22×Q8—28no—
214C22×Q8—24no—
215C22×Q8—24no—
216C22×Q8—24no—
217C22×Q8—24no—
218C22×Q8—24no—
219C22×Q8—42no—
220C22×Q8—44no—
221C22×Q8—42no—
222C22×Q8—432no—
223C22×Q8—416no—
224C22×Q8—416no—
225C22×Q8—432no—
226C22×Q8—416no—
227C22×Q8C2×D418yes—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—41no—
233C22×D4—41no—
234C22×D4—42no—
235C22×D4—41no—
236C22×D4—41no—
237C22×D4—42no—
238C22×D4C2×D414yes—
239C22×D4C2×Q818yes—
240C22×D4C2×Q814yes—
241C22×D4#4114yes—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—28no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—41no—
268C23×C4—42no—
269C23×C4—41no—
270C23×C4—42no—
271C23×C4—44no—
272C23×C4—42no—
273C23×C4—432no—
274C23×C4—416no—
275C23×C4—416no—
276C23×C4—432no—
277C23×C4—416no—
278C23×C4C2×D414yes—
279C23×C4C2×D418yes—
280C23×C4C2×D414yes—
281C23×C4C2414yes—
282C23×C4C2414yes—
283C23×C4C2412yes—
284C23×C4C2414yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2414yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C22⋊Q8—432no—
294C22⋊Q8—432no—
295C22⋊Q8—432no—
296#120—232no—
297C4×D4—416no—
298C4×D4—432no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D418yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D4116yes—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D414yes—
376C2×C22⋊C4C2×D4116yes—
377C2×C22⋊C4C2×Q814yescomplemented
378C2×C22⋊C4C2×Q818yescomplemented
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42C2×D414yes—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—24no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—44no—
403#95—44no—
404#95—42no—
405#95—44no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—28no—
435C24—216no—
436C24—44no—
437C24—48no—
438C24—44no—
439C24—44no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24—48no—
444C24—48no—
445C24—44no—
446C24—48no—
447C24—44no—
448C24—44no—
449C24—48no—
450C24—44no—
451C24—44no—
452C24—48no—
453C24—48no—
454C24—44no—
455C24—48no—
456C24—44no—
457C24C22×D412yes—
458C24C22×D412yes—
459C24C22×D414yes—
460C24C22×Q812yes—
461C24C22×Q812yes—
462C24C22×Q814yes—
463C24C2×#4112yes—
464C24C2×#4112yes—
465C242−1+414yes—
466C24C2511yescharacteristic
467C2×Q8—216no—
468C2×Q8—216no—
469C2×Q8—216no—
470C2×Q8—416no—
471C2×Q8—48no—
472C2×Q8—48no—
473C2×Q8—416no—
474C2×Q8—4128no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—48no—
480C2×D4—216no—
481C2×D4—216no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4C22⋊Q8116yescomplemented
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—216no—
537C22×C4—216no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—216no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—48no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—416no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—416no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—44no—
578C22×C4—4128no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4C22×D412yes—
591C22×C4C22×D418yes—
592C22×C4C22×D418yes—
593C22×C4C22×D412yes—
594C22×C4C22×D414yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D414yes—
599C22×C4C22×Q814yes—
600C22×C4C22×Q812yes—
601C22×C4C2×#4112yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C4H(5,𝔽2)14yes—
605C4⋊C4—216no—
606C4⋊C4—44no—
607C4⋊C4—416no—
608C4⋊C4—48no—
609C4⋊C4—416no—
610C4⋊C4—416no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C4⋊C4—88no—
616C22⋊C4—28no—
617C22⋊C4—216no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—416no—
621C22⋊C4—416no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—416no—
628C22⋊C4—416no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—416no—
632C42—28no—
633C42—48no—
634C42—84no—
635C23—24no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—416no—
678C23—432no—
679C23—432no—
680C23—416no—
681C23—416no—
682C23—432no—
683C23—416no—
684C23—416no—
685C23—432no—
686C23—416no—
687C23—416no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23C2×C22⋊Q814yes—
725C23C2×C22⋊Q814yes—
726C23D4×Q818yes—
727C23C23×D411yescharacteristic
728C23C23×D412yes—
729C23C23×Q811yescharacteristic
730C23C22×#4111yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×H(5,𝔽2)12yes—
734C23C2×2−1+412yes—
735C23#58511yescharacteristic
736C23#58511yescharacteristic
737C23#58512yes—
738Q8—432no—
739Q8—432no—
740D4—416no—
741D4—432no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—28no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—432no—
767C2×C4—416no—
768C2×C4—432no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—416no—
795C2×C4—432no—
796C2×C4—416no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4C2×C22⋊Q814yes—
819C2×C4#53414yes—
820C2×C4#53418yes—
821C2×C4D4218yes—
822C2×C4D4214yes—
823C2×C4H(3,𝔽4)14yes—
824C22—28no—
825C22—28no—
826C22—24no—
827C22—24no—
828C22—28no—
829C22—28no—
830C22—28no—
831C22—464no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—44no—
843C22—42no—
844C22—42no—
845C22—44no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—44no—
856C22—42no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—42no—
861C22—44no—
862C22C22×C22⋊Q811yescharacteristic
863C22C2×#53412yes—
864C22C2×#53411yescharacteristic
865C22#344911yescharacteristic
866C22C2×D4212yes—
867C22C2×D4211yescharacteristic
868C22C2×D4×Q812yes—
869C22D4×#4112yes—
870C22#348712yes—
871C22#348912yes—
872C22#348912yes—
873C22#350111yescharacteristic
874C22#350111yescharacteristic
875C22#350112yes—
876C22#350511yescharacteristic
877C22#350511yescharacteristic
878C22#352012yes—
879C22C2×H(3,𝔽4)11yescharacteristic
880C22#353811yescharacteristic
881C22#354012yes—
882C22#354011yescharacteristic
883C22#354112yes—
884C22#354112yes—
885C4—24no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—48no—
890C4—48no—
891C4—44no—
892C4—42no—
893C4—82no—
894C4—84no—
895C4—84no—
896C4#267918yes—
897C2—44no—
898C2—48no—
899C2—44no—
900C2#3501011yescharacteristic
901C2D4×C22⋊Q812yes—
902C2#3737411yescharacteristic
903C2#3765912yes—
904C2#3959512yes—
905C2#3986012yes—
906C2#4549411yescharacteristic
907C2#4566711yescharacteristic
908C2C2×#267911yescharacteristic
909C2#5899811yescharacteristic
910C2#5900111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2848C2semidirect
2. C2×#2409C2semidirect
3. C2×#2409C2semidirect
5. #16318C2semidirect
6. #16297C2semidirect
7. #15961C2semidirect
8. #15622C2semidirect
9. #15182C2semidirect
10. #15181C2semidirect
11. #15179C2semidirect
12. #14440C2semidirect
14. #13997C2semidirect
15. #13906C2semidirect
16. C24×Q8C22semidirect
27. C2×#395C22semidirect
28. C2×#395C22semidirect
32. C2×#391C22semidirect
33. C2×#391C22semidirect
34. C2×#391C22semidirect
36. C2×#389C22semidirect
46. C2×#385C22semidirect
47. C2×#385C22semidirect
48. C2×#384C22semidirect
52. C2×#380C22semidirect
53. C2×#380C22semidirect
56. C2×C4×C4⋊C4C22semidirect
59. #1445C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
78. C4⋊#95C22semidirect
108. C2×C22⋊Q8D4semidirect
111. C2×#120Q8semidirect
207. C25C2×Q8semidirect
377. C2×C22⋊C4C2×Q8semidirect
378. C2×C22⋊C4C2×Q8semidirect
493. C2×D4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#24092
C2×C4×#1202
#163182
#162972
#159612
#156222
#151822
#151812
#151792
#144402
#143572
#139972
#139062