Finite Group Databasebeta

← #648049

Subgroups — #648049

Order 512.

6058 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C2×#2848C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2427C212yesmaximal, complemented
5C2×#2339C211yesmaximal, characteristic, complemented
6#15269C214yesmaximal, complemented
7#15266C214yesmaximal, complemented
8#15179C212yesmaximal, complemented
9#15178C212yesmaximal, complemented
10#14731C214yesmaximal, complemented
11#14138C211yesmaximal, characteristic, complemented
12#14129C211yesmaximal, characteristic, complemented
13#13975C214yesmaximal, complemented
14#13970C212yesmaximal, complemented
15C4×#379C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic, complemented
19C22×#124C2211yescharacteristic, complemented
20C2×#525—28no—
21C2×#525—216no—
22C22×#123C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×#121C2212yes—
27C22×#120C2212yes—
28C22×C4×D4C2214yes—
29C22×C4×D4C2212yescomplemented
30C22×#117C2211yescharacteristic
31#2848—28no—
32#2432—28no—
33#2427—216no—
34C2×#397C2214yescomplemented
35C2×#394C2214yes—
36C2×#394C2214yes—
37#2339—28no—
38C2×#391C2212yescomplemented
39C2×#391C2212yescomplemented
40C2×#391C2211yescharacteristic, complemented
41C2×#390C2211yescharacteristic, complemented
42C2×#389C2212yescomplemented
43C2×#386C2214yes—
44C2×#386C2214yes—
45C2×#386C2214yes—
46C2×#385C2214yes—
47C2×#385C2212yes—
48C2×#385C2214yescomplemented
49C2×#381C2212yescomplemented
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2214yescomplemented
53C2×#379C2212yes—
54C2×#379C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C22×#95C2212yescomplemented
60#1444C2214yescomplemented
61#1444C2214yescomplemented
62#1442C2214yescomplemented
63#1441C2214yescomplemented
64#1440C2214yes—
65#1440C2214yes—
66#1440C2214yescomplemented
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1438C2214yes—
72#1436C2214yescomplemented
73#1436C2212yescomplemented
74#1436C2212yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2214yescomplemented
81C26C2311yescharacteristic
82C22×#41—28no—
83C22×#41—24no—
84C22×#41—24no—
85C22×#41—44no—
86C22×#41D418yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×D4C2312yes—
90C23×D4C2314yes—
91C23×D4C2311yescharacteristic
92C24×C4—28no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—24no—
96C24×C4—44no—
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2314yes—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—44no—
105C2×#124—28no—
106C2×#124—24no—
107#525—2128no—
108C2×#123—28no—
109C2×#123—216no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—28no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—44no—
119C2×#121—28no—
120C2×#121—28no—
121C2×#121D4116yes—
122C2×#120—28no—
123C2×#120—216no—
124C2×C4×D4—216no—
125C2×C4×D4—216no—
126C2×C4×D4—28no—
127C2×C4×D4—28no—
128C2×C4×D4—216no—
129C2×C4×D4—44no—
130C2×#117—24no—
131C2×#117—28no—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#397—216no—
161#394—216no—
162#394—216no—
163#391—24no—
164#391—28no—
165#391—28no—
166#390—24no—
167#389—28no—
168#386—216no—
169#386—216no—
170#386—216no—
171#385—216no—
172#385—28no—
173#385—216no—
174#381—28no—
175#380—28no—
176#380—216no—
177#380D418yescomplemented
178#379—28no—
179#379—28no—
180C4×C22⋊C4—24no—
181C4×C22⋊C4—28no—
182C4×C22⋊C4—24no—
183C4×C22⋊C4—44no—
184C2×#95—28no—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C25—24no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—24no—
209C25—24no—
210C25—42no—
211C25—42no—
212C25—42no—
213C25C2412yes—
214C25C2411yescharacteristic
215C25C2412yes—
216C2×#41—232no—
217C2×#41—232no—
218C2×#41—416no—
219C2×#41—432no—
220C2×#41—432no—
221C22×Q8—24no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—24no—
229C22×Q8—24no—
230C22×Q8C2×D414yes—
231C22×D4—28no—
232C22×D4—28no—
233C22×D4—28no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4C2×D4116yes—
245C22×D4C2×D418yes—
246C22×D4C2×D418yes—
247C22×D4C2×D414yes—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—232no—
251C23×C4—24no—
252C23×C4—28no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—28no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—44no—
276C23×C4—432no—
277C23×C4—432no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—416no—
283C23×C4—416no—
284C23×C4C2×D418yes—
285C23×C4C2×D418yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4#4114yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2414yes—
294C23×C4C2414yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C4⋊Q8—416no—
302#124—416no—
303#123—264no—
304C22⋊Q8—264no—
305C22⋊Q8—432no—
306C22⋊Q8—416no—
307#121—264no—
308#120—264no—
309C4×D4—2128no—
310C4×D4—432no—
311#117—232no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4C2×D418yes—
335C2×C4⋊C4C2×D418yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4C2×D4116yes—
380C2×C22⋊C4C2×D418yes—
381C2×C22⋊C4#4118yescomplemented
382C2×C42—28no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—24no—
391#95—22no—
392#95—28no—
393#95—24no—
394#95—22no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—44no—
406#95—44no—
407#95—42no—
408#95—42no—
409#95C2×D418yes—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—22no—
434C24—22no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24—48no—
444C24—48no—
445C24—48no—
446C24—48no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—44no—
455C24—48no—
456C24C22×D414yes—
457C24C22×D418yes—
458C24C22×D412yes—
459C24C22×D412yes—
460C24C22×D414yes—
461C24C2×#4112yes—
462C24C2×#4114yes—
463C242−1+414yes—
464C24C2511yescharacteristic
465#41—4128no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—48no—
473C2×Q8—48no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×D4—232no—
477C2×D4—216no—
478C2×D4—216no—
479C2×D4—232no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—216no—
483C2×D4—216no—
484C2×D4—416no—
485C2×D4—48no—
486C2×D4—416no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—416no—
490C2×D4—416no—
491C2×D4—416no—
492C2×D4#120116yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—28no—
501C22×C4—216no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—216no—
537C22×C4—216no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—416no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—416no—
573C22×C4—416no—
574C22×C4—48no—
575C22×C4—4128no—
576C22×C4—416no—
577C22×C4—416no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—88no—
586C22×C4—88no—
587C22×C4—88no—
588C22×C4—88no—
589C22×C4#121116yes—
590C22×C4C22×D418yes—
591C22×C4C22×D418yes—
592C22×C4C22×D414yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4H(5,𝔽2)14yes—
604C4⋊C4—232no—
605C4⋊C4—216no—
606C4⋊C4—216no—
607C4⋊C4—416no—
608C4⋊C4—416no—
609C4⋊C4—44no—
610C4⋊C4—48no—
611C4⋊C4—88no—
612C22⋊C4—216no—
613C22⋊C4—232no—
614C22⋊C4—232no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—416no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—416no—
622C22⋊C4—48no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—416no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C42—216no—
629C42—44no—
630C42—44no—
631C42—48no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—28no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—28no—
646C23—28no—
647C23—24no—
648C23—28no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—28no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—28no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—28no—
663C23—28no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—416no—
673C23—432no—
674C23—416no—
675C23—432no—
676C23—432no—
677C23—416no—
678C23—432no—
679C23—432no—
680C23—432no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—44no—
702C23—42no—
703C23—44no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—44no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—42no—
714C23—42no—
715C23C2×#12018yes—
716C23C2×#12114yes—
717C23#54718yes—
718C23C23×D411yescharacteristic
719C23C23×D412yes—
720C23C23×D411yescharacteristic
721C23C22×#4111yescharacteristic
722C23C22×#4112yes—
723C23C2×H(5,𝔽2)12yes—
724C23C2×2−1+412yes—
725C23#58512yes—
726C23#58512yes—
727Q8—416no—
728Q8—88no—
729D4—232no—
730D4—464no—
731D4—432no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—232no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—416no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—432no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—832no—
806C2×C4C2×#12014yes—
807C2×C4C2×#12114yes—
808C2×C4C2×#12114yes—
809C2×C4#53414yes—
810C2×C4D4218yes—
811C2×C4#54618yes—
812C22—28no—
813C22—24no—
814C22—24no—
815C22—28no—
816C22—28no—
817C22—216no—
818C22—28no—
819C22—24no—
820C22—464no—
821C22—48no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—48no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—48no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—48no—
838C22—44no—
839C22—44no—
840C22—48no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22C22×#12011yescharacteristic
847C22C22×#12111yescharacteristic
848C22#344411yescharacteristic
849C22C2×#53411yescharacteristic
850C22#345511yescharacteristic
851C22C2×D4212yes—
852C22C2×#54612yes—
853C22C2×#54712yes—
854C22D4×#4112yes—
855C22D4×#4112yes—
856C22D4×#4112yes—
857C22#348512yes—
858C22#348511yescharacteristic
859C22#348611yescharacteristic
860C22#348912yes—
861C22#348912yes—
862C22#349512yes—
863C22#350512yes—
864C22#352012yes—
865C22#354012yes—
866C22#354112yes—
867C4—24no—
868C4—44no—
869C4—44no—
870C4—48no—
871C4—48no—
872C4—44no—
873C4—44no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4#241018yes—
879C2—48no—
880C2—48no—
881C2—44no—
882C2C2×#241011yescharacteristic
883C2#3474311yescharacteristic
884C2#3563311yescharacteristic
885C2#3614312yes—
886C2#3621312yes—
887C2#3766812yes—
888C2#3986012yes—
889C2#5900012yes—
890C2#5900212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#525C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2848C2semidirect
3. C2×#2432C2semidirect
4. C2×#2427C2semidirect
5. C2×#2339C2semidirect
6. #15269C2semidirect
7. #15266C2semidirect
8. #15179C2semidirect
9. #15178C2semidirect
10. #14731C2semidirect
11. #14138C2semidirect
12. #14129C2semidirect
13. #13975C2semidirect
14. #13970C2semidirect
15. C4×#379C2semidirect
18. C22×C4⋊Q8C22semidirect
19. C22×#124C22semidirect
29. C22×C4×D4C22semidirect
34. C2×#397C22semidirect
38. C2×#391C22semidirect
39. C2×#391C22semidirect
40. C2×#391C22semidirect
41. C2×#390C22semidirect
42. C2×#389C22semidirect
48. C2×#385C22semidirect
49. C2×#381C22semidirect
52. C2×#380C22semidirect
59. C22×#95C22semidirect
60. #1444C22semidirect
61. #1444C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
66. #1440C22semidirect
72. #1436C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
80. C22⋊#95C22semidirect
177. #380D4semidirect
381. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#28482
C2×#24322
C2×#24272
C2×#23392
#152692
#152662
#151792
#151782
#147312
#141382
#141292
#139752
#139702
C4×#3792