Finite Group Databasebeta

← #823425

Subgroups — #823425

Order 512.

4242 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C212yesmaximal, complemented
2C2×#2416C212yesmaximal, complemented
3C2×#2361C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5#16518C212yesmaximal, complemented
6#15324C214yesmaximal, complemented
7#15277C214yesmaximal, complemented
8#15150C211yesmaximal, characteristic, complemented
9#15136C211yesmaximal, characteristic, complemented
10#15123C211yesmaximal, characteristic, complemented
11#14868C212yesmaximal, complemented
12#14795C212yesmaximal, complemented
13#13970C212yesmaximal, complemented
14#13918C211yesmaximal, characteristic, complemented
15#13907C212yesmaximal, complemented
16#13872C212yesmaximal, complemented
17C4×#392C211yesmaximal, characteristic, complemented
18C22×#121C2212yes—
19C22×#121C2214yes—
20C22×#121C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2212yes—
24C22×C4×D4C2212yes—
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28#2535—216no—
29#2416—216no—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#397C2212yes—
33C2×#397C2212yes—
34C2×#396C2214yes—
35C2×#394C2214yes—
36C2×#392C2212yes—
37C2×#392C2211yescharacteristic
38#2361—28no—
39D4×C4⋊C4—28no—
40C2×#390C2211yescharacteristic
41C2×#390C2212yes—
42C2×#389C2212yes—
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#388C2212yes—
46C2×#386C2214yes—
47C2×#386C2214yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2214yes—
51C2×#385C2212yes—
52C2×#384C2211yescharacteristic
53C2×#382C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2214yes—
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61#1445C2212yes—
62#1445C2212yes—
63#1444C2211yescharacteristic
64#1442C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1439C2212yes—
70#1439C2211yescharacteristic
71#1439C2214yes—
72#1439C2212yes—
73#1439C2214yes—
74#1438C2214yes—
75#1438C2212yes—
76#1438C2211yescharacteristic
77#1438C2214yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82#1434C2212yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2214yes—
86C4×#95C2211yescharacteristic
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2314yes—
90C23×D4C2312yes—
91C23×D4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2314yes—
95C24×C4C2312yes—
96C24×C4C2312yes—
97C2×#121—216no—
98C2×#121—28no—
99C2×#121—216no—
100C2×#121—28no—
101C2×#121—24no—
102C2×#121—24no—
103C2×#121—48no—
104C2×#121—44no—
105C2×#121D418yescomplemented
106C2×C4×D4—28no—
107C2×C4×D4—28no—
108C2×C4×D4—28no—
109C2×C4×D4—28no—
110C2×C4×D4—24no—
111C2×C4×D4—28no—
112C2×C4×D4—24no—
113C2×C4×D4—28no—
114C2×C4×D4—28no—
115C2×C4×D4—44no—
116C2×C4×D4—44no—
117C2×C4×D4—44no—
118C2×C4×D4—44no—
119C22×C4⋊C4—28no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—28no—
122C22×C4⋊C4—28no—
123C22×C4⋊C4—44no—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158#397—28no—
159#397—28no—
160#397—44no—
161#397—44no—
162#396—216no—
163#394—216no—
164#392—28no—
165#392D418yescomplemented
166#390—28no—
167#390—24no—
168#389—24no—
169#389—28no—
170#389—28no—
171#388—28no—
172#386—216no—
173#386—216no—
174#386—216no—
175#386—28no—
176#385—216no—
177#385—28no—
178#384—24no—
179#382—28no—
180#380—28no—
181#380—28no—
182#380—216no—
183#380—44no—
184C4×C4⋊C4D418yescomplemented
185C4×C22⋊C4—24no—
186C4×C22⋊C4—44no—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2311yescharacteristic
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C25C2412yes—
209C25C2411yescharacteristic
210C25C2412yes—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—28no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4—22no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—44no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4C2×D414yes—
239C22×D4C2×D414yes—
240C22×D4C2×D418yes—
241C22×D4C2×D418yes—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—28no—
253C23×C4—24no—
254C23×C4—28no—
255C23×C4—24no—
256C23×C4—28no—
257C23×C4—24no—
258C23×C4—28no—
259C23×C4—24no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4C2×D414yes—
270C23×C4#4118yes—
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2414yes—
274C23×C4C2412yes—
275C23×C4C2414yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285#121—232no—
286#121—432no—
287#121—464no—
288C4×D4—232no—
289C4×D4—432no—
290C4×D4—432no—
291C4×D4—416no—
292C4×D4—432no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—28no—
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—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—416no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—432no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4C2×D414yes—
327C2×C4⋊C4C2×D414yes—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4#4114yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D418yes—
378C2×C22⋊C4C2×D418yes—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42C2×D418yes—
388C2×C42C2×D414yes—
389#95—22no—
390#95—22no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—24no—
397#95—24no—
398#95—28no—
399#95—22no—
400#95—42no—
401#95—44no—
402#95—42no—
403#95—42no—
404#95—44no—
405#95—42no—
406#95—44no—
407#95—44no—
408#95C2×D418yes—
409#95C2×D414yes—
410C24—22no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—24no—
434C24—22no—
435C24—24no—
436C24—22no—
437C24—24no—
438C24—22no—
439C24—24no—
440C24C22×D414yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C22×D414yes—
444C24C2×#4114yes—
445C24H(5,𝔽2)12yes—
446C242−1+414yes—
447C24C2511yescharacteristic
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—216no—
451C2×D4—216no—
452C2×D4—216no—
453C2×D4—216no—
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—216no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—416no—
470C2×D4—416no—
471C2×D4—416no—
472C2×D4—416no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—48no—
476C2×D4—88no—
477C2×D4—88no—
478C2×D4—88no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—28no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—216no—
517C22×C4—216no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—48no—
550C22×C4—416no—
551C22×C4—48no—
552C22×C4—416no—
553C22×C4—416no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—416no—
564C22×C4—88no—
565C22×C4—88no—
566C22×C4—88no—
567C22×C4—88no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—88no—
571C22×C4—88no—
572C22×C4—88no—
573C22×C4C22×D414yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D414yes—
577C22×C4C22×D412yes—
578C22×C4C22×D414yes—
579C22×C4C22×D414yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4114yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)14yes—
590C4⋊C4—28no—
591C4⋊C4—28no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—416no—
595C4⋊C4—48no—
596C4⋊C4—416no—
597C4⋊C4—48no—
598C4⋊C4—44no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—84no—
602C4⋊C4#121116yes—
603C22⋊C4—216no—
604C22⋊C4—216no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—44no—
608C22⋊C4—416no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—416no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—416no—
616C22⋊C4—48no—
617C22⋊C4—84no—
618C22⋊C4—88no—
619C22⋊C4—88no—
620C42—28no—
621C42—216no—
622C42—44no—
623C42—48no—
624C23—22no—
625C23—24no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—28no—
657C23—28no—
658C23—24no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23D4214yes—
704C23#54718yes—
705C23C23×D411yescharacteristic
706C23C23×D411yescharacteristic
707C23C23×D411yescharacteristic
708C23C22×#4111yescharacteristic
709C23C22×#4112yes—
710C23C2×H(5,𝔽2)12yes—
711C23C2×H(5,𝔽2)11yescharacteristic
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×2−1+412yes—
714C23#58511yescharacteristic
715C23#58512yes—
716D4—232no—
717D4—432no—
718D4—432no—
719D4—416no—
720D4—832no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—416no—
766C2×C4—432no—
767C2×C4—44no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—832no—
799C2×C4—816no—
800C2×C4—816no—
801C2×C4C2×#12118yes—
802C2×C4C2×#12114yes—
803C2×C4#52514yes—
804C2×C4#53514yes—
805C2×C4D4214yes—
806C2×C4#54618yes—
807C2×C4#55318yes—
808C22—28no—
809C22—28no—
810C22—28no—
811C22—28no—
812C22—24no—
813C22—42no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—44no—
831C22—44no—
832C22—42no—
833C22—44no—
834C22—48no—
835C22—44no—
836C22—48no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—84no—
842C22—84no—
843C22—82no—
844C22—82no—
845C22C22×#12111yescharacteristic
846C22C2×#52511yescharacteristic
847C22C2×#53511yescharacteristic
848C22C2×D4211yescharacteristic
849C22C2×D4211yescharacteristic
850C22C2×#54612yes—
851C22C2×#54712yes—
852C22D4×#4111yescharacteristic
853C22C2×#55312yes—
854C22#348611yescharacteristic
855C22#348811yescharacteristic
856C22#348912yes—
857C22#349212yes—
858C22#349412yes—
859C22#349611yescharacteristic
860C22#349612yes—
861C22#350011yescharacteristic
862C22#351212yes—
863C22#351612yes—
864C22#351911yescharacteristic
865C22#353612yes—
866C22#354112yes—
867C22#354612yes—
868C4—24no—
869C4—28no—
870C4—42no—
871C4—44no—
872C4—44no—
873C4—44no—
874C4—42no—
875C4—42no—
876C4—82no—
877C4—81no—
878C4—84no—
879C4—82no—
880C4—84no—
881C4#253518yescomplemented
882C2—48no—
883C2—44no—
884C2—84no—
885C2C2×#253511yescharacteristic
886C2#3573711yescharacteristic
887C2#3608311yescharacteristic
888C2D4×#12111yescharacteristic
889C2#3610311yescharacteristic
890C2#3936211yescharacteristic
891C2#4281011yescharacteristic
892C2#4510412yes—
893C2#4537312yes—
894C2#5901512yes—
895C2#5982612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2535C2semidirect
2. C2×#2416C2semidirect
3. C2×#2361C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. #16518C2semidirect
6. #15324C2semidirect
7. #15277C2semidirect
8. #15150C2semidirect
9. #15136C2semidirect
10. #15123C2semidirect
11. #14868C2semidirect
12. #14795C2semidirect
13. #13970C2semidirect
14. #13918C2semidirect
15. #13907C2semidirect
16. #13872C2semidirect
17. C4×#392C2semidirect
105. C2×#121D4semidirect
165. #392D4semidirect
184. C4×C4⋊C4D4semidirect
881. C4#2535semidirect

Maximal subgroups

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

subgroupindex
C2×#25352
C2×#24162
C2×#23612
C2×D4×C4⋊C42
#165182
#153242
#152772
#151502
#151362
#151232
#148682
#147952
#139702
#139182
#139072
#138722
C4×#3922