Finite Group Databasebeta

← #777328

Subgroups — #777328

Order 512.

5048 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#2407C212yesmaximal, complemented
3C2×#2341C211yesmaximal, characteristic, complemented
4#16633C212yesmaximal, complemented
5#15453C214yesmaximal, complemented
6#15323C214yesmaximal, complemented
7#15144C211yesmaximal, characteristic, complemented
8#15125C211yesmaximal, characteristic, complemented
9#15123C211yesmaximal, characteristic, complemented
10#14916C212yesmaximal, complemented
11#14811C212yesmaximal, complemented
12#14175C212yesmaximal, complemented
13#14137C212yesmaximal, complemented
14#13969C212yesmaximal, complemented
15#13931C211yesmaximal, characteristic, complemented
16#13872C212yesmaximal, complemented
17C4×#392C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C2×#554—216no—
20C2×#554—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#125C2212yes—
23C22×C22⋊Q8C2214yes—
24C22×C22⋊Q8C2212yes—
25C22×#121C2212yes—
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2212yes—
30C22×C4×D4C2212yes—
31C23×C4⋊C4C2212yes—
32#2407—216no—
33C2×#394C2214yes—
34C2×#393C2212yes—
35C2×#393C2214yes—
36C2×#392C2212yes—
37C2×#392C2211yescharacteristic
38C2×#392C2214yes—
39#2341—28no—
40C2×#391C2212yes—
41C2×#390C2211yescharacteristic
42C2×#390C2212yes—
43C2×#390C2211yescharacteristic
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#386C2214yes—
47C2×#386C2214yes—
48C2×#386C2214yes—
49C2×#386C2214yes—
50C2×#385C2214yes—
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58#1446C2212yes—
59#1445C2214yes—
60#1444C2211yescharacteristic
61#1442C2212yes—
62#1441C2214yes—
63#1441C2214yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2211yescharacteristic
68#1439C2212yes—
69#1439C2212yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2214yes—
75#1438C2212yes—
76#1438C2211yescharacteristic
77#1437C2214yes—
78#1436C2214yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83#1434C2212yes—
84#1434C2212yes—
85C22⋊#95C2214yes—
86C4×#95C2211yescharacteristic
87C22×#41—24no—
88C22×#41—28no—
89C22×#41—24no—
90C22×#41—24no—
91C22×#41—44no—
92C23×Q8C2311yescharacteristic
93C23×Q8C2312yes—
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2312yes—
98C23×D4C2314yes—
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2314yes—
103#554—2128no—
104C2×C4⋊Q8—28no—
105C2×C4⋊Q8—24no—
106C2×#125—216no—
107C2×#125—28no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—216no—
111C2×C22⋊Q8—216no—
112C2×C22⋊Q8—216no—
113C2×C22⋊Q8D4116yescomplemented
114C2×#121—28no—
115C2×#121—28no—
116C2×#121—44no—
117C2×C4×Q8—28no—
118C2×C4×Q8—24no—
119C2×C4×Q8—44no—
120C2×C4×Q8D418yescomplemented
121C2×C4×D4—28no—
122C2×C4×D4—28no—
123C2×C4×D4—28no—
124C2×C4×D4—216no—
125C2×C4×D4—28no—
126C2×C4×D4—24no—
127C2×C4×D4—44no—
128C22×C4⋊C4—28no—
129C22×C4⋊C4—28no—
130C22×C4⋊C4—28no—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165#394—216no—
166#393—44no—
167#393—48no—
168#392—24no—
169#392—28no—
170#392—216no—
171#391—28no—
172#390—24no—
173#390—28no—
174#390—28no—
175#390—28no—
176#390—24no—
177#386—216no—
178#386—48no—
179#386—48no—
180#386—48no—
181#385—216no—
182#380—24no—
183#380—28no—
184#380—28no—
185#380—44no—
186C4×C22⋊C4—28no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—44no—
189C2×#95C2311yescharacteristic
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2311yescharacteristic
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C25C2411yescharacteristic
210C25C2412yes—
211C25C2412yes—
212C2×#41—232no—
213C2×#41—432no—
214C2×#41—432no—
215C2×#41—416no—
216C2×#41—416no—
217C22×Q8—28no—
218C22×Q8—24no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—24no—
222C22×Q8—42no—
223C22×Q8—42no—
224C22×Q8—44no—
225C22×Q8C2×D414yes—
226C22×Q8C2×D418yes—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—28no—
235C22×D4—24no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—28no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4#4114yes—
255C22×D4#4114yescomplemented
256C23×C4—24no—
257C23×C4—28no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—28no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×D418yes—
279C23×C4#4114yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2414yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2414yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C4⋊Q8—232no—
295#125—264no—
296C22⋊Q8—2128no—
297C22⋊Q8—264no—
298#121—432no—
299C4×Q8—232no—
300C4×Q8—416no—
301C4×D4—264no—
302C4×D4—232no—
303C4×D4—432no—
304C2×C4⋊C4—264no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4C2×D418yes—
331C2×C4⋊C4C2×D4116yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4C2×D4116yes—
383C2×C42—28no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—44no—
392C2×C42C2×D418yes—
393C2×C42C2×D414yes—
394#95—22no—
395#95—22no—
396#95—24no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—22no—
401#95—24no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—24no—
406#95—22no—
407#95—42no—
408#95—42no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—42no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—22no—
429C24—24no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—24no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—24no—
444C24—22no—
445C24—21no—
446C24C22×D414yes—
447C24C2×#4114yes—
448C24C2×#4112yes—
449C24C2×#4114yes—
450C242−1+414yes—
451C24C2511yescharacteristic
452#41—4128no—
453C2×Q8—216no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—216no—
457C2×Q8—216no—
458C2×Q8—88no—
459C2×Q8—84no—
460C2×Q8—88no—
461C2×Q8—84no—
462C2×Q8#120116yes—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—216no—
466C2×D4—216no—
467C2×D4—216no—
468C2×D4—216no—
469C2×D4—28no—
470C2×D4—216no—
471C2×D4—28no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—416no—
482C2×D4—416no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—48no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—48no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—216no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—232no—
533C22×C4—216no—
534C22×C4—28no—
535C22×C4—216no—
536C22×C4—216no—
537C22×C4—216no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—24no—
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—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—416no—
563C22×C4—416no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—88no—
574C22×C4—88no—
575C22×C4—88no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4C22×D412yes—
580C22×C4C22×D414yes—
581C22×C4C22×D418yes—
582C22×C4C22×D414yes—
583C22×C4C22×D418yes—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D414yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4H(5,𝔽2)14yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)14yes—
595C22×C42−1+412yes—
596C4⋊C4—232no—
597C4⋊C4—28no—
598C4⋊C4—216no—
599C4⋊C4—28no—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—232no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—44no—
606C4⋊C4—48no—
607C22⋊C4—216no—
608C22⋊C4—232no—
609C22⋊C4—48no—
610C22⋊C4—44no—
611C22⋊C4—416no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—416no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C22⋊C4—88no—
622C22⋊C4—88no—
623C22⋊C4—84no—
624C22⋊C4—88no—
625C42—216no—
626C42—28no—
627C42—48no—
628C42—44no—
629C42—48no—
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—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—28no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—28no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—44no—
680C23—41no—
681C23—42no—
682C23—44no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—44no—
690C23—41no—
691C23—42no—
692C23—44no—
693C23—42no—
694C23—44no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—44no—
699C23—42no—
700C23—41no—
701C23—42no—
702C23—44no—
703C23—42no—
704C23—44no—
705C23—42no—
706C23—42no—
707C23—44no—
708C23—42no—
709C23—44no—
710C23#54818yes—
711C23C23×D411yescharacteristic
712C23C23×D412yes—
713C23C22×#4111yescharacteristic
714C23C22×#4111yescharacteristic
715C23C22×#4111yescharacteristic
716C23C2×H(5,𝔽2)12yes—
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)12yes—
719C23C2×2−1+412yes—
720C23C2×2−1+411yescharacteristic
721C23#58511yescharacteristic
722Q8—232no—
723Q8—816no—
724D4—232no—
725D4—432no—
726D4—432no—
727D4—416no—
728D4—832no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—432no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—432no—
780C2×C4—416no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—832no—
806C2×C4C2×#12018yes—
807C2×C4C2×#12014yes—
808C2×C4#52514yes—
809C2×C4#53514yes—
810C2×C4#54618yes—
811C2×C4#54618yes—
812C2×C4#54814yes—
813C22—28no—
814C22—28no—
815C22—28no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—48no—
829C22—44no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—48no—
838C22—81no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—81no—
843C22—84no—
844C22—84no—
845C22—82no—
846C22—82no—
847C22—81no—
848C22—82no—
849C22—81no—
850C22C22×#12011yescharacteristic
851C22C2×#52511yescharacteristic
852C22C2×#53511yescharacteristic
853C22C2×#54612yes—
854C22C2×#54612yes—
855C22C2×#54811yescharacteristic
856C22C2×#54812yes—
857C22#347511yescharacteristic
858C22#348111yescharacteristic
859C22#348611yescharacteristic
860C22#348612yes—
861C22#348811yescharacteristic
862C22#348812yes—
863C22#349212yes—
864C22#349811yescharacteristic
865C22#349812yes—
866C22#351111yescharacteristic
867C22#351511yescharacteristic
868C22#351912yes—
869C22#352012yes—
870C22#353612yes—
871C22#354112yes—
872C22#354812yes—
873C4—28no—
874C4—24no—
875C4—42no—
876C4—44no—
877C4—44no—
878C4—42no—
879C4—44no—
880C4—48no—
881C4—42no—
882C4—81no—
883C4—82no—
884C4—84no—
885C4—82no—
886C4#240418yes—
887C2—48no—
888C2—84no—
889C2—82no—
890C2C2×#240411yescharacteristic
891C2#3570111yescharacteristic
892C2#3609111yescharacteristic
893C2#3649211yescharacteristic
894C2#3657511yescharacteristic
895C2#3916911yescharacteristic
896C2#4281011yescharacteristic
897C2#4491512yes—
898C2#4499612yes—
899C2#5902412yes—
900C2#5965012yes—
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. C22×#554C2semidirect
2. C2×#2407C2semidirect
3. C2×#2341C2semidirect
4. #16633C2semidirect
5. #15453C2semidirect
6. #15323C2semidirect
7. #15144C2semidirect
8. #15125C2semidirect
9. #15123C2semidirect
10. #14916C2semidirect
11. #14811C2semidirect
12. #14175C2semidirect
13. #14137C2semidirect
14. #13969C2semidirect
15. #13931C2semidirect
16. #13872C2semidirect
17. C4×#392C2semidirect
113. C2×C22⋊Q8D4semidirect
120. C2×C4×Q8D4semidirect
255. C22×D4#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#24072
C2×#23412
#166332
#154532
#153232
#151442
#151252
#151232
#149162
#148112
#141752
#141372
#139692
#139312
#138722
C4×#3922