Finite Group Databasebeta

← #686584

Subgroups — #686584

Order 512.

5290 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
1C22×#537C211yesmaximal, characteristic
2C2×#2422C212yesmaximal, complemented
3C2×#2339C211yesmaximal, characteristic, complemented
4#16364C212yesmaximal, complemented
5#16361C212yesmaximal, complemented
6#15950C214yesmaximal, complemented
7#15277C214yesmaximal, complemented
8#15182C212yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#14926C212yesmaximal, complemented
11#14914C212yesmaximal, complemented
12#14337C211yesmaximal, characteristic, complemented
13#14130C211yesmaximal, characteristic, complemented
14#13970C212yesmaximal, complemented
15#13937C211yesmaximal, characteristic, complemented
16#13880C211yesmaximal, characteristic, complemented
17#13851C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C23×#41C2211yescharacteristic
20C2×#537—28no—
21C2×#537—216no—
22C22×#123C2214yes—
23C22×C22⋊Q8C2212yes—
24C22×C22⋊Q8C2212yes—
25C22×#121C2212yes—
26C22×#121C2214yes—
27C22×#121C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31#2422—216no—
32C2×#397C2214yes—
33C2×#394C2214yes—
34#2339—28no—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2212yes—
38C2×#390C2212yes—
39C2×#389C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2214yes—
43C2×#385C2214yes—
44C2×#385C2212yes—
45C2×#385C2214yes—
46C2×#384C2212yes—
47C2×#381C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C22×#95C2212yes—
57#1446C2212yes—
58#1446C2211yescharacteristic
59#1446C2211yescharacteristic
60#1444C2212yes—
61#1444C2212yes—
62#1444C2212yes—
63#1442C2212yes—
64#1442C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1438C2212yes—
74#1438C2214yes—
75#1438C2211yescharacteristic
76#1438C2212yes—
77#1438C2212yes—
78#1438C2211yescharacteristic
79#1438C2214yes—
80#1438C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2214yes—
86C22⋊#95C2212yes—
87C22×#41—28no—
88C22×#41—28no—
89C22×#41—24no—
90C22×#41—24no—
91C22×#41—24no—
92C22×#41—24no—
93C22×#41—24no—
94C22×#41—44no—
95C22×#41—44no—
96C22×#41D418yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2312yes—
100C23×D4C2311yescharacteristic
101C23×D4C2312yes—
102C23×D4C2311yescharacteristic
103C23×D4C2314yes—
104C24×C4C2312yes—
105C24×C4C2312yes—
106C24×C4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110#537—2128no—
111C2×#123—216no—
112C2×#123—48no—
113C2×#123—48no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—216no—
119C2×#121—28no—
120C2×#121—28no—
121C2×#121—216no—
122C2×#121—216no—
123C2×#121—216no—
124C2×#121—28no—
125C2×#121—216no—
126C2×#121D4116yes—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C2×C4×D4—28no—
130C2×C4×D4—44no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—28no—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162#397—216no—
163#394—216no—
164#391—24no—
165#391—24no—
166#391—44no—
167#390—28no—
168#389—28no—
169#386—28no—
170#386—28no—
171#386—48no—
172#385—216no—
173#385—48no—
174#385—44no—
175#384—28no—
176#381—28no—
177#380—24no—
178#380—28no—
179#380—24no—
180#380—44no—
181C4×C22⋊C4—24no—
182C4×C22⋊C4—28no—
183C4×C22⋊C4—24no—
184C4×C22⋊C4—44no—
185C2×#95—28no—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C25C2412yes—
210C25C2412yes—
211C25C2411yescharacteristic
212C2×#41—232no—
213C2×#41—232no—
214C2×#41—232no—
215C2×#41—432no—
216C2×#41—432no—
217C2×#41—416no—
218C2×#41—432no—
219C2×#41—432no—
220C2×#41—416no—
221C2×#41—416no—
222C22×Q8—24no—
223C22×Q8—22no—
224C22×Q8—24no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—24no—
230C22×Q8—42no—
231C22×Q8C2×D414yes—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—28no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—28no—
239C22×D4—28no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4C2×D418yes—
258C22×D4C2×D414yes—
259C22×D4C2×D418yes—
260C22×D4C2×D4116yes—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—28no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—28no—
274C23×C4—28no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—44no—
286C23×C4—42no—
287C23×C4—44no—
288C23×C4C2×D418yes—
289C23×C4C2×D418yes—
290C23×C4C2×D414yes—
291C23×C4#4114yes—
292C23×C4#4114yes—
293C23×C4C2414yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2414yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307#123—464no—
308C22⋊Q8—264no—
309C22⋊Q8—264no—
310#121—264no—
311#121—2128no—
312#121—264no—
313C4×D4—416no—
314C4×D4—416no—
315C2×C4⋊C4—232no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4C2×D418yes—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
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—28no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4C2×D4116yes—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395#95—22no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—22no—
400#95—24no—
401#95—24no—
402#95—28no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—28no—
410#95—42no—
411#95—42no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—21no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—22no—
427C24—21no—
428C24—24no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24C22×D414yes—
450C24C22×D418yes—
451C24C22×D414yes—
452C24C22×D412yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24C2511yescharacteristic
456#41—4128no—
457#41—4128no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×D4—28no—
469C2×D4—216no—
470C2×D4—216no—
471C2×D4—216no—
472C2×D4—232no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—216no—
476C2×D4—216no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—416no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—44no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C2×D4#120116yes—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—216no—
541C22×C4—216no—
542C22×C4—216no—
543C22×C4—216no—
544C22×C4—216no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—48no—
573C22×C4—416no—
574C22×C4—416no—
575C22×C4—416no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—88no—
585C22×C4—88no—
586C22×C4—88no—
587C22×C4—84no—
588C22×C4—88no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—88no—
593C22×C4#123116yescomplemented
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D418yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D414yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)14yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C4H(5,𝔽2)14yes—
607C22×C42−1+414yes—
608C22×C42−1+412yes—
609C4⋊C4—216no—
610C4⋊C4—232no—
611C4⋊C4—216no—
612C4⋊C4—416no—
613C4⋊C4—416no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—88no—
618C22⋊C4—216no—
619C22⋊C4—232no—
620C22⋊C4—216no—
621C22⋊C4—232no—
622C22⋊C4—48no—
623C22⋊C4—44no—
624C22⋊C4—416no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—416no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—416no—
632C22⋊C4—48no—
633C22⋊C4—84no—
634C22⋊C4—88no—
635C42—44no—
636C42—44no—
637C42—48no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—28no—
653C23—24no—
654C23—24no—
655C23—28no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—28no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—42no—
677C23—42no—
678C23—44no—
679C23—42no—
680C23—42no—
681C23—44no—
682C23—42no—
683C23—44no—
684C23—42no—
685C23—44no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23C2×#12018yes—
718C23C2×#12314yes—
719C23C23×D411yescharacteristic
720C23C23×D412yes—
721C23C22×#4111yescharacteristic
722C23C22×#4111yescharacteristic
723C23C2×H(5,𝔽2)12yes—
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)12yes—
726C23C2×2−1+411yescharacteristic
727C23C2×2−1+412yes—
728C23#58511yescharacteristic
729C23#58511yescharacteristic
730Q8—416no—
731Q8—416no—
732D4—232no—
733D4—416no—
734D4—432no—
735D4—432no—
736D4—832no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—232no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—28no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—432no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—432no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—816no—
815C2×C4—816no—
816C2×C4—816no—
817C2×C4C2×#12014yes—
818C2×C4C2×#12314yes—
819C2×C4C2×#12314yes—
820C2×C4#53414yes—
821C2×C4#54618yes—
822C2×C4#54618yes—
823C22—24no—
824C22—28no—
825C22—28no—
826C22—24no—
827C22—24no—
828C22—28no—
829C22—44no—
830C22—48no—
831C22—44no—
832C22—48no—
833C22—44no—
834C22—48no—
835C22—42no—
836C22—44no—
837C22—48no—
838C22—44no—
839C22—42no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—42no—
844C22—42no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22C22×#12011yescharacteristic
861C22C22×#12311yescharacteristic
862C22C2×#53411yescharacteristic
863C22#346011yescharacteristic
864C22#346111yescharacteristic
865C22C2×#54612yes—
866C22C2×#54612yes—
867C22#348412yes—
868C22#348811yescharacteristic
869C22#348912yes—
870C22#348911yescharacteristic
871C22#349212yes—
872C22#349612yes—
873C22#349811yescharacteristic
874C22#349912yes—
875C22#349911yescharacteristic
876C22#351112yes—
877C22#351111yescharacteristic
878C22#351211yescharacteristic
879C22#353612yes—
880C22#354112yes—
881C22#354612yes—
882C22#354812yes—
883C4—24no—
884C4—44no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—42no—
889C4—48no—
890C4—42no—
891C4—82no—
892C4—84no—
893C4—81no—
894C4—82no—
895C4—81no—
896C4#240518yes—
897C2—44no—
898C2—48no—
899C2—84no—
900C2C2×#240511yescharacteristic
901C2#3525511yescharacteristic
902C2#3553011yescharacteristic
903C2#3568011yescharacteristic
904C2#3608511yescharacteristic
905C2#3778012yes—
906C2#3943212yes—
907C2#4291611yescharacteristic
908C2#4298811yescharacteristic
909C2#4486912yes—
910C2#4510412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#537C2
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×#2422C2semidirect
3. C2×#2339C2semidirect
4. #16364C2semidirect
5. #16361C2semidirect
6. #15950C2semidirect
7. #15277C2semidirect
8. #15182C2semidirect
9. #15179C2semidirect
10. #14926C2semidirect
11. #14914C2semidirect
12. #14337C2semidirect
13. #14130C2semidirect
14. #13970C2semidirect
15. #13937C2semidirect
16. #13880C2semidirect
17. #13851C2semidirect
593. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C22×#5372
C2×#24222
C2×#23392
#163642
#163612
#159502
#152772
#151822
#151792
#149262
#149142
#143372
#141302
#139702
#139372
#138802
#138512