Finite Group Databasebeta

← #4930355

Subgroups — #4930355

Order 512.

5714 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#518C211yesmaximal, characteristic
2C2×#2439C211yesmaximal, characteristic, complemented
3C2×#2452C212yesmaximal, complemented
4#15203C212yesmaximal, complemented
5#15177C212yesmaximal, complemented
6#14865C212yesmaximal, complemented
7#14812C212yesmaximal, complemented
8#14726C214yesmaximal, complemented
9#14717C214yesmaximal, complemented
10#14264C211yesmaximal, characteristic, complemented
11#14018C212yesmaximal, complemented
12#13979C212yesmaximal, complemented
13#13951C211yesmaximal, characteristic, complemented
14#13920C212yesmaximal, complemented
15#13902C211yesmaximal, characteristic
16#13902C211yesmaximal, characteristic
17#13844C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic, complemented
20C22×C22⋊Q8C2214yescomplemented
21C2×#518—216no—
22C2×#518—28no—
23C22×C4×D4C2212yes—
24C22×C4×D4C2212yes—
25C22×C4×D4C2212yes—
26C22×C4×D4C2212yes—
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C22⋊C4C2214yes—
30#2452—216no—
31#2439—28no—
32C2×#396C2212yes—
33C2×#396C2214yescomplemented
34C2×#393C2212yes—
35C2×#393C2214yescomplemented
36C2×#391C2212yescomplemented
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#390C2212yes—
41C2×#389C2211yescharacteristic, complemented
42C2×#389C2212yescomplemented
43C2×#389C2212yescomplemented
44C2×#389C2211yescharacteristic, complemented
45C2×#387C2212yescomplemented
46C2×#385C2214yescomplemented
47C2×#385C2214yescomplemented
48C2×#382C2211yescharacteristic, complemented
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2214yescomplemented
52C2×#379C2212yes—
53C2×#379C2214yes—
54C2×#379C2212yes—
55C2×C4×C4⋊C4C2212yescomplemented
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58#1444C2211yescharacteristic, complemented
59#1444C2211yescharacteristic, complemented
60#1444C2212yescomplemented
61#1442C2211yescharacteristic, complemented
62#1442C2212yescomplemented
63#1442C2211yescharacteristic, complemented
64#1439C2212yes—
65#1439C2212yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1439C2214yescomplemented
74#1438C2212yes—
75#1438C2212yes—
76#1438C2212yes—
77#1438C2212yes—
78C4⋊#95C2212yescomplemented
79C4⋊#95C2212yescomplemented
80C4⋊#95C2212yescomplemented
81#1434C2212yescomplemented
82C22⋊#95C2214yescomplemented
83C22⋊#95C2214yescomplemented
84C22⋊#95C2214yescomplemented
85C22⋊#95C2214yescomplemented
86C4×#95C2212yescomplemented
87C26C2312yes—
88C23×Q8C2312yes—
89C23×D4—28no—
90C23×D4—28no—
91C23×D4—24no—
92C23×D4—24no—
93C23×D4Q818yescomplemented
94C23×D4C2312yes—
95C23×D4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2314yes—
98C24×C4C2314yes—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—28no—
101C2×C22⋊Q8—216no—
102C2×C22⋊Q8—48no—
103C2×C22⋊Q8—48no—
104#518—2128no—
105C2×C4×D4—28no—
106C2×C4×D4—216no—
107C2×C4×D4—28no—
108C2×C4×D4—28no—
109C2×C4×D4—28no—
110C2×C4×D4—216no—
111C2×C4×D4—28no—
112C2×C4×D4—28no—
113C2×C4×D4—28no—
114C2×C4×D4D4116yes—
115C2×#117—24no—
116C2×#117—28no—
117C2×#117—28no—
118C2×#117D418yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—216no—
134C22×C22⋊C4—216no—
135C22×C22⋊C4—216no—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158#396—28no—
159#396—216no—
160#393—28no—
161#393—216no—
162#391—28no—
163#390—28no—
164#390—28no—
165#390—28no—
166#390—28no—
167#389—24no—
168#389—24no—
169#389—28no—
170#389—28no—
171#387—28no—
172#385—216no—
173#385—48no—
174#382—24no—
175#380—24no—
176#380—24no—
177#380—48no—
178#379—44no—
179#379—48no—
180#379—44no—
181C4×C4⋊C4—28no—
182C4×C22⋊C4—24no—
183C4×C22⋊C4—24no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C25—28no—
207C25—24no—
208C25—28no—
209C25—24no—
210C25—44no—
211C25—42no—
212C25—42no—
213C25—42no—
214C25—44no—
215C25—42no—
216C25C2×Q818yes—
217C25C2411yescharacteristic
218C25C2414yes—
219C22×Q8—28no—
220C22×Q8—24no—
221C22×Q8—24no—
222C22×Q8—44no—
223C22×Q8—42no—
224C22×D4—232no—
225C22×D4—232no—
226C22×D4—264no—
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—264no—
230C22×D4—232no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4C2×D418yes—
238C22×D4C2×Q818yes—
239C22×D4C2×Q818yes—
240C22×D4#4118yes—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—28no—
244C23×C4—28no—
245C23×C4—28no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—44no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4C2×D414yes—
257C23×C4C2×D4116yes—
258C23×C4C2×Q814yes—
259C23×C4#4114yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2414yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C4⋊Q8—416no—
276C22⋊Q8—464no—
277C4×D4—264no—
278C4×D4—264no—
279C4×D4—264no—
280C4×D4—264no—
281#117—232no—
282#117—232no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4C2×D414yes—
315C2×C4⋊C4C2×D418yes—
316C2×C4⋊C4C2×D414yes—
317C2×C22⋊C4—2128no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4C2×D418yes—
366C2×C22⋊C4C2×D4116yes—
367C2×C42—28no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42C2×D418yes—
378C2×C42C2×D418yes—
379#95—22no—
380#95—22no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—24no—
388#95—24no—
389#95—28no—
390#95—22no—
391#95—22no—
392#95—24no—
393#95—24no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401C24—216no—
402C24—216no—
403C24—232no—
404C24—22no—
405C24—24no—
406C24—24no—
407C24—22no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—232no—
425C24—216no—
426C24—48no—
427C24—48no—
428C24—416no—
429C24—88no—
430C24—88no—
431C24—84no—
432C24—84no—
433C24—88no—
434C24—88no—
435C24—84no—
436C24—88no—
437C24—84no—
438C24—84no—
439C24—84no—
440C24—88no—
441C24—88no—
442C24—88no—
443C24—88no—
444C24C22×D412yes—
445C24C22×D418yes—
446C24C22×Q812yes—
447C24C22×Q818yes—
448C24C2×#4112yes—
449C24C2×#4118yes—
450C24C2511yescharacteristic
451C2×Q8—416no—
452C2×Q8—48no—
453C2×Q8—48no—
454C2×Q8—88no—
455C2×Q8—84no—
456C2×D4—216no—
457C2×D4—216no—
458C2×D4—232no—
459C2×D4—2256no—
460C2×D4—232no—
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—216no—
464C2×D4—216no—
465C2×D4—216no—
466C2×D4—216no—
467C2×D4—216no—
468C2×D4C22⋊Q8132yescomplemented
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—28no—
475C22×C4—216no—
476C22×C4—28no—
477C22×C4—216no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—232no—
509C22×C4—232no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—416no—
545C22×C4—416no—
546C22×C4—88no—
547C22×C4—88no—
548C22×C4—88no—
549C22×C4—88no—
550C22×C4—88no—
551C22×C4—88no—
552C22×C4—88no—
553C22×C4—88no—
554C22×C4—88no—
555C22×C4—88no—
556C22×C4C22⋊Q8116yescomplemented
557C22×C4C22×D414yes—
558C22×C4C22×D414yes—
559C22×C4C22×D414yes—
560C22×C4C22×D418yes—
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D414yes—
565C22×C4C22×Q812yes—
566C22×C4C22×Q812yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4114yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)14yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—216no—
576C4⋊C4—28no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—416no—
580C4⋊C4—416no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—48no—
585C4⋊C4—84no—
586C4⋊C4#120116yes—
587C22⋊C4—216no—
588C22⋊C4—232no—
589C22⋊C4—216no—
590C22⋊C4—232no—
591C22⋊C4—416no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—48no—
595C22⋊C4—416no—
596C22⋊C4—416no—
597C22⋊C4—416no—
598C22⋊C4—88no—
599C22⋊C4—84no—
600C22⋊C4—84no—
601C22⋊C4—88no—
602C22⋊C4—88no—
603C22⋊C4—88no—
604C42—216no—
605C42—216no—
606C42—44no—
607C42—48no—
608C42—44no—
609C23—264no—
610C23—22no—
611C23—28no—
612C23—24no—
613C23—28no—
614C23—28no—
615C23—22no—
616C23—24no—
617C23—28no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—28no—
626C23—22no—
627C23—28no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—22no—
637C23—22no—
638C23—28no—
639C23—28no—
640C23—28no—
641C23—28no—
642C23—44no—
643C23—42no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—42no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—42no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—42no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—42no—
664C23—44no—
665C23—42no—
666C23—832no—
667C23—816no—
668C23—832no—
669C23—816no—
670C23—832no—
671C23—816no—
672C23—816no—
673C23—832no—
674C23—816no—
675C23—816no—
676C23C2×C22⋊Q814yes—
677C23C2×C22⋊Q8116yes—
678C23C23×D412yes—
679C23C23×D411yescharacteristic
680C23C23×Q811yescharacteristic
681C23C22×#4111yescharacteristic
682C23C22×#4112yes—
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)12yes—
685C23C2×H(5,𝔽2)11yescharacteristic
686C23#58512yes—
687C23#58511yescharacteristic
688C23#58511yescharacteristic
689Q8—816no—
690D4—264no—
691D4—264no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—24no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—232no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—832no—
772C2×C4—832no—
773C2×C4C2×#12018yes—
774C2×C4C2×#12014yes—
775C2×C4C2×C22⋊Q814yes—
776C2×C4C2×C22⋊Q818yes—
777C2×C4C2×C22⋊Q814yes—
778C2×C4#52518yes—
779C2×C4#52514yes—
780C22—24no—
781C22—216no—
782C22—216no—
783C22—24no—
784C22—216no—
785C22—24no—
786C22—48no—
787C22—48no—
788C22—44no—
789C22—48no—
790C22—42no—
791C22—48no—
792C22—44no—
793C22—48no—
794C22—42no—
795C22—48no—
796C22—48no—
797C22—44no—
798C22—48no—
799C22—48no—
800C22—44no—
801C22—48no—
802C22—48no—
803C22—42no—
804C22—48no—
805C22—42no—
806C22—864no—
807C22C22×#12011yescharacteristic
808C22C22×C22⋊Q812yes—
809C22C22×C22⋊Q811yescharacteristic
810C22C2×#52512yes—
811C22C2×#52511yescharacteristic
812C22#348412yes—
813C22#348811yescharacteristic
814C22#348811yescharacteristic
815C22#348812yes—
816C22#349412yes—
817C22#349612yes—
818C22#349811yescharacteristic
819C22#350012yes—
820C22#350011yescharacteristic
821C22#350111yescharacteristic
822C22#350112yes—
823C22#350111yescharacteristic
824C22#350811yescharacteristic
825C22#351011yescharacteristic
826C22#351412yes—
827C22#351412yes—
828C22#351912yes—
829C22#352112yes—
830C4—24no—
831C4—28no—
832C4—44no—
833C4—42no—
834C4—44no—
835C4—42no—
836C4—44no—
837C4—44no—
838C4—82no—
839C4—82no—
840C4—81no—
841C4—82no—
842C4—84no—
843C4—81no—
844C4#284818yes—
845C2—416no—
846C2—44no—
847C2#3551511yescharacteristic
848C2#3552412yes—
849C2#3552911yescharacteristic
850C2#3561112yes—
851C2#3568011yescharacteristic
852C2#3570212yes—
853C2#3577612yes—
854C2#3600411yescharacteristic
855C2#3607511yescharacteristic
856C2#3608211yescharacteristic
857C2C2×#284811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2439C2semidirect
3. C2×#2452C2semidirect
4. #15203C2semidirect
5. #15177C2semidirect
6. #14865C2semidirect
7. #14812C2semidirect
8. #14726C2semidirect
9. #14717C2semidirect
10. #14264C2semidirect
11. #14018C2semidirect
12. #13979C2semidirect
13. #13951C2semidirect
14. #13920C2semidirect
17. #13844C2semidirect
19. C22×C4⋊Q8C22semidirect
20. C22×C22⋊Q8C22semidirect
33. C2×#396C22semidirect
35. C2×#393C22semidirect
36. C2×#391C22semidirect
41. C2×#389C22semidirect
42. C2×#389C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
45. C2×#387C22semidirect
46. C2×#385C22semidirect
47. C2×#385C22semidirect
48. C2×#382C22semidirect
51. C2×#380C22semidirect
55. C2×C4×C4⋊C4C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
78. C4⋊#95C22semidirect
79. C4⋊#95C22semidirect
80. C4⋊#95C22semidirect
81. #1434C22semidirect
82. C22⋊#95C22semidirect
83. C22⋊#95C22semidirect
84. C22⋊#95C22semidirect
85. C22⋊#95C22semidirect
86. C4×#95C22semidirect
93. C23×D4Q8semidirect
468. C2×D4C22⋊Q8semidirect
556. C22×C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#5182
C2×#24392
C2×#24522
#152032
#151772
#148652
#148122
#147262
#147172
#142642
#140182
#139792
#139512
#139202
#139022
#138442