Finite Group Databasebeta

← #4414572

Subgroups — #4414572

Order 512.

3238 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16831C211yesmaximal, characteristic, complemented
2#16831C212yesmaximal, complemented
3#16470C212yesmaximal, complemented
4#16417C212yesmaximal, complemented
5#16417C212yesmaximal, complemented
6#16339C211yesmaximal, characteristic, complemented
7#16307C212yesmaximal, complemented
8#15026C212yesmaximal, complemented
9#14914C212yesmaximal, complemented
10#14820C211yesmaximal, characteristic
11#14767C212yesmaximal, complemented
12#14738C212yesmaximal, complemented
13#14727C212yesmaximal
14#14717C211yesmaximal, characteristic
15#14693C212yesmaximal
16#14669C212yesmaximal, complemented
17#14635C211yesmaximal, characteristic, complemented
18#14627C211yesmaximal, characteristic, complemented
19C2×C22⋊#95C211yesmaximal, characteristic
20C25×C4C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C2×#400C2212yescomplemented
25C2×#400C2212yescomplemented
26C2×#397C2211yescharacteristic
27C2×#397C2211yescharacteristic
28C2×#397C2212yes—
29C2×#397C2212yes—
30C2×#393C2211yescharacteristic
31C2×#393C2211yescharacteristic
32C2×#385C2212yes—
33C2×#385C2212yes—
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#380C2211yescharacteristic
40C2×#379C2212yes—
41C2×#379C2212yes—
42C22×#95C2212yes—
43C22×#95C2212yes—
44#1446C2212yescomplemented
45#1446C2212yescomplemented
46#1445C2212yescomplemented
47#1445C2212yescomplemented
48#1444C2212yescomplemented
49#1444C2212yescomplemented
50#1443C2212yescomplemented
51#1443C2212yescomplemented
52#1443C2212yescomplemented
53#1443C2212yescomplemented
54#1443C2212yescomplemented
55#1443C2212yescomplemented
56#1443C2212yescomplemented
57#1443C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1442C2212yescomplemented
62#1442C2212yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1441C2212yescomplemented
73#1441C2212yescomplemented
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1439C2211yescharacteristic
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2211yescharacteristic
85#1439C2211yescharacteristic
86#1439C2212yes—
87#1439C2211yescharacteristic
88C22⋊#95C2211yescharacteristic
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2211yescharacteristic
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2212yes—
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C26C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C24×C4—24no—
110C24×C4—44no—
111C24×C4—44no—
112C24×C4—42no—
113C24×C4—42no—
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C24×C4C2311yescharacteristic
118C24×C4C2312yes—
119C24×C4C2312yes—
120C24×C4C2311yescharacteristic
121C2×C22⋊Q8—44no—
122C2×C22⋊Q8—42no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158#400—44no—
159#400—44no—
160#397—24no—
161#397—44no—
162#397—42no—
163#397—44no—
164#393—24no—
165#393—42no—
166#385—28no—
167#385—44no—
168#385—44no—
169#385—44no—
170#385—44no—
171#385—44no—
172#385—44no—
173#380—42no—
174#379—28no—
175#379—44no—
176C2×#95—44no—
177C2×#95—44no—
178C2×#95C2312yes—
179C2×#95C2311yescharacteristic
180C2×#95C2311yescharacteristic
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2311yescharacteristic
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—24no—
234C25—24no—
235C25—42no—
236C25—42no—
237C25#4114yes—
238C25C2411yescharacteristic
239C25C2411yescharacteristic
240C25C2411yescharacteristic
241C22×Q8—22no—
242C22×Q8—42no—
243C22×Q8—41no—
244C22×Q8—42no—
245C22×Q8—41no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—41no—
272C23×C4—41no—
273C23×C4—41no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—41no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—432no—
287C23×C4—416no—
288C23×C4—416no—
289C23×C4—432no—
290C23×C4—416no—
291C23×C4#4114yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2412yes—
308C22⋊Q8—416no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—416no—
386C2×C22⋊C4—416no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4#4114yes—
396#95—24no—
397#95—24no—
398#95—22no—
399#95—24no—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—41no—
430#95—42no—
431#95—41no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—28no—
452C24—28no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—28no—
457C24—28no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—216no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—48no—
484C24—44no—
485C24—44no—
486C24—48no—
487C24—44no—
488C24—48no—
489C24—44no—
490C24C2×#4112yes—
491C24C2×#4112yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24C2×#4112yes—
495C24H(5,𝔽2)12yes—
496C24H(5,𝔽2)12yes—
497C24H(5,𝔽2)14yes—
498C24H(5,𝔽2)12yes—
499C242−1+412yes—
500C242−1+414yes—
501C24C2511yescharacteristic
502C2×Q8—44no—
503C2×Q8—82no—
504C2×Q8—84no—
505C2×Q8—82no—
506C2×Q8—84no—
507C22×C4—216no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—48no—
629C22×C4—4128no—
630C22×C4—44no—
631C22×C4—48no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—82no—
642C22×C4—82no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—84no—
646C22×C4—84no—
647C22×C4—84no—
648C22×C4—84no—
649C22×C4C2×#4112yes—
650C22×C4C2×#4112yes—
651C22×C4C2×#4114yes—
652C22×C4H(5,𝔽2)14yes—
653C4⋊C4—44no—
654C4⋊C4—48no—
655C4⋊C4—82no—
656C4⋊C4—84no—
657C4⋊C4—84no—
658C4⋊C4—84no—
659C4⋊C4—84no—
660C4⋊C4—82no—
661C4⋊C4—84no—
662C4⋊C4—84no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C22⋊C4—84no—
681C22⋊C4—84no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—24no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—232no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—432no—
726C23—432no—
727C23—416no—
728C23—416no—
729C23—416no—
730C23—432no—
731C23—416no—
732C23—416no—
733C23—432no—
734C23—416no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—41no—
740C23—41no—
741C23—42no—
742C23—42no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23#52914yes—
756C23#53814yes—
757C23#53914yes—
758C23#53918yes—
759C23H(3,𝔽4)14yes—
760C23#56318yes—
761C23#56314yes—
762C23C22×#4111yescharacteristic
763C23C22×#4111yescharacteristic
764C23C22×#4111yescharacteristic
765C23C2×H(5,𝔽2)11yescharacteristic
766C23C2×H(5,𝔽2)11yescharacteristic
767C23C2×H(5,𝔽2)11yescharacteristic
768C23C2×H(5,𝔽2)12yes—
769C23C2×H(5,𝔽2)12yes—
770C23C2×2−1+411yescharacteristic
771C23C2×2−1+412yes—
772C23#58512yes—
773Q8—88no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—432no—
785C2×C4—416no—
786C2×C4—432no—
787C2×C4—416no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—88no—
883C2×C4—88no—
884C2×C4—816no—
885C22—24no—
886C22—24no—
887C22—28no—
888C22—24no—
889C22—28no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—28no—
894C22—28no—
895C22—28no—
896C22—24no—
897C22—24no—
898C22—28no—
899C22—464no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—44no—
907C22—42no—
908C22—42no—
909C22—44no—
910C22—44no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22#283518yes—
919C22C2×#52911yescharacteristic
920C22C2×#53811yescharacteristic
921C22C2×#53911yescharacteristic
922C22C2×#53912yes—
923C22#345912yes—
924C22#349011yescharacteristic
925C22#349012yes—
926C22#349011yescharacteristic
927C22#349211yescharacteristic
928C22#349211yescharacteristic
929C22#349512yes—
930C22#351312yes—
931C22#352012yes—
932C22C2×H(3,𝔽4)11yescharacteristic
933C22C2×#56312yes—
934C22C2×#56311yescharacteristic
935C22#353211yescharacteristic
936C22#353212yes—
937C22#353311yescharacteristic
938C22#353412yes—
939C22#353512yes—
940C22#353612yes—
941C22#354112yes—
942C4—42no—
943C4—44no—
944C4—44no—
945C4—42no—
946C4—81no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—82no—
953C4—82no—
954C4—81no—
955C4—82no—
956C4—82no—
957C4—82no—
958C2—28no—
959C2—44no—
960C2—44no—
961C2#3499711yescharacteristic
962C2#3499912yes—
963C2C2×#283511yescharacteristic
964C2#3745711yescharacteristic
965C2#3748212yes—
966C2#4545811yescharacteristic
967C2#4546312yes—
968C2#4547411yescharacteristic
969C2#4553112yes—
970C2#4556811yescharacteristic
971C2#4572811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16831C2semidirect
2. #16831C2semidirect
3. #16470C2semidirect
4. #16417C2semidirect
5. #16417C2semidirect
6. #16339C2semidirect
7. #16307C2semidirect
8. #15026C2semidirect
9. #14914C2semidirect
11. #14767C2semidirect
12. #14738C2semidirect
16. #14669C2semidirect
17. #14635C2semidirect
18. #14627C2semidirect
24. C2×#400C22semidirect
25. C2×#400C22semidirect
44. #1446C22semidirect
45. #1446C22semidirect
46. #1445C22semidirect
47. #1445C22semidirect
48. #1444C22semidirect
49. #1444C22semidirect
50. #1443C22semidirect
51. #1443C22semidirect
52. #1443C22semidirect
53. #1443C22semidirect
54. #1443C22semidirect
55. #1443C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect

Maximal subgroups

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

subgroupindex
#168312
#164702
#164172
#163392
#163072
#150262
#149142
#148202
#147672
#147382
#147272
#147172
#146932
#146692
#146352
#146272
C2×C22⋊#952