Finite Group Databasebeta

← #873871

Subgroups — #873871

Order 512.

2882 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic
2C2×#2566C211yesmaximal, characteristic, complemented
3C2×#2489C211yesmaximal, characteristic, complemented
4C2×#2420C211yesmaximal, characteristic
5#16285C214yesmaximal, complemented
6#15706C214yesmaximal, complemented
7#15288C214yesmaximal, complemented
8#15240C211yesmaximal, characteristic, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15228C211yesmaximal, characteristic, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15130C211yesmaximal, characteristic
14#14682C211yesmaximal, characteristic, complemented
15#14517C214yesmaximal, complemented
16#14027C211yesmaximal, characteristic, complemented
17#14002C211yesmaximal, characteristic, complemented
18#13909C211yesmaximal, characteristic, complemented
19C4×#385C211yesmaximal, characteristic, complemented
20C22×#125C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2850—28no—
27#2566—28no—
28#2489—28no—
29#2420—28no—
30C2×#400C2212yes—
31C2×#397C2212yes—
32C2×#397C2212yes—
33C2×#396C2214yes—
34C2×#394C2214yes—
35C2×#394C2212yes—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#388C2214yes—
47C2×#388C2212yes—
48C2×#386C2214yes—
49C2×#386C2212yes—
50C2×#385C2214yes—
51C2×#385C2212yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2212yes—
58C2×#382C2211yescharacteristic
59C2×#381C2212yes—
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67#1445C2214yes—
68#1445C2214yes—
69#1444C2214yes—
70#1443C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83#1436C2212yes—
84#1436C2212yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89#1434C2214yes—
90C22⋊#95C2214yes—
91C22⋊#95C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C2×#125—24no—
102C2×#125—24no—
103C2×#125—42no—
104C2×#124—24no—
105C2×#124—24no—
106C2×#124—42no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—42no—
110C2×#121—24no—
111C2×#121—24no—
112C2×#121—42no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—42no—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—42no—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155#400—28no—
156#397—28no—
157#397—28no—
158#396—216no—
159#394—28no—
160#394—216no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—42no—
165#391—42no—
166#390—24no—
167#390—24no—
168#390—42no—
169#390D418yes—
170#389—24no—
171#388—216no—
172#388—28no—
173#386—216no—
174#386—28no—
175#385—216no—
176#385—28no—
177#384—24no—
178#384—42no—
179#382—24no—
180#382—24no—
181#382—24no—
182#382—28no—
183#382—42no—
184#381—28no—
185#380—24no—
186#380—24no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—24no—
190C4×C22⋊C4—42no—
191C4×C22⋊C4D418yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C25C2412yes—
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—28no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—42no—
240C22×D4—44no—
241C22×D4C2×D414yes—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4C2×D414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278#125—416no—
279#124—416no—
280C22⋊Q8—416no—
281#121—416no—
282C4×D4—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4C2×D414yes—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
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—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C2×D414yes—
357C2×C22⋊C4C2×D414yes—
358C2×C22⋊C4C2×D4116yes—
359C2×C22⋊C4#4118yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—416no—
378C2×C42—42no—
379C2×C42—44no—
380C2×C42C2×D414yes—
381C2×C42C2×D414yes—
382C2×C42C2×D414yes—
383C2×C42#4114yes—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—28no—
391#95—28no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—28no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—28no—
402#95—44no—
403#95—42no—
404#95—44no—
405#95—44no—
406#95—42no—
407#95—42no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95C2×D414yes—
412#95C2×D414yes—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24C22×D414yes—
433C24C22×D412yes—
434C24C2×#4114yes—
435C24C2511yescharacteristic
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—48no—
447C2×D4—416no—
448C2×D4—48no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—84no—
454C2×D4—88no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—84no—
554C22×C4—88no—
555C22×C4—88no—
556C22×C4C22×D412yes—
557C22×C4C22×D414yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4114yes—
568C22×C4C2×#4112yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C42−1+412yes—
572C22×C42−1+412yes—
573C4⋊C4—28no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—88no—
585C4⋊C4—84no—
586C4⋊C4—88no—
587C22⋊C4—28no—
588C22⋊C4—44no—
589C22⋊C4—416no—
590C22⋊C4—48no—
591C22⋊C4—416no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—416no—
596C22⋊C4—48no—
597C22⋊C4—84no—
598C22⋊C4—84no—
599C22⋊C4—88no—
600C22⋊C4—84no—
601C42—28no—
602C42—28no—
603C42—28no—
604C42—28no—
605C42—48no—
606C42—48no—
607C42—44no—
608C42—44no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—28no—
625C23—28no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—44no—
642C23—44no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—42no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23#53214yes—
655C23C23×D411yescharacteristic
656C23C23×D411yescharacteristic
657C23C22×#4112yes—
658C23C22×#4111yescharacteristic
659C23C2×H(5,𝔽2)11yescharacteristic
660C23C2×H(5,𝔽2)11yescharacteristic
661C23C2×2−1+411yescharacteristic
662C23C2×2−1+411yescharacteristic
663C23#58512yes—
664C23#58512yes—
665C23#58512yes—
666Q8—88no—
667D4—416no—
668D4—816no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—28no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—432no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—416no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—816no—
764C2×C4#53614yes—
765C2×C4#53714yes—
766C2×C4#54214yes—
767C2×C4D4214yes—
768C2×C4#54614yes—
769C2×C4#54714yes—
770C2×C4#56214yes—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—44no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—48no—
786C22—48no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—84no—
791C22—82no—
792C22—84no—
793C22C2×#53211yescharacteristic
794C22C2×#53611yescharacteristic
795C22C2×#53711yescharacteristic
796C22#344911yescharacteristic
797C22C2×#54211yescharacteristic
798C22C2×D4211yescharacteristic
799C22C2×#54611yescharacteristic
800C22C2×#54711yescharacteristic
801C22D4×#4112yes—
802C22#347512yes—
803C22#348512yes—
804C22#349312yes—
805C22#350011yescharacteristic
806C22#350011yescharacteristic
807C22#350512yes—
808C22#350712yes—
809C22#351412yes—
810C22#351512yes—
811C22C2×#56211yescharacteristic
812C22#353912yes—
813C22#355712yes—
814C22#356212yes—
815C22#356512yes—
816C4—42no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—44no—
821C4—42no—
822C4—44no—
823C4—44no—
824C4—44no—
825C4—42no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4#267218yes—
833C2—44no—
834C2—84no—
835C2#3510311yescharacteristic
836C2#3612411yescharacteristic
837C2#3618411yescharacteristic
838C2#3742011yescharacteristic
839C2#3768211yescharacteristic
840C2#3787111yescharacteristic
841C2#3988012yes—
842C2#3993012yes—
843C2#4568212yes—
844C2C2×#267211yescharacteristic
845C2#5902012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2566C2semidirect
3. C2×#2489C2semidirect
5. #16285C2semidirect
6. #15706C2semidirect
7. #15288C2semidirect
8. #15240C2semidirect
9. #15237C2semidirect
10. #15228C2semidirect
11. #15217C2semidirect
12. #15182C2semidirect
14. #14682C2semidirect
15. #14517C2semidirect
16. #14027C2semidirect
17. #14002C2semidirect
18. #13909C2semidirect
19. C4×#385C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×#25662
C2×#24892
C2×#24202
#162852
#157062
#152882
#152402
#152372
#152282
#152172
#151822
#151302
#146822
#145172
#140272
#140022
#139092
C4×#3852