Finite Group Databasebeta

← #873959

Subgroups — #873959

Order 512.

2686 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2862C211yesmaximal, characteristic
2C2×#2546C211yesmaximal, characteristic
3C2×#2546C211yesmaximal, characteristic
4C2×#2451C211yesmaximal, characteristic
5#16525C214yesmaximal
6#15698C214yesmaximal
7#15333C214yesmaximal
8#15191C211yesmaximal, characteristic
9#15190C211yesmaximal, characteristic
10#15190C211yesmaximal, characteristic
11#15188C211yesmaximal, characteristic
12#15188C211yesmaximal, characteristic
13#15184C211yesmaximal, characteristic
14#14714C211yesmaximal, characteristic
15#14404C214yesmaximal
16#14024C211yesmaximal, characteristic
17#14024C211yesmaximal, characteristic
18#13976C211yesmaximal, characteristic
19C4×#387C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29#2862—28no—
30#2546—28no—
31#2546—28no—
32#2451—28no—
33C2×#398C2214yes—
34C2×#398C2212yes—
35C2×#398C2212yes—
36C2×#398C2212yes—
37C2×#395C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2214yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2212yes—
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#389C2212yes—
55C2×#389C2214yes—
56C2×#389C2211yescharacteristic
57C2×#389C2212yes—
58C2×#389C2211yescharacteristic
59C2×#387C2212yes—
60C2×#387C2212yes—
61C2×#384C2211yescharacteristic
62C2×#382C2214yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C43C2211yescharacteristic
66#1446C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2212yes—
85#1436C2212yes—
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2214yes—
89C4⋊#95C2211yescharacteristic
90#1434C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2312yes—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—42no—
113C2×C4⋊Q8—42no—
114C2×C4⋊Q8—42no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8—42no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—42no—
125C2×C4×Q8—42no—
126C2×C4×Q8—42no—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160#398—28no—
161#398—216no—
162#398—28no—
163#398—28no—
164#395—28no—
165#391—24no—
166#391—24no—
167#391—24no—
168#391—24no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—216no—
174#391—28no—
175#391—42no—
176#391—42no—
177#391—42no—
178#391—42no—
179#391—42no—
180#391D418yes—
181#389—28no—
182#389—28no—
183#389—24no—
184#389—24no—
185#389—216no—
186#387—28no—
187#387Q8116yescomplemented
188#384—42no—
189#382—216no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4D418yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C43—24no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—28no—
255C22×Q8—42no—
256C22×Q8—44no—
257C22×Q8C2×D414yes—
258C22×Q8#4114yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C4⋊Q8—416no—
279C4⋊Q8—416no—
280C4⋊Q8—416no—
281C4⋊Q8—416no—
282C4⋊Q8—416no—
283C4⋊Q8—416no—
284C4⋊Q8—416no—
285C4×Q8—416no—
286C4×Q8—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×Q818yes—
348C2×C4⋊C4C2×Q818yes—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42C2×Q818yes—
382#95—24no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—28no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—42no—
400#95—42no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95C2×D414yes—
409#95C2×D414yes—
410#95C2×D4116yes—
411#95C2×Q818yes—
412#95C2×Q818yes—
413#95C2×Q818yes—
414#95C2×Q818yes—
415C24C2511yescharacteristic
416C2×Q8—28no—
417C2×Q8—28no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8—28no—
422C2×Q8—48no—
423C2×Q8—416no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—48no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—84no—
448C2×Q8—88no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
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—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
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—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4C22×D414yes—
537C22×C4C22×D412yes—
538C22×C4C22×D414yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D414yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×Q814yes—
548C22×C4C22×Q814yes—
549C22×C4C22×Q814yes—
550C22×C4C22×Q814yes—
551C22×C4C22×Q814yes—
552C22×C4C22×Q814yes—
553C22×C4C22×Q814yes—
554C22×C4C2×#4114yes—
555C22×C4C2×#4112yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4H(5,𝔽2)12yes—
559C22×C42−1+414yes—
560C22×C42−1+414yes—
561C22×C42−1+412yes—
562C4⋊C4—28no—
563C4⋊C4—28no—
564C4⋊C4—216no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—416no—
571C4⋊C4—48no—
572C4⋊C4—416no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—416no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—88no—
581C4⋊C4—84no—
582C4⋊C4—84no—
583C4⋊C4C4⋊Q8116yescomplemented
584C42—28no—
585C42—28no—
586C42—28no—
587C42—28no—
588C42—216no—
589C42—48no—
590C42—48no—
591C42—48no—
592C42—44no—
593C42—44no—
594C42—44no—
595C23C23×D411yescharacteristic
596C23C23×D411yescharacteristic
597C23C23×Q812yes—
598C23C22×#4111yescharacteristic
599C23C2×H(5,𝔽2)11yescharacteristic
600C23C2×H(5,𝔽2)11yescharacteristic
601C23C2×H(5,𝔽2)11yescharacteristic
602C23C2×2−1+412yes—
603C23C2×2−1+411yescharacteristic
604C23C2×2−1+412yes—
605C23#58512yes—
606Q8—416no—
607Q8—416no—
608Q8—816no—
609Q8—88no—
610Q8—88no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4C2×C4⋊Q814yes—
713C2×C4C2×C4⋊Q814yes—
714C2×C4C2×C4⋊Q814yes—
715C2×C4#53514yes—
716C2×C4#53614yes—
717C2×C4#53714yes—
718C2×C4#53814yes—
719C2×C4D4214yes—
720C2×C4#54614yes—
721C2×C4#54814yes—
722C2×C4D4×Q818yes—
723C2×C4#56214yes—
724C22C22×C4⋊Q811yescharacteristic
725C22C2×#53511yescharacteristic
726C22C2×#53611yescharacteristic
727C22C2×#53711yescharacteristic
728C22C2×#53811yescharacteristic
729C22C2×D4211yescharacteristic
730C22C2×#54611yescharacteristic
731C22C2×#54811yescharacteristic
732C22C2×D4×Q812yes—
733C22Q8×#4112yes—
734C22#348912yes—
735C22#349911yescharacteristic
736C22#350011yescharacteristic
737C22#350212yes—
738C22#350312yes—
739C22#350312yes—
740C22#350312yes—
741C22#352312yes—
742C22C2×#56211yescharacteristic
743C22#355412yes—
744C22#355612yes—
745C22#356112yes—
746C22#356112yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—28no—
752C4—42no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—44no—
757C4—44no—
758C4—44no—
759C4—44no—
760C4—82no—
761C4—82no—
762C4—82no—
763C4—82no—
764C4—82no—
765C4#267618yes—
766C2#3528111yescharacteristic
767C2D4×C4⋊Q811yescharacteristic
768C2#3647411yescharacteristic
769C2#3739111yescharacteristic
770C2#3767611yescharacteristic
771C2#3917011yescharacteristic
772C2#3959912yes—
773C2#3966312yes—
774C2#4600712yes—
775C2C2×#267611yescharacteristic
776C2#5909612yes—
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
187. #387Q8semidirect
583. C4⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28622
C2×#25462
C2×#24512
#165252
#156982
#153332
#151912
#151902
#151882
#151842
#147142
#144042
#140242
#139762
C4×#3872