Finite Group Databasebeta

← #525263

Subgroups — #525263

Order 512.

3654 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×#2322C212yesmaximal
4C22×#389C211yesmaximal, characteristic, complemented
5#14697C211yesmaximal, characteristic, complemented
6#14548C214yesmaximal, complemented
7#14526C214yesmaximal, complemented
8#14263C212yesmaximal, complemented
9#14133C212yesmaximal, complemented
10#14130C212yesmaximal, complemented
11#14005C212yesmaximal, complemented
12#13994C212yesmaximal, complemented
13#13972C212yesmaximal, complemented
14#13968C212yesmaximal
15#13904C211yesmaximal, characteristic, complemented
16C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
17C4×#386C211yesmaximal, characteristic
18C22×#123C2212yes—
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C23×C4⋊C4C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2486C4116yescomplemented
27C2×#398C2212yes—
28C2×#397C2212yes—
29D4×C4⋊C4—28no—
30#2322—216no—
31C2×#389—28no—
32C2×#389C2214yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2214yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#388C2214yes—
40C2×#387C2214yes—
41C2×#386C2211yescharacteristic
42C2×#386C2211yescharacteristic
43C2×#385C2214yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#384C2211yescharacteristic
48C2×#381C2212yes—
49C2×#381C2212yes—
50C2×#381C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C22×#95C2212yes—
61#1445C2214yes—
62#1444C2214yes—
63#1444C2214yes—
64#1443C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1440C2214yes—
70#1437C2212yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80#1434C2214yes—
81C22⋊#95C2214yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2211yescharacteristic
85C22⋊#95C2211yescharacteristic
86C4×#95C2212yes—
87C23×D4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2312yes—
95C2×#123—28no—
96C2×#123—28no—
97C2×#123C2×C4116yes—
98C2×C4×D4—24no—
99C2×C4×D4—24no—
100C2×C4×D4—28no—
101C2×C4×D4—28no—
102C2×C4×D4—44no—
103C2×C4×D4C2×C418yes—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—28no—
107C22×C4⋊C4—28no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—44no—
110C22×C4⋊C4—44no—
111C22×C4⋊C4—44no—
112C22×C4⋊C4C2×C418yescomplemented
113C22×C4⋊C4D418yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C42—24no—
141C22×C42—44no—
142C22×C42C2312yes—
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2311yescharacteristic
146C22×C42C2312yes—
147C22×C42C2314yes—
148#398C2×C4116yescomplemented
149#397C2×C4116yescomplemented
150#389—28no—
151#389—28no—
152#389—28no—
153#389—216no—
154#389—216no—
155#389—44no—
156#389C2×C4116yescomplemented
157#388—216no—
158#387—216no—
159#386—24no—
160#386D418yes—
161#385—28no—
162#385—28no—
163#385—28no—
164#385—216no—
165#384—24no—
166#381—28no—
167#381—44no—
168#381C2×C4116yescomplemented
169#380—24no—
170#380—24no—
171#380C2×C4116yescomplemented
172#380C2×C418yescomplemented
173C4×C4⋊C4—24no—
174C4×C4⋊C4—44no—
175C4×C22⋊C4—24no—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—44no—
178C2×#95—28no—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C25C2411yescharacteristic
205C25C2411yescharacteristic
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4C22×C414yes—
211C22×D4C2×D414yes—
212C22×D4#4114yes—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—22no—
217C23×C4—24no—
218C23×C4—22no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—44no—
239C23×C4—44no—
240C23×C4—42no—
241C23×C4—44no—
242C23×C4—44no—
243C23×C4C22×C418yes—
244C23×C4C22×C414yes—
245C23×C4C22×C414yes—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2×D418yes—
249C23×C4#4114yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2414yes—
254C23×C4C2411yescharacteristic
255C23×C4C2414yes—
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265#123—264no—
266C4×D4—232no—
267C4×D4—432no—
268C2×C4⋊C4—232no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—416no—
295C2×C4⋊C4—416no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—432no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4C22×C418yes—
306C2×C4⋊C4C22×C418yes—
307C2×C4⋊C4C22×C414yes—
308C2×C4⋊C4C22×C4116yes—
309C2×C4⋊C4C22×C418yes—
310C2×C4⋊C4C2×D414yes—
311C2×C4⋊C4C2×D414yes—
312C2×C4⋊C4C2×D418yes—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4C22×C414yes—
338C2×C22⋊C4C22×C414yes—
339C2×C22⋊C4C22×C418yes—
340C2×C22⋊C4C22×C4116yes—
341C2×C22⋊C4C2×D414yes—
342C2×C22⋊C4C2×D418yes—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—28no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—416no—
359C2×C42—44no—
360C2×C42—44no—
361C2×C42C22×C414yes—
362#95—28no—
363#95—28no—
364#95—28no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—44no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95C22×C4116yes—
384#95C22×C418yes—
385#95C22×C4116yes—
386#95C2×D418yes—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—21no—
395C24—22no—
396C24—22no—
397C24—21no—
398C24—22no—
399C24C23×C412yes—
400C24C23×C412yes—
401C24C22×D412yes—
402C24C22×D412yes—
403C24C22×D412yes—
404C24C2×#4112yes—
405C24C2×#4112yes—
406C24C2×#4112yes—
407C24H(5,𝔽2)12yes—
408C242−1+412yes—
409C24C2511yescharacteristic
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4C4×D4116yes—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—216no—
424C22×C4—28no—
425C22×C4—28no—
426C22×C4—216no—
427C22×C4—28no—
428C22×C4—216no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—28no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—216no—
479C22×C4—28no—
480C22×C4—216no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—44no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—48no—
517C22×C4—84no—
518C22×C4—88no—
519C22×C4—88no—
520C22×C4—88no—
521C22×C4—88no—
522C22×C4C4×D4116yes—
523C22×C4C23×C412yes—
524C22×C4C23×C412yes—
525C22×C4C23×C418yes—
526C22×C4C23×C418yes—
527C22×C4C23×C412yes—
528C22×C4C23×C412yes—
529C22×C4C23×C412yes—
530C22×C4C22×D414yes—
531C22×C4C22×D414yes—
532C22×C4C22×D414yes—
533C22×C4C22×D414yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4H(5,𝔽2)14yes—
541C22×C42−1+414yes—
542C22×C42−1+414yes—
543C4⋊C4—216no—
544C4⋊C4—216no—
545C4⋊C4—28no—
546C4⋊C4—232no—
547C4⋊C4—216no—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—48no—
551C4⋊C4—416no—
552C4⋊C4—416no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—84no—
558C4⋊C4—88no—
559C22⋊C4—28no—
560C22⋊C4—216no—
561C22⋊C4—232no—
562C22⋊C4—28no—
563C22⋊C4—28no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—44no—
569C42—28no—
570C42—48no—
571C42—48no—
572C42—48no—
573C42—48no—
574C42—88no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23—22no—
579C23—24no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—24no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23C2×C4×D414yes—
614C23C2×C4×D414yes—
615C23C2×C4×D414yes—
616C23#52014yes—
617C23D4214yes—
618C23#54714yes—
619C23#54814yes—
620C23#55314yes—
621C23C24×C411yescharacteristic
622C23C23×D411yescharacteristic
623C23C23×D411yescharacteristic
624C23C22×#4111yescharacteristic
625C23C22×#4111yescharacteristic
626C23C2×H(5,𝔽2)12yes—
627C23C2×H(5,𝔽2)11yescharacteristic
628C23C2×2−1+412yes—
629C23C2×2−1+411yescharacteristic
630C23C2×2−1+412yes—
631C23#58512yes—
632D4—232no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—232no—
644C2×C4—22no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—24no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—416no—
670C2×C4—416no—
671C2×C4—432no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—416no—
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—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—816no—
721C2×C4—816no—
722C2×C4C2×C4×D414yes—
723C2×C4C2×C4×D414yes—
724C2×C4C2×C4×D414yes—
725C2×C4#52018yes—
726C2×C4#53414yes—
727C2×C4#53614yes—
728C2×C4#53918yes—
729C22—28no—
730C22—24no—
731C22—28no—
732C22—28no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—28no—
740C22—24no—
741C22—42no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22#236118yes—
751C22C22×C4×D411yescharacteristic
752C22C22×C4×D411yescharacteristic
753C22C2×#52012yes—
754C22C2×#52011yescharacteristic
755C22C4×2−1+412yes—
756C22C2×#53411yescharacteristic
757C22C2×#53611yescharacteristic
758C22C2×#53912yes—
759C22C2×D4211yescharacteristic
760C22C2×#54711yescharacteristic
761C22C2×#54811yescharacteristic
762C22C2×#55311yescharacteristic
763C22#348511yescharacteristic
764C22#348611yescharacteristic
765C22#349612yes—
766C22#349912yes—
767C22#350712yes—
768C22#351512yes—
769C22#352012yes—
770C22#353812yes—
771C22#354212yes—
772C22#354412yes—
773C22#356312yes—
774C4—24no—
775C4—24no—
776C4—48no—
777C4—42no—
778C4—48no—
779C4—44no—
780C4—44no—
781C4—44no—
782C4—44no—
783C4—44no—
784C4—42no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#232218yescomplemented
789C2—28no—
790C2—44no—
791C2C2×#232211yescharacteristic
792C2C2×#236111yescharacteristic
793C2#3426611yescharacteristic
794C2#3430812yes—
795C2#3446512yes—
796C2#3912111yescharacteristic
797C2#3912211yescharacteristic
798C2#3919012yes—
799C2#3933711yescharacteristic
800C2#3933811yescharacteristic
801C2#3937612yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#389C2semidirect
5. #14697C2semidirect
6. #14548C2semidirect
7. #14526C2semidirect
8. #14263C2semidirect
9. #14133C2semidirect
10. #14130C2semidirect
11. #14005C2semidirect
12. #13994C2semidirect
13. #13972C2semidirect
15. #13904C2semidirect
16. C22⋊C4×C4⋊C4C2semidirect
26. #2486C4semidirect
112. C22×C4⋊C4C2×C4semidirect
148. #398C2×C4semidirect
149. #397C2×C4semidirect
156. #389C2×C4semidirect
168. #381C2×C4semidirect
171. #380C2×C4semidirect
172. #380C2×C4semidirect
788. C4#2322semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×D4×C4⋊C42
C2×#23222
C22×#3892
#146972
#145482
#145262
#142632
#141332
#141302
#140052
#139942
#139722
#139682
#139042
C22⋊C4×C4⋊C42
C4×#3862