Finite Group Databasebeta

← #796914

Subgroups — #796914

Order 512.

4050 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2354C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3#16392C212yesmaximal, complemented
4#15343C214yesmaximal, complemented
5#15282C214yesmaximal, complemented
6#15195C211yesmaximal, characteristic, complemented
7#15148C211yesmaximal, characteristic, complemented
8#15136C211yesmaximal, characteristic, complemented
9#15113C212yesmaximal, complemented
10#14734C212yesmaximal, complemented
11#14022C212yesmaximal, complemented
12#14018C212yesmaximal, complemented
13#13973C212yesmaximal, complemented
14#13916C211yesmaximal, characteristic, complemented
15#13902C212yesmaximal
16#13868C212yesmaximal, complemented
17C4×#399C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yescomplemented
22C23×C22⋊C4C2212yes—
23C2×#399C2211yescharacteristic
24C2×#399C2212yescomplemented
25C2×#397C2214yescomplemented
26#2354—28no—
27D4×C22⋊C4—28no—
28C2×#390C2211yescharacteristic
29C2×#390C2212yes—
30C2×#390C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2212yes—
33C2×#390C2212yes—
34C2×#389C2212yescomplemented
35C2×#388C2214yescomplemented
36C2×#388C2214yescomplemented
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#385C2214yescomplemented
40C2×#384C2211yescharacteristic, complemented
41C2×#381C2212yescomplemented
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yescomplemented
45C2×#379C2212yes—
46C2×#379C2214yes—
47C2×#379C2214yes—
48C2×C4×C4⋊C4C2211yescharacteristic, complemented
49C2×C4×C4⋊C4C2212yescomplemented
50C2×C4×C4⋊C4C2212yescomplemented
51C2×C4×C22⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2212yes—
53#1445C2211yescharacteristic, complemented
54#1445C2212yescomplemented
55#1444C2211yescharacteristic, complemented
56#1442C2212yescomplemented
57#1442C2214yescomplemented
58#1442C2212yescomplemented
59#1440C2214yescomplemented
60#1440C2214yescomplemented
61#1439C2211yescharacteristic
62#1439C2212yes—
63#1439C2212yes—
64#1439C2212yes—
65#1439C2214yes—
66#1439C2212yescomplemented
67#1439C2214yescomplemented
68#1439C2212yescomplemented
69#1439C2212yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1438C2214yes—
74#1438C2214yes—
75#1437C2214yes—
76#1437C2214yescomplemented
77C4⋊#95C2212yescomplemented
78C4⋊#95C2211yescharacteristic, complemented
79C4⋊#95C2212yescomplemented
80C4⋊#95C2212yescomplemented
81#1434C2214yescomplemented
82C22⋊#95C2212yescomplemented
83C22⋊#95C2214yescomplemented
84C4×#95C2211yescharacteristic, complemented
85C26C2312yes—
86C23×D4—24no—
87C23×D4—24no—
88C23×D4—28no—
89C23×D4—24no—
90C23×D4—44no—
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C23×D4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2312yes—
97C2×C4×D4—28no—
98C2×C4×D4—24no—
99C2×C4×D4—44no—
100C2×C4×D4D418yes—
101C2×#117—28no—
102C2×#117—48no—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C22⋊C4—28no—
115C22×C22⋊C4—28no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C42C2311yescharacteristic
138C22×C42C2312yes—
139C22×C42C2312yes—
140C22×C42C2314yes—
141C22×C42C2311yescharacteristic
142#399—24no—
143#399—44no—
144#397—48no—
145#390—28no—
146#390—28no—
147#390—28no—
148#390—24no—
149#390—24no—
150#390—44no—
151#389—44no—
152#388—216no—
153#388—48no—
154#386—28no—
155#386—28no—
156#385—48no—
157#384—24no—
158#381—44no—
159#380—28no—
160#380—28no—
161#380—24no—
162#379—28no—
163#379—48no—
164#379—48no—
165C4×C4⋊C4—28no—
166C4×C4⋊C4—24no—
167C4×C4⋊C4—44no—
168C4×C22⋊C4—24no—
169C4×C22⋊C4—44no—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2311yescharacteristic
173C2×#95C2312yes—
174C2×#95C2311yescharacteristic
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2311yescharacteristic
180C2×#95C2311yescharacteristic
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C25—24no—
193C25—24no—
194C25—24no—
195C25—24no—
196C25—28no—
197C25—24no—
198C25—42no—
199C25—44no—
200C25—42no—
201C25—44no—
202C25—44no—
203C25C2412yes—
204C25C2412yes—
205C25C2411yescharacteristic
206C22×D4—232no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—28no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—22no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—432no—
219C22×D4—44no—
220C22×D4—432no—
221C22×D4—416no—
222C22×D4—416no—
223C22×D4C2×D414yes—
224C22×D4#4114yes—
225C22×D4#4118yes—
226C23×C4—28no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—44no—
236C23×C4—42no—
237C23×C4—44no—
238C23×C4—44no—
239C23×C4C2×D418yes—
240C23×C4#4114yes—
241C23×C4C2412yes—
242C23×C4C2414yes—
243C23×C4C2414yes—
244C23×C4C2411yescharacteristic
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C4×D4—232no—
256C4×D4—416no—
257#117—432no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4C2×D414yes—
286C2×C22⋊C4—28no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—28no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—28no—
293C2×C22⋊C4—28no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—432no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4C2×D418yes—
342C2×C22⋊C4#4114yes—
343C2×C42—24no—
344C2×C42—28no—
345C2×C42—22no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—28no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—44no—
355C2×C42C2×D414yes—
356#95—22no—
357#95—22no—
358#95—28no—
359#95—24no—
360#95—24no—
361#95—28no—
362#95—22no—
363#95—22no—
364#95—24no—
365#95—28no—
366#95—24no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378C24—21no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—24no—
385C24—24no—
386C24—21no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—22no—
393C24—22no—
394C24—21no—
395C24—216no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—22no—
403C24—24no—
404C24—22no—
405C24—22no—
406C24—48no—
407C24—416no—
408C24—416no—
409C24—48no—
410C24—48no—
411C24—48no—
412C24—416no—
413C24—416no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—48no—
418C24—84no—
419C24—84no—
420C24—88no—
421C24—88no—
422C24—88no—
423C24—88no—
424C24—88no—
425C24—88no—
426C24—88no—
427C24—88no—
428C24C22×D414yes—
429C24C2×#4114yes—
430C24C2×#4118yes—
431C24C2×#4112yes—
432C24C2×#4112yes—
433C242−1+412yes—
434C24C2511yescharacteristic
435C2×D4—216no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—216no—
440C2×D4—216no—
441C2×D4—216no—
442C2×D4—416no—
443C2×D4—4128no—
444C2×D4—416no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—48no—
450C2×D4#123116yes—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—216no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—216no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—48no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—88no—
532C22×C4—84no—
533C22×C4—88no—
534C22×C4C22×D414yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4114yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4H(5,𝔽2)14yes—
545C22×C4H(5,𝔽2)14yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C4H(5,𝔽2)14yes—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C4⋊C4—84no—
558C4⋊C4—88no—
559C22⋊C4—216no—
560C22⋊C4—28no—
561C22⋊C4—48no—
562C22⋊C4—44no—
563C22⋊C4—416no—
564C22⋊C4—416no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—416no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—84no—
572C22⋊C4—84no—
573C22⋊C4—88no—
574C22⋊C4—88no—
575C22⋊C4—88no—
576C22⋊C4—88no—
577C22⋊C4—88no—
578C22⋊C4—88no—
579C42—28no—
580C42—416no—
581C42—48no—
582C42—44no—
583C42—48no—
584C23—22no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—24no—
589C23—24no—
590C23—28no—
591C23—28no—
592C23—22no—
593C23—28no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—22no—
600C23—24no—
601C23—28no—
602C23—24no—
603C23—28no—
604C23—24no—
605C23—22no—
606C23—28no—
607C23—24no—
608C23—24no—
609C23—28no—
610C23—24no—
611C23—28no—
612C23—24no—
613C23—432no—
614C23—432no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—44no—
624C23—42no—
625C23—44no—
626C23—44no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—44no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—44no—
639C23—42no—
640C23—44no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—832no—
654C23—816no—
655C23—816no—
656C23—816no—
657C23—832no—
658C23—832no—
659C23—816no—
660C23—832no—
661C23—816no—
662C23C2×#12318yes—
663C23#55614yes—
664C23C23×D411yescharacteristic
665C23C22×#4112yes—
666C23C22×#4111yescharacteristic
667C23C22×#4111yescharacteristic
668C23C22×#4111yescharacteristic
669C23C2×H(5,𝔽2)12yes—
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×H(5,𝔽2)12yes—
672C23C2×H(5,𝔽2)12yes—
673C23C2×2−1+411yescharacteristic
674C23#58511yescharacteristic
675D4—232no—
676D4—432no—
677D4—416no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
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—44no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—416no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—816no—
757C2×C4C2×#12314yes—
758C2×C4#52514yes—
759C2×C4#53514yes—
760C2×C4#54614yes—
761C2×C4#55118yes—
762C2×C4#55118yes—
763C22—28no—
764C22—24no—
765C22—28no—
766C22—28no—
767C22—28no—
768C22—48no—
769C22—44no—
770C22—48no—
771C22—44no—
772C22—42no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—44no—
777C22—42no—
778C22—48no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—48no—
784C22—44no—
785C22—48no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—48no—
790C22—864no—
791C22—84no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—84no—
796C22—82no—
797C22C22×#12311yescharacteristic
798C22C2×#52511yescharacteristic
799C22C2×#53511yescharacteristic
800C22C2×#54611yescharacteristic
801C22C2×#55112yes—
802C22C2×#55112yes—
803C22C2×#55611yescharacteristic
804C22#347511yescharacteristic
805C22#348112yes—
806C22#348411yescharacteristic
807C22#348911yescharacteristic
808C22#349811yescharacteristic
809C22#350611yescharacteristic
810C22#350812yes—
811C22#351312yes—
812C22#351912yes—
813C22#351912yes—
814C22#351912yes—
815C22#352011yescharacteristic
816C22#352012yes—
817C22#353612yes—
818C22#354212yes—
819C22#354912yes—
820C4—24no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—44no—
825C4—42no—
826C4—44no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—84no—
831C4—84no—
832C4—81no—
833C4#248218yes—
834C2—48no—
835C2—44no—
836C2—84no—
837C2C2×#248211yescharacteristic
838C2#3574111yescharacteristic
839C2#3598711yescharacteristic
840C2#3616111yescharacteristic
841C2#3623611yescharacteristic
842C2#3895311yescharacteristic
843C2#4247811yescharacteristic
844C2#4495912yes—
845C2#4508812yes—
846C2#5938212yes—
847C2#5942412yes—
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
1. C2×#2354C2semidirect
3. #16392C2semidirect
4. #15343C2semidirect
5. #15282C2semidirect
6. #15195C2semidirect
7. #15148C2semidirect
8. #15136C2semidirect
9. #15113C2semidirect
10. #14734C2semidirect
11. #14022C2semidirect
12. #14018C2semidirect
13. #13973C2semidirect
14. #13916C2semidirect
16. #13868C2semidirect
17. C4×#399C2semidirect
21. C22×#117C22semidirect
24. C2×#399C22semidirect
25. C2×#397C22semidirect
34. C2×#389C22semidirect
35. C2×#388C22semidirect
36. C2×#388C22semidirect
39. C2×#385C22semidirect
40. C2×#384C22semidirect
41. C2×#381C22semidirect
44. C2×#380C22semidirect
48. C2×C4×C4⋊C4C22semidirect
49. C2×C4×C4⋊C4C22semidirect
50. C2×C4×C4⋊C4C22semidirect
53. #1445C22semidirect
54. #1445C22semidirect
55. #1444C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1440C22semidirect
60. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
76. #1437C22semidirect
77. C4⋊#95C22semidirect
78. C4⋊#95C22semidirect
79. C4⋊#95C22semidirect
80. C4⋊#95C22semidirect
81. #1434C22semidirect
82. C22⋊#95C22semidirect
83. C22⋊#95C22semidirect
84. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#23542
C2×D4×C22⋊C42
#163922
#153432
#152822
#151952
#151482
#151362
#151132
#147342
#140222
#140182
#139732
#139162
#139022
#138682
C4×#3992