Finite Group Databasebeta

← #6377748

Subgroups — #6377748

Order 512.

2242 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3215C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3C2×C4×#124C211yesmaximal, characteristic
4#22273C212yesmaximal, complemented
5#22223C212yesmaximal, complemented
6#22150C214yesmaximal, complemented
7#22044C212yesmaximal, complemented
8#22043C212yesmaximal
9#21986C211yesmaximal, characteristic, complemented
10#21866C211yesmaximal, characteristic, complemented
11#21808C211yesmaximal, characteristic
12#21702C212yesmaximal, complemented
13#21655C212yesmaximal, complemented
14#21508C214yesmaximal, complemented
15#21455C212yesmaximal, complemented
16#21453C212yesmaximal
17C4×#432C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×#124C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22#3215C4116yescomplemented
23C2×#497C2212yes—
24C2×#489C2212yes—
25C2×#464C2214yes—
26C2×#451C2212yes—
27C2×#450C2212yes—
28C2×#441C2214yescomplemented
29C2×#440C2214yes—
30C2×#432C2211yescharacteristic
31C2×#432C2211yescharacteristic
32C4×C4⋊Q8C2211yescharacteristic, complemented
33C4×C4⋊Q8C2211yescharacteristic, complemented
34C4×C4⋊Q8C2211yescharacteristic, complemented
35C4×C4⋊Q8C2211yescharacteristic, complemented
36C4×#125—21no—
37C4×#125—21no—
38C4×#124—21no—
39C4×#124—21no—
40C4×#124—21no—
41C4×#124—21no—
42C4×#124C2212yes—
43C4×#124C2212yes—
44C4×#124C2212yes—
45C4×#124C2212yes—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8C2212yes—
49C4×C22⋊Q8C2212yes—
50#2296—21no—
51#2295—21no—
52#2295C2212yescomplemented
53C2×#391C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#388—21no—
56C2×#388—21no—
57#2285C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C42×Q8—21no—
60C42×Q8C2212yescomplemented
61C4×#117—21no—
62C2×C4×C22⋊C4—21no—
63C2×C4×C22⋊C4—21no—
64C2×C43C2211yescharacteristic
65#1993C2212yescomplemented
66#1983C2214yes—
67#1969C2214yescomplemented
68#1968C2214yes—
69#1960C2212yescomplemented
70#1959C2212yes—
71#1959C2212yes—
72#1949C2214yescomplemented
73#1934C2214yes—
74#1933C2214yescomplemented
75#1928C2214yescomplemented
76#1926C2214yes—
77#1880C2214yes—
78#1878C2214yescomplemented
79#1878C2214yescomplemented
80#1877C2214yes—
81#1872C2212yes—
82#1872C2212yes—
83#1865C2214yescomplemented
84#1862C2214yes—
85#1853C2212yes—
86#1852C2212yes—
87#1847C2212yescomplemented
88#1836C2212yescomplemented
89#1805C2214yescomplemented
90#1787C2212yes—
91#1786C2212yes—
92#1767C2212yescomplemented
93C4×C4⋊C8C2212yescomplemented
94#1763C2214yescomplemented
95#1762C2214yes—
96#1749C2212yes—
97C4×C22⋊C8C2212yes—
98#1745C2212yescomplemented
99C4×#97C2212yescomplemented
100C23×Q8C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C22×Q16C2314yes—
104C22×SD16C2314yes—
105#533—24no—
106#533C2×C418yescomplemented
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#125—21no—
110C2×#124—21no—
111C2×#124—21no—
112C2×#124—24no—
113C2×#124C2×C418yes—
114C2×#124C2312yes—
115C2×#124C2312yes—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8C2312yes—
118C2×C4×Q8—21no—
119C2×C4×Q8—21no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8—44no—
124C2×C4×Q8C2312yes—
125C2×C4×Q8C2312yes—
126C2×C4×Q8C2312yes—
127C2×C4×Q8C2312yes—
128C2×C4×Q8C2312yes—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—44no—
132C2×C4×D4C2312yes—
133C2×C4×D4C2312yes—
134C2×#117—21no—
135C2×#117—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C42—21no—
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#497C2×C4116yescomplemented
153#489C2×C4116yescomplemented
154#464C2×C4132yescomplemented
155#451C2×C4116yescomplemented
156#450C2×C4116yes—
157#441—48no—
158#440—48no—
159#432—24no—
160#432C2×C418yescomplemented
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×#97C2312yes—
176C2×#97C2314yes—
177C2×#97C2312yes—
178C2×C4×C8C2314yes—
179#391—21no—
180#391—21no—
181#391—21no—
182#391—21no—
183#391C2312yes—
184#391C2312yes—
185#391C2312yes—
186#391C2312yes—
187#390—21no—
188#390—21no—
189#390C2312yes—
190#390C2312yes—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389C2312yes—
198#389C2312yes—
199#388—22no—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#388—22no—
207#387—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#385—22no—
212#385—22no—
213#384C2311yescharacteristic
214#384C2311yescharacteristic
215#382—21no—
216#382—21no—
217#382—21no—
218#382C2312yes—
219#382C2312yes—
220#380—21no—
221#380C2312yes—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—22no—
227C4×C4⋊C4—22no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—22no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4C2312yes—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248#376—22no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C43—22no—
254C43D411yescharacteristic
255C43D411yescharacteristic
256C43D411yescharacteristic
257C43D411yescharacteristic
258C43C2311yescharacteristic
259C43C2311yescharacteristic
260C43C2311yescharacteristic
261C43C2311yescharacteristic
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#336C2314yes—
267#336C2314yes—
268C25—21no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—22no—
272C22×Q8—42no—
273C22×Q8—42no—
274C22×Q8C22×C414yes—
275C22×Q8C2412yes—
276C22×Q8C2412yes—
277C22×D4—21no—
278C22×D4—22no—
279C22×D4—42no—
280C22×D4—42no—
281C22×D4C22×C414yes—
282C22×D4C2412yes—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C2×Q16—44no—
299C2×Q16—44no—
300C2×Q16C22×C4116yescomplemented
301C2×SD16—44no—
302C2×SD16—44no—
303C2×SD16C22×C4116yes—
304C22×C8C2414yes—
305C22×C8C2414yes—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8C22×C414yescomplemented
309C4⋊Q8C22×C414yescomplemented
310#125—28no—
311#124—28no—
312#124—28no—
313#124—24no—
314#124—24no—
315#124C22×C418yes—
316#124C22×C418yes—
317C22⋊Q8—28no—
318C22⋊Q8—24no—
319C22⋊Q8C22×C418yes—
320C4×Q8—28no—
321C4×Q8—24no—
322C4×Q8—28no—
323C4×Q8—28no—
324C4×Q8—44no—
325C4×Q8—44no—
326C4×Q8—44no—
327C4×Q8—44no—
328C4×Q8—44no—
329C4×Q8—44no—
330C4×Q8C22×C418yescomplemented
331C4×D4—28no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—44no—
335#117—28no—
336#117—44no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C42—24no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—44no—
394C2×C42C22×C414yes—
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42#4114yes—
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424#107—44no—
425#106—44no—
426C4⋊C8—24no—
427C4⋊C8C22×C418yescomplemented
428#103—44no—
429#103—44no—
430#103—44no—
431#103—44no—
432#103C22×C4116yescomplemented
433#102—44no—
434#102—44no—
435#102C22×C4116yes—
436C22⋊C8—24no—
437C22⋊C8C22×C418yes—
438#97—24no—
439#97—28no—
440#97C22×C418yescomplemented
441C4×C8—44no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460C24—24no—
461C24—22no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24C22×D411yescharacteristic
469C2×Q8—24no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—48no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—48no—
483C2×Q8C23×C414yes—
484C2×Q8C23×C414yes—
485C2×D4—24no—
486C2×D4—22no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—48no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—48no—
493C2×D4C23×C414yes—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—816no—
534C22×C4C4×D414yes—
535C22×C4C4×D414yes—
536C22×C4#13714yes—
537C22×C4C23×C412yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C2×#4112yes—
552C22×C4C2511yescharacteristic
553Q16—416no—
554SD16—416no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8C23×C418yes—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—22no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—44no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4C23×C414yes—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—28no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C42—28no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—44no—
621C42—44no—
622C42—44no—
623C42—44no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42C4×D414yes—
628C42C4×D414yes—
629C42C23×C412yes—
630C42C23×C412yes—
631C42C2×#4112yes—
632C42C2×#4112yes—
633C42H(5,𝔽2)14yes—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—48no—
640C23—48no—
641C23—42no—
642C23—42no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23C2×C4×D412yes—
653C23C2×#13712yes—
654C23#57512yes—
655C23C23×D411yescharacteristic
656Q8—28no—
657Q8—28no—
658Q8—48no—
659Q8—48no—
660Q8—44no—
661Q8—44no—
662D4—28no—
663D4—48no—
664D4—44no—
665C2×C4—28no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—28no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—48no—
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—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—88no—
724C2×C4—88no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×C4×D412yes—
728C2×C4C2×C4×D412yes—
729C2×C4C2×C4×D412yes—
730C2×C4C2×C4×D412yes—
731C2×C4C2×C4×D412yes—
732C2×C4#53512yes—
733C2×C4#53512yes—
734C2×C4C2×#13712yes—
735C2×C4C2×#13712yes—
736C2×C4#57512yes—
737C2×C4#57512yes—
738C2×C4C24×C411yescharacteristic
739C2×C4C22×#4111yescharacteristic
740C2×C4C2×H(5,𝔽2)12yes—
741C2×C4#58512yes—
742C8—28no—
743C8—44no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—816no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22C4×#13714yes—
759C22C22×C4×D411yescharacteristic
760C22C2×#53511yescharacteristic
761C22#344911yescharacteristic
762C22C22×#13711yescharacteristic
763C22C2×#57511yescharacteristic
764C22C2×#57511yescharacteristic
765C22C2×#57511yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—44no—
779C4—44no—
780C4—41no—
781C4—44no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4C4×H(5,𝔽2)12yes—
787C4#346012yes—
788C2—24no—
789C2—84no—
790C2C4×#53511yescharacteristic
791C2C2×C4×#13711yescharacteristic
792C2C4×#57511yescharacteristic
793C2#6079911yescharacteristic
794C2#6080411yescharacteristic
795C2#6095911yescharacteristic
796C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#533C2semidirect
4. #22273C2semidirect
5. #22223C2semidirect
6. #22150C2semidirect
7. #22044C2semidirect
9. #21986C2semidirect
10. #21866C2semidirect
12. #21702C2semidirect
13. #21655C2semidirect
14. #21508C2semidirect
15. #21455C2semidirect
17. C4×#432C2semidirect
22. #3215C4semidirect
28. C2×#441C22semidirect
32. C4×C4⋊Q8C22semidirect
33. C4×C4⋊Q8C22semidirect
34. C4×C4⋊Q8C22semidirect
35. C4×C4⋊Q8C22semidirect
52. #2295C22semidirect
60. C42×Q8C22semidirect
65. #1993C22semidirect
67. #1969C22semidirect
69. #1960C22semidirect
72. #1949C22semidirect
74. #1933C22semidirect
75. #1928C22semidirect
78. #1878C22semidirect
79. #1878C22semidirect
83. #1865C22semidirect
87. #1847C22semidirect
88. #1836C22semidirect
89. #1805C22semidirect
92. #1767C22semidirect
93. C4×C4⋊C8C22semidirect
94. #1763C22semidirect
98. #1745C22semidirect
99. C4×#97C22semidirect
106. #533C2×C4semidirect
152. #497C2×C4semidirect
153. #489C2×C4semidirect
154. #464C2×C4semidirect
155. #451C2×C4semidirect
160. #432C2×C4semidirect
300. C2×Q16C22×C4semidirect
308. C4⋊Q8C22×C4semidirect
309. C4⋊Q8C22×C4semidirect
330. C4×Q8C22×C4semidirect
427. C4⋊C8C22×C4semidirect
432. #103C22×C4semidirect
440. #97C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32152
C4×#5332
C2×C4×#1242
#222732
#222232
#221502
#220442
#220432
#219862
#218662
#218082
#217022
#216552
#215082
#214552
#214532
C4×#4322