Finite Group Databasebeta

← #6375739

Subgroups — #6375739

Order 512.

2218 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3077C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3C2×#2293C211yesmaximal, characteristic
4#22120C214yesmaximal, complemented
5#22117C212yesmaximal, complemented
6#22116C212yesmaximal, complemented
7#22114C214yesmaximal, complemented
8#22111C212yesmaximal, complemented
9#22110C212yesmaximal, complemented
10#21312C211yesmaximal, characteristic, complemented
11#21170C211yesmaximal, characteristic, complemented
12#21159C212yesmaximal, complemented
13#21095C212yesmaximal
14#21060C212yesmaximal
15#21034C212yesmaximal, complemented
16#20646C211yesmaximal, characteristic
17C4×#423C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117—21no—
21#3077C4116yescomplemented
22C2×#478C2214yes—
23C2×#476C2212yes—
24C2×#474C2212yes—
25C2×#428C2212yes—
26C2×#428C2212yes—
27C2×#423C2211yescharacteristic
28C2×#423C2211yescharacteristic
29C2×#418C2212yes—
30C2×#418C2212yes—
31C2×C4×M16C2212yes—
32C4×C4⋊Q8C2211yescharacteristic, complemented
33C4×C4⋊Q8C2211yescharacteristic, complemented
34C4×C4⋊Q8C2211yescharacteristic, complemented
35C4×C4⋊Q8C2211yescharacteristic, complemented
36C4×#125C2212yescomplemented
37C4×#125C2212yescomplemented
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8—21no—
42#2296C2212yes—
43#2295—21no—
44#2295—21no—
45#2293—21no—
46#2293—21no—
47#2293—21no—
48#2293—21no—
49#2293C2212yes—
50#2293C2212yes—
51#2293C2212yes—
52#2293C2212yes—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388—21no—
58C2×#388—21no—
59#2285C2211yescharacteristic
60C42×Q8—21no—
61C42×Q8—21no—
62C4×#117C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4—21no—
65C2×C43C2211yescharacteristic
66#1989C2214yescomplemented
67#1988C2212yescomplemented
68#1987C2212yescomplemented
69#1949C2214yescomplemented
70#1948C2212yescomplemented
71#1947C2212yescomplemented
72#1944C2214yescomplemented
73#1943C2214yescomplemented
74#1942C2214yescomplemented
75#1941C2214yescomplemented
76#1936C2214yes—
77#1936C2214yes—
78#1934C2214yes—
79#1934C2214yes—
80#1926C2214yes—
81#1926C2214yes—
82#1925C2214yes—
83#1925C2214yes—
84#1921C2214yescomplemented
85#1920C2214yescomplemented
86#1919C2214yescomplemented
87#1918C2214yescomplemented
88#1804C2214yes—
89#1802C2212yes—
90#1802C2212yes—
91#1767C2212yescomplemented
92#1767C2212yescomplemented
93C4×C4⋊C8C2212yescomplemented
94C4×C4⋊C8C2212yescomplemented
95#1736C2212yes—
96#1736C2212yes—
97#1736C2212yes—
98#1736C2212yes—
99#1728C2212yes—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C22×M16C2312yes—
103C22×M16C2312yes—
104#533—24no—
105#533C2×C418yes—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#125C2312yes—
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—21no—
111C2×C4×Q8—21no—
112C2×C4×Q8—21no—
113C2×C4×Q8—21no—
114C2×C4×Q8—21no—
115C2×C4×Q8—21no—
116C2×C4×Q8—21no—
117C2×C4×D4—21no—
118C2×C4×D4—21no—
119C2×C4×D4—24no—
120C2×C4×D4C2×C418yes—
121C2×C4×D4C2312yes—
122C2×C4×D4C2312yes—
123C2×#117—22no—
124C2×#117—22no—
125C2×#117—22no—
126C2×#117—22no—
127C2×#117—48no—
128C2×#117C2312yes—
129C2×#117C2312yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C42—21no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148#478C2×C4132yescomplemented
149#476C2×C4116yescomplemented
150#474C2×C4116yescomplemented
151#428—44no—
152#428C2×C4116yes—
153C2×#107C2314yes—
154C2×#107C2314yes—
155C2×#106C2314yes—
156C2×#106C2314yes—
157#423—24no—
158#423C2×C418yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163#418—44no—
164#418C2×C4116yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C4×M16—44no—
170C2×#97C2314yes—
171C2×C4×C8C2314yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#389C2312yes—
197#389C2312yes—
198#389C2312yes—
199#389C2312yes—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#387—22no—
212#385—22no—
213#385—22no—
214#384C2311yescharacteristic
215#384C2311yescharacteristic
216#382C2312yes—
217#380—21no—
218#380—21no—
219C4×C4⋊C4—22no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4—22no—
222C4×C4⋊C4—22no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—22no—
232C4×C4⋊C4—22no—
233C4×C4⋊C4C2312yes—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245#376—22no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C43—22no—
250C43D411yescharacteristic
251C43D411yescharacteristic
252C43D411yescharacteristic
253C43D411yescharacteristic
254C43C2311yescharacteristic
255C43C2311yescharacteristic
256C43C2311yescharacteristic
257C43C2311yescharacteristic
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#336C2314yes—
267#336C2314yes—
268C25—21no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×D4—21no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4C22×C414yes—
278C22×D4C2412yes—
279C23×C4—21no—
280C23×C4—28no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2411yescharacteristic
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16C22×C418yes—
300C22×C8C2414yes—
301C22×C8C2414yes—
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304C4⋊Q8C22×C414yes—
305C4⋊Q8C22×C414yes—
306#125—24no—
307#125C22×C418yes—
308C22⋊Q8—28no—
309C22⋊Q8—28no—
310C4×Q8—28no—
311C4×Q8—28no—
312C4×Q8—44no—
313C4×Q8—44no—
314C4×Q8—44no—
315C4×Q8—44no—
316C4×D4—28no—
317C4×D4—28no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4C22×C418yes—
321C4×D4C22×C418yes—
322#117—24no—
323#117—24no—
324#117—24no—
325#117—48no—
326#117—48no—
327#117—48no—
328#117—48no—
329#117C22×C418yes—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
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—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4C22×C414yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—28no—
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—22no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—44no—
398C2×C42C22×C414yes—
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×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42#4114yes—
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428#107—44no—
429#107C22×C4116yes—
430#106—44no—
431#106C22×C4116yes—
432C4⋊C8—24no—
433C4⋊C8—24no—
434C4⋊C8C22×C418yes—
435C4⋊C8C22×C418yes—
436#102—44no—
437#102—44no—
438#102C22×C4116yes—
439#102C22×C4116yes—
440#97—44no—
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—
458C24—24no—
459C24—22no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24C22×D411yescharacteristic
467C2×Q8—24no—
468C2×Q8—24no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×D4—24no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4C23×C414yes—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—432no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4C4×D414yes—
526C22×C4C4×D414yes—
527C22×C4C23×C412yes—
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C2×#4112yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C42−1+412yes—
544C22×C42−1+412yes—
545C22×C42−1+412yes—
546C22×C4C2511yescharacteristic
547M16—216no—
548M16—48no—
549C2×C8—24no—
550C2×C8—24no—
551C2×C8—24no—
552C2×C8—24no—
553C2×C8—24no—
554C2×C8C23×C418yes—
555C4⋊C4—24no—
556C4⋊C4—28no—
557C4⋊C4—28no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—42no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4C23×C414yes—
586C4⋊C4C23×C414yes—
587C4⋊C4C23×C414yes—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C42—28no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42C4×D414yes—
636C42C4×D414yes—
637C42AGL(1,ℤ/8)14yes—
638C42C23×C412yes—
639C42C23×C412yes—
640C42C2×#4112yes—
641C42C2×#4112yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—24no—
647C23—48no—
648C23—48no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23C2×C4×D412yes—
661C23#53612yes—
662C23#53712yes—
663C23C23×D411yescharacteristic
664Q8—48no—
665Q8—48no—
666D4—24no—
667D4—24no—
668D4—48no—
669D4—42no—
670D4—42no—
671C2×C4—21no—
672C2×C4—21no—
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—28no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—416no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—416no—
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—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4C2×C4×D412yes—
730C2×C4C2×C4×D412yes—
731C2×C4C2×C4×D412yes—
732C2×C4C2×C4×D412yes—
733C2×C4C2×C4×D412yes—
734C2×C4#51914yes—
735C2×C4#52014yes—
736C2×C4#53612yes—
737C2×C4#53712yes—
738C2×C4#54114yes—
739C2×C4#54214yes—
740C2×C4C2×AGL(1,ℤ/8)12yes—
741C2×C4C2×AGL(1,ℤ/8)12yes—
742C2×C4C2×AGL(1,ℤ/8)12yes—
743C2×C4#57512yes—
744C2×C4#57512yes—
745C2×C4#57512yes—
746C2×C4C24×C411yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C2×C4C2×2−1+411yescharacteristic
750C2×C4C2×2−1+411yescharacteristic
751C2×C4C2×2−1+411yescharacteristic
752C8—28no—
753C8—44no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—816no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#232314yes—
769C22C22×C4×D411yescharacteristic
770C22C2×#53611yescharacteristic
771C22C2×#53711yescharacteristic
772C22C22×AGL(1,ℤ/8)11yescharacteristic
773C22C2×#57511yescharacteristic
774C22C2×#57511yescharacteristic
775C22C2×#57511yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—44no—
788C4—44no—
789C4—44no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4#232314yes—
795C4C4×AGL(1,ℤ/8)14yes—
796C4C2×#51911yescharacteristic
797C4C2×#52011yescharacteristic
798C4C2×#54111yescharacteristic
799C4C2×#54211yescharacteristic
800C2—24no—
801C2—84no—
802C2C2×#232311yescharacteristic
803C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
804C2C4×#57511yescharacteristic
805C2#6086411yescharacteristic
806C2#6086611yescharacteristic
807C2#6091611yescharacteristic
808C2#6091711yescharacteristic
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. #22120C2semidirect
5. #22117C2semidirect
6. #22116C2semidirect
7. #22114C2semidirect
8. #22111C2semidirect
9. #22110C2semidirect
10. #21312C2semidirect
11. #21170C2semidirect
12. #21159C2semidirect
15. #21034C2semidirect
17. C4×#423C2semidirect
21. #3077C4semidirect
32. C4×C4⋊Q8C22semidirect
33. C4×C4⋊Q8C22semidirect
34. C4×C4⋊Q8C22semidirect
35. C4×C4⋊Q8C22semidirect
36. C4×#125C22semidirect
37. C4×#125C22semidirect
66. #1989C22semidirect
67. #1988C22semidirect
68. #1987C22semidirect
69. #1949C22semidirect
70. #1948C22semidirect
71. #1947C22semidirect
72. #1944C22semidirect
73. #1943C22semidirect
74. #1942C22semidirect
75. #1941C22semidirect
84. #1921C22semidirect
85. #1920C22semidirect
86. #1919C22semidirect
87. #1918C22semidirect
91. #1767C22semidirect
92. #1767C22semidirect
93. C4×C4⋊C8C22semidirect
94. C4×C4⋊C8C22semidirect
148. #478C2×C4semidirect
149. #476C2×C4semidirect
150. #474C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#30772
C4×#5332
C2×#22932
#221202
#221172
#221162
#221142
#221112
#221102
#213122
#211702
#211592
#210952
#210602
#210342
#206462
C4×#4232