Finite Group Databasebeta

← #6403305

Subgroups — #6403305

Order 512.

2037 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3353C211yesmaximal, characteristic
2#34324C211yesmaximal, characteristic, complemented
3#34308C211yesmaximal, characteristic
4#23157C211yesmaximal, characteristic, complemented
5#23034C212yesmaximal, complemented
6#22964C211yesmaximal, characteristic, complemented
7#22962C211yesmaximal, characteristic, complemented
8#22925C212yesmaximal, complemented
9#22924C212yesmaximal, complemented
10C4⋊C4×SD16C211yesmaximal, characteristic, complemented
11#22663C211yesmaximal, characteristic, complemented
12#22624C212yesmaximal, complemented
13#22504C211yesmaximal, characteristic, complemented
14#22500C211yesmaximal, characteristic
15#22118C211yesmaximal, characteristic, complemented
16#22116C211yesmaximal, characteristic, complemented
17#22086C212yesmaximal, complemented
18#22085C212yesmaximal, complemented
19#21726C211yesmaximal, characteristic, complemented
20C4×#468C212yesmaximal, complemented
21#21279C211yesmaximal, characteristic, complemented
22#21159C212yesmaximal, complemented
23#20494C211yesmaximal, characteristic, complemented
24C2×#556C2211yescharacteristic
25C2×#547C2211yescharacteristic
26C2×#520—21no—
27#3353C4116yescomplemented
28C2×#500C2211yescharacteristic
29C2×#484C2212yes—
30C2×#482C2212yes—
31C2×#475C2211yescharacteristic
32C2×#474C2211yescharacteristic
33C2×#468C2212yes—
34C2×C4×SD16C2212yes—
35C2×C4×SD16C2211yescharacteristic
36C2×#436C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#428C2212yes—
39C2×#428C2212yes—
40C2×C4×M16C2212yes—
41#2373—22no—
42#2367—21no—
43#2365C2211yescharacteristic
44#2365C2211yescharacteristic
45#2362C2212yes—
46#2361C2212yes—
47#2360—21no—
48#2359—22no—
49#2355—21no—
50#2354C2211yescharacteristic
51Q8×C4⋊C4C2211yescharacteristic
52D4×C4⋊C4C2211yescharacteristic
53D4×C4⋊C4C2211yescharacteristic
54#2346C2212yes—
55#2344C2212yes—
56#2339—21no—
57#2334—22no—
58#2326—21no—
59#2323—21no—
60#2322—22no—
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2212yes—
64C4×#121C2212yes—
65#2296C2212yes—
66#2295C2211yescharacteristic
67#2293C2211yescharacteristic
68C2×#389C2212yes—
69#2276—21no—
70C42×D4C2211yescharacteristic
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1988C2211yescharacteristic
74#1988C2211yescharacteristic
75#1973C2211yescharacteristic
76#1973C2211yescharacteristic
77#1948C2211yescharacteristic
78#1947C2211yescharacteristic
79#1944C2211yescharacteristic
80#1944C2211yescharacteristic
81#1944C2212yes—
82#1943C2212yes—
83#1943C2212yes—
84#1943C2212yes—
85#1942C2212yes—
86#1942C2212yes—
87#1941C2212yes—
88#1941C2212yes—
89#1936C2212yes—
90#1936C2211yescharacteristic
91#1936C2211yescharacteristic
92#1935C2212yes—
93#1935C2211yescharacteristic
94#1935C2211yescharacteristic
95#1928C2212yes—
96#1926C2212yes—
97#1921C2212yes—
98#1920C2212yes—
99#1919C2212yes—
100#1918C2212yes—
101#1918C2212yes—
102#1918C2212yes—
103#1895C2212yes—
104#1894C2212yes—
105#1875C2212yes—
106#1872C2212yes—
107#1865C2212yes—
108#1865C2212yes—
109#1864C2212yes—
110#1862C2212yes—
111#1854C2212yes—
112#1853C2212yes—
113#1844C2211yescharacteristic
114#1825C2212yes—
115#1824C2212yes—
116#1809C2212yes—
117#1803C2211yescharacteristic
118#1802C2211yescharacteristic
119#1776C2212yes—
120#1776C2212yes—
121C4×#107C2212yes—
122C4×#107C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2211yescharacteristic
125#1767C2211yescharacteristic
126C4×#103C2212yes—
127C4×#103C2211yescharacteristic
128C4×#102C2212yes—
129C4×#102C2211yescharacteristic
130#1753C2212yes—
131#1753C2212yes—
132#1749C2212yes—
133#1736C2212yes—
134#1736C2212yes—
135C4×#97C2211yescharacteristic
136C22×#41—21no—
137C22×SD16C2311yescharacteristic
138C22×M16C2312yes—
139C22×M16C2312yes—
140#556—24no—
141#556C2×C418yescomplemented
142#547—24no—
143#547C2×C418yes—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×#126—22no—
147C2×#124—21no—
148C2×#123—22no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8C2312yes—
151C2×#121C2312yes—
152#520—48no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2312yes—
160C2×C4×D4—21no—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4D411yescharacteristic
164C2×C4×D4D411yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×#117—22no—
169C2×#117—21no—
170C2×#117C2312yes—
171C2×#117C2312yes—
172C22×C4⋊C4—22no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C42C2312yes—
177#500C2×C418yescomplemented
178#484C2×C4116yescomplemented
179#482C2×C4116yescomplemented
180#475C2×C418yescomplemented
181#474C2×C418yescomplemented
182#468C2×C4116yescomplemented
183C4×SD16—44no—
184C4×SD16C2×C418yescomplemented
185#436—24no—
186#436C2×C418yescomplemented
187#428—44no—
188#428C2×C4116yescomplemented
189C2×#107C2311yescharacteristic
190C2×#107C2311yescharacteristic
191C2×#107C2312yes—
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#107C2312yes—
195C2×#106C2312yes—
196C2×#106C2312yes—
197C2×#106C2312yes—
198C2×#106C2312yes—
199C2×#106C2311yescharacteristic
200C2×C4⋊C8C2311yescharacteristic
201C2×C4⋊C8C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2311yescharacteristic
205C2×#103C2312yes—
206C2×#103C2311yescharacteristic
207C2×#102C2311yescharacteristic
208C2×#102C2312yes—
209C2×#102C2311yescharacteristic
210C2×#102C2311yescharacteristic
211C2×#102C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C4×M16—44no—
215C2×#97C2311yescharacteristic
216C2×#97C2311yescharacteristic
217C2×#97C2311yescharacteristic
218C2×#97C2312yes—
219C2×#97C2311yescharacteristic
220C2×C4×C8C2312yes—
221C2×C4×C8C2311yescharacteristic
222C2×C4×C8C2312yes—
223C2×C4×C8C2311yescharacteristic
224#391—21no—
225#391—21no—
226#391—21no—
227#391—21no—
228#391C2311yescharacteristic
229#391C2311yescharacteristic
230#390—21no—
231#390C2311yescharacteristic
232#390C2311yescharacteristic
233#389—21no—
234#389—21no—
235#389—21no—
236#389—22no—
237#389—22no—
238#389—22no—
239#389C2312yes—
240#389C2312yes—
241#389C2311yescharacteristic
242#389C2312yes—
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—21no—
255#388—22no—
256#388—21no—
257#388—22no—
258#387—21no—
259#387—22no—
260#387—21no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#386—22no—
267#386—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385—22no—
274#384—21no—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#382—22no—
278#381—22no—
279#380—21no—
280#380C2312yes—
281#380C2312yes—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—22no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—22no—
290C4×C4⋊C4—22no—
291C4×C4⋊C4D411yescharacteristic
292C4×C4⋊C4D411yescharacteristic
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C22⋊C4—22no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4D412yes—
304C4×C22⋊C4D412yes—
305C4×C22⋊C4C2312yes—
306#376—21no—
307#376—22no—
308C2×#95—22no—
309C43C2311yescharacteristic
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2311yescharacteristic
327#340C2311yescharacteristic
328#336C2312yes—
329#336C2312yes—
330#336C2312yes—
331C2×#41—28no—
332C2×#41—44no—
333C2×#41—44no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8C2411yescharacteristic
337C22×D4—22no—
338C22×D4C2×D411yescharacteristic
339C22×D4C2411yescharacteristic
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4C2×D412yes—
345C23×C4C2×D412yes—
346C23×C4C2412yes—
347C2×SD16—22no—
348C2×SD16—22no—
349C2×SD16C22×C414yes—
350C2×M16—24no—
351C2×M16—24no—
352C2×M16—24no—
353C2×M16—24no—
354C2×M16—42no—
355C2×M16C22×C418yes—
356C22×C8C2412yes—
357C22×C8C2411yescharacteristic
358C22×C8C2412yes—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8C22×C414yes—
365C4⋊Q8C22×C414yes—
366#126—216no—
367#124—28no—
368#123—216no—
369C22⋊Q8—24no—
370C22⋊Q8—28no—
371C22⋊Q8C22×C418yes—
372#121—24no—
373#121C22×C418yes—
374C4×Q8—28no—
375C4×Q8—22no—
376C4×Q8—44no—
377C4×Q8—44no—
378C4×Q8—42no—
379C4×Q8—42no—
380C4×Q8—44no—
381C4×Q8—44no—
382C4×Q8C22×C414yes—
383C4×D4—24no—
384C4×D4—22no—
385C4×D4—42no—
386C4×D4—42no—
387C4×D4—42no—
388C4×D4—48no—
389C4×D4—48no—
390C4×D4—44no—
391C4×D4C22×C414yes—
392C4×D4C22×C414yes—
393C4×D4#4114yes—
394#117—24no—
395#117—44no—
396#117—48no—
397#117—42no—
398#117—42no—
399#117C22×C418yes—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—48no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4C22×C418yes—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C42—22no—
456C2×C42—21no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—42no—
466C2×C42—42no—
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D412yes—
472C2×C42C2×D412yes—
473C2×C42C2412yes—
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477#107—22no—
478#107—22no—
479#107—42no—
480#107C22×C418yes—
481#107C22×C418yes—
482#107C22×C418yes—
483#106—24no—
484#106—42no—
485#106—42no—
486#106C22×C414yes—
487#106C22×C418yes—
488C4⋊C8—22no—
489C4⋊C8C22×C414yes—
490#103—22no—
491#103—41no—
492#103—42no—
493#103C22×C414yes—
494#103C22×C418yes—
495#102—22no—
496#102—41no—
497#102—42no—
498#102C22×C414yes—
499#102C22×C418yes—
500C22⋊C8—24no—
501C22⋊C8C22×C418yes—
502#97—22no—
503#97—22no—
504#97—22no—
505#97—41no—
506#97—42no—
507C4×C8—24no—
508C4×C8—22no—
509C4×C8—42no—
510C4×C8C22×C414yes—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—21no—
516#95—22no—
517#95—21no—
518#95—21no—
519#95—22no—
520#95—21no—
521#95—21no—
522#95—22no—
523#95—22no—
524#95—21no—
525#95—22no—
526#95—21no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95C2×D412yes—
534#95C2×D412yes—
535#95C2×D412yes—
536C24—21no—
537C24C22×D412yes—
538#41—432no—
539C2×Q8—24no—
540C2×Q8—24no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8—42no—
549C2×Q8—42no—
550C2×Q8C23×C412yes—
551C2×D4—28no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4C4×D414yes—
562C2×D4C23×C412yes—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4C23×C414yes—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D412yes—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C2×#4114yes—
607C22×C4C2511yescharacteristic
608SD16—28no—
609M16—216no—
610M16—48no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—22no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—22no—
622C2×C8—21no—
623C2×C8C23×C412yes—
624C2×C8C23×C414yes—
625C2×C8C23×C412yes—
626C2×C8H(5,𝔽2)12yes—
627C2×C82−1+412yes—
628C2×C82−1+412yes—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—42no—
661C4⋊C4—81no—
662C4⋊C4—81no—
663C4⋊C4—81no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4C4×D414yes—
668C4⋊C4AGL(1,ℤ/8)14yes—
669C4⋊C4C23×C412yes—
670C4⋊C4C23×C414yes—
671C4⋊C4C23×C412yes—
672C4⋊C4C23×C414yes—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—24no—
676C22⋊C4—28no—
677C22⋊C4—24no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—81no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4C4×D418yes—
688C42—28no—
689C42—24no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—22no—
698C42—42no—
699C42—42no—
700C42—41no—
701C42—41no—
702C42—44no—
703C42—44no—
704C42—44no—
705C42—42no—
706C42—44no—
707C42—42no—
708C42—82no—
709C42—82no—
710C42C23×C412yes—
711C42C2×#4112yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23C2×C4×D414yes—
726C23C23×D411yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—48no—
730Q8—48no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—28no—
736D4—416no—
737D4—41no—
738D4—41no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—416no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—48no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—84no—
800C2×C4—84no—
801C2×C4—164no—
802C2×C4—164no—
803C2×C4C2×C4×D414yes—
804C2×C4C2×C4×D412yes—
805C2×C4C2×C4×D412yes—
806C2×C4C2×AGL(1,ℤ/8)14yes—
807C2×C4C2×AGL(1,ℤ/8)12yes—
808C2×C4#57512yes—
809C2×C4C24×C411yescharacteristic
810C2×C4C22×#4111yescharacteristic
811C2×C4C2×H(5,𝔽2)11yescharacteristic
812C2×C4C2×2−1+411yescharacteristic
813C2×C4C2×2−1+411yescharacteristic
814C2×C4#58511yescharacteristic
815C8—24no—
816C8—22no—
817C8—22no—
818C8—41no—
819C8—42no—
820C8#52014yescomplemented
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22C22×C4×D411yescharacteristic
836C22#349611yescharacteristic
837C22#349911yescharacteristic
838C22C22×AGL(1,ℤ/8)11yescharacteristic
839C22C2×#57511yescharacteristic
840C22#358611yescharacteristic
841C22#358611yescharacteristic
842C4—24no—
843C4—22no—
844C4—24no—
845C4—42no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—44no—
854C4—44no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4—82no—
860C4—82no—
861C4C4×AGL(1,ℤ/8)14yes—
862C4C2×#52011yescharacteristic
863C4C4×2−1+411yescharacteristic
864C4#351511yescharacteristic
865C4#352011yescharacteristic
866C2—44no—
867C2—82no—
868C2#3430811yescharacteristic
869C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
870C2#6017511yescharacteristic
871C2#6229511yescharacteristic
872C2#6230311yescharacteristic
873C2#6250911yescharacteristic
874C2#6251111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#547C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34324C2semidirect
4. #23157C2semidirect
5. #23034C2semidirect
6. #22964C2semidirect
7. #22962C2semidirect
8. #22925C2semidirect
9. #22924C2semidirect
10. C4⋊C4×SD16C2semidirect
11. #22663C2semidirect
12. #22624C2semidirect
13. #22504C2semidirect
15. #22118C2semidirect
16. #22116C2semidirect
17. #22086C2semidirect
18. #22085C2semidirect
19. #21726C2semidirect
20. C4×#468C2semidirect
21. #21279C2semidirect
22. #21159C2semidirect
23. #20494C2semidirect
27. #3353C4semidirect
141. #556C2×C4semidirect
177. #500C2×C4semidirect
178. #484C2×C4semidirect
179. #482C2×C4semidirect
180. #475C2×C4semidirect
181. #474C2×C4semidirect
182. #468C2×C4semidirect
184. C4×SD16C2×C4semidirect
186. #436C2×C4semidirect
188. #428C2×C4semidirect
820. C8#520semidirect

Maximal subgroups

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

subgroupindex
C2×#33532
#343242
#343082
#231572
#230342
#229642
#229622
#229252
#229242
C4⋊C4×SD162
#226632
#226242
#225042
#225002
#221182
#221162
#220862
#220852
#217262
C4×#4682
#212792
#211592
#204942