Finite Group Databasebeta

← C3×Dic3×AGL(1,ℤ/8) #11860271

Subgroups — C3×Dic3×AGL(1,ℤ/8) #11860271

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C3×Dic3×#41C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6C3×#5164C212yesmaximal, complemented
7C3×Dic3×SD16C212yesmaximal, complemented
8C3×#5152C212yesmaximal, complemented
9C3×Dic3×D8C212yesmaximal, complemented
10C3×#5121C211yesmaximal, characteristic, complemented
11C3×Dic3×M16C211yesmaximal, characteristic, complemented
12C3×C4×AGL(1,ℤ/8)—31nomaximal
13Dic3×AGL(1,ℤ/8)C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C3×Dic3—21no—
17C32×AGL(1,ℤ/8)C418yescomplemented
18C2×C32×SD16C2212yes—
19C2×C32×D8C2212yes—
20C2×C32×M16C2211yescharacteristic
21C2×C3×#217—21no—
22C3×Q8×Dic3C2211yescharacteristic, complemented
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C3×D4×Dic3—21no—
25C3×D4×Dic3—21no—
26C3×D4×Dic3—21no—
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2212yes—
29C3×D4×Dic3C2212yes—
30C3×D4×Dic3C2211yescharacteristic, complemented
31C3×D4×Dic3C2211yescharacteristic, complemented
32C3×#926—21no—
33C3×#926C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4×Dic3—21no—
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C3×#835C2212yescomplemented
39C3×#832C2212yes—
40C3×#832C2212yes—
41C3×#832C2212yescomplemented
42C3×#818C2212yescomplemented
43C3×#817C2212yescomplemented
44C3×#815C2212yescomplemented
45C3×C8×Dic3C2212yescomplemented
46C2×C3×AGL(1,ℤ/8)—21no—
47C2×C3×AGL(1,ℤ/8)D311yescharacteristic
48C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic
49C3×C4×#41—31no—
50C2×C3×C4×D4—31no—
51Dic3×#41C2×C311yescharacteristic, complemented
52C2×D4×Dic3C2×C311yescharacteristic, complemented
53C3×#442—32no—
54C3×#440—32no—
55C3×C4×SD16—32no—
56C3×C4×D8—32no—
57C3×#428—31no—
58C3×#418—31no—
59C3×#417—31no—
60C3×C4×M16—31no—
61#5232C2×C311yescharacteristic, complemented
62#5215C2×C311yescharacteristic, complemented
63#5164C2×C312yescomplemented
64Dic3×SD16C2×C312yescomplemented
65#5152C2×C312yescomplemented
66Dic3×D8C2×C312yescomplemented
67#5121C2×C311yescharacteristic, complemented
68Dic3×M16C2×C311yescharacteristic, complemented
69C24×C32—21no—
70C32×#41—22no—
71C32×#41C2×C414yescomplemented
72C2×C32×Q8C2311yescharacteristic
73C2×C32×D4—21no—
74C2×C32×D4—21no—
75C2×C32×D4—22no—
76C2×C32×D4C2×C414yescomplemented
77C2×C32×D4C2312yes—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4C2311yescharacteristic
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—22no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3—44no—
87C22×C3×Dic3D411yescharacteristic
88C22×C3×Dic3D411yescharacteristic
89C32×SD16C2×C418yescomplemented
90C32×D8C2×C418yescomplemented
91C32×M16C2×C414yescomplemented
92C2×C32×C8C2312yes—
93C3×#217—21no—
94C3×#217—21no—
95C3×#217—21no—
96C3×#217—22no—
97C3×#217—22no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2312yes—
102C3×C4⋊Dic3C2311yescharacteristic
103C3×C4⋊Dic3C2311yescharacteristic
104C3×C4×Dic3—21no—
105C3×C4×Dic3—21no—
106C3×C4×Dic3—21no—
107C3×C4×Dic3D411yescharacteristic
108C3×C4×Dic3D411yescharacteristic
109C3×C4×Dic3C2311yescharacteristic
110C3×C4×Dic3C2311yescharacteristic
111C3×#208—22no—
112C2×C3×C3⋊C8C2312yes—
113C4×AGL(1,ℤ/8)—31noSylow
114C2×C3×#41—21no—
115C2×C3×#41C2×D311yescharacteristic
116C2×C3×#41C22×C311yescharacteristic
117C22×C3×D4—21no—
118C22×C3×D4C2×D311yescharacteristic
119C22×C3×D4C22×C311yescharacteristic
120C23×C3×C4—61no—
121C23×Dic3—21no—
122C3×AGL(1,ℤ/8)—28no—
123C3×AGL(1,ℤ/8)Dic318yesdirect product factor
124C3×AGL(1,ℤ/8)C3×C418yescomplemented
125C2×C3×SD16—22no—
126C2×C3×SD16C2×D312yes—
127C2×C3×SD16C22×C312yes—
128C2×C3×D8—22no—
129C2×C3×D8C2×D312yes—
130C2×C3×D8C22×C312yes—
131C2×C3×M16—21no—
132C2×C3×M16—31no—
133C2×C3×M16C2×D311yescharacteristic
134C2×C3×M16C22×C311yescharacteristic
135C3×C4×Q8—31no—
136C3×C4×Q8—31no—
137C3×C4×D4—32no—
138C3×C4×D4—32no—
139C3×C4×D4—31no—
140C3×C4×D4—31no—
141C3×C4×D4—61no—
142C3×C4×D4—61no—
143C3×C4×D4—61no—
144C3×C4×D4—61no—
145C3×#117—31no—
146C3×#117—61no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C22⋊C4—61no—
149C2×C3×C42—31no—
150C2×C3×C42—61no—
151C2×#217—21no—
152Q8×Dic3C22×C311yescharacteristic, complemented
153Q8×Dic3C22×C311yescharacteristic, complemented
154D4×Dic3—21no—
155D4×Dic3—21no—
156D4×Dic3—21no—
157D4×Dic3—21no—
158D4×Dic3C22×C312yes—
159D4×Dic3C22×C312yes—
160D4×Dic3C22×C311yescharacteristic, complemented
161D4×Dic3C22×C311yescharacteristic, complemented
162#926—21no—
163#926C22×C311yescharacteristic
164C2×C4⋊Dic3C22×C311yescharacteristic
165C2×C4×Dic3—21no—
166C2×C4×Dic3C22×C311yescharacteristic
167C2×#208C22×C311yescharacteristic
168C3×#107—32no—
169C3×#106—32no—
170C3×#103—32no—
171C3×#102—32no—
172C3×#102—32no—
173C3×#102—32no—
174C3×#97—32no—
175C3×C4×C8—32no—
176#835C22×C312yescomplemented
177#832C22×C312yes—
178#832C22×C312yes—
179#832C22×C312yescomplemented
180#818C22×C312yescomplemented
181#817C22×C312yescomplemented
182#815C22×C312yescomplemented
183C8×Dic3C22×C312yescomplemented
184C23×C32—24no—
185C23×C32—22no—
186C23×C32—21no—
187C23×C32—42no—
188C23×C32—42no—
189C23×C32C2×D411yescharacteristic
190C32×Q8—21no—
191C32×Q8C22×C412yescomplemented
192C32×D4—24no—
193C32×D4—24no—
194C32×D4—22no—
195C32×D4—21no—
196C32×D4C22×C414yes—
197C32×D4C22×C412yescomplemented
198C2×C32×C4—21no—
199C2×C32×C4—24no—
200C2×C32×C4C22×C412yes—
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4#4112yes—
203C2×C32×C4C2411yescharacteristic
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—41no—
209C2×C3×Dic3—42no—
210C2×C3×Dic3—44no—
211C2×C3×Dic3—42no—
212C2×C3×Dic3—42no—
213C2×C3×Dic3—44no—
214C2×C3×Dic3C2×D411yescharacteristic
215C2×C3×Dic3C2×D411yescharacteristic
216C2×C3×Dic3C2×D411yescharacteristic
217C2×C3×Dic3C2×D411yescharacteristic
218C32×C8C22×C414yescomplemented
219C3×C3⋊C8—22no—
220C2×AGL(1,ℤ/8)C3×D311yescharacteristic
221C4×#41—31no—
222C2×C4×D4—31no—
223#442—32no—
224#440—32no—
225C4×SD16—32no—
226C4×D8—32no—
227#428—31no—
228#418—31no—
229#417—31no—
230C4×M16—31no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—41no—
234C3×#41—22no—
235C3×#41—22no—
236C3×#41—24no—
237C3×#41—42no—
238C3×#41C2×Dic314yescomplemented
239C3×#41C2×C3×C414yescomplemented
240C2×C3×Q8—21no—
241C2×C3×Q8C22×D311yescharacteristic
242C2×C3×Q8C23×C311yescharacteristic
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—22no—
247C2×C3×D4—21no—
248C2×C3×D4—22no—
249C2×C3×D4—24no—
250C2×C3×D4—21no—
251C2×C3×D4—22no—
252C2×C3×D4—41no—
253C2×C3×D4—42no—
254C2×C3×D4—41no—
255C2×C3×D4C2×Dic314yescomplemented
256C2×C3×D4C2×C3×C414yescomplemented
257C2×C3×D4C22×D312yes—
258C2×C3×D4C22×D311yescharacteristic
259C2×C3×D4C23×C312yes—
260C2×C3×D4C23×C311yescharacteristic
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—41no—
267C22×C3×C4—61no—
268C22×C3×C4—61no—
269C22×C3×C4—62no—
270C22×C3×C4—62no—
271C22×C3×C4—61no—
272C22×C3×C4—124no—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C23×C311yescharacteristic
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—44no—
281C22×Dic3C3×D411yescharacteristic
282C22×Dic3C3×D411yescharacteristic
283C3×SD16—28no—
284C3×SD16C2×Dic318yescomplemented
285C3×SD16C2×C3×C418yescomplemented
286C3×D8—28no—
287C3×D8C2×Dic318yescomplemented
288C3×D8C2×C3×C418yescomplemented
289C3×M16—24no—
290C3×M16—62no—
291C3×M16C2×Dic314yescomplemented
292C3×M16C2×C3×C414yescomplemented
293C2×C3×C8—22no—
294C2×C3×C8—32no—
295C2×C3×C8C22×D312yes—
296C2×C3×C8C23×C312yes—
297C3×C4⋊C4—31no—
298C3×C4⋊C4—31no—
299C3×C4⋊C4—32no—
300C3×C4⋊C4—61no—
301C3×C4⋊C4—61no—
302C3×C4⋊C4—61no—
303C3×C22⋊C4—62no—
304C3×C22⋊C4—62no—
305C3×C22⋊C4—61no—
306C3×C22⋊C4—61no—
307C3×C22⋊C4—61no—
308C3×C42—31no—
309C3×C42—31no—
310C3×C42—31no—
311C3×C42—31no—
312C3×C42—61no—
313C3×C42—61no—
314C3×C42—61no—
315#217—21no—
316#217—21no—
317#217—21no—
318#217—22no—
319#217—22no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3C23×C311yescharacteristic
324C4⋊Dic3C23×C312yes—
325C4⋊Dic3C23×C311yescharacteristic
326C4×Dic3—21no—
327C4×Dic3—21no—
328C4×Dic3—21no—
329C4×Dic3C3×D411yescharacteristic
330C4×Dic3C3×D411yescharacteristic
331C4×Dic3C23×C311yescharacteristic
332C4×Dic3C23×C311yescharacteristic
333#208—22no—
334C2×C3⋊C8C23×C312yes—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—22no—
338C22×C32—24no—
339C22×C32—48no—
340C22×C32—42no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—42no—
344C22×C32C4×D412yes—
345C22×C32C22×D411yescharacteristic
346C32×C4—22no—
347C32×C4C4×D412yes—
348C32×C4C23×C411yescharacteristic
349C32×C4C2×#4111yescharacteristic
350C3×Dic3—21no—
351C3×Dic3—21no—
352C3×Dic3—21no—
353C3×Dic3—41no—
354C3×Dic3—42no—
355C3×Dic3—41no—
356C3×Dic3AGL(1,ℤ/8)12yesdirect product factor
357C2×#41C2×C3×D311yescharacteristic
358C22×D4C2×C3×D311yescharacteristic
359C23×C4—61no—
360AGL(1,ℤ/8)C3×Dic318yesdirect product factor
361C2×SD16C2×C3×D312yes—
362C2×D8C2×C3×D312yes—
363C2×M16—31no—
364C2×M16C2×C3×D311yescharacteristic
365C4×Q8—31no—
366C4×Q8—31no—
367C4×D4—32no—
368C4×D4—32no—
369C4×D4—31no—
370C4×D4—31no—
371C4×D4—61no—
372C4×D4—61no—
373C4×D4—61no—
374C4×D4—61no—
375#117—31no—
376#117—61no—
377C2×C4⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C42—31no—
380C2×C42—61no—
381#107—32no—
382#106—32no—
383#103—32no—
384#102—32no—
385#102—32no—
386#102—32no—
387#97—32no—
388C4×C8—32no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—21no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—22no—
395C23×C3—21no—
396C23×C3—41no—
397C23×C3—44no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—82no—
404C23×C3—82no—
405C23×C3D3×D411yescharacteristic
406C23×C3C2×C3×D411yescharacteristic
407C3×Q8—21no—
408C3×Q8—21no—
409C3×Q8—22no—
410C3×Q8—41no—
411C3×Q8C22×Dic312yescomplemented
412C3×Q8C22×C3×C412yescomplemented
413C3×D4—24no—
414C3×D4—24no—
415C3×D4—24no—
416C3×D4—24no—
417C3×D4—22no—
418C3×D4—21no—
419C3×D4—22no—
420C3×D4—21no—
421C3×D4—24no—
422C3×D4—22no—
423C3×D4—44no—
424C3×D4—42no—
425C3×D4—41no—
426C3×D4—44no—
427C3×D4C22×Dic314yes—
428C3×D4C22×Dic312yescomplemented
429C3×D4C22×C3×C414yes—
430C3×D4C22×C3×C412yescomplemented
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—44no—
444C2×C3×C4—41no—
445C2×C3×C4—62no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—62no—
449C2×C3×C4—122no—
450C2×C3×C4—124no—
451C2×C3×C4—121no—
452C2×C3×C4—122no—
453C2×C3×C4—124no—
454C2×C3×C4—122no—
455C2×C3×C4D3×D411yescharacteristic
456C2×C3×C4#23712yes—
457C2×C3×C4C22×Dic312yes—
458C2×C3×C4C22×C3×C412yes—
459C2×C3×C4C2×C3×D411yescharacteristic
460C2×C3×C4C3×#4112yes—
461C2×C3×C4C23×D311yescharacteristic
462C2×C3×C4C24×C311yescharacteristic
463C2×Dic3—22no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—22no—
467C2×Dic3—41no—
468C2×Dic3—42no—
469C2×Dic3—44no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—44no—
473C2×Dic3C2×C3×D411yescharacteristic
474C2×Dic3C2×C3×D411yescharacteristic
475C2×Dic3C2×C3×D411yescharacteristic
476C2×Dic3C2×C3×D411yescharacteristic
477C3×C8—24no—
478C3×C8—62no—
479C3×C8C22×Dic314yescomplemented
480C3×C8C22×C3×C414yescomplemented
481C3⋊C8—22no—
482C2×C32—22no—
483C2×C32—42no—
484C2×C32—44no—
485C2×C32C2×C4×D411yescharacteristic
486C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
487C2×C32#57511yescharacteristic
488C24—21no—
489#41—22no—
490#41C2×C3×Dic314yescomplemented
491C2×Q8C22×C3×D311yescharacteristic
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4C2×C3×Dic314yescomplemented
496C2×D4C22×C3×D312yes—
497C2×D4C22×C3×D311yescharacteristic
498C22×C4—21no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—61no—
506C22×C4—124no—
507C22×C4C22×C3×D311yescharacteristic
508SD16C2×C3×Dic318yescomplemented
509D8C2×C3×Dic318yescomplemented
510M16—62no—
511M16C2×C3×Dic314yescomplemented
512C2×C8—32no—
513C2×C8C22×C3×D312yes—
514C4⋊C4—31no—
515C4⋊C4—31no—
516C4⋊C4—32no—
517C4⋊C4—61no—
518C4⋊C4—61no—
519C4⋊C4—61no—
520C22⋊C4—62no—
521C22⋊C4—62no—
522C22⋊C4—61no—
523C22⋊C4—61no—
524C22⋊C4—61no—
525C42—31no—
526C42—31no—
527C42—31no—
528C42—31no—
529C42—61no—
530C42—61no—
531C42—61no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—22no—
537C22×C3—24no—
538C22×C3—22no—
539C22×C3—24no—
540C22×C3—22no—
541C22×C3—21no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—42no—
545C22×C3—44no—
546C22×C3—48no—
547C22×C3—48no—
548C22×C3—42no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—42no—
556C22×C3—82no—
557C22×C3—82no—
558C22×C3—81no—
559C22×C3—81no—
560C22×C3—88no—
561C22×C3D4×Dic312yes—
562C22×C3C3×C4×D412yes—
563C22×C3C2×D3×D411yescharacteristic
564C22×C3C22×C3×D411yescharacteristic
565C3×C4—22no—
566C3×C4—22no—
567C3×C4—22no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—32no—
571C3×C4—42no—
572C3×C4—61no—
573C3×C4—61no—
574C3×C4—61no—
575C3×C4—122no—
576C3×C4—121no—
577C3×C4—121no—
578C3×C4D4×Dic312yes—
579C3×C4C3×C4×D412yes—
580C3×C4C2×#23711yescharacteristic
581C3×C4C23×Dic311yescharacteristic
582C3×C4C23×C3×C411yescharacteristic
583C3×C4C2×C3×#4111yescharacteristic
584Dic3—21no—
585Dic3—21no—
586Dic3—21no—
587Dic3—42no—
588Dic3—41no—
589Dic3—41no—
590Dic3C3×AGL(1,ℤ/8)12yesdirect product factor
591C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
592C23—24no—
593C23—21no—
594C23—22no—
595C23—42no—
596C23—42no—
597C23C3×D3×D411yescharacteristic
598Q8—21no—
599Q8C22×C3×Dic312yescomplemented
600D4—24no—
601D4—24no—
602D4—22no—
603D4—21no—
604D4C22×C3×Dic314yes—
605D4C22×C3×Dic312yescomplemented
606C2×C4—21no—
607C2×C4—24no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—31no—
611C2×C4—31no—
612C2×C4—62no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—62no—
616C2×C4—124no—
617C2×C4—122no—
618C2×C4—121no—
619C2×C4—124no—
620C2×C4—122no—
621C2×C4—122no—
622C2×C4C3×D3×D411yescharacteristic
623C2×C4C3×#23712yes—
624C2×C4C22×C3×Dic312yes—
625C2×C4C23×C3×D311yescharacteristic
626C8—62no—
627C8C22×C3×Dic314yescomplemented
628C2×C3—22no—
629C2×C3—22no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—42no—
634C2×C3—44no—
635C2×C3—42no—
636C2×C3—44no—
637C2×C3—42no—
638C2×C3—84no—
639C2×C3—82no—
640C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
641C2×C3#577311yescharacteristic
642C2×C3C2×D4×Dic311yescharacteristic
643C2×C3C2×C3×C4×D411yescharacteristic
644C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
645C2×C3C3×#57511yescharacteristic
646C22—21no—
647C22—21no—
648C22—22no—
649C22—24no—
650C22—48no—
651C22—42no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22C3×D4×Dic312yes—
656C22C2×C3×D3×D411yescharacteristic
657C4—22no—
658C4—32no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—122no—
663C4—121no—
664C4—121no—
665C4C3×D4×Dic312yes—
666C4C2×C3×#23711yescharacteristic
667C4C23×C3×Dic311yescharacteristic
668C3—21no—
669C3Dic3×AGL(1,ℤ/8)11yescharacteristic, direct product factor
670C3C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented
671C2—22no—
672C2—44no—
673C2—42no—
674C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
675C2C3×#577311yescharacteristic
676C2C2×C3×D4×Dic311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
2. C3×Dic3×#41C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C3×#5232C2semidirect
5. C3×#5215C2semidirect
6. C3×#5164C2semidirect
7. C3×Dic3×SD16C2semidirect
8. C3×#5152C2semidirect
9. C3×Dic3×D8C2semidirect
10. C3×#5121C2semidirect
11. C3×Dic3×M16C2semidirect
13. Dic3×AGL(1,ℤ/8)C3direct (N × H)
17. C32×AGL(1,ℤ/8)C4semidirect
22. C3×Q8×Dic3C22semidirect
23. C3×Q8×Dic3C22semidirect
30. C3×D4×Dic3C22semidirect
31. C3×D4×Dic3C22semidirect
38. C3×#835C22semidirect
41. C3×#832C22semidirect
42. C3×#818C22semidirect
43. C3×#817C22semidirect
44. C3×#815C22semidirect
45. C3×C8×Dic3C22semidirect
51. Dic3×#41C2×C3semidirect
52. C2×D4×Dic3C2×C3semidirect
61. #5232C2×C3semidirect
62. #5215C2×C3semidirect
63. #5164C2×C3semidirect
64. Dic3×SD16C2×C3semidirect
65. #5152C2×C3semidirect
66. Dic3×D8C2×C3semidirect
67. #5121C2×C3semidirect
68. Dic3×M16C2×C3semidirect
71. C32×#41C2×C4semidirect
76. C2×C32×D4C2×C4semidirect
89. C32×SD16C2×C4semidirect
90. C32×D8C2×C4semidirect
91. C32×M16C2×C4semidirect
123. C3×AGL(1,ℤ/8)Dic3direct (N × H)
124. C3×AGL(1,ℤ/8)C3×C4semidirect
152. Q8×Dic3C22×C3semidirect
153. Q8×Dic3C22×C3semidirect
160. D4×Dic3C22×C3semidirect
161. D4×Dic3C22×C3semidirect
176. #835C22×C3semidirect
179. #832C22×C3semidirect
180. #818C22×C3semidirect
181. #817C22×C3semidirect
182. #815C22×C3semidirect
183. C8×Dic3C22×C3semidirect
191. C32×Q8C22×C4semidirect
197. C32×D4C22×C4semidirect
218. C32×C8C22×C4semidirect
238. C3×#41C2×Dic3semidirect
239. C3×#41C2×C3×C4semidirect
255. C2×C3×D4C2×Dic3semidirect
256. C2×C3×D4C2×C3×C4semidirect
284. C3×SD16C2×Dic3semidirect
285. C3×SD16C2×C3×C4semidirect
287. C3×D8C2×Dic3semidirect
288. C3×D8C2×C3×C4semidirect
291. C3×M16C2×Dic3semidirect
292. C3×M16C2×C3×C4semidirect
356. C3×Dic3AGL(1,ℤ/8)direct (N × H)
360. AGL(1,ℤ/8)C3×Dic3direct (N × H)
411. C3×Q8C22×Dic3semidirect
412. C3×Q8C22×C3×C4semidirect
428. C3×D4C22×Dic3semidirect
430. C3×D4C22×C3×C4semidirect
479. C3×C8C22×Dic3semidirect
480. C3×C8C22×C3×C4semidirect
490. #41C2×C3×Dic3semidirect
495. C2×D4C2×C3×Dic3semidirect
508. SD16C2×C3×Dic3semidirect
509. D8C2×C3×Dic3semidirect
511. M16C2×C3×Dic3semidirect
590. Dic3C3×AGL(1,ℤ/8)direct (N × H)
591. C32C4×AGL(1,ℤ/8)semidirect
599. Q8C22×C3×Dic3semidirect
605. D4C22×C3×Dic3semidirect
627. C8C22×C3×Dic3semidirect
669. C3Dic3×AGL(1,ℤ/8)direct (N × H)
670. C3C3×C4×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
C3×Dic3×#412
C2×C3×D4×Dic32
C3×#52322
C3×#52152
C3×#51642
C3×Dic3×SD162
C3×#51522
C3×Dic3×D82
C3×#51212
C3×Dic3×M162
C3×C4×AGL(1,ℤ/8)3
Dic3×AGL(1,ℤ/8)3