Finite Group Databasebeta

← C3×#10595458 #13175055

Subgroups — C3×#10595458 #13175055

Order 1728.

1532 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#3802C211yesmaximal, characteristic, complemented
3C32×#949C212yesmaximal, complemented
4C3×#63941C212yesmaximal, complemented
5C3×#63940C212yesmaximal, complemented
6C3×#63927C212yesmaximal, complemented
7C3×#63926C212yesmaximal, complemented
8C3×#63830C212yesmaximal, complemented
9C3×#63818C211yesmaximal, characteristic, complemented
10C3×D3×AGL(1,ℤ/8)—32nomaximal
11#10595458C311yesmaximal, characteristic, direct product factor
12C22×C3×D32—21no—
13C33×#41C2211yescharacteristic, complemented
14C3×#3832C2211yescharacteristic, complemented
15C3×Q8×C3⋊D3C2211yescharacteristic, complemented
16C3×#3830—21no—
17C3×#3830C2211yescharacteristic, complemented
18C3×D4×C3⋊D3—21no—
19C3×D4×C3⋊D3C2211yescharacteristic, complemented
20C3×#3828—21no—
21C3×#3828C2211yescharacteristic, complemented
22C2×C3×C4×C3⋊D3—21no—
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C32×D12C2212yescomplemented
25C2×C3×#625—21no—
26C3×#3802—21no—
27C3×#3802—21no—
28C3×#3802C2212yes—
29C3×#3802C2212yescomplemented
30C32×#215C2214yescomplemented
31C32×#213C2214yescomplemented
32C32×#208C2212yescomplemented
33C3×#3716C2214yescomplemented
34C3×#3714C2214yescomplemented
35C3×#3712C2212yescomplemented
36C3×#3710C2212yescomplemented
37#41×C3⋊D3C2×C311yescharacteristic, complemented
38C3×D3×#41—32no—
39C3×D3×#41—61no—
40C2×C3×D3×D4—32no—
41C2×#3802C2×C311yescharacteristic, complemented
42C32×AGL(1,ℤ/8)—32no—
43C3×#949—22no—
44C3×#949D312yescomplemented
45C3×#949C2×C312yescomplemented
46C3×#932—32no—
47C3×#914—34no—
48C3×D3×SD16—34no—
49C3×#911—34no—
50C3×D3×D8—34no—
51C3×#908—32no—
52C3×D3×M16—32no—
53#63941C2×C312yescomplemented
54#63940C2×C312yescomplemented
55#63927C2×C312yescomplemented
56#63926C2×C312yescomplemented
57#63830C2×C312yescomplemented
58#63818C2×C311yescharacteristic, complemented
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3D411yescharacteristic
61C22×C32×D3—22no—
62C2×C3×D32—22no—
63C2×C3×D32—22no—
64C2×C3×D32—44no—
65C33×Q8C2311yescharacteristic, complemented
66C33×D4—21no—
67C33×D4C2311yescharacteristic, complemented
68C2×C33×C4—21no—
69C2×C33×C4C2311yescharacteristic
70C3×#638—21no—
71C3×#638—21no—
72C3×#638—21no—
73C2×C3×C3⋊Dic3—21no—
74C2×C3×C3⋊Dic3D411yescharacteristic
75C3×C4⋊(C3⋊D3)—21no—
76C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
77C3×C4×C3⋊D3—21no—
78C3×C4×C3⋊D3—21no—
79C3×C4×C3⋊D3—21no—
80C3×C4×C3⋊D3D411yescharacteristic
81C3×C4×C3⋊D3D411yescharacteristic
82C3×C4×C3⋊D3C2311yescharacteristic
83C3×C4×C3⋊D3C2311yescharacteristic
84C3×#634—21no—
85C3×#634C2311yescharacteristic, complemented
86C32×D12—22no—
87C32×D12C2314yes—
88C3×#625—22no—
89C3×#625—22no—
90C32×C3⋊C8C2314yescomplemented
91C2×C3×AGL(1,ℤ/8)—91no—
92D3×AGL(1,ℤ/8)—32no—
93C23×C3×D3—62no—
94C22×D32—21no—
95C32×#41—21no—
96C32×#41—22no—
97C32×#41—41no—
98C32×#41C2×D312yescomplemented
99C32×#41C22×C311yescharacteristic, complemented
100C2×C32×D4—32no—
101#3832C22×C311yescharacteristic, complemented
102Q8×C3⋊D3C22×C311yescharacteristic, complemented
103#3830—21no—
104#3830C22×C311yescharacteristic, complemented
105D4×C3⋊D3—21no—
106D4×C3⋊D3C22×C311yescharacteristic, complemented
107#3828—21no—
108#3828C22×C311yescharacteristic, complemented
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×C3×#67—62no—
112C3×#239—32no—
113C3×#239—61no—
114C3×D3×Q8—32no—
115C3×D3×Q8—61no—
116C3×#237—32no—
117C3×#237—62no—
118C3×#237—61no—
119C3×#237—62no—
120C3×D3×D4—32no—
121C3×D3×D4—34no—
122C3×D3×D4—34no—
123C3×D3×D4—62no—
124C3×D3×D4—62no—
125C3×D3×D4—62no—
126C3×D3×D4—61no—
127C3×D3×D4—62no—
128C3×#235—32no—
129C3×#235—62no—
130C3×#235—61no—
131C3×#235—62no—
132C2×C3×D12—22no—
133C2×C3×D12C2×D312yescomplemented
134C2×C3×D12C22×C312yescomplemented
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—62no—
137C2×C3×C4×D3—61no—
138C2×C3×C4×D3—62no—
139C2×#625—21no—
140#3802—21no—
141#3802—21no—
142#3802C22×C312yes—
143#3802C22×C312yescomplemented
144C32×SD16—34no—
145C32×D8—34no—
146C32×M16—32no—
147C3×#215—24no—
148C3×#215C2×D314yescomplemented
149C3×#215C22×C314yescomplemented
150C3×#214—34no—
151C3×#213—24no—
152C3×#213—34no—
153C3×#213C2×D314yescomplemented
154C3×#213C22×C314yescomplemented
155C3×#208—22no—
156C3×#208C2×D312yescomplemented
157C3×#208C22×C312yescomplemented
158C3×D24—34no—
159C3×#204—34no—
160C3×ΓL(1,𝔽25)—34no—
161C3×D3×C8—34no—
162#3716C22×C314yescomplemented
163#3714C22×C314yescomplemented
164#3712C22×C312yescomplemented
165#3710C22×C312yescomplemented
166C22×C33—21no—
167C22×C33C2×D411yescharacteristic
168C2×C3×C3⋊D3—22no—
169C2×C3×C3⋊D3—21no—
170C2×C3×C3⋊D3—42no—
171C2×C3×C3⋊D3C2×D411yescharacteristic
172C2×C3×C3⋊D3C2×D411yescharacteristic
173C2×C32×D3—24no—
174C2×C32×D3—44no—
175C3×D32—44no—
176C3×D32—44no—
177C33×C4—21no—
178C33×C4C2×D411yescharacteristic
179C33×C4C2411yescharacteristic
180C3×C3⋊Dic3—21no—
181C3×C3⋊Dic3C2×D411yescharacteristic
182C3×C3⋊Dic3C2×D411yescharacteristic
183C2×C3×#41—91no—
184C22×C3×D4—91no—
185D3×#41—32no—
186D3×#41—61no—
187C2×D3×D4—32no—
188C3×AGL(1,ℤ/8)—32no—
189C3×AGL(1,ℤ/8)—32no—
190C3×AGL(1,ℤ/8)—62no—
191C3×AGL(1,ℤ/8)—92no—
192C3×AGL(1,ℤ/8)—92no—
193C3×AGL(1,ℤ/8)—92no—
194C2×C3×SD16—92no—
195C2×C3×D8—92no—
196C2×C3×M16—91no—
197#949C3×D312yescomplemented
198#932—32no—
199#914—34no—
200D3×SD16—34no—
201#911—34no—
202D3×D8—34no—
203#908—32no—
204D3×M16—32no—
205C23×C32—62no—
206C22×C3⋊D3—21no—
207C22×C3⋊D3C3×D411yescharacteristic
208C22×C3×D3—22no—
209C22×C3×D3—22no—
210C22×C3×D3—32no—
211C22×C3×D3—42no—
212C22×C3×D3—61no—
213C22×C3×D3—64no—
214C22×C3×D3—64no—
215C22×C3×D3—62no—
216C22×C3×D3—62no—
217C22×C3×D3—128no—
218C2×D32—22no—
219C2×D32—22no—
220C2×D32—44no—
221C32×Q8—21no—
222C32×Q8—22no—
223C32×Q8—41no—
224C32×Q8C22×D312yescomplemented
225C32×Q8C23×C311yescharacteristic, complemented
226C32×D4—21no—
227C32×D4—22no—
228C32×D4—22no—
229C32×D4—21no—
230C32×D4—22no—
231C32×D4—34no—
232C32×D4—41no—
233C32×D4—42no—
234C32×D4—42no—
235C32×D4—62no—
236C32×D4C22×D312yescomplemented
237C32×D4C23×C311yescharacteristic, complemented
238C2×C32×C4—21no—
239C2×C32×C4—22no—
240C2×C32×C4—22no—
241C2×C32×C4—21no—
242C2×C32×C4—22no—
243C2×C32×C4—41no—
244C2×C32×C4—42no—
245C2×C32×C4—42no—
246C2×C32×C4C22×D312yes—
247C2×C32×C4C23×C311yescharacteristic
248#638—21no—
249#638—21no—
250#638—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C3×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C23×C311yescharacteristic, complemented
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3C3×D411yescharacteristic
259C4×C3⋊D3C3×D411yescharacteristic
260C4×C3⋊D3C23×C311yescharacteristic
261C4×C3⋊D3C23×C311yescharacteristic
262#634—21no—
263#634C23×C311yescharacteristic, complemented
264C3×#67—64no—
265C3×#67—64no—
266C3×#67—62no—
267C3×#67—62no—
268C3×#67—62no—
269C3×#67—62no—
270C3×#67—62no—
271C3×#67—62no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—62no—
276C3×D12—22no—
277C3×D12—22no—
278C3×D12—24no—
279C3×D12—32no—
280C3×D12—42no—
281C3×D12—61no—
282C3×D12—62no—
283C3×D12—62no—
284C3×D12C22×D314yes—
285C3×D12C23×C314yes—
286C3×C4×D3—32no—
287C3×C4×D3—32no—
288C3×C4×D3—32no—
289C3×C4×D3—32no—
290C3×C4×D3—61no—
291C3×C4×D3—61no—
292C3×C4×D3—61no—
293C3×C4×D3—61no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×Dic6—32no—
301C3×Dic6—61no—
302C3×Dic6—62no—
303C3×Dic6—62no—
304#625—22no—
305#625—22no—
306C32×C8—34no—
307C3×C3⋊C8—24no—
308C3×C3⋊C8C22×D314yescomplemented
309C3×C3⋊C8C23×C314yescomplemented
310C2×AGL(1,ℤ/8)—91noSylow
311C2×C33—21no—
312C2×C33—41no—
313C2×C33C22×D411yescharacteristic
314C3×C3⋊D3—21no—
315C3×C3⋊D3—41no—
316C3×C3⋊D3AGL(1,ℤ/8)12yescomplemented
317C32×D3—44no—
318C24×C3—181no—
319C23×D3—62no—
320C3×#41—21no—
321C3×#41—22no—
322C3×#41—41no—
323C3×#41—91no—
324C3×#41—91no—
325C3×#41—91no—
326C3×#41—181no—
327C3×#41—181no—
328C3×#41D3211yescharacteristic, complemented
329C3×#41C2×C3×D312yescomplemented
330C2×C3×Q8—91no—
331C2×C3×D4—32no—
332C2×C3×D4—32no—
333C2×C3×D4—62no—
334C2×C3×D4—92no—
335C2×C3×D4—92no—
336C2×C3×D4—91no—
337C2×C3×D4—181no—
338C2×C3×D4—181no—
339C2×C3×D4—181no—
340C2×C3×D4—181no—
341C22×C3×C4—91no—
342C22×C3×C4—181no—
343C2×#67—62no—
344#239—32no—
345#239—61no—
346D3×Q8—32no—
347D3×Q8—61no—
348#237—32no—
349#237—61no—
350#237—62no—
351#237—62no—
352D3×D4—32no—
353D3×D4—34no—
354D3×D4—34no—
355D3×D4—61no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—62no—
359D3×D4—62no—
360#235—32no—
361#235—61no—
362#235—62no—
363#235—62no—
364C2×D12C2×C3×D312yescomplemented
365C2×C4×D3—32no—
366C2×C4×D3—61no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C3×SD16—34no—
370C3×SD16—34no—
371C3×SD16—64no—
372C3×SD16—94no—
373C3×D8—34no—
374C3×D8—34no—
375C3×D8—64no—
376C3×D8—94no—
377C3×M16—32no—
378C3×M16—32no—
379C3×M16—62no—
380C3×M16—92no—
381C2×C3×C8—92no—
382#215C2×C3×D314yescomplemented
383#214—34no—
384#213—34no—
385#213C2×C3×D314yescomplemented
386#208C2×C3×D312yescomplemented
387D24—34no—
388#204—34no—
389ΓL(1,𝔽25)—34no—
390D3×C8—34no—
391C22×C32—21no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—21no—
395C22×C32—22no—
396C22×C32—41no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32—64no—
400C22×C32—124no—
401C22×C32D3×D412yes—
402C22×C32C2×C3×D411yescharacteristic
403C2×C3⋊D3—21no—
404C2×C3⋊D3—22no—
405C2×C3⋊D3—42no—
406C2×C3⋊D3C2×C3×D411yescharacteristic
407C2×C3⋊D3C2×C3×D411yescharacteristic
408C2×C3×D3—24no—
409C2×C3×D3—24no—
410C2×C3×D3—32no—
411C2×C3×D3—32no—
412C2×C3×D3—44no—
413C2×C3×D3—44no—
414C2×C3×D3—44no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—64no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—84no—
421C2×C3×D3—122no—
422C2×C3×D3—128no—
423C2×C3×D3—124no—
424C2×C3×D3—128no—
425C2×C3×D3—124no—
426D32—44no—
427D32—44no—
428C32×C4—21no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—21no—
432C32×C4—22no—
433C32×C4—21no—
434C32×C4—22no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4—42no—
438C32×C4—42no—
439C32×C4D3×D412yes—
440C32×C4C2×C3×D411yescharacteristic
441C32×C4C23×D312yes—
442C32×C4C24×C311yescharacteristic
443C3⋊Dic3—21no—
444C3⋊Dic3C2×C3×D411yescharacteristic
445C3⋊Dic3C2×C3×D411yescharacteristic
446C3×Dic3—32no—
447C3×Dic3—32no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C2×#41—91no—
453C22×D4—91no—
454AGL(1,ℤ/8)—32no—
455AGL(1,ℤ/8)—92no—
456AGL(1,ℤ/8)—92no—
457AGL(1,ℤ/8)—92no—
458C2×SD16—92no—
459C2×D8—92no—
460C2×M16—91no—
461C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
462C23×C3—62no—
463C23×C3—62no—
464C23×C3—91no—
465C23×C3—122no—
466C23×C3—181no—
467C23×C3—182no—
468C23×C3—182no—
469C23×C3—364no—
470C22×D3—22no—
471C22×D3—32no—
472C22×D3—61no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3—128no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—41no—
481C3×Q8—91no—
482C3×Q8—181no—
483C3×Q8C2×D3211yescharacteristic, complemented
484C3×Q8C22×C3×D312yescomplemented
485C3×D4—22no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—21no—
489C3×D4—22no—
490C3×D4—34no—
491C3×D4—34no—
492C3×D4—42no—
493C3×D4—42no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—62no—
497C3×D4—62no—
498C3×D4—91no—
499C3×D4—122no—
500C3×D4—181no—
501C3×D4—181no—
502C3×D4—182no—
503C3×D4—182no—
504C3×D4—181no—
505C3×D4—181no—
506C3×D4C2×D3211yescharacteristic, complemented
507C3×D4C22×C3×D312yescomplemented
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—41no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—181no—
522C2×C3×C4—181no—
523C2×C3×C4—181no—
524C2×C3×C4—181no—
525C2×C3×C4C2×D3211yescharacteristic
526C2×C3×C4C22×C3×D312yes—
527#67—64no—
528#67—64no—
529#67—62no—
530#67—62no—
531#67—62no—
532#67—62no—
533#67—62no—
534#67—62no—
535C2×Dic3—32no—
536C2×Dic3—61no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539D12—22no—
540D12—32no—
541D12—61no—
542D12—62no—
543D12—62no—
544D12C22×C3×D314yes—
545C4×D3—32no—
546C4×D3—32no—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—62no—
554C4×D3—62no—
555C4×D3—62no—
556C4×D3—62no—
557C4×D3—62no—
558C4×D3—62no—
559Dic6—32no—
560Dic6—61no—
561Dic6—62no—
562Dic6—62no—
563C3×C8—34no—
564C3×C8—34no—
565C3×C8—64no—
566C3⋊C8C22×C3×D314yescomplemented
567C2×C32—21no—
568C2×C32—22no—
569C2×C32—21no—
570C2×C32—22no—
571C2×C32—41no—
572C2×C32—42no—
573C2×C32—41no—
574C2×C32—41no—
575C2×C32—42no—
576C2×C32—42no—
577C2×C32—81no—
578C2×C32—82no—
579C2×C32—82no—
580C2×C32—124no—
581C2×C32C2×D3×D412yes—
582C2×C32C22×C3×D411yescharacteristic
583C3⋊D3—21no—
584C3⋊D3—41no—
585C3⋊D3C3×AGL(1,ℤ/8)12yescomplemented
586C3×D3—34no—
587C3×D3—44no—
588C3×D3—44no—
589C3×D3—62no—
590C3×D3—62no—
591C3×D3—84no—
592C3×D3—121no—
593C3×D3—122no—
594C3×D3—122no—
595C24—181no—
596#41—91no—
597#41—91no—
598#41—91no—
599#41—181no—
600#41—181no—
601#41C3×D3211yescharacteristic, complemented
602C2×Q8—91no—
603C2×D4—32no—
604C2×D4—92no—
605C2×D4—92no—
606C2×D4—91no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C22×C4—91no—
612C22×C4—181no—
613SD16—34no—
614SD16—94no—
615D8—34no—
616D8—94no—
617M16—32no—
618M16—92no—
619C2×C8—92no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—41no—
628C22×C3—64no—
629C22×C3—64no—
630C22×C3—91no—
631C22×C3—91no—
632C22×C3—124no—
633C22×C3—124no—
634C22×C3—124no—
635C22×C3—182no—
636C22×C3—181no—
637C22×C3—244no—
638C22×C3—362no—
639C22×C3—364no—
640C22×C3—364no—
641C22×C3#381111yescharacteristic
642C22×C3C3×D3×D412yes—
643C2×D3—24no—
644C2×D3—32no—
645C2×D3—32no—
646C2×D3—44no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—64no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—122no—
653C2×D3—128no—
654C2×D3—124no—
655C2×D3—128no—
656C2×D3—124no—
657C3×C4—22no—
658C3×C4—21no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—91no—
669C3×C4—91no—
670C3×C4—181no—
671C3×C4#381111yescharacteristic
672C3×C4C3×D3×D412yes—
673C3×C4C22×D3211yescharacteristic
674C3×C4C23×C3×D312yes—
675Dic3—32no—
676Dic3—32no—
677Dic3—61no—
678Dic3—61no—
679Dic3—62no—
680Dic3—62no—
681C32—22no—
682C32—21no—
683C32—41no—
684C32D3×AGL(1,ℤ/8)12yescomplemented
685C32C2×C3×AGL(1,ℤ/8)11yescharacteristic, complemented
686C23—62no—
687C23—91no—
688C23—181no—
689C23—182no—
690C23—182no—
691C23—364no—
692Q8—91no—
693Q8—181no—
694Q8C2×C3×D3211yescharacteristic, complemented
695D4—21no—
696D4—34no—
697D4—62no—
698D4—91no—
699D4—181no—
700D4—181no—
701D4—182no—
702D4—182no—
703D4—181no—
704D4—181no—
705D4C2×C3×D3211yescharacteristic, complemented
706C2×C4—21no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4C2×C3×D3211yescharacteristic
717C8—34no—
718C2×C3—22no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—42no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—81no—
729C2×C3—82no—
730C2×C3—82no—
731C2×C3—92no—
732C2×C3—124no—
733C2×C3—124no—
734C2×C3—181no—
735C2×C3—244no—
736C2×C3—361no—
737C2×C3C2×#381111yescharacteristic
738C2×C3C2×C3×D3×D412yes—
739D3—34no—
740D3—44no—
741D3—62no—
742D3—62no—
743D3—121no—
744D3—122no—
745D3—122no—
746C22—21no—
747C22—64no—
748C22—91no—
749C22—91no—
750C22—124no—
751C22—182no—
752C22—181no—
753C22—362no—
754C22—364no—
755C22—364no—
756C22C3×#381111yescharacteristic
757C4—21no—
758C4—91no—
759C4—91no—
760C4—181no—
761C4C3×#381111yescharacteristic
762C4C22×C3×D3211yescharacteristic
763C3—21no—
764C3—22no—
765C3—41no—
766C3#1059545811yescharacteristic, direct product factor
767C3C3×D3×AGL(1,ℤ/8)12yescomplemented
768C2—21no—
769C2—41no—
770C2—92no—
771C2—124no—
772C2—181no—
773C2—361no—
774C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3C2×#3811
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C2×C3×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
1. C3×#41×C3⋊D3C2semidirect
2. C2×C3×#3802C2semidirect
3. C32×#949C2semidirect
4. C3×#63941C2semidirect
5. C3×#63940C2semidirect
6. C3×#63927C2semidirect
7. C3×#63926C2semidirect
8. C3×#63830C2semidirect
9. C3×#63818C2semidirect
11. #10595458C3direct (N × H)
13. C33×#41C22semidirect
14. C3×#3832C22semidirect
15. C3×Q8×C3⋊D3C22semidirect
17. C3×#3830C22semidirect
19. C3×D4×C3⋊D3C22semidirect
21. C3×#3828C22semidirect
24. C2×C32×D12C22semidirect
29. C3×#3802C22semidirect
30. C32×#215C22semidirect
31. C32×#213C22semidirect
32. C32×#208C22semidirect
33. C3×#3716C22semidirect
34. C3×#3714C22semidirect
35. C3×#3712C22semidirect
36. C3×#3710C22semidirect
37. #41×C3⋊D3C2×C3semidirect
41. C2×#3802C2×C3semidirect
44. C3×#949D3semidirect
45. C3×#949C2×C3semidirect
53. #63941C2×C3semidirect
54. #63940C2×C3semidirect
55. #63927C2×C3semidirect
56. #63926C2×C3semidirect
57. #63830C2×C3semidirect
58. #63818C2×C3semidirect
65. C33×Q8C23semidirect
67. C33×D4C23semidirect
76. C3×C4⋊(C3⋊D3)C23semidirect
85. C3×#634C23semidirect
90. C32×C3⋊C8C23semidirect
98. C32×#41C2×D3semidirect
99. C32×#41C22×C3semidirect
101. #3832C22×C3semidirect
102. Q8×C3⋊D3C22×C3semidirect
104. #3830C22×C3semidirect
106. D4×C3⋊D3C22×C3semidirect
108. #3828C22×C3semidirect
133. C2×C3×D12C2×D3semidirect
134. C2×C3×D12C22×C3semidirect
143. #3802C22×C3semidirect
148. C3×#215C2×D3semidirect
149. C3×#215C22×C3semidirect
153. C3×#213C2×D3semidirect
154. C3×#213C22×C3semidirect
156. C3×#208C2×D3semidirect
157. C3×#208C22×C3semidirect
162. #3716C22×C3semidirect
163. #3714C22×C3semidirect
164. #3712C22×C3semidirect
165. #3710C22×C3semidirect
197. #949C3×D3semidirect
224. C32×Q8C22×D3semidirect
225. C32×Q8C23×C3semidirect
236. C32×D4C22×D3semidirect
237. C32×D4C23×C3semidirect
254. C4⋊(C3⋊D3)C23×C3semidirect
263. #634C23×C3semidirect
308. C3×C3⋊C8C22×D3semidirect
309. C3×C3⋊C8C23×C3semidirect
316. C3×C3⋊D3AGL(1,ℤ/8)semidirect
328. C3×#41D32semidirect
329. C3×#41C2×C3×D3semidirect
364. C2×D12C2×C3×D3semidirect
382. #215C2×C3×D3semidirect
385. #213C2×C3×D3semidirect
386. #208C2×C3×D3semidirect
461. C33C2×AGL(1,ℤ/8)semidirect
483. C3×Q8C2×D32semidirect
484. C3×Q8C22×C3×D3semidirect
506. C3×D4C2×D32semidirect
507. C3×D4C22×C3×D3semidirect
566. C3⋊C8C22×C3×D3semidirect
585. C3⋊D3C3×AGL(1,ℤ/8)semidirect
601. #41C3×D32semidirect
684. C32D3×AGL(1,ℤ/8)semidirect
685. C32C2×C3×AGL(1,ℤ/8)semidirect
694. Q8C2×C3×D32semidirect
705. D4C2×C3×D32semidirect
766. C3#10595458direct (N × H)
767. C3C3×D3×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
C3×#41×C3⋊D32
C2×C3×#38022
C32×#9492
C3×#639412
C3×#639402
C3×#639272
C3×#639262
C3×#638302
C3×#638182
C3×D3×AGL(1,ℤ/8)3
#105954583