Finite Group Databasebeta

← C2×C3×#63925 #13174788

Subgroups — C2×C3×#63925 #13174788

Order 1728.

1562 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C2×C3×#3753C211yesmaximal, characteristic, complemented
4C2×C32×#213C211yesmaximal, characteristic, complemented
5C3×#63925C218yesmaximal, direct product factor
6C2×C3×#3717C211yesmaximal, characteristic, complemented
7C2×C3×#3715C211yesmaximal, characteristic, complemented
8C2×C3×#3711C211yesmaximal, characteristic, complemented
9C2×C3×#949—31nomaximal
10C2×C3×#911—31nomaximal
11C2×#63925C311yesmaximal, characteristic, direct product factor
12C22×C3×D32—21no—
13C2×C33×D4C2211yescharacteristic, complemented
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C32×#67—21no—
16C22×C32×Dic3—21no—
17C32×#237—22no—
18C32×#237C2214yescomplemented
19C2×C32×D12C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic, complemented
22C2×C3×#626—21no—
23C3×D3×D12—22no—
24C3×D3×D12C2214yescomplemented
25C3×#3753C2214yescomplemented
26C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27C32×#213C2214yescomplemented
28C2×C32×C3⋊C8C2211yescharacteristic, complemented
29C3×#3717C2214yescomplemented
30C3×#3715C2214yescomplemented
31C3×#3711C2214yescomplemented
32C2×C32×#41—31no—
33C2×C3×#237—21no—
34C2×C3×#237D311yescharacteristic, complemented
35C2×C3×#237C2×C311yescharacteristic, complemented
36C2×C3×D3×D4—31no—
37C22×C3×D12—31no—
38C2×D3×D12C2×C311yescharacteristic, complemented
39C2×C32×D8—31no—
40C2×#3753C2×C311yescharacteristic, complemented
41C3×#949—38no—
42C2×C3×#215—31no—
43C2×C3×#215—31no—
44C2×C3×#214—31no—
45C2×C3×#213—21no—
46C2×C3×#213—31no—
47C2×C3×#213—31no—
48C2×C3×#213—61no—
49C2×C3×#213D311yescharacteristic, complemented
50C2×C3×#213C2×C311yescharacteristic, complemented
51C2×C3×#208—31no—
52C3×#911—38no—
53C2×C3×#204—31no—
54C2×C3×ΓL(1,𝔽25)—31no—
55#63925C2×C318yesdirect product factor
56C2×#3717C2×C311yescharacteristic, complemented
57C2×#3715C2×C311yescharacteristic, complemented
58C2×#3711C2×C311yescharacteristic, complemented
59C23×C33—21no—
60C22×C3×C3⋊D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3D411yescharacteristic
63C2×C3×D32—24no—
64C2×C3×D32—44no—
65C33×D4—21no—
66C33×D4C2312yescomplemented
67C2×C33×C4C2311yescharacteristic
68C3×C4⋊(C3⋊D3)—21no—
69C3×C4⋊(C3⋊D3)C2312yes—
70C32×#67—24no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3—24no—
73C2×C32×Dic3D411yescharacteristic
74C32×D12—21no—
75C32×D12C2312yes—
76C32×C4×D3D412yes—
77C32×C4×D3C2312yes—
78C32×Dic6—21no—
79C32×Dic6C2312yescomplemented
80C3×#626—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C2×C3×AGL(1,ℤ/8)—91no—
84C2×#949—31no—
85C2×#911—31no—
86C23×C3×D3—61no—
87C23×C3×D3—61no—
88C22×D32—21no—
89C32×#41—34no—
90C32×#41—62no—
91C2×C32×Q8—31no—
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4—21no—
95C2×C32×D4—31no—
96C2×C32×D4—41no—
97C2×C32×D4—61no—
98C2×C32×D4C2×D311yescharacteristic, complemented
99C2×C32×D4C2×D311yescharacteristic, complemented
100C2×C32×D4C22×C311yescharacteristic, complemented
101C22×C32×C4—31no—
102C22×C32×C4—61no—
103C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
104C2×C3×#67—22no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—61no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C3×#237—24no—
112C3×#237—24no—
113C3×#237—22no—
114C3×#237—22no—
115C3×#237C2×D314yescomplemented
116C3×#237C22×C314yescomplemented
117C3×D3×D4—34no—
118C3×D3×D4—62no—
119C2×C3×D12—21no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×C3×D12—34no—
123C2×C3×D12—62no—
124C2×C3×D12—61no—
125C2×C3×D12—61no—
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×D12C22×C311yescharacteristic
128C2×C3×C4×D3—21no—
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×C3×C4×D3C22×C311yescharacteristic
131C2×C3×Dic6—21no—
132C2×C3×Dic6C2×D311yescharacteristic, complemented
133C2×C3×Dic6C22×C311yescharacteristic, complemented
134C2×#626—21no—
135D3×D12—22no—
136D3×D12C22×C314yescomplemented
137C32×D8—34no—
138C2×C32×C8—31no—
139#3753C22×C314yescomplemented
140C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
141C3×#215—34no—
142C3×#215—34no—
143C3×#214—34no—
144C3×#213—24no—
145C3×#213—34no—
146C3×#213—34no—
147C3×#213—64no—
148C3×#213C2×D314yescomplemented
149C3×#213C22×C314yescomplemented
150C3×#208—34no—
151C2×C3×C3⋊C8—21no—
152C2×C3×C3⋊C8—31no—
153C2×C3×C3⋊C8—31no—
154C2×C3×C3⋊C8—61no—
155C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
156C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
157C3×#204—34no—
158C3×ΓL(1,𝔽25)—34no—
159#3717C22×C314yescomplemented
160#3715C22×C314yescomplemented
161#3711C22×C314yescomplemented
162C22×C33—22no—
163C22×C33—42no—
164C22×C33C2×D411yescharacteristic
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—42no—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3—42no—
170C2×C32×D3C2×D412yes—
171C3×D32—48no—
172C33×C4C2×D411yescharacteristic
173C33×C4C2411yescharacteristic
174C32×Dic3—22no—
175C32×Dic3C2×D412yes—
176C2×C3×#41—31no—
177C2×C3×#41—31no—
178C2×C3×#41—61no—
179C22×C3×D4—91no—
180C2×#237C3×D311yescharacteristic, complemented
181C2×D3×D4—31no—
182C22×D12—31no—
183C3×AGL(1,ℤ/8)—98no—
184C2×C3×SD16—91no—
185C2×C3×SD16—91no—
186C2×C3×D8—31no—
187C2×C3×D8—31no—
188C2×C3×D8—61no—
189C2×C3×D8—91no—
190C2×C3×M16—91no—
191#949—38no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#214—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—61no—
198C2×#213C3×D311yescharacteristic, complemented
199C2×#208—31no—
200#911—38no—
201C2×#204—31no—
202C2×ΓL(1,𝔽25)—31no—
203C23×C32—21no—
204C23×C32—22no—
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—31no—
208C23×C32—41no—
209C23×C32—41no—
210C23×C32—42no—
211C23×C32—61no—
212C22×C3⋊D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—41no—
217C22×C3×D3—64no—
218C22×C3×D3—61no—
219C22×C3×D3—61no—
220C22×C3×D3—64no—
221C22×C3×D3—121no—
222C22×C3×D3—124no—
223C22×C3×D3—124no—
224C22×C3×D3#6711yescharacteristic
225C22×C3×D3C3×D411yescharacteristic
226C2×D32—24no—
227C2×D32—44no—
228C32×Q8—32no—
229C32×Q8—61no—
230C32×D4—21no—
231C32×D4—22no—
232C32×D4—21no—
233C32×D4—21no—
234C32×D4—22no—
235C32×D4—22no—
236C32×D4—22no—
237C32×D4—32no—
238C32×D4—42no—
239C32×D4—41no—
240C32×D4—41no—
241C32×D4—42no—
242C32×D4—64no—
243C32×D4—61no—
244C32×D4C22×D312yescomplemented
245C32×D4C22×D312yescomplemented
246C32×D4C23×C312yescomplemented
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—31no—
251C2×C32×C4—32no—
252C2×C32×C4—32no—
253C2×C32×C4—41no—
254C2×C32×C4—64no—
255C2×C32×C4—61no—
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C23×C311yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)C23×C312yes—
261C3×#67—28no—
262C3×#67—24no—
263C3×#67—24no—
264C3×#67—64no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—28no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—24no—
270C2×C3×Dic3—24no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3#6711yescharacteristic
273C2×C3×Dic3C3×D411yescharacteristic
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—22no—
277C3×D12—32no—
278C3×D12—32no—
279C3×D12—41no—
280C3×D12—62no—
281C3×D12—64no—
282C3×D12—61no—
283C3×D12—61no—
284C3×D12—121no—
285C3×D12C22×D312yes—
286C3×D12C23×C312yes—
287C3×C4×D3—22no—
288C3×C4×D3—22no—
289C3×C4×D3#6712yes—
290C3×C4×D3C3×D412yes—
291C3×C4×D3C22×D312yes—
292C3×C4×D3C23×C312yes—
293C3×Dic6—22no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—22no—
297C3×Dic6C22×D312yescomplemented
298C3×Dic6C23×C312yescomplemented
299#626—24no—
300C32×C8—32no—
301C3⋊(C3⋊C8)C23×C312yescomplemented
302C3×C3⋊C8—22no—
303C3×C3⋊C8—32no—
304C3×C3⋊C8—32no—
305C3×C3⋊C8—62no—
306C3×C3⋊C8C22×D312yescomplemented
307C3×C3⋊C8C23×C312yescomplemented
308C2×AGL(1,ℤ/8)—91noSylow
309C2×C33—42no—
310C2×C33AGL(1,ℤ/8)12yescomplemented
311C2×C33C22×D411yescharacteristic
312C3×C3⋊D3—42no—
313C32×D3—22no—
314C32×D3—42no—
315C24×C3—181no—
316C23×D3—61no—
317C23×D3—61no—
318C3×#41—34no—
319C3×#41—34no—
320C3×#41—64no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—64no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×Q8—61no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—41no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—62no—
337C2×C3×D4—94no—
338C2×C3×D4—91no—
339C2×C3×D4—182no—
340C2×C3×D4—181no—
341C2×C3×D4D3211yescharacteristic, complemented
342C2×C3×D4C2×C3×D311yescharacteristic, complemented
343C2×C3×D4C2×C3×D311yescharacteristic, complemented
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4—62no—
350C2×#67—21no—
351C2×#67—61no—
352C22×Dic3—21no—
353#237—22no—
354#237C2×C3×D314yescomplemented
355D3×D4—34no—
356D3×D4—62no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—34no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12C2×C3×D311yescharacteristic
364C2×C4×D3C2×C3×D311yescharacteristic
365C2×Dic6C2×C3×D311yescharacteristic, complemented
366C3×SD16—94no—
367C3×SD16—94no—
368C3×D8—34no—
369C3×D8—34no—
370C3×D8—64no—
371C3×D8—94no—
372C3×M16—94no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
375C2×C3×C8—61no—
376C2×C3×C8—91no—
377#215—34no—
378#215—34no—
379#214—34no—
380#213—34no—
381#213—34no—
382#213—64no—
383#213C2×C3×D314yescomplemented
384#208—34no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
389#204—34no—
390ΓL(1,𝔽25)—34no—
391C22×C32—22no—
392C22×C32—24no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—32no—
399C22×C32—41no—
400C22×C32—42no—
401C22×C32—42no—
402C22×C32—44no—
403C22×C32—42no—
404C22×C32—44no—
405C22×C32—42no—
406C22×C32—42no—
407C22×C32—62no—
408C22×C32—62no—
409C22×C32—82no—
410C22×C32—82no—
411C22×C32—84no—
412C22×C32—122no—
413C22×C32D3×D411yescharacteristic
414C22×C32C2×#6711yescharacteristic
415C22×C32C2×C3×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—42no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—42no—
424C2×C3×D3—42no—
425C2×C3×D3—42no—
426C2×C3×D3—42no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—82no—
430C2×C3×D3—122no—
431C2×C3×D3—128no—
432C2×C3×D3—128no—
433C2×C3×D3—122no—
434C2×C3×D3—122no—
435C2×C3×D3—242no—
436C2×C3×D3C2×#6712yes—
437C2×C3×D3C2×C3×D412yes—
438D32—48no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—32no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4—62no—
449C32×C4D3×D411yescharacteristic
450C32×C4C2×#6711yescharacteristic
451C32×C4C2×C3×D411yescharacteristic
452C32×C4C23×D311yescharacteristic
453C32×C4C23×D311yescharacteristic
454C32×C4C24×C311yescharacteristic
455C3×Dic3—24no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3C2×#6712yes—
460C3×Dic3C2×C3×D412yes—
461C2×#41—31no—
462C22×D4—91no—
463AGL(1,ℤ/8)—98no—
464C2×SD16—91no—
465C2×SD16—91no—
466C2×D8—31no—
467C2×D8—91no—
468C2×M16—91no—
469C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
470C23×C3—22no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3—31no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—42no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—121no—
483C23×C3—184no—
484C23×C3—181no—
485C23×C3—364no—
486C22×D3—21no—
487C22×D3—64no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—64no—
491C22×D3—121no—
492C22×D3—124no—
493C22×D3—124no—
494C22×D3C3×#6711yescharacteristic
495C3×Q8—32no—
496C3×Q8—32no—
497C3×Q8—62no—
498C3×Q8—62no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×D4—22no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—32no—
509C3×D4—32no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—42no—
513C3×D4—42no—
514C3×D4—62no—
515C3×D4—64no—
516C3×D4—64no—
517C3×D4—68no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—92no—
521C3×D4—121no—
522C3×D4—184no—
523C3×D4—181no—
524C3×D4C2×D3212yescomplemented
525C3×D4C22×C3×D312yescomplemented
526C3×D4C22×C3×D312yescomplemented
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—41no—
537C2×C3×C4—62no—
538C2×C3×C4—62no—
539C2×C3×C4—61no—
540C2×C3×C4—64no—
541C2×C3×C4—64no—
542C2×C3×C4—62no—
543C2×C3×C4—68no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4C2×D3211yescharacteristic
547C2×C3×C4C22×C3×D311yescharacteristic
548C2×C3×C4C22×C3×D311yescharacteristic
549#67—24no—
550#67—64no—
551C2×Dic3—21no—
552C2×Dic3—24no—
553C2×Dic3C3×#6711yescharacteristic
554D12—21no—
555D12—32no—
556D12—32no—
557D12—62no—
558D12—64no—
559D12—61no—
560D12—61no—
561D12—121no—
562D12C22×C3×D312yes—
563C4×D3C3×#6712yes—
564C4×D3C22×C3×D312yes—
565Dic6—21no—
566Dic6C22×C3×D312yescomplemented
567C3×C8—32no—
568C3×C8—32no—
569C3×C8—62no—
570C3×C8—92no—
571C3⋊C8—32no—
572C3⋊C8—32no—
573C3⋊C8—62no—
574C3⋊C8C22×C3×D312yescomplemented
575C2×C32—22no—
576C2×C32—22no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—22no—
581C2×C32—42no—
582C2×C32—41no—
583C2×C32—42no—
584C2×C32—44no—
585C2×C32—42no—
586C2×C32—42no—
587C2×C32—62no—
588C2×C32—82no—
589C2×C32—82no—
590C2×C32—84no—
591C2×C32—122no—
592C2×C32#91112yescomplemented
593C2×C32#94912yescomplemented
594C2×C32C3×AGL(1,ℤ/8)12yescomplemented
595C2×C32C2×D3×D411yescharacteristic
596C2×C32C22×#6711yescharacteristic
597C2×C32C22×C3×D411yescharacteristic
598C3⋊D3—42no—
599C3×D3—22no—
600C3×D3—22no—
601C3×D3—42no—
602C3×D3—42no—
603C3×D3—42no—
604C3×D3—82no—
605C3×D3—122no—
606C3×D3—122no—
607C3×D3—242no—
608C24—181no—
609#41—34no—
610#41—62no—
611C2×Q8—31no—
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—94no—
615C2×D4—91no—
616C2×D4—182no—
617C2×D4—181no—
618C2×D4C3×D3211yescharacteristic, complemented
619C22×C4—31no—
620C22×C4—61no—
621SD16—94no—
622SD16—94no—
623D8—34no—
624D8—94no—
625M16—94no—
626C2×C8—31no—
627C2×C8—91no—
628C22×C3—24no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—32no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—44no—
640C22×C3—44no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—41no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—62no—
649C22×C3—62no—
650C22×C3—82no—
651C22×C3—82no—
652C22×C3—84no—
653C22×C3—122no—
654C22×C3—122no—
655C22×C3—122no—
656C22×C3—122no—
657C22×C3—182no—
658C22×C3—242no—
659C22×C3—368no—
660C22×C3—362no—
661C22×C3D3×#6711yescharacteristic
662C22×C3C3×D3×D411yescharacteristic
663C22×C3C2×C3×#6711yescharacteristic
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—42no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—122no—
670C2×D3—128no—
671C2×D3—128no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3—242no—
675C2×D3C2×C3×#6712yes—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—32no—
683C3×C4—32no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—62no—
687C3×C4—64no—
688C3×C4—62no—
689C3×C4—62no—
690C3×C4D3×#6711yescharacteristic
691C3×C4C3×D3×D411yescharacteristic
692C3×C4C2×C3×#6711yescharacteristic
693C3×C4C22×D3211yescharacteristic
694C3×C4C23×C3×D311yescharacteristic
695C3×C4C23×C3×D311yescharacteristic
696Dic3—22no—
697Dic3C2×C3×#6712yes—
698C32—21no—
699C32—21no—
700C32—21no—
701C32—41no—
702C32C2×#91111yescharacteristic, complemented
703C32C2×#94911yescharacteristic, complemented
704C32C2×C3×AGL(1,ℤ/8)11yescharacteristic, complemented
705C23—21no—
706C23—31no—
707C23—61no—
708C23—184no—
709C23—181no—
710C23—364no—
711Q8—32no—
712Q8—61no—
713D4—21no—
714D4—32no—
715D4—64no—
716D4—61no—
717D4—92no—
718D4—184no—
719D4—181no—
720D4C2×C3×D3212yescomplemented
721C2×C4—31no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—64no—
725C2×C4—61no—
726C2×C4C2×C3×D3211yescharacteristic
727C8—32no—
728C8—92no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—22no—
735C2×C3—44no—
736C2×C3—42no—
737C2×C3—42no—
738C2×C3—42no—
739C2×C3—41no—
740C2×C3—42no—
741C2×C3—62no—
742C2×C3—62no—
743C2×C3—82no—
744C2×C3—82no—
745C2×C3—84no—
746C2×C3—122no—
747C2×C3—122no—
748C2×C3—122no—
749C2×C3—242no—
750C2×C3—362no—
751C2×C3#6392512yesdirect product factor
752C2×C3C3×#91112yescomplemented
753C2×C3C3×#94912yescomplemented
754C2×C3C2×D3×#6711yescharacteristic
755C2×C3C2×C3×D3×D411yescharacteristic
756C2×C3C22×C3×#6711yescharacteristic
757D3—22no—
758D3—42no—
759D3—122no—
760D3—122no—
761D3—242no—
762C22—22no—
763C22—32no—
764C22—42no—
765C22—62no—
766C22—62no—
767C22—122no—
768C22—182no—
769C22—368no—
770C22—362no—
771C22C3×D3×#6711yescharacteristic
772C4—32no—
773C4—62no—
774C4C3×D3×#6711yescharacteristic
775C4C22×C3×D3211yescharacteristic
776C3—21no—
777C3—21no—
778C3—21no—
779C3—41no—
780C3C2×#6392511yescharacteristic, direct product factor
781C3C2×C3×#91111yescharacteristic, complemented
782C3C2×C3×#94911yescharacteristic, complemented
783C2—42no—
784C2—62no—
785C2—122no—
786C2—362no—
787C2C3×#6392512yesdirect product factor
788C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×C3×D4D32
hypocenterC32C2×C3×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C2×C3×#3753C2semidirect
4. C2×C32×#213C2semidirect
5. C3×#63925C2direct (N × H)
6. C2×C3×#3717C2semidirect
7. C2×C3×#3715C2semidirect
8. C2×C3×#3711C2semidirect
11. C2×#63925C3direct (N × H)
13. C2×C33×D4C22semidirect
18. C32×#237C22semidirect
21. C2×C32×Dic6C22semidirect
24. C3×D3×D12C22semidirect
25. C3×#3753C22semidirect
26. C2×C3×C3⋊(C3⋊C8)C22semidirect
27. C32×#213C22semidirect
28. C2×C32×C3⋊C8C22semidirect
29. C3×#3717C22semidirect
30. C3×#3715C22semidirect
31. C3×#3711C22semidirect
34. C2×C3×#237D3semidirect
35. C2×C3×#237C2×C3semidirect
38. C2×D3×D12C2×C3semidirect
40. C2×#3753C2×C3semidirect
49. C2×C3×#213D3semidirect
50. C2×C3×#213C2×C3semidirect
55. #63925C2×C3direct (N × H)
56. C2×#3717C2×C3semidirect
57. C2×#3715C2×C3semidirect
58. C2×#3711C2×C3semidirect
66. C33×D4C23semidirect
79. C32×Dic6C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
98. C2×C32×D4C2×D3semidirect
99. C2×C32×D4C2×D3semidirect
100. C2×C32×D4C22×C3semidirect
115. C3×#237C2×D3semidirect
116. C3×#237C22×C3semidirect
132. C2×C3×Dic6C2×D3semidirect
133. C2×C3×Dic6C22×C3semidirect
136. D3×D12C22×C3semidirect
139. #3753C22×C3semidirect
140. C2×C3⋊(C3⋊C8)C22×C3semidirect
148. C3×#213C2×D3semidirect
149. C3×#213C22×C3semidirect
155. C2×C3×C3⋊C8C2×D3semidirect
156. C2×C3×C3⋊C8C22×C3semidirect
159. #3717C22×C3semidirect
160. #3715C22×C3semidirect
161. #3711C22×C3semidirect
180. C2×#237C3×D3semidirect
198. C2×#213C3×D3semidirect
244. C32×D4C22×D3semidirect
245. C32×D4C22×D3semidirect
246. C32×D4C23×C3semidirect
297. C3×Dic6C22×D3semidirect
298. C3×Dic6C23×C3semidirect
301. C3⋊(C3⋊C8)C23×C3semidirect
306. C3×C3⋊C8C22×D3semidirect
307. C3×C3⋊C8C23×C3semidirect
310. C2×C33AGL(1,ℤ/8)semidirect
341. C2×C3×D4D32semidirect
342. C2×C3×D4C2×C3×D3semidirect
343. C2×C3×D4C2×C3×D3semidirect
354. #237C2×C3×D3semidirect
365. C2×Dic6C2×C3×D3semidirect
383. #213C2×C3×D3semidirect
388. C2×C3⋊C8C2×C3×D3semidirect
469. C33C2×AGL(1,ℤ/8)semidirect
524. C3×D4C2×D32semidirect
525. C3×D4C22×C3×D3semidirect
526. C3×D4C22×C3×D3semidirect
566. Dic6C22×C3×D3semidirect
574. C3⋊C8C22×C3×D3semidirect
592. C2×C32#911semidirect
593. C2×C32#949semidirect
594. C2×C32C3×AGL(1,ℤ/8)semidirect
618. C2×D4C3×D32semidirect
702. C32C2×#911semidirect
703. C32C2×#949semidirect
704. C32C2×C3×AGL(1,ℤ/8)semidirect
720. D4C2×C3×D32semidirect
751. C2×C3#63925direct (N × H)
752. C2×C3C3×#911semidirect
753. C2×C3C3×#949semidirect
780. C3C2×#63925direct (N × H)
781. C3C2×C3×#911semidirect
782. C3C2×C3×#949semidirect
787. C2C3×#63925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C3×D3×D122
C2×C3×#37532
C2×C32×#2132
C3×#639252
C2×C3×#37172
C2×C3×#37152
C2×C3×#37112
C2×C3×#9493
C2×C3×#9113
C2×#639253