Finite Group Databasebeta

← C2×C3×#63861 #13174389

Subgroups — C2×C3×#63861 #13174389

Order 1728.

1354 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#3724C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8C3×#63861C218yesmaximal, direct product factor
9C2×C3×#898—31nomaximal
10C2×C3×#879—31nomaximal
11C2×#63861C311yesmaximal, characteristic, direct product factor
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C3×C4⋊(C3⋊Dic3)C2214yescomplemented
20C32×(C2×D3)⋊C4C2214yes—
21C32×Dic3⋊C4C2214yescomplemented
22C3×#3724C2214yescomplemented
23C3×(C2×D3)⋊Dic3C2214yes—
24C3×(C2×D3)⋊Dic3C2214yes—
25C3×Dic32C2214yescomplemented
26C2×C32×C4⋊C4—31no—
27C2×C32×C22⋊C4—31no—
28C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
29C2×C3×#217—31no—
30C2×C3×#217—31no—
31C2×C3×(C2×D3)⋊C4—21no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4—31no—
34C2×C3×(C2×D3)⋊C4D311yescharacteristic
35C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
36C2×C3×C4⋊Dic3—31no—
37C2×C3×C4⋊Dic3—31no—
38C2×C3×C4⋊Dic3—61no—
39C2×C3×Dic3⋊C4—21no—
40C2×C3×Dic3⋊C4—31no—
41C2×C3×Dic3⋊C4—31no—
42C2×C3×Dic3⋊C4D311yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
44C2×C3×C4×Dic3—31no—
45C2×C3×C4×Dic3—31no—
46C3×#898—38no—
47C3×#879—38no—
48C2×#3724C2×C311yescharacteristic, complemented
49C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
50C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
51C2×Dic32C2×C311yescharacteristic, complemented
52#63861C2×C318yesdirect product factor
53C23×C33C2311yescharacteristic
54C22×C32×D3—22no—
55C22×C32×D3—22no—
56C22×C32×D3—22no—
57C22×C32×D3C2312yes—
58C2×C33×C4—22no—
59C2×C33×C4C2312yes—
60C2×C3×C3⋊Dic3—22no—
61C2×C3×C3⋊Dic3—22no—
62C2×C3×C3⋊Dic3C2312yes—
63C2×C3×C3⋊Dic3C2312yes—
64C2×C32×Dic3—22no—
65C2×C32×Dic3—22no—
66C2×C32×Dic3—22no—
67C2×C32×Dic3C2312yes—
68C2×C32×Dic3C2312yes—
69C2×C32×Dic3C2312yes—
70C2×C3×#126—91no—
71C2×#898—31no—
72C2×#879—31no—
73C24×C32—31no—
74C23×C3×D3—21no—
75C23×C3×D3C2×D311yescharacteristic
76C23×C3×D3C22×C311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4—31no—
81C22×C32×C4—31no—
82C22×C32×C4—31no—
83C22×C32×C4—41no—
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C2×D311yescharacteristic
86C22×C32×C4C22×C311yescharacteristic
87C22×C3⋊Dic3C22×C311yescharacteristic
88C22×C3⋊Dic3C22×C311yescharacteristic
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—61no—
97C22×C3×Dic3—61no—
98C22×C3×Dic3C2×D311yescharacteristic
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C2×D311yescharacteristic
101C22×C3×Dic3C22×C311yescharacteristic
102C22×C3×Dic3C22×C311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C32×C4⋊C4—34no—
105C32×C22⋊C4—34no—
106C4⋊(C3⋊Dic3)C22×C314yescomplemented
107C3×#217—34no—
108C3×#217—34no—
109C3×(C2×D3)⋊C4—24no—
110C3×(C2×D3)⋊C4—34no—
111C3×(C2×D3)⋊C4—34no—
112C3×(C2×D3)⋊C4C2×D314yes—
113C3×(C2×D3)⋊C4C22×C314yes—
114C3×C4⋊Dic3—34no—
115C3×C4⋊Dic3—34no—
116C3×C4⋊Dic3—64no—
117C3×Dic3⋊C4—24no—
118C3×Dic3⋊C4—34no—
119C3×Dic3⋊C4—34no—
120C3×Dic3⋊C4C2×D314yescomplemented
121C3×Dic3⋊C4C22×C314yescomplemented
122C3×C4×Dic3—34no—
123C3×C4×Dic3—34no—
124#3724C22×C314yescomplemented
125(C2×D3)⋊Dic3C22×C314yes—
126(C2×D3)⋊Dic3C22×C314yes—
127Dic32C22×C314yescomplemented
128C22×C33#4112yes—
129C22×C33#4112yes—
130C22×C33#4112yes—
131C22×C33C2411yescharacteristic
132C2×C32×D3—22no—
133C2×C32×D3—22no—
134C2×C32×D3—22no—
135C2×C32×D3—44no—
136C33×C4—22no—
137C3×C3⋊Dic3—22no—
138C3×C3⋊Dic3—22no—
139C32×Dic3—22no—
140C32×Dic3—22no—
141C32×Dic3—22no—
142C3×#126—98no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—61no—
146C2×C3×C4⋊C4—91no—
147C2×C3×C4⋊C4—91no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—61no—
151C2×C3×C22⋊C4—91no—
152C2×C3×C22⋊C4—91no—
153C2×C3×C42—91no—
154C2×#217—31no—
155C2×#217—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4C3×D311yescharacteristic
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—61no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4C3×D311yescharacteristic, complemented
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167#898—38no—
168#879—38no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—32no—
173C23×C32—41no—
174C23×C32—62no—
175C23×C32—62no—
176C23×C32—62no—
177C23×C32C22×D311yescharacteristic
178C23×C32C22×D311yescharacteristic
179C23×C32C23×C311yescharacteristic
180C22×C3×D3—24no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—42no—
189C22×C3×D3—42no—
190C22×C3×D3C22×D312yes—
191C22×C3×D3C23×C312yes—
192C2×C32×C4—22no—
193C2×C32×C4—24no—
194C2×C32×C4—22no—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4—22no—
199C2×C32×C4—32no—
200C2×C32×C4—32no—
201C2×C32×C4—32no—
202C2×C32×C4—42no—
203C2×C32×C4—42no—
204C2×C32×C4—42no—
205C2×C32×C4—44no—
206C2×C32×C4—62no—
207C2×C32×C4—62no—
208C2×C32×C4—62no—
209C2×C32×C4C22×D312yes—
210C2×C32×C4C22×D312yes—
211C2×C32×C4C23×C312yes—
212C2×C3⋊Dic3—22no—
213C2×C3⋊Dic3—22no—
214C2×C3⋊Dic3C23×C312yes—
215C2×C3⋊Dic3C23×C312yes—
216C2×C3×Dic3—24no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—32no—
227C2×C3×Dic3—32no—
228C2×C3×Dic3—32no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—42no—
231C2×C3×Dic3—42no—
232C2×C3×Dic3—62no—
233C2×C3×Dic3—62no—
234C2×C3×Dic3—62no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—62no—
238C2×C3×Dic3—122no—
239C2×C3×Dic3—122no—
240C2×C3×Dic3C22×D312yes—
241C2×C3×Dic3C22×D312yes—
242C2×C3×Dic3C22×D312yes—
243C2×C3×Dic3C23×C312yes—
244C2×C3×Dic3C23×C312yes—
245C2×C3×Dic3C23×C312yes—
246C2×#126—91noSylow
247C2×C33#12614yescomplemented
248C2×C33C2×#4111yescharacteristic
249C2×C33C2×#4111yescharacteristic
250C2×C33C2×#4111yescharacteristic
251C32×D3—42no—
252C24×C3—31no—
253C24×C3—31no—
254C24×C3—61no—
255C23×D3C2×C3×D311yescharacteristic
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—41no—
266C22×C3×C4—61no—
267C22×C3×C4—61no—
268C22×C3×C4—61no—
269C22×C3×C4—91no—
270C22×C3×C4—91no—
271C22×C3×C4D3211yescharacteristic
272C22×C3×C4C2×C3×D311yescharacteristic
273C22×C3×C4C2×C3×D311yescharacteristic
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—61no—
279C22×Dic3—61no—
280C22×Dic3C2×C3×D311yescharacteristic
281C22×Dic3C2×C3×D311yescharacteristic
282C22×Dic3C2×C3×D311yescharacteristic
283C3×C4⋊C4—34no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—64no—
286C3×C4⋊C4—94no—
287C3×C4⋊C4—94no—
288C3×C22⋊C4—34no—
289C3×C22⋊C4—34no—
290C3×C22⋊C4—64no—
291C3×C22⋊C4—94no—
292C3×C22⋊C4—94no—
293C3×C42—94no—
294#217—34no—
295#217—34no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4C2×C3×D314yes—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—64no—
302Dic3⋊C4—34no—
303Dic3⋊C4—34no—
304Dic3⋊C4C2×C3×D314yescomplemented
305C4×Dic3—34no—
306C4×Dic3—34no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—42no—
320C22×C32—42no—
321C22×C32—42no—
322C22×C32—41no—
323C22×C32—62no—
324C22×C32—62no—
325C22×C32—62no—
326C22×C32—124no—
327C22×C32#23512yes—
328C22×C32#23512yes—
329C22×C32#23712yes—
330C22×C32#23712yes—
331C22×C32#23712yes—
332C22×C32#23912yes—
333C22×C32C3×#4112yes—
334C22×C32C3×#4112yes—
335C22×C32C3×#4112yes—
336C22×C32C23×D311yescharacteristic
337C22×C32C23×D311yescharacteristic
338C22×C32C24×C311yescharacteristic
339C2×C3×D3—24no—
340C2×C3×D3—22no—
341C2×C3×D3—22no—
342C2×C3×D3—22no—
343C2×C3×D3—22no—
344C2×C3×D3—22no—
345C2×C3×D3—22no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C2×C3×D3—48no—
349C2×C3×D3—44no—
350C2×C3×D3—44no—
351C32×C4—22no—
352C32×C4—24no—
353C32×C4—22no—
354C32×C4—22no—
355C32×C4—42no—
356C32×C4—42no—
357C32×C4—44no—
358C32×C4—62no—
359C32×C4—62no—
360C32×C4—62no—
361C3⋊Dic3—22no—
362C3⋊Dic3—22no—
363C3×Dic3—24no—
364C3×Dic3—22no—
365C3×Dic3—22no—
366C3×Dic3—22no—
367C3×Dic3—22no—
368C3×Dic3—22no—
369C3×Dic3—22no—
370C3×Dic3—42no—
371C3×Dic3—42no—
372C3×Dic3—62no—
373C3×Dic3—62no—
374C3×Dic3—62no—
375C3×Dic3—62no—
376C3×Dic3—122no—
377C3×Dic3—122no—
378#126—98no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—91no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C42—91no—
386C33C2×#12611yescharacteristic, complemented, Sylow
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—32no—
391C23×C3—32no—
392C23×C3—41no—
393C23×C3—62no—
394C23×C3—64no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—62no—
401C23×C3—122no—
402C23×C3—122no—
403C23×C3C2×D3211yescharacteristic
404C23×C3C22×C3×D311yescharacteristic
405C23×C3C22×C3×D311yescharacteristic
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3C22×C3×D312yes—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—32no—
418C2×C3×C4—32no—
419C2×C3×C4—32no—
420C2×C3×C4—32no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—44no—
426C2×C3×C4—42no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—64no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—92no—
438C2×C3×C4—92no—
439C2×C3×C4—122no—
440C2×C3×C4—122no—
441C2×C3×C4—182no—
442C2×C3×C4—182no—
443C2×C3×C4C2×D3212yes—
444C2×C3×C4C22×C3×D312yes—
445C2×C3×C4C22×C3×D312yes—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—32no—
450C2×Dic3—32no—
451C2×Dic3—32no—
452C2×Dic3—32no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—122no—
460C2×Dic3—122no—
461C2×Dic3C22×C3×D312yes—
462C2×Dic3C22×C3×D312yes—
463C2×Dic3C22×C3×D312yes—
464C2×C32—24no—
465C2×C32—24no—
466C2×C32—21no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32—21no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—24no—
476C2×C32—44no—
477C2×C32—41no—
478C2×C32—41no—
479C2×C32—41no—
480C2×C32—122no—
481C2×C32#87914yescomplemented
482C2×C32#89814yescomplemented
483C2×C32C3×#12614yescomplemented
484C2×C32C2×#23511yescharacteristic
485C2×C32C2×#23511yescharacteristic
486C2×C32C2×#23711yescharacteristic
487C2×C32C2×#23711yescharacteristic
488C2×C32C2×#23711yescharacteristic
489C2×C32C2×#23911yescharacteristic
490C2×C32C2×C3×#4111yescharacteristic
491C2×C32C2×C3×#4111yescharacteristic
492C2×C32C2×C3×#4111yescharacteristic
493C3×D3—44no—
494C3×D3—42no—
495C3×D3—42no—
496C24—31no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—31no—
500C22×C4—91no—
501C22×C4—91no—
502C22×C4C3×D3211yescharacteristic
503C4⋊C4—34no—
504C4⋊C4—94no—
505C4⋊C4—94no—
506C22⋊C4—34no—
507C22⋊C4—94no—
508C22⋊C4—94no—
509C42—94no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—41no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—64no—
527C22×C3—62no—
528C22×C3—62no—
529C22×C3—62no—
530C22×C3—62no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3—122no—
534C22×C3—122no—
535C22×C3—128no—
536C22×C3—124no—
537C22×C3—124no—
538C22×C3#379512yes—
539C22×C3#379912yes—
540C22×C3#380512yes—
541C22×C3C3×#23512yes—
542C22×C3C3×#23512yes—
543C22×C3C3×#23712yes—
544C22×C3C3×#23712yes—
545C22×C3C3×#23712yes—
546C22×C3C3×#23912yes—
547C22×C3C22×D3211yescharacteristic
548C22×C3C23×C3×D311yescharacteristic
549C22×C3C23×C3×D311yescharacteristic
550C2×D3—22no—
551C2×D3—22no—
552C2×D3—22no—
553C2×D3—44no—
554C3×C4—24no—
555C3×C4—22no—
556C3×C4—22no—
557C3×C4—22no—
558C3×C4—42no—
559C3×C4—42no—
560C3×C4—44no—
561C3×C4—64no—
562C3×C4—62no—
563C3×C4—62no—
564C3×C4—62no—
565C3×C4—62no—
566C3×C4—62no—
567C3×C4—62no—
568C3×C4—122no—
569C3×C4—122no—
570C3×C4—182no—
571C3×C4—182no—
572Dic3—22no—
573Dic3—22no—
574Dic3—22no—
575Dic3—62no—
576Dic3—62no—
577Dic3—62no—
578Dic3—62no—
579Dic3—122no—
580Dic3—122no—
581C32—21no—
582C32—21no—
583C32—21no—
584C32—41no—
585C32C2×#87911yescharacteristic, complemented
586C32C2×#89811yescharacteristic, complemented
587C32C2×C3×#12611yescharacteristic, complemented
588C23—32no—
589C23—62no—
590C23—62no—
591C23—62no—
592C23C2×C3×D3211yescharacteristic
593C2×C4—22no—
594C2×C4—32no—
595C2×C4—32no—
596C2×C4—32no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—92no—
601C2×C4—92no—
602C2×C4—182no—
603C2×C4—182no—
604C2×C4C2×C3×D3212yes—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—24no—
609C2×C3—24no—
610C2×C3—24no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—41no—
618C2×C3—44no—
619C2×C3—41no—
620C2×C3—41no—
621C2×C3—124no—
622C2×C3—122no—
623C2×C3—122no—
624C2×C3#6386114yesdirect product factor
625C2×C3C3×#87914yescomplemented
626C2×C3C3×#89814yescomplemented
627C2×C3C2×#379511yescharacteristic
628C2×C3C2×#379911yescharacteristic
629C2×C3C2×#380511yescharacteristic
630C2×C3C2×C3×#23511yescharacteristic
631C2×C3C2×C3×#23511yescharacteristic
632C2×C3C2×C3×#23711yescharacteristic
633C2×C3C2×C3×#23711yescharacteristic
634C2×C3C2×C3×#23711yescharacteristic
635C2×C3C2×C3×#23911yescharacteristic
636D3—42no—
637C22—62no—
638C22—62no—
639C22—62no—
640C22—124no—
641C22C3×#379512yes—
642C22C3×#379912yes—
643C22C3×#380512yes—
644C22C22×C3×D3211yescharacteristic
645C4—22no—
646C4—62no—
647C4—62no—
648C4—62no—
649C4—182no—
650C4—182no—
651C3—21no—
652C3—21no—
653C3—21no—
654C3—41no—
655C3C2×#6386111yescharacteristic, direct product factor
656C3C2×C3×#87911yescharacteristic, complemented
657C3C2×C3×#89811yescharacteristic, complemented
658C2—122no—
659C2C3×#6386114yesdirect product factor
660C2C2×C3×#379511yescharacteristic
661C2C2×C3×#379911yescharacteristic
662C2C2×C3×#380511yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4⋊(C3⋊Dic3)C2semidirect
3. C2×C32×Dic3⋊C4C2semidirect
4. C2×C3×#3724C2semidirect
7. C2×C3×Dic32C2semidirect
8. C3×#63861C2direct (N × H)
11. C2×#63861C3direct (N × H)
19. C3×C4⋊(C3⋊Dic3)C22semidirect
21. C32×Dic3⋊C4C22semidirect
22. C3×#3724C22semidirect
25. C3×Dic32C22semidirect
28. C2×C4⋊(C3⋊Dic3)C2×C3semidirect
42. C2×C3×Dic3⋊C4D3semidirect
43. C2×C3×Dic3⋊C4C2×C3semidirect
48. C2×#3724C2×C3semidirect
51. C2×Dic32C2×C3semidirect
52. #63861C2×C3direct (N × H)
106. C4⋊(C3⋊Dic3)C22×C3semidirect
120. C3×Dic3⋊C4C2×D3semidirect
121. C3×Dic3⋊C4C22×C3semidirect
124. #3724C22×C3semidirect
127. Dic32C22×C3semidirect
164. C2×Dic3⋊C4C3×D3semidirect
247. C2×C33#126semidirect
304. Dic3⋊C4C2×C3×D3semidirect
386. C33C2×#126semidirect
481. C2×C32#879semidirect
482. C2×C32#898semidirect
483. C2×C32C3×#126semidirect
585. C32C2×#879semidirect
586. C32C2×#898semidirect
587. C32C2×C3×#126semidirect
624. C2×C3#63861direct (N × H)
625. C2×C3C3×#879semidirect
626. C2×C3C3×#898semidirect
655. C3C2×#63861direct (N × H)
656. C3C2×C3×#879semidirect
657. C3C2×C3×#898semidirect
659. C2C3×#63861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4⋊(C3⋊Dic3)2
C2×C32×(C2×D3)⋊C42
C2×C32×Dic3⋊C42
C2×C3×#37242
C2×C3×(C2×D3)⋊Dic32
C2×C3×Dic322
C3×#638612
C2×C3×#8983
C2×C3×#8793
C2×#638613