Finite Group Databasebeta

← C2×C3×#63868 #13174399

Subgroups — C2×C3×#63868 #13174399

Order 1728.

1370 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×#3752C211yesmaximal, characteristic
2C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#3724C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×#3722C211yesmaximal, characteristic
7C2×C3×#3722C211yesmaximal, characteristic
8C3×#63868C218yesmaximal, direct product factor
9C2×C3×#898—31nomaximal
10C2×C3×#876—31nomaximal
11C2×#63868C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C3×#3752C2214yes—
20C32×Dic3⋊C4C2214yescomplemented
21C32×C4×Dic3C2214yescomplemented
22C3×#3724C2214yescomplemented
23C3×Dic3⋊Dic3C2214yescomplemented
24C3×#3722C2214yes—
25C3×#3722C2214yes—
26C2×C32×C4⋊C4—31no—
27C2×C32×C42—31no—
28C2×#3752C2×C311yescharacteristic
29C2×C3×(C2×D3)⋊C4—31no—
30C2×C3×(C2×D3)⋊C4—31no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4—31no—
34C2×C3×(C2×D3)⋊C4—31no—
35C2×C3×(C2×D3)⋊C4—61no—
36C2×C3×C4⋊Dic3—31no—
37C2×C3×Dic3⋊C4—21no—
38C2×C3×Dic3⋊C4—31no—
39C2×C3×Dic3⋊C4—31no—
40C2×C3×Dic3⋊C4—31no—
41C2×C3×Dic3⋊C4D311yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
43C2×C3×C4×Dic3—21no—
44C2×C3×C4×Dic3D311yescharacteristic, complemented
45C2×C3×C4×Dic3C2×C311yescharacteristic, complemented
46C3×#898—38no—
47C3×#876—38no—
48C2×#3724C2×C311yescharacteristic, complemented
49C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
50C2×#3722C2×C311yescharacteristic
51C2×#3722C2×C311yescharacteristic
52#63868C2×C318yesdirect product factor
53C23×C33C2311yescharacteristic
54C22×C3×C3⋊D3—22no—
55C22×C3×C3⋊D3—22no—
56C22×C3×C3⋊D3—22no—
57C22×C3×C3⋊D3C2312yes—
58C2×C33×C4—22no—
59C2×C33×C4C2312yes—
60C2×C3×C3⋊Dic3—22no—
61C2×C3×C3⋊Dic3C2312yes—
62C2×C32×Dic3—22no—
63C2×C32×Dic3—22no—
64C2×C32×Dic3—22no—
65C2×C32×Dic3—22no—
66C2×C32×Dic3C2312yes—
67C2×C32×Dic3C2312yes—
68C2×C32×Dic3C2312yes—
69C2×C32×Dic3C2312yes—
70C2×C3×#126—91no—
71C2×#898—31no—
72C2×#876—31no—
73C23×C3⋊D3C22×C311yescharacteristic
74C23×C3×D3—31no—
75C23×C3×D3—31no—
76C23×C3×D3—61no—
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—31no—
84C22×C32×C4—41no—
85C22×C32×C4C2×D311yescharacteristic
86C22×C32×C4C2×D311yescharacteristic
87C22×C32×C4C22×C311yescharacteristic
88C22×C3⋊Dic3C22×C311yescharacteristic
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—61no—
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C2×D311yescharacteristic
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C22×C311yescharacteristic
101C22×C3×Dic3C22×C311yescharacteristic
102C22×C3×Dic3C22×C311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C32×C4⋊C4—34no—
105C32×C42—34no—
106#3752C22×C314yes—
107C3×(C2×D3)⋊C4—34no—
108C3×(C2×D3)⋊C4—34no—
109C3×(C2×D3)⋊C4—34no—
110C3×(C2×D3)⋊C4—34no—
111C3×(C2×D3)⋊C4—34no—
112C3×(C2×D3)⋊C4—34no—
113C3×(C2×D3)⋊C4—64no—
114C3×C4⋊Dic3—34no—
115C3×Dic3⋊C4—24no—
116C3×Dic3⋊C4—34no—
117C3×Dic3⋊C4—34no—
118C3×Dic3⋊C4—34no—
119C3×Dic3⋊C4C2×D314yescomplemented
120C3×Dic3⋊C4C22×C314yescomplemented
121C3×C4×Dic3—24no—
122C3×C4×Dic3C2×D314yescomplemented
123C3×C4×Dic3C22×C314yescomplemented
124#3724C22×C314yescomplemented
125Dic3⋊Dic3C22×C314yescomplemented
126#3722C22×C314yes—
127#3722C22×C314yes—
128C22×C33#4112yes—
129C22×C33#4112yes—
130C22×C33#4112yes—
131C22×C33C2411yescharacteristic
132C2×C3×C3⋊D3—22no—
133C2×C3×C3⋊D3—22no—
134C2×C3×C3⋊D3—22no—
135C2×C3×C3⋊D3—44no—
136C33×C4—22no—
137C3×C3⋊Dic3—22no—
138C32×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—91no—
149C2×C3×C22⋊C4—91no—
150C2×C3×C22⋊C4—91no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×C3×C42—61no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—61no—
161C2×C4⋊Dic3—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4C3×D311yescharacteristic, complemented
166C2×C4×Dic3C3×D311yescharacteristic, complemented
167#898—38no—
168#876—38no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—41no—
173C23×C32C22×D311yescharacteristic
174C23×C32C22×D311yescharacteristic
175C23×C32C23×C311yescharacteristic
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3C23×C312yes—
180C22×C3×D3—32no—
181C22×C3×D3—32no—
182C22×C3×D3—62no—
183C22×C3×D3—64no—
184C22×C3×D3—62no—
185C22×C3×D3—62no—
186C22×C3×D3—62no—
187C22×C3×D3—62no—
188C22×C3×D3—62no—
189C22×C3×D3—62no—
190C22×C3×D3—122no—
191C22×C3×D3—122no—
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—32no—
203C2×C32×C4—42no—
204C2×C32×C4—42no—
205C2×C32×C4—42no—
206C2×C32×C4—44no—
207C2×C32×C4—62no—
208C2×C32×C4—62no—
209C2×C32×C4—62no—
210C2×C32×C4—62no—
211C2×C32×C4C22×D312yes—
212C2×C32×C4C22×D312yes—
213C2×C32×C4C23×C312yes—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3C23×C312yes—
216C2×C3×Dic3—24no—
217C2×C3×Dic3—24no—
218C2×C3×Dic3—24no—
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—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—32no—
233C2×C3×Dic3—42no—
234C2×C3×Dic3—62no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—122no—
238C2×C3×Dic3C22×D312yes—
239C2×C3×Dic3C22×D312yes—
240C2×C3×Dic3C22×D312yes—
241C2×C3×Dic3C22×D312yes—
242C2×C3×Dic3C23×C312yes—
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
251C3×C3⋊D3—42no—
252C24×C3—91no—
253C23×D3—31no—
254C23×D3—31no—
255C23×D3—61no—
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—31no—
266C22×C3×C4—31no—
267C22×C3×C4—41no—
268C22×C3×C4—61no—
269C22×C3×C4—61no—
270C22×C3×C4—61no—
271C22×C3×C4—61no—
272C22×C3×C4—91no—
273C22×C3×C4D3211yescharacteristic
274C22×C3×C4C2×C3×D311yescharacteristic
275C22×C3×C4C2×C3×D311yescharacteristic
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—61no—
279C22×Dic3C2×C3×D311yescharacteristic
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—94no—
289C3×C22⋊C4—94no—
290C3×C22⋊C4—94no—
291C3×C42—34no—
292C3×C42—34no—
293C3×C42—64no—
294(C2×D3)⋊C4—34no—
295(C2×D3)⋊C4—34no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—64no—
301C4⋊Dic3—34no—
302Dic3⋊C4—34no—
303Dic3⋊C4—34no—
304Dic3⋊C4—34no—
305Dic3⋊C4C2×C3×D314yescomplemented
306C4×Dic3C2×C3×D314yescomplemented
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#23512yes—
324C22×C32#23512yes—
325C22×C32#23512yes—
326C22×C32#23512yes—
327C22×C32#23712yes—
328C22×C32#23912yes—
329C22×C32C3×#4112yes—
330C22×C32C3×#4112yes—
331C22×C32C3×#4112yes—
332C22×C32C23×D311yescharacteristic
333C22×C32C23×D311yescharacteristic
334C22×C32C24×C311yescharacteristic
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—22no—
338C2×C3⋊D3—44no—
339C2×C3×D3—64no—
340C2×C3×D3—62no—
341C2×C3×D3—62no—
342C2×C3×D3—62no—
343C2×C3×D3—62no—
344C2×C3×D3—62no—
345C2×C3×D3—62no—
346C2×C3×D3—122no—
347C2×C3×D3—122no—
348C2×C3×D3—128no—
349C2×C3×D3—124no—
350C2×C3×D3—124no—
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—
361C32×C4—62no—
362C3⋊Dic3—22no—
363C3×Dic3—24no—
364C3×Dic3—24no—
365C3×Dic3—24no—
366C3×Dic3—22no—
367C3×Dic3—22no—
368C3×Dic3—22no—
369C3×Dic3—22no—
370C3×Dic3—22no—
371C3×Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3—42no—
375C3×Dic3—62no—
376C3×Dic3—62no—
377C3×Dic3—122no—
378#126—98no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C42—31no—
386C33C2×#12611yescharacteristic, complemented, Sylow
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—41no—
391C23×C3—92no—
392C23×C3—182no—
393C23×C3—182no—
394C23×C3—182no—
395C23×C3C2×D3211yescharacteristic
396C23×C3C22×C3×D311yescharacteristic
397C23×C3C22×C3×D311yescharacteristic
398C22×D3—32no—
399C22×D3—32no—
400C22×D3—62no—
401C22×D3—64no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—122no—
409C22×D3—122no—
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—32no—
424C2×C3×C4—32no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—44no—
428C2×C3×C4—42no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—64no—
434C2×C3×C4—64no—
435C2×C3×C4—64no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4—92no—
445C2×C3×C4—122no—
446C2×C3×C4—182no—
447C2×C3×C4C2×D3212yes—
448C2×C3×C4C22×C3×D312yes—
449C2×C3×C4C22×C3×D312yes—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—32no—
455C2×Dic3—32no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—122no—
460C2×Dic3C22×C3×D312yes—
461C2×Dic3C22×C3×D312yes—
462C2×Dic3C22×C3×D312yes—
463C2×Dic3C22×C3×D312yes—
464C2×C32—24no—
465C2×C32—21no—
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—24no—
475C2×C32—24no—
476C2×C32—44no—
477C2×C32—41no—
478C2×C32—41no—
479C2×C32—41no—
480C2×C32#87614yescomplemented
481C2×C32#89814yescomplemented
482C2×C32C3×#12614yescomplemented
483C2×C32C2×#23511yescharacteristic
484C2×C32C2×#23511yescharacteristic
485C2×C32C2×#23511yescharacteristic
486C2×C32C2×#23511yescharacteristic
487C2×C32C2×#23711yescharacteristic
488C2×C32C2×#23911yescharacteristic
489C2×C32C2×C3×#4111yescharacteristic
490C2×C32C2×C3×#4111yescharacteristic
491C2×C32C2×C3×#4111yescharacteristic
492C3⋊D3—42no—
493C3×D3—124no—
494C3×D3—122no—
495C3×D3—122no—
496C24—91no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—91no—
502C22×C4C3×D3211yescharacteristic
503C4⋊C4—34no—
504C4⋊C4—94no—
505C4⋊C4—94no—
506C22⋊C4—94no—
507C22⋊C4—94no—
508C22⋊C4—94no—
509C42—34no—
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—182no—
527C22×C3—182no—
528C22×C3—182no—
529C22×C3—364no—
530C22×C3#379812yes—
531C22×C3#379912yes—
532C22×C3#380412yes—
533C22×C3C3×#23512yes—
534C22×C3C3×#23512yes—
535C22×C3C3×#23512yes—
536C22×C3C3×#23512yes—
537C22×C3C3×#23712yes—
538C22×C3C3×#23912yes—
539C22×C3C22×D3211yescharacteristic
540C22×C3C23×C3×D311yescharacteristic
541C22×C3C23×C3×D311yescharacteristic
542C2×D3—64no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—62no—
549C2×D3—122no—
550C2×D3—122no—
551C2×D3—128no—
552C2×D3—124no—
553C2×D3—124no—
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—64no—
563C3×C4—64no—
564C3×C4—62no—
565C3×C4—62no—
566C3×C4—62no—
567C3×C4—62no—
568C3×C4—62no—
569C3×C4—62no—
570C3×C4—62no—
571C3×C4—62no—
572C3×C4—122no—
573C3×C4—182no—
574Dic3—22no—
575Dic3—22no—
576Dic3—22no—
577Dic3—22no—
578Dic3—62no—
579Dic3—62no—
580Dic3—122no—
581C32—21no—
582C32—21no—
583C32—21no—
584C32—41no—
585C32C2×#87611yescharacteristic, complemented
586C32C2×#89811yescharacteristic, complemented
587C32C2×C3×#12611yescharacteristic, complemented
588C23—92no—
589C23—182no—
590C23—182no—
591C23—182no—
592C23C2×C3×D3211yescharacteristic
593C2×C4—22no—
594C2×C4—32no—
595C2×C4—32no—
596C2×C4—32no—
597C2×C4—32no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—92no—
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—362no—
622C2×C3#6386814yesdirect product factor
623C2×C3C3×#87614yescomplemented
624C2×C3C3×#89814yescomplemented
625C2×C3C2×#379811yescharacteristic
626C2×C3C2×#379911yescharacteristic
627C2×C3C2×#380411yescharacteristic
628C2×C3C2×C3×#23511yescharacteristic
629C2×C3C2×C3×#23511yescharacteristic
630C2×C3C2×C3×#23511yescharacteristic
631C2×C3C2×C3×#23511yescharacteristic
632C2×C3C2×C3×#23711yescharacteristic
633C2×C3C2×C3×#23911yescharacteristic
634D3—124no—
635D3—122no—
636D3—122no—
637C22—182no—
638C22—182no—
639C22—182no—
640C22—364no—
641C22C3×#379812yes—
642C22C3×#379912yes—
643C22C3×#380412yes—
644C22C22×C3×D3211yescharacteristic
645C4—22no—
646C4—62no—
647C4—62no—
648C4—62no—
649C4—62no—
650C4—182no—
651C3—21no—
652C3—21no—
653C3—21no—
654C3—41no—
655C3C2×#6386811yescharacteristic, direct product factor
656C3C2×C3×#87611yescharacteristic, complemented
657C3C2×C3×#89811yescharacteristic, complemented
658C2—362no—
659C2C3×#6386814yesdirect product factor
660C2C2×C3×#379811yescharacteristic
661C2C2×C3×#379911yescharacteristic
662C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×C3⋊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
2. C2×C32×Dic3⋊C4C2semidirect
3. C2×C32×C4×Dic3C2semidirect
4. C2×C3×#3724C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
8. C3×#63868C2direct (N × H)
11. C2×#63868C3direct (N × H)
20. C32×Dic3⋊C4C22semidirect
21. C32×C4×Dic3C22semidirect
22. C3×#3724C22semidirect
23. C3×Dic3⋊Dic3C22semidirect
41. C2×C3×Dic3⋊C4D3semidirect
42. C2×C3×Dic3⋊C4C2×C3semidirect
44. C2×C3×C4×Dic3D3semidirect
45. C2×C3×C4×Dic3C2×C3semidirect
48. C2×#3724C2×C3semidirect
49. C2×Dic3⋊Dic3C2×C3semidirect
52. #63868C2×C3direct (N × H)
119. C3×Dic3⋊C4C2×D3semidirect
120. C3×Dic3⋊C4C22×C3semidirect
122. C3×C4×Dic3C2×D3semidirect
123. C3×C4×Dic3C22×C3semidirect
124. #3724C22×C3semidirect
125. Dic3⋊Dic3C22×C3semidirect
165. C2×Dic3⋊C4C3×D3semidirect
166. C2×C4×Dic3C3×D3semidirect
247. C2×C33#126semidirect
305. Dic3⋊C4C2×C3×D3semidirect
306. C4×Dic3C2×C3×D3semidirect
386. C33C2×#126semidirect
480. C2×C32#876semidirect
481. C2×C32#898semidirect
482. C2×C32C3×#126semidirect
585. C32C2×#876semidirect
586. C32C2×#898semidirect
587. C32C2×C3×#126semidirect
622. C2×C3#63868direct (N × H)
623. C2×C3C3×#876semidirect
624. C2×C3C3×#898semidirect
655. C3C2×#63868direct (N × H)
656. C3C2×C3×#876semidirect
657. C3C2×C3×#898semidirect
659. C2C3×#63868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#37522
C2×C32×Dic3⋊C42
C2×C32×C4×Dic32
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C2×C3×#37222
C3×#638682
C2×C3×#8983
C2×C3×#8763
C2×#638683