Finite Group Databasebeta

← C3×C4×(C2×D3)⋊Dic3 #13158194

Subgroups — C3×C4×(C2×D3)⋊Dic3 #13158194

Order 1728.

1538 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
1C22×C32×C4×D3C211yesmaximal, characteristic
2C2×C3×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊Dic3C212yesmaximal
5C3×#63579C212yesmaximal, complemented
6C3×C4×#217—31nomaximal
7C3×C4×(C2×D3)⋊C4—31nomaximal
8C4×(C2×D3)⋊Dic3C311yesmaximal, characteristic, direct product factor
9C23×C32×D3C2211yescharacteristic
10C22×C33×C4C2211yescharacteristic
11C22×C3×C3⋊Dic3C2212yes—
12C22×C32×Dic3C2211yescharacteristic
13C22×C32×Dic3C2212yes—
14C2×C32×C4×D3—22no—
15C2×C32×C4×D3—22no—
16C2×C32×C4×D3C414yescomplemented
17C3×C4×C3⋊Dic3—22no—
18C32×C4×Dic3—22no—
19C3×(C2×D3)⋊Dic3C418yesdirect product factor
20C23×C32×C4—31no—
21C22×C3×C4×D3—21no—
22C22×C3×C4×D3D311yescharacteristic
23C22×C3×C4×D3C2×C311yescharacteristic
24C2×C32×C42—31no—
25C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
26C2×C3×#217—32no—
27C2×C3×(C2×D3)⋊C4—32no—
28C2×C3×C4×Dic3—21no—
29C2×C3×C4×Dic3—31no—
30C2×C3×C4×Dic3—31no—
31C2×C3×C4×Dic3—61no—
32C2×C3×C4×Dic3D311yescharacteristic, complemented
33C2×C3×C4×Dic3C2×C311yescharacteristic, complemented
34C2×(C2×D3)⋊Dic3C2×C312yes—
35C3×C3⋊#95—32no—
36C3×C3⋊#95—32no—
37#63579C2×C312yescomplemented
38C23×C33C2311yescharacteristic
39C22×C32×D3—21no—
40C22×C32×D3—21no—
41C22×C32×D3—22no—
42C22×C32×D3C2×C414yes—
43C22×C32×D3C2×C412yes—
44C2×C33×C4C2×C412yes—
45C2×C33×C4D412yes—
46C2×C33×C4D412yes—
47C2×C3×C3⋊Dic3—22no—
48C2×C3×C3⋊Dic3—22no—
49C2×C3×C3⋊Dic3C2×C414yescomplemented
50C2×C32×Dic3—21no—
51C2×C32×Dic3—21no—
52C2×C32×Dic3—22no—
53C2×C32×Dic3—22no—
54C2×C32×Dic3C2×C412yes—
55C2×C32×Dic3C2×C414yescomplemented
56C32×C4×D3—28no—
57C3×C4×C22⋊C4—91no—
58C4×#217—31no—
59C4×(C2×D3)⋊C4—31no—
60C24×C32—31no—
61C23×C3×D3—21no—
62C23×C3×D3C2×D311yescharacteristic
63C23×C3×D3C22×C311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—32no—
68C22×C32×C4—31no—
69C22×C32×C4—34no—
70C22×C32×C4—41no—
71C22×C32×C4—62no—
72C22×C32×C4—62no—
73C22×C32×C4C2×D311yescharacteristic
74C22×C32×C4C2×D311yescharacteristic
75C22×C32×C4C22×C311yescharacteristic
76C22×C3⋊Dic3C22×C312yes—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—32no—
80C22×C3×Dic3—32no—
81C22×C3×Dic3—62no—
82C22×C3×Dic3C2×D312yes—
83C22×C3×Dic3C2×D311yescharacteristic
84C22×C3×Dic3C22×C311yescharacteristic
85C22×C3×Dic3C22×C312yes—
86C2×C3×C4×D3—24no—
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3Dic314yescomplemented
94C2×C3×C4×D3C3×C414yescomplemented
95C32×C42—62no—
96C4×C3⋊Dic3—22no—
97C3×#217—38no—
98C3×(C2×D3)⋊C4—38no—
99C3×C4×Dic3—24no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3—22no—
102C3×C4×Dic3—64no—
103C3×C4×Dic3—62no—
104C3×C4×Dic3—62no—
105(C2×D3)⋊Dic3C3×C418yesdirect product factor
106C22×C33C22×C411yescharacteristic
107C22×C33C22×C412yes—
108C22×C33C2×D411yescharacteristic
109C22×C33C2×D411yescharacteristic
110C22×C33#4112yes—
111C2×C32×D3—22no—
112C2×C32×D3—22no—
113C2×C32×D3—24no—
114C2×C32×D3—24no—
115C2×C32×D3C4214yescomplemented
116C33×C4C22⋊C414yescomplemented
117C3×C3⋊Dic3—24no—
118C32×Dic3—22no—
119C32×Dic3—24no—
120C23×C3×C4—31no—
121C23×C3×C4—31no—
122C23×C3×C4—61no—
123C22×C4×D3C3×D311yescharacteristic
124C2×C3×C22⋊C4—92no—
125C2×C3×C42—31no—
126C2×C3×C42—31no—
127C2×C3×C42—61no—
128C2×C3×C42—91no—
129C2×#217—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3C3×D311yescharacteristic, complemented
135C3×#95—92no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C23×C32—21no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32—34no—
142C23×C32—32no—
143C23×C32—41no—
144C23×C32—61no—
145C23×C32—62no—
146C23×C32—61no—
147C23×C32C22×D311yescharacteristic
148C23×C32C22×D311yescharacteristic
149C23×C32C23×C311yescharacteristic
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—22no—
159C22×C3×D3—24no—
160C22×C3×D3—22no—
161C22×C3×D3C4×D314yes—
162C22×C3×D3C2×Dic312yes—
163C22×C3×D3C2×C3×C414yes—
164C22×C3×D3C2×C3×C412yes—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—34no—
175C2×C32×C4—32no—
176C2×C32×C4—42no—
177C2×C32×C4—42no—
178C2×C32×C4—42no—
179C2×C32×C4—61no—
180C2×C32×C4—62no—
181C2×C32×C4—62no—
182C2×C32×C4—61no—
183C2×C32×C4—68no—
184C2×C32×C4C4×D312yes—
185C2×C32×C4D1212yes—
186C2×C32×C4C2×Dic312yes—
187C2×C32×C4#6712yes—
188C2×C32×C4#6712yes—
189C2×C32×C4#6712yes—
190C2×C32×C4C2×C3×C412yes—
191C2×C32×C4C3×D412yes—
192C2×C32×C4C3×D412yes—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3C2×C3×C414yescomplemented
196C2×C3×Dic3—24no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—24no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—34no—
211C2×C3×Dic3—34no—
212C2×C3×Dic3—64no—
213C2×C3×Dic3—64no—
214C2×C3×Dic3—64no—
215C2×C3×Dic3—62no—
216C2×C3×Dic3—62no—
217C2×C3×Dic3—62no—
218C2×C3×Dic3—62no—
219C2×C3×Dic3C4×D314yescomplemented
220C2×C3×Dic3C2×Dic312yes—
221C2×C3×Dic3C2×C3×C412yes—
222C2×C3×Dic3C2×C3×C414yescomplemented
223C3×C4×D3—216no—
224C3×C4×D3—28no—
225C3×C4×D3—28no—
226C4×C22⋊C4—91noSylow
227C2×C33C2×C4211yescharacteristic
228C2×C33C2×C22⋊C411yescharacteristic
229C2×C33#11711yescharacteristic
230C2×C33C4×D412yes—
231C2×C33C4×D412yes—
232C32×D3—24no—
233C24×C3—31no—
234C24×C3—31no—
235C24×C3—61no—
236C23×D3C2×C3×D311yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—34no—
245C22×C3×C4—34no—
246C22×C3×C4—41no—
247C22×C3×C4—64no—
248C22×C3×C4—62no—
249C22×C3×C4—61no—
250C22×C3×C4—64no—
251C22×C3×C4—64no—
252C22×C3×C4—62no—
253C22×C3×C4—62no—
254C22×C3×C4—62no—
255C22×C3×C4—62no—
256C22×C3×C4—92no—
257C22×C3×C4D3211yescharacteristic
258C22×C3×C4C2×C3×D311yescharacteristic
259C22×C3×C4C2×C3×D311yescharacteristic
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—62no—
263C22×Dic3C2×C3×D312yes—
264C22×Dic3C2×C3×D311yescharacteristic
265C2×C4×D3—22no—
266C2×C4×D3—22no—
267C2×C4×D3C3×Dic314yescomplemented
268C3×C22⋊C4—98no—
269C3×C42—64no—
270C3×C42—62no—
271C3×C42—62no—
272C3×C42—182no—
273#217—38no—
274(C2×D3)⋊C4—38no—
275C4×Dic3—22no—
276C4×Dic3—64no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C22×C32—22no—
280C22×C32—22no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—22no—
285C22×C32—21no—
286C22×C32—22no—
287C22×C32—21no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—34no—
295C22×C32—41no—
296C22×C32—42no—
297C22×C32—41no—
298C22×C32—41no—
299C22×C32—42no—
300C22×C32—62no—
301C22×C32—64no—
302C22×C32—62no—
303C22×C32—64no—
304C22×C32C2×C4×D312yes—
305C22×C32C2×C4×D312yes—
306C22×C32C2×C4×D311yescharacteristic
307C22×C32C2×D1211yescharacteristic
308C22×C32#23512yes—
309C22×C32#23512yes—
310C22×C32C22×Dic311yescharacteristic
311C22×C32C2×#6711yescharacteristic
312C22×C32C2×#6711yescharacteristic
313C22×C32C2×#6711yescharacteristic
314C22×C32C22×C3×C412yes—
315C22×C32C22×C3×C411yescharacteristic
316C22×C32C2×C3×D411yescharacteristic
317C22×C32C2×C3×D411yescharacteristic
318C22×C32C3×#4112yes—
319C2×C3×D3—24no—
320C2×C3×D3—24no—
321C2×C3×D3—28no—
322C2×C3×D3—28no—
323C2×C3×D3—22no—
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—22no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3C4×Dic314yescomplemented
333C2×C3×D3C3×C4214yescomplemented
334C32×C4—24no—
335C32×C4—24no—
336C32×C4—24no—
337C32×C4—44no—
338C32×C4—62no—
339C32×C4—64no—
340C32×C4(C2×D3)⋊C414yescomplemented
341C32×C4#21714yescomplemented
342C32×C4C3×C22⋊C414yescomplemented
343C3⋊Dic3—24no—
344C3×Dic3—24no—
345C3×Dic3—28no—
346C3×Dic3—24no—
347C3×Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—24no—
350C3×Dic3—68no—
351C3×Dic3—64no—
352C3×Dic3—64no—
353C23×C4—31no—
354C2×C22⋊C4—92no—
355C2×C42—31no—
356C2×C42—91no—
357#95—92no—
358C33C4×C22⋊C411yescharacteristic, complemented, Sylow
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—34no—
363C23×C3—32no—
364C23×C3—34no—
365C23×C3—32no—
366C23×C3—41no—
367C23×C3—62no—
368C23×C3—64no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—64no—
372C23×C3—62no—
373C23×C3—61no—
374C23×C3—61no—
375C23×C3—61no—
376C23×C3—62no—
377C23×C3—61no—
378C23×C3C2×D3211yescharacteristic
379C23×C3C22×C3×D311yescharacteristic
380C23×C3C22×C3×D311yescharacteristic
381C22×D3—22no—
382C22×D3—21no—
383C22×D3—21no—
384C22×D3C3×C4×D314yes—
385C22×D3C2×C3×Dic312yes—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—34no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—64no—
403C2×C3×C4—62no—
404C2×C3×C4—616no—
405C2×C3×C4—64no—
406C2×C3×C4—64no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—61no—
417C2×C3×C4—68no—
418C2×C3×C4—68no—
419C2×C3×C4—94no—
420C2×C3×C4—182no—
421C2×C3×C4—182no—
422C2×C3×C4D3×Dic312yes—
423C2×C3×C4#62512yes—
424C2×C3×C4#62612yes—
425C2×C3×C4C3×C4×D312yes—
426C2×C3×C4C3×D1212yes—
427C2×C3×C4C2×C3×Dic312yes—
428C2×C3×C4C3×#6712yes—
429C2×C3×C4C3×#6712yes—
430C2×C3×C4C3×#6712yes—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—34no—
436C2×Dic3—34no—
437C2×Dic3—64no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3C3×C4×D314yescomplemented
445C2×Dic3C2×C3×Dic312yes—
446C4×D3—28no—
447C2×C32—21no—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—22no—
451C2×C32—22no—
452C2×C32—22no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32—21no—
456C2×C32—22no—
457C2×C32—22no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—22no—
462C2×C32—41no—
463C2×C32—41no—
464C2×C32—41no—
465C2×C32—42no—
466C2×C32—42no—
467C2×C32—64no—
468C2×C32C42×D311yescharacteristic
469C2×C32#87211yescharacteristic
470C2×C32C4×D1212yes—
471C2×C32C2×C4×Dic311yescharacteristic
472C2×C32#92611yescharacteristic
473C2×C32C2×(C2×D3)⋊C411yescharacteristic
474C2×C32C4×#6712yes—
475C2×C32C4×#6712yes—
476C2×C32C4×#6712yes—
477C2×C32C2×#21711yescharacteristic
478C2×C32C2×C3×C4211yescharacteristic
479C2×C32C2×C3×C22⋊C411yescharacteristic
480C2×C32C3×#11711yescharacteristic
481C2×C32C3×C4×D412yes—
482C2×C32C3×C4×D412yes—
483C3×D3—28no—
484C3×D3—24no—
485C3×D3—24no—
486C24—31no—
487C22×C4—31no—
488C22×C4—32no—
489C22×C4—34no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—92no—
493C22×C4C3×D3211yescharacteristic
494C22⋊C4—98no—
495C42—62no—
496C42—182no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—34no—
513C22×C3—34no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—68no—
523C22×C3—68no—
524C22×C3—62no—
525C22×C3—64no—
526C22×C3—62no—
527C22×C3—64no—
528C22×C3—64no—
529C22×C3—62no—
530C22×C3—62no—
531C22×C3—64no—
532C22×C3#379812yes—
533C22×C3C4×D3212yes—
534C22×C3C2×D3×Dic311yescharacteristic
535C22×C3C2×#62511yescharacteristic
536C22×C3C2×#62611yescharacteristic
537C22×C3C2×C3×C4×D312yes—
538C22×C3C2×C3×C4×D312yes—
539C22×C3C2×C3×C4×D311yescharacteristic
540C22×C3C2×C3×D1211yescharacteristic
541C22×C3C3×#23512yes—
542C22×C3C3×#23512yes—
543C22×C3C22×C3×Dic311yescharacteristic
544C22×C3C2×C3×#6711yescharacteristic
545C22×C3C2×C3×#6711yescharacteristic
546C22×C3C2×C3×#6711yescharacteristic
547C2×D3—22no—
548C2×D3—24no—
549C2×D3—24no—
550C2×D3—22no—
551C2×D3C3×C4×Dic314yescomplemented
552C3×C4—24no—
553C3×C4—24no—
554C3×C4—24no—
555C3×C4—44no—
556C3×C4—64no—
557C3×C4—68no—
558C3×C4—62no—
559C3×C4—64no—
560C3×C4—64no—
561C3×C4—62no—
562C3×C4—184no—
563C3×C4(C2×D3)⋊Dic314yesdirect product factor
564C3×C4C3×(C2×D3)⋊C414yescomplemented
565C3×C4C3×#21714yescomplemented
566Dic3—24no—
567Dic3—22no—
568Dic3—68no—
569Dic3—64no—
570Dic3—64no—
571C32—21no—
572C32—21no—
573C32—21no—
574C32—41no—
575C32C4×(C2×D3)⋊C411yescharacteristic, complemented
576C32C4×#21711yescharacteristic, complemented
577C32C3×C4×C22⋊C411yescharacteristic, complemented
578C23—34no—
579C23—32no—
580C23—62no—
581C23—61no—
582C23—61no—
583C23C2×C3×D3211yescharacteristic
584C2×C4—34no—
585C2×C4—32no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—61no—
589C2×C4—61no—
590C2×C4—68no—
591C2×C4—94no—
592C2×C4—182no—
593C2×C4—182no—
594C2×C4C3×D3×Dic312yes—
595C2×C4C3×#62512yes—
596C2×C4C3×#62612yes—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—22no—
607C2×C3—22no—
608C2×C3—22no—
609C2×C3—22no—
610C2×C3—22no—
611C2×C3—22no—
612C2×C3—41no—
613C2×C3—41no—
614C2×C3—41no—
615C2×C3—42no—
616C2×C3—42no—
617C2×C3—68no—
618C2×C3—64no—
619C2×C3—64no—
620C2×C3#6385511yescharacteristic
621C2×C3C4×D3×Dic311yescharacteristic
622C2×C3C4×#62512yes—
623C2×C3C4×#62612yes—
624C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
625C2×C3C3×C42×D311yescharacteristic
626C2×C3C3×#87211yescharacteristic
627C2×C3C3×C4×D1212yes—
628C2×C3C2×C3×C4×Dic311yescharacteristic
629C2×C3C3×#92611yescharacteristic
630C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
631C2×C3C3×C4×#6712yes—
632C2×C3C3×C4×#6712yes—
633C2×C3C3×C4×#6712yes—
634C2×C3C2×C3×#21711yescharacteristic
635D3—24no—
636C22—34no—
637C22—62no—
638C22—62no—
639C22—64no—
640C22—64no—
641C22C3×#379812yes—
642C22C3×C4×D3212yes—
643C22C2×C3×D3×Dic311yescharacteristic
644C22C2×C3×#62511yescharacteristic
645C22C2×C3×#62611yescharacteristic
646C4—62no—
647C4—64no—
648C4—184no—
649C4C3×(C2×D3)⋊Dic314yesdirect product factor
650C3—21no—
651C3—21no—
652C3—21no—
653C3—41no—
654C3C4×(C2×D3)⋊Dic311yescharacteristic, direct product factor
655C3C3×C4×(C2×D3)⋊C411yescharacteristic, complemented
656C3C3×C4×#21711yescharacteristic, complemented
657C2—64no—
658C2C3×#6385511yescharacteristic
659C2C3×C4×D3×Dic311yescharacteristic
660C2C3×C4×#62512yes—
661C2C3×C4×#62612yes—
662C2C2×C3×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
center, hypercenterC22×C3×C4D32
commutatorC2×C32C2×C3×C42
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC23×C32C23×C3
hypocenterC32C3×C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C3⋊Dic3C2semidirect
3. C2×C32×C4×Dic3C2semidirect
5. C3×#63579C2semidirect
8. C4×(C2×D3)⋊Dic3C3direct (N × H)
16. C2×C32×C4×D3C4semidirect
19. C3×(C2×D3)⋊Dic3C4direct (N × H)
25. C2×C4×C3⋊Dic3C2×C3semidirect
32. C2×C3×C4×Dic3D3semidirect
33. C2×C3×C4×Dic3C2×C3semidirect
37. #63579C2×C3semidirect
49. C2×C3×C3⋊Dic3C2×C4semidirect
55. C2×C32×Dic3C2×C4semidirect
93. C2×C3×C4×D3Dic3semidirect
94. C2×C3×C4×D3C3×C4semidirect
105. (C2×D3)⋊Dic3C3×C4direct (N × H)
115. C2×C32×D3C42semidirect
116. C33×C4C22⋊C4semidirect
134. C2×C4×Dic3C3×D3semidirect
195. C2×C3⋊Dic3C2×C3×C4semidirect
219. C2×C3×Dic3C4×D3semidirect
222. C2×C3×Dic3C2×C3×C4semidirect
267. C2×C4×D3C3×Dic3semidirect
332. C2×C3×D3C4×Dic3semidirect
333. C2×C3×D3C3×C42semidirect
340. C32×C4(C2×D3)⋊C4semidirect
341. C32×C4#217semidirect
342. C32×C4C3×C22⋊C4semidirect
358. C33C4×C22⋊C4semidirect
444. C2×Dic3C3×C4×D3semidirect
551. C2×D3C3×C4×Dic3semidirect
563. C3×C4(C2×D3)⋊Dic3direct (N × H)
564. C3×C4C3×(C2×D3)⋊C4semidirect
565. C3×C4C3×#217semidirect
575. C32C4×(C2×D3)⋊C4semidirect
576. C32C4×#217semidirect
577. C32C3×C4×C22⋊C4semidirect
649. C4C3×(C2×D3)⋊Dic3direct (N × H)
654. C3C4×(C2×D3)⋊Dic3direct (N × H)
655. C3C3×C4×(C2×D3)⋊C4semidirect
656. C3C3×C4×#217semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×C3×C4×C3⋊Dic32
C2×C32×C4×Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#635792
C3×C4×#2173
C3×C4×(C2×D3)⋊C43
C4×(C2×D3)⋊Dic33