Finite Group Databasebeta

← C2×C3×#63837 #13174631

Subgroups — C2×C3×#63837 #13174631

Order 1728.

1538 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#627C211yesmaximal, characteristic
2C2×C3×#3750C211yesmaximal, characteristic
3C2×C32×Dic3⋊C4C211yesmaximal, characteristic
4C2×C32×C4×Dic3C211yesmaximal, characteristic
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
6C2×C3×Dic32C211yesmaximal, characteristic
7C2×C3×Dic32C211yesmaximal, characteristic
8C3×#63837C218yesmaximal, direct product factor
9C2×C3×#887—31nomaximal
10C2×C3×C4×Dic6—31nomaximal
11C2×#63837C311yesmaximal, characteristic, direct product factor
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×C3×#627C418yescomplemented
20C2×C3×#627C2214yes—
21C3×#3750C2214yes—
22C32×Dic3⋊C4C2214yes—
23C32×C4×Dic3C2214yes—
24C3×Dic3⋊Dic3C2214yes—
25C3×Dic32C2214yes—
26C3×Dic32C2214yes—
27C22×C3×Dic6—31no—
28C22×C3×Dic6—31no—
29C22×#627C2×C311yescharacteristic
30C2×C32×C4⋊C4—31no—
31C2×C32×C42—31no—
32C2×#3750C2×C311yescharacteristic
33C2×C3×C4⋊Dic3—31no—
34C2×C3×Dic3⋊C4—21no—
35C2×C3×Dic3⋊C4—31no—
36C2×C3×Dic3⋊C4—31no—
37C2×C3×Dic3⋊C4—31no—
38C2×C3×Dic3⋊C4—61no—
39C2×C3×Dic3⋊C4D311yescharacteristic
40C2×C3×Dic3⋊C4C2×C311yescharacteristic
41C2×C3×C4×Dic3—21no—
42C2×C3×C4×Dic3—31no—
43C2×C3×C4×Dic3—31no—
44C2×C3×C4×Dic3—31no—
45C2×C3×C4×Dic3—31no—
46C2×C3×C4×Dic3D311yescharacteristic
47C2×C3×C4×Dic3C2×C311yescharacteristic
48C3×#887—38no—
49C3×C4×Dic6—38no—
50C2×Dic3⋊Dic3C2×C311yescharacteristic
51C2×Dic32C2×C311yescharacteristic
52C2×Dic32C2×C311yescharacteristic
53#63837C2×C318yesdirect product factor
54C23×C33C2311yescharacteristic
55C2×C33×C4—22no—
56C2×C33×C4C2312yes—
57C2×C3×C3⋊Dic3—22no—
58C2×C3×C3⋊Dic3C2×C414yes—
59C2×C3×C3⋊Dic3C2312yes—
60C2×C3×C3⋊Dic3C2312yes—
61C2×C32×Dic3—22no—
62C2×C32×Dic3C2×C414yes—
63C2×C32×Dic3C2×C414yes—
64C2×C32×Dic3Q814yescomplemented
65C2×C32×Dic3C2312yes—
66C2×C32×Dic3C2312yes—
67C2×C32×Dic3C2312yes—
68C2×C32×Dic3C2312yes—
69C3×#627C2×C4116yescomplemented
70C2×C3×C4×Q8—91no—
71C2×#887—31no—
72C2×C4×Dic6—31no—
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4—31no—
77C22×C32×C4—31no—
78C22×C32×C4—31no—
79C22×C32×C4—31no—
80C22×C32×C4—41no—
81C22×C32×C4C2×D311yescharacteristic
82C22×C32×C4C2×D311yescharacteristic
83C22×C32×C4C22×C311yescharacteristic
84C22×C3⋊Dic3C22×C311yescharacteristic
85C22×C3⋊Dic3C22×C311yescharacteristic
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—61no—
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
104C2×C3×Dic6—38no—
105C2×C3×Dic6—38no—
106C2×C3×Dic6—34no—
107C2×C3×Dic6—34no—
108C2×#627C3×C418yescomplemented
109C2×#627C22×C314yes—
110C32×C4⋊C4—34no—
111C32×C42—34no—
112#3750C22×C314yes—
113C3×C4⋊Dic3—34no—
114C3×Dic3⋊C4—24no—
115C3×Dic3⋊C4—34no—
116C3×Dic3⋊C4—34no—
117C3×Dic3⋊C4—34no—
118C3×Dic3⋊C4—64no—
119C3×Dic3⋊C4C2×D314yes—
120C3×Dic3⋊C4C22×C314yes—
121C3×C4×Dic3—24no—
122C3×C4×Dic3—34no—
123C3×C4×Dic3—34no—
124C3×C4×Dic3—34no—
125C3×C4×Dic3—34no—
126C3×C4×Dic3C2×D314yes—
127C3×C4×Dic3C22×C314yes—
128Dic3⋊Dic3C22×C314yes—
129Dic32C22×C314yes—
130Dic32C22×C314yes—
131C22×C33C22×C412yes—
132C22×C33C2×Q812yes—
133C22×C33#4112yes—
134C22×C33C2411yescharacteristic
135C33×C4—22no—
136C3×C3⋊Dic3—22no—
137C3×C3⋊Dic3C22×C414yes—
138C32×Dic3—22no—
139C32×Dic3C22×C414yes—
140C32×Dic3C22×C414yes—
141C32×Dic3C2×Q814yescomplemented
142C22×C3×Q8—91no—
143C22×Dic6—31no—
144C22×Dic6—31no—
145C3×C4×Q8—98no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—61no—
149C2×C3×C4⋊C4—91no—
150C2×C3×C4⋊C4—91no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×C3×C42—61no—
154C2×C3×C42—91no—
155C2×C3×C42—91no—
156C2×C4⋊Dic3—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—61no—
161C2×Dic3⋊C4C3×D311yescharacteristic
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3C3×D311yescharacteristic
167#887—38no—
168C4×Dic6—38no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—41no—
173C23×C32C22×D311yescharacteristic
174C23×C32C22×D311yescharacteristic
175C23×C32C23×C311yescharacteristic
176C2×C32×C4—22no—
177C2×C32×C4—24no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—34no—
184C2×C32×C4—34no—
185C2×C32×C4—34no—
186C2×C32×C4—32no—
187C2×C32×C4—32no—
188C2×C32×C4—32no—
189C2×C32×C4—32no—
190C2×C32×C4—42no—
191C2×C32×C4—42no—
192C2×C32×C4—42no—
193C2×C32×C4—44no—
194C2×C32×C4—62no—
195C2×C32×C4C22×D312yes—
196C2×C32×C4C22×D312yes—
197C2×C32×C4C23×C312yes—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3C2×C3×C414yes—
200C2×C3⋊Dic3C23×C312yes—
201C2×C3⋊Dic3C23×C312yes—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—34no—
212C2×C3×Dic3—34no—
213C2×C3×Dic3—32no—
214C2×C3×Dic3—32no—
215C2×C3×Dic3—32no—
216C2×C3×Dic3—32no—
217C2×C3×Dic3—42no—
218C2×C3×Dic3—62no—
219C2×C3×Dic3—64no—
220C2×C3×Dic3—62no—
221C2×C3×Dic3—62no—
222C2×C3×Dic3—62no—
223C2×C3×Dic3—122no—
224C2×C3×Dic3Dic614yescomplemented
225C2×C3×Dic3C4×D314yes—
226C2×C3×Dic3C4×D314yes—
227C2×C3×Dic3C2×C3×C414yes—
228C2×C3×Dic3C2×C3×C414yes—
229C2×C3×Dic3C3×Q814yescomplemented
230C2×C3×Dic3C22×D312yes—
231C2×C3×Dic3C22×D312yes—
232C2×C3×Dic3C22×D312yes—
233C2×C3×Dic3C22×D312yes—
234C2×C3×Dic3C23×C312yes—
235C2×C3×Dic3C23×C312yes—
236C2×C3×Dic3C23×C312yes—
237C2×C3×Dic3C23×C312yes—
238C3×Dic6—316no—
239C3×Dic6—316no—
240#627C2×C3×C4116yescomplemented
241C2×C4×Q8—91noSylow
242C2×C33C4×Q814yescomplemented
243C2×C33C23×C411yescharacteristic
244C2×C33C22×Q811yescharacteristic
245C2×C33C2×#4111yescharacteristic
246C2×C3×Q8—94no—
247C2×C3×Q8—98no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—31no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—41no—
260C22×C3×C4—61no—
261C22×C3×C4—61no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4—91no—
265C22×C3×C4—91no—
266C22×C3×C4D3211yescharacteristic
267C22×C3×C4C2×C3×D311yescharacteristic
268C22×C3×C4C2×C3×D311yescharacteristic
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—61no—
274C22×Dic3—61no—
275C22×Dic3C2×C3×D311yescharacteristic
276C22×Dic3C2×C3×D311yescharacteristic
277C22×Dic3C2×C3×D311yescharacteristic
278C22×Dic3C2×C3×D311yescharacteristic
279C2×Dic6—38no—
280C2×Dic6—38no—
281C2×Dic6—34no—
282C2×Dic6—34no—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—64no—
286C3×C4⋊C4—94no—
287C3×C4⋊C4—94no—
288C3×C42—34no—
289C3×C42—34no—
290C3×C42—64no—
291C3×C42—94no—
292C3×C42—94no—
293C4⋊Dic3—34no—
294Dic3⋊C4—34no—
295Dic3⋊C4—34no—
296Dic3⋊C4—34no—
297Dic3⋊C4—64no—
298Dic3⋊C4C2×C3×D314yes—
299C4×Dic3—34no—
300C4×Dic3—34no—
301C4×Dic3—34no—
302C4×Dic3—34no—
303C4×Dic3C2×C3×D314yes—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32—42no—
319C22×C32—41no—
320C22×C32C2×Dic612yes—
321C22×C32C2×C4×D312yes—
322C22×C32C2×C4×D312yes—
323C22×C32#23512yes—
324C22×C32#23712yes—
325C22×C32D3×Q812yes—
326C22×C32C22×C3×C412yes—
327C22×C32C2×C3×Q812yes—
328C22×C32C3×#4112yes—
329C22×C32C23×D311yescharacteristic
330C22×C32C23×D311yescharacteristic
331C22×C32C24×C311yescharacteristic
332C32×C4—22no—
333C32×C4—24no—
334C32×C4—22no—
335C32×C4—22no—
336C32×C4—34no—
337C32×C4—34no—
338C32×C4—34no—
339C32×C4—42no—
340C32×C4—42no—
341C32×C4—44no—
342C32×C4—62no—
343C3⋊Dic3—22no—
344C3⋊Dic3C22×C3×C414yes—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—24no—
348C3×Dic3—24no—
349C3×Dic3—24no—
350C3×Dic3—34no—
351C3×Dic3—34no—
352C3×Dic3—42no—
353C3×Dic3—64no—
354C3×Dic3—62no—
355C3×Dic3—62no—
356C3×Dic3—122no—
357C3×Dic3C2×Dic614yescomplemented
358C3×Dic3C2×C4×D314yes—
359C3×Dic3C2×C4×D314yes—
360C3×Dic3C22×C3×C414yes—
361C3×Dic3C22×C3×C414yes—
362C3×Dic3C2×C3×Q814yescomplemented
363C22×Q8—91no—
364C4×Q8—98no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C42—31no—
369C2×C42—91no—
370C2×C42—91no—
371C33C2×C4×Q811yescharacteristic, complemented, Sylow
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—41no—
376C23×C3C2×D3211yescharacteristic
377C23×C3C22×C3×D311yescharacteristic
378C23×C3C22×C3×D311yescharacteristic
379C3×Q8—916no—
380C2×C3×C4—24no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—32no—
388C2×C3×C4—32no—
389C2×C3×C4—32no—
390C2×C3×C4—32no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—34no—
397C2×C3×C4—34no—
398C2×C3×C4—34no—
399C2×C3×C4—32no—
400C2×C3×C4—32no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—44no—
404C2×C3×C4—42no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—64no—
409C2×C3×C4—64no—
410C2×C3×C4—64no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—92no—
415C2×C3×C4—94no—
416C2×C3×C4—92no—
417C2×C3×C4—122no—
418C2×C3×C4—182no—
419C2×C3×C4C2×D3212yes—
420C2×C3×C4C22×C3×D312yes—
421C2×C3×C4C22×C3×D312yes—
422C2×Dic3—22no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—34no—
426C2×Dic3—34no—
427C2×Dic3—32no—
428C2×Dic3—32no—
429C2×Dic3—64no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435C2×Dic3C3×Dic614yescomplemented
436C2×Dic3C3×C4×D314yes—
437C2×Dic3C3×C4×D314yes—
438C2×Dic3C22×C3×D312yes—
439C2×Dic3C22×C3×D312yes—
440C2×Dic3C22×C3×D312yes—
441C2×Dic3C22×C3×D312yes—
442Dic6—316no—
443Dic6—316no—
444C2×C32—24no—
445C2×C32—21no—
446C2×C32—21no—
447C2×C32—21no—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—24no—
455C2×C32—24no—
456C2×C32—44no—
457C2×C32—41no—
458C2×C32—41no—
459C2×C32—41no—
460C2×C32C4×Dic614yescomplemented
461C2×C32#88714yescomplemented
462C2×C32C3×C4×Q814yescomplemented
463C2×C32C22×Dic611yescharacteristic
464C2×C32C22×C4×D311yescharacteristic
465C2×C32C22×C4×D311yescharacteristic
466C2×C32C2×#23511yescharacteristic
467C2×C32C2×#23711yescharacteristic
468C2×C32C2×D3×Q811yescharacteristic
469C2×C32C23×C3×C411yescharacteristic
470C2×C32C22×C3×Q811yescharacteristic
471C2×C32C2×C3×#4111yescharacteristic
472C2×Q8—94no—
473C2×Q8—98no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—91no—
479C22×C4—91no—
480C22×C4C3×D3211yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—94no—
483C4⋊C4—94no—
484C42—34no—
485C42—94no—
486C42—94no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—41no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3D3×Dic612yes—
504C22×C3C4×D3212yes—
505C22×C3#380412yes—
506C22×C3C2×C3×Dic612yes—
507C22×C3C2×C3×C4×D312yes—
508C22×C3C2×C3×C4×D312yes—
509C22×C3C3×#23512yes—
510C22×C3C3×#23712yes—
511C22×C3C3×D3×Q812yes—
512C22×C3C22×D3211yescharacteristic
513C22×C3C23×C3×D311yescharacteristic
514C22×C3C23×C3×D311yescharacteristic
515C3×C4—24no—
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—22no—
519C3×C4—34no—
520C3×C4—34no—
521C3×C4—34no—
522C3×C4—34no—
523C3×C4—34no—
524C3×C4—34no—
525C3×C4—42no—
526C3×C4—42no—
527C3×C4—44no—
528C3×C4—64no—
529C3×C4—64no—
530C3×C4—64no—
531C3×C4—62no—
532C3×C4—62no—
533C3×C4—94no—
534C3×C4—122no—
535C3×C4—182no—
536Dic3—22no—
537Dic3—34no—
538Dic3—34no—
539Dic3—64no—
540Dic3—62no—
541Dic3—62no—
542Dic3—122no—
543Dic3C2×C3×Dic614yescomplemented
544Dic3C2×C3×C4×D314yes—
545Dic3C2×C3×C4×D314yes—
546C32—21no—
547C32—21no—
548C32—21no—
549C32—41no—
550C32C2×C4×Dic611yescharacteristic, complemented
551C32C2×#88711yescharacteristic, complemented
552C32C2×C3×C4×Q811yescharacteristic, complemented
553C23C2×C3×D3211yescharacteristic
554Q8—916no—
555C2×C4—22no—
556C2×C4—32no—
557C2×C4—32no—
558C2×C4—32no—
559C2×C4—34no—
560C2×C4—34no—
561C2×C4—34no—
562C2×C4—32no—
563C2×C4—62no—
564C2×C4—92no—
565C2×C4—94no—
566C2×C4—92no—
567C2×C4—182no—
568C2×C4C2×C3×D3212yes—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—24no—
573C2×C3—24no—
574C2×C3—24no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—41no—
582C2×C3—44no—
583C2×C3—41no—
584C2×C3—41no—
585C2×C3#6383714yesdirect product factor
586C2×C3C3×C4×Dic614yescomplemented
587C2×C3C3×#88714yescomplemented
588C2×C3C2×D3×Dic611yescharacteristic
589C2×C3C2×C4×D3211yescharacteristic
590C2×C3C2×#380411yescharacteristic
591C2×C3C22×C3×Dic611yescharacteristic
592C2×C3C22×C3×C4×D311yescharacteristic
593C2×C3C22×C3×C4×D311yescharacteristic
594C2×C3C2×C3×#23511yescharacteristic
595C2×C3C2×C3×#23711yescharacteristic
596C2×C3C2×C3×D3×Q811yescharacteristic
597C22C3×D3×Dic612yes—
598C22C3×C4×D3212yes—
599C22C3×#380412yes—
600C22C22×C3×D3211yescharacteristic
601C4—22no—
602C4—34no—
603C4—34no—
604C4—34no—
605C4—62no—
606C4—94no—
607C4—182no—
608C3—21no—
609C3—21no—
610C3—21no—
611C3—41no—
612C3C2×#6383711yescharacteristic, direct product factor
613C3C2×C3×C4×Dic611yescharacteristic, complemented
614C3C2×C3×#88711yescharacteristic, complemented
615C2C3×#6383714yesdirect product factor
616C2C2×C3×D3×Dic611yescharacteristic
617C2C2×C3×C4×D3211yescharacteristic
618C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×C4×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
8. C3×#63837C2direct (N × H)
11. C2×#63837C3direct (N × H)
19. C2×C3×#627C4semidirect
53. #63837C2×C3direct (N × H)
64. C2×C32×Dic3Q8semidirect
69. C3×#627C2×C4semidirect
108. C2×#627C3×C4semidirect
141. C32×Dic3C2×Q8semidirect
224. C2×C3×Dic3Dic6semidirect
229. C2×C3×Dic3C3×Q8semidirect
240. #627C2×C3×C4semidirect
242. C2×C33C4×Q8semidirect
357. C3×Dic3C2×Dic6semidirect
362. C3×Dic3C2×C3×Q8semidirect
371. C33C2×C4×Q8semidirect
435. C2×Dic3C3×Dic6semidirect
460. C2×C32C4×Dic6semidirect
461. C2×C32#887semidirect
462. C2×C32C3×C4×Q8semidirect
543. Dic3C2×C3×Dic6semidirect
550. C32C2×C4×Dic6semidirect
551. C32C2×#887semidirect
552. C32C2×C3×C4×Q8semidirect
585. C2×C3#63837direct (N × H)
586. C2×C3C3×C4×Dic6semidirect
587. C2×C3C3×#887semidirect
612. C3C2×#63837direct (N × H)
613. C3C2×C3×C4×Dic6semidirect
614. C3C2×C3×#887semidirect
615. C2C3×#63837direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6272
C2×C3×#37502
C2×C32×Dic3⋊C42
C2×C32×C4×Dic32
C2×C3×Dic3⋊Dic32
C2×C3×Dic322
C3×#638372
C2×C3×#8873
C2×C3×C4×Dic63
C2×#638373