Finite Group Databasebeta

← D3×D4×C3⋊Dic3 #13177364

Subgroups — D3×D4×C3⋊Dic3 #13177364

Order 1728.

2932 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic
2C22×D3×C3⋊Dic3C212yesmaximal, complemented
3D4×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊Dic3)C212yesmaximal, complemented
6#67×C3⋊Dic3C212yesmaximal, complemented
7D3×#3757C212yesmaximal, complemented
8#11723499C211yesmaximal, characteristic, complemented
9D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
10D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
12C2×D4×C3⋊Dic3—31nomaximal
13D3×D4×Dic3—34nomaximal
14C23×C32×D3C2212yes—
15C2×C33×D4C2211yescharacteristic
16C22×C3⋊(C3⋊Dic3)C2212yescomplemented
17C22×C3×C3⋊Dic3C2212yescomplemented
18C2×C32×#67C2212yes—
19C32×D3×D4C418yescomplemented
20C2×C32×D12C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×D3×C3⋊Dic3—28no—
23C2×D3×C3⋊Dic3C2212yes—
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2212yescomplemented
27C2×D3×C3⋊Dic3C2212yescomplemented
28#88864C2212yescomplemented
29C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
30C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C3×#3757C2212yescomplemented
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
34Dic3⋊(C3⋊Dic3)C2212yescomplemented
35(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37Dic3×C3⋊Dic3C2211yescharacteristic, complemented
38Dic3×C3⋊Dic3C2211yescharacteristic, complemented
39C22×C32×D4—31no—
40C23×C3⋊Dic3—32no—
41C2×C3×D3×D4D314yes—
42C22×D3×Dic3—38no—
43C2×#3757—32no—
44D4×C3⋊Dic3—31no—
45D4×C3⋊Dic3—32no—
46D4×C3⋊Dic3—32no—
47D4×C3⋊Dic3—31no—
48D4×C3⋊Dic3—34no—
49D4×C3⋊Dic3—31no—
50D4×C3⋊Dic3—64no—
51D4×C3⋊Dic3D311yescharacteristic, direct product factor
52C2×C4⋊(C3⋊Dic3)—31no—
53C2×C4×C3⋊Dic3—31no—
54C3×D4×Dic3—34no—
55#67⋊Dic3—38no—
56Dic3×#67—38no—
57D3×#217—38no—
58#63898—34no—
59Dic3×D12—34no—
60D3×C4⋊Dic3—34no—
61C4×D3×Dic3—34no—
62C23×C33C2312yes—
63C22×C32×D3—24no—
64C22×C32×D3—24no—
65C22×C32×D3C2×C418yescomplemented
66C22×C32×D3C2312yes—
67C22×C32×D3C2311yescharacteristic
68C33×D4C2×C414yescomplemented
69C2×C33×C4C2311yescharacteristic
70C2×C3⋊(C3⋊Dic3)—24no—
71C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
72C2×C3⋊(C3⋊Dic3)C2312yes—
73C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
74C2×C3×C3⋊Dic3—24no—
75C2×C3×C3⋊Dic3C2311yescharacteristic
76C2×C3×C3⋊Dic3C2312yes—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C32×#67C2×C418yescomplemented
79C2×C32×Dic3C2311yescharacteristic
80C32×D12C2×C414yescomplemented
81C32×C4×D3C2×C414yescomplemented
82D3×C3⋊Dic3—24no—
83D3×C3⋊Dic3—22no—
84D3×C3⋊Dic3—24no—
85D3×C3⋊Dic3—24no—
86D3×C3⋊Dic3D414yesdirect product factor
87C2×D4×Dic3—94no—
88C4×D3×D4—91no—
89C24×C32—32no—
90C23×C3×D3C2×D318yes—
91C2×C32×D4—24no—
92C2×C32×D4—32no—
93C2×C32×D4—38no—
94C2×C32×D4—31no—
95C2×C32×D4C2×D311yescharacteristic
96C2×C32×D4C2×D314yes—
97C22×C32×C4—31no—
98C22×C3⋊Dic3—31no—
99C22×C3⋊Dic3—32no—
100C22×C3⋊Dic3—38no—
101C22×C3⋊Dic3—32no—
102C22×C3⋊Dic3—32no—
103C22×C3⋊Dic3—32no—
104C22×C3⋊Dic3—31no—
105C22×C3⋊Dic3—68no—
106C22×C3⋊Dic3—68no—
107C22×C3⋊Dic3C2×D312yescomplemented
108C2×C3×#67C2×D318yes—
109C22×C3×Dic3—38no—
110C3×D3×D4Dic3132yescomplemented
111C2×C3×D12C2×D314yes—
112C2×C3×C4×D3C2×D314yes—
113C2×D3×Dic3—34no—
114C2×D3×Dic3—38no—
115C2×D3×Dic3—38no—
116C2×D3×Dic3—38no—
117C2×D3×Dic3—34no—
118C2×D3×Dic3—632no—
119#3757—32no—
120#3757—38no—
121#3757—32no—
122#3757—32no—
123#3757—68no—
124#3757C2×D312yescomplemented
125C4⋊(C3⋊Dic3)—31no—
126C4⋊(C3⋊Dic3)—34no—
127C4⋊(C3⋊Dic3)—32no—
128C4⋊(C3⋊Dic3)—64no—
129C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
130C4×C3⋊Dic3—31no—
131C4×C3⋊Dic3—34no—
132C4×C3⋊Dic3—31no—
133C4×C3⋊Dic3—31no—
134C4×C3⋊Dic3—64no—
135C4×C3⋊Dic3C2×D311yescharacteristic, complemented
136C3×#217—38no—
137C3×C4⋊Dic3—34no—
138C3×C4×Dic3—34no—
139Dic3⋊Dic3—38no—
140(C2×D3)⋊Dic3—38no—
141(C2×D3)⋊Dic3—38no—
142Dic32—34no—
143Dic32—34no—
144C22×C33—22no—
145C22×C33—22no—
146C22×C33C22×C414yescomplemented
147C22×C33C2411yescharacteristic
148C2×C32×D3—22no—
149C2×C32×D3—22no—
150C2×C32×D3—216no—
151C2×C32×D3C22×C412yes—
152C2×C32×D3C22×C414yescomplemented
153C2×C32×D3C2×D412yes—
154C2×C32×D3#4112yes—
155C33×C4C22×C412yescomplemented
156C3⋊(C3⋊Dic3)—22no—
157C3⋊(C3⋊Dic3)—21no—
158C3⋊(C3⋊Dic3)C2×D412yescomplemented
159C3×C3⋊Dic3—22no—
160C3×C3⋊Dic3—21no—
161C3×C3⋊Dic3C2×D412yescomplemented
162C32×Dic3C22×C412yescomplemented
163C22×C3×D4—34no—
164C23×Dic3—98no—
165C2×D3×D4C3⋊D311yescharacteristic
166C22×C4×D3—92no—
167C3×C4×D4—91no—
168C2×#217—98no—
169D4×Dic3—34no—
170D4×Dic3—94no—
171D4×Dic3—94no—
172D4×Dic3—98no—
173D4×Dic3—98no—
174D4×Dic3—94no—
175D4×Dic3—91no—
176D4×Dic3—184no—
177C4×#67—92no—
178C2×C4⋊Dic3—94no—
179C2×C4×Dic3—94no—
180#893—91no—
181D3×C4⋊C4—91no—
182#67⋊C4—92no—
183D3×C22⋊C4—92no—
184C4×D12—91no—
185C42×D3—91no—
186C23×C32—28no—
187C23×C32—31no—
188C23×C32—38no—
189C23×C32—32no—
190C23×C32—64no—
191C23×C32—64no—
192C23×C32C22×D318yes—
193C23×C32C22×D312yes—
194C22×C3×D3—216no—
195C22×C3×D3—216no—
196C22×C3×D3C2×Dic3132yescomplemented
197C22×C3×D3C22×D318yes—
198C22×C3×D3C22×D314yes—
199C32×D4—216no—
200C32×D4—38no—
201C32×D4—34no—
202C32×D4C4×D314yescomplemented
203C32×D4C2×Dic3116yescomplemented
204C2×C32×C4—24no—
205C2×C32×C4—31no—
206C2×C32×C4—34no—
207C2×C32×C4C22×D314yes—
208C2×C32×C4C22×D311yescharacteristic
209C2×C3⋊Dic3—24no—
210C2×C3⋊Dic3—31no—
211C2×C3⋊Dic3—34no—
212C2×C3⋊Dic3—31no—
213C2×C3⋊Dic3—32no—
214C2×C3⋊Dic3—34no—
215C2×C3⋊Dic3—34no—
216C2×C3⋊Dic3—38no—
217C2×C3⋊Dic3—64no—
218C2×C3⋊Dic3—64no—
219C2×C3⋊Dic3—68no—
220C2×C3⋊Dic3—64no—
221C2×C3⋊Dic3—62no—
222C2×C3⋊Dic3—64no—
223C2×C3⋊Dic3—64no—
224C2×C3⋊Dic3—64no—
225C2×C3⋊Dic3—616no—
226C2×C3⋊Dic3—1216no—
227C2×C3⋊Dic3C22×D311yescharacteristic
228C2×C3⋊Dic3C22×D312yes—
229C2×C3⋊Dic3C22×D311yescharacteristic
230C3×#67C2×Dic3132yescomplemented
231C2×C3×Dic3—34no—
232C2×C3×Dic3—34no—
233C2×C3×Dic3—38no—
234C2×C3×Dic3—616no—
235C2×C3×Dic3C22×D314yes—
236C3×D12C2×Dic3116yescomplemented
237C3×C4×D3C2×Dic3116yescomplemented
238D3×Dic3—316no—
239D3×Dic3—616no—
240D3×Dic3—616no—
241D3×Dic3—616no—
242D3×Dic3—68no—
243C2×C4×D4—271noSylow
244C2×C33—24no—
245C2×C33C23×C411yescharacteristic
246C2×C33C22×D411yescharacteristic
247C2×C33C2×#4111yescharacteristic
248C32×D3—24no—
249C32×D3C4×D414yescomplemented
250C24×C3—38no—
251C23×D3C2×C3⋊D312yes—
252C2×C3×D4—24no—
253C2×C3×D4—38no—
254C2×C3×D4—332no—
255C2×C3×D4—34no—
256C2×C3×D4D3214yes—
257C2×C3×D4C2×C3⋊D311yescharacteristic
258C22×C3×C4—34no—
259C22×C3×C4—92no—
260C2×#67C2×C3⋊D312yes—
261C22×Dic3—38no—
262C22×Dic3—94no—
263C22×Dic3—94no—
264C22×Dic3—98no—
265C22×Dic3—98no—
266C22×Dic3—98no—
267C22×Dic3—98no—
268C22×Dic3—92no—
269C22×Dic3—188no—
270C22×Dic3—1832no—
271D3×D4C3⋊Dic318yesdirect product factor
272C2×D12C2×C3⋊D311yescharacteristic
273C2×C4×D3—91no—
274C2×C4×D3—91no—
275C2×C4×D3—92no—
276C2×C4×D3—92no—
277C2×C4×D3—92no—
278C2×C4×D3—188no—
279C2×C4×D3C2×C3⋊D311yescharacteristic
280C3×C4⋊C4—91no—
281C3×C22⋊C4—92no—
282C3×C42—91no—
283#217—38no—
284#217—98no—
285#217—98no—
286#217—98no—
287#217—92no—
288#217—188no—
289(C2×D3)⋊C4—92no—
290(C2×D3)⋊C4—92no—
291C4⋊Dic3—34no—
292C4⋊Dic3—98no—
293C4⋊Dic3—94no—
294C4⋊Dic3—91no—
295C4⋊Dic3—184no—
296Dic3⋊C4—92no—
297C4×Dic3—34no—
298C4×Dic3—94no—
299C4×Dic3—94no—
300C4×Dic3—94no—
301C4×Dic3—91no—
302C4×Dic3—91no—
303C4×Dic3—91no—
304C4×Dic3—184no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—24no—
308C22×C32—216no—
309C22×C32—28no—
310C22×C32—28no—
311C22×C32—32no—
312C22×C32—32no—
313C22×C32—32no—
314C22×C32—34no—
315C22×C32—48no—
316C22×C32—48no—
317C22×C32—616no—
318C22×C32—62no—
319C22×C32—62no—
320C22×C32C2×C4×D314yescomplemented
321C22×C32C22×Dic3116yescomplemented
322C22×C32C23×D314yes—
323C22×C32C23×D311yescharacteristic
324C2×C3×D3—28no—
325C2×C3×D3—28no—
326C2×C3×D3—264no—
327C2×C3×D3D3×D418yes—
328C2×C3×D3#23718yes—
329C2×C3×D3C22×Dic318yes—
330C2×C3×D3C22×Dic3116yescomplemented
331C32×C4—28no—
332C32×C4—32no—
333C32×C4C2×C4×D312yescomplemented
334C32×C4C22×Dic318yescomplemented
335C3⋊Dic3—22no—
336C3⋊Dic3—21no—
337C3⋊Dic3—32no—
338C3⋊Dic3—38no—
339C3⋊Dic3—68no—
340C3⋊Dic3—62no—
341C3⋊Dic3—61no—
342C3⋊Dic3—68no—
343C3⋊Dic3—64no—
344C3⋊Dic3—124no—
345C3⋊Dic3—128no—
346C3⋊Dic3D3×D412yesdirect product factor
347C3×Dic3—38no—
348C3×Dic3—68no—
349C3×Dic3—64no—
350C3×Dic3C22×Dic318yescomplemented
351C22×D4—31no—
352C23×C4—272no—
353C4×D4—91no—
354C4×D4—271no—
355C4×D4—272no—
356C4×D4—271no—
357C4×D4—272no—
358C4×D4—271no—
359C2×C4⋊C4—271no—
360C2×C22⋊C4—272no—
361C2×C42—271no—
362C33C2×C4×D411yescharacteristic, complemented, Sylow
363C23×C3—28no—
364C23×C3—34no—
365C23×C3—38no—
366C23×C3—332no—
367C23×C3—616no—
368C23×C3—616no—
369C23×C3C2×D3218yes—
370C23×C3C22×C3⋊D312yes—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3C2×C3⋊Dic318yescomplemented
374C22×D3C22×C3⋊D312yes—
375C22×D3C22×C3⋊D311yescharacteristic
376C3×D4—216no—
377C3×D4—332no—
378C3×D4—316no—
379C3×D4D3×Dic3116yescomplemented
380C3×D4C2×C3⋊Dic314yescomplemented
381C2×C3×C4—24no—
382C2×C3×C4—34no—
383C2×C3×C4—316no—
384C2×C3×C4—91no—
385C2×C3×C4—91no—
386C2×C3×C4—92no—
387C2×C3×C4—184no—
388C2×C3×C4C2×D3214yes—
389C2×C3×C4C22×C3⋊D311yescharacteristic
390#67C2×C3⋊Dic318yescomplemented
391C2×Dic3—34no—
392C2×Dic3—34no—
393C2×Dic3—38no—
394C2×Dic3—616no—
395C2×Dic3—916no—
396C2×Dic3—94no—
397C2×Dic3—91no—
398C2×Dic3—94no—
399C2×Dic3—98no—
400C2×Dic3—91no—
401C2×Dic3—92no—
402C2×Dic3—184no—
403C2×Dic3—184no—
404C2×Dic3—188no—
405C2×Dic3—1816no—
406C2×Dic3—1816no—
407C2×Dic3—188no—
408C2×Dic3—1816no—
409C2×Dic3—184no—
410C2×Dic3—1816no—
411C2×Dic3—3616no—
412C2×Dic3C22×C3⋊D311yescharacteristic
413D12C2×C3⋊Dic314yescomplemented
414C4×D3—94no—
415C4×D3—184no—
416C4×D3—184no—
417C4×D3—184no—
418C4×D3—182no—
419C4×D3C2×C3⋊Dic314yescomplemented
420C2×C32—24no—
421C2×C32—24no—
422C2×C32—24no—
423C2×C32—24no—
424C2×C32—216no—
425C2×C32—34no—
426C2×C32—416no—
427C2×C32—64no—
428C2×C32C22×C4×D311yescharacteristic
429C2×C32C2×D3×D414yes—
430C2×C32C2×D3×D411yescharacteristic
431C2×C32C2×#23714yes—
432C2×C32D3×#4111yescharacteristic
433C2×C32C23×Dic314yes—
434C3×D3—216no—
435C3×D3D4×Dic3116yescomplemented
436C24—32no—
437C2×D4—32no—
438C2×D4—38no—
439C2×D4—31no—
440C2×D4D3×C3⋊D311yescharacteristic
441C22×C4—31no—
442C22×C4—92no—
443C22×C4—271no—
444C22×C4—271no—
445C22×C4—272no—
446C22×C4—272no—
447C22×C4—272no—
448C22×C4—272no—
449C22×C4—548no—
450C4⋊C4—91no—
451C4⋊C4—272no—
452C4⋊C4—271no—
453C22⋊C4—92no—
454C22⋊C4—272no—
455C22⋊C4—272no—
456C22⋊C4—272no—
457C42—91no—
458C42—271no—
459C42—271no—
460C42—271no—
461C22×C3—28no—
462C22×C3—28no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—24no—
466C22×C3—216no—
467C22×C3—38no—
468C22×C3—38no—
469C22×C3—38no—
470C22×C3—316no—
471C22×C3—48no—
472C22×C3—48no—
473C22×C3—664no—
474C22×C3—68no—
475C22×C3—68no—
476C22×C3C2×D3×Dic3116yescomplemented
477C22×C3C22×C3⋊Dic314yescomplemented
478C22×C3C22×D3214yes—
479C22×C3C23×C3⋊D311yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—216no—
483C2×D3D4×C3⋊D312yes—
484C2×D3#383012yes—
485C2×D3C22×C3⋊Dic312yes—
486C2×D3C22×C3⋊Dic314yescomplemented
487C3×C4—28no—
488C3×C4—38no—
489C3×C4—92no—
490C3×C4—182no—
491C3×C4—181no—
492C3×C4C2×D3×Dic318yescomplemented
493C3×C4C22×C3⋊Dic312yescomplemented
494Dic3—38no—
495Dic3—68no—
496Dic3—64no—
497Dic3—98no—
498Dic3—92no—
499Dic3—188no—
500Dic3—188no—
501Dic3—184no—
502Dic3—182no—
503Dic3—181no—
504Dic3—368no—
505Dic3—364no—
506Dic3C22×C3⋊Dic312yescomplemented
507C32—24no—
508C32C4×D3×D411yescharacteristic, complemented
509C32C2×D4×Dic314yescomplemented
510C23—31no—
511C23—32no—
512C23—38no—
513C23—64no—
514C23—64no—
515C23C2×D3×C3⋊D312yes—
516D4—38no—
517D4—34no—
518D4D3×C3⋊Dic314yesdirect product factor
519C2×C4—31no—
520C2×C4—34no—
521C2×C4—91no—
522C2×C4—91no—
523C2×C4—92no—
524C2×C4—184no—
525C2×C4—274no—
526C2×C4—271no—
527C2×C4—271no—
528C2×C4—272no—
529C2×C4—544no—
530C2×C4—544no—
531C2×C4—544no—
532C2×C4—542no—
533C2×C4—544no—
534C2×C4C2×D3×C3⋊D311yescharacteristic
535C2×C3—216no—
536C2×C3—24no—
537C2×C3—24no—
538C2×C3—24no—
539C2×C3—24no—
540C2×C3—316no—
541C2×C3—416no—
542C2×C3—616no—
543C2×C3D32×D414yes—
544C2×C3D3×#23714yes—
545C2×C3C22×D3×Dic314yes—
546C2×C3C2×D4×C3⋊D311yescharacteristic
547C2×C3C2×#383011yescharacteristic
548C2×C3C23×C3⋊Dic311yescharacteristic
549D3—24no—
550D3D4×C3⋊Dic314yesdirect product factor
551C22—22no—
552C22—22no—
553C22—32no—
554C22—32no—
555C22—32no—
556C22—34no—
557C22—616no—
558C22—62no—
559C22—62no—
560C22C2×D3×C3⋊Dic314yescomplemented
561C22C22×D3×C3⋊D311yescharacteristic
562C4—32no—
563C4—92no—
564C4—182no—
565C4—181no—
566C4—272no—
567C4—542no—
568C4—541no—
569C4C2×D3×C3⋊Dic312yescomplemented
570C3—24no—
571C3D3×D4×Dic314yescomplemented
572C3C2×D4×C3⋊Dic311yescharacteristic, complemented
573C2—24no—
574C2—34no—
575C2—64no—
576C2D3×D4×C3⋊D311yescharacteristic
577C2D3×#383011yescharacteristic
578C2C22×D3×C3⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC2×C33×D4C22
socle, cosocleC22×C33C24
prime radicalC2×C32×D3×D4C2
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×D3×C3⋊Dic3C2semidirect
3. D4×C3⋊(C3⋊Dic3)C2semidirect
4. C3×D4×C3⋊Dic3C2semidirect
5. #67⋊(C3⋊Dic3)C2semidirect
6. #67×C3⋊Dic3C2semidirect
7. D3×#3757C2semidirect
8. #11723499C2semidirect
9. D12×C3⋊Dic3C2semidirect
10. D3×C4⋊(C3⋊Dic3)C2semidirect
11. C4×D3×C3⋊Dic3C2semidirect
16. C22×C3⋊(C3⋊Dic3)C22semidirect
17. C22×C3×C3⋊Dic3C22semidirect
19. C32×D3×D4C4semidirect
26. C2×D3×C3⋊Dic3C22semidirect
27. C2×D3×C3⋊Dic3C22semidirect
28. #88864C22semidirect
29. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
30. C4×C3⋊(C3⋊Dic3)C22semidirect
31. C3×#3757C22semidirect
32. C3×C4⋊(C3⋊Dic3)C22semidirect
33. C3×C4×C3⋊Dic3C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
35. (C2×D3)⋊(C3⋊Dic3)C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. Dic3×C3⋊Dic3C22semidirect
38. Dic3×C3⋊Dic3C22semidirect
51. D4×C3⋊Dic3D3direct (N × H)
65. C22×C32×D3C2×C4semidirect
68. C33×D4C2×C4semidirect
78. C32×#67C2×C4semidirect
80. C32×D12C2×C4semidirect
81. C32×C4×D3C2×C4semidirect
86. D3×C3⋊Dic3D4direct (N × H)
107. C22×C3⋊Dic3C2×D3semidirect
110. C3×D3×D4Dic3semidirect
124. #3757C2×D3semidirect
129. C4⋊(C3⋊Dic3)C2×D3semidirect
135. C4×C3⋊Dic3C2×D3semidirect
146. C22×C33C22×C4semidirect
152. C2×C32×D3C22×C4semidirect
155. C33×C4C22×C4semidirect
158. C3⋊(C3⋊Dic3)C2×D4semidirect
161. C3×C3⋊Dic3C2×D4semidirect
162. C32×Dic3C22×C4semidirect
196. C22×C3×D3C2×Dic3semidirect
202. C32×D4C4×D3semidirect
203. C32×D4C2×Dic3semidirect
230. C3×#67C2×Dic3semidirect
236. C3×D12C2×Dic3semidirect
237. C3×C4×D3C2×Dic3semidirect
249. C32×D3C4×D4semidirect
271. D3×D4C3⋊Dic3direct (N × H)
320. C22×C32C2×C4×D3semidirect
321. C22×C32C22×Dic3semidirect
330. C2×C3×D3C22×Dic3semidirect
333. C32×C4C2×C4×D3semidirect
334. C32×C4C22×Dic3semidirect
346. C3⋊Dic3D3×D4direct (N × H)
350. C3×Dic3C22×Dic3semidirect
362. C33C2×C4×D4semidirect
373. C22×D3C2×C3⋊Dic3semidirect
379. C3×D4D3×Dic3semidirect
380. C3×D4C2×C3⋊Dic3semidirect
390. #67C2×C3⋊Dic3semidirect
413. D12C2×C3⋊Dic3semidirect
419. C4×D3C2×C3⋊Dic3semidirect
435. C3×D3D4×Dic3semidirect
476. C22×C3C2×D3×Dic3semidirect
477. C22×C3C22×C3⋊Dic3semidirect
486. C2×D3C22×C3⋊Dic3semidirect
492. C3×C4C2×D3×Dic3semidirect
493. C3×C4C22×C3⋊Dic3semidirect
506. Dic3C22×C3⋊Dic3semidirect
508. C32C4×D3×D4semidirect
509. C32C2×D4×Dic3semidirect
518. D4D3×C3⋊Dic3direct (N × H)
550. D3D4×C3⋊Dic3direct (N × H)
560. C22C2×D3×C3⋊Dic3semidirect
569. C4C2×D3×C3⋊Dic3semidirect
571. C3D3×D4×Dic3semidirect
572. C3C2×D4×C3⋊Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C22×D3×C3⋊Dic32
D4×C3⋊(C3⋊Dic3)2
C3×D4×C3⋊Dic32
#67⋊(C3⋊Dic3)2
#67×C3⋊Dic32
D3×#37572
#117234992
D12×C3⋊Dic32
D3×C4⋊(C3⋊Dic3)2
C4×D3×C3⋊Dic32
C2×D4×C3⋊Dic33
D3×D4×Dic33