Finite Group Databasebeta

← C2×C3×#63916 #13174596

Subgroups — C2×C3×#63916 #13174596

Order 1728.

2322 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C32×D12C211yesmaximal, characteristic, complemented
3C22×C3×#626C212yesmaximal, complemented
4C2×C32×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C212yesmaximal, complemented
6C3×#63916C218yesmaximal, direct product factor
7C2×C3×#938—31nomaximal
8C2×C3×#895—31nomaximal
9C2×#63916C311yesmaximal, characteristic, direct product factor
10C23×C3×C3⋊D3C2211yescharacteristic
11C23×C32×D3C2212yes—
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4×C3⋊D3—24no—
15C2×C3×C4×C3⋊D3C2214yescomplemented
16C22×C32×Dic3C2212yes—
17C2×C32×D12—24no—
18C2×C32×D12C2214yescomplemented
19C2×C3×#626—28no—
20C2×C3×#626C2218yescomplemented
21C32×C4⋊Dic3C2214yescomplemented
22C3×(C2×D3)⋊Dic3C2218yescomplemented
23C22×C32×D4—31no—
24C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
25C22×C3×#67—32no—
26C22×C3×D12—21no—
27C22×C3×D12—32no—
28C22×C3×D12D311yescharacteristic, complemented
29C22×C3×D12C2×C311yescharacteristic, complemented
30C22×C3×C4×D3—31no—
31C22×C3×C4×D3—31no—
32C22×C3×C4×D3—61no—
33C22×#626C2×C312yescomplemented
34C2×C32×C4⋊C4—31no—
35C2×C3×#217—32no—
36C3×#938—38no—
37C2×C3×(C2×D3)⋊C4—32no—
38C2×C3×C4⋊Dic3—21no—
39C2×C3×C4⋊Dic3D311yescharacteristic, complemented
40C2×C3×C4⋊Dic3C2×C311yescharacteristic, complemented
41C3×#895—38no—
42C2×(C2×D3)⋊Dic3C2×C312yescomplemented
43#63916C2×C318yesdirect product factor
44C23×C33C2311yescharacteristic
45C22×C3×C3⋊D3—22no—
46C22×C3×C3⋊D3—22no—
47C22×C3×C3⋊D3D414yescomplemented
48C22×C3×C3⋊D3C2312yes—
49C22×C32×D3—24no—
50C22×C32×D3—24no—
51C22×C32×D3—24no—
52C22×C32×D3C2314yes—
53C2×C33×C4D414yescomplemented
54C2×C33×C4C2312yes—
55C2×C3×C3⋊Dic3—22no—
56C2×C3×C3⋊Dic3C2312yes—
57C3×C4×C3⋊D3—28no—
58C2×C32×Dic3—24no—
59C2×C32×Dic3C2314yes—
60C32×D12—28no—
61C3×#626—216no—
62C2×C3×#121—91no—
63C2×#938—31no—
64C2×#895—31no—
65C24×C32—32no—
66C23×C3⋊D3C22×C311yescharacteristic
67C23×C3×D3—22no—
68C23×C3×D3—31no—
69C23×C3×D3—31no—
70C23×C3×D3—61no—
71C23×C3×D3C2×D312yes—
72C23×C3×D3C22×C312yes—
73C2×C32×D4—34no—
74C2×C32×D4—64no—
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4—32no—
79C22×C32×C4—41no—
80C22×C32×C4C2×D311yescharacteristic
81C22×C32×C4C2×D311yescharacteristic
82C22×C32×C4C22×C311yescharacteristic
83C22×C3⋊Dic3C22×C311yescharacteristic
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3C22×C314yescomplemented
86C2×C3×#67—38no—
87C2×C3×#67—68no—
88C22×C3×Dic3—22no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—61no—
92C22×C3×Dic3C2×D312yes—
93C22×C3×Dic3C22×C312yes—
94C2×C3×D12—28no—
95C2×C3×D12—24no—
96C2×C3×D12—24no—
97C2×C3×D12—24no—
98C2×C3×D12—38no—
99C2×C3×D12—68no—
100C2×C3×D12C2×D314yescomplemented
101C2×C3×D12C22×C314yescomplemented
102C2×C3×C4×D3—34no—
103C2×C3×C4×D3—34no—
104C2×C3×C4×D3—64no—
105C2×C3×C4×D3—68no—
106C2×C3×C4×D3—64no—
107C2×C3×C4×D3—64no—
108C2×#626—28no—
109C2×#626C22×C318yescomplemented
110C32×C4⋊C4—34no—
111C3×#217—38no—
112C3×(C2×D3)⋊C4—38no—
113C3×C4⋊Dic3—24no—
114C3×C4⋊Dic3C2×D314yescomplemented
115C3×C4⋊Dic3C22×C314yescomplemented
116(C2×D3)⋊Dic3C22×C318yescomplemented
117C22×C33C2×D412yes—
118C22×C33C2×D412yes—
119C22×C33#4112yes—
120C22×C33C2411yescharacteristic
121C2×C3×C3⋊D3—28no—
122C2×C3×C3⋊D3—22no—
123C2×C3×C3⋊D3—22no—
124C2×C3×C3⋊D3C2×D414yescomplemented
125C2×C32×D3—24no—
126C2×C32×D3—24no—
127C2×C32×D3—24no—
128C2×C32×D3—48no—
129C33×C4C2×D414yescomplemented
130C3×C3⋊Dic3—22no—
131C32×Dic3—24no—
132C22×C3×D4—31no—
133C22×C3×D4—31no—
134C22×C3×D4—61no—
135C22×C3×D4—92no—
136C23×C3×C4—91no—
137C22×#67—32no—
138C22×D12—32no—
139C22×D12C3×D311yescharacteristic, complemented
140C22×C4×D3—31no—
141C22×C4×D3—31no—
142C22×C4×D3—61no—
143C3×#121—98no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—61no—
147C2×C3×C22⋊C4—92no—
148C2×#217—32no—
149#938—38no—
150C2×(C2×D3)⋊C4—32no—
151C2×C4⋊Dic3C3×D311yescharacteristic, complemented
152#895—38no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—34no—
157C23×C32—41no—
158C23×C32—64no—
159C23×C32—64no—
160C23×C32—64no—
161C23×C32C22×D311yescharacteristic
162C23×C32C22×D311yescharacteristic
163C23×C32C23×C311yescharacteristic
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3C3×D414yescomplemented
167C22×C3⋊D3C23×C312yes—
168C22×C3×D3—28no—
169C22×C3×D3—24no—
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3—24no—
174C22×C3×D3—24no—
175C22×C3×D3—24no—
176C22×C3×D3—34no—
177C22×C3×D3—34no—
178C22×C3×D3—32no—
179C22×C3×D3—32no—
180C22×C3×D3—44no—
181C22×C3×D3—44no—
182C22×C3×D3—64no—
183C22×C3×D3—62no—
184C22×C3×D3—64no—
185C22×C3×D3—64no—
186C22×C3×D3—62no—
187C22×C3×D3—62no—
188C22×C3×D3—62no—
189C22×C3×D3—62no—
190C22×C3×D3C22×D314yes—
191C22×C3×D3C23×C314yes—
192C32×D4—68no—
193C2×C32×C4—24no—
194C2×C32×C4—24no—
195C2×C32×C4—24no—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4—22no—
199C2×C32×C4—34no—
200C2×C32×C4—44no—
201C2×C32×C4—42no—
202C2×C32×C4—64no—
203C2×C32×C4D1214yescomplemented
204C2×C32×C4#6714yescomplemented
205C2×C32×C4C3×D414yescomplemented
206C2×C32×C4C22×D312yes—
207C2×C32×C4C22×D312yes—
208C2×C32×C4C23×C312yes—
209C2×C3⋊Dic3—22no—
210C2×C3⋊Dic3C23×C312yes—
211C4×C3⋊D3—28no—
212C3×#67—616no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—24no—
216C2×C3×Dic3—32no—
217C2×C3×Dic3—32no—
218C2×C3×Dic3—44no—
219C2×C3×Dic3—62no—
220C2×C3×Dic3—64no—
221C2×C3×Dic3—62no—
222C2×C3×Dic3—62no—
223C2×C3×Dic3C22×D314yes—
224C2×C3×Dic3C23×C314yes—
225C3×D12—216no—
226C3×D12—28no—
227C3×D12—28no—
228C3×D12—616no—
229C3×C4×D3—616no—
230C3×C4×D3—68no—
231C3×C4×D3—68no—
232#626—216no—
233C2×#121—91noSylow
234C2×C33#12114yescomplemented
235C2×C33C22×D411yescharacteristic
236C2×C33C22×D411yescharacteristic
237C2×C33C2×#4111yescharacteristic
238C3×C3⋊D3—24no—
239C32×D3—44no—
240C24×C3—32no—
241C24×C3—32no—
242C24×C3—62no—
243C24×C3—91no—
244C23×D3—31no—
245C23×D3—31no—
246C23×D3—61no—
247C23×D3C2×C3×D312yes—
248C2×C3×D4—34no—
249C2×C3×D4—34no—
250C2×C3×D4—64no—
251C2×C3×D4—68no—
252C2×C3×D4—64no—
253C2×C3×D4—64no—
254C2×C3×D4—98no—
255C2×C3×D4—188no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—32no—
260C22×C3×C4—32no—
261C22×C3×C4—41no—
262C22×C3×C4—62no—
263C22×C3×C4—91no—
264C22×C3×C4—94no—
265C22×C3×C4—184no—
266C22×C3×C4D3211yescharacteristic
267C22×C3×C4C2×C3×D311yescharacteristic
268C22×C3×C4C2×C3×D311yescharacteristic
269C2×#67—38no—
270C2×#67—68no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—61no—
274C22×Dic3C2×C3×D312yes—
275C2×D12—24no—
276C2×D12—38no—
277C2×D12—68no—
278C2×D12C2×C3×D314yescomplemented
279C2×C4×D3—34no—
280C2×C4×D3—34no—
281C2×C4×D3—64no—
282C2×C4×D3—68no—
283C2×C4×D3—64no—
284C2×C4×D3—64no—
285C3×C4⋊C4—34no—
286C3×C4⋊C4—34no—
287C3×C4⋊C4—64no—
288C3×C22⋊C4—98no—
289#217—38no—
290(C2×D3)⋊C4—38no—
291C4⋊Dic3C2×C3×D314yescomplemented
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—42no—
305C22×C32—42no—
306C22×C32—42no—
307C22×C32—41no—
308C22×C32—64no—
309C22×C32—64no—
310C22×C32—64no—
311C22×C32—128no—
312C22×C32C2×D1212yes—
313C22×C32D3×D412yes—
314C22×C32D3×D412yes—
315C22×C32#23712yes—
316C22×C32#23912yes—
317C22×C32C2×#6712yes—
318C22×C32C2×C3×D412yes—
319C22×C32C2×C3×D412yes—
320C22×C32C3×#4112yes—
321C22×C32C23×D311yescharacteristic
322C22×C32C23×D311yescharacteristic
323C22×C32C24×C311yescharacteristic
324C2×C3⋊D3—28no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3C2×C3×D414yescomplemented
328C2×C3×D3—28no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—24no—
333C2×C3×D3—24no—
334C2×C3×D3—24no—
335C2×C3×D3—34no—
336C2×C3×D3—34no—
337C2×C3×D3—44no—
338C2×C3×D3—44no—
339C2×C3×D3—416no—
340C2×C3×D3—48no—
341C2×C3×D3—48no—
342C2×C3×D3—64no—
343C2×C3×D3—64no—
344C2×C3×D3—64no—
345C2×C3×D3—616no—
346C2×C3×D3—68no—
347C2×C3×D3—68no—
348C2×C3×D3—62no—
349C2×C3×D3—62no—
350C2×C3×D3—62no—
351C2×C3×D3—62no—
352C32×C4—24no—
353C32×C4—24no—
354C32×C4—24no—
355C32×C4—44no—
356C32×C4—64no—
357C32×C4C2×D1214yescomplemented
358C32×C4C2×#6714yescomplemented
359C32×C4C2×C3×D414yescomplemented
360C3⋊Dic3—22no—
361C3×Dic3—24no—
362C3×Dic3—24no—
363C3×Dic3—44no—
364C3×Dic3—64no—
365C3×Dic3—62no—
366C3×Dic3—62no—
367C22×D4—31no—
368C22×D4—92no—
369C23×C4—91no—
370#121—98no—
371C2×C4⋊C4—31no—
372C2×C22⋊C4—92no—
373C33C2×#12111yescharacteristic, complemented, Sylow
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—34no—
378C23×C3—34no—
379C23×C3—41no—
380C23×C3—64no—
381C23×C3—68no—
382C23×C3—64no—
383C23×C3—64no—
384C23×C3—64no—
385C23×C3—64no—
386C23×C3—64no—
387C23×C3—64no—
388C23×C3—92no—
389C23×C3—94no—
390C23×C3—124no—
391C23×C3—124no—
392C23×C3—182no—
393C23×C3—182no—
394C23×C3C2×D3211yescharacteristic
395C23×C3C22×C3×D311yescharacteristic
396C23×C3C22×C3×D311yescharacteristic
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—32no—
401C22×D3—32no—
402C22×D3—34no—
403C22×D3—34no—
404C22×D3—64no—
405C22×D3—62no—
406C22×D3—64no—
407C22×D3—64no—
408C22×D3—62no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3C22×C3×D314yes—
413C3×D4—616no—
414C3×D4—68no—
415C3×D4—68no—
416C3×D4—1816no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—34no—
424C2×C3×C4—34no—
425C2×C3×C4—44no—
426C2×C3×C4—42no—
427C2×C3×C4—64no—
428C2×C3×C4—64no—
429C2×C3×C4—64no—
430C2×C3×C4—92no—
431C2×C3×C4—124no—
432C2×C3×C4—182no—
433C2×C3×C4—188no—
434C2×C3×C4#62614yescomplemented
435C2×C3×C4C3×D1214yescomplemented
436C2×C3×C4C3×#6714yescomplemented
437C2×C3×C4C2×D3212yes—
438C2×C3×C4C22×C3×D312yes—
439C2×C3×C4C22×C3×D312yes—
440#67—616no—
441C2×Dic3—24no—
442C2×Dic3—32no—
443C2×Dic3—32no—
444C2×Dic3—62no—
445C2×Dic3—64no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3C22×C3×D314yes—
449D12—28no—
450D12—616no—
451C4×D3—616no—
452C4×D3—68no—
453C4×D3—68no—
454C2×C32—24no—
455C2×C32—21no—
456C2×C32—21no—
457C2×C32—24no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—24no—
466C2×C32—44no—
467C2×C32—41no—
468C2×C32—41no—
469C2×C32—41no—
470C2×C32—124no—
471C2×C32#89514yescomplemented
472C2×C32#93814yescomplemented
473C2×C32C3×#12114yescomplemented
474C2×C32C22×D1211yescharacteristic
475C2×C32C2×D3×D411yescharacteristic
476C2×C32C2×D3×D411yescharacteristic
477C2×C32C2×#23711yescharacteristic
478C2×C32C2×#23911yescharacteristic
479C2×C32C22×#6711yescharacteristic
480C2×C32C22×C3×D411yescharacteristic
481C2×C32C22×C3×D411yescharacteristic
482C2×C32C2×C3×#4111yescharacteristic
483C3⋊D3—24no—
484C3×D3—48no—
485C3×D3—44no—
486C3×D3—44no—
487C3×D3—68no—
488C3×D3—64no—
489C3×D3—64no—
490C24—32no—
491C24—91no—
492C2×D4—34no—
493C2×D4—64no—
494C2×D4—98no—
495C2×D4—188no—
496C22×C4—32no—
497C22×C4—91no—
498C22×C4—94no—
499C22×C4—184no—
500C22×C4C3×D3211yescharacteristic
501C4⋊C4—34no—
502C22⋊C4—98no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—41no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—68no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—64no—
523C22×C3—64no—
524C22×C3—64no—
525C22×C3—64no—
526C22×C3—94no—
527C22×C3—124no—
528C22×C3—124no—
529C22×C3—1216no—
530C22×C3—128no—
531C22×C3—128no—
532C22×C3—182no—
533C22×C3—182no—
534C22×C3—188no—
535C22×C3#379612yes—
536C22×C3#380212yes—
537C22×C3C2×#62612yes—
538C22×C3C2×C3×D1212yes—
539C22×C3C3×D3×D412yes—
540C22×C3C3×D3×D412yes—
541C22×C3C3×#23712yes—
542C22×C3C3×#23912yes—
543C22×C3C2×C3×#6712yes—
544C22×C3C22×D3211yescharacteristic
545C22×C3C23×C3×D311yescharacteristic
546C22×C3C23×C3×D311yescharacteristic
547C2×D3—24no—
548C2×D3—24no—
549C2×D3—24no—
550C2×D3—34no—
551C2×D3—34no—
552C2×D3—48no—
553C2×D3—64no—
554C2×D3—64no—
555C2×D3—616no—
556C2×D3—64no—
557C2×D3—68no—
558C2×D3—68no—
559C2×D3—62no—
560C2×D3—62no—
561C2×D3—62no—
562C2×D3—62no—
563C3×C4—24no—
564C3×C4—24no—
565C3×C4—24no—
566C3×C4—44no—
567C3×C4—64no—
568C3×C4—64no—
569C3×C4—124no—
570C3×C4—182no—
571C3×C4C2×#62614yescomplemented
572C3×C4C2×C3×D1214yescomplemented
573C3×C4C2×C3×#6714yescomplemented
574Dic3—24no—
575Dic3—64no—
576Dic3—62no—
577Dic3—62no—
578C32—21no—
579C32—21no—
580C32—21no—
581C32—41no—
582C32C2×#89511yescharacteristic, complemented
583C32C2×#93811yescharacteristic, complemented
584C32C2×C3×#12111yescharacteristic, complemented
585C23—34no—
586C23—64no—
587C23—64no—
588C23—64no—
589C23—92no—
590C23—94no—
591C23—182no—
592C23—182no—
593C23C2×C3×D3211yescharacteristic
594D4—68no—
595D4—1816no—
596C2×C4—34no—
597C2×C4—64no—
598C2×C4—92no—
599C2×C4—182no—
600C2×C4—188no—
601C2×C4C3×#62614yescomplemented
602C2×C4C2×C3×D3212yes—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—24no—
607C2×C3—24no—
608C2×C3—24no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—41no—
616C2×C3—44no—
617C2×C3—41no—
618C2×C3—41no—
619C2×C3—128no—
620C2×C3—124no—
621C2×C3—124no—
622C2×C3—184no—
623C2×C3#6391614yesdirect product factor
624C2×C3C3×#89514yescomplemented
625C2×C3C3×#93814yescomplemented
626C2×C3C2×#379611yescharacteristic
627C2×C3C2×#380211yescharacteristic
628C2×C3C22×#62611yescharacteristic
629C2×C3C22×C3×D1211yescharacteristic
630C2×C3C2×C3×D3×D411yescharacteristic
631C2×C3C2×C3×D3×D411yescharacteristic
632C2×C3C2×C3×#23711yescharacteristic
633C2×C3C2×C3×#23911yescharacteristic
634C2×C3C22×C3×#6711yescharacteristic
635D3—44no—
636D3—68no—
637D3—64no—
638D3—64no—
639C22—64no—
640C22—64no—
641C22—64no—
642C22—94no—
643C22—128no—
644C22—182no—
645C22—188no—
646C22—182no—
647C22C3×#379612yes—
648C22C3×#380212yes—
649C22C2×C3×#62612yes—
650C22C22×C3×D3211yescharacteristic
651C4—64no—
652C4—182no—
653C4C2×C3×#62614yescomplemented
654C3—21no—
655C3—21no—
656C3—21no—
657C3—41no—
658C3C2×#6391611yescharacteristic, direct product factor
659C3C2×C3×#89511yescharacteristic, complemented
660C3C2×C3×#93811yescharacteristic, complemented
661C2—124no—
662C2—184no—
663C2C3×#6391614yesdirect product factor
664C2C2×C3×#379611yescharacteristic
665C2C2×C3×#380211yescharacteristic
666C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#121
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. C22×C3×C4×C3⋊D3C2semidirect
2. C22×C32×D12C2semidirect
3. C22×C3×#626C2semidirect
4. C2×C32×C4⋊Dic3C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. C3×#63916C2direct (N × H)
9. C2×#63916C3direct (N × H)
15. C2×C3×C4×C3⋊D3C22semidirect
18. C2×C32×D12C22semidirect
20. C2×C3×#626C22semidirect
21. C32×C4⋊Dic3C22semidirect
22. C3×(C2×D3)⋊Dic3C22semidirect
24. C22×C4×C3⋊D3C2×C3semidirect
28. C22×C3×D12D3semidirect
29. C22×C3×D12C2×C3semidirect
33. C22×#626C2×C3semidirect
39. C2×C3×C4⋊Dic3D3semidirect
40. C2×C3×C4⋊Dic3C2×C3semidirect
42. C2×(C2×D3)⋊Dic3C2×C3semidirect
43. #63916C2×C3direct (N × H)
47. C22×C3×C3⋊D3D4semidirect
53. C2×C33×C4D4semidirect
85. C2×C4×C3⋊D3C22×C3semidirect
100. C2×C3×D12C2×D3semidirect
101. C2×C3×D12C22×C3semidirect
109. C2×#626C22×C3semidirect
114. C3×C4⋊Dic3C2×D3semidirect
115. C3×C4⋊Dic3C22×C3semidirect
116. (C2×D3)⋊Dic3C22×C3semidirect
124. C2×C3×C3⋊D3C2×D4semidirect
129. C33×C4C2×D4semidirect
139. C22×D12C3×D3semidirect
151. C2×C4⋊Dic3C3×D3semidirect
166. C22×C3⋊D3C3×D4semidirect
203. C2×C32×C4D12semidirect
204. C2×C32×C4#67semidirect
205. C2×C32×C4C3×D4semidirect
234. C2×C33#121semidirect
278. C2×D12C2×C3×D3semidirect
291. C4⋊Dic3C2×C3×D3semidirect
327. C2×C3⋊D3C2×C3×D4semidirect
357. C32×C4C2×D12semidirect
358. C32×C4C2×#67semidirect
359. C32×C4C2×C3×D4semidirect
373. C33C2×#121semidirect
434. C2×C3×C4#626semidirect
435. C2×C3×C4C3×D12semidirect
436. C2×C3×C4C3×#67semidirect
471. C2×C32#895semidirect
472. C2×C32#938semidirect
473. C2×C32C3×#121semidirect
571. C3×C4C2×#626semidirect
572. C3×C4C2×C3×D12semidirect
573. C3×C4C2×C3×#67semidirect
582. C32C2×#895semidirect
583. C32C2×#938semidirect
584. C32C2×C3×#121semidirect
601. C2×C4C3×#626semidirect
623. C2×C3#63916direct (N × H)
624. C2×C3C3×#895semidirect
625. C2×C3C3×#938semidirect
653. C4C2×C3×#626semidirect
658. C3C2×#63916direct (N × H)
659. C3C2×C3×#895semidirect
660. C3C2×C3×#938semidirect
663. C2C3×#63916direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C22×C32×D122
C22×C3×#6262
C2×C32×C4⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#639162
C2×C3×#9383
C2×C3×#8953
C2×#639163