Finite Group Databasebeta

← D3×#64139 #13177321

Subgroups — D3×#64139 #13177321

Order 1728.

2932 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×D3×#638C212yesmaximal, complemented
3C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#11723971C211yesmaximal, characteristic, complemented
5C3×#64139C211yesmaximal, characteristic, complemented
6#11723632C212yesmaximal, complemented
7D3×#3752C212yesmaximal, complemented
8#11723516C211yesmaximal, characteristic, complemented
9#11723515C211yesmaximal, characteristic, complemented
10#11723514C212yesmaximal, complemented
11D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
12C2×#64139—31nomaximal
13D3×#930—34nomaximal
14C23×C32×D3C2211yescharacteristic
15C22×D3×C3⋊D3C2212yes—
16C22×C33×C4C2211yescharacteristic, complemented
17C2×#6312C2212yescomplemented
18C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
19C2×C3×#638C2212yescomplemented
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C22×C32×Dic3C2211yescharacteristic, complemented
22C2×C32×C4×D3—24no—
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C2×C32×C4×D3C2211yescharacteristic, complemented
27D3×#638—28no—
28C2×#6292C2212yescomplemented
29C2×#6291C2212yescomplemented
30C2×#6290C2212yescomplemented
31C2×D3×C3⋊Dic3C2212yes—
32D3×C4⋊(C3⋊D3)—24no—
33#88859C2212yescomplemented
34C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
35C3×#3752C2212yescomplemented
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37Dic3⋊(C3⋊Dic3)C2212yescomplemented
38#88804C2212yescomplemented
39#88803C2212yescomplemented
40C23×C32×C4—31no—
41C22×#638—32no—
42C22×C4⋊(C3⋊D3)—31no—
43C22×C3×C4×D3D314yescomplemented
44C2×D3×#67—38no—
45C2×D3×D12—34no—
46#64139—31no—
47#64139—32no—
48#64139—31no—
49#64139—32no—
50#64139—31no—
51#64139—34no—
52#64139—64no—
53#64139D311yescharacteristic, direct product factor
54C2×#3752—32no—
55C2×C4⋊(C3⋊Dic3)—31no—
56C3×#930—34no—
57#63978—38no—
58D3×(C2×D3)⋊C4—38no—
59#63909—34no—
60#63908—34no—
61#63906—38no—
62D3×C4⋊Dic3—34no—
63C23×C33C2311yescharacteristic
64C22×C3⋊(C3⋊D3)C2312yes—
65C22×C3×C3⋊D3C2312yes—
66C22×C32×D3—22no—
67C22×C32×D3—22no—
68C22×C32×D3D414yescomplemented
69C22×C32×D3C2311yescharacteristic
70C22×C32×D3C2311yescharacteristic
71C2×D3×C3⋊D3—24no—
72C2×D3×C3⋊D3—24no—
73C2×D3×C3⋊D3—24no—
74C2×C33×C4—22no—
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77#6312—24no—
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C4⋊(C3⋊(C3⋊D3))—22no—
80C3×#638—24no—
81C2×C3×C3⋊Dic3C2312yes—
82C3×C4⋊(C3⋊D3)—22no—
83C2×C32×Dic3—22no—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×C4×D3—22no—
88C32×C4×D3—22no—
89C32×C4×D3D414yescomplemented
90#6292—24no—
91#6291—24no—
92#6290—24no—
93D3×C3⋊Dic3—24no—
94C2×#930—94no—
95D3×#121—91no—
96C24×C32—31no—
97C23×C3⋊D3—32no—
98C23×C3×D3C2×D314yes—
99C22×D32—38no—
100C22×C32×C4—24no—
101C22×C32×C4—31no—
102C22×C32×C4—31no—
103C22×C32×C4—31no—
104C22×C32×C4—31no—
105C22×C32×C4—31no—
106C22×C32×C4—64no—
107C22×C32×C4C2×D314yescomplemented
108C22×C32×C4C2×D311yescharacteristic, complemented
109C2×#638—32no—
110C2×#638—38no—
111C2×#638—32no—
112C2×#638—32no—
113C2×#638—68no—
114C2×#638—68no—
115C2×#638C2×D312yescomplemented
116C22×C3⋊Dic3—32no—
117C2×C4⋊(C3⋊D3)—32no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—34no—
120C2×C4⋊(C3⋊D3)—64no—
121C2×C4⋊(C3⋊D3)—64no—
122C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
123C2×C3×#67—38no—
124C22×C3×Dic3C2×D314yescomplemented
125C2×C3×D12—34no—
126C2×C3×C4×D3—216no—
127C2×C3×C4×D3C2×D314yes—
128C2×C3×C4×D3C2×D314yes—
129C2×C3×C4×D3C2×D314yescomplemented
130C2×C3×C4×D3C2×D314yescomplemented
131D3×#67—632no—
132C2×#626—38no—
133C2×#626—38no—
134C2×#625—38no—
135C2×D3×Dic3—38no—
136D3×D12—616no—
137#3752—32no—
138#3752—32no—
139#3752—38no—
140#3752—32no—
141#3752—68no—
142#3752C2×D312yescomplemented
143C4⋊(C3⋊Dic3)—31no—
144C4⋊(C3⋊Dic3)—34no—
145C4⋊(C3⋊Dic3)—32no—
146C4⋊(C3⋊Dic3)—64no—
147C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
148C3×(C2×D3)⋊C4—38no—
149C3×C4⋊Dic3—34no—
150Dic3⋊Dic3—38no—
151#3722—38no—
152(C2×D3)⋊Dic3—38no—
153C22×C33—21no—
154C22×C33—21no—
155C22×C33C2×D412yescomplemented
156C22×C33C2411yescharacteristic
157C2×C3⋊(C3⋊D3)—22no—
158C2×C3⋊(C3⋊D3)—22no—
159C2×C3⋊(C3⋊D3)—22no—
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3—22no—
162C2×C3×C3⋊D3—22no—
163C2×C32×D3—21no—
164C2×C32×D3—21no—
165C2×C32×D3—28no—
166C2×C32×D3C2×D412yes—
167C2×C32×D3C2×D412yes—
168C2×C32×D3C2×D412yescomplemented
169C2×C32×D3#4112yes—
170D3×C3⋊D3—48no—
171C33×C4—21no—
172C33×C4C2×D412yescomplemented
173C3⋊(C3⋊Dic3)—22no—
174C3×C3⋊Dic3—22no—
175C32×Dic3—21no—
176C32×Dic3C2×D412yescomplemented
177C23×C3×C4—34no—
178C22×#67—98no—
179C2×D3×D4—92no—
180C2×D3×D4—91no—
181C22×D12—94no—
182C22×C4×D3C3⋊D311yescharacteristic, complemented
183C3×#121—91no—
184#939—92no—
185#938—91no—
186#930—34no—
187#930—94no—
188#930—98no—
189#930—94no—
190#930—98no—
191#930—94no—
192#930—91no—
193#930—184no—
194C2×(C2×D3)⋊C4—98no—
195C2×C4⋊Dic3—94no—
196#895—91no—
197D3×C4⋊C4—91no—
198#884—92no—
199D3×C22⋊C4—92no—
200C23×C32—24no—
201C23×C32—31no—
202C23×C32—34no—
203C23×C32—31no—
204C23×C32—62no—
205C23×C32—62no—
206C23×C32C22×D314yes—
207C23×C32C22×D311yescharacteristic
208C22×C3⋊D3—32no—
209C22×C3⋊D3—38no—
210C22×C3⋊D3—68no—
211C22×C3⋊D3—64no—
212C22×C3⋊D3—64no—
213C22×C3⋊D3—64no—
214C22×C3⋊D3C22×D312yes—
215C22×C3×D3—28no—
216C22×C3×D3—28no—
217C22×C3×D3—38no—
218C22×C3×D3D12116yescomplemented
219C22×C3×D3C22×D314yes—
220C22×C3×D3C22×D314yes—
221C2×D32—616no—
222C2×D32—616no—
223C2×D32—616no—
224C2×C32×C4—22no—
225C2×C32×C4—24no—
226C2×C32×C4—24no—
227C2×C32×C4—28no—
228C2×C32×C4—31no—
229C2×C32×C4—34no—
230C2×C32×C4—31no—
231C2×C32×C4—48no—
232C2×C32×C4—62no—
233C2×C32×C4—62no—
234C2×C32×C4—62no—
235C2×C32×C4—62no—
236C2×C32×C4C22×D314yes—
237C2×C32×C4C22×D314yes—
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240#638—24no—
241#638—64no—
242#638—64no—
243#638—64no—
244#638—616no—
245#638—1216no—
246C2×C3⋊Dic3—32no—
247C2×C3⋊Dic3—38no—
248C2×C3⋊Dic3—68no—
249C2×C3⋊Dic3—64no—
250C2×C3⋊Dic3C22×D312yes—
251C4⋊(C3⋊D3)—22no—
252C4⋊(C3⋊D3)—64no—
253C4⋊(C3⋊D3)—62no—
254C4⋊(C3⋊D3)—68no—
255C4⋊(C3⋊D3)—128no—
256C3×#67—616no—
257C2×C3×Dic3—28no—
258C2×C3×Dic3—38no—
259C2×C3×Dic3C22×D314yes—
260C2×C3×Dic3C22×D314yes—
261C3×D12—68no—
262C3×C4×D3—28no—
263C3×C4×D3—28no—
264C3×C4×D3—28no—
265C3×C4×D3#67116yescomplemented
266#626—616no—
267#626—616no—
268#625—616no—
269D3×Dic3—616no—
270C2×#121—271noSylow
271C2×C33—22no—
272C2×C33C22×D411yescharacteristic
273C2×C33C22×D411yescharacteristic
274C2×C33C2×#4111yescharacteristic
275C3⋊(C3⋊D3)—42no—
276C3×C3⋊D3—42no—
277C32×D3—22no—
278C32×D3#12114yescomplemented
279C24×C3—34no—
280C23×D3—98no—
281C23×D3—92no—
282C23×D3C2×C3⋊D311yescharacteristic
283C2×C3×D4—92no—
284C2×C3×D4—91no—
285C22×C3×C4—24no—
286C22×C3×C4—34no—
287C22×C3×C4—34no—
288C22×C3×C4—34no—
289C22×C3×C4—34no—
290C22×C3×C4—34no—
291C22×C3×C4—616no—
292C22×C3×C4D3214yescomplemented
293C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
294C2×#67—38no—
295C2×#67—98no—
296C2×#67—98no—
297C2×#67—98no—
298C2×#67—92no—
299C2×#67—92no—
300C2×#67—92no—
301C2×#67—188no—
302C2×#67—1832no—
303C22×Dic3—98no—
304C22×Dic3C2×C3⋊D311yescharacteristic, complemented
305D3×D4—188no—
306D3×D4—184no—
307C2×D12—34no—
308C2×D12—98no—
309C2×D12—92no—
310C2×D12—94no—
311C2×D12—91no—
312C2×D12—184no—
313C2×D12—1816no—
314C2×C4×D3—24no—
315C2×C4×D3—92no—
316C2×C4×D3C2×C3⋊D311yescharacteristic
317C2×C4×D3C2×C3⋊D311yescharacteristic
318C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
319C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
320C3×C4⋊C4—91no—
321C3×C22⋊C4—92no—
322#217—92no—
323(C2×D3)⋊C4—38no—
324(C2×D3)⋊C4—98no—
325(C2×D3)⋊C4—98no—
326(C2×D3)⋊C4—98no—
327(C2×D3)⋊C4—92no—
328(C2×D3)⋊C4—92no—
329(C2×D3)⋊C4—188no—
330C4⋊Dic3—34no—
331C4⋊Dic3—98no—
332C4⋊Dic3—94no—
333C4⋊Dic3—91no—
334C4⋊Dic3—184no—
335Dic3⋊C4—92no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—24no—
339C22×C32—28no—
340C22×C32—24no—
341C22×C32—24no—
342C22×C32—32no—
343C22×C32—32no—
344C22×C32—32no—
345C22×C32—32no—
346C22×C32—44no—
347C22×C32—44no—
348C22×C32—68no—
349C22×C32—61no—
350C22×C32—61no—
351C22×C32C2×D1218yescomplemented
352C22×C32D3×D412yescomplemented
353C22×C32C23×D314yes—
354C22×C32C23×D311yescharacteristic
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—62no—
359C2×C3⋊D3—62no—
360C2×C3⋊D3—62no—
361C2×C3⋊D3—68no—
362C2×C3⋊D3—68no—
363C2×C3⋊D3—68no—
364C2×C3⋊D3—128no—
365C2×C3⋊D3—128no—
366C2×C3⋊D3—128no—
367C2×C3⋊D3—128no—
368C2×C3×D3—24no—
369C2×C3×D3—24no—
370C2×C3×D3—232no—
371C2×C3×D3—68no—
372C2×C3×D3—68no—
373C2×C3×D3—68no—
374C2×C3×D3C2×D1218yes—
375C2×C3×D3C2×D1218yescomplemented
376C2×C3×D3#23518yes—
377C2×C3×D3C2×#6718yes—
378D32—1232no—
379C32×C4—21no—
380C32×C4—28no—
381C32×C4—24no—
382C32×C4—32no—
383C32×C4—44no—
384C32×C4—61no—
385C32×C4D3×D412yescomplemented
386C32×C4C2×#6718yescomplemented
387C3⋊Dic3—22no—
388C3⋊Dic3—62no—
389C3⋊Dic3—68no—
390C3⋊Dic3—128no—
391C3×Dic3—24no—
392C3×Dic3—68no—
393C3×Dic3C2×#6718yescomplemented
394C22×D4—271no—
395C22×D4—272no—
396C23×C4—31no—
397#121—91no—
398#121—272no—
399#121—271no—
400#121—271no—
401#121—272no—
402#121—271no—
403C2×C4⋊C4—271no—
404C2×C22⋊C4—272no—
405C33C2×#12111yescharacteristic, complemented, Sylow
406C23×C3—24no—
407C23×C3—34no—
408C23×C3—34no—
409C23×C3—316no—
410C23×C3—68no—
411C23×C3—68no—
412C23×C3—92no—
413C23×C3C2×D3214yes—
414C23×C3C22×C3⋊D311yescharacteristic
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—38no—
418C22×D3—98no—
419C22×D3—92no—
420C22×D3—188no—
421C22×D3—1816no—
422C22×D3—1816no—
423C22×D3—1816no—
424C22×D3—184no—
425C22×D3—184no—
426C22×D3—184no—
427C22×D3C4⋊(C3⋊D3)14yescomplemented
428C22×D3C22×C3⋊D311yescharacteristic
429C22×D3C22×C3⋊D311yescharacteristic
430C3×D4—184no—
431C3×D4—182no—
432C2×C3×C4—28no—
433C2×C3×C4—22no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—34no—
437C2×C3×C4—316no—
438C2×C3×C4—34no—
439C2×C3×C4—48no—
440C2×C3×C4—68no—
441C2×C3×C4—68no—
442C2×C3×C4—68no—
443C2×C3×C4—68no—
444C2×C3×C4—92no—
445C2×C3×C4C2×D3214yes—
446C2×C3×C4C2×D3214yes—
447C2×C3×C4C22×C3⋊D311yescharacteristic
448C2×C3×C4C22×C3⋊D311yescharacteristic
449#67—616no—
450#67—1816no—
451#67—1816no—
452#67—1816no—
453#67—184no—
454#67—184no—
455#67—184no—
456#67—3616no—
457C2×Dic3—22no—
458C2×Dic3—38no—
459C2×Dic3—98no—
460C2×Dic3—92no—
461C2×Dic3—188no—
462C2×Dic3—1816no—
463C2×Dic3C22×C3⋊D311yescharacteristic
464C2×Dic3C22×C3⋊D311yescharacteristic
465D12—68no—
466D12—1816no—
467D12—184no—
468D12—188no—
469D12—182no—
470D12—368no—
471C4×D3—22no—
472C4×D3—22no—
473C4×D3—22no—
474C4×D3—184no—
475C4×D3#63814yescomplemented
476C2×C32—22no—
477C2×C32—24no—
478C2×C32—24no—
479C2×C32—24no—
480C2×C32—28no—
481C2×C32—34no—
482C2×C32—48no—
483C2×C32—62no—
484C2×C32C22×D1214yes—
485C2×C32C2×#23514yes—
486C2×C32C2×D3×D411yescharacteristic
487C2×C32C2×D3×D411yescharacteristic
488C2×C32D3×#4111yescharacteristic
489C2×C32C22×#6714yes—
490C3⋊D3—42no—
491C3⋊D3—122no—
492C3⋊D3—128no—
493C3⋊D3—248no—
494C3×D3—28no—
495C3×D3—128no—
496C3×D3#930116yescomplemented
497C24—31no—
498C24—272no—
499C2×D4—92no—
500C2×D4—91no—
501C2×D4—272no—
502C2×D4—272no—
503C2×D4—272no—
504C2×D4—272no—
505C2×D4—271no—
506C2×D4—544no—
507C2×D4—548no—
508C22×C4—31no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—64no—
514C22×C4—272no—
515C22×C4D3×C3⋊D311yescharacteristic, complemented
516C4⋊C4—91no—
517C4⋊C4—272no—
518C4⋊C4—271no—
519C22⋊C4—92no—
520C22⋊C4—272no—
521C22⋊C4—272no—
522C22⋊C4—272no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—24no—
528C22×C3—28no—
529C22×C3—38no—
530C22×C3—38no—
531C22×C3—38no—
532C22×C3—38no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3—632no—
536C22×C3—64no—
537C22×C3—64no—
538C22×C3—182no—
539C22×C3—182no—
540C22×C3—182no—
541C22×C3D3×D1218yescomplemented
542C22×C3C2×C4⋊(C3⋊D3)12yescomplemented
543C22×C3C22×D3214yes—
544C22×C3C23×C3⋊D311yescharacteristic
545C2×D3—21no—
546C2×D3—21no—
547C2×D3—28no—
548C2×D3—68no—
549C2×D3—68no—
550C2×D3—68no—
551C2×D3—188no—
552C2×D3—188no—
553C2×D3—188no—
554C2×D3—182no—
555C2×D3—182no—
556C2×D3—182no—
557C2×D3—368no—
558C2×D3—368no—
559C2×D3—368no—
560C2×D3—3632no—
561C2×D3—368no—
562C2×D3C2×C4⋊(C3⋊D3)12yes—
563C2×D3C2×C4⋊(C3⋊D3)12yescomplemented
564C2×D3#382812yes—
565C2×D3C2×#63812yes—
566C3×C4—24no—
567C3×C4—21no—
568C3×C4—28no—
569C3×C4—38no—
570C3×C4—44no—
571C3×C4—64no—
572C3×C4—182no—
573C3×C4D3×#6718yescomplemented
574C3×C4C2×#63812yescomplemented
575Dic3—21no—
576Dic3—68no—
577Dic3—188no—
578Dic3—182no—
579Dic3—368no—
580Dic3C2×#63812yescomplemented
581C32—24no—
582C32D3×#12111yescharacteristic, complemented
583C32C2×#93014yescomplemented
584C23—31no—
585C23—31no—
586C23—34no—
587C23—62no—
588C23—62no—
589C23—92no—
590C23—272no—
591C23—544no—
592C23—544no—
593C23—544no—
594C23C2×D3×C3⋊D311yescharacteristic
595D4—184no—
596D4—182no—
597D4—544no—
598D4—544no—
599D4—544no—
600D4—544no—
601D4—542no—
602C2×C4—22no—
603C2×C4—31no—
604C2×C4—34no—
605C2×C4—31no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—92no—
611C2×C4—272no—
612C2×C4—544no—
613C2×C4C2×D3×C3⋊D311yescharacteristic
614C2×C4C2×D3×C3⋊D311yescharacteristic
615C2×C3—22no—
616C2×C3—28no—
617C2×C3—24no—
618C2×C3—24no—
619C2×C3—24no—
620C2×C3—316no—
621C2×C3—48no—
622C2×C3—68no—
623C2×C3—362no—
624C2×C3C2×D3×D1214yes—
625C2×C3D3×#23514yes—
626C2×C3C2×D3×#6714yes—
627C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
628C2×C3C2×#382811yescharacteristic
629C2×C3C22×#63811yescharacteristic
630D3—22no—
631D3—128no—
632D3—362no—
633D3—368no—
634D3—728no—
635D3#6413914yesdirect product factor
636C22—21no—
637C22—21no—
638C22—32no—
639C22—32no—
640C22—32no—
641C22—32no—
642C22—68no—
643C22—61no—
644C22—61no—
645C22—182no—
646C22—182no—
647C22—182no—
648C22—542no—
649C22—542no—
650C22—542no—
651C22—1088no—
652C22D3×C4⋊(C3⋊D3)12yescomplemented
653C22C22×D3×C3⋊D311yescharacteristic
654C4—21no—
655C4—32no—
656C4—61no—
657C4—182no—
658C4—542no—
659C4D3×#63812yescomplemented
660C3—24no—
661C3D3×#93014yescomplemented
662C3C2×#6413911yescharacteristic, complemented
663C2—22no—
664C2—34no—
665C2—62no—
666C2—362no—
667C2—1082no—
668C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
669C2D3×#382811yescharacteristic
670C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4×D3C2semidirect
2. C2×D3×#638C2semidirect
3. C2×D3×C4⋊(C3⋊D3)C2semidirect
4. #11723971C2semidirect
5. C3×#64139C2semidirect
6. #11723632C2semidirect
7. D3×#3752C2semidirect
8. #11723516C2semidirect
9. #11723515C2semidirect
10. #11723514C2semidirect
11. D3×C4⋊(C3⋊Dic3)C2semidirect
16. C22×C33×C4C22semidirect
17. C2×#6312C22semidirect
18. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
19. C2×C3×#638C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C22×C32×Dic3C22semidirect
25. C2×C32×C4×D3C22semidirect
26. C2×C32×C4×D3C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6290C22semidirect
33. #88859C22semidirect
34. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
35. C3×#3752C22semidirect
36. C3×C4⋊(C3⋊Dic3)C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
38. #88804C22semidirect
39. #88803C22semidirect
43. C22×C3×C4×D3D3semidirect
53. #64139D3direct (N × H)
68. C22×C32×D3D4semidirect
89. C32×C4×D3D4semidirect
107. C22×C32×C4C2×D3semidirect
108. C22×C32×C4C2×D3semidirect
115. C2×#638C2×D3semidirect
122. C2×C4⋊(C3⋊D3)C2×D3semidirect
124. C22×C3×Dic3C2×D3semidirect
129. C2×C3×C4×D3C2×D3semidirect
130. C2×C3×C4×D3C2×D3semidirect
142. #3752C2×D3semidirect
147. C4⋊(C3⋊Dic3)C2×D3semidirect
155. C22×C33C2×D4semidirect
168. C2×C32×D3C2×D4semidirect
172. C33×C4C2×D4semidirect
176. C32×Dic3C2×D4semidirect
182. C22×C4×D3C3⋊D3semidirect
218. C22×C3×D3D12semidirect
265. C3×C4×D3#67semidirect
278. C32×D3#121semidirect
292. C22×C3×C4D32semidirect
293. C22×C3×C4C2×C3⋊D3semidirect
304. C22×Dic3C2×C3⋊D3semidirect
318. C2×C4×D3C2×C3⋊D3semidirect
319. C2×C4×D3C2×C3⋊D3semidirect
351. C22×C32C2×D12semidirect
352. C22×C32D3×D4semidirect
375. C2×C3×D3C2×D12semidirect
385. C32×C4D3×D4semidirect
386. C32×C4C2×#67semidirect
393. C3×Dic3C2×#67semidirect
405. C33C2×#121semidirect
427. C22×D3C4⋊(C3⋊D3)semidirect
475. C4×D3#638semidirect
496. C3×D3#930semidirect
515. C22×C4D3×C3⋊D3semidirect
541. C22×C3D3×D12semidirect
542. C22×C3C2×C4⋊(C3⋊D3)semidirect
563. C2×D3C2×C4⋊(C3⋊D3)semidirect
573. C3×C4D3×#67semidirect
574. C3×C4C2×#638semidirect
580. Dic3C2×#638semidirect
582. C32D3×#121semidirect
583. C32C2×#930semidirect
635. D3#64139direct (N × H)
652. C22D3×C4⋊(C3⋊D3)semidirect
659. C4D3×#638semidirect
661. C3D3×#930semidirect
662. C3C2×#64139semidirect

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×D3×#6382
C2×D3×C4⋊(C3⋊D3)2
#117239712
C3×#641392
#117236322
D3×#37522
#117235162
#117235152
#117235142
D3×C4⋊(C3⋊Dic3)2
C2×#641393
D3×#9303