Finite Group Databasebeta

← #67×C4⋊(C3⋊D3) #13177304

Subgroups — #67×C4⋊(C3⋊D3) #13177304

Order 1728.

2944 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C212yesmaximal, complemented
3C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#11723971C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6#11723636C212yesmaximal, complemented
7#11723541C212yesmaximal, complemented
8#11723517C211yesmaximal, characteristic, complemented
9#11723515C211yesmaximal, characteristic, complemented
10#11723482C212yesmaximal, complemented
11Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
12D4×C4⋊(C3⋊D3)—31nomaximal
13D12×#67—34nomaximal
14C23×C3×C3⋊D3C2212yescomplemented
15C22×D3×C3⋊D3C2212yescomplemented
16C22×C33×C4C2211yescharacteristic, complemented
17C2×#6312C2212yescomplemented
18C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
19C2×C3×C4⋊(C3⋊D3)—24no—
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C3⋊D3×#67—28no—
26C2×#6292C2212yescomplemented
27C2×#6292C2212yescomplemented
28C2×#6292C2212yescomplemented
29C2×#6290C2212yescomplemented
30C2×Dic3×C3⋊D3C2212yescomplemented
31D3×C4⋊(C3⋊D3)—24no—
32#88859C2212yescomplemented
33C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
34C32×#217C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C32×Dic3⋊C4C2211yescharacteristic, complemented
37C32×C4×Dic3C2211yescharacteristic, complemented
38#88803C2212yescomplemented
39#88803C2212yescomplemented
40C2×D4×C3⋊D3—32no—
41C22×C4⋊(C3⋊D3)—31no—
42C22×C4⋊(C3⋊D3)D311yescharacteristic, complemented
43C22×C3×D12—34no—
44C2×D3×#67—38no—
45C2×D3×D12—34no—
46C32×C4×D4—31no—
47#64139—31no—
48#64139—31no—
49#64139—34no—
50#64139—64no—
51#64104—32no—
52#64091—32no—
53#64091—32no—
54#64083—31no—
55C4×C4⋊(C3⋊D3)—31no—
56C3×C4×#67D314yescomplemented
57#63977—38no—
58#63922—38no—
59#63911—34no—
60#63908—34no—
61Dic3×D12—34no—
62#63886—38no—
63C23×C33C2311yescharacteristic
64C22×C3⋊(C3⋊D3)C2312yes—
65C22×C3×C3⋊D3—24no—
66C22×C3×C3⋊D3—24no—
67C22×C3×C3⋊D3—42no—
68C22×C3×C3⋊D3C2312yes—
69C22×C3×C3⋊D3C2312yes—
70C22×C32×D3C2311yescharacteristic
71C2×D3×C3⋊D3—24no—
72C2×D3×C3⋊D3—24no—
73C2×D3×C3⋊D3—42no—
74C2×C33×C4—22no—
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77#6312—24no—
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C4⋊(C3⋊(C3⋊D3))—22no—
80C3×C4⋊(C3⋊D3)—24no—
81C3×C4⋊(C3⋊D3)—22no—
82C3×C4⋊(C3⋊D3)D414yescomplemented
83C32×#67D414yescomplemented
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6292—24no—
89#6292—24no—
90#6292—42no—
91#6290—24no—
92Dic3×C3⋊D3—24no—
93D4×#67—91no—
94D4×D12—94no—
95C23×C3⋊D3—32no—
96C23×C3⋊D3C2×D312yescomplemented
97C23×C3×D3—38no—
98C22×D32—38no—
99C2×C32×D4—31no—
100C22×C32×C4—24no—
101C22×C32×C4—31no—
102C22×C32×C4C2×D314yescomplemented
103C22×C32×C4C2×D311yescharacteristic, complemented
104C2×#638—32no—
105C2×#638—38no—
106C2×#638—32no—
107C2×#638—68no—
108D4×C3⋊D3—68no—
109C2×C4⋊(C3⋊D3)—24no—
110C2×C4⋊(C3⋊D3)—32no—
111C2×C4⋊(C3⋊D3)—32no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4⋊(C3⋊D3)—34no—
114C2×C4⋊(C3⋊D3)—32no—
115C2×C4⋊(C3⋊D3)—64no—
116C2×C4⋊(C3⋊D3)—64no—
117C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
118C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
119C2×C4⋊(C3⋊D3)C2×D312yescomplemented
120C2×C4×C3⋊D3—32no—
121C2×C3×#67C2×D314yes—
122C2×C3×D12—34no—
123C2×C3×D12—38no—
124C2×C3×D12—34no—
125C2×C3×D12—616no—
126C2×C3×C4×D3C2×D314yescomplemented
127D3×#67—632no—
128C2×#626—38no—
129C2×#626—38no—
130C2×#626—38no—
131C2×#625—38no—
132C2×D3×Dic3—38no—
133D3×D12—616no—
134C32×C4⋊C4—31no—
135C32×C22⋊C4—31no—
136C32×C22⋊C4—31no—
137C32×C42—31no—
138#3752—32no—
139#3752—32no—
140#3752—32no—
141#3752—38no—
142#3752—68no—
143C4⋊(C3⋊Dic3)—31no—
144C4⋊(C3⋊Dic3)—34no—
145C4⋊(C3⋊Dic3)—64no—
146C3×#217C2×D314yescomplemented
147C3×(C2×D3)⋊C4C2×D314yescomplemented
148C3×Dic3⋊C4C2×D314yescomplemented
149C3×C4×Dic3C2×D314yescomplemented
150(C2×D3)⋊Dic3—38no—
151(C2×D3)⋊Dic3—38no—
152C22×C33—21no—
153C22×C33—21no—
154C22×C33C2×D412yescomplemented
155C22×C33C2411yescharacteristic
156C2×C3⋊(C3⋊D3)—22no—
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×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—48no—
165C2×C3×C3⋊D3C2×D414yescomplemented
166C2×C32×D3—21no—
167C2×C32×D3—21no—
168C2×C32×D3C2×D412yescomplemented
169D3×C3⋊D3—48no—
170C33×C4—21no—
171C33×C4C2×D412yescomplemented
172C3⋊(C3⋊Dic3)—22no—
173C32×Dic3—21no—
174C32×Dic3—21no—
175C32×Dic3C2×D412yescomplemented
176C22×C3×D4—91no—
177C22×#67—92no—
178C2×D3×D4—98no—
179C2×D3×D4—91no—
180C22×D12—34no—
181C22×D12—94no—
182C3×C4×D4—34no—
183#953—92no—
184#940—91no—
185#939—92no—
186#938—91no—
187#937—92no—
188D4×Dic3—91no—
189#930—94no—
190#930—94no—
191#930—91no—
192#930—184no—
193C4×#67C3⋊D311yescharacteristic, complemented
194#895—98no—
195#882—98no—
196#882—98no—
197#874—94no—
198C4×D12—94no—
199C23×C32—24no—
200C23×C32—31no—
201C23×C32C22×D314yes—
202C23×C32C22×D311yescharacteristic
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—32no—
206C22×C3⋊D3—38no—
207C22×C3⋊D3—42no—
208C22×C3⋊D3—68no—
209C22×C3⋊D3—64no—
210C22×C3⋊D3—64no—
211C22×C3⋊D3—122no—
212C22×C3⋊D3C22×D312yes—
213C22×C3⋊D3C22×D312yes—
214C22×C3×D3—38no—
215C22×C3×D3—38no—
216C22×C3×D3—616no—
217C22×C3×D3—616no—
218C22×C3×D3—128no—
219C22×C3×D3C22×D314yes—
220C2×D32—616no—
221C2×D32—616no—
222C2×D32—128no—
223C32×D4—34no—
224C2×C32×C4—22no—
225C2×C32×C4—24no—
226C2×C32×C4—24no—
227C2×C32×C4—28no—
228C2×C32×C4—31no—
229C2×C32×C4—31no—
230C2×C32×C4—31no—
231C2×C32×C4—48no—
232C2×C32×C4—62no—
233C2×C32×C4C22×D314yes—
234C2×C32×C4C22×D314yes—
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D311yescharacteristic
237#638—64no—
238#638—64no—
239#638—616no—
240#638—1216no—
241C2×C3⋊Dic3—32no—
242C2×C3⋊Dic3—38no—
243C2×C3⋊Dic3—68no—
244C4⋊(C3⋊D3)—24no—
245C4⋊(C3⋊D3)—22no—
246C4⋊(C3⋊D3)—64no—
247C4⋊(C3⋊D3)—64no—
248C4⋊(C3⋊D3)—62no—
249C4⋊(C3⋊D3)—68no—
250C4⋊(C3⋊D3)—128no—
251C4⋊(C3⋊D3)—122no—
252C4⋊(C3⋊D3)#6714yesdirect product factor
253C4×C3⋊D3—64no—
254C3×#67D12116yescomplemented
255C2×C3×Dic3C22×D314yes—
256C2×C3×Dic3C22×D314yes—
257C2×C3×Dic3C22×D314yes—
258C3×D12—316no—
259C3×D12—616no—
260C3×D12—68no—
261C3×C4×D3—28no—
262#626—616no—
263#626—616no—
264#626—128no—
265#625—616no—
266D3×Dic3—616no—
267D42—271noSylow
268C2×C33—22no—
269C2×C33C22×D411yescharacteristic
270C2×C33C22×D411yescharacteristic
271C2×C33H(5,𝔽2)11yescharacteristic
272C3⋊(C3⋊D3)—42no—
273C3×C3⋊D3—24no—
274C3×C3⋊D3—42no—
275C32×D3—22no—
276C24×C3—92no—
277C23×D3—38no—
278C23×D3—98no—
279C23×D3—92no—
280C2×C3×D4—34no—
281C2×C3×D4—91no—
282C2×C3×D4—92no—
283C2×C3×D4—91no—
284C2×C3×D4—184no—
285C22×C3×C4—24no—
286C22×C3×C4—34no—
287C22×C3×C4D3214yescomplemented
288C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
289C2×#67—98no—
290C2×#67—98no—
291C2×#67—92no—
292C2×#67—92no—
293C2×#67—92no—
294C2×#67—92no—
295C2×#67—92no—
296C2×#67—188no—
297C2×#67—188no—
298C2×#67C2×C3⋊D311yescharacteristic
299C22×Dic3—92no—
300D3×D4—184no—
301D3×D4—1832no—
302C2×D12—34no—
303C2×D12—34no—
304C2×D12—38no—
305C2×D12—616no—
306C2×D12—98no—
307C2×D12—98no—
308C2×D12—94no—
309C2×D12—91no—
310C2×D12—98no—
311C2×D12—184no—
312C2×D12—1816no—
313C2×C4×D3—98no—
314C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
315C3×C4⋊C4—34no—
316C3×C22⋊C4—34no—
317C3×C22⋊C4—34no—
318C3×C42—34no—
319#217—92no—
320#217—92no—
321#217C2×C3⋊D311yescharacteristic, complemented
322(C2×D3)⋊C4—98no—
323(C2×D3)⋊C4—98no—
324(C2×D3)⋊C4—98no—
325(C2×D3)⋊C4—92no—
326(C2×D3)⋊C4—188no—
327(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
328C4⋊Dic3—94no—
329C4⋊Dic3—91no—
330C4⋊Dic3—184no—
331Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
332C4×Dic3C2×C3⋊D311yescharacteristic, complemented
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—24no—
336C22×C32—28no—
337C22×C32—24no—
338C22×C32—24no—
339C22×C32—32no—
340C22×C32—44no—
341C22×C32—44no—
342C22×C32—61no—
343C22×C32—61no—
344C22×C32C2×D1218yescomplemented
345C22×C32D3×D412yescomplemented
346C22×C32C23×D314yes—
347C22×C32C23×D311yescharacteristic
348C2×C3⋊D3—22no—
349C2×C3⋊D3—22no—
350C2×C3⋊D3—22no—
351C2×C3⋊D3—22no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—48no—
354C2×C3⋊D3—62no—
355C2×C3⋊D3—62no—
356C2×C3⋊D3—62no—
357C2×C3⋊D3—68no—
358C2×C3⋊D3—68no—
359C2×C3⋊D3—68no—
360C2×C3⋊D3—128no—
361C2×C3⋊D3—128no—
362C2×C3⋊D3—128no—
363C2×C3⋊D3—128no—
364C2×C3⋊D3C2×#6714yescomplemented
365C2×C3×D3—24no—
366C2×C3×D3—24no—
367C2×C3×D3—316no—
368C2×C3×D3—68no—
369C2×C3×D3—68no—
370C2×C3×D3—68no—
371C2×C3×D3—68no—
372C2×C3×D3—68no—
373C2×C3×D3—1232no—
374C2×C3×D3C2×D1218yescomplemented
375D32—1232no—
376C32×C4—21no—
377C32×C4—28no—
378C32×C4—24no—
379C32×C4—32no—
380C32×C4—44no—
381C32×C4—61no—
382C32×C4—61no—
383C32×C4D3×D418yescomplemented
384C32×C4C2×#6712yescomplemented
385C3⋊Dic3—62no—
386C3⋊Dic3—68no—
387C3⋊Dic3—128no—
388C3×Dic3—24no—
389C3×Dic3—24no—
390C3×Dic3C2×D1218yescomplemented
391C22×D4—91no—
392C22×D4—271no—
393C22×D4—272no—
394#127—271no—
395#121—272no—
396#121—271no—
397#121—271no—
398#120—272no—
399#120—272no—
400C4×D4—31no—
401C4×D4—271no—
402C33D4211yescharacteristic, complemented, Sylow
403C23×C3—24no—
404C23×C3—34no—
405C23×C3—92no—
406C23×C3—92no—
407C23×C3—184no—
408C23×C3—184no—
409C23×C3—362no—
410C23×C3C2×D3214yes—
411C23×C3C22×C3⋊D311yescharacteristic
412C22×D3—38no—
413C22×D3—38no—
414C22×D3—616no—
415C22×D3—616no—
416C22×D3—98no—
417C22×D3—92no—
418C22×D3—128no—
419C22×D3—188no—
420C22×D3—184no—
421C22×D3—1816no—
422C22×D3—1816no—
423C22×D3—184no—
424C22×D3—362no—
425C22×D3—368no—
426C22×D3C22×C3⋊D311yescharacteristic
427C3×D4—316no—
428C3×D4—94no—
429C3×D4—184no—
430C3×D4—182no—
431C2×C3×C4—28no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—34no—
436C2×C3×C4—34no—
437C2×C3×C4—34no—
438C2×C3×C4—48no—
439C2×C3×C4—68no—
440C2×C3×C4C2×D3214yes—
441C2×C3×C4C2×D3214yes—
442C2×C3×C4C22×C3⋊D311yescharacteristic
443C2×C3×C4C22×C3⋊D311yescharacteristic
444#67—184no—
445#67—1816no—
446#67—1816no—
447#67—184no—
448#67—184no—
449#67—184no—
450#67—3616no—
451#67—362no—
452#67C4⋊(C3⋊D3)14yesdirect product factor
453C2×Dic3—98no—
454C2×Dic3—92no—
455C2×Dic3—188no—
456C2×Dic3—184no—
457C2×Dic3C22×C3⋊D311yescharacteristic
458C2×Dic3C22×C3⋊D311yescharacteristic
459C2×Dic3C22×C3⋊D311yescharacteristic
460D12—316no—
461D12—616no—
462D12—68no—
463D12—1816no—
464D12—1816no—
465D12—188no—
466D12—182no—
467D12—368no—
468D12—368no—
469C4×D3—22no—
470C4×D3—1816no—
471C2×C32—22no—
472C2×C32—24no—
473C2×C32—24no—
474C2×C32—24no—
475C2×C32—28no—
476C2×C32—48no—
477C2×C32—62no—
478C2×C32C22×D1214yes—
479C2×C32C2×D3×D414yes—
480C2×C32C2×D3×D411yescharacteristic
481C2×C32#100411yescharacteristic
482C2×C32#100914yes—
483C2×C32C22×#6711yescharacteristic
484C3⋊D3—24no—
485C3⋊D3—42no—
486C3⋊D3—122no—
487C3⋊D3—128no—
488C3⋊D3—248no—
489C3×D3—28no—
490C3×D3—616no—
491C3×D3—128no—
492C24—92no—
493C24—272no—
494C2×D4—31no—
495C2×D4—91no—
496C2×D4—92no—
497C2×D4—91no—
498C2×D4—184no—
499C2×D4—272no—
500C2×D4—272no—
501C2×D4—272no—
502C2×D4—272no—
503C2×D4—272no—
504C2×D4—271no—
505C2×D4—544no—
506C2×D4—548no—
507C22×C4—31no—
508C22×C4—272no—
509C22×C4D3×C3⋊D311yescharacteristic, complemented
510C4⋊C4—31no—
511C4⋊C4—271no—
512C22⋊C4—31no—
513C22⋊C4—31no—
514C22⋊C4—272no—
515C22⋊C4—272no—
516C22⋊C4—272no—
517C42—31no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—24no—
523C22×C3—28no—
524C22×C3—38no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—64no—
528C22×C3—64no—
529C22×C3—94no—
530C22×C3—182no—
531C22×C3—182no—
532C22×C3—182no—
533C22×C3—182no—
534C22×C3—182no—
535C22×C3—368no—
536C22×C3D3×D1218yescomplemented
537C22×C3C2×C4⋊(C3⋊D3)12yescomplemented
538C22×C3C22×D3214yes—
539C22×C3C23×C3⋊D311yescharacteristic
540C2×D3—21no—
541C2×D3—21no—
542C2×D3—316no—
543C2×D3—68no—
544C2×D3—68no—
545C2×D3—68no—
546C2×D3—68no—
547C2×D3—68no—
548C2×D3—1232no—
549C2×D3—188no—
550C2×D3—188no—
551C2×D3—188no—
552C2×D3—182no—
553C2×D3—182no—
554C2×D3—182no—
555C2×D3—368no—
556C2×D3—368no—
557C2×D3—368no—
558C2×D3—368no—
559C2×D3—3632no—
560C2×D3C2×C4⋊(C3⋊D3)12yescomplemented
561C3×C4—24no—
562C3×C4—21no—
563C3×C4—28no—
564C3×C4—38no—
565C3×C4—44no—
566C3×C4—64no—
567C3×C4—64no—
568C3×C4D3×#6718yescomplemented
569C3×C4D4×C3⋊D312yescomplemented
570Dic3—21no—
571Dic3—21no—
572Dic3—188no—
573Dic3—182no—
574Dic3—368no—
575Dic3C2×C4⋊(C3⋊D3)12yescomplemented
576C32—24no—
577C32D4×D1214yescomplemented
578C32D4×#6711yescharacteristic, complemented
579C23—31no—
580C23—92no—
581C23—92no—
582C23—184no—
583C23—184no—
584C23—272no—
585C23—362no—
586C23—544no—
587C23—544no—
588C23—1082no—
589C23C2×D3×C3⋊D311yescharacteristic
590D4—34no—
591D4—94no—
592D4—184no—
593D4—182no—
594D4—544no—
595D4—544no—
596D4—544no—
597D4—544no—
598D4—542no—
599D4—1082no—
600C2×C4—22no—
601C2×C4—31no—
602C2×C4—31no—
603C2×C4—31no—
604C2×C4—62no—
605C2×C4—272no—
606C2×C4—544no—
607C2×C4C2×D3×C3⋊D311yescharacteristic
608C2×C4C2×D3×C3⋊D311yescharacteristic
609C2×C3—22no—
610C2×C3—28no—
611C2×C3—24no—
612C2×C3—24no—
613C2×C3—24no—
614C2×C3—48no—
615C2×C3—68no—
616C2×C3—184no—
617C2×C3—362no—
618C2×C3C2×D3×D1214yes—
619C2×C3#6430714yes—
620C2×C3C2×D3×#6714yes—
621C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
622C2×C3C2×D4×C3⋊D311yescharacteristic
623C2×C3#6436611yescharacteristic
624D3—22no—
625D3—616no—
626D3—128no—
627D3—362no—
628D3—368no—
629D3—728no—
630C22—21no—
631C22—21no—
632C22—32no—
633C22—61no—
634C22—61no—
635C22—94no—
636C22—182no—
637C22—182no—
638C22—182no—
639C22—182no—
640C22—182no—
641C22—368no—
642C22—542no—
643C22—542no—
644C22—542no—
645C22—1088no—
646C22D3×C4⋊(C3⋊D3)12yescomplemented
647C22C22×D3×C3⋊D311yescharacteristic
648C4—21no—
649C4—32no—
650C4—61no—
651C4—61no—
652C4—542no—
653C4C3⋊D3×#6712yescomplemented
654C3—24no—
655C3D12×#6714yescomplemented
656C3D4×C4⋊(C3⋊D3)11yescharacteristic, complemented
657C2—22no—
658C2—62no—
659C2—184no—
660C2—362no—
661C2—1082no—
662C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
663C2#1172458011yescharacteristic
664C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊(C3⋊D3)C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. C2×D3×C4⋊(C3⋊D3)C2semidirect
4. #11723971C2semidirect
5. C32×C4×#67C2semidirect
6. #11723636C2semidirect
7. #11723541C2semidirect
8. #11723517C2semidirect
9. #11723515C2semidirect
10. #11723482C2semidirect
11. Dic3×C4⋊(C3⋊D3)C2semidirect
14. C23×C3×C3⋊D3C22semidirect
15. C22×D3×C3⋊D3C22semidirect
16. C22×C33×C4C22semidirect
17. C2×#6312C22semidirect
18. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
21. C2×C3×C4⋊(C3⋊D3)C22semidirect
22. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C2×C32×C4×D3C22semidirect
26. C2×#6292C22semidirect
27. C2×#6292C22semidirect
28. C2×#6292C22semidirect
29. C2×#6290C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
32. #88859C22semidirect
33. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
34. C32×#217C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C32×Dic3⋊C4C22semidirect
37. C32×C4×Dic3C22semidirect
38. #88803C22semidirect
39. #88803C22semidirect
42. C22×C4⋊(C3⋊D3)D3semidirect
56. C3×C4×#67D3semidirect
82. C3×C4⋊(C3⋊D3)D4semidirect
83. C32×#67D4semidirect
96. C23×C3⋊D3C2×D3semidirect
102. C22×C32×C4C2×D3semidirect
103. C22×C32×C4C2×D3semidirect
118. C2×C4⋊(C3⋊D3)C2×D3semidirect
119. C2×C4⋊(C3⋊D3)C2×D3semidirect
126. C2×C3×C4×D3C2×D3semidirect
146. C3×#217C2×D3semidirect
147. C3×(C2×D3)⋊C4C2×D3semidirect
148. C3×Dic3⋊C4C2×D3semidirect
149. C3×C4×Dic3C2×D3semidirect
154. C22×C33C2×D4semidirect
165. C2×C3×C3⋊D3C2×D4semidirect
168. C2×C32×D3C2×D4semidirect
171. C33×C4C2×D4semidirect
175. C32×Dic3C2×D4semidirect
193. C4×#67C3⋊D3semidirect
252. C4⋊(C3⋊D3)#67direct (N × H)
254. C3×#67D12semidirect
287. C22×C3×C4D32semidirect
288. C22×C3×C4C2×C3⋊D3semidirect
314. C2×C4×D3C2×C3⋊D3semidirect
321. #217C2×C3⋊D3semidirect
327. (C2×D3)⋊C4C2×C3⋊D3semidirect
331. Dic3⋊C4C2×C3⋊D3semidirect
332. C4×Dic3C2×C3⋊D3semidirect
344. C22×C32C2×D12semidirect
345. C22×C32D3×D4semidirect
364. C2×C3⋊D3C2×#67semidirect
374. C2×C3×D3C2×D12semidirect
383. C32×C4D3×D4semidirect
384. C32×C4C2×#67semidirect
390. C3×Dic3C2×D12semidirect
402. C33D42semidirect
452. #67C4⋊(C3⋊D3)direct (N × H)
509. C22×C4D3×C3⋊D3semidirect
536. C22×C3D3×D12semidirect
537. C22×C3C2×C4⋊(C3⋊D3)semidirect
560. C2×D3C2×C4⋊(C3⋊D3)semidirect
568. C3×C4D3×#67semidirect
569. C3×C4D4×C3⋊D3semidirect
575. Dic3C2×C4⋊(C3⋊D3)semidirect
577. C32D4×D12semidirect
578. C32D4×#67semidirect
646. C22D3×C4⋊(C3⋊D3)semidirect
653. C4C3⋊D3×#67semidirect
655. C3D12×#67semidirect
656. C3D4×C4⋊(C3⋊D3)semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊(C3⋊D3)2
C2×C3⋊D3×#672
C2×D3×C4⋊(C3⋊D3)2
#117239712
C32×C4×#672
#117236362
#117235412
#117235172
#117235152
#117234822
Dic3×C4⋊(C3⋊D3)2
D4×C4⋊(C3⋊D3)3
D12×#673