Finite Group Databasebeta

← D4×#6292 #13177514

Subgroups — D4×#6292 #13177514

Order 1728.

3512 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C22×#6292C212yesmaximal, complemented
4C32×D4×Dic3C211yesmaximal, characteristic, complemented
5#11723639C212yesmaximal, complemented
6#11723636C212yesmaximal, complemented
7#11723632C212yesmaximal, complemented
8#11723532C211yesmaximal, characteristic, complemented
9#11723526C211yesmaximal, characteristic, complemented
10#11723517C211yesmaximal, characteristic, complemented
11C4×#6292C211yesmaximal, characteristic, complemented
12D4×C4⋊(C3⋊D3)—31nomaximal
13D4×#626—34nomaximal
14C23×C3⋊(C3⋊D3)C2212yescomplemented
15C23×C3×C3⋊D3C2212yescomplemented
16C2×C33×D4C2211yescharacteristic
17C2×#6312C2212yescomplemented
18D4×C3⋊(C3⋊D3)—24no—
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×#638C2212yescomplemented
22C3×D4×C3⋊D3—24no—
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C32×Dic3C2212yescomplemented
26C2×#6292—28no—
27C2×#6292C2211yescharacteristic
28C2×#6292C2212yescomplemented
29C2×#6292C2212yescomplemented
30C2×#6292C2212yescomplemented
31C2×#6292C2212yescomplemented
32C32×#217C2212yescomplemented
33C32×C4⋊Dic3C2211yescharacteristic, complemented
34C32×C4×Dic3C2211yescharacteristic, complemented
35Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36#88804C2212yescomplemented
37#88804C2211yescharacteristic, complemented
38#88803C2212yescomplemented
39#88803C2211yescharacteristic, complemented
40C2×D4×C3⋊D3—31no—
41C2×D4×C3⋊D3—34no—
42C2×D4×C3⋊D3—64no—
43C2×D4×C3⋊D3D311yescharacteristic, complemented
44C22×C4⋊(C3⋊D3)—32no—
45C2×C3×D3×D4—34no—
46C22×#626—38no—
47C32×C4×D4—31no—
48#64139—32no—
49#64104—31no—
50#64104—31no—
51#64091—32no—
52#64091—32no—
53#64083—31no—
54C4×C4⋊(C3⋊D3)—31no—
55C3×D4×Dic3D314yescomplemented
56#63981—38no—
57#63978—38no—
58#63977—38no—
59#63916—34no—
60#63911—34no—
61#63909—34no—
62C4×#626—34no—
63C23×C33C2312yes—
64C22×C3⋊(C3⋊D3)—24no—
65C22×C3⋊(C3⋊D3)—24no—
66C22×C3⋊(C3⋊D3)—42no—
67C22×C3⋊(C3⋊D3)C2312yes—
68C22×C3⋊(C3⋊D3)C2311yescharacteristic
69C22×C3×C3⋊D3—24no—
70C22×C3×C3⋊D3—24no—
71C22×C3×C3⋊D3—42no—
72C22×C3×C3⋊D3C2312yes—
73C22×C3×C3⋊D3C2311yescharacteristic
74C33×D4D414yescomplemented
75C2×C33×C4C2311yescharacteristic
76#6312—24no—
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊(C3⋊D3))—22no—
79C4×C3⋊(C3⋊D3)—22no—
80C3×#638—24no—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4⋊(C3⋊D3)—22no—
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3—24no—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88#6292—24no—
89#6292—24no—
90#6292—24no—
91#6292—42no—
92#6292D414yesdirect product factor
93D4×#67—91no—
94D4×D12—94no—
95C23×C3⋊D3—32no—
96C23×C3⋊D3—38no—
97C23×C3⋊D3—68no—
98C23×C3⋊D3C2×D312yescomplemented
99C23×C3×D3—38no—
100C2×C32×D4—24no—
101C2×C32×D4C2×D314yes—
102C2×C32×D4C2×D311yescharacteristic
103C22×C32×C4—32no—
104C2×#638—32no—
105C2×#638—38no—
106C2×#638—68no—
107C2×#638C2×D312yescomplemented
108D4×C3⋊D3—24no—
109D4×C3⋊D3—632no—
110D4×C3⋊D3—616no—
111D4×C3⋊D3—64no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4⋊(C3⋊D3)—32no—
114C2×C4⋊(C3⋊D3)—32no—
115C2×C4⋊(C3⋊D3)—32no—
116C2×C4⋊(C3⋊D3)—31no—
117C2×C4⋊(C3⋊D3)—34no—
118C2×C4⋊(C3⋊D3)—32no—
119C2×C4⋊(C3⋊D3)—68no—
120C2×C4⋊(C3⋊D3)—64no—
121C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—34no—
124C2×C4×C3⋊D3—64no—
125C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
126C2×C3×#67—38no—
127C22×C3×Dic3C2×D318yescomplemented
128C3×D3×D4—616no—
129C2×C3×D12—34no—
130C2×C3×C4×D3—34no—
131C2×#626—34no—
132C2×#626—38no—
133C2×#626—38no—
134C2×#626—38no—
135C2×#626—38no—
136C2×#626—632no—
137C32×C4⋊C4—31no—
138C32×C22⋊C4—32no—
139C32×C42—31no—
140#3752—31no—
141#3752—32no—
142#3752—31no—
143#3752—32no—
144C4⋊(C3⋊Dic3)—31no—
145C3×#217C2×D318yescomplemented
146C3×C4⋊Dic3C2×D314yescomplemented
147C3×C4×Dic3C2×D314yescomplemented
148Dic3⋊Dic3—34no—
149#3722—34no—
150#3722—38no—
151(C2×D3)⋊Dic3—34no—
152(C2×D3)⋊Dic3—38no—
153C22×C33—22no—
154C22×C33—22no—
155C22×C33C2×D414yescomplemented
156C22×C33C2411yescharacteristic
157C2×C3⋊(C3⋊D3)—21no—
158C2×C3⋊(C3⋊D3)—21no—
159C2×C3⋊(C3⋊D3)—22no—
160C2×C3⋊(C3⋊D3)—22no—
161C2×C3⋊(C3⋊D3)—22no—
162C2×C3⋊(C3⋊D3)—48no—
163C2×C3⋊(C3⋊D3)C2×D412yescomplemented
164C2×C3×C3⋊D3—21no—
165C2×C3×C3⋊D3—21no—
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3—22no—
169C2×C3×C3⋊D3—48no—
170C2×C3×C3⋊D3C2×D412yescomplemented
171C33×C4C2×D412yescomplemented
172C3⋊(C3⋊Dic3)—21no—
173C3×C3⋊Dic3—21no—
174C32×Dic3—22no—
175C32×Dic3—21no—
176C32×Dic3C2×D412yescomplemented
177C22×C3×D4—91no—
178C22×#67—92no—
179C2×D3×D4—34no—
180C2×D3×D4—94no—
181C2×D3×D4—91no—
182C2×D3×D4—184no—
183C22×D12—98no—
184C3×C4×D4—34no—
185#953—92no—
186#940—91no—
187#939—92no—
188#938—91no—
189#937—92no—
190D4×Dic3C3⋊D311yescharacteristic, complemented
191#930—98no—
192#930—91no—
193C4×#67—91no—
194#895—94no—
195#895—94no—
196#882—98no—
197#882—98no—
198#874—94no—
199C4×D12—94no—
200C23×C32—28no—
201C23×C32C22×D318yes—
202C23×C32C22×D312yes—
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—31no—
206C22×C3⋊D3—32no—
207C22×C3⋊D3—34no—
208C22×C3⋊D3—38no—
209C22×C3⋊D3—42no—
210C22×C3⋊D3—64no—
211C22×C3⋊D3—68no—
212C22×C3⋊D3—64no—
213C22×C3⋊D3—632no—
214C22×C3⋊D3—616no—
215C22×C3⋊D3—64no—
216C22×C3⋊D3—616no—
217C22×C3⋊D3—1216no—
218C22×C3⋊D3—122no—
219C22×C3⋊D3—128no—
220C22×C3⋊D3—1216no—
221C22×C3⋊D3C22×D312yes—
222C22×C3⋊D3C22×D311yescharacteristic
223C22×C3×D3—34no—
224C22×C3×D3—38no—
225C22×C3×D3—616no—
226C22×C3×D3—616no—
227C22×C3×D3—128no—
228C32×D4—216no—
229C32×D4D12116yescomplemented
230C32×D4#6714yescomplemented
231C2×C32×C4—24no—
232C2×C32×C4—31no—
233C2×C32×C4—31no—
234C2×C32×C4—32no—
235C2×C32×C4—64no—
236C2×C32×C4C22×D314yes—
237C2×C32×C4C22×D311yescharacteristic
238#638—24no—
239#638—632no—
240#638—616no—
241#638—64no—
242C2×C3⋊Dic3—31no—
243C2×C3⋊Dic3—34no—
244C2×C3⋊Dic3—64no—
245C2×C3⋊Dic3C22×D311yescharacteristic
246C4⋊(C3⋊D3)—22no—
247C4⋊(C3⋊D3)—34no—
248C4⋊(C3⋊D3)—616no—
249C4⋊(C3⋊D3)—64no—
250C4⋊(C3⋊D3)—64no—
251C4⋊(C3⋊D3)—64no—
252C4⋊(C3⋊D3)—68no—
253C4⋊(C3⋊D3)—62no—
254C4⋊(C3⋊D3)—122no—
255C4×C3⋊D3—22no—
256C4×C3⋊D3—616no—
257C4×C3⋊D3—68no—
258C4×C3⋊D3—62no—
259C3×#67—616no—
260C2×C3×Dic3—216no—
261C2×C3×Dic3—34no—
262C2×C3×Dic3C22×D314yes—
263C2×C3×Dic3C22×D318yes—
264C2×C3×Dic3C22×D314yes—
265C3×D12—68no—
266C3×C4×D3—68no—
267#626—316no—
268#626—616no—
269#626—616no—
270#626—616no—
271#626—128no—
272D42—271noSylow
273C2×C33—24no—
274C2×C33C22×D411yescharacteristic
275C2×C33C22×D411yescharacteristic
276C2×C33H(5,𝔽2)11yescharacteristic
277C3⋊(C3⋊D3)—22no—
278C3⋊(C3⋊D3)—42no—
279C3×C3⋊D3—22no—
280C3×C3⋊D3—42no—
281C24×C3—92no—
282C23×D3—38no—
283C23×D3—98no—
284C23×D3—92no—
285C23×D3—188no—
286C2×C3×D4—24no—
287C2×C3×D4—92no—
288C2×C3×D4—91no—
289C2×C3×D4—184no—
290C2×C3×D4D3214yes—
291C2×C3×D4C2×C3⋊D311yescharacteristic
292C22×C3×C4—38no—
293C22×C3×C4—91no—
294C2×#67—38no—
295C2×#67—98no—
296C2×#67—92no—
297C2×#67—91no—
298C2×#67—92no—
299C2×#67—92no—
300C2×#67—92no—
301C2×#67—92no—
302C2×#67—188no—
303C2×#67—188no—
304C22×Dic3C2×C3⋊D312yescomplemented
305D3×D4—616no—
306D3×D4—1832no—
307D3×D4—1816no—
308D3×D4—184no—
309C2×D12—34no—
310C2×D12—94no—
311C2×D12—98no—
312C2×D12—98no—
313C2×D12—98no—
314C2×D12—94no—
315C2×D12—91no—
316C2×D12—98no—
317C2×D12—184no—
318C2×D12—1832no—
319C2×C4×D3—34no—
320C2×C4×D3—94no—
321C2×C4×D3—91no—
322C2×C4×D3—184no—
323C3×C4⋊C4—34no—
324C3×C22⋊C4—38no—
325C3×C42—34no—
326#217—91no—
327#217—92no—
328#217C2×C3⋊D312yescomplemented
329(C2×D3)⋊C4—94no—
330(C2×D3)⋊C4—98no—
331(C2×D3)⋊C4—94no—
332(C2×D3)⋊C4—98no—
333(C2×D3)⋊C4—91no—
334(C2×D3)⋊C4—92no—
335C4⋊Dic3—94no—
336C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
337Dic3⋊C4—91no—
338C4×Dic3C2×C3⋊D311yescharacteristic, complemented
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—24no—
342C22×C32—216no—
343C22×C32—28no—
344C22×C32—28no—
345C22×C32—48no—
346C22×C32—48no—
347C22×C32C2×D12116yescomplemented
348C22×C32C2×#6714yescomplemented
349C22×C32C23×D314yes—
350C22×C32C23×D311yescharacteristic
351C2×C3⋊D3—21no—
352C2×C3⋊D3—21no—
353C2×C3⋊D3—22no—
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—32no—
357C2×C3⋊D3—38no—
358C2×C3⋊D3—48no—
359C2×C3⋊D3—68no—
360C2×C3⋊D3—68no—
361C2×C3⋊D3—68no—
362C2×C3⋊D3—64no—
363C2×C3⋊D3—61no—
364C2×C3⋊D3—64no—
365C2×C3⋊D3—61no—
366C2×C3⋊D3—616no—
367C2×C3⋊D3—68no—
368C2×C3⋊D3—62no—
369C2×C3⋊D3—62no—
370C2×C3⋊D3—62no—
371C2×C3⋊D3—68no—
372C2×C3⋊D3—68no—
373C2×C3⋊D3—128no—
374C2×C3⋊D3—128no—
375C2×C3⋊D3—128no—
376C2×C3⋊D3—1232no—
377C2×C3⋊D3—1264no—
378C2×C3⋊D3D3×D412yescomplemented
379C2×C3×D3—38no—
380C2×C3×D3—64no—
381C2×C3×D3—64no—
382C2×C3×D3—68no—
383C2×C3×D3—68no—
384C2×C3×D3—68no—
385C2×C3×D3—1232no—
386C32×C4—28no—
387C32×C4—32no—
388C32×C4—62no—
389C32×C4—61no—
390C32×C4C2×D1218yescomplemented
391C32×C4C2×#6712yescomplemented
392C3⋊Dic3—21no—
393C3⋊Dic3—68no—
394C3⋊Dic3—64no—
395C3⋊Dic3—61no—
396C3×Dic3—28no—
397C3×Dic3—24no—
398C3×Dic3—64no—
399C3×Dic3D3×D418yescomplemented
400C22×D4—91no—
401C22×D4—272no—
402C22×D4—271no—
403#127—271no—
404#121—271no—
405#121—271no—
406#121—272no—
407#120—272no—
408#120—272no—
409C4×D4—31no—
410C4×D4—271no—
411C33D4211yescharacteristic, complemented, Sylow
412C23×C3—28no—
413C23×C3—91no—
414C23×C3—92no—
415C23×C3—184no—
416C23×C3—184no—
417C23×C3—362no—
418C23×C3C2×D3218yes—
419C23×C3C22×C3⋊D312yes—
420C22×D3—34no—
421C22×D3—38no—
422C22×D3—616no—
423C22×D3—616no—
424C22×D3—94no—
425C22×D3—91no—
426C22×D3—98no—
427C22×D3—92no—
428C22×D3—128no—
429C22×D3—184no—
430C22×D3—188no—
431C22×D3—184no—
432C22×D3—1816no—
433C22×D3—1832no—
434C22×D3—1816no—
435C22×D3—184no—
436C22×D3—3616no—
437C22×D3—368no—
438C22×D3—362no—
439C22×D3—3616no—
440C3×D4—216no—
441C3×D4—184no—
442C3×D4—182no—
443C3×D4#626116yescomplemented
444C3×D4C4⋊(C3⋊D3)14yescomplemented
445C2×C3×C4—24no—
446C2×C3×C4—34no—
447C2×C3×C4—34no—
448C2×C3×C4—38no—
449C2×C3×C4—616no—
450C2×C3×C4—91no—
451C2×C3×C4—182no—
452C2×C3×C4C2×D3214yes—
453C2×C3×C4C22×C3⋊D311yescharacteristic
454#67—616no—
455#67—94no—
456#67—184no—
457#67—184no—
458#67—1832no—
459#67—1816no—
460#67—184no—
461#67—184no—
462#67—362no—
463C2×Dic3—24no—
464C2×Dic3—34no—
465C2×Dic3—94no—
466C2×Dic3—91no—
467C2×Dic3—184no—
468C2×Dic3C22×C3⋊D311yescharacteristic
469C2×Dic3C22×C3⋊D312yes—
470C2×Dic3C22×C3⋊D311yescharacteristic
471D12—68no—
472D12—916no—
473D12—1816no—
474D12—1816no—
475D12—1816no—
476D12—1816no—
477D12—188no—
478D12—182no—
479D12—368no—
480C4×D3—68no—
481C4×D3—1816no—
482C4×D3—188no—
483C4×D3—182no—
484C2×C32—24no—
485C2×C32—24no—
486C2×C32—24no—
487C2×C32—24no—
488C2×C32—216no—
489C2×C32—416no—
490C2×C32C22×D1214yes—
491C2×C32C2×D3×D414yes—
492C2×C32C2×D3×D411yescharacteristic
493C2×C32#100411yescharacteristic
494C2×C32#100914yes—
495C2×C32C22×#6711yescharacteristic
496C3⋊D3—22no—
497C3⋊D3—42no—
498C3⋊D3—616no—
499C3⋊D3—62no—
500C3⋊D3—68no—
501C3⋊D3—1216no—
502C3⋊D3—122no—
503C3⋊D3—128no—
504C3×D3—68no—
505C3×D3—128no—
506C24—92no—
507C24—272no—
508C2×D4—92no—
509C2×D4—91no—
510C2×D4—184no—
511C2×D4—271no—
512C2×D4—272no—
513C2×D4—272no—
514C2×D4—272no—
515C2×D4—272no—
516C2×D4—272no—
517C2×D4—271no—
518C2×D4—548no—
519C2×D4—544no—
520C2×D4D3×C3⋊D311yescharacteristic
521C22×C4—32no—
522C22×C4—91no—
523C22×C4—271no—
524C4⋊C4—31no—
525C4⋊C4—271no—
526C22⋊C4—32no—
527C22⋊C4—271no—
528C22⋊C4—272no—
529C22⋊C4—271no—
530C22⋊C4—272no—
531C42—31no—
532C22×C3—28no—
533C22×C3—28no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—24no—
537C22×C3—216no—
538C22×C3—48no—
539C22×C3—48no—
540C22×C3—92no—
541C22×C3—181no—
542C22×C3—181no—
543C22×C3—182no—
544C22×C3—182no—
545C22×C3—182no—
546C22×C3—368no—
547C22×C3C2×#626116yescomplemented
548C22×C3C2×C4⋊(C3⋊D3)14yescomplemented
549C22×C3C22×D3214yes—
550C22×C3C23×C3⋊D311yescharacteristic
551C2×D3—38no—
552C2×D3—64no—
553C2×D3—64no—
554C2×D3—68no—
555C2×D3—68no—
556C2×D3—68no—
557C2×D3—98no—
558C2×D3—92no—
559C2×D3—1232no—
560C2×D3—188no—
561C2×D3—188no—
562C2×D3—188no—
563C2×D3—184no—
564C2×D3—184no—
565C2×D3—181no—
566C2×D3—181no—
567C2×D3—1816no—
568C2×D3—188no—
569C2×D3—188no—
570C2×D3—188no—
571C2×D3—182no—
572C2×D3—182no—
573C2×D3—182no—
574C2×D3—368no—
575C2×D3—368no—
576C2×D3—3632no—
577C2×D3—368no—
578C2×D3—3664no—
579C3×C4—28no—
580C3×C4—38no—
581C3×C4—68no—
582C3×C4—64no—
583C3×C4—181no—
584C3×C4C2×#62618yescomplemented
585C3×C4C2×C4⋊(C3⋊D3)12yescomplemented
586Dic3—22no—
587Dic3—21no—
588Dic3—64no—
589Dic3—188no—
590Dic3—184no—
591Dic3—181no—
592Dic3D4×C3⋊D312yescomplemented
593C32—24no—
594C32D4×D1214yescomplemented
595C32D4×#6711yescharacteristic, complemented
596C23—91no—
597C23—92no—
598C23—184no—
599C23—184no—
600C23—271no—
601C23—272no—
602C23—362no—
603C23—544no—
604C23—544no—
605C23—1082no—
606C23C2×D3×C3⋊D312yes—
607D4—184no—
608D4—182no—
609D4—274no—
610D4—544no—
611D4—544no—
612D4—544no—
613D4—544no—
614D4—542no—
615D4—1082no—
616D4#629214yesdirect product factor
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—32no—
620C2×C4—64no—
621C2×C4—91no—
622C2×C4—182no—
623C2×C4—271no—
624C2×C4—542no—
625C2×C4C2×D3×C3⋊D311yescharacteristic
626C2×C3—216no—
627C2×C3—24no—
628C2×C3—24no—
629C2×C3—24no—
630C2×C3—24no—
631C2×C3—416no—
632C2×C3—182no—
633C2×C3—362no—
634C2×C3D32×D414yes—
635C2×C3#6431414yes—
636C2×C3C22×#62614yes—
637C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
638C2×C3C2×D4×C3⋊D311yescharacteristic
639C2×C3#6436611yescharacteristic
640D3—68no—
641D3—128no—
642D3—1816no—
643D3—188no—
644D3—182no—
645D3—3616no—
646D3—368no—
647D3—362no—
648C22—22no—
649C22—22no—
650C22—92no—
651C22—181no—
652C22—181no—
653C22—182no—
654C22—182no—
655C22—182no—
656C22—272no—
657C22—368no—
658C22—541no—
659C22—541no—
660C22—542no—
661C22—542no—
662C22—542no—
663C22—1088no—
664C22C2×#629214yescomplemented
665C22C22×D3×C3⋊D311yescharacteristic
666C4—32no—
667C4—62no—
668C4—61no—
669C4—181no—
670C4—541no—
671C4C2×#629212yescomplemented
672C3—24no—
673C3D4×#62614yescomplemented
674C3D4×C4⋊(C3⋊D3)11yescharacteristic, complemented
675C2—24no—
676C2—182no—
677C2—362no—
678C2—542no—
679C2—1082no—
680C2D3×D4×C3⋊D311yescharacteristic
681C2#1172458911yescharacteristic
682C2C22×#629211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×C3×D4×C3⋊D3C2semidirect
3. C22×#6292C2semidirect
4. C32×D4×Dic3C2semidirect
5. #11723639C2semidirect
6. #11723636C2semidirect
7. #11723632C2semidirect
8. #11723532C2semidirect
9. #11723526C2semidirect
10. #11723517C2semidirect
11. C4×#6292C2semidirect
14. C23×C3⋊(C3⋊D3)C22semidirect
15. C23×C3×C3⋊D3C22semidirect
17. C2×#6312C22semidirect
19. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
21. C2×C3×#638C22semidirect
23. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C22×C32×Dic3C22semidirect
28. C2×#6292C22semidirect
29. C2×#6292C22semidirect
30. C2×#6292C22semidirect
31. C2×#6292C22semidirect
32. C32×#217C22semidirect
33. C32×C4⋊Dic3C22semidirect
34. C32×C4×Dic3C22semidirect
35. Dic3⋊(C3⋊Dic3)C22semidirect
36. #88804C22semidirect
37. #88804C22semidirect
38. #88803C22semidirect
39. #88803C22semidirect
43. C2×D4×C3⋊D3D3semidirect
55. C3×D4×Dic3D3semidirect
74. C33×D4D4semidirect
92. #6292D4direct (N × H)
98. C23×C3⋊D3C2×D3semidirect
107. C2×#638C2×D3semidirect
121. C2×C4⋊(C3⋊D3)C2×D3semidirect
125. C2×C4×C3⋊D3C2×D3semidirect
127. C22×C3×Dic3C2×D3semidirect
145. C3×#217C2×D3semidirect
146. C3×C4⋊Dic3C2×D3semidirect
147. C3×C4×Dic3C2×D3semidirect
155. C22×C33C2×D4semidirect
163. C2×C3⋊(C3⋊D3)C2×D4semidirect
170. C2×C3×C3⋊D3C2×D4semidirect
171. C33×C4C2×D4semidirect
176. C32×Dic3C2×D4semidirect
190. D4×Dic3C3⋊D3semidirect
229. C32×D4D12semidirect
230. C32×D4#67semidirect
304. C22×Dic3C2×C3⋊D3semidirect
328. #217C2×C3⋊D3semidirect
336. C4⋊Dic3C2×C3⋊D3semidirect
338. C4×Dic3C2×C3⋊D3semidirect
347. C22×C32C2×D12semidirect
348. C22×C32C2×#67semidirect
378. C2×C3⋊D3D3×D4semidirect
390. C32×C4C2×D12semidirect
391. C32×C4C2×#67semidirect
399. C3×Dic3D3×D4semidirect
411. C33D42semidirect
443. C3×D4#626semidirect
444. C3×D4C4⋊(C3⋊D3)semidirect
547. C22×C3C2×#626semidirect
548. C22×C3C2×C4⋊(C3⋊D3)semidirect
584. C3×C4C2×#626semidirect
585. C3×C4C2×C4⋊(C3⋊D3)semidirect
592. Dic3D4×C3⋊D3semidirect
594. C32D4×D12semidirect
595. C32D4×#67semidirect
616. D4#6292direct (N × H)
664. C22C2×#6292semidirect
671. C4C2×#6292semidirect
673. C3D4×#626semidirect
674. 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
C2×D4×C3⋊(C3⋊D3)2
C2×C3×D4×C3⋊D32
C22×#62922
C32×D4×Dic32
#117236392
#117236362
#117236322
#117235322
#117235262
#117235172
C4×#62922
D4×C4⋊(C3⋊D3)3
D4×#6263