Finite Group Databasebeta

← C3×C4×D4×C3⋊D3 #13179297

Subgroups — C3×C4×D4×C3⋊D3 #13179297

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×C3×D4×C3⋊D3C211yesmaximal, characteristic
2C22×C3×C4×C3⋊D3C212yesmaximal, complemented
3C33×C4×D4C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×C4×#638C212yesmaximal, complemented
6C3×#64102C211yesmaximal, characteristic, complemented
7C3×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
8C3×#64090C212yesmaximal, complemented
9C3×C22⋊C4×C3⋊D3C212yesmaximal, complemented
10C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
11C3×C42×C3⋊D3C211yesmaximal, characteristic, complemented
12C4×D4×C3⋊D3C311yesmaximal, characteristic, direct product factor
13C3×C4×D3×D4—34nomaximal
14C23×C3×C3⋊D3C2212yes—
15C2×C33×D4C2211yescharacteristic
16C22×C33×C4C2212yescomplemented
17C2×C3×#638C2212yes—
18C22×C3×C3⋊Dic3C2212yescomplemented
19C3×D4×C3⋊D3C418yesdirect product factor
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3—28no—
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2212yes—
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2212yescomplemented
27C2×C3×C4×C3⋊D3C2212yescomplemented
28C33×C4⋊C4C2211yescharacteristic, complemented
29C33×C22⋊C4C2212yescomplemented
30C33×C42C2211yescharacteristic, complemented
31C3×#3757C2212yescomplemented
32C3×#3752C2212yescomplemented
33C3×#3752C2212yescomplemented
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×#3750C2212yescomplemented
36C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
37C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C2×D4×C3⋊D3C2×C311yescharacteristic
40C22×C4×C3⋊D3C2×C312yescomplemented
41C2×C3×D3×D4—34no—
42C22×C3×C4×D3—38no—
43C32×C4×D4—24no—
44C32×C4×D4D314yescomplemented
45C32×C4×D4C2×C311yescharacteristic, complemented
46D4×C3⋊Dic3C2×C311yescharacteristic, complemented
47C4×#638C2×C312yescomplemented
48#64102C2×C311yescharacteristic, complemented
49C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
50#64090C2×C312yescomplemented
51C22⋊C4×C3⋊D3C2×C312yescomplemented
52C4×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
53C42×C3⋊D3C2×C311yescharacteristic, complemented
54C3×D4×Dic3—34no—
55C3×C4×#67—38no—
56C3×#893—34no—
57C3×D3×C4⋊C4—34no—
58C3×#67⋊C4—38no—
59C3×D3×C22⋊C4—38no—
60C3×C4×D12—34no—
61C3×C42×D3—34no—
62C23×C33C2312yes—
63C22×C3×C3⋊D3—24no—
64C22×C3×C3⋊D3—24no—
65C22×C3×C3⋊D3C2×C418yescomplemented
66C22×C3×C3⋊D3C2312yes—
67C22×C3×C3⋊D3C2311yescharacteristic
68C33×D4C2×C414yescomplemented
69C2×C33×C4—24no—
70C2×C33×C4C2311yescharacteristic
71C2×C33×C4C2312yes—
72C2×C33×C4C2311yescharacteristic
73C2×C33×C4C2311yescharacteristic
74C3×#638C2×C418yescomplemented
75C2×C3×C3⋊Dic3—24no—
76C2×C3×C3⋊Dic3C2311yescharacteristic
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C3×C4⋊(C3⋊D3)C2×C414yescomplemented
81C3×C4×C3⋊D3—24no—
82C3×C4×C3⋊D3—22no—
83C3×C4×C3⋊D3—24no—
84C3×C4×C3⋊D3—24no—
85C3×C4×C3⋊D3C2×C414yescomplemented
86C3×C4×C3⋊D3D414yesdirect product factor
87C2×C3×C4×D4—91no—
88C4×D3×D4—34no—
89C23×C3⋊D3C22×C312yes—
90C23×C3×D3—38no—
91C2×C32×D4—24no—
92C2×C32×D4C2×D314yes—
93C2×C32×D4C22×C311yescharacteristic
94C22×C32×C4—28no—
95C22×C32×C4C2×D318yescomplemented
96C22×C32×C4C22×C312yescomplemented
97C2×#638C22×C312yes—
98C22×C3⋊Dic3C22×C312yescomplemented
99D4×C3⋊D3C3×C418yesdirect product factor
100C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
101C2×C4×C3⋊D3—28no—
102C2×C4×C3⋊D3C22×C311yescharacteristic
103C2×C4×C3⋊D3C22×C312yes—
104C2×C4×C3⋊D3C22×C311yescharacteristic
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×C4×C3⋊D3C22×C312yescomplemented
107C2×C4×C3⋊D3C22×C312yescomplemented
108C2×C3×#67—38no—
109C22×C3×Dic3—38no—
110C3×D3×D4—332no—
111C2×C3×D12—34no—
112C2×C3×C4×D3—34no—
113C2×C3×C4×D3—34no—
114C2×C3×C4×D3—34no—
115C2×C3×C4×D3—38no—
116C2×C3×C4×D3—38no—
117C2×C3×C4×D3—38no—
118C2×C3×C4×D3—632no—
119C32×C4⋊C4—24no—
120C32×C4⋊C4C2×D314yescomplemented
121C32×C4⋊C4C22×C311yescharacteristic, complemented
122C32×C22⋊C4—28no—
123C32×C22⋊C4C2×D318yescomplemented
124C32×C22⋊C4C22×C312yescomplemented
125C32×C42—24no—
126C32×C42C2×D314yescomplemented
127C32×C42C22×C311yescharacteristic, complemented
128#3757C22×C312yescomplemented
129#3752C22×C312yescomplemented
130#3752C22×C312yescomplemented
131C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
132#3750C22×C312yescomplemented
133C4×C3⋊Dic3C22×C311yescharacteristic, complemented
134C4×C3⋊Dic3C22×C311yescharacteristic, complemented
135C4×C3⋊Dic3C22×C311yescharacteristic, complemented
136C3×#217—38no—
137C3×(C2×D3)⋊C4—38no—
138C3×(C2×D3)⋊C4—38no—
139C3×C4⋊Dic3—34no—
140C3×Dic3⋊C4—38no—
141C3×C4×Dic3—34no—
142C3×C4×Dic3—34no—
143C3×C4×Dic3—34no—
144C22×C33—22no—
145C22×C33—22no—
146C22×C33C22×C414yescomplemented
147C22×C33C2411yescharacteristic
148C2×C3×C3⋊D3—22no—
149C2×C3×C3⋊D3—22no—
150C2×C3×C3⋊D3—216no—
151C2×C3×C3⋊D3C22×C412yes—
152C2×C3×C3⋊D3C22×C414yescomplemented
153C2×C3×C3⋊D3C2×D412yes—
154C2×C3×C3⋊D3#4112yes—
155C33×C4—22no—
156C33×C4—21no—
157C33×C4C22×C412yescomplemented
158C33×C4C2×D412yescomplemented
159C3×C3⋊Dic3—22no—
160C3×C3⋊Dic3—21no—
161C3×C3⋊Dic3C22×C412yescomplemented
162C3×C3⋊Dic3C2×D412yescomplemented
163C22×C3×D4—91no—
164C23×C3×C4—92no—
165C2×D3×D4—34no—
166C22×C4×D3—38no—
167C3×C4×D4—24no—
168C3×C4×D4—91no—
169C3×C4×D4—92no—
170C3×C4×D4—91no—
171C3×C4×D4—92no—
172C3×C4×D4—91no—
173C3×C4×D4C3×D314yescomplemented
174C3×C4×D4C3⋊D311yescharacteristic, direct product factor
175C2×C3×C4⋊C4—91no—
176C2×C3×C22⋊C4—92no—
177C2×C3×C42—91no—
178D4×Dic3—34no—
179C4×#67—38no—
180#893—34no—
181D3×C4⋊C4—34no—
182#67⋊C4—38no—
183D3×C22⋊C4—38no—
184C4×D12—34no—
185C42×D3—34no—
186C23×C32—28no—
187C23×C32C22×D318yes—
188C23×C32C23×C312yes—
189C22×C3⋊D3—24no—
190C22×C3⋊D3—24no—
191C22×C3⋊D3C2×C3×C418yescomplemented
192C22×C3⋊D3C23×C312yes—
193C22×C3⋊D3C23×C311yescharacteristic
194C22×C3×D3—34no—
195C22×C3×D3—332no—
196C22×C3×D3—38no—
197C22×C3×D3—616no—
198C22×C3×D3—616no—
199C32×D4—216no—
200C32×D4C4×D3116yescomplemented
201C32×D4C2×C3×C414yescomplemented
202C2×C32×C4—24no—
203C2×C32×C4—24no—
204C2×C32×C4—24no—
205C2×C32×C4—24no—
206C2×C32×C4—28no—
207C2×C32×C4—216no—
208C2×C32×C4—416no—
209C2×C32×C4C22×D314yes—
210C2×C32×C4C22×D318yes—
211C2×C32×C4C22×D314yes—
212C2×C32×C4C22×D314yes—
213C2×C32×C4C23×C311yescharacteristic
214C2×C32×C4C23×C312yes—
215C2×C32×C4C23×C311yescharacteristic
216C2×C32×C4C23×C311yescharacteristic
217#638C2×C3×C418yescomplemented
218C2×C3⋊Dic3—24no—
219C2×C3⋊Dic3C23×C311yescharacteristic
220C2×C3⋊Dic3C23×C312yes—
221C2×C3⋊Dic3C23×C311yescharacteristic
222C2×C3⋊Dic3C23×C311yescharacteristic
223C4⋊(C3⋊D3)C2×C3×C414yescomplemented
224C4×C3⋊D3—24no—
225C4×C3⋊D3—22no—
226C4×C3⋊D3—24no—
227C4×C3⋊D3—24no—
228C4×C3⋊D3C2×C3×C414yescomplemented
229C4×C3⋊D3C3×D414yesdirect product factor
230C3×#67—332no—
231C2×C3×Dic3—34no—
232C2×C3×Dic3—34no—
233C2×C3×Dic3—34no—
234C2×C3×Dic3—38no—
235C2×C3×Dic3—616no—
236C3×D12—316no—
237C3×C4×D3—316no—
238C3×C4×D3—316no—
239C3×C4×D3—616no—
240C3×C4×D3—68no—
241C3×C4×D3—616no—
242C3×C4×D3—616no—
243C2×C4×D4—91noSylow
244C2×C33—24no—
245C2×C33C23×C411yescharacteristic
246C2×C33C22×D411yescharacteristic
247C2×C33C2×#4111yescharacteristic
248C3×C3⋊D3—24no—
249C3×C3⋊D3C4×D414yesdirect product factor
250C24×C3—92no—
251C23×D3—38no—
252C2×C3×D4—24no—
253C2×C3×D4—92no—
254C2×C3×D4—98no—
255C2×C3×D4—91no—
256C2×C3×D4C2×C3×D314yes—
257C2×C3×D4C2×C3⋊D311yescharacteristic
258C22×C3×C4—28no—
259C22×C3×C4—91no—
260C22×C3×C4—91no—
261C22×C3×C4—92no—
262C22×C3×C4—91no—
263C22×C3×C4—92no—
264C22×C3×C4—92no—
265C22×C3×C4—92no—
266C22×C3×C4—188no—
267C22×C3×C4C2×C3×D318yescomplemented
268C22×C3×C4C2×C3⋊D312yescomplemented
269C2×#67—38no—
270C22×Dic3—38no—
271D3×D4—332no—
272C2×D12—34no—
273C2×C4×D3—34no—
274C2×C4×D3—34no—
275C2×C4×D3—34no—
276C2×C4×D3—38no—
277C2×C4×D3—38no—
278C2×C4×D3—38no—
279C2×C4×D3—632no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—92no—
282C3×C4⋊C4—91no—
283C3×C4⋊C4C2×C3×D314yescomplemented
284C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
285C3×C22⋊C4—28no—
286C3×C22⋊C4—92no—
287C3×C22⋊C4—92no—
288C3×C22⋊C4—92no—
289C3×C22⋊C4C2×C3×D318yescomplemented
290C3×C22⋊C4C2×C3⋊D312yescomplemented
291C3×C42—24no—
292C3×C42—91no—
293C3×C42—91no—
294C3×C42—91no—
295C3×C42C2×C3×D314yescomplemented
296C3×C42C2×C3⋊D311yescharacteristic, complemented
297#217—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—38no—
300C4⋊Dic3—34no—
301Dic3⋊C4—38no—
302C4×Dic3—34no—
303C4×Dic3—34no—
304C4×Dic3—34no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—24no—
308C22×C32—216no—
309C22×C32—28no—
310C22×C32—28no—
311C22×C32—48no—
312C22×C32—48no—
313C22×C32C2×C4×D3116yescomplemented
314C22×C32C22×C3×C414yescomplemented
315C22×C32C23×D314yes—
316C22×C32C24×C311yescharacteristic
317C2×C3⋊D3—22no—
318C2×C3⋊D3—22no—
319C2×C3⋊D3—216no—
320C2×C3⋊D3C22×C3×C412yes—
321C2×C3⋊D3C22×C3×C414yescomplemented
322C2×C3⋊D3C2×C3×D412yes—
323C2×C3⋊D3C3×#4112yes—
324C2×C3×D3—38no—
325C2×C3×D3—38no—
326C2×C3×D3—38no—
327C2×C3×D3—316no—
328C2×C3×D3—664no—
329C2×C3×D3—68no—
330C2×C3×D3—68no—
331C32×C4—22no—
332C32×C4—21no—
333C32×C4—28no—
334C32×C4—28no—
335C32×C4—28no—
336C32×C4—24no—
337C32×C4—44no—
338C32×C4—48no—
339C32×C4C2×C4×D318yescomplemented
340C32×C4D3×D418yescomplemented
341C32×C4C22×C3×C412yescomplemented
342C32×C4C2×C3×D412yescomplemented
343C3⋊Dic3—22no—
344C3⋊Dic3—21no—
345C3⋊Dic3C22×C3×C412yescomplemented
346C3⋊Dic3C2×C3×D412yescomplemented
347C3×Dic3—38no—
348C3×Dic3—38no—
349C3×Dic3—68no—
350C3×Dic3—64no—
351C22×D4—91no—
352C23×C4—92no—
353C4×D4—91no—
354C4×D4—92no—
355C4×D4—91no—
356C4×D4—92no—
357C4×D4—91no—
358C4×D4C3×C3⋊D311yescharacteristic, direct product factor
359C2×C4⋊C4—91no—
360C2×C22⋊C4—92no—
361C2×C42—91no—
362C33C2×C4×D411yescharacteristic, complemented, Sylow
363C23×C3—28no—
364C23×C3—91no—
365C23×C3—92no—
366C23×C3—98no—
367C23×C3—184no—
368C23×C3—184no—
369C23×C3C22×C3×D318yes—
370C23×C3C22×C3⋊D312yes—
371C22×D3—34no—
372C22×D3—38no—
373C22×D3—332no—
374C22×D3—616no—
375C22×D3—616no—
376C3×D4—216no—
377C3×D4—98no—
378C3×D4—94no—
379C3×D4C3×C4×D3116yescomplemented
380C3×D4C4×C3⋊D314yesdirect product factor
381C2×C3×C4—216no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—28no—
387C2×C3×C4—416no—
388C2×C3×C4—91no—
389C2×C3×C4—91no—
390C2×C3×C4—94no—
391C2×C3×C4—94no—
392C2×C3×C4—91no—
393C2×C3×C4—92no—
394C2×C3×C4—184no—
395C2×C3×C4—182no—
396C2×C3×C4—184no—
397C2×C3×C4—184no—
398C2×C3×C4—184no—
399C2×C3×C4C22×C3×D314yes—
400C2×C3×C4C22×C3×D318yes—
401C2×C3×C4C22×C3×D314yes—
402C2×C3×C4C22×C3×D314yes—
403C2×C3×C4C22×C3⋊D311yescharacteristic
404C2×C3×C4C22×C3⋊D312yes—
405C2×C3×C4C22×C3⋊D311yescharacteristic
406C2×C3×C4C22×C3⋊D311yescharacteristic
407#67—332no—
408C2×Dic3—34no—
409C2×Dic3—34no—
410C2×Dic3—34no—
411C2×Dic3—38no—
412C2×Dic3—616no—
413D12—316no—
414C4×D3—316no—
415C4×D3—316no—
416C4×D3—616no—
417C4×D3—68no—
418C4×D3—616no—
419C4×D3—616no—
420C2×C32—24no—
421C2×C32—24no—
422C2×C32—24no—
423C2×C32—24no—
424C2×C32—216no—
425C2×C32—416no—
426C2×C32C22×C4×D314yes—
427C2×C32C2×D3×D414yes—
428C2×C32D3×#4114yes—
429C2×C32C23×C3×C411yescharacteristic
430C2×C32C22×C3×D411yescharacteristic
431C2×C32C2×C3×#4111yescharacteristic
432C3⋊D3—24no—
433C3⋊D3C3×C4×D414yesdirect product factor
434C3×D3—316no—
435C3×D3—616no—
436C24—92no—
437C2×D4—92no—
438C2×D4—98no—
439C2×D4—91no—
440C2×D4C2×C3×C3⋊D311yescharacteristic
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—92no—
444C22×C4—91no—
445C22×C4—92no—
446C22×C4—92no—
447C22×C4—92no—
448C22×C4—188no—
449C22×C4C2×C3×C3⋊D312yescomplemented
450C4⋊C4—92no—
451C4⋊C4—91no—
452C4⋊C4C2×C3×C3⋊D311yescharacteristic, complemented
453C22⋊C4—92no—
454C22⋊C4—92no—
455C22⋊C4—92no—
456C22⋊C4C2×C3×C3⋊D312yescomplemented
457C42—91no—
458C42—91no—
459C42—91no—
460C42C2×C3×C3⋊D311yescharacteristic, complemented
461C22×C3—28no—
462C22×C3—28no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—24no—
466C22×C3—216no—
467C22×C3—48no—
468C22×C3—48no—
469C22×C3—92no—
470C22×C3—92no—
471C22×C3—92no—
472C22×C3—94no—
473C22×C3—1816no—
474C22×C3—182no—
475C22×C3—182no—
476C22×C3C2×C3×C4×D3116yescomplemented
477C22×C3C2×C4×C3⋊D314yescomplemented
478C22×C3C23×C3×D314yes—
479C22×C3C23×C3⋊D311yescharacteristic
480C2×D3—38no—
481C2×D3—38no—
482C2×D3—38no—
483C2×D3—316no—
484C2×D3—664no—
485C2×D3—68no—
486C2×D3—68no—
487C3×C4—28no—
488C3×C4—24no—
489C3×C4—22no—
490C3×C4—21no—
491C3×C4—28no—
492C3×C4—28no—
493C3×C4—48no—
494C3×C4—44no—
495C3×C4—92no—
496C3×C4—92no—
497C3×C4—182no—
498C3×C4—181no—
499C3×C4C2×C3×C4×D318yescomplemented
500C3×C4C3×D3×D418yescomplemented
501C3×C4C2×C4×C3⋊D312yescomplemented
502C3×C4D4×C3⋊D312yesdirect product factor
503Dic3—38no—
504Dic3—38no—
505Dic3—68no—
506Dic3—64no—
507C32—24no—
508C32C4×D3×D414yescomplemented
509C32C2×C3×C4×D411yescharacteristic, complemented
510C23—91no—
511C23—92no—
512C23—98no—
513C23—184no—
514C23—184no—
515C23C22×C3×C3⋊D312yes—
516D4—98no—
517D4—94no—
518D4C3×C4×C3⋊D314yesdirect product factor
519C2×C4—24no—
520C2×C4—91no—
521C2×C4—91no—
522C2×C4—94no—
523C2×C4—94no—
524C2×C4—91no—
525C2×C4—92no—
526C2×C4—184no—
527C2×C4—184no—
528C2×C4—182no—
529C2×C4—184no—
530C2×C4—184no—
531C2×C4C22×C3×C3⋊D311yescharacteristic
532C2×C4C22×C3×C3⋊D312yes—
533C2×C4C22×C3×C3⋊D311yescharacteristic
534C2×C4C22×C3×C3⋊D311yescharacteristic
535C2×C3—216no—
536C2×C3—24no—
537C2×C3—24no—
538C2×C3—24no—
539C2×C3—24no—
540C2×C3—416no—
541C2×C3—94no—
542C2×C3—184no—
543C2×C3C22×C3×C4×D314yes—
544C2×C3C2×C3×D3×D414yes—
545C2×C3C3×D3×#4114yes—
546C2×C3C22×C4×C3⋊D311yescharacteristic
547C2×C3C2×D4×C3⋊D311yescharacteristic
548C2×C3#41×C3⋊D311yescharacteristic
549D3—316no—
550D3—616no—
551C22—22no—
552C22—22no—
553C22—92no—
554C22—92no—
555C22—92no—
556C22—94no—
557C22—1816no—
558C22—182no—
559C22—182no—
560C22C2×C3×C4×C3⋊D314yescomplemented
561C22C23×C3×C3⋊D311yescharacteristic
562C4—22no—
563C4—21no—
564C4—92no—
565C4—92no—
566C4—182no—
567C4—181no—
568C4C2×C3×C4×C3⋊D312yescomplemented
569C4C3×D4×C3⋊D312yesdirect product factor
570C3—24no—
571C3C3×C4×D3×D414yescomplemented
572C3C4×D4×C3⋊D311yescharacteristic, direct product factor
573C2—24no—
574C2—94no—
575C2—184no—
576C2C22×C3×C4×C3⋊D311yescharacteristic
577C2C2×C3×D4×C3⋊D311yescharacteristic
578C2C3×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C3×C4C22×C3⋊D3
commutatorC2×C32C23×C3×C4
FrattiniC22C23×C3×C3⋊D3
FittingC33×C4×D4C2
socleC22×C33C24
prime radicalC2×C3×D4×C3⋊D3C2
cosocleC22×C32C24×C3
hypercenterC3×C4×D4C3⋊D3
hypocenterC32C2×C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×C3⋊D3C2semidirect
3. C33×C4×D4C2semidirect
4. C3×D4×C3⋊Dic3C2semidirect
5. C3×C4×#638C2semidirect
6. C3×#64102C2semidirect
7. C3×C4⋊C4×C3⋊D3C2semidirect
8. C3×#64090C2semidirect
9. C3×C22⋊C4×C3⋊D3C2semidirect
10. C3×C4×C4⋊(C3⋊D3)C2semidirect
11. C3×C42×C3⋊D3C2semidirect
12. C4×D4×C3⋊D3C3direct (N × H)
16. C22×C33×C4C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
19. C3×D4×C3⋊D3C4direct (N × H)
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C33×C4⋊C4C22semidirect
29. C33×C22⋊C4C22semidirect
30. C33×C42C22semidirect
31. C3×#3757C22semidirect
32. C3×#3752C22semidirect
33. C3×#3752C22semidirect
34. C3×C4⋊(C3⋊Dic3)C22semidirect
35. C3×#3750C22semidirect
36. C3×C4×C3⋊Dic3C22semidirect
37. C3×C4×C3⋊Dic3C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
40. C22×C4×C3⋊D3C2×C3semidirect
44. C32×C4×D4D3semidirect
45. C32×C4×D4C2×C3semidirect
46. D4×C3⋊Dic3C2×C3semidirect
47. C4×#638C2×C3semidirect
48. #64102C2×C3semidirect
49. C4⋊C4×C3⋊D3C2×C3semidirect
50. #64090C2×C3semidirect
51. C22⋊C4×C3⋊D3C2×C3semidirect
52. C4×C4⋊(C3⋊D3)C2×C3semidirect
53. C42×C3⋊D3C2×C3semidirect
65. C22×C3×C3⋊D3C2×C4semidirect
68. C33×D4C2×C4semidirect
74. C3×#638C2×C4semidirect
80. C3×C4⋊(C3⋊D3)C2×C4semidirect
85. C3×C4×C3⋊D3C2×C4semidirect
86. C3×C4×C3⋊D3D4direct (N × H)
95. C22×C32×C4C2×D3semidirect
96. C22×C32×C4C22×C3semidirect
98. C22×C3⋊Dic3C22×C3semidirect
99. D4×C3⋊D3C3×C4direct (N × H)
106. C2×C4×C3⋊D3C22×C3semidirect
107. C2×C4×C3⋊D3C22×C3semidirect
120. C32×C4⋊C4C2×D3semidirect
121. C32×C4⋊C4C22×C3semidirect
123. C32×C22⋊C4C2×D3semidirect
124. C32×C22⋊C4C22×C3semidirect
126. C32×C42C2×D3semidirect
127. C32×C42C22×C3semidirect
128. #3757C22×C3semidirect
129. #3752C22×C3semidirect
130. #3752C22×C3semidirect
131. C4⋊(C3⋊Dic3)C22×C3semidirect
132. #3750C22×C3semidirect
133. C4×C3⋊Dic3C22×C3semidirect
134. C4×C3⋊Dic3C22×C3semidirect
135. C4×C3⋊Dic3C22×C3semidirect
146. C22×C33C22×C4semidirect
152. C2×C3×C3⋊D3C22×C4semidirect
157. C33×C4C22×C4semidirect
158. C33×C4C2×D4semidirect
161. C3×C3⋊Dic3C22×C4semidirect
162. C3×C3⋊Dic3C2×D4semidirect
173. C3×C4×D4C3×D3semidirect
174. C3×C4×D4C3⋊D3direct (N × H)
191. C22×C3⋊D3C2×C3×C4semidirect
200. C32×D4C4×D3semidirect
201. C32×D4C2×C3×C4semidirect
217. #638C2×C3×C4semidirect
223. C4⋊(C3⋊D3)C2×C3×C4semidirect
228. C4×C3⋊D3C2×C3×C4semidirect
229. C4×C3⋊D3C3×D4direct (N × H)
249. C3×C3⋊D3C4×D4direct (N × H)
267. C22×C3×C4C2×C3×D3semidirect
268. C22×C3×C4C2×C3⋊D3semidirect
283. C3×C4⋊C4C2×C3×D3semidirect
284. C3×C4⋊C4C2×C3⋊D3semidirect
289. C3×C22⋊C4C2×C3×D3semidirect
290. C3×C22⋊C4C2×C3⋊D3semidirect
295. C3×C42C2×C3×D3semidirect
296. C3×C42C2×C3⋊D3semidirect
313. C22×C32C2×C4×D3semidirect
314. C22×C32C22×C3×C4semidirect
321. C2×C3⋊D3C22×C3×C4semidirect
339. C32×C4C2×C4×D3semidirect
340. C32×C4D3×D4semidirect
341. C32×C4C22×C3×C4semidirect
342. C32×C4C2×C3×D4semidirect
345. C3⋊Dic3C22×C3×C4semidirect
346. C3⋊Dic3C2×C3×D4semidirect
358. C4×D4C3×C3⋊D3direct (N × H)
362. C33C2×C4×D4semidirect
379. C3×D4C3×C4×D3semidirect
380. C3×D4C4×C3⋊D3direct (N × H)
433. C3⋊D3C3×C4×D4direct (N × H)
449. C22×C4C2×C3×C3⋊D3semidirect
452. C4⋊C4C2×C3×C3⋊D3semidirect
456. C22⋊C4C2×C3×C3⋊D3semidirect
460. C42C2×C3×C3⋊D3semidirect
476. C22×C3C2×C3×C4×D3semidirect
477. C22×C3C2×C4×C3⋊D3semidirect
499. C3×C4C2×C3×C4×D3semidirect
500. C3×C4C3×D3×D4semidirect
501. C3×C4C2×C4×C3⋊D3semidirect
502. C3×C4D4×C3⋊D3direct (N × H)
508. C32C4×D3×D4semidirect
509. C32C2×C3×C4×D4semidirect
518. D4C3×C4×C3⋊D3direct (N × H)
560. C22C2×C3×C4×C3⋊D3semidirect
568. C4C2×C3×C4×C3⋊D3semidirect
569. C4C3×D4×C3⋊D3direct (N × H)
571. C3C3×C4×D3×D4semidirect
572. C3C4×D4×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C22×C3×C4×C3⋊D32
C33×C4×D42
C3×D4×C3⋊Dic32
C3×C4×#6382
C3×#641022
C3×C4⋊C4×C3⋊D32
C3×#640902
C3×C22⋊C4×C3⋊D32
C3×C4×C4⋊(C3⋊D3)2
C3×C42×C3⋊D32
C4×D4×C3⋊D33
C3×C4×D3×D43