Finite Group Databasebeta

← D3×C4⋊C4×C3⋊D3 #13176520

Subgroups — D3×C4⋊C4×C3⋊D3 #13176520

Order 1728.

2876 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×C3⋊D3C212yesmaximal
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic
3C4⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
6#11723503C211yesmaximal, characteristic, complemented
7C3⋊D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
9#11723470C212yesmaximal, complemented
10C3⋊D3×Dic3⋊C4C212yesmaximal, complemented
11D3×#3750C212yesmaximal, complemented
12C2×C4⋊C4×C3⋊D3—31nomaximal
13D32×C4⋊C4—34nomaximal
14C22×D3×C3⋊D3C2211yescharacteristic
15C2×C4×C3⋊(C3⋊D3)C2212yes—
16C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2212yes—
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C32×C4×D3C2212yes—
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6289C2212yes—
22C2×#6289C2211yescharacteristic
23C2×Dic3×C3⋊D3C2212yes—
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2212yes—
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C4×D3×C3⋊D3—28no—
28C4×D3×C3⋊D3C418yescomplemented
29C33×C4⋊C4C2211yescharacteristic, complemented
30C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
31#88857C2212yescomplemented
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C3×#3750C2212yescomplemented
34C32×C4⋊Dic3C2211yescharacteristic, complemented
35C32×Dic3⋊C4C2212yescomplemented
36#88807C2212yescomplemented
37#88806C2212yescomplemented
38Dic3⋊(C3⋊Dic3)C2212yescomplemented
39C22×C4×C3⋊D3—31no—
40C22×C4×C3⋊D3—32no—
41C2×C4×D32—34no—
42C2×C4×D32—38no—
43C2×C32×C4⋊C4—31no—
44C2×C4⋊(C3⋊Dic3)—31no—
45C2×#3750—32no—
46C4⋊C4×C3⋊D3—32no—
47C4⋊C4×C3⋊D3—31no—
48C4⋊C4×C3⋊D3—31no—
49C4⋊C4×C3⋊D3—31no—
50C4⋊C4×C3⋊D3—32no—
51C4⋊C4×C3⋊D3—34no—
52C4⋊C4×C3⋊D3—64no—
53C4⋊C4×C3⋊D3D311yescharacteristic, direct product factor
54C3×D3×C4⋊C4—34no—
55C3×D3×C4⋊C4D314yescomplemented
56#63900—34no—
57D3×C4⋊Dic3—34no—
58D3×C4⋊Dic3—34no—
59#63883—38no—
60D3×Dic3⋊C4—38no—
61D3×Dic3⋊C4—38no—
62C22×C3⋊(C3⋊D3)C2311yescharacteristic
63C22×C3×C3⋊D3C2311yescharacteristic
64C22×C32×D3C2311yescharacteristic
65C2×D3×C3⋊D3C2×C414yes—
66C2×D3×C3⋊D3D414yes—
67C2×D3×C3⋊D3Q814yes—
68C2×C33×C4C2312yes—
69C2×C33×C4C2311yescharacteristic
70C2×C3⋊(C3⋊Dic3)C2312yes—
71C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
72C4×C3⋊(C3⋊D3)—24no—
73C4×C3⋊(C3⋊D3)C2×C414yescomplemented
74C2×C3×C3⋊Dic3C2312yes—
75C2×C3×C3⋊Dic3C2311yescharacteristic
76C3×C4×C3⋊D3—24no—
77C3×C4×C3⋊D3C2×C414yescomplemented
78C2×C32×Dic3C2312yes—
79C2×C32×Dic3C2311yescharacteristic
80C32×C4×D3—24no—
81C32×C4×D3C2×C414yescomplemented
82#6289—24no—
83#6289C2×C414yescomplemented
84Dic3×C3⋊D3—24no—
85Dic3×C3⋊D3C2×C414yescomplemented
86D3×C3⋊Dic3—24no—
87D3×C3⋊Dic3C2×C414yescomplemented
88C2×D3×C4⋊C4—94no—
89C2×D3×C4⋊C4—91no—
90C23×C3⋊D3—31no—
91C22×D32—34no—
92C22×C32×C4—31no—
93C22×C32×C4—32no—
94C22×C3⋊Dic3—31no—
95C22×C3⋊Dic3—32no—
96C2×C4×C3⋊D3—31no—
97C2×C4×C3⋊D3—31no—
98C2×C4×C3⋊D3—34no—
99C2×C4×C3⋊D3—31no—
100C2×C4×C3⋊D3—38no—
101C2×C4×C3⋊D3—32no—
102C2×C4×C3⋊D3—32no—
103C2×C4×C3⋊D3—38no—
104C2×C4×C3⋊D3—32no—
105C2×C4×C3⋊D3—68no—
106C2×C4×C3⋊D3—64no—
107C2×C4×C3⋊D3—68no—
108C2×C4×C3⋊D3C2×D312yes—
109C2×C4×C3⋊D3C2×D311yescharacteristic
110C2×C3×C4×D3—34no—
111C2×C3×C4×D3—38no—
112C2×C3×C4×D3C2×D318yes—
113C2×C3×C4×D3C2×D314yes—
114C2×#624—34no—
115C2×#624—38no—
116C2×D3×Dic3—34no—
117C2×D3×Dic3—34no—
118C2×D3×Dic3—38no—
119C2×D3×Dic3—38no—
120C4×D32—332no—
121C4×D32—632no—
122C32×C4⋊C4—24no—
123C32×C4⋊C4—32no—
124C32×C4⋊C4—31no—
125C32×C4⋊C4C2×D314yescomplemented
126C32×C4⋊C4C2×D311yescharacteristic, complemented
127C4⋊(C3⋊Dic3)—31no—
128C4⋊(C3⋊Dic3)—34no—
129C4⋊(C3⋊Dic3)—32no—
130C4⋊(C3⋊Dic3)—64no—
131C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
132#3750—32no—
133#3750—38no—
134#3750—32no—
135#3750—32no—
136#3750—68no—
137#3750C2×D312yescomplemented
138C3×C4⋊Dic3—34no—
139C3×C4⋊Dic3C2×D314yescomplemented
140C3×Dic3⋊C4—38no—
141C3×Dic3⋊C4C2×D318yescomplemented
142#3724—38no—
143Dic3⋊Dic3—38no—
144Dic3⋊Dic3—38no—
145C22×C33C2411yescharacteristic
146C2×C3⋊(C3⋊D3)C22×C412yes—
147C2×C3⋊(C3⋊D3)C2×D412yes—
148C2×C3⋊(C3⋊D3)C2×Q812yes—
149C2×C3×C3⋊D3C22×C412yes—
150C2×C3×C3⋊D3C2×D412yes—
151C2×C3×C3⋊D3C2×Q812yes—
152C2×C32×D3C22×C412yes—
153C2×C32×D3C2×D412yes—
154C2×C32×D3C2×Q812yes—
155D3×C3⋊D3C4⋊C4116yesdirect product factor
156C33×C4—22no—
157C33×C4C22×C412yescomplemented
158C3⋊(C3⋊Dic3)—22no—
159C3⋊(C3⋊Dic3)C22×C412yescomplemented
160C3×C3⋊Dic3—22no—
161C3×C3⋊Dic3C22×C412yescomplemented
162C32×Dic3—22no—
163C32×Dic3C22×C412yescomplemented
164C22×C4×D3—94no—
165C22×C4×D3—98no—
166C22×C4×D3—91no—
167C22×C4×D3—92no—
168C2×C3×C4⋊C4—34no—
169C2×C3×C4⋊C4—91no—
170C2×C4⋊Dic3—94no—
171C2×C4⋊Dic3—91no—
172C2×Dic3⋊C4—98no—
173C2×Dic3⋊C4—92no—
174D3×C4⋊C4—34no—
175D3×C4⋊C4—98no—
176D3×C4⋊C4—94no—
177D3×C4⋊C4—98no—
178D3×C4⋊C4—94no—
179D3×C4⋊C4—92no—
180D3×C4⋊C4—91no—
181D3×C4⋊C4—94no—
182D3×C4⋊C4—91no—
183D3×C4⋊C4—91no—
184D3×C4⋊C4—92no—
185D3×C4⋊C4—184no—
186D3×C4⋊C4C3⋊D311yescharacteristic, direct product factor
187C23×C32—31no—
188C22×C3⋊D3—31no—
189C22×C3⋊D3—34no—
190C22×C3⋊D3—34no—
191C22×C3⋊D3—34no—
192C22×C3⋊D3—34no—
193C22×C3⋊D3—64no—
194C22×C3⋊D3C22×D311yescharacteristic
195C22×C3×D3—34no—
196C22×C3×D3C22×D314yes—
197C2×D32—316no—
198C2×D32—316no—
199C2×D32—316no—
200C2×C32×C4—24no—
201C2×C32×C4—28no—
202C2×C32×C4—31no—
203C2×C32×C4—34no—
204C2×C32×C4—32no—
205C2×C32×C4—64no—
206C2×C32×C4C22×D318yes—
207C2×C32×C4C22×D314yes—
208C2×C32×C4C22×D312yes—
209C2×C32×C4C22×D311yescharacteristic
210C2×C3⋊Dic3—31no—
211C2×C3⋊Dic3—34no—
212C2×C3⋊Dic3—32no—
213C2×C3⋊Dic3—34no—
214C2×C3⋊Dic3—38no—
215C2×C3⋊Dic3—64no—
216C2×C3⋊Dic3—68no—
217C2×C3⋊Dic3—64no—
218C2×C3⋊Dic3C22×D312yes—
219C2×C3⋊Dic3C22×D311yescharacteristic
220C4×C3⋊D3—24no—
221C4×C3⋊D3—34no—
222C4×C3⋊D3—34no—
223C4×C3⋊D3—34no—
224C4×C3⋊D3—316no—
225C4×C3⋊D3—616no—
226C4×C3⋊D3—64no—
227C4×C3⋊D3—64no—
228C4×C3⋊D3—64no—
229C4×C3⋊D3—616no—
230C4×C3⋊D3—1216no—
231C4×C3⋊D3C4×D314yescomplemented
232C2×C3×Dic3—34no—
233C2×C3×Dic3—38no—
234C2×C3×Dic3C22×D318yes—
235C2×C3×Dic3C22×D314yes—
236C3×C4×D3—216no—
237C3×C4×D3—316no—
238C3×C4×D3—616no—
239C3×C4×D3C4×D3116yescomplemented
240#624—316no—
241#624—616no—
242D3×Dic3—316no—
243D3×Dic3—316no—
244D3×Dic3—616no—
245D3×Dic3—616no—
246C22×C4⋊C4—271noSylow
247C2×C33C23×C411yescharacteristic
248C2×C33C22×D411yescharacteristic
249C2×C33C22×Q811yescharacteristic
250C3⋊(C3⋊D3)C2×C4⋊C414yescomplemented
251C3×C3⋊D3C2×C4⋊C414yescomplemented
252C32×D3C2×C4⋊C414yescomplemented
253C23×D3—94no—
254C23×D3—91no—
255C22×C3×C4—34no—
256C22×C3×C4—38no—
257C22×C3×C4—91no—
258C22×C3×C4—92no—
259C22×Dic3—94no—
260C22×Dic3—98no—
261C22×Dic3—91no—
262C22×Dic3—92no—
263C2×C4×D3—34no—
264C2×C4×D3—38no—
265C2×C4×D3—932no—
266C2×C4×D3—94no—
267C2×C4×D3—94no—
268C2×C4×D3—91no—
269C2×C4×D3—94no—
270C2×C4×D3—91no—
271C2×C4×D3—91no—
272C2×C4×D3—98no—
273C2×C4×D3—98no—
274C2×C4×D3—98no—
275C2×C4×D3—92no—
276C2×C4×D3—98no—
277C2×C4×D3—92no—
278C2×C4×D3—92no—
279C2×C4×D3—184no—
280C2×C4×D3—188no—
281C2×C4×D3—188no—
282C2×C4×D3—1832no—
283C2×C4×D3C2×C3⋊D312yes—
284C2×C4×D3C2×C3⋊D311yescharacteristic
285C3×C4⋊C4—24no—
286C3×C4⋊C4—38no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—92no—
289C3×C4⋊C4—91no—
290C3×C4⋊C4D3214yescomplemented
291C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
292C4⋊Dic3—34no—
293C4⋊Dic3—98no—
294C4⋊Dic3—94no—
295C4⋊Dic3—91no—
296C4⋊Dic3—92no—
297C4⋊Dic3—184no—
298C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
299Dic3⋊C4—38no—
300Dic3⋊C4—98no—
301Dic3⋊C4—98no—
302Dic3⋊C4—98no—
303Dic3⋊C4—92no—
304Dic3⋊C4—92no—
305Dic3⋊C4—92no—
306Dic3⋊C4—188no—
307Dic3⋊C4C2×C3⋊D312yescomplemented
308C22×C32—24no—
309C22×C32—32no—
310C22×C32—32no—
311C22×C32—32no—
312C22×C32C23×D314yes—
313C22×C32C23×D311yescharacteristic
314C2×C3⋊D3—32no—
315C2×C3⋊D3—32no—
316C2×C3⋊D3—32no—
317C2×C3⋊D3—316no—
318C2×C3⋊D3—38no—
319C2×C3⋊D3—38no—
320C2×C3⋊D3—38no—
321C2×C3⋊D3—68no—
322C2×C3⋊D3—68no—
323C2×C3⋊D3—68no—
324C2×C3⋊D3C2×C4×D312yes—
325C2×C3⋊D3D3×D412yes—
326C2×C3⋊D3D3×Q812yes—
327C2×C3×D3—38no—
328C2×C3×D3—38no—
329C2×C3×D3—38no—
330C2×C3×D3C2×C4×D318yes—
331C2×C3×D3D3×D418yes—
332C2×C3×D3D3×Q818yes—
333D32—364no—
334C32×C4—22no—
335C32×C4—28no—
336C32×C4—28no—
337C32×C4—32no—
338C32×C4—48no—
339C32×C4—62no—
340C32×C4C2×C4×D318yescomplemented
341C32×C4C2×C4×D312yescomplemented
342C3⋊Dic3—22no—
343C3⋊Dic3—32no—
344C3⋊Dic3—38no—
345C3⋊Dic3—68no—
346C3⋊Dic3—62no—
347C3⋊Dic3—68no—
348C3⋊Dic3—128no—
349C3⋊Dic3C2×C4×D312yescomplemented
350C3×Dic3—28no—
351C3×Dic3—38no—
352C3×Dic3—68no—
353C3×Dic3C2×C4×D318yescomplemented
354C23×C4—271no—
355C23×C4—272no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—272no—
359C2×C4⋊C4—271no—
360C2×C4⋊C4—272no—
361C2×C4⋊C4—271no—
362C2×C4⋊C4—272no—
363C2×C4⋊C4—271no—
364C2×C4⋊C4—271no—
365C33C22×C4⋊C411yescharacteristic, complemented, Sylow
366C23×C3—34no—
367C23×C3—91no—
368C22×D3—34no—
369C22×D3—916no—
370C22×D3—916no—
371C22×D3—916no—
372C22×D3—94no—
373C22×D3—91no—
374C22×D3—94no—
375C22×D3—94no—
376C22×D3—94no—
377C22×D3—184no—
378C22×D3C22×C3⋊D311yescharacteristic
379C2×C3×C4—24no—
380C2×C3×C4—28no—
381C2×C3×C4—34no—
382C2×C3×C4—316no—
383C2×C3×C4—38no—
384C2×C3×C4—616no—
385C2×C3×C4—91no—
386C2×C3×C4—94no—
387C2×C3×C4—92no—
388C2×C3×C4—184no—
389C2×C3×C4C2×D3218yes—
390C2×C3×C4C2×D3214yes—
391C2×C3×C4C22×C3⋊D312yes—
392C2×C3×C4C22×C3⋊D311yescharacteristic
393C2×Dic3—34no—
394C2×Dic3—38no—
395C2×Dic3—916no—
396C2×Dic3—94no—
397C2×Dic3—91no—
398C2×Dic3—94no—
399C2×Dic3—98no—
400C2×Dic3—92no—
401C2×Dic3—184no—
402C2×Dic3—188no—
403C2×Dic3—184no—
404C2×Dic3—1816no—
405C2×Dic3C22×C3⋊D312yes—
406C2×Dic3C22×C3⋊D311yescharacteristic
407C4×D3—24no—
408C4×D3—316no—
409C4×D3—616no—
410C4×D3—916no—
411C4×D3—916no—
412C4×D3—94no—
413C4×D3—916no—
414C4×D3—94no—
415C4×D3—94no—
416C4×D3—1816no—
417C4×D3—184no—
418C4×D3—1816no—
419C4×D3—184no—
420C4×D3—1816no—
421C4×D3—1816no—
422C4×D3—184no—
423C4×D3—3616no—
424C4×D3C4×C3⋊D314yescomplemented
425C2×C32—24no—
426C2×C32—24no—
427C2×C32—24no—
428C2×C32—34no—
429C2×C32C22×C4×D314yes—
430C2×C32C22×C4×D311yescharacteristic
431C2×C32C2×D3×D414yes—
432C2×C32C2×D3×D411yescharacteristic
433C2×C32C2×D3×Q814yes—
434C2×C32C2×D3×Q811yescharacteristic
435C3⋊D3—34no—
436C3⋊D3—316no—
437C3⋊D3—616no—
438C3⋊D3D3×C4⋊C414yesdirect product factor
439C3×D3—316no—
440C3×D3D3×C4⋊C4116yescomplemented
441C24—271no—
442C22×C4—31no—
443C22×C4—32no—
444C22×C4—91no—
445C22×C4—92no—
446C22×C4—271no—
447C22×C4—278no—
448C22×C4—272no—
449C22×C4—271no—
450C22×C4—272no—
451C22×C4—271no—
452C22×C4—272no—
453C22×C4—271no—
454C22×C4—272no—
455C22×C4—548no—
456C4⋊C4—32no—
457C4⋊C4—31no—
458C4⋊C4—92no—
459C4⋊C4—91no—
460C4⋊C4—272no—
461C4⋊C4—272no—
462C4⋊C4—272no—
463C4⋊C4—272no—
464C4⋊C4—271no—
465C4⋊C4D3×C3⋊D311yescharacteristic, direct product factor
466C22×C3—24no—
467C22×C3—38no—
468C22×C3—38no—
469C22×C3—38no—
470C22×C3—92no—
471C22×C3—92no—
472C22×C3—92no—
473C22×C3C22×D3214yes—
474C22×C3C23×C3⋊D311yescharacteristic
475C2×D3—38no—
476C2×D3—38no—
477C2×D3—38no—
478C2×D3—964no—
479C2×D3—98no—
480C2×D3—98no—
481C2×D3—98no—
482C2×D3—92no—
483C2×D3—92no—
484C2×D3—92no—
485C2×D3—916no—
486C2×D3—188no—
487C2×D3—188no—
488C2×D3—188no—
489C2×D3C2×C4×C3⋊D312yes—
490C2×D3D4×C3⋊D312yes—
491C2×D3Q8×C3⋊D312yes—
492C3×C4—28no—
493C3×C4—22no—
494C3×C4—28no—
495C3×C4—38no—
496C3×C4—48no—
497C3×C4—68no—
498C3×C4—92no—
499C3×C4—182no—
500C3×C4C4×D3218yescomplemented
501C3×C4C2×C4×C3⋊D312yescomplemented
502Dic3—22no—
503Dic3—38no—
504Dic3—68no—
505Dic3—98no—
506Dic3—92no—
507Dic3—188no—
508Dic3—188no—
509Dic3—182no—
510Dic3—368no—
511Dic3C2×C4×C3⋊D312yescomplemented
512C32—24no—
513C32C2×D3×C4⋊C414yescomplemented
514C32C2×D3×C4⋊C411yescharacteristic, complemented
515C23—31no—
516C23—91no—
517C23—274no—
518C23—274no—
519C23—274no—
520C23—271no—
521C2×C4—31no—
522C2×C4—34no—
523C2×C4—32no—
524C2×C4—64no—
525C2×C4—91no—
526C2×C4—94no—
527C2×C4—92no—
528C2×C4—184no—
529C2×C4—274no—
530C2×C4—274no—
531C2×C4—274no—
532C2×C4—271no—
533C2×C4—274no—
534C2×C4—272no—
535C2×C4—544no—
536C2×C4—544no—
537C2×C4—544no—
538C2×C4—544no—
539C2×C4C2×D3×C3⋊D312yes—
540C2×C4C2×D3×C3⋊D311yescharacteristic
541C2×C3—24no—
542C2×C3—24no—
543C2×C3—24no—
544C2×C3—316no—
545C2×C3—94no—
546C2×C3C2×C4×D3214yes—
547C2×C3D32×D414yes—
548C2×C3D32×Q814yes—
549C2×C3C22×C4×C3⋊D311yescharacteristic
550C2×C3C2×D4×C3⋊D311yescharacteristic
551C2×C3C2×Q8×C3⋊D311yescharacteristic
552D3—316no—
553D3—916no—
554D3—94no—
555D3—1816no—
556D3C4⋊C4×C3⋊D314yesdirect product factor
557C22—32no—
558C22—32no—
559C22—32no—
560C22—92no—
561C22—92no—
562C22—92no—
563C22—2716no—
564C22—272no—
565C22—272no—
566C22—272no—
567C22C22×D3×C3⋊D311yescharacteristic
568C4—22no—
569C4—32no—
570C4—62no—
571C4—92no—
572C4—182no—
573C4—272no—
574C4—542no—
575C4C4×D3×C3⋊D312yescomplemented
576C3—24no—
577C3D32×C4⋊C414yescomplemented
578C3C2×C4⋊C4×C3⋊D311yescharacteristic, complemented
579C2—34no—
580C2—94no—
581C2—274no—
582C2C2×C4×D3×C3⋊D311yescharacteristic
583C2D3×D4×C3⋊D311yescharacteristic
584C2D3×Q8×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC33×C4⋊C4C22
socle, cosocleC22×C33C24
prime radicalC22×D3×C3⋊D3C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C22×C4⋊C4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×C3⋊(C3⋊D3)C2semidirect
4. C3×C4⋊C4×C3⋊D3C2semidirect
5. C32×D3×C4⋊C4C2semidirect
6. #11723503C2semidirect
7. C3⋊D3×C4⋊Dic3C2semidirect
8. D3×C4⋊(C3⋊Dic3)C2semidirect
9. #11723470C2semidirect
10. C3⋊D3×Dic3⋊C4C2semidirect
11. D3×#3750C2semidirect
28. C4×D3×C3⋊D3C4semidirect
29. C33×C4⋊C4C22semidirect
30. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
31. #88857C22semidirect
32. C3×C4⋊(C3⋊Dic3)C22semidirect
33. C3×#3750C22semidirect
34. C32×C4⋊Dic3C22semidirect
35. C32×Dic3⋊C4C22semidirect
36. #88807C22semidirect
37. #88806C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
53. C4⋊C4×C3⋊D3D3direct (N × H)
55. C3×D3×C4⋊C4D3semidirect
73. C4×C3⋊(C3⋊D3)C2×C4semidirect
77. C3×C4×C3⋊D3C2×C4semidirect
81. C32×C4×D3C2×C4semidirect
83. #6289C2×C4semidirect
85. Dic3×C3⋊D3C2×C4semidirect
87. D3×C3⋊Dic3C2×C4semidirect
125. C32×C4⋊C4C2×D3semidirect
126. C32×C4⋊C4C2×D3semidirect
131. C4⋊(C3⋊Dic3)C2×D3semidirect
137. #3750C2×D3semidirect
139. C3×C4⋊Dic3C2×D3semidirect
141. C3×Dic3⋊C4C2×D3semidirect
155. D3×C3⋊D3C4⋊C4direct (N × H)
157. C33×C4C22×C4semidirect
159. C3⋊(C3⋊Dic3)C22×C4semidirect
161. C3×C3⋊Dic3C22×C4semidirect
163. C32×Dic3C22×C4semidirect
186. D3×C4⋊C4C3⋊D3direct (N × H)
231. C4×C3⋊D3C4×D3semidirect
239. C3×C4×D3C4×D3semidirect
250. C3⋊(C3⋊D3)C2×C4⋊C4semidirect
251. C3×C3⋊D3C2×C4⋊C4semidirect
252. C32×D3C2×C4⋊C4semidirect
290. C3×C4⋊C4D32semidirect
291. C3×C4⋊C4C2×C3⋊D3semidirect
298. C4⋊Dic3C2×C3⋊D3semidirect
307. Dic3⋊C4C2×C3⋊D3semidirect
340. C32×C4C2×C4×D3semidirect
341. C32×C4C2×C4×D3semidirect
349. C3⋊Dic3C2×C4×D3semidirect
353. C3×Dic3C2×C4×D3semidirect
365. C33C22×C4⋊C4semidirect
424. C4×D3C4×C3⋊D3semidirect
438. C3⋊D3D3×C4⋊C4direct (N × H)
440. C3×D3D3×C4⋊C4semidirect
465. C4⋊C4D3×C3⋊D3direct (N × H)
500. C3×C4C4×D32semidirect
501. C3×C4C2×C4×C3⋊D3semidirect
511. Dic3C2×C4×C3⋊D3semidirect
513. C32C2×D3×C4⋊C4semidirect
514. C32C2×D3×C4⋊C4semidirect
556. D3C4⋊C4×C3⋊D3direct (N × H)
575. C4C4×D3×C3⋊D3semidirect
577. C3D32×C4⋊C4semidirect
578. C3C2×C4⋊C4×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×C3⋊D32
C4⋊C4×C3⋊(C3⋊D3)2
C3×C4⋊C4×C3⋊D32
C32×D3×C4⋊C42
#117235032
C3⋊D3×C4⋊Dic32
D3×C4⋊(C3⋊Dic3)2
#117234702
C3⋊D3×Dic3⋊C42
D3×#37502
C2×C4⋊C4×C3⋊D33
D32×C4⋊C43