Finite Group Databasebeta

← C4×#89026 #13175395

Subgroups — C4×#89026 #13175395

Order 1728.

2988 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89026C211yesmaximal, characteristic
2C2×C4×D3×C3⋊D3C212yesmaximal, complemented
3C42×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C32×C4×D12C211yesmaximal, characteristic, complemented
6#11723539C212yesmaximal, complemented
7#11723508C212yesmaximal, complemented
8C4×#6290C212yesmaximal, complemented
9#11723503C211yesmaximal, characteristic, complemented
10#11723501C211yesmaximal, characteristic, complemented
11#11723499C211yesmaximal, characteristic, complemented
12C4×D4×C3⋊D3—31nomaximal
13C4×#3802—34nomaximal
14C22×D3×C3⋊D3C2212yes—
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
17C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2212yescomplemented
20C2×C32×D12C2211yescharacteristic
21C2×C32×C4×D3C2212yescomplemented
22C2×#6290C2212yes—
23C2×#6289C2212yes—
24C2×Dic3×C3⋊D3C2212yescomplemented
25C2×D3×C3⋊Dic3C2212yescomplemented
26#89026C418yesdirect product factor
27C4×D3×C3⋊D3—28no—
28C33×C42C2211yescharacteristic, complemented
29C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
32C3×#3752C2212yescomplemented
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C32×(C2×D3)⋊C4C2212yescomplemented
35C32×C4⋊Dic3C2211yescharacteristic, complemented
36#88806C2212yescomplemented
37#88803C2212yescomplemented
38(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
39C2×D4×C3⋊D3—31no—
40C22×C4×C3⋊D3—32no—
41C2×#3802—34no—
42C2×C4×D32—38no—
43C32×C4×D4—31no—
44D4×C3⋊Dic3—31no—
45C4×#638—32no—
46#64102—31no—
47C4⋊C4×C3⋊D3—31no—
48#64090—32no—
49C22⋊C4×C3⋊D3—32no—
50C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
51C42×C3⋊D3—31no—
52C42×C3⋊D3—34no—
53C42×C3⋊D3—64no—
54C3×C4×D12—34no—
55C3×C4×D12D314yescomplemented
56#63921—38no—
57#63902—38no—
58C4×#625—38no—
59#63900—34no—
60#63898—34no—
61#63898—34no—
62C22×C3⋊(C3⋊D3)C2311yescharacteristic
63C22×C3×C3⋊D3C2312yes—
64C22×C32×D3C2312yes—
65C2×D3×C3⋊D3—24no—
66C2×D3×C3⋊D3—24no—
67C2×D3×C3⋊D3C2×C418yescomplemented
68C2×C33×C4C2311yescharacteristic
69C2×C33×C4C2311yescharacteristic
70C2×C33×C4C2311yescharacteristic
71C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
72C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
73C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
74C4×C3⋊(C3⋊D3)—22no—
75C4×C3⋊(C3⋊D3)C2×C414yescomplemented
76C4×C3⋊(C3⋊D3)D414yescomplemented
77C2×C3×C3⋊Dic3C2312yes—
78C3×C4⋊(C3⋊D3)C2×C414yescomplemented
79C3×C4×C3⋊D3—24no—
80C2×C32×Dic3C2312yes—
81C32×D12C2×C414yescomplemented
82C32×C4×D3—24no—
83#6290C2×C418yescomplemented
84#6289—24no—
85Dic3×C3⋊D3—24no—
86D3×C3⋊Dic3—24no—
87C4×D3×D4—94no—
88C4×D3×D4—91no—
89C23×C3⋊D3—32no—
90C22×D32—38no—
91C2×C32×D4—31no—
92C22×C32×C4—32no—
93C2×#638—32no—
94C22×C3⋊Dic3—32no—
95D4×C3⋊D3—38no—
96C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
97C2×C4×C3⋊D3—31no—
98C2×C4×C3⋊D3—31no—
99C2×C4×C3⋊D3—34no—
100C2×C4×C3⋊D3—34no—
101C2×C4×C3⋊D3—32no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3—34no—
104C2×C4×C3⋊D3—32no—
105C2×C4×C3⋊D3—68no—
106C2×C4×C3⋊D3—64no—
107C2×C4×C3⋊D3—64no—
108C2×C4×C3⋊D3—64no—
109C2×C4×C3⋊D3C2×D312yescomplemented
110C2×C3×D12—34no—
111C2×C3×D12C2×D314yes—
112C2×C3×C4×D3—38no—
113C2×C3×C4×D3C2×D318yescomplemented
114C2×#625—38no—
115C2×#624—38no—
116C2×D3×Dic3—38no—
117C2×D3×Dic3—38no—
118#3802—332no—
119C4×D32—632no—
120C32×C4⋊C4—31no—
121C32×C22⋊C4—32no—
122C32×C42—24no—
123C32×C42C2×D314yescomplemented
124C32×C42C2×D311yescharacteristic, complemented
125#3757—32no—
126#3752—32no—
127#3752C2×D312yescomplemented
128C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
129#3750—32no—
130C4×C3⋊Dic3—31no—
131C4×C3⋊Dic3—31no—
132C4×C3⋊Dic3—31no—
133C4×C3⋊Dic3—34no—
134C4×C3⋊Dic3—34no—
135C4×C3⋊Dic3—34no—
136C4×C3⋊Dic3—64no—
137C4×C3⋊Dic3—64no—
138C4×C3⋊Dic3—64no—
139C3×(C2×D3)⋊C4—38no—
140C3×(C2×D3)⋊C4C2×D318yescomplemented
141C3×C4⋊Dic3—34no—
142C3×C4⋊Dic3C2×D314yescomplemented
143#3724—38no—
144(C2×D3)⋊Dic3—38no—
145(C2×D3)⋊Dic3—38no—
146C22×C33C2411yescharacteristic
147C2×C3⋊(C3⋊D3)C22×C412yes—
148C2×C3⋊(C3⋊D3)C2×D412yes—
149C2×C3⋊(C3⋊D3)#4112yes—
150C2×C3×C3⋊D3—22no—
151C2×C3×C3⋊D3—22no—
152C2×C3×C3⋊D3C22×C414yescomplemented
153C2×C32×D3—22no—
154C2×C32×D3—22no—
155C2×C32×D3C22×C414yescomplemented
156D3×C3⋊D3—216no—
157C33×C4—21no—
158C33×C4C22×C412yescomplemented
159C33×C4C2×D412yescomplemented
160C3⋊(C3⋊Dic3)—21no—
161C3⋊(C3⋊Dic3)C22×C412yescomplemented
162C3⋊(C3⋊Dic3)C2×D412yescomplemented
163C3×C3⋊Dic3—22no—
164C32×Dic3—22no—
165C2×D3×D4—94no—
166C2×D3×D4—91no—
167C22×C4×D3—98no—
168C22×C4×D3—92no—
169C3×C4×D4—34no—
170C3×C4×D4—91no—
171D4×Dic3—94no—
172D4×Dic3—91no—
173C4×#67—98no—
174C4×#67—92no—
175#893—94no—
176#893—91no—
177D3×C4⋊C4—94no—
178D3×C4⋊C4—91no—
179#67⋊C4—98no—
180#67⋊C4—92no—
181D3×C22⋊C4—98no—
182D3×C22⋊C4—92no—
183C4×D12—34no—
184C4×D12C3⋊D311yescharacteristic, complemented
185C42×D3—94no—
186C42×D3—91no—
187C42×D3—184no—
188C23×C32—32no—
189C22×C3⋊D3—31no—
190C22×C3⋊D3—38no—
191C22×C3⋊D3—34no—
192C22×C3⋊D3—64no—
193C22×C3⋊D3—64no—
194C22×C3⋊D3—64no—
195C22×C3⋊D3C22×D312yes—
196C22×C3×D3—38no—
197C22×C3×D3C22×D318yes—
198C2×D32—332no—
199C2×D32—616no—
200C2×D32—616no—
201C32×D4—34no—
202C2×C32×C4—24no—
203C2×C32×C4—24no—
204C2×C32×C4—24no—
205C2×C32×C4—32no—
206C2×C32×C4—64no—
207C2×C32×C4C22×D314yes—
208C2×C32×C4C22×D314yes—
209C2×C32×C4C22×D314yes—
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C22×D311yescharacteristic
212C2×C32×C4C22×D311yescharacteristic
213#638—38no—
214C2×C3⋊Dic3—31no—
215C2×C3⋊Dic3—31no—
216C2×C3⋊Dic3—31no—
217C2×C3⋊Dic3—34no—
218C2×C3⋊Dic3—34no—
219C2×C3⋊Dic3—34no—
220C2×C3⋊Dic3—64no—
221C2×C3⋊Dic3—64no—
222C2×C3⋊Dic3—64no—
223C2×C3⋊Dic3—64no—
224C2×C3⋊Dic3C22×D312yes—
225C4⋊(C3⋊D3)C4×D314yescomplemented
226C4×C3⋊D3—24no—
227C4×C3⋊D3—34no—
228C4×C3⋊D3—34no—
229C4×C3⋊D3—316no—
230C4×C3⋊D3—316no—
231C4×C3⋊D3—616no—
232C4×C3⋊D3—616no—
233C4×C3⋊D3—64no—
234C4×C3⋊D3—64no—
235C4×C3⋊D3—62no—
236C4×C3⋊D3—68no—
237C4×C3⋊D3—616no—
238C2×C3×Dic3—38no—
239C2×C3×Dic3C22×D318yes—
240C3×D12—316no—
241C3×D12C4×D3116yescomplemented
242C3×C4×D3—216no—
243C3×C4×D3—616no—
244#625—332no—
245#624—616no—
246D3×Dic3—616no—
247D3×Dic3—616no—
248C2×C4×D4—271noSylow
249C2×C33C23×C411yescharacteristic
250C2×C33C22×D411yescharacteristic
251C2×C33C2×#4111yescharacteristic
252C3⋊(C3⋊D3)C4×D414yescomplemented
253C3×C3⋊D3—24no—
254C32×D3—24no—
255C23×D3—98no—
256C23×D3—92no—
257C2×C3×D4—34no—
258C2×C3×D4—91no—
259C22×C3×C4—38no—
260C22×C3×C4—92no—
261C2×#67—98no—
262C2×#67—92no—
263C22×Dic3—98no—
264C22×Dic3—92no—
265D3×D4—932no—
266D3×D4—98no—
267C2×D12—34no—
268C2×D12C2×C3⋊D311yescharacteristic
269C2×C4×D3—38no—
270C2×C4×D3—94no—
271C2×C4×D3—94no—
272C2×C4×D3—91no—
273C2×C4×D3—91no—
274C2×C4×D3—98no—
275C2×C4×D3—98no—
276C2×C4×D3—92no—
277C2×C4×D3—94no—
278C2×C4×D3—91no—
279C2×C4×D3—92no—
280C2×C4×D3—184no—
281C2×C4×D3—184no—
282C2×C4×D3—184no—
283C2×C4×D3—188no—
284C2×C4×D3—1832no—
285C2×C4×D3C2×C3⋊D312yescomplemented
286C3×C4⋊C4—34no—
287C3×C4⋊C4—91no—
288C3×C22⋊C4—38no—
289C3×C22⋊C4—92no—
290C3×C42—24no—
291C3×C42D3214yescomplemented
292C3×C42C2×C3⋊D311yescharacteristic, complemented
293#217—98no—
294#217—92no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—98no—
297(C2×D3)⋊C4—92no—
298(C2×D3)⋊C4C2×C3⋊D312yescomplemented
299C4⋊Dic3—34no—
300C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
301Dic3⋊C4—98no—
302Dic3⋊C4—92no—
303C4×Dic3—94no—
304C4×Dic3—94no—
305C4×Dic3—94no—
306C4×Dic3—91no—
307C4×Dic3—91no—
308C4×Dic3—91no—
309C4×Dic3—184no—
310C4×Dic3—184no—
311C4×Dic3—184no—
312C22×C32—24no—
313C22×C32—34no—
314C22×C32—62no—
315C22×C32—62no—
316C22×C32C23×D314yes—
317C22×C32C23×D311yescharacteristic
318C2×C3⋊D3—22no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—32no—
321C2×C3⋊D3—32no—
322C2×C3⋊D3—32no—
323C2×C3⋊D3—38no—
324C2×C3⋊D3—38no—
325C2×C3⋊D3—38no—
326C2×C3⋊D3—68no—
327C2×C3⋊D3—68no—
328C2×C3⋊D3—68no—
329C2×C3⋊D3—616no—
330C2×C3⋊D3C2×C4×D314yescomplemented
331C2×C3×D3—28no—
332C2×C3×D3—28no—
333C2×C3×D3—316no—
334C2×C3×D3—68no—
335C2×C3×D3—68no—
336C2×C3×D3C2×C4×D3116yescomplemented
337D32—664no—
338C32×C4—28no—
339C32×C4—24no—
340C32×C4—21no—
341C32×C4—28no—
342C32×C4—28no—
343C32×C4—62no—
344C32×C4C2×C4×D318yescomplemented
345C32×C4C2×C4×D312yescomplemented
346C32×C4D3×D418yescomplemented
347C32×C4D3×D412yescomplemented
348C3⋊Dic3—22no—
349C3⋊Dic3—32no—
350C3⋊Dic3—32no—
351C3⋊Dic3—38no—
352C3⋊Dic3—38no—
353C3⋊Dic3—68no—
354C3⋊Dic3—68no—
355C3⋊Dic3—68no—
356C3⋊Dic3—64no—
357C3⋊Dic3—61no—
358C3×Dic3—28no—
359C3×Dic3—68no—
360C22×D4—271no—
361C23×C4—272no—
362C4×D4—31no—
363C4×D4—91no—
364C4×D4—272no—
365C4×D4—271no—
366C4×D4—271no—
367C4×D4—272no—
368C2×C4⋊C4—271no—
369C2×C22⋊C4—272no—
370C2×C42—271no—
371C33C2×C4×D411yescharacteristic, complemented, Sylow
372C23×C3—38no—
373C23×C3—92no—
374C22×D3—38no—
375C22×D3—932no—
376C22×D3—94no—
377C22×D3—91no—
378C22×D3—98no—
379C22×D3—184no—
380C22×D3—184no—
381C22×D3—184no—
382C22×D3—1816no—
383C22×D3—1816no—
384C22×D3C22×C3⋊D312yes—
385C3×D4—316no—
386C3×D4—94no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—38no—
391C2×C3×C4—616no—
392C2×C3×C4—92no—
393C2×C3×C4—184no—
394C2×C3×C4C2×D3214yes—
395C2×C3×C4C2×D3214yes—
396C2×C3×C4C2×D3214yes—
397C2×C3×C4C22×C3⋊D311yescharacteristic
398C2×C3×C4C22×C3⋊D311yescharacteristic
399C2×C3×C4C22×C3⋊D311yescharacteristic
400#67—932no—
401#67—98no—
402C2×Dic3—38no—
403C2×Dic3—94no—
404C2×Dic3—94no—
405C2×Dic3—91no—
406C2×Dic3—91no—
407C2×Dic3—94no—
408C2×Dic3—91no—
409C2×Dic3—184no—
410C2×Dic3—184no—
411C2×Dic3—184no—
412C2×Dic3—184no—
413C2×Dic3—1816no—
414C2×Dic3C22×C3⋊D312yes—
415D12—316no—
416D12C4×C3⋊D314yescomplemented
417C4×D3—24no—
418C4×D3—616no—
419C4×D3—916no—
420C4×D3—916no—
421C4×D3—94no—
422C4×D3—94no—
423C4×D3—1816no—
424C4×D3—1816no—
425C4×D3—184no—
426C4×D3—1816no—
427C4×D3—1816no—
428C4×D3—184no—
429C4×D3—188no—
430C4×D3—182no—
431C4×D3—1816no—
432C2×C32—24no—
433C2×C32—24no—
434C2×C32—24no—
435C2×C32—64no—
436C2×C32C22×C4×D314yes—
437C2×C32C22×C4×D311yescharacteristic
438C2×C32C2×D3×D414yes—
439C2×C32C2×D3×D411yescharacteristic
440C2×C32D3×#4114yes—
441C2×C32D3×#4111yescharacteristic
442C3⋊D3—24no—
443C3⋊D3—34no—
444C3⋊D3—316no—
445C3⋊D3—616no—
446C3×D3—216no—
447C3×D3—616no—
448C24—272no—
449C2×D4—31no—
450C2×D4—91no—
451C2×D4—278no—
452C2×D4—272no—
453C22×C4—32no—
454C22×C4—92no—
455C22×C4—272no—
456C22×C4—272no—
457C22×C4—272no—
458C22×C4—271no—
459C22×C4—271no—
460C22×C4—271no—
461C22×C4—548no—
462C4⋊C4—31no—
463C4⋊C4—91no—
464C4⋊C4—272no—
465C22⋊C4—32no—
466C22⋊C4—92no—
467C22⋊C4—272no—
468C22⋊C4—272no—
469C42—271no—
470C42—271no—
471C42—271no—
472C42D3×C3⋊D311yescharacteristic, complemented
473C22×C3—24no—
474C22×C3—316no—
475C22×C3—68no—
476C22×C3—68no—
477C22×C3—94no—
478C22×C3—182no—
479C22×C3—182no—
480C22×C3C22×D3214yes—
481C22×C3C23×C3⋊D311yescharacteristic
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—316no—
485C2×D3—68no—
486C2×D3—68no—
487C2×D3—98no—
488C2×D3—98no—
489C2×D3—98no—
490C2×D3—92no—
491C2×D3—92no—
492C2×D3—92no—
493C2×D3—188no—
494C2×D3—188no—
495C2×D3—188no—
496C2×D3—1816no—
497C2×D3—1864no—
498C2×D3C2×C4×C3⋊D314yescomplemented
499C3×C4—28no—
500C3×C4—24no—
501C3×C4—21no—
502C3×C4—28no—
503C3×C4—28no—
504C3×C4—68no—
505C3×C4—182no—
506C3×C4C4×D3218yescomplemented
507C3×C4#380218yescomplemented
508C3×C4C2×C4×C3⋊D312yescomplemented
509C3×C4D4×C3⋊D312yescomplemented
510Dic3—22no—
511Dic3—68no—
512Dic3—98no—
513Dic3—98no—
514Dic3—92no—
515Dic3—92no—
516Dic3—188no—
517Dic3—188no—
518Dic3—188no—
519Dic3—184no—
520Dic3—181no—
521C32—24no—
522C32C4×D3×D414yescomplemented
523C32C4×D3×D411yescharacteristic, complemented
524C23—32no—
525C23—92no—
526C23—278no—
527C23—271no—
528C23—544no—
529C23—544no—
530D4—34no—
531D4—94no—
532D4—278no—
533C2×C4—32no—
534C2×C4—64no—
535C2×C4—92no—
536C2×C4—184no—
537C2×C4—271no—
538C2×C4—271no—
539C2×C4—274no—
540C2×C4—274no—
541C2×C4—271no—
542C2×C4—542no—
543C2×C4—544no—
544C2×C4—544no—
545C2×C4—544no—
546C2×C4C2×D3×C3⋊D311yescharacteristic
547C2×C4C2×D3×C3⋊D311yescharacteristic
548C2×C4C2×D3×C3⋊D311yescharacteristic
549C2×C3—24no—
550C2×C3—24no—
551C2×C3—24no—
552C2×C3—616no—
553C2×C3—184no—
554C2×C3C2×C4×D3214yes—
555C2×C3C2×#380214yes—
556C2×C3#6430614yes—
557C2×C3C22×C4×C3⋊D311yescharacteristic
558C2×C3C2×D4×C3⋊D311yescharacteristic
559C2×C3#41×C3⋊D311yescharacteristic
560D3—24no—
561D3—616no—
562D3—94no—
563D3—916no—
564D3—1816no—
565C22—34no—
566C22—62no—
567C22—62no—
568C22—94no—
569C22—182no—
570C22—182no—
571C22—272no—
572C22—272no—
573C22—272no—
574C22—5416no—
575C22C22×D3×C3⋊D311yescharacteristic
576C4—21no—
577C4—62no—
578C4—182no—
579C4—272no—
580C4—272no—
581C4—541no—
582C4C4×D3×C3⋊D312yescomplemented
583C4#8902612yesdirect product factor
584C3—24no—
585C3C4×#380214yescomplemented
586C3C4×D4×C3⋊D311yescharacteristic, complemented
587C2—64no—
588C2—184no—
589C2—274no—
590C2C2×C4×D3×C3⋊D311yescharacteristic
591C2C2×#8902611yescharacteristic
592C2#1172457811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutatorC2×C33C23×C4
FrattiniC22C22×D3×C3⋊D3
FittingC33×C42C22
socle, cosocleC22×C33C24
prime radicalC2×#89026C2
hypercenterC42D3×C3⋊D3
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×C3⋊D3C2semidirect
3. C42×C3⋊(C3⋊D3)C2semidirect
4. C3×C4×C4⋊(C3⋊D3)C2semidirect
5. C32×C4×D12C2semidirect
6. #11723539C2semidirect
7. #11723508C2semidirect
8. C4×#6290C2semidirect
9. #11723503C2semidirect
10. #11723501C2semidirect
11. #11723499C2semidirect
19. C2×C3×C4×C3⋊D3C22semidirect
21. C2×C32×C4×D3C22semidirect
24. C2×Dic3×C3⋊D3C22semidirect
25. C2×D3×C3⋊Dic3C22semidirect
26. #89026C4direct (N × H)
28. C33×C42C22semidirect
29. C4×C3⋊(C3⋊Dic3)C22semidirect
30. C4×C3⋊(C3⋊Dic3)C22semidirect
31. C4×C3⋊(C3⋊Dic3)C22semidirect
32. C3×#3752C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C32×(C2×D3)⋊C4C22semidirect
35. C32×C4⋊Dic3C22semidirect
36. #88806C22semidirect
37. #88803C22semidirect
38. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. C4×C4⋊(C3⋊D3)D3semidirect
55. C3×C4×D12D3semidirect
67. C2×D3×C3⋊D3C2×C4semidirect
75. C4×C3⋊(C3⋊D3)C2×C4semidirect
76. C4×C3⋊(C3⋊D3)D4semidirect
78. C3×C4⋊(C3⋊D3)C2×C4semidirect
81. C32×D12C2×C4semidirect
83. #6290C2×C4semidirect
109. C2×C4×C3⋊D3C2×D3semidirect
113. C2×C3×C4×D3C2×D3semidirect
123. C32×C42C2×D3semidirect
124. C32×C42C2×D3semidirect
127. #3752C2×D3semidirect
128. C4⋊(C3⋊Dic3)C2×D3semidirect
140. C3×(C2×D3)⋊C4C2×D3semidirect
142. C3×C4⋊Dic3C2×D3semidirect
152. C2×C3×C3⋊D3C22×C4semidirect
155. C2×C32×D3C22×C4semidirect
158. C33×C4C22×C4semidirect
159. C33×C4C2×D4semidirect
161. C3⋊(C3⋊Dic3)C22×C4semidirect
162. C3⋊(C3⋊Dic3)C2×D4semidirect
184. C4×D12C3⋊D3semidirect
225. C4⋊(C3⋊D3)C4×D3semidirect
241. C3×D12C4×D3semidirect
252. C3⋊(C3⋊D3)C4×D4semidirect
285. C2×C4×D3C2×C3⋊D3semidirect
291. C3×C42D32semidirect
292. C3×C42C2×C3⋊D3semidirect
298. (C2×D3)⋊C4C2×C3⋊D3semidirect
300. C4⋊Dic3C2×C3⋊D3semidirect
330. C2×C3⋊D3C2×C4×D3semidirect
336. C2×C3×D3C2×C4×D3semidirect
344. C32×C4C2×C4×D3semidirect
345. C32×C4C2×C4×D3semidirect
346. C32×C4D3×D4semidirect
347. C32×C4D3×D4semidirect
371. C33C2×C4×D4semidirect
416. D12C4×C3⋊D3semidirect
472. C42D3×C3⋊D3semidirect
498. C2×D3C2×C4×C3⋊D3semidirect
506. C3×C4C4×D32semidirect
507. C3×C4#3802semidirect
508. C3×C4C2×C4×C3⋊D3semidirect
509. C3×C4D4×C3⋊D3semidirect
522. C32C4×D3×D4semidirect
523. C32C4×D3×D4semidirect
582. C4C4×D3×C3⋊D3semidirect
583. C4#89026direct (N × H)
585. C3C4×#3802semidirect
586. C3C4×D4×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C2×#890262
C2×C4×D3×C3⋊D32
C42×C3⋊(C3⋊D3)2
C3×C4×C4⋊(C3⋊D3)2
C32×C4×D122
#117235392
#117235082
C4×#62902
#117235032
#117235012
#117234992
C4×D4×C3⋊D33
C4×#38023