Finite Group Databasebeta

← C4×D3×C4⋊(C3⋊D3) #13175393

Subgroups — C4×D3×C4⋊(C3⋊D3) #13175393

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×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C4×D3×C3⋊D3C212yesmaximal, complemented
3C4×C4⋊(C3⋊(C3⋊D3))C211yesmaximal, characteristic, complemented
4C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C32×C42×D3C211yesmaximal, characteristic, complemented
6D3×#3752C212yesmaximal, complemented
7C4×#6292C212yesmaximal, complemented
8#11723484C211yesmaximal, characteristic, complemented
9Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
10D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11#11723471C212yesmaximal, complemented
12C2×C4×C4⋊(C3⋊D3)—31nomaximal
13C4×D3×D12—34nomaximal
14C22×D3×C3⋊D3C2212yes—
15C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
16C2×C4×C3⋊(C3⋊D3)C2212yescomplemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2212yescomplemented
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×#6292C2212yes—
23C2×#6289C2212yescomplemented
24C2×Dic3×C3⋊D3C2212yescomplemented
25C2×D3×C3⋊Dic3C2212yes—
26D3×C4⋊(C3⋊D3)C418yesdirect product factor
27C4×D3×C3⋊D3—28no—
28C33×C42C2211yescharacteristic, complemented
29#88859C2212yescomplemented
30C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
31C3×#3752C2212yescomplemented
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C32×C4×Dic3C2211yescharacteristic, complemented
34C32×C4×Dic3C2211yescharacteristic, complemented
35C32×C4×Dic3C2211yescharacteristic, complemented
36Dic3⋊(C3⋊Dic3)C2212yescomplemented
37#88804C2212yescomplemented
38#88803C2212yescomplemented
39C22×C4⋊(C3⋊D3)—31no—
40C22×C4×C3⋊D3—32no—
41C2×D3×D12—34no—
42C2×C4×D32—38no—
43C2×C32×C42—31no—
44C2×#3752—32no—
45C2×C4⋊(C3⋊Dic3)—31no—
46C4×C4⋊(C3⋊D3)—31no—
47C4×C4⋊(C3⋊D3)—32no—
48C4×C4⋊(C3⋊D3)—31no—
49C4×C4⋊(C3⋊D3)—32no—
50C4×C4⋊(C3⋊D3)—31no—
51C4×C4⋊(C3⋊D3)—34no—
52C4×C4⋊(C3⋊D3)—64no—
53C4×C4⋊(C3⋊D3)D311yescharacteristic, direct product factor
54C3×C4×D12—34no—
55C3×C42×D3D314yescomplemented
56D3×(C2×D3)⋊C4—38no—
57C4×#626—38no—
58#63894—34no—
59Dic3×D12—34no—
60D3×C4⋊Dic3—34no—
61#63880—38no—
62C22×C3⋊(C3⋊D3)C2312yes—
63C22×C3×C3⋊D3C2312yes—
64C22×C32×D3C2311yescharacteristic
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)C2312yes—
72C4⋊(C3⋊(C3⋊D3))C2×C414yescomplemented
73C4×C3⋊(C3⋊D3)—24no—
74C2×C3×C3⋊Dic3C2312yes—
75C3×C4⋊(C3⋊D3)C2×C414yescomplemented
76C3×C4×C3⋊D3—24no—
77C2×C32×Dic3C2311yescharacteristic
78C2×C32×Dic3C2311yescharacteristic
79C2×C32×Dic3C2311yescharacteristic
80C32×C4×D3—22no—
81C32×C4×D3C2×C414yescomplemented
82C32×C4×D3D414yescomplemented
83#6292C2×C418yescomplemented
84#6289—24no—
85Dic3×C3⋊D3—24no—
86D3×C3⋊Dic3—24no—
87C4×D3×D4—91no—
88C2×C4×D12—94no—
89C23×C3⋊D3—32no—
90C22×D32—38no—
91C22×C32×C4—31no—
92C22×C32×C4—31no—
93C22×C32×C4—31no—
94C22×C3⋊Dic3—32no—
95C2×C4⋊(C3⋊D3)—32no—
96C2×C4⋊(C3⋊D3)—31no—
97C2×C4⋊(C3⋊D3)—34no—
98C2×C4⋊(C3⋊D3)—38no—
99C2×C4⋊(C3⋊D3)—64no—
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
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—68no—
107C2×C4×C3⋊D3C2×D312yescomplemented
108C2×C3×D12—34no—
109C2×C3×C4×D3—38no—
110C2×C3×C4×D3C2×D314yes—
111C2×C3×C4×D3C2×D314yes—
112C2×C3×C4×D3C2×D314yes—
113C2×#626—38no—
114C2×#624—38no—
115C2×D3×Dic3—38no—
116C2×D3×Dic3—38no—
117D3×D12—332no—
118C4×D32—632no—
119C32×C42—24no—
120C32×C42—31no—
121C32×C42—31no—
122C32×C42—31no—
123C32×C42C2×D314yescomplemented
124C32×C42C2×D311yescharacteristic, complemented
125#3752—32no—
126#3752—32no—
127#3752—38no—
128#3752—32no—
129#3752—68no—
130#3752C2×D312yescomplemented
131C4⋊(C3⋊Dic3)—31no—
132C4⋊(C3⋊Dic3)—34no—
133C4⋊(C3⋊Dic3)—32no—
134C4⋊(C3⋊Dic3)—64no—
135C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
136C3×(C2×D3)⋊C4—38no—
137C3×C4⋊Dic3—34no—
138C3×C4×Dic3C2×D314yescomplemented
139C3×C4×Dic3C2×D314yescomplemented
140C3×C4×Dic3C2×D314yescomplemented
141Dic3⋊Dic3—38no—
142#3722—38no—
143(C2×D3)⋊Dic3—38no—
144C22×C33C2411yescharacteristic
145C2×C3⋊(C3⋊D3)—22no—
146C2×C3⋊(C3⋊D3)—22no—
147C2×C3⋊(C3⋊D3)C22×C414yescomplemented
148C2×C3×C3⋊D3—22no—
149C2×C3×C3⋊D3—22no—
150C2×C3×C3⋊D3C22×C414yescomplemented
151C2×C32×D3C22×C412yes—
152C2×C32×D3C2×D412yes—
153C2×C32×D3#4112yes—
154D3×C3⋊D3—216no—
155C33×C4—21no—
156C33×C4C22×C412yescomplemented
157C33×C4C2×D412yescomplemented
158C3⋊(C3⋊Dic3)—22no—
159C3×C3⋊Dic3—22no—
160C32×Dic3—21no—
161C32×Dic3C22×C412yescomplemented
162C32×Dic3C2×D412yescomplemented
163C2×D3×D4—91no—
164C22×D12—94no—
165C22×C4×D3—98no—
166C22×C4×D3—92no—
167C3×C4×D4—91no—
168C2×C3×C42—34no—
169D4×Dic3—91no—
170C4×#67—92no—
171C2×(C2×D3)⋊C4—98no—
172C2×C4⋊Dic3—94no—
173#893—91no—
174D3×C4⋊C4—91no—
175#67⋊C4—92no—
176D3×C22⋊C4—92no—
177C4×D12—34no—
178C4×D12—94no—
179C4×D12—98no—
180C4×D12—98no—
181C4×D12—94no—
182C4×D12—94no—
183C4×D12—91no—
184C4×D12—184no—
185C42×D3C3⋊D311yescharacteristic, complemented
186C23×C32—31no—
187C22×C3⋊D3—32no—
188C22×C3⋊D3—38no—
189C22×C3⋊D3—38no—
190C22×C3⋊D3—68no—
191C22×C3⋊D3—64no—
192C22×C3⋊D3—64no—
193C22×C3⋊D3C22×D312yes—
194C22×C3×D3—38no—
195C22×C3×D3C22×D314yes—
196C2×D32—332no—
197C2×D32—616no—
198C2×D32—616no—
199C2×C32×C4—24no—
200C2×C32×C4—24no—
201C2×C32×C4—24no—
202C2×C32×C4—31no—
203C2×C32×C4—31no—
204C2×C32×C4—34no—
205C2×C32×C4—34no—
206C2×C32×C4—31no—
207C2×C32×C4—62no—
208C2×C32×C4C22×D314yes—
209C2×C32×C4C22×D314yes—
210C2×C32×C4C22×D314yes—
211C2×C32×C4C22×D311yescharacteristic
212C2×C32×C4C22×D311yescharacteristic
213C2×C32×C4C22×D311yescharacteristic
214C2×C3⋊Dic3—32no—
215C2×C3⋊Dic3—38no—
216C2×C3⋊Dic3—68no—
217C2×C3⋊Dic3—64no—
218C2×C3⋊Dic3C22×D312yes—
219C4⋊(C3⋊D3)—38no—
220C4⋊(C3⋊D3)—34no—
221C4⋊(C3⋊D3)—316no—
222C4⋊(C3⋊D3)—616no—
223C4⋊(C3⋊D3)C4×D314yesdirect product factor
224C4×C3⋊D3—24no—
225C4×C3⋊D3—64no—
226C4×C3⋊D3—64no—
227C4×C3⋊D3—64no—
228C4×C3⋊D3—616no—
229C4×C3⋊D3—1216no—
230C2×C3×Dic3—38no—
231C2×C3×Dic3C22×D314yes—
232C2×C3×Dic3C22×D314yes—
233C2×C3×Dic3C22×D314yes—
234C3×D12—316no—
235C3×C4×D3—28no—
236C3×C4×D3—616no—
237C3×C4×D3C4×D3116yescomplemented
238C3×C4×D3D12116yescomplemented
239#626—332no—
240#624—616no—
241D3×Dic3—616no—
242D3×Dic3—616no—
243C2×C4×D4—271noSylow
244C2×C33C23×C411yescharacteristic
245C2×C33C22×D411yescharacteristic
246C2×C33C2×#4111yescharacteristic
247C3⋊(C3⋊D3)—24no—
248C3×C3⋊D3—24no—
249C32×D3C4×D414yescomplemented
250C23×D3—98no—
251C23×D3—92no—
252C2×C3×D4—91no—
253C22×C3×C4—34no—
254C22×C3×C4—34no—
255C22×C3×C4—34no—
256C22×C3×C4—92no—
257C2×#67—92no—
258C22×Dic3—98no—
259C22×Dic3—92no—
260D3×D4—98no—
261C2×D12—34no—
262C2×D12—932no—
263C2×D12—98no—
264C2×D12—94no—
265C2×D12—91no—
266C2×D12—184no—
267C2×C4×D3—38no—
268C2×C4×D3—98no—
269C2×C4×D3—98no—
270C2×C4×D3—92no—
271C2×C4×D3—98no—
272C2×C4×D3—92no—
273C2×C4×D3—92no—
274C2×C4×D3—188no—
275C2×C4×D3—1832no—
276C2×C4×D3—188no—
277C2×C4×D3C2×C3⋊D311yescharacteristic
278C2×C4×D3C2×C3⋊D311yescharacteristic
279C2×C4×D3C2×C3⋊D311yescharacteristic
280C3×C4⋊C4—91no—
281C3×C22⋊C4—92no—
282C3×C42—24no—
283C3×C42—34no—
284C3×C42—34no—
285C3×C42—34no—
286C3×C42D3214yescomplemented
287C3×C42C2×C3⋊D311yescharacteristic, complemented
288#217—92no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—98no—
291(C2×D3)⋊C4—98no—
292(C2×D3)⋊C4—98no—
293(C2×D3)⋊C4—92no—
294(C2×D3)⋊C4—92no—
295(C2×D3)⋊C4—188no—
296C4⋊Dic3—34no—
297C4⋊Dic3—98no—
298C4⋊Dic3—94no—
299C4⋊Dic3—91no—
300C4⋊Dic3—184no—
301Dic3⋊C4—92no—
302C4×Dic3C2×C3⋊D311yescharacteristic, complemented
303C4×Dic3C2×C3⋊D311yescharacteristic, complemented
304C4×Dic3C2×C3⋊D311yescharacteristic, complemented
305C22×C32—24no—
306C22×C32—32no—
307C22×C32—32no—
308C22×C32—32no—
309C22×C32C23×D314yes—
310C22×C32C23×D311yescharacteristic
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3—34no—
314C2×C3⋊D3—316no—
315C2×C3⋊D3—616no—
316C2×C3⋊D3—616no—
317C2×C3⋊D3—62no—
318C2×C3⋊D3—62no—
319C2×C3⋊D3—68no—
320C2×C3⋊D3—68no—
321C2×C3⋊D3—128no—
322C2×C3⋊D3—128no—
323C2×C3⋊D3C2×C4×D314yescomplemented
324C2×C3×D3—316no—
325C2×C3×D3—68no—
326C2×C3×D3—68no—
327C2×C3×D3C2×C4×D318yes—
328C2×C3×D3C2×D1218yes—
329C2×C3×D3#23518yes—
330D32—664no—
331C32×C4—21no—
332C32×C4—28no—
333C32×C4—28no—
334C32×C4—24no—
335C32×C4—32no—
336C32×C4—32no—
337C32×C4—44no—
338C32×C4—61no—
339C32×C4C2×C4×D318yescomplemented
340C32×C4C2×C4×D312yescomplemented
341C32×C4C2×D1218yescomplemented
342C32×C4D3×D412yescomplemented
343C3⋊Dic3—22no—
344C3⋊Dic3—62no—
345C3⋊Dic3—68no—
346C3⋊Dic3—128no—
347C3×Dic3—24no—
348C3×Dic3—68no—
349C3×Dic3C2×C4×D318yescomplemented
350C3×Dic3C2×D1218yescomplemented
351C22×D4—271no—
352C23×C4—272no—
353C4×D4—91no—
354C4×D4—272no—
355C4×D4—271no—
356C4×D4—272no—
357C4×D4—271no—
358C4×D4—271no—
359C2×C4⋊C4—271no—
360C2×C22⋊C4—272no—
361C2×C42—31no—
362C33C2×C4×D411yescharacteristic, complemented, Sylow
363C23×C3—34no—
364C23×C3—92no—
365C22×D3—38no—
366C22×D3—932no—
367C22×D3—98no—
368C22×D3—92no—
369C22×D3—98no—
370C22×D3—188no—
371C22×D3—1816no—
372C22×D3—1816no—
373C22×D3—184no—
374C22×D3—184no—
375C22×D3C22×C3⋊D311yescharacteristic
376C3×D4—94no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—34no—
381C2×C3×C4—34no—
382C2×C3×C4—316no—
383C2×C3×C4—316no—
384C2×C3×C4—34no—
385C2×C3×C4—68no—
386C2×C3×C4—92no—
387C2×C3×C4—184no—
388C2×C3×C4C2×D3214yes—
389C2×C3×C4C2×D3214yes—
390C2×C3×C4C2×D3214yes—
391C2×C3×C4C22×C3⋊D311yescharacteristic
392C2×C3×C4C22×C3⋊D311yescharacteristic
393C2×C3×C4C22×C3⋊D311yescharacteristic
394#67—98no—
395C2×Dic3—38no—
396C2×Dic3—98no—
397C2×Dic3—92no—
398C2×Dic3—188no—
399C2×Dic3—1816no—
400C2×Dic3—184no—
401C2×Dic3C22×C3⋊D311yescharacteristic
402C2×Dic3C22×C3⋊D311yescharacteristic
403C2×Dic3C22×C3⋊D311yescharacteristic
404D12—316no—
405D12—932no—
406D12—916no—
407D12—94no—
408D12—1816no—
409C4×D3—22no—
410C4×D3—616no—
411C4×D3—1816no—
412C4×D3—1816no—
413C4×D3—184no—
414C4×D3—1816no—
415C4×D3—184no—
416C4×D3—184no—
417C4×D3—3616no—
418C4×D3C4×C3⋊D314yescomplemented
419C4×D3C4⋊(C3⋊D3)14yesdirect product factor
420C2×C32—24no—
421C2×C32—24no—
422C2×C32—24no—
423C2×C32—34no—
424C2×C32C22×C4×D314yes—
425C2×C32C22×C4×D311yescharacteristic
426C2×C32C22×D1214yes—
427C2×C32C2×#23514yes—
428C2×C32C2×D3×D411yescharacteristic
429C2×C32D3×#4111yescharacteristic
430C3⋊D3—24no—
431C3⋊D3—64no—
432C3⋊D3—616no—
433C3⋊D3—1216no—
434C3×D3—616no—
435C3×D3C4×D12116yescomplemented
436C24—272no—
437C2×D4—91no—
438C2×D4—278no—
439C2×D4—272no—
440C2×D4—271no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—92no—
445C22×C4—272no—
446C22×C4—272no—
447C22×C4—272no—
448C22×C4—272no—
449C22×C4—548no—
450C4⋊C4—91no—
451C4⋊C4—272no—
452C4⋊C4—271no—
453C22⋊C4—92no—
454C22⋊C4—272no—
455C22⋊C4—272no—
456C22⋊C4—272no—
457C42—31no—
458C42—31no—
459C42—31no—
460C42D3×C3⋊D311yescharacteristic, complemented
461C22×C3—24no—
462C22×C3—38no—
463C22×C3—38no—
464C22×C3—38no—
465C22×C3—94no—
466C22×C3—182no—
467C22×C3—182no—
468C22×C3C22×D3214yes—
469C22×C3C23×C3⋊D311yescharacteristic
470C2×D3—316no—
471C2×D3—68no—
472C2×D3—68no—
473C2×D3—916no—
474C2×D3—94no—
475C2×D3—1816no—
476C2×D3—1864no—
477C2×D3—188no—
478C2×D3—188no—
479C2×D3—182no—
480C2×D3—182no—
481C2×D3—1816no—
482C2×D3—368no—
483C2×D3—368no—
484C2×D3C2×C4×C3⋊D312yes—
485C2×D3C2×C4⋊(C3⋊D3)12yes—
486C2×D3#382812yes—
487C3×C4—24no—
488C3×C4—21no—
489C3×C4—28no—
490C3×C4—28no—
491C3×C4—38no—
492C3×C4—38no—
493C3×C4—44no—
494C3×C4—64no—
495C3×C4—182no—
496C3×C4C4×D3218yescomplemented
497C3×C4D3×D1218yescomplemented
498C3×C4C2×C4×C3⋊D312yescomplemented
499C3×C4C2×C4⋊(C3⋊D3)12yescomplemented
500Dic3—21no—
501Dic3—68no—
502Dic3—188no—
503Dic3—182no—
504Dic3—368no—
505Dic3C2×C4×C3⋊D312yescomplemented
506Dic3C2×C4⋊(C3⋊D3)12yescomplemented
507C32—24no—
508C32C2×C4×D1214yescomplemented
509C32C4×D3×D411yescharacteristic, complemented
510C23—31no—
511C23—92no—
512C23—278no—
513C23—272no—
514C23—544no—
515C23—544no—
516D4—94no—
517D4—278no—
518D4—274no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—34no—
522C2×C4—34no—
523C2×C4—31no—
524C2×C4—62no—
525C2×C4—92no—
526C2×C4—184no—
527C2×C4—272no—
528C2×C4—544no—
529C2×C4—544no—
530C2×C4—544no—
531C2×C4—544no—
532C2×C4C2×D3×C3⋊D311yescharacteristic
533C2×C4C2×D3×C3⋊D311yescharacteristic
534C2×C4C2×D3×C3⋊D311yescharacteristic
535C2×C3—24no—
536C2×C3—24no—
537C2×C3—24no—
538C2×C3—316no—
539C2×C3—184no—
540C2×C3C2×C4×D3214yes—
541C2×C3C2×D3×D1214yes—
542C2×C3D3×#23514yes—
543C2×C3C22×C4×C3⋊D311yescharacteristic
544C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
545C2×C3C2×#382811yescharacteristic
546D3—616no—
547D3—184no—
548D3—1816no—
549D3—3616no—
550D3C4×C4⋊(C3⋊D3)14yesdirect product factor
551C22—32no—
552C22—32no—
553C22—32no—
554C22—94no—
555C22—182no—
556C22—182no—
557C22—274no—
558C22—5416no—
559C22—542no—
560C22—542no—
561C22C22×D3×C3⋊D311yescharacteristic
562C4—21no—
563C4—32no—
564C4—32no—
565C4—61no—
566C4—182no—
567C4—542no—
568C4C4×D3×C3⋊D312yescomplemented
569C4D3×C4⋊(C3⋊D3)12yesdirect product factor
570C3—24no—
571C3C4×D3×D1214yescomplemented
572C3C2×C4×C4⋊(C3⋊D3)11yescharacteristic, complemented
573C2—34no—
574C2—184no—
575C2—544no—
576C2C2×C4×D3×C3⋊D311yescharacteristic
577C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
578C2D3×#382811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutatorC2×C33C23×C4
FrattiniC22C22×D3×C3⋊D3
FittingC33×C42C22
socle, cosocleC22×C33C24
prime radicalC2×D3×C4⋊(C3⋊D3)C2
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. C4×C4⋊(C3⋊(C3⋊D3))C2semidirect
4. C3×C4×C4⋊(C3⋊D3)C2semidirect
5. C32×C42×D3C2semidirect
6. D3×#3752C2semidirect
7. C4×#6292C2semidirect
8. #11723484C2semidirect
9. Dic3×C4⋊(C3⋊D3)C2semidirect
10. D3×C4⋊(C3⋊Dic3)C2semidirect
11. #11723471C2semidirect
16. C2×C4×C3⋊(C3⋊D3)C22semidirect
18. C2×C3×C4×C3⋊D3C22semidirect
23. C2×#6289C22semidirect
24. C2×Dic3×C3⋊D3C22semidirect
26. D3×C4⋊(C3⋊D3)C4direct (N × H)
28. C33×C42C22semidirect
29. #88859C22semidirect
30. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
31. C3×#3752C22semidirect
32. C3×C4⋊(C3⋊Dic3)C22semidirect
33. C32×C4×Dic3C22semidirect
34. C32×C4×Dic3C22semidirect
35. C32×C4×Dic3C22semidirect
36. Dic3⋊(C3⋊Dic3)C22semidirect
37. #88804C22semidirect
38. #88803C22semidirect
53. C4×C4⋊(C3⋊D3)D3direct (N × H)
55. C3×C42×D3D3semidirect
67. C2×D3×C3⋊D3C2×C4semidirect
72. C4⋊(C3⋊(C3⋊D3))C2×C4semidirect
75. C3×C4⋊(C3⋊D3)C2×C4semidirect
81. C32×C4×D3C2×C4semidirect
82. C32×C4×D3D4semidirect
83. #6292C2×C4semidirect
107. C2×C4×C3⋊D3C2×D3semidirect
123. C32×C42C2×D3semidirect
124. C32×C42C2×D3semidirect
130. #3752C2×D3semidirect
135. C4⋊(C3⋊Dic3)C2×D3semidirect
138. C3×C4×Dic3C2×D3semidirect
139. C3×C4×Dic3C2×D3semidirect
140. C3×C4×Dic3C2×D3semidirect
147. C2×C3⋊(C3⋊D3)C22×C4semidirect
150. C2×C3×C3⋊D3C22×C4semidirect
156. C33×C4C22×C4semidirect
157. C33×C4C2×D4semidirect
161. C32×Dic3C22×C4semidirect
162. C32×Dic3C2×D4semidirect
185. C42×D3C3⋊D3semidirect
223. C4⋊(C3⋊D3)C4×D3direct (N × H)
237. C3×C4×D3C4×D3semidirect
238. C3×C4×D3D12semidirect
249. C32×D3C4×D4semidirect
286. C3×C42D32semidirect
287. C3×C42C2×C3⋊D3semidirect
302. C4×Dic3C2×C3⋊D3semidirect
303. C4×Dic3C2×C3⋊D3semidirect
304. C4×Dic3C2×C3⋊D3semidirect
323. C2×C3⋊D3C2×C4×D3semidirect
339. C32×C4C2×C4×D3semidirect
340. C32×C4C2×C4×D3semidirect
341. C32×C4C2×D12semidirect
342. C32×C4D3×D4semidirect
349. C3×Dic3C2×C4×D3semidirect
350. C3×Dic3C2×D12semidirect
362. C33C2×C4×D4semidirect
418. C4×D3C4×C3⋊D3semidirect
419. C4×D3C4⋊(C3⋊D3)direct (N × H)
435. C3×D3C4×D12semidirect
460. C42D3×C3⋊D3semidirect
496. C3×C4C4×D32semidirect
497. C3×C4D3×D12semidirect
498. C3×C4C2×C4×C3⋊D3semidirect
499. C3×C4C2×C4⋊(C3⋊D3)semidirect
505. Dic3C2×C4×C3⋊D3semidirect
506. Dic3C2×C4⋊(C3⋊D3)semidirect
508. C32C2×C4×D12semidirect
509. C32C4×D3×D4semidirect
550. D3C4×C4⋊(C3⋊D3)direct (N × H)
568. C4C4×D3×C3⋊D3semidirect
569. C4D3×C4⋊(C3⋊D3)direct (N × H)
571. C3C4×D3×D12semidirect
572. C3C2×C4×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×D3×C4⋊(C3⋊D3)2
C2×C4×D3×C3⋊D32
C4×C4⋊(C3⋊(C3⋊D3))2
C3×C4×C4⋊(C3⋊D3)2
C32×C42×D32
D3×#37522
C4×#62922
#117234842
Dic3×C4⋊(C3⋊D3)2
D3×C4⋊(C3⋊Dic3)2
#117234712
C2×C4×C4⋊(C3⋊D3)3
C4×D3×D123