Finite Group Databasebeta

← C4×D3×#638 #13177293

Subgroups — C4×D3×#638 #13177293

Order 1728.

2932 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×D3×#638C211yesmaximal, characteristic
3C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
4C4×#6312C211yesmaximal, characteristic, complemented
5C3×C4×#638C211yesmaximal, characteristic, complemented
6#11723618C211yesmaximal, characteristic, complemented
7Dic3×#638C211yesmaximal, characteristic, complemented
8D3×#3757C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10#11723510C211yesmaximal, characteristic, complemented
11C4×#6291C211yesmaximal, characteristic, complemented
12#11723506C211yesmaximal, characteristic, complemented
13C4×#6290C211yesmaximal, characteristic, complemented
14D3×#3750C211yesmaximal, characteristic, complemented
15C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
16C2×C4×#638—31nomaximal
17C4×D3×#67—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×C32×C4×D3—24no—
27C2×C32×C4×D3C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C2×C32×C4×D3C2211yescharacteristic, complemented
31D3×#638C418yesdirect product factor
32C2×#6291C2211yescharacteristic
33C2×#6290C2211yescharacteristic
34C2×#6289C2211yescharacteristic, complemented
35C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
36C2×D3×C3⋊Dic3C2211yescharacteristic
37C2×D3×C3⋊Dic3C2211yescharacteristic
38C2×D3×C3⋊Dic3C2211yescharacteristic
39C4×D3×C3⋊D3—24no—
40#88864C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42#88857C2211yescharacteristic, complemented
43C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C3×#3757C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×#3750C2211yescharacteristic, complemented
47C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55Dic3×C3⋊Dic3C2211yescharacteristic, complemented
56C23×C32×C4—31no—
57C22×#638—31no—
58C22×C4×C3⋊D3—31no—
59C22×C3×C4×D3D314yescomplemented
60C2×D3×#67—34no—
61C2×C4×D32—34no—
62C2×#3757—31no—
63C4×#638—31no—
64C4×#638—31no—
65C4×#638—31no—
66C4×#638—31no—
67C4×#638—31no—
68C4×#638—31no—
69C4×#638—31no—
70C4×#638—34no—
71C4×#638—64no—
72C4×#638D311yescharacteristic, direct product factor
73C2×#3752—31no—
74C2×#3750—31no—
75C2×C4×C3⋊Dic3—31no—
76C3×C4×#67—34no—
77Dic3×#67—34no—
78D3×#217—34no—
79#63952—34no—
80D3×(C2×D3)⋊C4—34no—
81#63904—34no—
82C4×#626—34no—
83C4×#625—34no—
84#63879—34no—
85D3×Dic3⋊C4—34no—
86C4×D3×Dic3—34no—
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3C2×C414yescomplemented
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3C2×C414yescomplemented
98C2×C33×C4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101#6312C2×C414yescomplemented
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4×C3⋊(C3⋊D3)—22no—
106C3×#638C2×C414yescomplemented
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C3×C4×C3⋊D3—22no—
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×C4×D3—22no—
115C32×C4×D3—22no—
116C32×C4×D3—22no—
117C32×C4×D3D414yescomplemented
118#6291C2×C414yescomplemented
119#6290C2×C414yescomplemented
120#6289—22no—
121Dic3×C3⋊D3—22no—
122D3×C3⋊Dic3—22no—
123D3×C3⋊Dic3—22no—
124D3×C3⋊Dic3C2×C414yescomplemented
125C2×C4×#67—94no—
126C4×D3×D4—91no—
127C24×C32—31no—
128C23×C3⋊D3—31no—
129C23×C3×D3C2×D314yes—
130C22×D32—34no—
131C22×C32×C4—24no—
132C22×C32×C4—31no—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C22×C32×C4—31no—
137C22×C32×C4—64no—
138C22×C32×C4C2×D314yescomplemented
139C22×C32×C4C2×D311yescharacteristic, complemented
140C2×#638—31no—
141C2×#638—34no—
142C2×#638—31no—
143C2×#638—38no—
144C2×#638—31no—
145C2×#638—64no—
146C2×#638C2×D311yescharacteristic
147C22×C3⋊Dic3—31no—
148C22×C3⋊Dic3—31no—
149C22×C3⋊Dic3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—34no—
153C2×C4×C3⋊D3—31no—
154C2×C4×C3⋊D3—64no—
155C2×C4×C3⋊D3—64no—
156C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
157C2×C3×#67—34no—
158C22×C3×Dic3C2×D314yescomplemented
159C2×C3×C4×D3—216no—
160C2×C3×C4×D3—34no—
161C2×C3×C4×D3C2×D314yes—
162C2×C3×C4×D3C2×D314yes—
163C2×C3×C4×D3C2×D314yescomplemented
164C2×C3×C4×D3C2×D314yescomplemented
165D3×#67—332no—
166C2×#626—34no—
167C2×#625—34no—
168C2×#624—34no—
169C2×D3×Dic3—34no—
170C2×D3×Dic3—34no—
171C2×D3×Dic3—34no—
172C2×D3×Dic3—34no—
173C4×D32—616no—
174#3757—31no—
175#3757—34no—
176#3757—31no—
177#3757—31no—
178#3757—64no—
179#3757C2×D311yescharacteristic, complemented
180#3752—31no—
181#3752—31no—
182#3752—34no—
183#3752—31no—
184#3752—64no—
185#3752C2×D311yescharacteristic, complemented
186#3750—31no—
187#3750—34no—
188#3750—31no—
189#3750—31no—
190#3750—64no—
191#3750C2×D311yescharacteristic, complemented
192C4×C3⋊Dic3—31no—
193C4×C3⋊Dic3—34no—
194C4×C3⋊Dic3—31no—
195C4×C3⋊Dic3—31no—
196C4×C3⋊Dic3—64no—
197C4×C3⋊Dic3C2×D311yescharacteristic, complemented
198C3×#217—34no—
199C3×(C2×D3)⋊C4—34no—
200C3×Dic3⋊C4—34no—
201C3×C4×Dic3—34no—
202#3724—34no—
203Dic3⋊Dic3—34no—
204#3722—34no—
205(C2×D3)⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208Dic32—34no—
209Dic32—34no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C22×C412yescomplemented
213C22×C33C2411yescharacteristic
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)C22×C412yescomplemented
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3C22×C412yescomplemented
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—28no—
223C2×C32×D3C22×C412yes—
224C2×C32×D3C22×C412yescomplemented
225C2×C32×D3C2×D412yes—
226C2×C32×D3#4112yes—
227D3×C3⋊D3—28no—
228C33×C4—21no—
229C33×C4C2×D412yescomplemented
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)—21no—
232C3⋊(C3⋊Dic3)C22×C412yescomplemented
233C3×C3⋊Dic3—21no—
234C3×C3⋊Dic3—21no—
235C3×C3⋊Dic3C22×C412yescomplemented
236C32×Dic3—21no—
237C32×Dic3C2×D412yescomplemented
238C23×C3×C4—34no—
239C22×#67—94no—
240C2×D3×D4—91no—
241C22×C4×D3—94no—
242C22×C4×D3—91no—
243C22×C4×D3C3⋊D311yescharacteristic, complemented
244C3×C4×D4—91no—
245C2×#217—94no—
246D4×Dic3—91no—
247C4×#67—34no—
248C4×#67—94no—
249C4×#67—94no—
250C4×#67—94no—
251C4×#67—94no—
252C4×#67—94no—
253C4×#67—94no—
254C4×#67—94no—
255C4×#67—91no—
256C4×#67—91no—
257C4×#67—184no—
258C2×(C2×D3)⋊C4—94no—
259C2×Dic3⋊C4—94no—
260C2×C4×Dic3—94no—
261#893—91no—
262D3×C4⋊C4—91no—
263#67⋊C4—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267C4×D12—91no—
268C42×D3—91no—
269C23×C32—24no—
270C23×C32—31no—
271C23×C32—34no—
272C23×C32—31no—
273C23×C32—62no—
274C23×C32—62no—
275C23×C32C22×D314yes—
276C23×C32C22×D311yescharacteristic
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—64no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3C22×D311yescharacteristic
284C22×C3×D3—28no—
285C22×C3×D3—28no—
286C22×C3×D3—34no—
287C22×C3×D3C4×D3116yescomplemented
288C22×C3×D3C22×D314yes—
289C22×C3×D3C22×D314yes—
290C2×D32—316no—
291C2×D32—68no—
292C2×D32—68no—
293C2×C32×C4—22no—
294C2×C32×C4—24no—
295C2×C32×C4—24no—
296C2×C32×C4—28no—
297C2×C32×C4—31no—
298C2×C32×C4—34no—
299C2×C32×C4—31no—
300C2×C32×C4—48no—
301C2×C32×C4—62no—
302C2×C32×C4—62no—
303C2×C32×C4—62no—
304C2×C32×C4—62no—
305C2×C32×C4C22×D314yes—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D311yescharacteristic
308C2×C32×C4C22×D311yescharacteristic
309#638—34no—
310#638—34no—
311#638—34no—
312#638—316no—
313#638—616no—
314#638C4×D314yesdirect product factor
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—31no—
318C2×C3⋊Dic3—31no—
319C2×C3⋊Dic3—34no—
320C2×C3⋊Dic3—34no—
321C2×C3⋊Dic3—34no—
322C2×C3⋊Dic3—64no—
323C2×C3⋊Dic3—64no—
324C2×C3⋊Dic3—64no—
325C2×C3⋊Dic3—62no—
326C2×C3⋊Dic3—62no—
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4×C3⋊D3—22no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—62no—
334C4×C3⋊D3—68no—
335C4×C3⋊D3—128no—
336C3×#67—316no—
337C2×C3×Dic3—28no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3C22×D314yes—
342C2×C3×Dic3C22×D314yes—
343C3×C4×D3—28no—
344C3×C4×D3—28no—
345C3×C4×D3—28no—
346C3×C4×D3—68no—
347C3×C4×D3#67116yescomplemented
348#626—316no—
349#625—316no—
350#624—68no—
351D3×Dic3—316no—
352D3×Dic3—68no—
353D3×Dic3—68no—
354D3×Dic3—68no—
355C2×C4×D4—271noSylow
356C2×C33—22no—
357C2×C33C23×C411yescharacteristic
358C2×C33C22×D411yescharacteristic
359C2×C33C2×#4111yescharacteristic
360C3⋊(C3⋊D3)—22no—
361C3×C3⋊D3—22no—
362C32×D3—22no—
363C32×D3C4×D414yescomplemented
364C24×C3—34no—
365C23×D3—94no—
366C23×D3—91no—
367C23×D3C2×C3⋊D311yescharacteristic
368C2×C3×D4—91no—
369C22×C3×C4—24no—
370C22×C3×C4—34no—
371C22×C3×C4—34no—
372C22×C3×C4—34no—
373C22×C3×C4—34no—
374C22×C3×C4—34no—
375C22×C3×C4—616no—
376C22×C3×C4—91no—
377C22×C3×C4D3214yescomplemented
378C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
379C2×#67—34no—
380C2×#67—94no—
381C2×#67—932no—
382C2×#67—94no—
383C2×#67—94no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—184no—
387C22×Dic3—94no—
388C22×Dic3—94no—
389C22×Dic3—94no—
390C22×Dic3—91no—
391C22×Dic3C2×C3⋊D311yescharacteristic, complemented
392D3×D4—98no—
393C2×D12—91no—
394C2×C4×D3—24no—
395C2×C4×D3—34no—
396C2×C4×D3—91no—
397C2×C4×D3—94no—
398C2×C4×D3—94no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—184no—
405C2×C4×D3—1816no—
406C2×C4×D3—184no—
407C2×C4×D3C2×C3⋊D311yescharacteristic
408C2×C4×D3C2×C3⋊D311yescharacteristic
409C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
410C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
411C3×C4⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4—91no—
414C3×C42—91no—
415#217—34no—
416#217—94no—
417#217—94no—
418#217—94no—
419#217—91no—
420#217—91no—
421#217—184no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—184no—
431C4⋊Dic3—91no—
432Dic3⋊C4—34no—
433Dic3⋊C4—94no—
434Dic3⋊C4—94no—
435Dic3⋊C4—94no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—184no—
439C4×Dic3—34no—
440C4×Dic3—94no—
441C4×Dic3—94no—
442C4×Dic3—94no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—184no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—24no—
450C22×C32—28no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—32no—
454C22×C32—32no—
455C22×C32—32no—
456C22×C32—32no—
457C22×C32—44no—
458C22×C32—44no—
459C22×C32—68no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32C2×C4×D318yescomplemented
463C22×C32C2×C4×D312yescomplemented
464C22×C32C23×D314yes—
465C22×C32C23×D311yescharacteristic
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—32no—
469C2×C3⋊D3—38no—
470C2×C3⋊D3—68no—
471C2×C3⋊D3—68no—
472C2×C3⋊D3—61no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—64no—
475C2×C3⋊D3—64no—
476C2×C3⋊D3—124no—
477C2×C3⋊D3—124no—
478C2×C3⋊D3C2×C4×D312yescomplemented
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—232no—
482C2×C3×D3—38no—
483C2×C3×D3—64no—
484C2×C3×D3—64no—
485C2×C3×D3C2×C4×D318yes—
486C2×C3×D3C2×C4×D318yescomplemented
487C2×C3×D3#23518yes—
488C2×C3×D3C2×#6718yes—
489D32—632no—
490C32×C4—21no—
491C32×C4—28no—
492C32×C4—24no—
493C32×C4—32no—
494C32×C4—44no—
495C32×C4—61no—
496C32×C4D3×D412yescomplemented
497C32×C4C2×#6718yescomplemented
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3⋊Dic3—32no—
501C3⋊Dic3—38no—
502C3⋊Dic3—68no—
503C3⋊Dic3—61no—
504C3⋊Dic3—61no—
505C3⋊Dic3—64no—
506C3⋊Dic3—64no—
507C3⋊Dic3—124no—
508C3⋊Dic3—124no—
509C3⋊Dic3C2×C4×D312yescomplemented
510C3×Dic3—24no—
511C3×Dic3—38no—
512C3×Dic3—64no—
513C3×Dic3—64no—
514C3×Dic3C2×#6718yescomplemented
515C22×D4—271no—
516C23×C4—31no—
517C23×C4—271no—
518C4×D4—91no—
519C4×D4—271no—
520C4×D4—271no—
521C4×D4—271no—
522C4×D4—271no—
523C4×D4—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C4⋊C4—271no—
527C2×C22⋊C4—271no—
528C2×C22⋊C4—271no—
529C2×C42—271no—
530C33C2×C4×D411yescharacteristic, complemented, Sylow
531C23×C3—24no—
532C23×C3—34no—
533C23×C3—34no—
534C23×C3—316no—
535C23×C3—68no—
536C23×C3—68no—
537C23×C3—91no—
538C23×C3C2×D3214yes—
539C23×C3C22×C3⋊D311yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—34no—
543C22×D3—916no—
544C22×D3—94no—
545C22×D3—91no—
546C22×D3—94no—
547C22×D3—184no—
548C22×D3—188no—
549C22×D3—188no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3C4×C3⋊D314yescomplemented
553C22×D3C22×C3⋊D311yescharacteristic
554C22×D3C22×C3⋊D311yescharacteristic
555C3×D4—94no—
556C2×C3×C4—28no—
557C2×C3×C4—22no—
558C2×C3×C4—24no—
559C2×C3×C4—24no—
560C2×C3×C4—34no—
561C2×C3×C4—316no—
562C2×C3×C4—34no—
563C2×C3×C4—48no—
564C2×C3×C4—68no—
565C2×C3×C4—68no—
566C2×C3×C4—68no—
567C2×C3×C4—68no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—182no—
572C2×C3×C4C2×D3214yes—
573C2×C3×C4C2×D3214yes—
574C2×C3×C4C22×C3⋊D311yescharacteristic
575C2×C3×C4C22×C3⋊D311yescharacteristic
576#67—316no—
577#67—916no—
578#67—916no—
579#67—916no—
580#67—94no—
581#67—94no—
582#67—1816no—
583C2×Dic3—22no—
584C2×Dic3—34no—
585C2×Dic3—34no—
586C2×Dic3—34no—
587C2×Dic3—916no—
588C2×Dic3—94no—
589C2×Dic3—91no—
590C2×Dic3—94no—
591C2×Dic3—94no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—184no—
595C2×Dic3—184no—
596C2×Dic3—184no—
597C2×Dic3—188no—
598C2×Dic3—188no—
599C2×Dic3—182no—
600C2×Dic3C22×C3⋊D311yescharacteristic
601C2×Dic3C22×C3⋊D311yescharacteristic
602D12—94no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—22no—
606C4×D3—68no—
607C4×D3—94no—
608C4×D3—188no—
609C4×D3—188no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—188no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—368no—
616C4×D3#63814yesdirect product factor
617C2×C32—22no—
618C2×C32—24no—
619C2×C32—24no—
620C2×C32—24no—
621C2×C32—28no—
622C2×C32—34no—
623C2×C32—48no—
624C2×C32—62no—
625C2×C32C22×C4×D314yes—
626C2×C32C22×C4×D311yescharacteristic
627C2×C32C2×#23514yes—
628C2×C32C2×D3×D411yescharacteristic
629C2×C32D3×#4111yescharacteristic
630C2×C32C22×#6714yes—
631C3⋊D3—22no—
632C3⋊D3—62no—
633C3⋊D3—68no—
634C3⋊D3—128no—
635C3×D3—28no—
636C3×D3—68no—
637C3×D3C4×#67116yescomplemented
638C24—31no—
639C24—271no—
640C2×D4—91no—
641C2×D4—271no—
642C2×D4—278no—
643C2×D4—271no—
644C2×D4—271no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—64no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C22×C4—271no—
658C22×C4—544no—
659C22×C4D3×C3⋊D311yescharacteristic, complemented
660C4⋊C4—91no—
661C4⋊C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C42—91no—
673C42—271no—
674C42—271no—
675C42—271no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—24no—
681C22×C3—28no—
682C22×C3—38no—
683C22×C3—38no—
684C22×C3—38no—
685C22×C3—38no—
686C22×C3—44no—
687C22×C3—44no—
688C22×C3—632no—
689C22×C3—64no—
690C22×C3—64no—
691C22×C3—92no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3C4×D3218yescomplemented
695C22×C3C2×C4×C3⋊D312yescomplemented
696C22×C3C22×D3214yes—
697C22×C3C23×C3⋊D311yescharacteristic
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—28no—
701C2×D3—38no—
702C2×D3—64no—
703C2×D3—64no—
704C2×D3—98no—
705C2×D3—92no—
706C2×D3—188no—
707C2×D3—1832no—
708C2×D3—184no—
709C2×D3—184no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—188no—
713C2×D3—364no—
714C2×D3—364no—
715C2×D3C2×C4×C3⋊D312yes—
716C2×D3C2×C4×C3⋊D312yescomplemented
717C2×D3#382812yes—
718C2×D3C2×#63812yes—
719C3×C4—24no—
720C3×C4—21no—
721C3×C4—28no—
722C3×C4—38no—
723C3×C4—44no—
724C3×C4—64no—
725C3×C4—92no—
726C3×C4—181no—
727C3×C4—181no—
728C3×C4D3×#6718yescomplemented
729C3×C4C2×#63812yescomplemented
730Dic3—21no—
731Dic3—38no—
732Dic3—64no—
733Dic3—64no—
734Dic3—98no—
735Dic3—92no—
736Dic3—188no—
737Dic3—184no—
738Dic3—184no—
739Dic3—181no—
740Dic3—181no—
741Dic3—364no—
742Dic3—364no—
743Dic3C2×#63812yescomplemented
744C32—24no—
745C32C4×D3×D411yescharacteristic, complemented
746C32C2×C4×#6714yescomplemented
747C23—31no—
748C23—31no—
749C23—34no—
750C23—62no—
751C23—62no—
752C23—91no—
753C23—274no—
754C23—271no—
755C23—542no—
756C23—542no—
757C23C2×D3×C3⋊D311yescharacteristic
758D4—94no—
759D4—274no—
760D4—274no—
761D4—274no—
762C2×C4—22no—
763C2×C4—31no—
764C2×C4—34no—
765C2×C4—31no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—182no—
774C2×C4—274no—
775C2×C4—271no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—542no—
783C2×C4C2×D3×C3⋊D311yescharacteristic
784C2×C4C2×D3×C3⋊D311yescharacteristic
785C2×C3—22no—
786C2×C3—28no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—24no—
790C2×C3—316no—
791C2×C3—48no—
792C2×C3—68no—
793C2×C3—182no—
794C2×C3C2×C4×D3214yes—
795C2×C3D3×#23514yes—
796C2×C3C2×D3×#6714yes—
797C2×C3C22×C4×C3⋊D311yescharacteristic
798C2×C3C2×#382811yescharacteristic
799C2×C3C22×#63811yescharacteristic
800D3—22no—
801D3—68no—
802D3—182no—
803D3—188no—
804D3—368no—
805D3C4×#63814yesdirect product factor
806C22—21no—
807C22—21no—
808C22—32no—
809C22—32no—
810C22—32no—
811C22—32no—
812C22—68no—
813C22—61no—
814C22—61no—
815C22—92no—
816C22—181no—
817C22—181no—
818C22—272no—
819C22—548no—
820C22—541no—
821C22—541no—
822C22C4×D3×C3⋊D312yescomplemented
823C22C22×D3×C3⋊D311yescharacteristic
824C4—21no—
825C4—32no—
826C4—61no—
827C4—92no—
828C4—181no—
829C4—181no—
830C4—272no—
831C4—541no—
832C4—541no—
833C4D3×#63812yesdirect product factor
834C3—24no—
835C3C4×D3×#6714yescomplemented
836C3C2×C4×#63811yescharacteristic, complemented
837C2—22no—
838C2—34no—
839C2—62no—
840C2—182no—
841C2—542no—
842C2C2×C4×D3×C3⋊D311yescharacteristic
843C2D3×#382811yescharacteristic
844C2C2×D3×#63811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutatorC2×C33C23×C4
FrattiniC22C22×D3×C3⋊D3
FittingC22×C33×C4C22
socle, cosocleC22×C33C24
prime radicalC2×D3×#638C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4×D3C2semidirect
3. C2×C4×D3×C3⋊D3C2semidirect
4. C4×#6312C2semidirect
5. C3×C4×#638C2semidirect
6. #11723618C2semidirect
7. Dic3×#638C2semidirect
8. D3×#3757C2semidirect
9. D3×#3752C2semidirect
10. #11723510C2semidirect
11. C4×#6291C2semidirect
12. #11723506C2semidirect
13. C4×#6290C2semidirect
14. D3×#3750C2semidirect
15. C4×D3×C3⋊Dic3C2semidirect
20. C22×C33×C4C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C22×C32×Dic3C22semidirect
29. C2×C32×C4×D3C22semidirect
30. C2×C32×C4×D3C22semidirect
31. D3×#638C4direct (N × H)
34. C2×#6289C22semidirect
35. C2×Dic3×C3⋊D3C22semidirect
40. #88864C22semidirect
41. #88859C22semidirect
42. #88857C22semidirect
43. C4×C3⋊(C3⋊Dic3)C22semidirect
44. C3×#3757C22semidirect
45. C3×#3752C22semidirect
46. C3×#3750C22semidirect
47. C3×C4×C3⋊Dic3C22semidirect
48. #88807C22semidirect
49. #88806C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. Dic3×C3⋊Dic3C22semidirect
59. C22×C3×C4×D3D3semidirect
72. C4×#638D3direct (N × H)
92. C22×C32×D3C2×C4semidirect
97. C2×D3×C3⋊D3C2×C4semidirect
101. #6312C2×C4semidirect
106. C3×#638C2×C4semidirect
117. C32×C4×D3D4semidirect
118. #6291C2×C4semidirect
119. #6290C2×C4semidirect
124. D3×C3⋊Dic3C2×C4semidirect
138. C22×C32×C4C2×D3semidirect
139. C22×C32×C4C2×D3semidirect
156. C2×C4×C3⋊D3C2×D3semidirect
158. C22×C3×Dic3C2×D3semidirect
163. C2×C3×C4×D3C2×D3semidirect
164. C2×C3×C4×D3C2×D3semidirect
179. #3757C2×D3semidirect
185. #3752C2×D3semidirect
191. #3750C2×D3semidirect
197. C4×C3⋊Dic3C2×D3semidirect
212. C22×C33C22×C4semidirect
216. C2×C3⋊(C3⋊D3)C22×C4semidirect
219. C2×C3×C3⋊D3C22×C4semidirect
224. C2×C32×D3C22×C4semidirect
229. C33×C4C2×D4semidirect
232. C3⋊(C3⋊Dic3)C22×C4semidirect
235. C3×C3⋊Dic3C22×C4semidirect
237. C32×Dic3C2×D4semidirect
243. C22×C4×D3C3⋊D3semidirect
287. C22×C3×D3C4×D3semidirect
314. #638C4×D3direct (N × H)
347. C3×C4×D3#67semidirect
363. C32×D3C4×D4semidirect
377. C22×C3×C4D32semidirect
378. C22×C3×C4C2×C3⋊D3semidirect
391. C22×Dic3C2×C3⋊D3semidirect
409. C2×C4×D3C2×C3⋊D3semidirect
410. C2×C4×D3C2×C3⋊D3semidirect
462. C22×C32C2×C4×D3semidirect
463. C22×C32C2×C4×D3semidirect
478. C2×C3⋊D3C2×C4×D3semidirect
486. C2×C3×D3C2×C4×D3semidirect
496. C32×C4D3×D4semidirect
497. C32×C4C2×#67semidirect
509. C3⋊Dic3C2×C4×D3semidirect
514. C3×Dic3C2×#67semidirect
530. C33C2×C4×D4semidirect
552. C22×D3C4×C3⋊D3semidirect
616. C4×D3#638direct (N × H)
637. C3×D3C4×#67semidirect
659. C22×C4D3×C3⋊D3semidirect
694. C22×C3C4×D32semidirect
695. C22×C3C2×C4×C3⋊D3semidirect
716. C2×D3C2×C4×C3⋊D3semidirect
728. C3×C4D3×#67semidirect
729. C3×C4C2×#638semidirect
743. Dic3C2×#638semidirect
745. C32C4×D3×D4semidirect
746. C32C2×C4×#67semidirect
805. D3C4×#638direct (N × H)
822. C22C4×D3×C3⋊D3semidirect
833. C4D3×#638direct (N × H)
835. C3C4×D3×#67semidirect
836. C3C2×C4×#638semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×D3×#6382
C2×C4×D3×C3⋊D32
C4×#63122
C3×C4×#6382
#117236182
Dic3×#6382
D3×#37572
D3×#37522
#117235102
C4×#62912
#117235062
C4×#62902
D3×#37502
C4×D3×C3⋊Dic32
C2×C4×#6383
C4×D3×#673