Finite Group Databasebeta

← C2×D3×D4×Dic3 #11899893

Subgroups — C2×D3×D4×Dic3 #11899893

Order 1152.

5269 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic
2C23×D3×Dic3C212yesmaximal, complemented
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C212yesmaximal, complemented
6C2×Dic3×#67C212yesmaximal, complemented
7C2×D3×#217C212yesmaximal, complemented
8D3×D4×Dic3C2116yesmaximal, direct product factor
9C2×#63898C211yesmaximal, characteristic, complemented
10C2×Dic3×D12C211yesmaximal, characteristic, complemented
11C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
13C22×D4×Dic3—31nomaximal
14C2×C4×D3×D4—31nomaximal
15C24×C3×D3C2212yes—
16C22×C32×D4C2211yescharacteristic
17C23×C3⋊Dic3C2212yescomplemented
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yescomplemented
20C2×C3×D3×D4C4116yescomplemented
21C2×C3×D3×D4C2218yes—
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×D3×Dic3—216no—
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2212yes—
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C22116yescomplemented
29C22×D3×Dic3C2212yescomplemented
30C22×D3×Dic3C2212yescomplemented
31C2×#3757C2212yescomplemented
32D4×C3⋊Dic3C2218yescomplemented
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C2×C3×#217C2212yescomplemented
36C3×D4×Dic3C2218yescomplemented
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39#67⋊Dic3C22116yescomplemented
40Dic3×#67C22116yescomplemented
41D3×#217C22116yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×Dic32C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63898C2218yescomplemented
48Dic3×D12C2218yescomplemented
49D3×C4⋊Dic3C2218yescomplemented
50C4×D3×Dic3C2218yescomplemented
51C23×C3×D4—31no—
52C24×Dic3—32no—
53C22×D3×D4D311yescharacteristic
54C23×C4×D3—32no—
55C2×C3×C4×D4—31no—
56C22×#217—32no—
57C2×D4×Dic3—31no—
58C2×D4×Dic3—31no—
59C2×D4×Dic3—32no—
60C2×D4×Dic3—32no—
61C2×D4×Dic3—316no—
62C2×D4×Dic3—31no—
63C2×D4×Dic3—31no—
64C2×D4×Dic3—61no—
65C2×D4×Dic3D311yescharacteristic, direct product factor
66C2×C4×#67—32no—
67C22×C4⋊Dic3—31no—
68C22×C4×Dic3—31no—
69C4×D3×D4—316no—
70C2×#893—31no—
71C2×D3×C4⋊C4—31no—
72C2×#67⋊C4—32no—
73C2×D3×C22⋊C4—32no—
74C2×C4×D12—31no—
75C2×C42×D3—31no—
76C24×C32C2312yes—
77C23×C3×D3—28no—
78C23×C3×D3—28no—
79C23×C3×D3C2×C4116yescomplemented
80C23×C3×D3C2312yes—
81C23×C3×D3C2318yes—
82C23×C3×D3C2311yescharacteristic
83C2×C32×D4C2×C418yescomplemented
84C2×C32×D4C2314yes—
85C22×C32×C4C2311yescharacteristic
86C22×C3⋊Dic3—28no—
87C22×C3⋊Dic3C2312yes—
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2318yescomplemented
91C2×C3×#67C2×C4116yescomplemented
92C2×C3×#67C2318yes—
93C22×C3×Dic3—28no—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2318yescomplemented
99C3×D3×D4C2×C4164yescomplemented
100C2×C3×D12C2×C418yescomplemented
101C2×C3×D12C2314yes—
102C2×C3×C4×D3C2×C418yescomplemented
103C2×C3×C4×D3C2314yes—
104C2×D3×Dic3—28no—
105C2×D3×Dic3—24no—
106C2×D3×Dic3—28no—
107C2×D3×Dic3—28no—
108C2×D3×Dic3—264no—
109C2×D3×Dic3D418yesdirect product factor
110C2×D3×Dic3C2318yes—
111C2×D3×Dic3C2314yes—
112C2×D3×Dic3C2314yes—
113C2×D3×Dic3C2318yescomplemented
114C2×D3×Dic3C2318yescomplemented
115#3757C2318yescomplemented
116C4⋊(C3⋊Dic3)C2314yescomplemented
117C4×C3⋊Dic3C2314yescomplemented
118C3×#217C2318yescomplemented
119C3×C4⋊Dic3C2314yescomplemented
120C3×C4×Dic3C2314yescomplemented
121Dic3⋊Dic3C2318yescomplemented
122(C2×D3)⋊Dic3C2318yescomplemented
123(C2×D3)⋊Dic3C2318yescomplemented
124Dic32C2314yescomplemented
125Dic32C2314yescomplemented
126C22×C4×D4—91noSylow
127C25×C3—32no—
128C24×D3C2×D312yes—
129C22×C3×D4—21no—
130C22×C3×D4—32no—
131C22×C3×D4—316no—
132C22×C3×D4—38no—
133C22×C3×D4—31no—
134C22×C3×D4C2×D311yescharacteristic
135C22×C3×D4C2×D311yescharacteristic
136C23×C3×C4—31no—
137C23×C3×C4—32no—
138C22×#67C2×D312yes—
139C23×Dic3—31no—
140C23×Dic3—32no—
141C23×Dic3—32no—
142C23×Dic3—32no—
143C23×Dic3—31no—
144C23×Dic3—32no—
145C23×Dic3—32no—
146C23×Dic3—316no—
147C23×Dic3—62no—
148C23×Dic3—616no—
149C23×Dic3C2×D312yescomplemented
150C2×D3×D4Dic3116yesdirect product factor
151C2×D3×D4C2×D318yes—
152C22×D12C2×D311yescharacteristic
153C22×C4×D3—31no—
154C22×C4×D3—32no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—316no—
158C22×C4×D3—31no—
159C22×C4×D3—616no—
160C22×C4×D3C2×D311yescharacteristic
161C3×C4×D4—38no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C42—31no—
165C2×#217—32no—
166C2×#217—32no—
167C2×#217—32no—
168C2×#217—32no—
169C2×#217—316no—
170C2×#217—62no—
171C2×#217C2×D312yescomplemented
172D4×Dic3—38no—
173D4×Dic3—38no—
174D4×Dic3—316no—
175D4×Dic3—316no—
176D4×Dic3—38no—
177D4×Dic3—38no—
178D4×Dic3—68no—
179D4×Dic3C2×D318yesdirect product factor
180C4×#67—316no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—32no—
186C2×C4⋊Dic3—38no—
187C2×C4⋊Dic3—61no—
188C2×C4⋊Dic3C2×D311yescharacteristic, complemented
189C2×Dic3⋊C4—32no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—38no—
197C2×C4×Dic3—61no—
198C2×C4×Dic3C2×D311yescharacteristic, complemented
199#893—38no—
200D3×C4⋊C4—38no—
201#67⋊C4—316no—
202D3×C22⋊C4—316no—
203C4×D12—38no—
204C42×D3—38no—
205C23×C32—24no—
206C23×C32—24no—
207C23×C32C22×C418yescomplemented
208C23×C32C2414yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—24no—
211C22×C3×D3—24no—
212C22×C3×D3—264no—
213C22×C3×D3—216no—
214C22×C3×D3—216no—
215C22×C3×D3C22×C414yes—
216C22×C3×D3C22×C4132yescomplemented
217C22×C3×D3C22×C418yescomplemented
218C22×C3×D3C2×D414yes—
219C22×C3×D3#4114yes—
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C32×D4C22×C4116yescomplemented
223C2×C32×C4C22×C414yescomplemented
224C2×C32×C4C2412yes—
225C2×C3⋊Dic3—24no—
226C2×C3⋊Dic3—22no—
227C2×C3⋊Dic3—216no—
228C2×C3⋊Dic3C2×D414yescomplemented
229C2×C3⋊Dic3C2412yes—
230C2×C3⋊Dic3C2414yes—
231C2×C3⋊Dic3C2412yes—
232C3×#67C22×C4132yescomplemented
233C2×C3×Dic3—24no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—216no—
236C2×C3×Dic3C22×C414yescomplemented
237C2×C3×Dic3C2×D414yescomplemented
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C3×D12C22×C4116yescomplemented
243C3×C4×D3C22×C4116yescomplemented
244D3×Dic3—216no—
245D3×Dic3—28no—
246D3×Dic3—216no—
247D3×Dic3—216no—
248D3×Dic3C2×D4116yesdirect product factor
249C23×D4—31no—
250C24×C4—92no—
251C2×C4×D4—31no—
252C2×C4×D4—91no—
253C2×C4×D4—92no—
254C2×C4×D4—91no—
255C2×C4×D4—916no—
256C2×C4×D4—92no—
257C2×C4×D4—91no—
258C22×C4⋊C4—91no—
259C22×C22⋊C4—92no—
260C22×C42—91no—
261C24×C3—22no—
262C24×C3—31no—
263C24×C3—316no—
264C24×C3—38no—
265C24×C3—32no—
266C24×C3—68no—
267C24×C3—68no—
268C24×C3C22×D312yes—
269C24×C3C22×D312yes—
270C23×D3—28no—
271C23×D3—28no—
272C23×D3C2×Dic3116yescomplemented
273C23×D3C22×D318yes—
274C23×D3C22×D312yes—
275C23×D3C22×D311yescharacteristic
276C2×C3×D4—28no—
277C2×C3×D4—24no—
278C2×C3×D4—316no—
279C2×C3×D4—38no—
280C2×C3×D4—364no—
281C2×C3×D4—38no—
282C2×C3×D4—34no—
283C2×C3×D4C4×D318yescomplemented
284C2×C3×D4C2×Dic318yescomplemented
285C2×C3×D4C22×D314yes—
286C2×C3×D4C22×D314yes—
287C22×C3×C4—21no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—38no—
291C22×C3×C4—34no—
292C22×C3×C4—31no—
293C22×C3×C4—32no—
294C22×C3×C4—38no—
295C22×C3×C4—68no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C2×#67C2×Dic3116yescomplemented
299C2×#67C22×D318yes—
300C22×Dic3—28no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—38no—
304C22×Dic3—34no—
305C22×Dic3—38no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—32no—
309C22×Dic3—32no—
310C22×Dic3—38no—
311C22×Dic3—34no—
312C22×Dic3—38no—
313C22×Dic3—38no—
314C22×Dic3—38no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—62no—
318C22×Dic3—68no—
319C22×Dic3—68no—
320C22×Dic3—664no—
321C22×Dic3—64no—
322C22×Dic3—68no—
323C22×Dic3—68no—
324C22×Dic3—68no—
325C22×Dic3—68no—
326C22×Dic3—128no—
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D312yes—
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D318yescomplemented
332D3×D4C2×Dic3164yesdirect product factor
333C2×D12C2×Dic318yescomplemented
334C2×D12C22×D314yes—
335C2×C4×D3—38no—
336C2×C4×D3—34no—
337C2×C4×D3—34no—
338C2×C4×D3—38no—
339C2×C4×D3—38no—
340C2×C4×D3—38no—
341C2×C4×D3—664no—
342C2×C4×D3—68no—
343C2×C4×D3—68no—
344C2×C4×D3—68no—
345C2×C4×D3—64no—
346C2×C4×D3C2×Dic318yescomplemented
347C2×C4×D3C22×D314yes—
348C3×C4⋊C4—34no—
349C3×C22⋊C4—38no—
350C3×C42—34no—
351#217—38no—
352#217—38no—
353#217—38no—
354#217—38no—
355#217—68no—
356#217C22×D318yescomplemented
357(C2×D3)⋊C4—38no—
358(C2×D3)⋊C4—38no—
359C4⋊Dic3—34no—
360C4⋊Dic3—34no—
361C4⋊Dic3—38no—
362C4⋊Dic3—64no—
363C4⋊Dic3C22×D314yescomplemented
364Dic3⋊C4—38no—
365C4×Dic3—34no—
366C4×Dic3—34no—
367C4×Dic3—34no—
368C4×Dic3—34no—
369C4×Dic3—34no—
370C4×Dic3—34no—
371C4×Dic3—64no—
372C4×Dic3C22×D314yescomplemented
373C22×C32—216no—
374C22×C32—24no—
375C22×C32—24no—
376C22×C32C23×C412yes—
377C22×C32C23×C418yescomplemented
378C22×C32C22×D412yes—
379C22×C32C2×#4112yes—
380C22×C32C2511yescharacteristic
381C2×C3×D3—216no—
382C2×C3×D3—24no—
383C2×C3×D3—24no—
384C2×C3×D3—264no—
385C2×C3×D3C4×D4116yescomplemented
386C2×C3×D3C23×C414yes—
387C2×C3×D3C23×C418yescomplemented
388C2×C3×D3C22×D414yes—
389C2×C3×D3C2×#4114yes—
390C32×C4C23×C414yescomplemented
391C3⋊Dic3—24no—
392C3⋊Dic3—22no—
393C3⋊Dic3C22×D414yescomplemented
394C3×Dic3—24no—
395C3×Dic3—22no—
396C3×Dic3C23×C414yescomplemented
397C3×Dic3C22×D414yescomplemented
398C25—32no—
399C22×D4—32no—
400C22×D4—316no—
401C22×D4—38no—
402C22×D4—31no—
403C22×D4D3211yescharacteristic
404C23×C4—31no—
405C23×C4—32no—
406C23×C4—91no—
407C23×C4—91no—
408C23×C4—92no—
409C23×C4—92no—
410C23×C4—916no—
411C23×C4—92no—
412C23×C4—92no—
413C23×C4—1816no—
414C4×D4—38no—
415C4×D4—98no—
416C4×D4—916no—
417C4×D4—98no—
418C4×D4—916no—
419C4×D4—98no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—98no—
422C2×C4⋊C4—92no—
423C2×C4⋊C4—91no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—916no—
426C2×C22⋊C4—92no—
427C2×C22⋊C4—92no—
428C2×C22⋊C4—92no—
429C2×C42—31no—
430C2×C42—98no—
431C2×C42—91no—
432C2×C42—91no—
433C2×C42—91no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—21no—
440C23×C3—28no—
441C23×C3—34no—
442C23×C3—34no—
443C23×C3—34no—
444C23×C3—32no—
445C23×C3—38no—
446C23×C3—332no—
447C23×C3—34no—
448C23×C3—44no—
449C23×C3—44no—
450C23×C3—616no—
451C23×C3—616no—
452C23×C3—664no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3C2×C4×D318yescomplemented
456C23×C3C22×Dic318yescomplemented
457C23×C3C23×D314yes—
458C23×C3C23×D314yes—
459C23×C3C23×D311yescharacteristic
460C23×C3C23×D311yescharacteristic
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—264no—
464C22×D3—216no—
465C22×D3—216no—
466C22×D3D3×D414yes—
467C22×D3#23714yes—
468C22×D3C22×Dic314yes—
469C22×D3C22×Dic3132yescomplemented
470C22×D3C22×Dic318yescomplemented
471C22×D3C23×D314yes—
472C22×D3C23×D312yes—
473C3×D4—216no—
474C3×D4—332no—
475C3×D4—316no—
476C3×D4C2×C4×D3116yescomplemented
477C3×D4C22×Dic3116yescomplemented
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—34no—
481C2×C3×C4—34no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—316no—
485C2×C3×C4—32no—
486C2×C3×C4—34no—
487C2×C3×C4—616no—
488C2×C3×C4—64no—
489C2×C3×C4—62no—
490C2×C3×C4C2×C4×D314yescomplemented
491C2×C3×C4C22×Dic314yescomplemented
492C2×C3×C4C23×D312yes—
493C2×C3×C4C23×D312yes—
494#67C22×Dic3132yescomplemented
495C2×Dic3—24no—
496C2×Dic3—22no—
497C2×Dic3—216no—
498C2×Dic3—34no—
499C2×Dic3—34no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—316no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—64no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—64no—
511C2×Dic3—616no—
512C2×Dic3—68no—
513C2×Dic3—616no—
514C2×Dic3—616no—
515C2×Dic3—616no—
516C2×Dic3—64no—
517C2×Dic3—64no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—616no—
521C2×Dic3—1216no—
522C2×Dic3—122no—
523C2×Dic3—124no—
524C2×Dic3D3×D414yesdirect product factor
525C2×Dic3C22×Dic314yescomplemented
526C2×Dic3C23×D312yes—
527C2×Dic3C23×D314yes—
528C2×Dic3C23×D312yes—
529C2×Dic3C23×D312yes—
530D12C22×Dic3116yescomplemented
531C4×D3—316no—
532C4×D3—616no—
533C4×D3—616no—
534C4×D3—616no—
535C4×D3—68no—
536C4×D3C22×Dic3116yescomplemented
537C2×C32—28no—
538C2×C32C2×C4×D414yescomplemented
539C2×C32C24×C411yescharacteristic
540C2×C32C23×D411yescharacteristic
541C2×C32C22×#4111yescharacteristic
542C3×D3—28no—
543C3×D3C2×C4×D418yescomplemented
544C24—31no—
545C24—38no—
546C24—32no—
547C24—316no—
548C24—68no—
549C24—68no—
550C24C2×D3212yes—
551C2×D4—38no—
552C2×D4—316no—
553C2×D4—364no—
554C2×D4—34no—
555C2×D4—38no—
556C2×D4D3×Dic318yesdirect product factor
557C2×D4C2×D3214yes—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—34no—
561C22×C4—38no—
562C22×C4—38no—
563C22×C4—31no—
564C22×C4—32no—
565C22×C4—68no—
566C22×C4—94no—
567C22×C4—98no—
568C22×C4—94no—
569C22×C4—98no—
570C22×C4—98no—
571C22×C4—98no—
572C22×C4—91no—
573C22×C4—98no—
574C22×C4—91no—
575C22×C4—92no—
576C22×C4—188no—
577C22×C4—1864no—
578C22×C4—188no—
579C22×C4—188no—
580C22×C4—184no—
581C22×C4—188no—
582C22×C4C2×D3211yescharacteristic
583C4⋊C4—34no—
584C4⋊C4—98no—
585C4⋊C4—94no—
586C22⋊C4—38no—
587C22⋊C4—98no—
588C22⋊C4—98no—
589C22⋊C4—98no—
590C42—34no—
591C42—94no—
592C42—94no—
593C42—94no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—216no—
599C22×C3—216no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—28no—
604C22×C3—21no—
605C22×C3—34no—
606C22×C3—34no—
607C22×C3—34no—
608C22×C3—316no—
609C22×C3—38no—
610C22×C3—44no—
611C22×C3—416no—
612C22×C3—44no—
613C22×C3—664no—
614C22×C3—64no—
615C22×C3—64no—
616C22×C3—616no—
617C22×C3C22×C4×D312yes—
618C22×C3C22×C4×D318yescomplemented
619C22×C3C2×D3×D412yes—
620C22×C3C2×D3×D412yes—
621C22×C3C2×#23712yes—
622C22×C3D3×#4112yes—
623C22×C3C23×Dic312yes—
624C22×C3C23×Dic318yescomplemented
625C22×C3C24×D311yescharacteristic
626C22×C3C24×D311yescharacteristic
627C2×D3—24no—
628C2×D3—24no—
629C2×D3—216no—
630C2×D3—264no—
631C2×D3D4×Dic3116yesdirect product factor
632C2×D3C2×D3×D414yes—
633C2×D3C2×#23714yes—
634C2×D3C23×Dic314yes—
635C2×D3C23×Dic318yescomplemented
636C3×C4—24no—
637C3×C4—34no—
638C3×C4—34no—
639C3×C4—64no—
640C3×C4—62no—
641C3×C4C22×C4×D314yescomplemented
642C3×C4C23×Dic314yescomplemented
643Dic3—24no—
644Dic3—22no—
645Dic3—34no—
646Dic3—34no—
647Dic3—64no—
648Dic3—64no—
649Dic3—64no—
650Dic3—62no—
651Dic3—62no—
652Dic3—124no—
653Dic3—122no—
654Dic3C2×D3×D414yesdirect product factor
655Dic3C23×Dic314yescomplemented
656C32C22×C4×D411yescharacteristic, complemented, Sylow
657C23—24no—
658C23—24no—
659C23—34no—
660C23—34no—
661C23—34no—
662C23—32no—
663C23—38no—
664C23—332no—
665C23—34no—
666C23—616no—
667C23—664no—
668C23—616no—
669C23—64no—
670C23—64no—
671C23C2×D3×Dic318yescomplemented
672C23C22×D3214yes—
673C23C22×D3211yescharacteristic
674D4—332no—
675D4—316no—
676D4C2×D3×Dic3116yesdirect product factor
677C2×C4—34no—
678C2×C4—34no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—316no—
682C2×C4—32no—
683C2×C4—34no—
684C2×C4—616no—
685C2×C4—64no—
686C2×C4—62no—
687C2×C4—916no—
688C2×C4—94no—
689C2×C4—92no—
690C2×C4—92no—
691C2×C4—94no—
692C2×C4—1816no—
693C2×C4—1816no—
694C2×C4—1816no—
695C2×C4—188no—
696C2×C4—1816no—
697C2×C4—184no—
698C2×C4—182no—
699C2×C4C2×D3×Dic314yescomplemented
700C2×C4C22×D3212yes—
701C2×C3—28no—
702C2×C3—28no—
703C2×C3—24no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—38no—
708C2×C3—48no—
709C2×C3—68no—
710C2×C3C4×D3×D414yescomplemented
711C2×C3C2×D4×Dic314yescomplemented
712C2×C3C23×C4×D311yescharacteristic
713C2×C3C22×D3×D411yescharacteristic
714C2×C3C22×D3×D411yescharacteristic
715C2×C3C22×#23711yescharacteristic
716C2×C3C2×D3×#4111yescharacteristic
717C2×C3C24×Dic311yescharacteristic
718D3—28no—
719D3C2×D4×Dic318yesdirect product factor
720C22—216no—
721C22—24no—
722C22—24no—
723C22—316no—
724C22—34no—
725C22—34no—
726C22—34no—
727C22—38no—
728C22—664no—
729C22—616no—
730C22—64no—
731C22—64no—
732C22D32×D412yes—
733C22D3×#23712yes—
734C22C22×D3×Dic312yes—
735C22C22×D3×Dic318yescomplemented
736C22C23×D3211yescharacteristic
737C4—34no—
738C4—34no—
739C4—64no—
740C4—62no—
741C4—94no—
742C4—184no—
743C4—182no—
744C4C22×D3×Dic314yescomplemented
745C3—21no—
746C3C2×C4×D3×D411yescharacteristic, complemented
747C3C22×D4×Dic311yescharacteristic, complemented
748C2—28no—
749C2—38no—
750C2—68no—
751C2D3×D4×Dic314yesdirect product factor
752C2C2×D32×D411yescharacteristic
753C2C2×D3×#23711yescharacteristic
754C2C23×D3×Dic311yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC22×C3×D3×D4C2
cosocleC22×C32C25
hypercenterC22×D4D32
hypocenterC32C22×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C23×D3×Dic3C2semidirect
3. C2×D4×C3⋊Dic3C2semidirect
4. C2×C3×D4×Dic3C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×D3×#217C2semidirect
8. D3×D4×Dic3C2direct (N × H)
9. C2×#63898C2semidirect
10. C2×Dic3×D12C2semidirect
11. C2×D3×C4⋊Dic3C2semidirect
12. C2×C4×D3×Dic3C2semidirect
17. C23×C3⋊Dic3C22semidirect
19. C23×C3×Dic3C22semidirect
20. C2×C3×D3×D4C4semidirect
28. C22×D3×Dic3C22semidirect
29. C22×D3×Dic3C22semidirect
30. C22×D3×Dic3C22semidirect
31. C2×#3757C22semidirect
32. D4×C3⋊Dic3C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×C4×C3⋊Dic3C22semidirect
35. C2×C3×#217C22semidirect
36. C3×D4×Dic3C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×C4×Dic3C22semidirect
39. #67⋊Dic3C22semidirect
40. Dic3×#67C22semidirect
41. D3×#217C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. C2×Dic32C22semidirect
47. #63898C22semidirect
48. Dic3×D12C22semidirect
49. D3×C4⋊Dic3C22semidirect
50. C4×D3×Dic3C22semidirect
65. C2×D4×Dic3D3direct (N × H)
79. C23×C3×D3C2×C4semidirect
83. C2×C32×D4C2×C4semidirect
90. C22×C3⋊Dic3C23semidirect
91. C2×C3×#67C2×C4semidirect
98. C22×C3×Dic3C23semidirect
99. C3×D3×D4C2×C4semidirect
100. C2×C3×D12C2×C4semidirect
102. C2×C3×C4×D3C2×C4semidirect
109. C2×D3×Dic3D4direct (N × H)
113. C2×D3×Dic3C23semidirect
114. C2×D3×Dic3C23semidirect
115. #3757C23semidirect
116. C4⋊(C3⋊Dic3)C23semidirect
117. C4×C3⋊Dic3C23semidirect
118. C3×#217C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×C4×Dic3C23semidirect
121. Dic3⋊Dic3C23semidirect
122. (C2×D3)⋊Dic3C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. Dic32C23semidirect
125. Dic32C23semidirect
149. C23×Dic3C2×D3semidirect
150. C2×D3×D4Dic3direct (N × H)
171. C2×#217C2×D3semidirect
179. D4×Dic3C2×D3direct (N × H)
188. C2×C4⋊Dic3C2×D3semidirect
198. C2×C4×Dic3C2×D3semidirect
207. C23×C32C22×C4semidirect
216. C22×C3×D3C22×C4semidirect
217. C22×C3×D3C22×C4semidirect
222. C32×D4C22×C4semidirect
223. C2×C32×C4C22×C4semidirect
228. C2×C3⋊Dic3C2×D4semidirect
232. C3×#67C22×C4semidirect
236. C2×C3×Dic3C22×C4semidirect
237. C2×C3×Dic3C2×D4semidirect
242. C3×D12C22×C4semidirect
243. C3×C4×D3C22×C4semidirect
248. D3×Dic3C2×D4direct (N × H)
272. C23×D3C2×Dic3semidirect
283. C2×C3×D4C4×D3semidirect
284. C2×C3×D4C2×Dic3semidirect
298. C2×#67C2×Dic3semidirect
331. C22×Dic3C22×D3semidirect
332. D3×D4C2×Dic3direct (N × H)
333. C2×D12C2×Dic3semidirect
346. C2×C4×D3C2×Dic3semidirect
356. #217C22×D3semidirect
363. C4⋊Dic3C22×D3semidirect
372. C4×Dic3C22×D3semidirect
377. C22×C32C23×C4semidirect
385. C2×C3×D3C4×D4semidirect
387. C2×C3×D3C23×C4semidirect
390. C32×C4C23×C4semidirect
393. C3⋊Dic3C22×D4semidirect
396. C3×Dic3C23×C4semidirect
397. C3×Dic3C22×D4semidirect
455. C23×C3C2×C4×D3semidirect
456. C23×C3C22×Dic3semidirect
469. C22×D3C22×Dic3semidirect
470. C22×D3C22×Dic3semidirect
476. C3×D4C2×C4×D3semidirect
477. C3×D4C22×Dic3semidirect
490. C2×C3×C4C2×C4×D3semidirect
491. C2×C3×C4C22×Dic3semidirect
494. #67C22×Dic3semidirect
524. C2×Dic3D3×D4direct (N × H)
525. C2×Dic3C22×Dic3semidirect
530. D12C22×Dic3semidirect
536. C4×D3C22×Dic3semidirect
538. C2×C32C2×C4×D4semidirect
543. C3×D3C2×C4×D4semidirect
556. C2×D4D3×Dic3direct (N × H)
618. C22×C3C22×C4×D3semidirect
624. C22×C3C23×Dic3semidirect
631. C2×D3D4×Dic3direct (N × H)
635. C2×D3C23×Dic3semidirect
641. C3×C4C22×C4×D3semidirect
642. C3×C4C23×Dic3semidirect
654. Dic3C2×D3×D4direct (N × H)
655. Dic3C23×Dic3semidirect
656. C32C22×C4×D4semidirect
671. C23C2×D3×Dic3semidirect
676. D4C2×D3×Dic3direct (N × H)
699. C2×C4C2×D3×Dic3semidirect
710. C2×C3C4×D3×D4semidirect
711. C2×C3C2×D4×Dic3semidirect
719. D3C2×D4×Dic3direct (N × H)
735. C22C22×D3×Dic3semidirect
744. C4C22×D3×Dic3semidirect
746. C3C2×C4×D3×D4semidirect
747. C3C22×D4×Dic3semidirect
751. C2D3×D4×Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C23×D3×Dic32
C2×D4×C3⋊Dic32
C2×C3×D4×Dic32
C2×#67⋊Dic32
C2×Dic3×#672
C2×D3×#2172
D3×D4×Dic32
C2×#638982
C2×Dic3×D122
C2×D3×C4⋊Dic32
C2×C4×D3×Dic32
C22×D4×Dic33
C2×C4×D3×D43