Finite Group Databasebeta

← D3×#64361 #13181614

Subgroups — D3×#64361 #13181614

Order 1728.

6052 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724679C211yesmaximal, characteristic, complemented
2C3×#64361C211yesmaximal, characteristic, complemented
3C2×C32×D3×D4C211yesmaximal, characteristic, complemented
4#11724611C214yesmaximal, complemented
5C2×D3×#638C214yesmaximal, complemented
6#11724588C214yesmaximal, complemented
7#11724587C214yesmaximal, complemented
8D3×#3830C214yesmaximal, complemented
9D3×D4×C3⋊D3C214yesmaximal, complemented
10#11724579C212yesmaximal, complemented
11D3×#3828C212yesmaximal, complemented
12C2×#64361—31nomaximal
13D3×#1004—34nomaximal
14C23×C32×D3C2212yescomplemented
15C22×D3×C3⋊D3C2214yescomplemented
16C2×C33×D4C2211yescharacteristic, complemented
17C2×#6312C2214yescomplemented
18#89078C2214yescomplemented
19D4×C3⋊(C3⋊D3)C2214yescomplemented
20#89076C2212yescomplemented
21C2×C3×#638C2214yescomplemented
22C3×#3830C2214yescomplemented
23C3×D4×C3⋊D3C2214yescomplemented
24C3×#3828C2212yescomplemented
25C2×C32×#67C2212yescomplemented
26C32×D3×D4C2214yescomplemented
27C32×D3×D4C2214yescomplemented
28C2×C32×D12C2211yescharacteristic, complemented
29C2×C32×C4×D3C2211yescharacteristic, complemented
30#89039C2218yescomplemented
31C3⋊D3×#67C2218yescomplemented
32D3×#638C2214yescomplemented
33D3×#638C2218yescomplemented
34D3×#638C2218yescomplemented
35D3×#638C2218yescomplemented
36C2×#6291C2214yescomplemented
37C2×#6290C2214yescomplemented
38#89031C2214yescomplemented
39#89029C2218yescomplemented
40#89028C2218yescomplemented
41C2×D3×C3⋊Dic3C2214yescomplemented
42#89026C2214yescomplemented
43C3⋊D3×D12C2214yescomplemented
44D3×C4⋊(C3⋊D3)C2212yescomplemented
45C4×D3×C3⋊D3C2214yescomplemented
46#89022C2212yescomplemented
47#89021C2212yescomplemented
48#89020C2214yescomplemented
49#89015C2214yescomplemented
50#89014C2214yescomplemented
51D3×#634C2212yescomplemented
52C22×C32×D4—31no—
53C22×#638—34no—
54#64361—31no—
55#64361—34no—
56#64361—34no—
57#64361—34no—
58#64361—32no—
59#64361—34no—
60#64361—64no—
61#64361D311yescharacteristic, direct product factor
62C2×#3830—34no—
63C2×D4×C3⋊D3—34no—
64C2×#3828—32no—
65C3×#1004—34no—
66C2×C3×D3×D4D314yescomplemented
67#64330—316no—
68C2×D3×#67—316no—
69#64314—316no—
70#64313—316no—
71D3×#237—316no—
72D32×D4—316no—
73#64307—38no—
74D3×#235—38no—
75C23×C33C2312yescomplemented
76C22×C3⋊(C3⋊D3)C2314yescomplemented
77C22×C3×C3⋊D3C2314yescomplemented
78C22×C32×D3—44no—
79C22×C32×D3C2314yes—
80C22×C32×D3C2311yescharacteristic
81C22×C32×D3C2314yescomplemented
82C22×C32×D3C2312yescomplemented
83C2×D3×C3⋊D3—48no—
84C2×D3×C3⋊D3C2314yes—
85C2×D3×C3⋊D3C2318yescomplemented
86C33×D4C2314yescomplemented
87C2×C33×C4C2311yescharacteristic, complemented
88#6312C2318yescomplemented
89#6312C2314yescomplemented
90C2×C3⋊(C3⋊Dic3)C2314yescomplemented
91C4⋊(C3⋊(C3⋊D3))C2312yescomplemented
92C4×C3⋊(C3⋊D3)C2314yescomplemented
93#6308C2312yescomplemented
94C3×#638C2318yescomplemented
95C3×#638C2314yescomplemented
96C2×C3×C3⋊Dic3C2314yescomplemented
97C3×C4⋊(C3⋊D3)C2312yescomplemented
98C3×C4×C3⋊D3C2314yescomplemented
99C3×#634C2312yescomplemented
100C32×#67C2318yescomplemented
101C2×C32×Dic3C2311yescharacteristic, complemented
102C32×D12C2314yescomplemented
103C32×C4×D3C2312yes—
104C32×C4×D3C2312yescomplemented
105#6293C2314yescomplemented
106#6292C2314yescomplemented
107#6291C2318yescomplemented
108#6291C2314yescomplemented
109#6290C2318yescomplemented
110#6290C2314yescomplemented
111#6289C2314yescomplemented
112Dic3×C3⋊D3C2314yescomplemented
113D3×C3⋊Dic3C2314yes—
114D3×C3⋊Dic3C2318yescomplemented
115D3×H(5,𝔽2)—91no—
116C2×#1004—94no—
117C24×C32—32no—
118C23×C3⋊D3—34no—
119C23×C3×D3C2×D318yescomplemented
120C22×D32—316no—
121C2×C32×D4—24no—
122C2×C32×D4—32no—
123C2×C32×D4—34no—
124C2×C32×D4—34no—
125C2×C32×D4—31no—
126C2×C32×D4C2×D314yescomplemented
127C2×C32×D4C2×D311yescharacteristic, complemented
128C22×C32×C4—31no—
129C2×#638—34no—
130C2×#638—316no—
131C2×#638—34no—
132C2×#638—34no—
133C2×#638—38no—
134C2×#638—38no—
135C2×#638—38no—
136C2×#638—34no—
137C2×#638—616no—
138C2×#638C2×D314yescomplemented
139C22×C3⋊Dic3—34no—
140#3830—34no—
141#3830—316no—
142#3830—38no—
143#3830—38no—
144#3830—34no—
145#3830—34no—
146#3830—616no—
147#3830C2×D314yescomplemented
148D4×C3⋊D3—38no—
149D4×C3⋊D3—34no—
150D4×C3⋊D3—316no—
151D4×C3⋊D3—38no—
152D4×C3⋊D3—34no—
153D4×C3⋊D3—34no—
154D4×C3⋊D3—616no—
155D4×C3⋊D3C2×D314yescomplemented
156#3828—32no—
157#3828—38no—
158#3828—34no—
159#3828—32no—
160#3828—34no—
161#3828—32no—
162#3828—68no—
163#3828C2×D312yescomplemented
164C2×C4⋊(C3⋊D3)—32no—
165C2×C4×C3⋊D3—34no—
166C2×#634—32no—
167C2×C3×#67—316no—
168C2×C3×#67C2×D318yescomplemented
169C3×#237—316no—
170C3×D3×D4—316no—
171C3×D3×D4C2×D3116yescomplemented
172C3×D3×D4C2×D3116yescomplemented
173C3×#235—38no—
174C2×C3×D12C2×D314yescomplemented
175C2×C3×C4×D3C2×D314yescomplemented
176#3811—332no—
177D3×#67—316no—
178D3×#67—332no—
179D3×#67—332no—
180D3×#67—332no—
181D3×#67—332no—
182C2×#626—316no—
183C2×#625—316no—
184#3805—332no—
185#3804—332no—
186#3804—316no—
187C2×D3×Dic3—316no—
188#3802—316no—
189D3×D12—316no—
190D3×D12—38no—
191C4×D32—316no—
192#3799—38no—
193#3798—316no—
194#3796—316no—
195#3795—316no—
196#3795—38no—
197D3×Dic6—38no—
198C22×C33—42no—
199C22×C33C2411yescharacteristic
200C22×C33C2414yes—
201C2×C3⋊(C3⋊D3)—44no—
202C2×C3⋊(C3⋊D3)C2414yes—
203C2×C3×C3⋊D3—44no—
204C2×C3×C3⋊D3C2414yes—
205C2×C32×D3—28no—
206C2×C32×D3—22no—
207C2×C32×D3—42no—
208C2×C32×D3—44no—
209C2×C32×D3C2414yes—
210C2×C32×D3C2411yescharacteristic
211C2×C32×D3C2411yescharacteristic
212D3×C3⋊D3—28no—
213D3×C3⋊D3—48no—
214C33×C4C2412yes—
215C3⋊(C3⋊Dic3)C2414yes—
216C3×C3⋊Dic3C2414yes—
217C32×Dic3C2412yes—
218C3×H(5,𝔽2)—91no—
219C22×C3×D4—34no—
220C22×#67—916no—
221#1009—94no—
222#1009—92no—
223D3×#41—94no—
224D3×#41—92no—
225#1004—34no—
226#1004—98no—
227#1004—916no—
228#1004—916no—
229#1004—916no—
230#1004—94no—
231#1004—91no—
232#1004—94no—
233#1004—94no—
234#1004—184no—
235C2×#237—916no—
236C2×D3×D4—916no—
237C2×D3×D4—94no—
238C2×D3×D4—94no—
239C2×D3×D4C3⋊D311yescharacteristic, complemented
240C2×#235—98no—
241C23×C32—28no—
242C23×C32—34no—
243C23×C32—31no—
244C23×C32—32no—
245C23×C32—34no—
246C23×C32—124no—
247C23×C32C22×D318yescomplemented
248C23×C32C22×D312yescomplemented
249C22×C3⋊D3—34no—
250C22×C3⋊D3—34no—
251C22×C3⋊D3—38no—
252C22×C3⋊D3—316no—
253C22×C3⋊D3—616no—
254C22×C3⋊D3—128no—
255C22×C3⋊D3C22×D314yescomplemented
256C22×C3×D3—316no—
257C22×C3×D3—416no—
258C22×C3×D3C22×D3116yes—
259C22×C3×D3C22×D314yes—
260C22×C3×D3C22×D3116yescomplemented
261C22×C3×D3C22×D318yescomplemented
262C2×D32—316no—
263C2×D32—332no—
264C2×D32—1232no—
265C32×D4—216no—
266C32×D4—38no—
267C32×D4—34no—
268C32×D4C22×D3116yescomplemented
269C32×D4C22×D314yescomplemented
270C2×C32×C4—24no—
271C2×C32×C4—31no—
272C2×C32×C4—32no—
273C2×C32×C4—32no—
274C2×C32×C4C22×D314yescomplemented
275C2×C32×C4C22×D311yescharacteristic, complemented
276#638—34no—
277#638—38no—
278#638—34no—
279#638—38no—
280#638—34no—
281#638—38no—
282#638—316no—
283#638—332no—
284#638—616no—
285#638—632no—
286#638C22×D314yescomplemented
287#638C22×D318yescomplemented
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—38no—
291C2×C3⋊Dic3—316no—
292C2×C3⋊Dic3—616no—
293C2×C3⋊Dic3C22×D314yescomplemented
294C4⋊(C3⋊D3)—34no—
295C4⋊(C3⋊D3)—32no—
296C4⋊(C3⋊D3)—38no—
297C4⋊(C3⋊D3)—68no—
298C4⋊(C3⋊D3)C22×D312yescomplemented
299C4×C3⋊D3—34no—
300C4×C3⋊D3—34no—
301C4×C3⋊D3—34no—
302C4×C3⋊D3—316no—
303C4×C3⋊D3—616no—
304C4×C3⋊D3C22×D314yescomplemented
305#634—32no—
306#634—34no—
307#634—38no—
308#634—68no—
309#634C22×D312yescomplemented
310C3×#67—316no—
311C3×#67—332no—
312C3×#67C22×D3132yescomplemented
313C2×C3×Dic3—316no—
314C2×C3×Dic3C22×D314yescomplemented
315C3×D12—38no—
316C3×D12C22×D3116yescomplemented
317C3×C4×D3—316no—
318C3×C4×D3C22×D318yes—
319C3×C4×D3C22×D318yescomplemented
320C3×Dic6—38no—
321#627—316no—
322#626—332no—
323#626—316no—
324#626—316no—
325#625—316no—
326#625—332no—
327#624—316no—
328D3×Dic3—316no—
329D3×Dic3—332no—
330D3×Dic3—316no—
331C2×H(5,𝔽2)—271noSylow
332C2×C33—21no—
333C2×C33—24no—
334C2×C33C2511yescharacteristic
335C3⋊(C3⋊D3)—24no—
336C3×C3⋊D3—24no—
337C32×D3—24no—
338C32×D3—21no—
339C32×D3H(5,𝔽2)12yescomplemented
340C24×C3—38no—
341C23×D3—916no—
342C23×D3—94no—
343C23×D3C2×C3⋊D312yescomplemented
344C3×#41—94no—
345C3×#41—92no—
346C2×C3×D4—24no—
347C2×C3×D4—38no—
348C2×C3×D4—316no—
349C2×C3×D4—316no—
350C2×C3×D4—34no—
351C2×C3×D4—94no—
352C2×C3×D4—94no—
353C2×C3×D4D3214yescomplemented
354C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
355C22×C3×C4—34no—
356C2×#67—316no—
357C2×#67—916no—
358C2×#67—916no—
359C2×#67—932no—
360C2×#67—932no—
361C2×#67—932no—
362C2×#67—916no—
363C2×#67—916no—
364C2×#67—94no—
365C2×#67—94no—
366C2×#67—98no—
367C2×#67—1816no—
368C2×#67C2×C3⋊D312yescomplemented
369C22×Dic3—916no—
370#239—94no—
371#239—92no—
372D3×Q8—92no—
373#237—316no—
374#237—916no—
375#237—916no—
376#237—932no—
377#237—932no—
378#237—916no—
379#237—94no—
380#237—98no—
381#237—94no—
382#237—92no—
383#237—1816no—
384D3×D4—316no—
385D3×D4—916no—
386D3×D4—916no—
387D3×D4—932no—
388D3×D4—932no—
389D3×D4—98no—
390D3×D4—94no—
391D3×D4—98no—
392D3×D4—98no—
393D3×D4—916no—
394D3×D4—94no—
395D3×D4—98no—
396D3×D4—94no—
397D3×D4—92no—
398D3×D4—1816no—
399D3×D4C2×C3⋊D314yescomplemented
400D3×D4C2×C3⋊D314yescomplemented
401#235—38no—
402#235—98no—
403#235—916no—
404#235—98no—
405#235—916no—
406#235—98no—
407#235—92no—
408#235—98no—
409#235—94no—
410#235—94no—
411#235—188no—
412C2×D12—98no—
413C2×D12—94no—
414C2×D12—94no—
415C2×D12C2×C3⋊D311yescharacteristic, complemented
416C2×C4×D3—916no—
417C2×C4×D3—94no—
418C2×C4×D3—94no—
419C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
420C2×Dic6—98no—
421C22×C32—216no—
422C22×C32—24no—
423C22×C32—31no—
424C22×C32—34no—
425C22×C32—31no—
426C22×C32—42no—
427C22×C32—48no—
428C22×C32—68no—
429C22×C32—62no—
430C22×C32—88no—
431C22×C32—124no—
432C22×C32—122no—
433C22×C32C23×D3116yes—
434C22×C32C23×D314yes—
435C22×C32C23×D314yes—
436C22×C32C23×D311yescharacteristic
437C2×C3⋊D3—34no—
438C2×C3⋊D3—316no—
439C2×C3⋊D3—44no—
440C2×C3⋊D3—616no—
441C2×C3⋊D3—68no—
442C2×C3⋊D3—128no—
443C2×C3⋊D3—124no—
444C2×C3⋊D3—1216no—
445C2×C3⋊D3—2416no—
446C2×C3⋊D3C23×D314yes—
447C2×C3×D3—232no—
448C2×C3×D3—28no—
449C2×C3×D3—316no—
450C2×C3×D3—48no—
451C2×C3×D3—416no—
452C2×C3×D3—1216no—
453C2×C3×D3C23×D3116yes—
454C2×C3×D3C23×D314yes—
455C2×C3×D3C23×D314yes—
456D32—632no—
457D32—1232no—
458C32×C4—28no—
459C32×C4—32no—
460C32×C4C23×D318yes—
461C32×C4C23×D312yes—
462C3⋊Dic3—34no—
463C3⋊Dic3—316no—
464C3⋊Dic3—616no—
465C3⋊Dic3C23×D314yes—
466C3×Dic3—316no—
467C3×Dic3C23×D318yes—
468H(5,𝔽2)—91no—
469H(5,𝔽2)—274no—
470H(5,𝔽2)—274no—
471H(5,𝔽2)—274no—
472H(5,𝔽2)—272no—
473H(5,𝔽2)—271no—
474C2×#41—272no—
475C2×#41—274no—
476C22×D4—31no—
477C22×D4—274no—
478C22×D4—274no—
479C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
480C23×C3—28no—
481C23×C3—316no—
482C23×C3—34no—
483C23×C3—38no—
484C23×C3—316no—
485C23×C3—94no—
486C23×C3—1216no—
487C23×C3C2×D3218yescomplemented
488C23×C3C22×C3⋊D312yescomplemented
489C22×D3—316no—
490C22×D3—44no—
491C22×D3—916no—
492C22×D3—932no—
493C22×D3—916no—
494C22×D3—94no—
495C22×D3—94no—
496C22×D3—98no—
497C22×D3—1816no—
498C22×D3—368no—
499C22×D3—3632no—
500C22×D3C22×C3⋊D314yes—
501C22×D3C22×C3⋊D311yescharacteristic
502C22×D3C22×C3⋊D314yescomplemented
503C22×D3C22×C3⋊D312yescomplemented
504C3×Q8—92no—
505C3×D4—216no—
506C3×D4—332no—
507C3×D4—316no—
508C3×D4—98no—
509C3×D4—94no—
510C3×D4—92no—
511C3×D4C2×D32116yescomplemented
512C3×D4C22×C3⋊D314yescomplemented
513C2×C3×C4—24no—
514C2×C3×C4—34no—
515C2×C3×C4—38no—
516C2×C3×C4—38no—
517C2×C3×C4—94no—
518C2×C3×C4—94no—
519C2×C3×C4C2×D3214yescomplemented
520C2×C3×C4C22×C3⋊D311yescharacteristic, complemented
521#67—316no—
522#67—332no—
523#67—916no—
524#67—932no—
525#67—916no—
526#67—932no—
527#67—916no—
528#67—932no—
529#67—98no—
530#67—94no—
531#67—98no—
532#67—94no—
533#67—94no—
534#67—1816no—
535#67—1832no—
536#67C22×C3⋊D318yescomplemented
537C2×Dic3—316no—
538C2×Dic3—916no—
539C2×Dic3—932no—
540C2×Dic3—916no—
541C2×Dic3—94no—
542C2×Dic3—94no—
543C2×Dic3—1816no—
544C2×Dic3C22×C3⋊D311yescharacteristic, complemented
545D12—38no—
546D12—916no—
547D12—98no—
548D12—94no—
549D12—98no—
550D12—92no—
551D12—188no—
552D12C22×C3⋊D314yescomplemented
553C4×D3—316no—
554C4×D3—916no—
555C4×D3—916no—
556C4×D3—94no—
557C4×D3—98no—
558C4×D3—916no—
559C4×D3—94no—
560C4×D3—94no—
561C4×D3—1816no—
562C4×D3C22×C3⋊D312yes—
563C4×D3C22×C3⋊D312yescomplemented
564Dic6—38no—
565Dic6—916no—
566Dic6—98no—
567Dic6—92no—
568Dic6—94no—
569Dic6—188no—
570C2×C32—24no—
571C2×C32—21no—
572C2×C32—24no—
573C2×C32—24no—
574C2×C32—216no—
575C2×C32—32no—
576C2×C32—416no—
577C2×C32—44no—
578C2×C32—64no—
579C2×C32—61no—
580C2×C32C24×D314yes—
581C2×C32C24×D311yescharacteristic
582C3⋊D3—24no—
583C3⋊D3—64no—
584C3⋊D3—616no—
585C3⋊D3—1216no—
586C3×D3—216no—
587C3×D3—24no—
588C3×D3—616no—
589C3×D3#100418yescomplemented
590C24—32no—
591C24—274no—
592#41—94no—
593#41—92no—
594#41—274no—
595#41—274no—
596#41—272no—
597#41—272no—
598#41—278no—
599#41—274no—
600#41—278no—
601#41—274no—
602#41—274no—
603#41—272no—
604C2×Q8—272no—
605C2×D4—32no—
606C2×D4—34no—
607C2×D4—34no—
608C2×D4—31no—
609C2×D4—94no—
610C2×D4—94no—
611C2×D4—272no—
612C2×D4—274no—
613C2×D4—274no—
614C2×D4—278no—
615C2×D4—274no—
616C2×D4—278no—
617C2×D4—274no—
618C2×D4—278no—
619C2×D4—278no—
620C2×D4—278no—
621C2×D4—274no—
622C2×D4—274no—
623C2×D4—274no—
624C2×D4D3×C3⋊D311yescharacteristic, complemented
625C22×C4—31no—
626C22×C4—274no—
627C22×C4—274no—
628C22×C3—216no—
629C22×C3—24no—
630C22×C3—34no—
631C22×C3—316no—
632C22×C3—34no—
633C22×C3—42no—
634C22×C3—48no—
635C22×C3—632no—
636C22×C3—68no—
637C22×C3—88no—
638C22×C3—94no—
639C22×C3—1216no—
640C22×C3—128no—
641C22×C3—364no—
642C22×C3C22×D32116yes—
643C22×C3C22×D3214yes—
644C22×C3C23×C3⋊D314yes—
645C22×C3C23×C3⋊D311yescharacteristic
646C2×D3—22no—
647C2×D3—28no—
648C2×D3—316no—
649C2×D3—44no—
650C2×D3—42no—
651C2×D3—916no—
652C2×D3—94no—
653C2×D3—1216no—
654C2×D3—1816no—
655C2×D3—1832no—
656C2×D3—188no—
657C2×D3—368no—
658C2×D3—3632no—
659C2×D3—364no—
660C2×D3—3616no—
661C2×D3—7216no—
662C2×D3C23×C3⋊D314yes—
663C2×D3C23×C3⋊D311yescharacteristic
664C2×D3C23×C3⋊D311yescharacteristic
665C3×C4—28no—
666C3×C4—38no—
667C3×C4—94no—
668C3×C4C22×D3218yes—
669C3×C4C23×C3⋊D312yes—
670Dic3—316no—
671Dic3—916no—
672Dic3—94no—
673Dic3—1816no—
674Dic3C23×C3⋊D312yes—
675C32—24no—
676C32C2×#100414yescomplemented
677C32D3×H(5,𝔽2)11yescharacteristic, complemented
678C23—31no—
679C23—34no—
680C23—34no—
681C23—32no—
682C23—94no—
683C23—124no—
684C23—274no—
685C23—278no—
686C23—274no—
687C23—1088no—
688C23C2×D3×C3⋊D312yescomplemented
689Q8—92no—
690Q8—274no—
691Q8—272no—
692D4—38no—
693D4—34no—
694D4—94no—
695D4—98no—
696D4—92no—
697D4—274no—
698D4—274no—
699D4—278no—
700D4—274no—
701D4—278no—
702D4—274no—
703D4—278no—
704D4—272no—
705D4C2×D3×C3⋊D314yescomplemented
706C2×C4—31no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—94no—
710C2×C4—94no—
711C2×C4—274no—
712C2×C4—274no—
713C2×C4—274no—
714C2×C4—278no—
715C2×C4—274no—
716C2×C4—274no—
717C2×C4C2×D3×C3⋊D311yescharacteristic, complemented
718C2×C3—216no—
719C2×C3—24no—
720C2×C3—21no—
721C2×C3—24no—
722C2×C3—24no—
723C2×C3—38no—
724C2×C3—416no—
725C2×C3—44no—
726C2×C3—616no—
727C2×C3—64no—
728C2×C3—184no—
729C2×C3C23×D3214yes—
730C2×C3C24×C3⋊D311yescharacteristic
731D3—21no—
732D3—24no—
733D3—616no—
734D3—1816no—
735D3—184no—
736D3—3616no—
737D3#6436112yesdirect product factor
738C22—31no—
739C22—31no—
740C22—34no—
741C22—42no—
742C22—62no—
743C22—68no—
744C22—94no—
745C22—122no—
746C22—124no—
747C22—274no—
748C22—364no—
749C22—548no—
750C22—1084no—
751C22—1088no—
752C22C22×D3×C3⋊D311yescharacteristic
753C22C22×D3×C3⋊D314yes—
754C4—32no—
755C4—94no—
756C4—274no—
757C4C22×D3×C3⋊D312yes—
758C3—24no—
759C3D3×#100414yescomplemented
760C3C2×#6436111yescharacteristic, complemented
761C2—21no—
762C2—24no—
763C2—32no—
764C2—61no—
765C2—64no—
766C2—184no—
767C2—544no—
768C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C23×D3×C3⋊D3
commutator, socle, cosocleC2×C33C25
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11724679C2semidirect
2. C3×#64361C2semidirect
3. C2×C32×D3×D4C2semidirect
4. #11724611C2semidirect
5. C2×D3×#638C2semidirect
6. #11724588C2semidirect
7. #11724587C2semidirect
8. D3×#3830C2semidirect
9. D3×D4×C3⋊D3C2semidirect
10. #11724579C2semidirect
11. D3×#3828C2semidirect
14. C23×C32×D3C22semidirect
15. C22×D3×C3⋊D3C22semidirect
16. C2×C33×D4C22semidirect
17. C2×#6312C22semidirect
18. #89078C22semidirect
19. D4×C3⋊(C3⋊D3)C22semidirect
20. #89076C22semidirect
21. C2×C3×#638C22semidirect
22. C3×#3830C22semidirect
23. C3×D4×C3⋊D3C22semidirect
24. C3×#3828C22semidirect
25. C2×C32×#67C22semidirect
26. C32×D3×D4C22semidirect
27. C32×D3×D4C22semidirect
28. C2×C32×D12C22semidirect
29. C2×C32×C4×D3C22semidirect
30. #89039C22semidirect
31. C3⋊D3×#67C22semidirect
32. D3×#638C22semidirect
33. D3×#638C22semidirect
34. D3×#638C22semidirect
35. D3×#638C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
38. #89031C22semidirect
39. #89029C22semidirect
40. #89028C22semidirect
41. C2×D3×C3⋊Dic3C22semidirect
42. #89026C22semidirect
43. C3⋊D3×D12C22semidirect
44. D3×C4⋊(C3⋊D3)C22semidirect
45. C4×D3×C3⋊D3C22semidirect
46. #89022C22semidirect
47. #89021C22semidirect
48. #89020C22semidirect
49. #89015C22semidirect
50. #89014C22semidirect
51. D3×#634C22semidirect
61. #64361D3direct (N × H)
66. C2×C3×D3×D4D3semidirect
75. C23×C33C23semidirect
76. C22×C3⋊(C3⋊D3)C23semidirect
77. C22×C3×C3⋊D3C23semidirect
81. C22×C32×D3C23semidirect
82. C22×C32×D3C23semidirect
85. C2×D3×C3⋊D3C23semidirect
86. C33×D4C23semidirect
87. C2×C33×C4C23semidirect
88. #6312C23semidirect
89. #6312C23semidirect
90. C2×C3⋊(C3⋊Dic3)C23semidirect
91. C4⋊(C3⋊(C3⋊D3))C23semidirect
92. C4×C3⋊(C3⋊D3)C23semidirect
93. #6308C23semidirect
94. C3×#638C23semidirect
95. C3×#638C23semidirect
96. C2×C3×C3⋊Dic3C23semidirect
97. C3×C4⋊(C3⋊D3)C23semidirect
98. C3×C4×C3⋊D3C23semidirect
99. C3×#634C23semidirect
100. C32×#67C23semidirect
101. C2×C32×Dic3C23semidirect
102. C32×D12C23semidirect
104. C32×C4×D3C23semidirect
105. #6293C23semidirect
106. #6292C23semidirect
107. #6291C23semidirect
108. #6291C23semidirect
109. #6290C23semidirect
110. #6290C23semidirect
111. #6289C23semidirect
112. Dic3×C3⋊D3C23semidirect
114. D3×C3⋊Dic3C23semidirect
119. C23×C3×D3C2×D3semidirect
126. C2×C32×D4C2×D3semidirect
127. C2×C32×D4C2×D3semidirect
138. C2×#638C2×D3semidirect
147. #3830C2×D3semidirect
155. D4×C3⋊D3C2×D3semidirect
163. #3828C2×D3semidirect
168. C2×C3×#67C2×D3semidirect
171. C3×D3×D4C2×D3semidirect
172. C3×D3×D4C2×D3semidirect
174. C2×C3×D12C2×D3semidirect
175. C2×C3×C4×D3C2×D3semidirect
239. C2×D3×D4C3⋊D3semidirect
247. C23×C32C22×D3semidirect
248. C23×C32C22×D3semidirect
255. C22×C3⋊D3C22×D3semidirect
260. C22×C3×D3C22×D3semidirect
261. C22×C3×D3C22×D3semidirect
268. C32×D4C22×D3semidirect
269. C32×D4C22×D3semidirect
274. C2×C32×C4C22×D3semidirect
275. C2×C32×C4C22×D3semidirect
286. #638C22×D3semidirect
287. #638C22×D3semidirect
293. C2×C3⋊Dic3C22×D3semidirect
298. C4⋊(C3⋊D3)C22×D3semidirect
304. C4×C3⋊D3C22×D3semidirect
309. #634C22×D3semidirect
312. C3×#67C22×D3semidirect
314. C2×C3×Dic3C22×D3semidirect
316. C3×D12C22×D3semidirect
319. C3×C4×D3C22×D3semidirect
339. C32×D3H(5,𝔽2)semidirect
343. C23×D3C2×C3⋊D3semidirect
353. C2×C3×D4D32semidirect
354. C2×C3×D4C2×C3⋊D3semidirect
368. C2×#67C2×C3⋊D3semidirect
399. D3×D4C2×C3⋊D3semidirect
400. D3×D4C2×C3⋊D3semidirect
415. C2×D12C2×C3⋊D3semidirect
419. C2×C4×D3C2×C3⋊D3semidirect
479. C33C2×H(5,𝔽2)semidirect
487. C23×C3C2×D32semidirect
488. C23×C3C22×C3⋊D3semidirect
502. C22×D3C22×C3⋊D3semidirect
503. C22×D3C22×C3⋊D3semidirect
511. C3×D4C2×D32semidirect
512. C3×D4C22×C3⋊D3semidirect
519. C2×C3×C4C2×D32semidirect
520. C2×C3×C4C22×C3⋊D3semidirect
536. #67C22×C3⋊D3semidirect
544. C2×Dic3C22×C3⋊D3semidirect
552. D12C22×C3⋊D3semidirect
563. C4×D3C22×C3⋊D3semidirect
589. C3×D3#1004semidirect
624. C2×D4D3×C3⋊D3semidirect
676. C32C2×#1004semidirect
677. C32D3×H(5,𝔽2)semidirect
688. C23C2×D3×C3⋊D3semidirect
705. D4C2×D3×C3⋊D3semidirect
717. C2×C4C2×D3×C3⋊D3semidirect
737. D3#64361direct (N × H)
759. C3D3×#1004semidirect
760. C3C2×#64361semidirect

Maximal subgroups

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

subgroupindex
#117246792
C3×#643612
C2×C32×D3×D42
#117246112
C2×D3×#6382
#117245882
#117245872
D3×#38302
D3×D4×C3⋊D32
#117245792
D3×#38282
C2×#643613
D3×#10043