Finite Group Databasebeta

← C3⋊D3×#912 #13176715

Subgroups — C3⋊D3×#912 #13176715

Order 1728.

1844 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#237C212yesmaximal, complemented
2#11723953C211yesmaximal, characteristic, complemented
3C3×D8×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#912C211yesmaximal, characteristic, complemented
5#11723565C212yesmaximal, complemented
6#11723556C212yesmaximal, complemented
7C3⋊D3×#214C212yesmaximal, complemented
8#11723345C211yesmaximal, characteristic, complemented
9#11723336C211yesmaximal, characteristic, complemented
10C3⋊D3×Dic12C211yesmaximal, characteristic, complemented
11D3×C8×C3⋊D3C211yesmaximal, characteristic, complemented
12C3⋊D3×#135—31nomaximal
13D3×#912—34nomaximal
14#89078C2212yescomplemented
15C3×D4×C3⋊D3C2212yes—
16C32×#237C2212yescomplemented
17C3⋊D3×#67—22no—
18#89031—22no—
19C2×Dic3×C3⋊D3—22no—
20#89029—22no—
21C4×D3×C3⋊D3C2211yescharacteristic
22#89021C2212yescomplemented
23#89017C2212yescomplemented
24C3⋊D3×Dic6C2212yes—
25C33×D8C2211yescharacteristic, complemented
26#88861C2212yescomplemented
27#88853C2211yescharacteristic, complemented
28C8×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
29C3×#3753C2212yescomplemented
30C3×#3745C2211yescharacteristic, complemented
31C3×C8×C3⋊D3C2211yescharacteristic
32C32×#214C2212yescomplemented
33C32×Dic12C2211yescharacteristic, complemented
34C32×D3×C8C2211yescharacteristic, complemented
35#88799C2212yescomplemented
36#88796C2212yescomplemented
37#88793C2212yescomplemented
38#88785C2211yescharacteristic, complemented
39C3⋊D3×C3⋊C8C2211yescharacteristic
40D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
41#41×C3⋊D3—32no—
42D3×#237—38no—
43C32×#135—31no—
44#64159—32no—
45#64128—31no—
46Q16×C3⋊D3—31no—
47#64125—32no—
48SD16×C3⋊D3—32no—
49#64121—31no—
50#64121—34no—
51#64121—64no—
52D8×C3⋊D3D311yescharacteristic, complemented
53#64113—31no—
54C2×C8×C3⋊D3—31no—
55C3×#912D314yescomplemented
56C3×D3×D8—34no—
57#63936—38no—
58#63933—38no—
59D3×#214—38no—
60#63810—34no—
61#63807—34no—
62D3×Dic12—34no—
63D32×C8—34no—
64C22×C3×C3⋊D3—22no—
65C2×D3×C3⋊D3D411yescharacteristic
66C33×D4C2312yes—
67#6312—22no—
68C2×C3⋊(C3⋊Dic3)—22no—
69C4×C3⋊(C3⋊D3)C2311yescharacteristic
70#6308C2312yes—
71C3×#638—22no—
72C3×C4⋊(C3⋊D3)C2312yes—
73C3×C4×C3⋊D3C2311yescharacteristic
74C32×#67—22no—
75C2×C32×Dic3—22no—
76C32×C4×D3C2311yescharacteristic
77C32×Dic6C2312yes—
78#6293—22no—
79#6292—22no—
80#6290—22no—
81#6289D411yescharacteristic
82Dic3×C3⋊D3—22no—
83Dic3×C3⋊D3—22no—
84Dic3×C3⋊D3—22no—
85Dic3×C3⋊D3D411yescharacteristic
86D3×C3⋊Dic3D411yescharacteristic
87C33×C8C2311yescharacteristic
88C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
89C3×C3⋊(C3⋊C8)C2311yescharacteristic
90C32×C3⋊C8C2311yescharacteristic
91D3×#135—94no—
92C2×#912—91no—
93C32×#41—32no—
94#3832—32no—
95Q8×C3⋊D3—32no—
96#3830—32no—
97#3830—38no—
98#3830—62no—
99#3830—68no—
100D4×C3⋊D3—62no—
101D4×C3⋊D3C2×D312yes—
102#3828—32no—
103#3828—62no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—62no—
106C3×#237C2×D318yescomplemented
107C3×D3×D4—38no—
108D3×#67—68no—
109#3805—68no—
110#3804—68no—
111C2×D3×Dic3—68no—
112C4×D32—34no—
113#3796—38no—
114#3795—38no—
115D3×Dic6—38no—
116C32×Q16—31no—
117C32×SD16—32no—
118C32×D8—24no—
119C32×D8C2×D314yescomplemented
120C32×D8C2×D311yescharacteristic, complemented
121C2×C32×C8—31no—
122#3756—32no—
123#3755—32no—
124#3754—32no—
125#3754—38no—
126#3754—68no—
127#3753C2×D312yescomplemented
128C2×C3⋊(C3⋊C8)—31no—
129#3746—31no—
130#3746—34no—
131#3746—64no—
132#3745C2×D311yescharacteristic, complemented
133#3744—32no—
134C8×C3⋊D3—31no—
135C8×C3⋊D3—31no—
136C8×C3⋊D3—34no—
137C8×C3⋊D3—31no—
138C8×C3⋊D3—64no—
139C8×C3⋊D3C2×D311yescharacteristic
140C3×#214C2×D318yescomplemented
141C3×#213—38no—
142C3×Dic12C2×D314yescomplemented
143C3×D24—34no—
144C3×D3×C8—34no—
145C3×D3×C8C2×D314yescomplemented
146#3719—38no—
147#3716—38no—
148#3715—38no—
149#3710—34no—
150D3×C3⋊C8—34no—
151D3×C3⋊C8—34no—
152C22×C33—22no—
153C2×C3⋊(C3⋊D3)C2×D411yescharacteristic
154C2×C3×C3⋊D3—22no—
155C2×C3×C3⋊D3—44no—
156C2×C3×C3⋊D3C2×D411yescharacteristic
157C2×C32×D3C2×D411yescharacteristic
158D3×C3⋊D3—22no—
159C33×C4C2411yescharacteristic
160C3⋊(C3⋊Dic3)—22no—
161C3⋊(C3⋊Dic3)C2×D411yescharacteristic
162C3×C3⋊Dic3C2×D411yescharacteristic
163C32×Dic3—22no—
164C32×Dic3C2×D411yescharacteristic
165D3×#41—98no—
166C2×#237—92no—
167C3×#135—34no—
168C2×C3×D8—91no—
169#950—98no—
170C2×#214—92no—
171#919—94no—
172D3×Q16—94no—
173#916—98no—
174D3×SD16—98no—
175#912—92no—
176#912—94no—
177#912—91no—
178#912—92no—
179#912—91no—
180#912—91no—
181#912—184no—
182#912C3⋊D311yescharacteristic, direct product factor
183D3×D8—34no—
184C2×Dic12—91no—
185#904—94no—
186C2×D3×C8—94no—
187C2×D3×C8—91no—
188C22×C3⋊D3—22no—
189C22×C3⋊D3—31no—
190C22×C3×D3—68no—
191C2×D32—34no—
192C32×Q8—32no—
193C32×D4—28no—
194C32×D4—62no—
195C32×D4C22×D318yes—
196C32×D4C22×D312yes—
197C2×C32×C4—31no—
198C2×C32×C4—62no—
199#638—22no—
200#638—62no—
201#638—62no—
202#638—68no—
203#638—128no—
204C2×C3⋊Dic3—31no—
205C2×C3⋊Dic3—62no—
206C2×C3⋊Dic3—68no—
207C2×C3⋊Dic3—128no—
208C4⋊(C3⋊D3)—62no—
209C4⋊(C3⋊D3)C22×D312yes—
210C4×C3⋊D3—31no—
211C4×C3⋊D3—31no—
212C4×C3⋊D3—31no—
213C4×C3⋊D3—34no—
214C4×C3⋊D3—64no—
215C4×C3⋊D3—62no—
216C4×C3⋊D3—62no—
217C4×C3⋊D3—62no—
218C4×C3⋊D3C22×D311yescharacteristic
219#634—32no—
220#634—38no—
221#634—68no—
222#634—62no—
223C3×#67—28no—
224C3×#67—68no—
225C2×C3×Dic3—28no—
226C3×D12—38no—
227C3×C4×D3—34no—
228C3×C4×D3C22×D314yes—
229C3×Dic6C22×D318yes—
230#627—68no—
231#626—68no—
232#625—68no—
233#624—34no—
234D3×Dic3—34no—
235D3×Dic3—34no—
236D3×Dic3—68no—
237D3×Dic3—68no—
238D3×Dic3—68no—
239C32×C8—24no—
240C32×C8—31no—
241C32×C8C22×D314yes—
242C32×C8C22×D311yescharacteristic
243C3⋊(C3⋊C8)—31no—
244C3⋊(C3⋊C8)—34no—
245C3⋊(C3⋊C8)—64no—
246C3⋊(C3⋊C8)C22×D311yescharacteristic
247C3×C3⋊C8—34no—
248C3×C3⋊C8C22×D314yes—
249C2×#135—271noSylow
250C2×C33—42no—
251C2×C33C22×D411yescharacteristic
252C3⋊(C3⋊D3)—21no—
253C3×C3⋊D3—42no—
254C3×C3⋊D3#13512yescomplemented
255C32×D3—21no—
256C3×#41—38no—
257C2×C3×D4—92no—
258C2×#67—182no—
259C22×Dic3—182no—
260#239—98no—
261D3×Q8—98no—
262#237—98no—
263#237—92no—
264#237—92no—
265#237—92no—
266#237—188no—
267#237—182no—
268#237—182no—
269#237—188no—
270#237C2×C3⋊D312yescomplemented
271D3×D4—38no—
272D3×D4—188no—
273#235—98no—
274#235—188no—
275C2×C4×D3—94no—
276C2×C4×D3—91no—
277C2×C4×D3—188no—
278C2×Dic6—92no—
279C3×Q16—34no—
280C3×SD16—38no—
281C3×D8—24no—
282C3×D8—92no—
283C3×D8—91no—
284C3×D8D3214yescomplemented
285C3×D8C2×C3⋊D311yescharacteristic, complemented
286C2×C3×C8—34no—
287C2×C3×C8—91no—
288#216—98no—
289#215—98no—
290#214—98no—
291#214—92no—
292#214—92no—
293#214—92no—
294#214—188no—
295#214C2×C3⋊D312yescomplemented
296#213—38no—
297C2×C3⋊C8—94no—
298C2×C3⋊C8—91no—
299Dic12—92no—
300Dic12—94no—
301Dic12—91no—
302Dic12—184no—
303Dic12C2×C3⋊D311yescharacteristic, complemented
304D24—34no—
305#204—98no—
306D3×C8—34no—
307D3×C8—94no—
308D3×C8—94no—
309D3×C8—91no—
310D3×C8—94no—
311D3×C8—91no—
312D3×C8—91no—
313D3×C8—184no—
314D3×C8C2×C3⋊D311yescharacteristic, complemented
315C22×C32—22no—
316C22×C32—28no—
317C22×C32—31no—
318C22×C32—48no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—31no—
321C2×C3⋊D3—34no—
322C2×C3⋊D3—44no—
323C2×C3⋊D3—64no—
324C2×C3⋊D3—62no—
325C2×C3⋊D3D3×D411yescharacteristic
326C2×C3×D3—34no—
327C2×C3×D3—68no—
328C2×C3×D3—1216no—
329C2×C3×D3D3×D414yes—
330D32—68no—
331C32×C4—24no—
332C32×C4—31no—
333C32×C4—62no—
334C32×C4C23×D314yes—
335C32×C4C23×D311yescharacteristic
336C3⋊Dic3—31no—
337C3⋊Dic3—34no—
338C3⋊Dic3—64no—
339C3⋊Dic3—62no—
340C3⋊Dic3—68no—
341C3⋊Dic3—128no—
342C3⋊Dic3D3×D411yescharacteristic
343C3×Dic3—28no—
344C3×Dic3—34no—
345C3×Dic3D3×D414yes—
346C2×#41—272no—
347#135—31no—
348#135—271no—
349#135—272no—
350#135—271no—
351#135—272no—
352#135—271no—
353C2×Q16—271no—
354C2×SD16—272no—
355C2×D8—91no—
356C22×C8—271no—
357C33C2×#13511yescharacteristic, complemented, Sylow
358C23×C3—182no—
359C22×D3—68no—
360C22×D3—94no—
361C22×D3—91no—
362C3×Q8—38no—
363C3×D4—28no—
364C3×D4—68no—
365C3×D4—92no—
366C3×D4—182no—
367C3×D4C2×D3218yes—
368C3×D4C22×C3⋊D312yes—
369C2×C3×C4—34no—
370C2×C3×C4—68no—
371C2×C3×C4—91no—
372#67—22no—
373#67—68no—
374#67—182no—
375#67—188no—
376#67—182no—
377#67—188no—
378#67—182no—
379#67—368no—
380C2×Dic3—22no—
381C2×Dic3—94no—
382C2×Dic3—91no—
383C2×Dic3—182no—
384C2×Dic3—182no—
385C2×Dic3—182no—
386C2×Dic3—188no—
387C2×Dic3—182no—
388C2×Dic3—368no—
389D12—38no—
390D12—188no—
391C4×D3—34no—
392C4×D3—94no—
393C4×D3—94no—
394C4×D3—91no—
395C4×D3—94no—
396C4×D3—91no—
397C4×D3—91no—
398C4×D3—184no—
399C4×D3—188no—
400C4×D3—188no—
401C4×D3—188no—
402C4×D3C22×C3⋊D311yescharacteristic
403Dic6—98no—
404Dic6—92no—
405Dic6—188no—
406Dic6—182no—
407Dic6—188no—
408Dic6C22×C3⋊D312yes—
409C3×C8—24no—
410C3×C8—34no—
411C3×C8—91no—
412C3×C8C2×D3214yes—
413C3×C8C22×C3⋊D311yescharacteristic
414C3⋊C8—34no—
415C3⋊C8—94no—
416C3⋊C8—91no—
417C3⋊C8—184no—
418C3⋊C8C22×C3⋊D311yescharacteristic
419C2×C32—24no—
420C2×C32—42no—
421C2×C32—48no—
422C2×C32—61no—
423C2×C32—88no—
424C2×C32C2×D3×D414yes—
425C2×C32C2×D3×D411yescharacteristic
426C3⋊D3—42no—
427C3⋊D3—61no—
428C3⋊D3—64no—
429C3⋊D3—124no—
430C3⋊D3#91212yesdirect product factor
431C3×D3—24no—
432C3×D3—38no—
433C3×D3—128no—
434#41—32no—
435#41—272no—
436#41—272no—
437#41—272no—
438#41—542no—
439#41—542no—
440C2×Q8—272no—
441C2×D4—92no—
442C2×D4—542no—
443C22×C4—271no—
444C22×C4—542no—
445Q16—31no—
446Q16—272no—
447Q16—271no—
448SD16—32no—
449SD16—272no—
450SD16—272no—
451SD16—272no—
452D8—92no—
453D8—91no—
454D8D3×C3⋊D311yescharacteristic, complemented
455C2×C8—31no—
456C2×C8—91no—
457C2×C8—271no—
458C2×C8—271no—
459C2×C8—271no—
460C2×C8—271no—
461C22×C3—28no—
462C22×C3—22no—
463C22×C3—34no—
464C22×C3—48no—
465C22×C3—91no—
466C22×C3—182no—
467C22×C3—364no—
468C2×D3—34no—
469C2×D3—68no—
470C2×D3—94no—
471C2×D3—91no—
472C2×D3—1216no—
473C2×D3—184no—
474C2×D3—182no—
475C2×D3—188no—
476C2×D3D4×C3⋊D311yescharacteristic
477C3×C4—24no—
478C3×C4—34no—
479C3×C4—68no—
480C3×C4—91no—
481C3×C4C22×D3214yes—
482C3×C4C23×C3⋊D311yescharacteristic
483Dic3—22no—
484Dic3—34no—
485Dic3—94no—
486Dic3—91no—
487Dic3—184no—
488Dic3—188no—
489Dic3—182no—
490Dic3—368no—
491Dic3D4×C3⋊D311yescharacteristic
492C32—24no—
493C32C2×#91211yescharacteristic, complemented
494C32D3×#13514yescomplemented
495C23—182no—
496C23—271no—
497Q8—32no—
498Q8—272no—
499Q8—542no—
500D4—62no—
501D4—92no—
502D4—182no—
503D4—542no—
504D4—542no—
505D4—542no—
506D4C2×D3×C3⋊D312yes—
507C2×C4—31no—
508C2×C4—62no—
509C2×C4—91no—
510C2×C4—271no—
511C2×C4—271no—
512C2×C4—271no—
513C2×C4—271no—
514C2×C4—542no—
515C2×C4—542no—
516C2×C4—542no—
517C2×C4—542no—
518C8—31no—
519C8—91no—
520C8—271no—
521C8C2×D3×C3⋊D311yescharacteristic
522C2×C3—24no—
523C2×C3—42no—
524C2×C3—48no—
525C2×C3—64no—
526C2×C3—88no—
527C2×C3—92no—
528C2×C3—362no—
529C2×C3D32×D414yes—
530C2×C3C2×D4×C3⋊D311yescharacteristic
531D3—21no—
532D3—38no—
533D3—128no—
534D3—181no—
535D3—184no—
536D3—364no—
537C22—22no—
538C22—31no—
539C22—91no—
540C22—182no—
541C22—271no—
542C22—364no—
543C22—542no—
544C4—31no—
545C4—62no—
546C4—91no—
547C4—271no—
548C4—542no—
549C4C22×D3×C3⋊D311yescharacteristic
550C3—24no—
551C3D3×#91214yescomplemented
552C3C3⋊D3×#13511yescharacteristic, complemented
553C2—42no—
554C2—61no—
555C2—92no—
556C2—362no—
557C2—541no—
558C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2D3×D4×C3⋊D3
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC33×D8C22
socleC2×C33C22×D4
hypercenterD8D3×C3⋊D3
hypocenterC33C2×#135
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#237C2semidirect
2. #11723953C2semidirect
3. C3×D8×C3⋊D3C2semidirect
4. C32×#912C2semidirect
5. #11723565C2semidirect
6. #11723556C2semidirect
7. C3⋊D3×#214C2semidirect
8. #11723345C2semidirect
9. #11723336C2semidirect
10. C3⋊D3×Dic12C2semidirect
11. D3×C8×C3⋊D3C2semidirect
14. #89078C22semidirect
16. C32×#237C22semidirect
22. #89021C22semidirect
23. #89017C22semidirect
25. C33×D8C22semidirect
26. #88861C22semidirect
27. #88853C22semidirect
28. C8×C3⋊(C3⋊D3)C22semidirect
29. C3×#3753C22semidirect
30. C3×#3745C22semidirect
32. C32×#214C22semidirect
33. C32×Dic12C22semidirect
34. C32×D3×C8C22semidirect
35. #88799C22semidirect
36. #88796C22semidirect
37. #88793C22semidirect
38. #88785C22semidirect
40. D3×C3⋊(C3⋊C8)C22semidirect
52. D8×C3⋊D3D3semidirect
55. C3×#912D3semidirect
106. C3×#237C2×D3semidirect
119. C32×D8C2×D3semidirect
120. C32×D8C2×D3semidirect
127. #3753C2×D3semidirect
132. #3745C2×D3semidirect
140. C3×#214C2×D3semidirect
142. C3×Dic12C2×D3semidirect
145. C3×D3×C8C2×D3semidirect
182. #912C3⋊D3direct (N × H)
254. C3×C3⋊D3#135semidirect
270. #237C2×C3⋊D3semidirect
284. C3×D8D32semidirect
285. C3×D8C2×C3⋊D3semidirect
295. #214C2×C3⋊D3semidirect
303. Dic12C2×C3⋊D3semidirect
314. D3×C8C2×C3⋊D3semidirect
357. C33C2×#135semidirect
430. C3⋊D3#912direct (N × H)
454. D8D3×C3⋊D3semidirect
493. C32C2×#912semidirect
494. C32D3×#135semidirect
551. C3D3×#912semidirect
552. C3C3⋊D3×#135semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#2372
#117239532
C3×D8×C3⋊D32
C32×#9122
#117235652
#117235562
C3⋊D3×#2142
#117233452
#117233362
C3⋊D3×Dic122
D3×C8×C3⋊D32
C3⋊D3×#1353
D3×#9123