Finite Group Databasebeta

← C3⋊D3×#464 #11865663

Subgroups — C3⋊D3×#464 #11865663

Order 1152.

1500 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×SD16×C3⋊D3C211yesmaximal, characteristic
3C3⋊D3×#124C211yesmaximal, characteristic
4C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×#464C211yesmaximal, characteristic, complemented
6#10592884C211yesmaximal, characteristic, complemented
7#10592865C211yesmaximal, characteristic, complemented
8#10592753C211yesmaximal, characteristic, complemented
9#10592727C211yesmaximal, characteristic, complemented
10#10592544C211yesmaximal, characteristic, complemented
11C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
12C3⋊D3×#103C211yesmaximal, characteristic, complemented
13#10592497C211yesmaximal, characteristic, complemented
14C3⋊D3×#102C211yesmaximal, characteristic
15#10592466C211yesmaximal, characteristic, complemented
16D3×#464—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic, complemented
21C2×C32×SD16C2211yescharacteristic
22C32×#124C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic, complemented
24#64156C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3756C2211yescharacteristic, complemented
27C2×#3756C2211yescharacteristic, complemented
28C2×#3755C2211yescharacteristic
29#64145C2211yescharacteristic
30C2×#3754C2211yescharacteristic
31Q16×C3⋊D3—24no—
32SD16×C3⋊D3—24no—
33C2×#3746C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic
35C2×C8×C3⋊D3C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37C4⋊C4×C3⋊D3—21no—
38C4⋊C4×C3⋊D3C2211yescharacteristic
39#64096—21no—
40#64096C2211yescharacteristic, complemented
41#64094—21no—
42#64094—21no—
43C22⋊C4×C3⋊D3—21no—
44C22⋊C4×C3⋊D3—21no—
45#64084C2211yescharacteristic
46C42×C3⋊D3—21no—
47C42×C3⋊D3C2211yescharacteristic
48C4×#634—21no—
49C4×#634C2211yescharacteristic, complemented
50C32×C4⋊C8C2211yescharacteristic, complemented
51C32×#103C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic
55#63648C2211yescharacteristic
56#63643C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63636C2211yescharacteristic
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×D3×Q16—34no—
63C2×D3×SD16—34no—
64D3×#124—34no—
65C4×D3×Q8—34no—
66C3×#464D314yescomplemented
67#5185—34no—
68#5166—34no—
69#5054—34no—
70#5028—34no—
71#4845—34no—
72D3×C4⋊C8—34no—
73D3×#103—34no—
74#4798—34no—
75D3×#102—34no—
76#4767—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C2×#638—21no—
82Q8×C3⋊D3—22no—
83Q8×C3⋊D3—22no—
84Q8×C3⋊D3—22no—
85Q8×C3⋊D3D414yes—
86D4×C3⋊D3—22no—
87D4×C3⋊D3—22no—
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3D411yescharacteristic
93C2×C4×C3⋊D3D411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634—21no—
96C2×#634—21no—
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C32×Q16—22no—
100C32×SD16—22no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4—21no—
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106C32×C22⋊C4—21no—
107C32×C42—21no—
108C32×C42C2311yescharacteristic
109#3757—21no—
110#3757—21no—
111#3756—22no—
112#3756—22no—
113#3755—22no—
114#3754—22no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123#3750—21no—
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3D411yescharacteristic
128C4×C3⋊Dic3D411yescharacteristic
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3746—22no—
133#3744—22no—
134C8×C3⋊D3—22no—
135C8×C3⋊D3—22no—
136C2×#464—91noSylow
137C2×D3×Q8—34no—
138C2×D3×Q8—34no—
139C2×D3×D4—34no—
140C2×C3×Q16C2×D314yescomplemented
141C2×C3×SD16C2×D314yes—
142C3×#124C2×D314yes—
143C3×C4×Q8C2×D314yescomplemented
144#947—34no—
145Q8×Dic3—34no—
146C2×#216—34no—
147C2×#216—34no—
148C2×#215—34no—
149#936—34no—
150C2×#214—34no—
151D3×Q16—616no—
152D3×SD16—616no—
153C2×Dic12—34no—
154C2×#204—34no—
155C2×D3×C8—34no—
156C2×D3×C8—34no—
157D3×C4⋊C4—34no—
158D3×C4⋊C4—64no—
159#887—34no—
160#887—64no—
161#885—64no—
162#885—64no—
163D3×C22⋊C4—64no—
164D3×C22⋊C4—64no—
165#875—34no—
166C42×D3—34no—
167C42×D3—64no—
168C4×Dic6—34no—
169C4×Dic6—64no—
170C3×C4⋊C8C2×D314yescomplemented
171C3×#103C2×D314yescomplemented
172C3×#102C2×D314yes—
173#835—34no—
174#832—34no—
175#821—34no—
176#816—34no—
177Dic3⋊C8—34no—
178Dic3⋊C8—34no—
179#810—34no—
180#809—34no—
181C4⋊(C3⋊C8)—34no—
182C23×C32—21no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3—42no—
185C22×C3⋊D3—42no—
186C22×C3⋊D3—42no—
187C22×C3⋊D3C2×D411yescharacteristic
188C32×Q8—21no—
189C32×Q8—21no—
190C32×Q8—21no—
191C32×Q8C2×D412yes—
192C32×D4—21no—
193C32×D4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2411yescharacteristic
200#638—42no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3C2×D411yescharacteristic
205C2×C3⋊Dic3C2×D411yescharacteristic
206C2×C3⋊Dic3C2×D411yescharacteristic
207C4⋊(C3⋊D3)—21no—
208C4⋊(C3⋊D3)—21no—
209C4×C3⋊D3—24no—
210C4×C3⋊D3—22no—
211C4×C3⋊D3—22no—
212C4×C3⋊D3—42no—
213C4×C3⋊D3—42no—
214C4×C3⋊D3C2×D412yes—
215C4×C3⋊D3#4112yes—
216#634—21no—
217#634—24no—
218#634—21no—
219#634—21no—
220#634—42no—
221#634C2×D412yes—
222C32×C8—21no—
223C32×C8—21no—
224C3⋊(C3⋊C8)—21no—
225C3⋊(C3⋊C8)—21no—
226C22×Q16—91no—
227C22×SD16—91no—
228C2×#124—91no—
229C2×C4×Q8—91no—
230#464—91no—
231#464—91no—
232#464—91no—
233#464—91no—
234#464—91no—
235#464—91no—
236#464—91no—
237#464C3⋊D311yescharacteristic, direct product factor
238C2×C4⋊C8—91no—
239C2×#103—91no—
240C2×#102—91no—
241C23×D3—64no—
242C2×C3×Q8C22×D314yes—
243C2×C3×Q8C22×D314yes—
244C2×C3×D4C22×D314yes—
245C2×#67—64no—
246D3×Q8—316no—
247D3×Q8—68no—
248D3×Q8—68no—
249D3×Q8—68no—
250D3×D4—68no—
251D3×D4—68no—
252C2×D12—34no—
253C2×C4×D3—34no—
254C2×C4×D3—34no—
255C2×C4×D3—34no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×Dic6—34no—
260C2×Dic6—34no—
261C2×Dic6—64no—
262C2×Dic6—64no—
263C3×Q16—28no—
264C3×SD16—28no—
265C2×C3×C8C22×D314yes—
266C2×C3×C8C22×D314yes—
267C3×C4⋊C4—24no—
268C3×C4⋊C4C22×D314yes—
269C3×C22⋊C4—24no—
270C3×C22⋊C4—24no—
271C3×C42—24no—
272C3×C42C22×D314yes—
273#217—64no—
274#217—64no—
275#216—68no—
276#216—68no—
277#215—68no—
278#214—68no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283C4⋊Dic3—34no—
284C4⋊Dic3—64no—
285Dic3⋊C4—64no—
286Dic3⋊C4—64no—
287Dic3⋊C4—64no—
288C4×Dic3—34no—
289C4×Dic3—34no—
290C4×Dic3—34no—
291C4×Dic3—64no—
292C4×Dic3—64no—
293C4×Dic3—64no—
294C2×C3⋊C8—34no—
295C2×C3⋊C8—34no—
296Dic12—68no—
297#204—68no—
298D3×C8—68no—
299D3×C8—68no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32C22×D411yescharacteristic
304C2×C3⋊D3—41no—
305C2×C3⋊D3—41no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—84no—
308C2×C3⋊D3#12112yes—
309C2×C3⋊D3#13512yes—
310C2×C3⋊D3#13712yes—
311C32×C4—22no—
312C32×C4—21no—
313C32×C4—21no—
314C32×C4—41no—
315C32×C4—41no—
316C32×C4C22×D411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—22no—
319C3⋊Dic3—21no—
320C3⋊Dic3—21no—
321C3⋊Dic3—41no—
322C3⋊Dic3—41no—
323C3⋊Dic3#12112yes—
324C22×Q8—91no—
325C22×Q8—91no—
326C22×D4—91no—
327C2×Q16—91no—
328C2×Q16—91no—
329C2×Q16—91no—
330C2×Q16—184no—
331C2×Q16C2×C3⋊D311yescharacteristic, complemented
332C2×SD16—91no—
333C2×SD16—91no—
334C2×SD16—91no—
335C2×SD16—184no—
336C2×SD16C2×C3⋊D311yescharacteristic
337C22×C8—91no—
338C22×C8—91no—
339#124—91no—
340#124—91no—
341#124—91no—
342#124—181no—
343#124—181no—
344#124C2×C3⋊D311yescharacteristic
345C4×Q8—91no—
346C4×Q8—91no—
347C4×Q8—91no—
348C4×Q8—181no—
349C4×Q8—181no—
350C4×Q8C2×C3⋊D311yescharacteristic, complemented
351C2×C4⋊C4—91no—
352C2×C4⋊C4—181no—
353C2×C22⋊C4—181no—
354C2×C22⋊C4—181no—
355C2×C42—91no—
356C2×C42—181no—
357C4⋊C8—91no—
358C4⋊C8—91no—
359C4⋊C8—91no—
360C4⋊C8C2×C3⋊D311yescharacteristic, complemented
361#103—91no—
362#103—91no—
363#103—91no—
364#103C2×C3⋊D311yescharacteristic, complemented
365#102—91no—
366#102—91no—
367#102—91no—
368#102C2×C3⋊D311yescharacteristic
369C23×C3—24no—
370C22×D3—34no—
371C22×D3—64no—
372C22×D3—128no—
373C22×D3—128no—
374C22×D3—128no—
375C3×Q8—24no—
376C3×Q8—24no—
377C3×Q8—24no—
378C3×Q8D3×D418yes—
379C3×D4—24no—
380C3×D4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4D3×D414yes—
385C2×C3×C4D3×D414yes—
386C2×C3×C4C23×D314yes—
387#67—128no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—34no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394D12—64no—
395D12—64no—
396C4×D3—38no—
397C4×D3—38no—
398C4×D3—68no—
399C4×D3—68no—
400C4×D3—616no—
401C4×D3—128no—
402C4×D3—128no—
403Dic6—38no—
404Dic6—616no—
405Dic6—64no—
406Dic6—64no—
407Dic6—64no—
408Dic6—128no—
409C3×C8—24no—
410C3×C8—24no—
411C3⋊C8—64no—
412C3⋊C8—64no—
413C2×C32—81no—
414C2×C32C2×#12111yescharacteristic
415C2×C32C2×#13511yescharacteristic
416C2×C32C2×#13711yescharacteristic
417C3⋊D3—81no—
418C3⋊D3#46414yesdirect product factor
419C24—181no—
420C2×Q8—94no—
421C2×Q8—91no—
422C2×Q8—91no—
423C2×Q8—181no—
424C2×Q8—181no—
425C2×Q8—182no—
426C2×Q8—182no—
427C2×Q8—182no—
428C2×Q8C22×C3⋊D311yescharacteristic
429C2×Q8C22×C3⋊D311yescharacteristic
430C2×D4—91no—
431C2×D4—182no—
432C2×D4—182no—
433C2×D4—181no—
434C2×D4C22×C3⋊D311yescharacteristic
435C22×C4—91no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4—181no—
441Q16—22no—
442Q16—182no—
443Q16—182no—
444Q16—182no—
445SD16—22no—
446SD16—182no—
447SD16—182no—
448SD16—182no—
449C2×C8—91no—
450C2×C8—91no—
451C2×C8—182no—
452C2×C8—182no—
453C2×C8C22×C3⋊D311yescharacteristic
454C2×C8C22×C3⋊D311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—91no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4C22×C3⋊D311yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C22⋊C4—181no—
469C22⋊C4—181no—
470C42—21no—
471C42—91no—
472C42—91no—
473C42—91no—
474C42—181no—
475C42—181no—
476C42—181no—
477C42C22×C3⋊D311yescharacteristic
478C22×C3—44no—
479C22×C3—44no—
480C22×C3—44no—
481C22×C3C2×D3×D414yes—
482C2×D3—38no—
483C2×D3—38no—
484C2×D3—38no—
485C2×D3—124no—
486C2×D3—124no—
487C2×D3—124no—
488C2×D3—2416no—
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—28no—
492C3×C4—44no—
493C3×C4—44no—
494C3×C4C2×D3×D414yes—
495C3×C4D3×#4114yes—
496Dic3—38no—
497Dic3—64no—
498Dic3—64no—
499Dic3—68no—
500Dic3—124no—
501Dic3—124no—
502C32C2×#46411yescharacteristic, complemented, Sylow
503C23—21no—
504C23—91no—
505C23—181no—
506C23—362no—
507C23—362no—
508C23—362no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—92no—
513Q8—184no—
514Q8—181no—
515Q8—181no—
516Q8—181no—
517Q8—362no—
518Q8D4×C3⋊D312yes—
519D4—21no—
520D4—21no—
521D4—181no—
522D4—181no—
523D4—362no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—91no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—91no—
531C2×C4—91no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—184no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—362no—
539C2×C4—362no—
540C2×C4D4×C3⋊D311yescharacteristic
541C2×C4D4×C3⋊D311yescharacteristic
542C2×C4C23×C3⋊D311yescharacteristic
543C8—21no—
544C8—21no—
545C8—181no—
546C8—181no—
547C2×C3—84no—
548C2×C3D3×#12114yes—
549C2×C3D3×#13514yes—
550C2×C3D3×#13714yes—
551D3—316no—
552D3—244no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—92no—
557C22—92no—
558C22—92no—
559C22—361no—
560C22—361no—
561C22—361no—
562C22—724no—
563C22C2×D4×C3⋊D311yescharacteristic
564C4—21no—
565C4—21no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—92no—
570C4—181no—
571C4—181no—
572C4—182no—
573C4—361no—
574C4—361no—
575C4C2×D4×C3⋊D311yescharacteristic
576C4#41×C3⋊D311yescharacteristic
577C3D3×#46414yescomplemented
578C2—81no—
579C2—94no—
580C2—721no—
581C2C3⋊D3×#12111yescharacteristic
582C2C3⋊D3×#13511yescharacteristic
583C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#464C3⋊D3
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×C3⋊D3C2semidirect
4. C4×Q8×C3⋊D3C2semidirect
5. C32×#464C2semidirect
6. #10592884C2semidirect
7. #10592865C2semidirect
8. #10592753C2semidirect
9. #10592727C2semidirect
10. #10592544C2semidirect
11. C3⋊D3×C4⋊C8C2semidirect
12. C3⋊D3×#103C2semidirect
13. #10592497C2semidirect
15. #10592466C2semidirect
20. C2×C32×Q16C22semidirect
23. C32×C4×Q8C22semidirect
25. Q8×C3⋊Dic3C22semidirect
26. C2×#3756C22semidirect
27. C2×#3756C22semidirect
33. C2×#3746C22semidirect
40. #64096C22semidirect
49. C4×#634C22semidirect
50. C32×C4⋊C8C22semidirect
51. C32×#103C22semidirect
53. #63662C22semidirect
56. #63643C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. #63637C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#464D3semidirect
140. C2×C3×Q16C2×D3semidirect
143. C3×C4×Q8C2×D3semidirect
170. C3×C4⋊C8C2×D3semidirect
171. C3×#103C2×D3semidirect
237. #464C3⋊D3direct (N × H)
331. C2×Q16C2×C3⋊D3semidirect
350. C4×Q8C2×C3⋊D3semidirect
360. C4⋊C8C2×C3⋊D3semidirect
364. #103C2×C3⋊D3semidirect
418. C3⋊D3#464direct (N × H)
502. C32C2×#464semidirect
577. C3D3×#464semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
C2×SD16×C3⋊D32
C3⋊D3×#1242
C4×Q8×C3⋊D32
C32×#4642
#105928842
#105928652
#105927532
#105927272
#105925442
C3⋊D3×C4⋊C82
C3⋊D3×#1032
#105924972
C3⋊D3×#1022
#105924662
D3×#4643