Finite Group Databasebeta

← D3×#63782 #13166525

Subgroups — D3×#63782 #13166525

Order 1728.

984 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D4×C3⋊D3C211yesmaximal, characteristic
2D3×C4⋊#157C211yesmaximal, characteristic, complemented
3D3×#3787C211yesmaximal, characteristic, complemented
4#11723107C211yesmaximal, characteristic, complemented
5C3×#63782C211yesmaximal, characteristic, complemented
6#11722707C211yesmaximal, characteristic, complemented
7#11722706C211yesmaximal, characteristic, complemented
8C2×#63782—31nomaximal
9C22×D3×C3⋊D3—21no—
10C2×D3×#157—21no—
11D4×C3⋊(C3⋊D3)C411yescharacteristic, complemented
12C3×D4×C3⋊D3C2211yescharacteristic
13C32×D3×D4C411yescharacteristic, complemented
14#89039—21no—
15C3⋊D3×#67—21no—
16D3×#638—21no—
17#89026C411yescharacteristic, complemented
18C3⋊D3×D12C2211yescharacteristic
19D3×C4⋊(C3⋊D3)C411yescharacteristic, complemented
20C4×D3×C3⋊D3C2211yescharacteristic
21C4⋊(C3⋊#157)C2211yescharacteristic, complemented
22#88988C2211yescharacteristic, complemented
23C3×C4⋊#157C2211yescharacteristic, complemented
24C3×#3787C2211yescharacteristic, complemented
25#88924—21no—
26D3×#622—21no—
27Dic3⋊#157—21no—
28C2×D4×C3⋊D3—31no—
29D32×D4—62no—
30C2×C4⋊#157—31no—
31C2×#3787—31no—
32#63782—31no—
33#63782—31no—
34#63782—31no—
35#63782D311yescharacteristic, direct product factor
36C22×C3⋊(C3⋊D3)—21no—
37C22×C3×C3⋊D3—21no—
38C22×C32×D3—21no—
39C2×D3×C3⋊D3—21no—
40C2×D3×C3⋊D3—21no—
41C2×D3×C3⋊D3—21no—
42C2×D3×C3⋊D3—42no—
43C2×D3×C3⋊D3—42no—
44C2×D3×C3⋊D3D411yescharacteristic
45C2×C3⋊#157—21no—
46C2×C3×#157—21no—
47D3×#157—42no—
48C33×D4C2×C411yescharacteristic, complemented
49#6312—21no—
50C4⋊(C3⋊(C3⋊D3))C2×C411yescharacteristic, complemented
51C4×C3⋊(C3⋊D3)C2×C411yescharacteristic
52C3×#638—21no—
53C3×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
54C3×C4×C3⋊D3C2311yescharacteristic
55C32×#67—21no—
56C32×D12C2×C411yescharacteristic, complemented
57C32×C4×D3C2×C411yescharacteristic
58#6292—21no—
59#6291—21no—
60#6290—21no—
61#6289D411yescharacteristic
62Dic3×C3⋊D3D411yescharacteristic
63D3×C3⋊Dic3D411yescharacteristic
64C3⋊#622—21no—
65C3×#622—21no—
66D3×#102—91nomaximal
67C23×C3⋊D3—61no—
68C22×D32—64no—
69C22×#157—61no—
70C2×C32×D4—31no—
71C2×#638—61no—
72D4×C3⋊D3—31no—
73D4×C3⋊D3—31no—
74D4×C3⋊D3—31no—
75D4×C3⋊D3—61no—
76D4×C3⋊D3—61no—
77D4×C3⋊D3—62no—
78D4×C3⋊D3—122no—
79D4×C3⋊D3C2×D311yescharacteristic
80C2×C4⋊(C3⋊D3)—31no—
81C2×C4×C3⋊D3—31no—
82C3×D3×D4—22no—
83C3×D3×D4—62no—
84#3811—64no—
85D3×#67—64no—
86D3×#67—64no—
87#3802—62no—
88D3×D12—62no—
89D3×D12—62no—
90C4×D32—62no—
91C2×#622—61no—
92C4⋊#157—31no—
93C4⋊#157—61no—
94C4⋊#157C2×D311yescharacteristic, complemented
95#3787—31no—
96#3787—61no—
97#3787C2×D311yescharacteristic, complemented
98C22×C33—21no—
99C2×C3⋊(C3⋊D3)—21no—
100C2×C3⋊(C3⋊D3)—42no—
101C2×C3⋊(C3⋊D3)C22⋊C411yescharacteristic
102C2×C3×C3⋊D3—21no—
103C2×C3×C3⋊D3—41no—
104C2×C3×C3⋊D3—41no—
105C2×C3×C3⋊D3C2×D411yescharacteristic
106C2×C32×D3—21no—
107C2×C32×D3—42no—
108C2×C32×D3C22⋊C411yescharacteristic
109D3×C3⋊D3—42no—
110D3×C3⋊D3—41no—
111D3×C3⋊D3—41no—
112D3×C3⋊D3—42no—
113D3×C3⋊D3D812yes—
114D3×C3⋊D3SD1612yes—
115C3⋊#157—41no—
116C3×#157—41no—
117C33×C4C22×C411yescharacteristic
118C3⋊(C3⋊Dic3)C22⋊C411yescharacteristic
119C3×C3⋊Dic3C2×D411yescharacteristic
120C32×Dic3C22⋊C411yescharacteristic
121C2×D3×D4—91no—
122C2×D3×D4—182no—
123C2×D3×C8—91no—
124D3×C4⋊C4—91no—
125C3×#102—91no—
126#832—91no—
127#821—91no—
128#809—91no—
129C23×C32—61no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—31no—
132C22×C3⋊D3—61no—
133C22×C3⋊D3—61no—
134C22×C3⋊D3—61no—
135C22×C3⋊D3—61no—
136C22×C3⋊D3—64no—
137C22×C3⋊D3—124no—
138C22×C3⋊D3—122no—
139C22×C3⋊D3—122no—
140C22×C3×D3—24no—
141C22×C3×D3—64no—
142C2×D32—62no—
143C2×D32—64no—
144C2×D32—64no—
145C2×D32—64no—
146C2×D32—128no—
147C2×D32—128no—
148C2×#157—21no—
149C2×#157—61no—
150C2×#157—122no—
151C32×D4—22no—
152C32×D4—31no—
153C32×D4—42no—
154C32×D4—61no—
155C32×D4C4×D311yescharacteristic, complemented
156C2×C32×C4—31no—
157#638—21no—
158#638—61no—
159#638—61no—
160#638—61no—
161#638—64no—
162#638—124no—
163C2×C3⋊Dic3—31no—
164C4⋊(C3⋊D3)—31no—
165C4⋊(C3⋊D3)—62no—
166C4⋊(C3⋊D3)—61no—
167C4⋊(C3⋊D3)—122no—
168C4⋊(C3⋊D3)C4×D311yescharacteristic, complemented
169C4×C3⋊D3—31no—
170C4×C3⋊D3—31no—
171C4×C3⋊D3—31no—
172C4×C3⋊D3—62no—
173C4×C3⋊D3—122no—
174C4×C3⋊D3C22×D311yescharacteristic
175C3×#67—24no—
176C3×#67—64no—
177C3×D12—22no—
178C3×D12—62no—
179C3×C4×D3—22no—
180C3×C4×D3—62no—
181#626—64no—
182#626—64no—
183#625—64no—
184#624—62no—
185D3×Dic3—62no—
186D3×Dic3—62no—
187#622—21no—
188#622—61no—
189C2×#102—271noSylow
190C2×C33—41no—
191C2×C33C2×C22⋊C411yescharacteristic
192C3⋊(C3⋊D3)—41no—
193C3⋊(C3⋊D3)#10212yescomplemented
194C3×C3⋊D3—41no—
195C3×C3⋊D3C2×D811yescharacteristic
196C3×C3⋊D3C2×SD1611yescharacteristic
197C32×D3—41no—
198C32×D3#10212yescomplemented
199C23×D3—181no—
200C23×D3—184no—
201C2×C3×D4—62no—
202C2×C3×D4—91no—
203C2×#67—181no—
204C2×#67—184no—
205D3×D4—62no—
206D3×D4—91no—
207D3×D4—91no—
208D3×D4—91no—
209D3×D4—182no—
210D3×D4—182no—
211D3×D4—182no—
212D3×D4—181no—
213D3×D4—181no—
214D3×D4—184no—
215D3×D4—184no—
216D3×D4—362no—
217D3×D4#15711yescharacteristic, complemented
218C2×D12—91no—
219C2×D12—182no—
220C2×C4×D3—91no—
221C2×C4×D3—182no—
222C2×C4×D3—181no—
223C2×C3×C8—91no—
224C3×C4⋊C4—91no—
225C4⋊Dic3—91no—
226Dic3⋊C4—181no—
227C2×C3⋊C8—91no—
228D3×C8—181no—
229D3×C8—181no—
230C22×C32—21no—
231C22×C32—24no—
232C22×C32—31no—
233C22×C32—44no—
234C22×C32—61no—
235C22×C32—122no—
236C2×C3⋊D3—21no—
237C2×C3⋊D3—31no—
238C2×C3⋊D3—32no—
239C2×C3⋊D3—32no—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—62no—
243C2×C3⋊D3—61no—
244C2×C3⋊D3—64no—
245C2×C3⋊D3—124no—
246C2×C3⋊D3—122no—
247C2×C3⋊D3—122no—
248C2×C3⋊D3—122no—
249C2×C3⋊D3—122no—
250C2×C3⋊D3—121no—
251C2×C3⋊D3—121no—
252C2×C3⋊D3—128no—
253C2×C3⋊D3—248no—
254C2×C3⋊D3D3×D411yescharacteristic
255C2×C3×D3—24no—
256C2×C3×D3—22no—
257C2×C3×D3—48no—
258C2×C3×D3—62no—
259C2×C3×D3—64no—
260C2×C3×D3—124no—
261C2×C3×D3—124no—
262D32—64no—
263D32—64no—
264D32—128no—
265D32—124no—
266D32—124no—
267D32—128no—
268#157—41no—
269#157—121no—
270C32×C4—22no—
271C32×C4—31no—
272C32×C4—42no—
273C32×C4C2×C4×D311yescharacteristic
274C3⋊Dic3—31no—
275C3⋊Dic3—62no—
276C3⋊Dic3—122no—
277C3⋊Dic3D3×D411yescharacteristic
278C3×Dic3—22no—
279C3×Dic3—62no—
280C22×D4—271no—
281C22×C8—271no—
282C2×C4⋊C4—271no—
283#102—91no—
284#102—271no—
285#102—271no—
286#102—271no—
287C33C2×#10211yescharacteristic, complemented, Sylow
288C23×C3—64no—
289C23×C3—181no—
290C22×D3—21no—
291C22×D3—64no—
292C22×D3—91no—
293C22×D3—182no—
294C22×D3—181no—
295C22×D3—181no—
296C22×D3—184no—
297C22×D3—184no—
298C22×D3—184no—
299C22×D3—181no—
300C22×D3—184no—
301C22×D3—181no—
302C22×D3—364no—
303C22×D3—362no—
304C22×D3—362no—
305C22×D3—368no—
306C22×D3—368no—
307C3×D4—22no—
308C3×D4—42no—
309C3×D4—62no—
310C3×D4—64no—
311C3×D4—91no—
312C3×D4—181no—
313C3×D4C2×#15711yescharacteristic, complemented
314C2×C3×C4—62no—
315C2×C3×C4—91no—
316C2×C3×C4—181no—
317#67—21no—
318#67—64no—
319#67—184no—
320#67—181no—
321#67—181no—
322#67—184no—
323#67—184no—
324#67—181no—
325#67—364no—
326C2×Dic3—91no—
327C2×Dic3—182no—
328C2×Dic3—181no—
329D12—62no—
330D12—91no—
331D12—182no—
332D12—184no—
333D12—181no—
334D12—362no—
335D12C2×#15711yescharacteristic, complemented
336C4×D3—62no—
337C4×D3—91no—
338C4×D3—91no—
339C4×D3—91no—
340C4×D3—182no—
341C4×D3—182no—
342C4×D3—182no—
343C4×D3—362no—
344C4×D3—362no—
345C4×D3C2×#15711yescharacteristic
346C3×C8—181no—
347C3⋊C8—181no—
348C2×C32—22no—
349C2×C32—32no—
350C2×C32—42no—
351C2×C32—41no—
352C2×C32—44no—
353C2×C32—84no—
354C2×C32—121no—
355C2×C32D3×C22⋊C411yescharacteristic
356C3⋊D3—32no—
357C3⋊D3—41no—
358C3⋊D3—64no—
359C3⋊D3—124no—
360C3⋊D3—121no—
361C3⋊D3—124no—
362C3⋊D3—244no—
363C3⋊D3D3×D811yescharacteristic
364C3⋊D3D3×SD1611yescharacteristic
365C3×D3—24no—
366C3×D3—44no—
367C3×D3—62no—
368C3×D3—62no—
369C3×D3—124no—
370C24—541no—
371C2×D4—31no—
372C2×D4—91no—
373C2×D4—271no—
374C2×D4—271no—
375C2×D4—271no—
376C2×D4—271no—
377C2×D4—541no—
378C2×D4—541no—
379C2×D4—541no—
380C22×C4—271no—
381C22×C4—541no—
382C2×C8—91no—
383C2×C8—271no—
384C2×C8—541no—
385C2×C8—541no—
386C4⋊C4—91no—
387C4⋊C4—271no—
388C4⋊C4—541no—
389C22×C3—24no—
390C22×C3—21no—
391C22×C3—44no—
392C22×C3—62no—
393C22×C3—64no—
394C22×C3—91no—
395C22×C3—128no—
396C22×C3—181no—
397C22×C3—361no—
398C22×C3—361no—
399C2×D3—21no—
400C2×D3—42no—
401C2×D3—62no—
402C2×D3—64no—
403C2×D3—91no—
404C2×D3—92no—
405C2×D3—92no—
406C2×D3—124no—
407C2×D3—124no—
408C2×D3—184no—
409C2×D3—184no—
410C2×D3—182no—
411C2×D3—184no—
412C2×D3—181no—
413C2×D3—362no—
414C2×D3—364no—
415C2×D3—362no—
416C2×D3—361no—
417C2×D3—361no—
418C2×D3—364no—
419C2×D3—364no—
420C2×D3—362no—
421C2×D3—368no—
422C2×D3—368no—
423C2×D3—368no—
424C2×D3—362no—
425C2×D3—728no—
426C2×D3C22⋊#15711yescharacteristic
427C3×C4—22no—
428C3×C4—42no—
429C3×C4—62no—
430C3×C4—91no—
431C3×C4—361no—
432C3×C4C22×#15711yescharacteristic
433Dic3—62no—
434Dic3—91no—
435Dic3—182no—
436Dic3—362no—
437Dic3—361no—
438Dic3C22⋊#15711yescharacteristic
439C32—22no—
440C32—42no—
441C32D3×#10211yescharacteristic, complemented
442C23—61no—
443C23—181no—
444C23—271no—
445C23—541no—
446C23—541no—
447C23—541no—
448C23—541no—
449C23—1082no—
450C23—1082no—
451D4—31no—
452D4—61no—
453D4—91no—
454D4—181no—
455D4—271no—
456D4—541no—
457D4—541no—
458D4—541no—
459D4—541no—
460D4D3×#15711yescharacteristic, complemented
461C2×C4—31no—
462C2×C4—91no—
463C2×C4—181no—
464C2×C4—271no—
465C2×C4—271no—
466C2×C4—271no—
467C2×C4—271no—
468C2×C4—541no—
469C2×C4—1082no—
470C8—181no—
471C8—541no—
472C2×C3—22no—
473C2×C3—44no—
474C2×C3—41no—
475C2×C3—42no—
476C2×C3—64no—
477C2×C3—84no—
478C2×C3—91no—
479C2×C3—91no—
480C2×C3—124no—
481C2×C3—361no—
482C2×C3C2×C22⋊#15711yescharacteristic
483D3—41no—
484D3—62no—
485D3—62no—
486D3—92no—
487D3—124no—
488D3—184no—
489D3—364no—
490D3—364no—
491D3—361no—
492D3—724no—
493D3#6378212yesdirect product factor
494C22—21no—
495C22—31no—
496C22—61no—
497C22—91no—
498C22—122no—
499C22—181no—
500C22—272no—
501C22—272no—
502C22—271no—
503C22—361no—
504C22—361no—
505C22—541no—
506C22—1082no—
507C22—1082no—
508C22—1081no—
509C22—1081no—
510C22—1082no—
511C4—31no—
512C4—91no—
513C4—271no—
514C4—361no—
515C4—1081no—
516C4C2×D3×#15711yescharacteristic
517C3—22no—
518C3—42no—
519C3C2×#6378211yescharacteristic, complemented
520C2—32no—
521C2—41no—
522C2—91no—
523C2—91no—
524C2—121no—
525C2—272no—
526C2—361no—
527C2—1081no—
528C2D3×C22⋊#15711yescharacteristic
subgroupG/H
centerC2D3×C22⋊#157
commutatorC33×C4C22×C4
FrattiniC4C2×D3×#157
FittingC33×D4C2×C4
socleC2×C33C2×C22⋊C4
prime radicalD3×D4×C3⋊D3C2
cosocleC3×C4×C3⋊D3C23
hypercenterD4D3×#157
hypocenterC33C2×#102
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
2. D3×C4⋊#157C2semidirect
3. D3×#3787C2semidirect
4. #11723107C2semidirect
5. C3×#63782C2semidirect
6. #11722707C2semidirect
7. #11722706C2semidirect
11. D4×C3⋊(C3⋊D3)C4semidirect
13. C32×D3×D4C4semidirect
17. #89026C4semidirect
19. D3×C4⋊(C3⋊D3)C4semidirect
21. C4⋊(C3⋊#157)C22semidirect
22. #88988C22semidirect
23. C3×C4⋊#157C22semidirect
24. C3×#3787C22semidirect
35. #63782D3direct (N × H)
48. C33×D4C2×C4semidirect
50. C4⋊(C3⋊(C3⋊D3))C2×C4semidirect
53. C3×C4⋊(C3⋊D3)C2×C4semidirect
56. C32×D12C2×C4semidirect
94. C4⋊#157C2×D3semidirect
97. #3787C2×D3semidirect
155. C32×D4C4×D3semidirect
168. C4⋊(C3⋊D3)C4×D3semidirect
193. C3⋊(C3⋊D3)#102semidirect
198. C32×D3#102semidirect
217. D3×D4#157semidirect
287. C33C2×#102semidirect
313. C3×D4C2×#157semidirect
335. D12C2×#157semidirect
441. C32D3×#102semidirect
460. D4D3×#157semidirect
493. D3#63782direct (N × H)
519. C3C2×#63782semidirect

Maximal subgroups

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

subgroupindex
D3×D4×C3⋊D32
D3×C4⋊#1572
D3×#37872
#117231072
C3×#637822
#117227072
#117227062
C2×#637823
D3×#1029