Finite Group Databasebeta

← D3×#63636 #13159413

Subgroups — D3×#63636 #13159413

Order 1728.

1412 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#11722179C211yesmaximal, characteristic, complemented
5C3×#63636C211yesmaximal, characteristic, complemented
6#11722035C211yesmaximal, characteristic, complemented
7#11722033C211yesmaximal, characteristic, complemented
8C2×#63636—31nomaximal
9D3×#809—34nomaximal
10C22×D3×C3⋊D3—21no—
11C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×C4×D3—21no—
14C2×C32×C4×D3C2211yescharacteristic
15C2×#6292—21no—
16D3×C4⋊(C3⋊D3)—22no—
17D3×C4⋊(C3⋊D3)C414yescomplemented
18C33×C4⋊C4C2211yescharacteristic, complemented
19C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
21C32×C4⋊Dic3C2211yescharacteristic, complemented
22C32×Dic3⋊C4—21no—
23D3×C3⋊(C3⋊C8)—22no—
24C22×C4⋊(C3⋊D3)—31no—
25C2×D3×D12—34no—
26C2×C32×C4⋊C4—31no—
27C22×C3⋊(C3⋊C8)—31no—
28C3×D3×C4⋊C4D314yescomplemented
29C2×D3×C3⋊C8—34no—
30#63636—31no—
31#63636—31no—
32#63636—31no—
33#63636—34no—
34#63636—64no—
35#63636D311yescharacteristic, direct product factor
36C3×#809—34no—
37#63564—34no—
38#63562—34no—
39C22×C3⋊(C3⋊D3)—21no—
40C22×C3×C3⋊D3—21no—
41C22×C32×D3D411yescharacteristic
42C2×D3×C3⋊D3—24no—
43C2×D3×C3⋊D3—42no—
44C2×D3×C3⋊D3—42no—
45C2×C33×C4—21no—
46C2×C33×C4C2311yescharacteristic
47C4⋊(C3⋊(C3⋊D3))—21no—
48C4⋊(C3⋊(C3⋊D3))C2×C412yescomplemented
49C3×C4⋊(C3⋊D3)—21no—
50C3×C4⋊(C3⋊D3)C2×C412yescomplemented
51C2×C32×Dic3—21no—
52C2×C32×Dic3D411yescharacteristic
53C32×C4×D3—42no—
54C32×C4×D3C2×C412yes—
55C32×C4×D3D412yes—
56#6292—24no—
57C3⋊(C3⋊(C3⋊C8))—21no—
58C3×C3⋊(C3⋊C8)—21no—
59C2×#809—94no—
60D3×#102—91no—
61C23×C3⋊D3—61no—
62C22×D32—64no—
63C22×C32×C4—31no—
64C22×C32×C4—61no—
65C2×C4⋊(C3⋊D3)—31no—
66C2×C4⋊(C3⋊D3)—34no—
67C2×C4⋊(C3⋊D3)—34no—
68C2×C4⋊(C3⋊D3)—62no—
69C2×C4⋊(C3⋊D3)—61no—
70C2×C4⋊(C3⋊D3)—64no—
71C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
72C2×C3×D12—34no—
73C2×C3×C4×D3—24no—
74C2×C3×C4×D3C2×D314yes—
75C2×#626—64no—
76D3×D12—316no—
77D3×D12—68no—
78C32×C4⋊C4—24no—
79C32×C4⋊C4—31no—
80C32×C4⋊C4—61no—
81C32×C4⋊C4C2×D314yescomplemented
82C32×C4⋊C4C2×D311yescharacteristic, complemented
83C2×C3⋊(C3⋊C8)—31no—
84C2×C3⋊(C3⋊C8)—34no—
85C2×C3⋊(C3⋊C8)—62no—
86C2×C3⋊(C3⋊C8)—64no—
87C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
88C3×C4⋊Dic3C2×D314yescomplemented
89C3×Dic3⋊C4—24no—
90C2×C3×C3⋊C8—34no—
91D3×C3⋊C8—68no—
92C22×C33C2×D411yescharacteristic
93C2×C3⋊(C3⋊D3)—22no—
94C2×C3⋊(C3⋊D3)—41no—
95C2×C3⋊(C3⋊D3)—41no—
96C2×C3×C3⋊D3—22no—
97C2×C3×C3⋊D3—41no—
98C2×C3×C3⋊D3—41no—
99C2×C32×D3C22⋊C412yes—
100C2×C32×D3D812yes—
101C2×C32×D3SD1612yes—
102D3×C3⋊D3—48no—
103C33×C4—41no—
104C33×C4C22×C411yescharacteristic
105C33×C4C2×D411yescharacteristic
106C32×Dic3—41no—
107C32×Dic3C22⋊C412yes—
108C2×D3×D4—91no—
109C22×D12—94no—
110C2×C3×C4⋊C4—34no—
111C22×C3⋊C8—94no—
112C2×D3×C8—91no—
113D3×C4⋊C4C3⋊D311yescharacteristic, complemented
114C3×#102—91no—
115#832—91no—
116#821—91no—
117#809—34no—
118#809—94no—
119#809—94no—
120#809—94no—
121#809—91no—
122#809—184no—
123C23×C32—31no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—64no—
126C22×C3⋊D3—61no—
127C22×C3⋊D3—64no—
128C22×C3⋊D3—124no—
129C22×C3⋊D3—122no—
130C22×C3⋊D3—122no—
131C22×C3×D3—64no—
132C22×C3×D3#6714yes—
133C2×D32—616no—
134C2×D32—128no—
135C2×D32—128no—
136C2×C32×C4—21no—
137C2×C32×C4—24no—
138C2×C32×C4—24no—
139C2×C32×C4—31no—
140C2×C32×C4—32no—
141C2×C32×C4—32no—
142C2×C32×C4—44no—
143C2×C32×C4—61no—
144C2×C32×C4—122no—
145C2×C32×C4C22×D314yes—
146C2×C32×C4C22×D311yescharacteristic
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)—32no—
149C4⋊(C3⋊D3)—38no—
150C4⋊(C3⋊D3)—68no—
151C4⋊(C3⋊D3)—64no—
152C4⋊(C3⋊D3)—61no—
153C4⋊(C3⋊D3)—64no—
154C4⋊(C3⋊D3)—124no—
155C4⋊(C3⋊D3)C4×D312yescomplemented
156C2×C3×Dic3—24no—
157C2×C3×Dic3#6714yes—
158C3×D12—38no—
159C3×D12—64no—
160C3×C4×D3—48no—
161C3×C4×D3C4×D318yes—
162C3×C4×D3D1218yes—
163#626—616no—
164C3⋊(C3⋊C8)—21no—
165C3⋊(C3⋊C8)—61no—
166C3⋊(C3⋊C8)—64no—
167C3⋊(C3⋊C8)—124no—
168C3×C3⋊C8—64no—
169C2×#102—271noSylow
170C2×C33C2×C22⋊C411yescharacteristic
171C2×C33C2×D811yescharacteristic
172C2×C33C2×SD1611yescharacteristic
173C3⋊(C3⋊D3)—42no—
174C3×C3⋊D3—42no—
175C32×D3#10214yescomplemented
176C23×D3—184no—
177C23×D3—181no—
178C2×C3×D4—91no—
179C22×C3×C4—34no—
180C22×C3×C4—64no—
181C2×#67—181no—
182D3×D4—94no—
183D3×D4—182no—
184C2×D12—34no—
185C2×D12—916no—
186C2×D12—94no—
187C2×D12—91no—
188C2×D12—184no—
189C2×D12—188no—
190C2×D12—184no—
191C2×C4×D3—21no—
192C2×C4×D3C2×C3⋊D311yescharacteristic
193C2×C3×C8—91no—
194C3×C4⋊C4—24no—
195C3×C4⋊C4—34no—
196C3×C4⋊C4—64no—
197C3×C4⋊C4D3214yescomplemented
198C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
199C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
200Dic3⋊C4—21no—
201C2×C3⋊C8—34no—
202C2×C3⋊C8—94no—
203C2×C3⋊C8—91no—
204C2×C3⋊C8—184no—
205C2×C3⋊C8—188no—
206D3×C8—182no—
207C22×C32—24no—
208C22×C32—32no—
209C22×C32—32no—
210C22×C32—32no—
211C22×C32D3×D411yescharacteristic
212C22×C32C2×#6714yes—
213C2×C3⋊D3—22no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—62no—
217C2×C3⋊D3—68no—
218C2×C3⋊D3—128no—
219C2×C3⋊D3—128no—
220C2×C3⋊D3—121no—
221C2×C3⋊D3—121no—
222C2×C3⋊D3—124no—
223C2×C3⋊D3—124no—
224C2×C3⋊D3—244no—
225C2×C3⋊D3—244no—
226C2×C3×D3—68no—
227C2×C3×D3—124no—
228C2×C3×D3—124no—
229C2×C3×D3(C2×D3)⋊C418yes—
230C2×C3×D3#21318yes—
231C2×C3×D3#21518yes—
232D32—1232no—
233C32×C4—24no—
234C32×C4—24no—
235C32×C4—32no—
236C32×C4—41no—
237C32×C4—44no—
238C32×C4—84no—
239C32×C4—121no—
240C32×C4C2×C4×D314yes—
241C32×C4C2×C4×D311yescharacteristic
242C32×C4C2×D1214yes—
243C32×C4D3×D411yescharacteristic
244C3×Dic3—44no—
245C3×Dic3(C2×D3)⋊C418yes—
246C22×D4—271no—
247C22×C8—271no—
248C2×C4⋊C4—31no—
249#102—91no—
250#102—271no—
251#102—271no—
252#102—271no—
253C33C2×#10211yescharacteristic, complemented, Sylow
254C23×C3—34no—
255C23×C3—181no—
256C22×D3—64no—
257C22×D3—1816no—
258C22×D3—184no—
259C22×D3—181no—
260C22×D3—184no—
261C22×D3—364no—
262C22×D3—368no—
263C22×D3—368no—
264C22×D3—362no—
265C22×D3—362no—
266C22×D3#63811yescharacteristic
267C3×D4—92no—
268C3×D4—181no—
269C2×C3×C4—24no—
270C2×C3×C4—21no—
271C2×C3×C4—24no—
272C2×C3×C4—34no—
273C2×C3×C4—38no—
274C2×C3×C4—38no—
275C2×C3×C4—44no—
276C2×C3×C4—64no—
277C2×C3×C4—128no—
278C2×C3×C4C2×D3214yes—
279C2×C3×C4C22×C3⋊D311yescharacteristic
280#67—184no—
281C2×Dic3—21no—
282C2×Dic3#63811yescharacteristic
283D12—38no—
284D12—64no—
285D12—98no—
286D12—92no—
287D12—188no—
288D12—1816no—
289D12—184no—
290D12—181no—
291D12—364no—
292C4×D3—42no—
293C4×D3C4×C3⋊D312yes—
294C4×D3C4⋊(C3⋊D3)12yes—
295C3×C8—181no—
296C3⋊C8—64no—
297C3⋊C8—184no—
298C3⋊C8—181no—
299C3⋊C8—364no—
300C2×C32—24no—
301C2×C32—24no—
302C2×C32—24no—
303C2×C32—34no—
304C2×C32D3×C22⋊C411yescharacteristic
305C2×C32D3×D811yescharacteristic
306C2×C32D3×SD1611yescharacteristic
307C2×C32C2×(C2×D3)⋊C414yes—
308C2×C32C2×#21314yes—
309C2×C32C2×#21514yes—
310C3⋊D3—42no—
311C3⋊D3—122no—
312C3⋊D3—128no—
313C3⋊D3—248no—
314C3×D3—128no—
315C3×D3#809116yescomplemented
316C24—541no—
317C2×D4—91no—
318C2×D4—274no—
319C2×D4—271no—
320C2×D4—542no—
321C2×D4—541no—
322C22×C4—31no—
323C22×C4—61no—
324C2×C8—91no—
325C2×C8—271no—
326C2×C8—542no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4D3×C3⋊D311yescharacteristic, complemented
330C22×C3—24no—
331C22×C3—38no—
332C22×C3—38no—
333C22×C3—38no—
334C22×C3—182no—
335C22×C3—361no—
336C22×C3—361no—
337C22×C3D3×#6714yes—
338C22×C3C2×#63811yescharacteristic
339C2×D3—68no—
340C2×D3—124no—
341C2×D3—124no—
342C2×D3—182no—
343C2×D3—188no—
344C2×D3—368no—
345C2×D3—3632no—
346C2×D3—361no—
347C2×D3—361no—
348C2×D3—364no—
349C2×D3—364no—
350C2×D3—368no—
351C2×D3—724no—
352C2×D3—724no—
353C2×D3#375212yes—
354C2×D3#375312yes—
355C2×D3#375512yes—
356C3×C4—24no—
357C3×C4—24no—
358C3×C4—38no—
359C3×C4—41no—
360C3×C4—44no—
361C3×C4—84no—
362C3×C4—124no—
363C3×C4C4×D3214yes—
364C3×C4D3×D1214yes—
365C3×C4C2×C4×C3⋊D311yescharacteristic
366C3×C4C2×C4⋊(C3⋊D3)11yescharacteristic
367Dic3—41no—
368Dic3#375212yes—
369C32—24no—
370C32D3×#10211yescharacteristic, complemented
371C32C2×#80914yescomplemented
372C23—31no—
373C23—181no—
374C23—544no—
375C23—541no—
376C23—1082no—
377C23—1082no—
378D4—92no—
379D4—181no—
380D4—272no—
381D4—544no—
382D4—541no—
383C2×C4—21no—
384C2×C4—31no—
385C2×C4—32no—
386C2×C4—32no—
387C2×C4—61no—
388C2×C4—122no—
389C2×C4C2×D3×C3⋊D311yescharacteristic
390C8—181no—
391C8—541no—
392C2×C3—24no—
393C2×C3—24no—
394C2×C3—24no—
395C2×C3—316no—
396C2×C3—362no—
397C2×C3D3×(C2×D3)⋊C414yes—
398C2×C3D3×#21314yes—
399C2×C3D3×#21514yes—
400C2×C3C2×#375211yescharacteristic
401C2×C3C2×#375311yescharacteristic
402C2×C3C2×#375511yescharacteristic
403D3—128no—
404D3—368no—
405D3—362no—
406D3—728no—
407D3#6363614yesdirect product factor
408C22—32no—
409C22—32no—
410C22—32no—
411C22—182no—
412C22—361no—
413C22—361no—
414C22—542no—
415C22—1088no—
416C22—1081no—
417C22—1081no—
418C22D3×#63811yescharacteristic
419C4—32no—
420C4—41no—
421C4—121no—
422C4C4×D3×C3⋊D311yescharacteristic
423C4D3×C4⋊(C3⋊D3)11yescharacteristic
424C3—24no—
425C3D3×#80914yescomplemented
426C3C2×#6363611yescharacteristic, complemented
427C2—34no—
428C2—362no—
429C2—1082no—
430C2D3×#375211yescharacteristic
431C2D3×#375311yescharacteristic
432C2D3×#375511yescharacteristic
subgroupG/H
centerC22D3×#638
commutatorC33×C4C22×C4
FrattiniC2×C4C2×D3×C3⋊D3
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
prime radicalC2×D3×C4⋊(C3⋊D3)C2
cosocleC2×C33×C4C23
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#102
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×D3×C4⋊C4C2semidirect
3. C2×D3×C3⋊(C3⋊C8)C2semidirect
4. #11722179C2semidirect
5. C3×#63636C2semidirect
6. #11722035C2semidirect
7. #11722033C2semidirect
17. D3×C4⋊(C3⋊D3)C4semidirect
18. C33×C4⋊C4C22semidirect
19. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
20. C2×C3×C3⋊(C3⋊C8)C22semidirect
21. C32×C4⋊Dic3C22semidirect
28. C3×D3×C4⋊C4D3semidirect
35. #63636D3direct (N × H)
48. C4⋊(C3⋊(C3⋊D3))C2×C4semidirect
50. C3×C4⋊(C3⋊D3)C2×C4semidirect
81. C32×C4⋊C4C2×D3semidirect
82. C32×C4⋊C4C2×D3semidirect
87. C2×C3⋊(C3⋊C8)C2×D3semidirect
88. C3×C4⋊Dic3C2×D3semidirect
113. D3×C4⋊C4C3⋊D3semidirect
155. C4⋊(C3⋊D3)C4×D3semidirect
175. C32×D3#102semidirect
197. C3×C4⋊C4D32semidirect
198. C3×C4⋊C4C2×C3⋊D3semidirect
199. C4⋊Dic3C2×C3⋊D3semidirect
253. C33C2×#102semidirect
315. C3×D3#809semidirect
329. C4⋊C4D3×C3⋊D3semidirect
370. C32D3×#102semidirect
371. C32C2×#809semidirect
407. D3#63636direct (N × H)
425. C3D3×#809semidirect
426. C3C2×#63636semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C32×D3×C4⋊C42
C2×D3×C3⋊(C3⋊C8)2
#117221792
C3×#636362
#117220352
#117220332
C2×#636363
D3×#8093