Finite Group Databasebeta

← D3×#64145 #13177413

Subgroups — D3×#64145 #13177413

Order 1728.

2284 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic
2C2×D3×#634C211yesmaximal, characteristic, complemented
3#11723977C211yesmaximal, characteristic, complemented
4C3×#64145C211yesmaximal, characteristic, complemented
5D3×#3757C214yesmaximal, complemented
6#11723600C214yesmaximal, complemented
7C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#11723434C211yesmaximal, characteristic, complemented
9#11723429C211yesmaximal, characteristic, complemented
10C2×#64145—31nomaximal
11D3×#936—34nomaximal
12C23×C32×D3C2212yes—
13C2×C33×D4C2211yescharacteristic
14C2×#6308C2211yescharacteristic, complemented
15C2×C3×#634C2211yescharacteristic, complemented
16C2×C32×#67C2212yes—
17C32×D3×D4—24no—
18C2×C32×D12C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6293C2212yescomplemented
21C2×D3×C3⋊Dic3C2212yes—
22C2×D3×C3⋊Dic3C2212yes—
23D3×#634—24no—
24#88864C2214yescomplemented
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C3×#3757C2214yescomplemented
27C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
28(C2×D3)⋊(C3⋊Dic3)C2214yescomplemented
29(C2×D3)⋊(C3⋊Dic3)C2214yescomplemented
30Dic3×C3⋊Dic3C2212yescomplemented
31C22×C32×D4—31no—
32C22×#634—31no—
33C2×C3×D3×D4D314yes—
34C2×D3×Dic6—34no—
35C2×#3757—34no—
36#64145—31no—
37#64145—31no—
38#64145—34no—
39#64145—34no—
40#64145—31no—
41#64145—64no—
42#64145D311yescharacteristic, direct product factor
43C2×C4×C3⋊Dic3—31no—
44C3×#936—34no—
45D3×#217—316no—
46#63959—316no—
47C4×D3×Dic3—34no—
48#63863—34no—
49#63860—34no—
50C23×C33C2312yes—
51C22×C32×D3—24no—
52C22×C32×D3—28no—
53C22×C32×D3C2312yes—
54C22×C32×D3C2311yescharacteristic
55C33×D4—22no—
56C2×C33×C4C2311yescharacteristic
57C2×C3⋊(C3⋊Dic3)C2312yes—
58C2×C3⋊(C3⋊Dic3)C2312yes—
59#6308—22no—
60C2×C3×C3⋊Dic3C2312yes—
61C2×C3×C3⋊Dic3C2312yes—
62C3×#634—22no—
63C32×#67—24no—
64C2×C32×Dic3C2311yescharacteristic
65C32×D12—22no—
66C32×C4×D3D414yes—
67#6293—24no—
68D3×C3⋊Dic3—24no—
69D3×C3⋊Dic3—24no—
70C2×#936—94no—
71D3×#124—91no—
72C24×C32—32no—
73C23×C3×D3C2×D318yes—
74C2×C32×D4—24no—
75C2×C32×D4—32no—
76C2×C32×D4—31no—
77C2×C32×D4—64no—
78C2×C32×D4C2×D314yes—
79C2×C32×D4C2×D311yescharacteristic
80C22×C32×C4—31no—
81C22×C3⋊Dic3—32no—
82C22×C3⋊Dic3—32no—
83C2×#634—31no—
84C2×#634—34no—
85C2×#634—32no—
86C2×#634—64no—
87C2×#634—64no—
88C2×#634C2×D311yescharacteristic, complemented
89C2×C3×#67C2×D318yes—
90C3×D3×D4—216no—
91C2×C3×D12C2×D314yes—
92C2×C3×C4×D3C2×D314yes—
93C2×C3×Dic6—34no—
94C2×#627—38no—
95C2×D3×Dic3—38no—
96C2×D3×Dic3—38no—
97D3×Dic6—616no—
98#3757—34no—
99#3757—316no—
100#3757—34no—
101#3757—34no—
102#3757—616no—
103#3757C2×D314yescomplemented
104C4×C3⋊Dic3—31no—
105C4×C3⋊Dic3—34no—
106C4×C3⋊Dic3—32no—
107C4×C3⋊Dic3—64no—
108C4×C3⋊Dic3C2×D311yescharacteristic, complemented
109C3×#217—316no—
110C3×C4×Dic3—34no—
111(C2×D3)⋊Dic3—316no—
112(C2×D3)⋊Dic3—316no—
113Dic32—38no—
114C22×C33—22no—
115C22×C33—24no—
116C22×C33C2411yescharacteristic
117C2×C32×D3—22no—
118C2×C32×D3—24no—
119C2×C32×D3—48no—
120C2×C32×D3C2×D412yes—
121C2×C32×D3#4114yes—
122C33×C4C2×D412yes—
123C3⋊(C3⋊Dic3)—22no—
124C3⋊(C3⋊Dic3)—22no—
125C3×C3⋊Dic3—22no—
126C3×C3⋊Dic3—22no—
127C32×Dic3C2×D412yes—
128C22×C3×D4—34no—
129C2×D3×Q8—91no—
130C2×D3×D4C3⋊D311yescharacteristic
131C22×Dic6—94no—
132C3×#124—91no—
133C2×#217—916no—
134#947—91no—
135#936—34no—
136#936—94no—
137#936—916no—
138#936—94no—
139#936—94no—
140#936—91no—
141#936—184no—
142C2×C4×Dic3—94no—
143#885—94no—
144D3×C22⋊C4—94no—
145#875—91no—
146C42×D3—91no—
147C23×C32—28no—
148C23×C32—31no—
149C23×C32—32no—
150C23×C32—68no—
151C23×C32—64no—
152C23×C32C22×D318yes—
153C23×C32C22×D312yes—
154C22×C3×D3—232no—
155C22×C3×D3—216no—
156C22×C3×D3C22×D318yes—
157C22×C3×D3C22×D314yes—
158C32×D4—22no—
159C32×D4—28no—
160C32×D4—48no—
161C32×D4—64no—
162C32×D4—62no—
163C2×C32×C4—24no—
164C2×C32×C4—31no—
165C2×C32×C4—34no—
166C2×C32×C4C22×D314yes—
167C2×C32×C4C22×D311yescharacteristic
168C2×C3⋊Dic3—32no—
169C2×C3⋊Dic3—32no—
170C2×C3⋊Dic3—38no—
171C2×C3⋊Dic3—38no—
172C2×C3⋊Dic3—68no—
173C2×C3⋊Dic3—68no—
174C2×C3⋊Dic3—64no—
175C2×C3⋊Dic3—64no—
176C2×C3⋊Dic3C22×D312yes—
177C2×C3⋊Dic3C22×D312yes—
178#634—22no—
179#634—64no—
180#634—62no—
181#634—68no—
182#634—128no—
183C3×#67—216no—
184C2×C3×Dic3—38no—
185C2×C3×Dic3—38no—
186C2×C3×Dic3C22×D314yes—
187C3×D12—28no—
188C3×C4×D3#67116yes—
189C3×Dic6—68no—
190#627—616no—
191D3×Dic3—616no—
192D3×Dic3—616no—
193C2×#124—271noSylow
194C2×C33—42no—
195C2×C33C22×D411yescharacteristic
196C2×C33C2×#4112yes—
197C32×D3—42no—
198C32×D3#12414yescomplemented
199C24×C3—38no—
200C23×D3C2×C3⋊D312yes—
201C2×C3×Q8—91no—
202C2×C3×D4—24no—
203C2×C3×D4—38no—
204C2×C3×D4—34no—
205C2×C3×D4—616no—
206C2×C3×D4D3214yes—
207C2×C3×D4C2×C3⋊D311yescharacteristic
208C22×C3×C4—34no—
209C2×#67C2×C3⋊D312yes—
210C22×Dic3—98no—
211C22×Dic3—98no—
212D3×Q8—184no—
213D3×D4—24no—
214C2×D12C2×C3⋊D311yescharacteristic
215C2×C4×D3—92no—
216C2×C4×D3—92no—
217C2×C4×D3C2×C3⋊D311yescharacteristic
218C2×Dic6—34no—
219C2×Dic6—98no—
220C2×Dic6—94no—
221C2×Dic6—91no—
222C2×Dic6—92no—
223C2×Dic6—184no—
224C2×Dic6—1816no—
225C3×C22⋊C4—94no—
226C3×C42—91no—
227#217—316no—
228#217—916no—
229#217—916no—
230#217—916no—
231#217—94no—
232#217—1816no—
233(C2×D3)⋊C4—94no—
234(C2×D3)⋊C4—94no—
235C4×Dic3—34no—
236C4×Dic3—98no—
237C4×Dic3—94no—
238C4×Dic3—91no—
239C4×Dic3—92no—
240C4×Dic3—184no—
241C22×C32—22no—
242C22×C32—24no—
243C22×C32—24no—
244C22×C32—216no—
245C22×C32—28no—
246C22×C32—32no—
247C22×C32—34no—
248C22×C32—48no—
249C22×C32—416no—
250C22×C32—62no—
251C22×C32—64no—
252C22×C32—128no—
253C22×C32C23×D314yes—
254C22×C32C23×D311yescharacteristic
255C2×C3×D3—216no—
256C2×C3×D3—28no—
257C2×C3×D3—432no—
258C2×C3×D3#237116yes—
259C2×C3×D3C2×#6718yes—
260C32×C4—28no—
261C32×C4—32no—
262C32×C4D3×D412yes—
263C32×C4C2×#6718yes—
264C3⋊Dic3—22no—
265C3⋊Dic3—22no—
266C3⋊Dic3—62no—
267C3⋊Dic3—62no—
268C3⋊Dic3—68no—
269C3⋊Dic3—68no—
270C3⋊Dic3—128no—
271C3⋊Dic3—128no—
272C3×Dic3—68no—
273C3×Dic3—68no—
274C3×Dic3C2×#6718yes—
275C22×Q8—271no—
276C22×D4—31no—
277#124—91no—
278#124—271no—
279#124—274no—
280#124—271no—
281#124—271no—
282C2×C22⋊C4—274no—
283C2×C42—271no—
284C33C2×#12411yescharacteristic, complemented, Sylow
285C23×C3—28no—
286C23×C3—34no—
287C23×C3—38no—
288C23×C3—616no—
289C23×C3—632no—
290C23×C3C2×D3218yes—
291C23×C3C22×C3⋊D312yes—
292C22×D3—28no—
293C22×D3—24no—
294C22×D3C22×C3⋊D312yes—
295C22×D3C22×C3⋊D311yescharacteristic
296C3×Q8—182no—
297C3×D4—28no—
298C3×D4—22no—
299C3×D4—48no—
300C3×D4—616no—
301C3×D4—68no—
302C2×C3×C4—24no—
303C2×C3×C4—34no—
304C2×C3×C4—316no—
305C2×C3×C4—92no—
306C2×C3×C4—92no—
307C2×C3×C4C2×D3214yes—
308C2×C3×C4C22×C3⋊D311yescharacteristic
309#67—24no—
310C2×Dic3—38no—
311C2×Dic3—38no—
312C2×Dic3—98no—
313C2×Dic3—98no—
314C2×Dic3—92no—
315C2×Dic3—92no—
316C2×Dic3—188no—
317C2×Dic3—188no—
318C2×Dic3—1816no—
319C2×Dic3—1816no—
320C2×Dic3C22×C3⋊D311yescharacteristic
321D12—22no—
322C4×D3—184no—
323C4×D3—184no—
324C4×D3#63814yes—
325Dic6—68no—
326Dic6—1816no—
327Dic6—188no—
328Dic6—182no—
329Dic6—184no—
330Dic6—368no—
331C2×C32—28no—
332C2×C32—24no—
333C2×C32—34no—
334C2×C32—42no—
335C2×C32—48no—
336C2×C32—88no—
337C2×C32—122no—
338C2×C32C2×D3×D411yescharacteristic
339C2×C32C2×#23718yes—
340C2×C32D3×#4112yes—
341C2×C32C22×#6714yes—
342C3×D3—48no—
343C3×D3#936116yescomplemented
344C24—32no—
345C2×Q8—91no—
346C2×Q8—272no—
347C2×Q8—271no—
348C2×Q8—544no—
349C2×D4—32no—
350C2×D4—31no—
351C2×D4—64no—
352C2×D4D3×C3⋊D311yescharacteristic
353C22×C4—31no—
354C22×C4—272no—
355C22×C4—272no—
356C22⋊C4—94no—
357C22⋊C4—274no—
358C22⋊C4—274no—
359C22⋊C4—274no—
360C42—91no—
361C42—272no—
362C42—271no—
363C22×C3—216no—
364C22×C3—28no—
365C22×C3—24no—
366C22×C3—22no—
367C22×C3—24no—
368C22×C3—316no—
369C22×C3—38no—
370C22×C3—48no—
371C22×C3—416no—
372C22×C3—616no—
373C22×C3—68no—
374C22×C3—1232no—
375C22×C3C22×D3214yes—
376C22×C3C23×C3⋊D311yescharacteristic
377C2×D3—24no—
378C2×D3—22no—
379C2×D3—48no—
380C2×D3#383014yes—
381C2×D3C2×#63812yes—
382C3×C4—28no—
383C3×C4—38no—
384C3×C4—182no—
385C3×C4—182no—
386C3×C4D3×#6718yes—
387C3×C4C2×#63812yes—
388Dic3—68no—
389Dic3—68no—
390Dic3—188no—
391Dic3—188no—
392Dic3—182no—
393Dic3—182no—
394Dic3—368no—
395Dic3—368no—
396Dic3C2×#63812yes—
397C32—24no—
398C32D3×#12411yescharacteristic, complemented
399C32C2×#93614yescomplemented
400C23—31no—
401C23—32no—
402C23—64no—
403C23—68no—
404C23C2×D3×C3⋊D312yes—
405Q8—182no—
406Q8—544no—
407Q8—542no—
408D4—22no—
409D4—64no—
410D4—62no—
411C2×C4—31no—
412C2×C4—34no—
413C2×C4—92no—
414C2×C4—92no—
415C2×C4—272no—
416C2×C4—272no—
417C2×C4—544no—
418C2×C4—544no—
419C2×C4C2×D3×C3⋊D311yescharacteristic
420C2×C3—28no—
421C2×C3—24no—
422C2×C3—316no—
423C2×C3—48no—
424C2×C3—42no—
425C2×C3—88no—
426C2×C3—128no—
427C2×C3D3×#23718yes—
428C2×C3C2×D3×#6714yes—
429C2×C3C2×#383012yes—
430C2×C3C22×#63811yescharacteristic
431D3—42no—
432D3#6414514yesdirect product factor
433C22—24no—
434C22—22no—
435C22—34no—
436C22—32no—
437C22—64no—
438C22—62no—
439C22—128no—
440C22C22×D3×C3⋊D311yescharacteristic
441C4—32no—
442C4—182no—
443C4—182no—
444C4—542no—
445C4—542no—
446C4D3×#63812yes—
447C3—24no—
448C3D3×#93614yescomplemented
449C3C2×#6414511yescharacteristic, complemented
450C2—34no—
451C2—42no—
452C2—122no—
453C2D3×#383012yes—
454C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radicalC2×C32×D3×D4C2
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×#124
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#634C2semidirect
3. #11723977C2semidirect
4. C3×#64145C2semidirect
5. D3×#3757C2semidirect
6. #11723600C2semidirect
7. C4×D3×C3⋊Dic3C2semidirect
8. #11723434C2semidirect
9. #11723429C2semidirect
14. C2×#6308C22semidirect
15. C2×C3×#634C22semidirect
20. C2×#6293C22semidirect
24. #88864C22semidirect
25. C4×C3⋊(C3⋊Dic3)C22semidirect
26. C3×#3757C22semidirect
27. C3×C4×C3⋊Dic3C22semidirect
28. (C2×D3)⋊(C3⋊Dic3)C22semidirect
29. (C2×D3)⋊(C3⋊Dic3)C22semidirect
30. Dic3×C3⋊Dic3C22semidirect
42. #64145D3direct (N × H)
88. C2×#634C2×D3semidirect
103. #3757C2×D3semidirect
108. C4×C3⋊Dic3C2×D3semidirect
198. C32×D3#124semidirect
284. C33C2×#124semidirect
343. C3×D3#936semidirect
398. C32D3×#124semidirect
399. C32C2×#936semidirect
432. D3#64145direct (N × H)
448. C3D3×#936semidirect
449. C3C2×#64145semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×D3×#6342
#117239772
C3×#641452
D3×#37572
#117236002
C4×D3×C3⋊Dic32
#117234342
#117234292
C2×#641453
D3×#9363