Finite Group Databasebeta

← D3×#5065 #11874915

Subgroups — D3×#5065 #11874915

Order 1152.

763 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#125C211yesmaximal, characteristic
2D3×#870C211yesmaximal, characteristic
3#10592764C211yesmaximal, characteristic, complemented
4C3×#5065C211yesmaximal, characteristic, complemented
5D3×#808C212yesmaximal
6D3×#807C212yesmaximal
7#10590414C212yesmaximal, complemented
8#10590413C212yesmaximal, complemented
9C4×D3×C3⋊C8C211yesmaximal, characteristic
10#10590314C211yesmaximal, characteristic, complemented
11#10590304C211yesmaximal, characteristic, complemented
12C2×#5065—31nomaximal
13D3×#499—31nomaximal
14C32×#125C2211yescharacteristic
15#64079C2211yescharacteristic
16C3×D3×C4⋊C4—22no—
17C3×D3×C4⋊C4C2212yes—
18C3×#890C2212yes—
19C3×#889—22no—
20C3×C42×D3C2211yescharacteristic
21C3×#870C2211yescharacteristic
22C3×#870C2211yescharacteristic
23D3×C4⋊Dic3C2212yes—
24D3×Dic3⋊C4—22no—
25#63869C2212yes—
26#63867—22no—
27C2×D3×C3⋊C8C2211yescharacteristic
28C2×D3×C3⋊C8C2211yescharacteristic
29#63635C2212yes—
30#63634C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×#808C2212yes—
33C3×#807C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63576C2212yes—
36#63575C2212yes—
37#63574C2212yes—
38#63573C2212yes—
39Dic3×C3⋊C8C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41C2×C3×#125—31no—
42D3×#125—31no—
43D3×#125D311yescharacteristic
44C2×#870—31no—
45C3×#499—31no—
46#5065—31no—
47#5065—31no—
48#5065—31no—
49#5065—31no—
50#5065—32no—
51#5065—32no—
52#5065—31no—
53#5065—61no—
54#5065D311yescharacteristic, direct product factor
55C2×#808—32no—
56C2×#807—32no—
57C2×C4×C3⋊C8—31no—
58D3×#107—32no—
59#4878—32no—
60D3×#106—32no—
61#4858—32no—
62C4×D3×C8—31no—
63#4683—31no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2311yescharacteristic
67C2×D3×Dic3—22no—
68C32×C4⋊C4—22no—
69C32×C4⋊C4C2312yes—
70C32×C42C2311yescharacteristic
71C4⋊(C3⋊Dic3)C2312yes—
72#3750—22no—
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C3×C4⋊Dic3—22no—
76C3×C4⋊Dic3C2312yes—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3D412yes—
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86#3724—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89D3×C3⋊C8Q814yes—
90D3×C3⋊C8Q814yes—
91C2×#499—91noSylow
92C3×#125—21no—
93C3×#125—32no—
94C3×#125—31no—
95C3×#125—31no—
96C3×#125—62no—
97C3×#125C2×D311yescharacteristic
98C3×#125C2×D311yescharacteristic
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—62no—
101C2×C3×C42—31no—
102C2×C4⋊Dic3—32no—
103C2×Dic3⋊C4—62no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—31no—
106C2×D3×C8—31no—
107C2×D3×C8—31no—
108D3×C4⋊C4—22no—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—62no—
111D3×C4⋊C4C2×D312yes—
112#890—32no—
113#890C2×D312yes—
114#889—22no—
115#889—62no—
116C42×D3C2×D311yescharacteristic
117#870—31no—
118#870—31no—
119#870—32no—
120#870—61no—
121#870—62no—
122#870C2×D311yescharacteristic
123#870C2×D311yescharacteristic
124C3×#107—32no—
125C3×#106—32no—
126C3×C4×C8—31no—
127#818—32no—
128#817—32no—
129C8×Dic3—31no—
130C8×Dic3—31no—
131#808—32no—
132#808—32no—
133#808—32no—
134#808—32no—
135#808—32no—
136#808—62no—
137#808C2×D312yes—
138#807—32no—
139#807—32no—
140#807—32no—
141#807—32no—
142#807—32no—
143#807—62no—
144#807C2×D312yes—
145C4×C3⋊C8—31no—
146C4×C3⋊C8—31no—
147C4×C3⋊C8—31no—
148C4×C3⋊C8—31no—
149C4×C3⋊C8—61no—
150C4×C3⋊C8C2×D311yescharacteristic
151C22×C3×D3C2×D411yescharacteristic
152C2×C32×C4—22no—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3C2×D412yes—
159C2×C3×Dic3C2×D411yescharacteristic
160C3×C4×D3—24no—
161C3×C4×D3—44no—
162C3×C4×D3C2×Q812yes—
163C3×C4×D3C2×Q812yes—
164D3×Dic3—44no—
165C3⋊(C3⋊C8)C2×Q812yes—
166C3⋊(C3⋊C8)C2×Q812yes—
167C3×C3⋊C8C2×Q812yes—
168C3×C3⋊C8C2×Q812yes—
169C2×#125—31no—
170C2×#125—91no—
171#499—31no—
172#499—91no—
173#499—92no—
174#499—92no—
175#499—91no—
176#499—91no—
177C2×#107—92no—
178C2×#106—92no—
179C2×C4×C8—91no—
180C22×C3×C4—31no—
181C22×C3×C4—32no—
182C22×C3×C4—62no—
183C22×Dic3—62no—
184C2×C4×D3—22no—
185C2×C4×D3—62no—
186C2×C4×D3#6712yes—
187C2×C4×D3C22×D311yescharacteristic
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4—32no—
195C3×C4⋊C4—42no—
196C3×C4⋊C4—62no—
197C3×C4⋊C4—62no—
198C3×C4⋊C4—62no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4—62no—
201C3×C4⋊C4C22×D312yes—
202C3×C4⋊C4C22×D312yes—
203C3×C42—21no—
204C3×C42—32no—
205C3×C42—31no—
206C3×C42C22×D311yescharacteristic
207C3×C42C22×D311yescharacteristic
208C4⋊Dic3—22no—
209C4⋊Dic3—32no—
210C4⋊Dic3—32no—
211C4⋊Dic3—62no—
212C4⋊Dic3—62no—
213C4⋊Dic3—62no—
214C4⋊Dic3C22×D312yes—
215C4⋊Dic3C22×D312yes—
216Dic3⋊C4—22no—
217Dic3⋊C4—22no—
218Dic3⋊C4—22no—
219Dic3⋊C4—22no—
220Dic3⋊C4—62no—
221Dic3⋊C4—62no—
222Dic3⋊C4—62no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—122no—
227C4×Dic3#6712yes—
228C4×Dic3C22×D311yescharacteristic
229C2×C3⋊C8—31no—
230C2×C3⋊C8—31no—
231C2×C3⋊C8—31no—
232C2×C3⋊C8—31no—
233C2×C3⋊C8—34no—
234C2×C3⋊C8—34no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8C22×D311yescharacteristic
238C2×C3⋊C8C22×D311yescharacteristic
239D3×C8—34no—
240D3×C8—34no—
241C22×C32C22×D411yescharacteristic
242C2×C3×D3C4⋊Q812yes—
243C2×C3×D3#13514yes—
244C32×C4—22no—
245C32×C4—42no—
246C32×C4C22×Q811yescharacteristic
247C32×C4C22×Q811yescharacteristic
248C3⋊Dic3—42no—
249C3×Dic3—22no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C3×Dic3C4⋊Q812yes—
253C22×C8—91no—
254C22×C8—91no—
255#125—32no—
256#125—31no—
257#125—31no—
258#125—62no—
259#125—92no—
260#125—91no—
261#125—182no—
262#125D3211yescharacteristic
263C2×C4⋊C4—32no—
264C2×C4⋊C4—62no—
265C2×C4⋊C4—92no—
266C2×C4⋊C4—182no—
267C2×C42—31no—
268#107—32no—
269#107—92no—
270#107—92no—
271#107—92no—
272#106—32no—
273#106—92no—
274#106—92no—
275#106—92no—
276C4×C8—31no—
277C4×C8—91no—
278C4×C8—91no—
279C4×C8—91no—
280C23×C3—31no—
281C22×D3C2×#6711yescharacteristic
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—22no—
286C2×C3×C4—31no—
287C2×C3×C4—32no—
288C2×C3×C4—32no—
289C2×C3×C4—32no—
290C2×C3×C4—42no—
291C2×C3×C4—64no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—124no—
295C2×C3×C4D3×D412yes—
296C2×C3×C4C2×#6712yes—
297C2×C3×C4C23×D311yescharacteristic
298C2×C3×C4C23×D311yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—124no—
305C2×Dic3C2×#6712yes—
306C2×Dic3C2×#6711yescharacteristic
307C4×D3—24no—
308C4×D3—44no—
309C4×D3—124no—
310C4×D3D3×Q812yes—
311C4×D3D3×Q812yes—
312C3×C8—32no—
313C3×C8—32no—
314C3⋊C8—32no—
315C3⋊C8—32no—
316C3⋊C8—32no—
317C3⋊C8—32no—
318C3⋊C8—62no—
319C3⋊C8—62no—
320C3⋊C8D3×Q812yes—
321C3⋊C8D3×Q812yes—
322C2×C32C2×C4⋊Q811yescharacteristic
323C2×C32C2×#13512yes—
324C3×D3#49914yescomplemented
325C22×C4—31no—
326C22×C4—32no—
327C22×C4—62no—
328C22×C4—182no—
329C2×C8—31no—
330C2×C8—31no—
331C2×C8—94no—
332C2×C8—94no—
333C2×C8—91no—
334C2×C8—91no—
335C4⋊C4—22no—
336C4⋊C4—32no—
337C4⋊C4—32no—
338C4⋊C4—62no—
339C4⋊C4—62no—
340C4⋊C4—62no—
341C4⋊C4—62no—
342C4⋊C4—62no—
343C4⋊C4—92no—
344C4⋊C4—182no—
345C4⋊C4—182no—
346C4⋊C4—182no—
347C4⋊C4—182no—
348C4⋊C4C2×D3212yes—
349C42—31no—
350C42—32no—
351C42C2×D3211yescharacteristic
352C22×C3—21no—
353C22×C3—32no—
354C22×C3—34no—
355C22×C3C2×D3×D411yescharacteristic
356C22×C3C22×#6711yescharacteristic
357C2×D3#94412yes—
358C2×D3#95014yes—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—32no—
364C3×C4—42no—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—62no—
368C3×C4—82no—
369C3×C4—122no—
370C3×C4—122no—
371C3×C4C2×D3×Q811yescharacteristic
372C3×C4C2×D3×Q811yescharacteristic
373C3×C4C2×D3×Q811yescharacteristic
374C3×C4C2×D3×Q811yescharacteristic
375Dic3—22no—
376Dic3—42no—
377Dic3—42no—
378Dic3—122no—
379Dic3—122no—
380Dic3—242no—
381Dic3#94412yes—
382C32C2×#49911yescharacteristic, complemented, Sylow
383C23—31no—
384C2×C4—22no—
385C2×C4—31no—
386C2×C4—32no—
387C2×C4—32no—
388C2×C4—32no—
389C2×C4—64no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—124no—
393C2×C4—182no—
394C2×C4—364no—
395C2×C4D3×#6712yes—
396C2×C4C22×D3211yescharacteristic
397C8—32no—
398C8—32no—
399C8—92no—
400C8—92no—
401C2×C3—21no—
402C2×C3—22no—
403C2×C3—34no—
404C2×C3D3×C4⋊Q811yescharacteristic
405C2×C3D3×#13512yes—
406C2×C3C2×#94411yescharacteristic
407C2×C3C2×#95012yes—
408D3#506514yesdirect product factor
409C22—32no—
410C22—34no—
411C22C2×D3×#6711yescharacteristic
412C4—22no—
413C4—32no—
414C4—42no—
415C4—62no—
416C4—122no—
417C4—122no—
418C4—362no—
419C4D32×Q811yescharacteristic
420C4D32×Q811yescharacteristic
421C3—21no—
422C3D3×#49911yescharacteristic, complemented
423C3C2×#506511yescharacteristic, complemented
424C2—34no—
425C2D3×#94411yescharacteristic
426C2D3×#95012yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#125D32
hypocenterC32C2×#499
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #10592764C2semidirect
4. C3×#5065C2semidirect
7. #10590414C2semidirect
8. #10590413C2semidirect
10. #10590314C2semidirect
11. #10590304C2semidirect
54. #5065D3direct (N × H)
324. C3×D3#499semidirect
382. C32C2×#499semidirect
408. D3#5065direct (N × H)
422. C3D3×#499semidirect
423. C3C2×#5065semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1252
D3×#8702
#105927642
C3×#50652
D3×#8082
D3×#8072
#105904142
#105904132
C4×D3×C3⋊C82
#105903142
#105903042
C2×#50653
D3×#4993