Finite Group Databasebeta

← D3×#5069 #11873624

Subgroups — D3×#5069 #11873624

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#125C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592768C211yesmaximal, characteristic, complemented
4C3×#5069C211yesmaximal, characteristic, complemented
5D3×#810C214yesmaximal
6#10590562C214yesmaximal, complemented
7D3×#803C211yesmaximal, characteristic
8#10590295C211yesmaximal, characteristic, complemented
9#10590291C211yesmaximal, characteristic, complemented
10C2×#5069—31nomaximal
11D3×#491—31nomaximal
12C2×D3×Dic6C2212yes—
13C32×#125C2211yescharacteristic
14#64078C2211yescharacteristic
15C3×D3×C4⋊C4—22no—
16C3×D3×C4⋊C4C2212yes—
17C3×#890C2212yes—
18C3×#889—22no—
19C3×C42×D3C2211yescharacteristic
20C3×#870C2211yescharacteristic
21C3×#869C2211yescharacteristic
22#63918—22no—
23D3×C4⋊Dic3—22no—
24#63866C2212yes—
25C2×D3×C3⋊C8C2212yes—
26#63637C2214yes—
27#63630C2211yescharacteristic
28C3×#810C2214yes—
29C3×#803C2211yescharacteristic
30#63567C2214yes—
31#63565C2214yes—
32#63554C2212yes—
33C2×C3×#125—31no—
34D3×C4⋊Q8—31no—
35D3×#125D311yescharacteristic
36C2×#869—31no—
37C3×#491—31no—
38#5082—31no—
39#5069—31no—
40#5069—31no—
41#5069—31no—
42#5069—34no—
43#5069—31no—
44#5069—61no—
45#5069D311yescharacteristic, direct product factor
46C2×#810—34no—
47C2×#803—31no—
48D3×#103—34no—
49#4797—34no—
50D3×#97—31no—
51#4703—31no—
52C2×#634C2312yes—
53C2×C3×C4×D3—22no—
54C2×C3×C4×D3D412yes—
55C2×C3×C4×D3C2311yescharacteristic
56C2×C3×Dic6C2312yes—
57C2×#627—22no—
58C2×D3×Dic3—22no—
59D3×Dic6—28no—
60C32×C4⋊C4—22no—
61C32×C4⋊C4C2312yes—
62C32×C42C2311yescharacteristic
63C4⋊(C3⋊Dic3)—22no—
64C2×C3⋊(C3⋊C8)C2312yes—
65C3×C4⋊Dic3—22no—
66C3×C4⋊Dic3—22no—
67C3×C4⋊Dic3C2312yes—
68C3×Dic3⋊C4—22no—
69C3×Dic3⋊C4—22no—
70C3×Dic3⋊C4—22no—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3C2311yescharacteristic
73C2×C3×C3⋊C8C2312yes—
74Dic3⋊Dic3—24no—
75D3×C3⋊C8—24no—
76C2×#491—91noSylow
77C2×D3×Q8—32no—
78C22×Dic6—32no—
79C3×C4⋊Q8—31no—
80C3×#125—21no—
81C3×#125—32no—
82C3×#125—31no—
83C3×#125—62no—
84C3×#125C2×D311yescharacteristic
85C3×#125C2×D311yescharacteristic
86C2×C3×C4⋊C4—32no—
87C2×C3×C4⋊C4—62no—
88C2×C3×C42—31no—
89#944—32no—
90C2×C4⋊Dic3—62no—
91C22×C3⋊C8—32no—
92C2×D3×C8—32no—
93D3×C4⋊C4—22no—
94D3×C4⋊C4—62no—
95D3×C4⋊C4C2×D312yes—
96#890C2×D312yes—
97#889—22no—
98#888—62no—
99C42×D3C2×D311yescharacteristic
100#870C2×D311yescharacteristic
101#869—32no—
102#869—31no—
103#869—31no—
104#869—61no—
105#869—62no—
106#869C2×D311yescharacteristic
107C3×#103—34no—
108C3×#97—31no—
109#835—34no—
110#816—34no—
111#815—32no—
112#810—34no—
113#810—34no—
114#810—34no—
115#810—34no—
116#810—64no—
117#810C2×D314yes—
118#803—31no—
119#803—31no—
120#803—32no—
121#803—61no—
122#803C2×D311yescharacteristic
123C22×C3×D3C2×D411yescharacteristic
124C2×C32×C4—22no—
125C2×C32×C4C2×D412yes—
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—22no—
128#634—24no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C2×D412yes—
132C2×C3×Dic3C2×D411yescharacteristic
133C3×C4×D3—24no—
134C3×C4×D3—44no—
135C3×C4×D3#4114yes—
136C3×Dic6—24no—
137#627—44no—
138D3×Dic3—44no—
139C3⋊(C3⋊C8)—22no—
140C3×C3⋊C8—22no—
141C2×C4⋊Q8—91no—
142C2×#125—31no—
143#491—31no—
144#491—91no—
145#491—94no—
146#491—91no—
147#491—91no—
148C2×#103—94no—
149C2×#97—91no—
150C2×C3×Q8—32no—
151C22×C3×C4—31no—
152C22×C3×C4—32no—
153C22×C3×C4—62no—
154C22×Dic3—62no—
155D3×Q8—68no—
156C2×C4×D3—22no—
157C2×C4×D3—62no—
158C2×C4×D3#6712yes—
159C2×C4×D3C22×D311yescharacteristic
160C2×Dic6—32no—
161C2×Dic6—32no—
162C2×Dic6—62no—
163C2×Dic6—68no—
164C2×Dic6—62no—
165C2×Dic6—62no—
166C2×Dic6C22×D312yes—
167C2×C3×C8—32no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—32no—
172C3×C4⋊C4—42no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—62no—
175C3×C4⋊C4—62no—
176C3×C4⋊C4—62no—
177C3×C4⋊C4—62no—
178C3×C4⋊C4C22×D312yes—
179C3×C4⋊C4C22×D312yes—
180C3×C42—21no—
181C3×C42—32no—
182C3×C42—31no—
183C3×C42C22×D311yescharacteristic
184C3×C42C22×D311yescharacteristic
185C4⋊Dic3—22no—
186C4⋊Dic3—22no—
187C4⋊Dic3—64no—
188C4⋊Dic3—62no—
189C4⋊Dic3—62no—
190C4⋊Dic3—122no—
191C4⋊Dic3C22×D312yes—
192Dic3⋊C4—22no—
193Dic3⋊C4—22no—
194Dic3⋊C4—22no—
195Dic3⋊C4—64no—
196C4×Dic3#6712yes—
197C4×Dic3C22×D311yescharacteristic
198C2×C3⋊C8—32no—
199C2×C3⋊C8—32no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—64no—
202C2×C3⋊C8C22×D312yes—
203D3×C8—64no—
204C22×C32C22×D411yescharacteristic
205C2×C3×D3#12412yes—
206C2×C3×D3#13714yes—
207C32×C4—22no—
208C32×C4—42no—
209C32×C4C2×#4112yes—
210C3⋊Dic3—42no—
211C3×Dic3—22no—
212C3×Dic3—42no—
213C3×Dic3—42no—
214C3×Dic3#12412yes—
215C22×Q8—92no—
216C22×C8—92no—
217C4⋊Q8—31no—
218C4⋊Q8—92no—
219C4⋊Q8—91no—
220C4⋊Q8—182no—
221#125—32no—
222#125—31no—
223#125—62no—
224#125D3211yescharacteristic
225C2×C4⋊C4—32no—
226C2×C4⋊C4—62no—
227C2×C4⋊C4—182no—
228C2×C42—31no—
229#103—34no—
230#103—94no—
231#103—94no—
232#103—94no—
233#97—31no—
234#97—92no—
235#97—91no—
236C23×C3—31no—
237C22×D3C2×#6711yescharacteristic
238C3×Q8—64no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—31no—
244C2×C3×C4—34no—
245C2×C3×C4—32no—
246C2×C3×C4—42no—
247C2×C3×C4—64no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—124no—
251C2×C3×C4D3×D412yes—
252C2×C3×C4C2×#6712yes—
253C2×C3×C4C23×D311yescharacteristic
254C2×C3×C4C23×D311yescharacteristic
255C2×Dic3—22no—
256C2×Dic3—22no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—122no—
260C2×Dic3—124no—
261C2×Dic3C2×#6712yes—
262C2×Dic3C2×#6711yescharacteristic
263C4×D3—24no—
264C4×D3—44no—
265C4×D3—124no—
266C4×D3#23914yes—
267Dic6—24no—
268Dic6—64no—
269Dic6—64no—
270Dic6—124no—
271Dic6—124no—
272Dic6—124no—
273C3×C8—62no—
274C3⋊C8—22no—
275C3⋊C8—62no—
276C3⋊C8—62no—
277C3⋊C8—122no—
278C2×C32C2×#12411yescharacteristic
279C2×C32C2×#13712yes—
280C3×D3#49114yescomplemented
281C2×Q8—32no—
282C2×Q8—92no—
283C2×Q8—182no—
284C2×Q8—188no—
285C22×C4—31no—
286C22×C4—32no—
287C22×C4—62no—
288C22×C4—182no—
289C2×C8—32no—
290C2×C8—92no—
291C2×C8—184no—
292C4⋊C4—22no—
293C4⋊C4—32no—
294C4⋊C4—62no—
295C4⋊C4—62no—
296C4⋊C4—62no—
297C4⋊C4—62no—
298C4⋊C4—62no—
299C4⋊C4—184no—
300C4⋊C4—182no—
301C4⋊C4C2×D3212yes—
302C42—31no—
303C42—32no—
304C42C2×D3211yescharacteristic
305C22×C3—21no—
306C22×C3—32no—
307C22×C3—34no—
308C22×C3C2×D3×D411yescharacteristic
309C22×C3C22×#6711yescharacteristic
310C2×D3#94712yes—
311C2×D3#95114yes—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—32no—
316C3×C4—42no—
317C3×C4—42no—
318C3×C4—42no—
319C3×C4—62no—
320C3×C4—82no—
321C3×C4—122no—
322C3×C4—122no—
323C3×C4C2×#23912yes—
324C3×C4D3×#4112yes—
325Dic3—22no—
326Dic3—42no—
327Dic3—42no—
328Dic3—122no—
329Dic3—122no—
330Dic3—242no—
331Dic3#94712yes—
332C32C2×#49111yescharacteristic, complemented, Sylow
333C23—31no—
334Q8—64no—
335Q8—184no—
336Q8—364no—
337C2×C4—22no—
338C2×C4—31no—
339C2×C4—34no—
340C2×C4—32no—
341C2×C4—64no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—124no—
345C2×C4—182no—
346C2×C4—364no—
347C2×C4D3×#6712yes—
348C2×C4C22×D3211yescharacteristic
349C8—62no—
350C8—182no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—34no—
354C2×C3D3×#12411yescharacteristic
355C2×C3D3×#13712yes—
356C2×C3C2×#94711yescharacteristic
357C2×C3C2×#95112yes—
358D3#506914yesdirect product factor
359C22—32no—
360C22—34no—
361C22C2×D3×#6711yescharacteristic
362C4—22no—
363C4—32no—
364C4—42no—
365C4—62no—
366C4—122no—
367C4—122no—
368C4—362no—
369C4D3×#23912yes—
370C3—21no—
371C3D3×#49111yescharacteristic, complemented
372C3C2×#506911yescharacteristic, complemented
373C2—34no—
374C2D3×#94711yescharacteristic
375C2D3×#95112yes—
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×#491
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. #10592768C2semidirect
4. C3×#5069C2semidirect
6. #10590562C2semidirect
8. #10590295C2semidirect
9. #10590291C2semidirect
45. #5069D3direct (N × H)
280. C3×D3#491semidirect
332. C32C2×#491semidirect
358. D3#5069direct (N × H)
371. C3D3×#491semidirect
372. C3C2×#5069semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1252
D3×#8692
#105927682
C3×#50692
D3×#8102
#105905622
D3×#8032
#105902952
#105902912
C2×#50693
D3×#4913