Finite Group Databasebeta

← D3×#4703 #11873611

Subgroups — D3×#4703 #11873611

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
1D3×#870C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592402C211yesmaximal, characteristic, complemented
4C3×D3×#97C211yesmaximal, characteristic
5C3×#4703C211yesmaximal, characteristic, complemented
6#10590898C214yesmaximal, complemented
7D3×#816C214yesmaximal
8#10590295C211yesmaximal, characteristic, complemented
9#10590289C211yesmaximal, characteristic, complemented
10D3×#491—31nomaximal
11C2×#4703—31nomaximal
12C2×D3×Dic6C2212yes—
13#64079C2211yescharacteristic
14#64078C2211yescharacteristic
15C2×C3×D3×C8C2212yes—
16C3×C42×D3C2211yescharacteristic
17C3×#870C2211yescharacteristic
18C3×#869C2211yescharacteristic
19#63918—22no—
20D3×C4⋊Dic3—22no—
21D3×C4⋊Dic3C2212yes—
22D3×Dic3⋊C4—22no—
23#63869C2212yes—
24#63867—22no—
25#63866C2212yes—
26C32×#97C2211yescharacteristic
27#63643C2214yes—
28C3×#816C2214yes—
29C3×#815C2212yes—
30C3×#803C2211yescharacteristic
31#63567C2214yes—
32#63566C2214yes—
33D3×C4⋊Q8—31no—
34D3×#125—31no—
35C2×#870—31no—
36C2×#869—31no—
37C3×#491—31no—
38C2×C3×#97—31no—
39C2×#816—34no—
40#5082—31no—
41#5069—31no—
42D3×#103—34no—
43#4797—34no—
44D3×#97D311yescharacteristic
45#4703—31no—
46#4703—31no—
47#4703—31no—
48#4703—31no—
49#4703—34no—
50#4703—61no—
51#4703D311yescharacteristic, direct product factor
52C2×#634C2312yes—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3C2311yescharacteristic
55C2×C3×Dic6C2312yes—
56C2×#627—22no—
57C2×D3×Dic3—22no—
58C2×D3×Dic3—22no—
59D3×Dic6—28no—
60C2×C32×C8C2312yes—
61C32×C42C2311yescharacteristic
62C4⋊(C3⋊Dic3)—22no—
63C4⋊(C3⋊Dic3)C2312yes—
64#3750—22no—
65C3×C4⋊Dic3—22no—
66C3×C4⋊Dic3C2312yes—
67C3×Dic3⋊C4—22no—
68C3×C4×Dic3D412yes—
69C3×C4×Dic3C2311yescharacteristic
70C2×C3×C3⋊C8C2312yes—
71C3×D3×C8—24no—
72#3724—22no—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3—22no—
75Dic3⋊Dic3—22no—
76C2×#491—91noSylow
77C2×D3×Q8—32no—
78C22×Dic6—32no—
79C22×C3×C8—32no—
80C3×C4⋊Q8—31no—
81C3×#125—31no—
82C2×C3×C42—31no—
83#944—32no—
84C2×C4⋊Dic3—32no—
85C2×C4⋊Dic3—62no—
86C2×Dic3⋊C4—62no—
87C2×D3×C8C2×D312yes—
88D3×C4⋊C4—32no—
89D3×C4⋊C4—62no—
90D3×C4⋊C4—62no—
91#890—32no—
92#889—62no—
93#888—62no—
94C42×D3C2×D311yescharacteristic
95#870—31no—
96#870—31no—
97#870—32no—
98#870—61no—
99#870—62no—
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—21no—
109C3×#97—32no—
110C3×#97—31no—
111C3×#97C2×D311yescharacteristic
112C3×#97C2×D311yescharacteristic
113#835—34no—
114#816—34no—
115#816—34no—
116#816—34no—
117#816—34no—
118#816—64no—
119#816C2×D314yes—
120#815C2×D312yes—
121#810—34no—
122#803C2×D311yescharacteristic
123C22×C3×D3C2×D411yescharacteristic
124C2×C32×C4C2×D412yes—
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
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#4114yes—
135C3×Dic6—24no—
136#627—44no—
137D3×Dic3—44no—
138D3×Dic3—44no—
139C32×C8—22no—
140C3×C3⋊C8—22no—
141C2×C4⋊Q8—91no—
142C2×#125—91no—
143#491—31no—
144#491—94no—
145#491—91no—
146#491—91no—
147#491—91no—
148C2×#103—94no—
149C2×#97—31no—
150C2×C3×Q8—32no—
151C22×C3×C4—31no—
152C22×C3×C4—32no—
153C22×Dic3—62no—
154C22×Dic3—62no—
155D3×Q8—68no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3D1212yes—
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—22no—
168C2×C3×C8—32no—
169C2×C3×C8—64no—
170C2×C3×C8C22×D312yes—
171C2×C3×C8C22×D312yes—
172C3×C4⋊C4—32no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—62no—
175C3×C42—21no—
176C3×C42—32no—
177C3×C42—31no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180C4⋊Dic3—22no—
181C4⋊Dic3—32no—
182C4⋊Dic3—32no—
183C4⋊Dic3—62no—
184C4⋊Dic3—64no—
185C4⋊Dic3—62no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189C4⋊Dic3—122no—
190C4⋊Dic3C22×D312yes—
191Dic3⋊C4—22no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—64no—
197Dic3⋊C4—62no—
198Dic3⋊C4—62no—
199Dic3⋊C4—122no—
200C4×Dic3D1212yes—
201C4×Dic3C22×D311yescharacteristic
202C2×C3⋊C8C22×D312yes—
203D3×C8—24no—
204C22×C32C22×D411yescharacteristic
205C2×C3×D3#12412yes—
206C2×C3×D3#13714yes—
207C32×C4—22no—
208C32×C4C2×#4112yes—
209C3⋊Dic3—42no—
210C3⋊Dic3—42no—
211C3×Dic3—22no—
212C3×Dic3—42no—
213C3×Dic3—42no—
214C3×Dic3#12412yes—
215C22×Q8—92no—
216C22×C8—32no—
217C4⋊Q8—31no—
218C4⋊Q8—92no—
219C4⋊Q8—91no—
220C4⋊Q8—182no—
221#125—31no—
222#125—92no—
223#125—91no—
224#125—182no—
225C2×C4⋊C4—92no—
226C2×C4⋊C4—182no—
227C2×C4⋊C4—182no—
228C2×C42—31no—
229#103—34no—
230#103—94no—
231#103—94no—
232#103—94no—
233#97—32no—
234#97—31no—
235#97D3211yescharacteristic
236C23×C3—31no—
237C22×D3C2×D1211yescharacteristic
238C3×Q8—64no—
239C2×C3×C4—21no—
240C2×C3×C4—22no—
241C2×C3×C4—31no—
242C2×C3×C4—34no—
243C2×C3×C4—32no—
244C2×C3×C4—64no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4C2×D1212yes—
248C2×C3×C4D3×D412yes—
249C2×C3×C4C23×D311yescharacteristic
250C2×C3×C4C23×D311yescharacteristic
251C2×Dic3—22no—
252C2×Dic3—22no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C2×Dic3—124no—
260C2×Dic3—124no—
261C2×Dic3C2×D1212yes—
262C2×Dic3C2×D1211yescharacteristic
263C4×D3—24no—
264C4×D3—124no—
265C4×D3—124no—
266C4×D3#23514yes—
267Dic6—24no—
268Dic6—64no—
269Dic6—64no—
270Dic6—124no—
271Dic6—124no—
272Dic6—124no—
273C3×C8—22no—
274C3×C8—22no—
275C3×C8—42no—
276C3×C8—62no—
277C3⋊C8—22no—
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—182no—
288C22×C4—182no—
289C2×C8—32no—
290C2×C8—64no—
291C2×C8C2×D3212yes—
292C4⋊C4—32no—
293C4⋊C4—62no—
294C4⋊C4—62no—
295C4⋊C4—92no—
296C4⋊C4—182no—
297C4⋊C4—182no—
298C4⋊C4—182no—
299C4⋊C4—184no—
300C4⋊C4—182no—
301C4⋊C4—182no—
302C42—31no—
303C42—32no—
304C42C2×D3211yescharacteristic
305C22×C3—21no—
306C22×C3—32no—
307C22×C3—34no—
308C22×C3C22×D1211yescharacteristic
309C22×C3C2×D3×D411yescharacteristic
310C2×D3#87512yes—
311C2×D3#90914yes—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—32no—
316C3×C4—42no—
317C3×C4—62no—
318C3×C4—122no—
319C3×C4—122no—
320C3×C4C2×#23512yes—
321C3×C4D3×#4112yes—
322Dic3—22no—
323Dic3—42no—
324Dic3—42no—
325Dic3—122no—
326Dic3—122no—
327Dic3—122no—
328Dic3—122no—
329Dic3—242no—
330Dic3—242no—
331Dic3#87512yes—
332C32C2×#49111yescharacteristic, complemented, Sylow
333C23—31no—
334Q8—64no—
335Q8—184no—
336Q8—364no—
337C2×C4—31no—
338C2×C4—34no—
339C2×C4—32no—
340C2×C4—64no—
341C2×C4—62no—
342C2×C4—62no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—364no—
346C2×C4—364no—
347C2×C4D3×D1212yes—
348C2×C4C22×D3211yescharacteristic
349C8—22no—
350C8—62no—
351C2×C3—22no—
352C2×C3—21no—
353C2×C3—34no—
354C2×C3C2×#87511yescharacteristic
355C2×C3D3×#12411yescharacteristic
356C2×C3C2×#90912yes—
357C2×C3D3×#13712yes—
358D3#470314yesdirect product factor
359C22—34no—
360C22—32no—
361C22C2×D3×D1211yescharacteristic
362C4—22no—
363C4—32no—
364C4—62no—
365C4—122no—
366C4—122no—
367C4—362no—
368C4—362no—
369C4D3×#23512yes—
370C3—21no—
371C3C2×#470311yescharacteristic, complemented
372C3D3×#49111yescharacteristic, complemented
373C2—34no—
374C2D3×#87511yescharacteristic
375C2D3×#90912yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#97D32
hypocenterC32C2×#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #10592402C2semidirect
5. C3×#4703C2semidirect
6. #10590898C2semidirect
8. #10590295C2semidirect
9. #10590289C2semidirect
51. #4703D3direct (N × H)
280. C3×D3#491semidirect
332. C32C2×#491semidirect
358. D3#4703direct (N × H)
371. C3C2×#4703semidirect
372. C3D3×#491semidirect

Maximal subgroups

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

subgroupindex
D3×#8702
D3×#8692
#105924022
C3×D3×#972
C3×#47032
#105908982
D3×#8162
#105902952
#105902892
D3×#4913
C2×#47033