Finite Group Databasebeta

← D3×#5231 #11808116

Subgroups — D3×#5231 #11808116

Order 1152.

2173 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×(C2×D3)⋊C4C213yesmaximal
3#10592930C211yesmaximal, characteristic, complemented
4C3×#5231C211yesmaximal, characteristic, complemented
5D3×C3⋊#95C213yesmaximal, complemented
6#10591310C213yesmaximal, complemented
7#10591304C213yesmaximal, complemented
8C2×#5231—31nomaximal
9D3×#393—31nomaximal
10C23×D32C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic, complemented
12C2×C3×D3×Q8—212no—
13C22×C3×C4×D3C2213yes—
14C22×C3×Dic6C2213yescomplemented
15C22×D3×Dic3C2213yes—
16C2×#3752C2213yes—
17C2×C3×(C2×D3)⋊C4C2213yes—
18C2×#3722C2213yes—
19C2×(C2×D3)⋊Dic3C2213yes—
20D3×(C2×D3)⋊C4—212no—
21#63658C2213yescomplemented
22C3×C3⋊#95C2213yescomplemented
23#63579C2216yescomplemented
24C23×C3×Q8—31no—
25C22×D3×Q8D311yescharacteristic, complemented
26C22×(C2×D3)⋊C4—33no—
27C2×D3×C22⋊C4—33no—
28C3×#393—31no—
29#5231—31no—
30#5231—31no—
31#5231—33no—
32#5231—33no—
33#5231—61no—
34#5231D311yescharacteristic, direct product factor
35C2×C3⋊#95—33no—
36#4947—33no—
37#4673—33no—
38D3×#95—33no—
39C23×C3⋊D3C2311yescharacteristic
40C23×C3×D3C2311yescharacteristic
41C23×C3×D3C2311yescharacteristic
42C22×D32—26no—
43C22×D32—26no—
44C22×D32Q814yescomplemented
45C2×C32×Q8—26no—
46C22×C32×C4C2313yes—
47C22×C3⋊Dic3C2313yes—
48C22×C3×Dic3C2313yes—
49C22×C3×Dic3C2313yes—
50C3×D3×Q8—232no—
51C2×C3×C4×D3—212no—
52C2×C3×C4×D3D4112yes—
53C2×C3×Dic6—26no—
54C2×C3×Dic6—212no—
55C2×D3×Dic3—26no—
56C2×D3×Dic3—212no—
57#3752—26no—
58C3×(C2×D3)⋊C4—26no—
59#3722—26no—
60(C2×D3)⋊Dic3—26no—
61C2×#393—91noSylow
62C24×D3—31no—
63C24×D3—31no—
64C22×C3×Q8—21no—
65C22×C3×Q8—33no—
66C22×C3×Q8—612no—
67C22×C3×Q8C2×D311yescharacteristic, complemented
68C22×C3×Q8C2×D311yescharacteristic, complemented
69C23×C3×C4—33no—
70C23×Dic3—33no—
71C2×D3×Q8—212no—
72C22×C4×D3—33no—
73C22×C4×D3C2×D313yes—
74C22×Dic6C2×D313yescomplemented
75C2×C3×C22⋊C4—33no—
76C2×#217—33no—
77C2×(C2×D3)⋊C4—33no—
78C2×(C2×D3)⋊C4—33no—
79C2×(C2×D3)⋊C4—33no—
80C2×(C2×D3)⋊C4—33no—
81C2×(C2×D3)⋊C4—33no—
82C2×(C2×D3)⋊C4—63no—
83C2×(C2×D3)⋊C4—612no—
84C2×(C2×D3)⋊C4C2×D313yes—
85D3×C22⋊C4—612no—
86C3×#95—33no—
87C3⋊#95—33no—
88C3⋊#95—33no—
89C3⋊#95—36no—
90C3⋊#95—36no—
91C3⋊#95—63no—
92C3⋊#95C2×D313yescomplemented
93C23×C32C2411yescharacteristic
94C22×C3⋊D3—23no—
95C22×C3⋊D3—23no—
96C22×C3⋊D3C2×Q812yescomplemented
97C22×C3×D3—23no—
98C22×C3×D3—23no—
99C22×C3×D3C2×D416yes—
100C22×C3×D3C2×Q812yes—
101C22×C3×D3C2×Q812yescomplemented
102C22×C3×D3#4116yes—
103C2×D32—224no—
104C2×D32—44no—
105C2×D32—412no—
106C32×Q8—28no—
107C2×C32×C4—26no—
108C2×C32×C4C2×D416yes—
109C2×C3⋊Dic3—23no—
110C2×C3⋊Dic3—26no—
111C2×C3×Dic3—26no—
112C2×C3×Dic3—23no—
113C2×C3×Dic3—26no—
114C2×C3×Dic3C2×D416yes—
115C3×C4×D3—224no—
116C3×Dic6—224no—
117D3×Dic3—412no—
118C23×Q8—31no—
119C22×C22⋊C4—93no—
120#393—31no—
121#393—93no—
122#393—93no—
123#393—91no—
124C2×#95—93no—
125C24×C3—31no—
126C24×C3—31no—
127C23×D3—31no—
128C23×D3—31no—
129C23×D3—34no—
130C23×D3—34no—
131C23×D3—61no—
132C23×D3—66no—
133C23×D3—66no—
134C23×D3—66no—
135C23×D3—66no—
136C23×D3C22×D311yescharacteristic
137C23×D3C22×D311yescharacteristic
138C2×C3×Q8—26no—
139C2×C3×Q8—26no—
140C2×C3×Q8—46no—
141C2×C3×Q8—612no—
142C2×C3×Q8—632no—
143C2×C3×Q8—66no—
144C22×C3×C4—23no—
145C22×C3×C4—33no—
146C22×C3×C4—312no—
147C22×C3×C4—33no—
148C22×C3×C4—612no—
149C22×C3×C4C22×D313yes—
150C22×C3×C4C22×D313yes—
151C22×Dic3—33no—
152C22×Dic3—33no—
153C22×Dic3—63no—
154C22×Dic3—66no—
155C22×Dic3—612no—
156C22×Dic3C22×D313yes—
157C22×Dic3C22×D313yes—
158D3×Q8—232no—
159C2×C4×D3—212no—
160C2×C4×D3—612no—
161C2×C4×D3—66no—
162C2×C4×D3#67112yes—
163C2×Dic6—26no—
164C2×Dic6—212no—
165C3×C22⋊C4—66no—
166#217—66no—
167(C2×D3)⋊C4—26no—
168(C2×D3)⋊C4—66no—
169(C2×D3)⋊C4—66no—
170(C2×D3)⋊C4—66no—
171(C2×D3)⋊C4—66no—
172(C2×D3)⋊C4—66no—
173(C2×D3)⋊C4—126no—
174C22×C32C22×D413yes—
175C22×C32C22×Q811yescharacteristic
176C22×C32C2×#4113yes—
177C2×C3⋊D3—26no—
178C2×C3⋊D3—41no—
179C2×C3⋊D3—43no—
180C2×C3×D3—26no—
181C2×C3×D3—41no—
182C2×C3×D3—43no—
183C2×C3×D3#12014yes—
184C2×C3×D3C22⋊Q8112yes—
185C2×C3×D3#124112yes—
186D32—416no—
187C32×C4—26no—
188C3⋊Dic3—43no—
189C3×Dic3—26no—
190C3×Dic3—43no—
191C25—91no—
192C22×Q8—33no—
193C22×Q8—612no—
194C22×Q8D3211yescharacteristic, complemented
195C23×C4—33no—
196C23×C4—93no—
197C2×C22⋊C4—33no—
198C2×C22⋊C4—93no—
199C2×C22⋊C4—93no—
200C2×C22⋊C4—93no—
201C2×C22⋊C4—1812no—
202#95—33no—
203#95—96no—
204#95—93no—
205C23×C3—21no—
206C23×C3—36no—
207C23×C3—32no—
208C23×C3—36no—
209C23×C3—32no—
210C23×C3—63no—
211C23×C3—63no—
212C23×C3C23×D311yescharacteristic
213C23×C3C23×D311yescharacteristic
214C22×D3—23no—
215C22×D3—23no—
216C22×D3—32no—
217C22×D3—32no—
218C22×D3—62no—
219C22×D3—624no—
220C22×D3—63no—
221C22×D3—63no—
222C22×D3—63no—
223C22×D3—63no—
224C22×D3—624no—
225C22×D3—123no—
226C22×D3—123no—
227C22×D3—1212no—
228C22×D3—124no—
229C22×D3—1212no—
230C22×D3—124no—
231C22×D3D3×Q812yes—
232C22×D3D3×Q812yescomplemented
233C22×D3#23916yes—
234C22×D3C2×#6716yes—
235C3×Q8—28no—
236C3×Q8—28no—
237C3×Q8—48no—
238C3×Q8—624no—
239C2×C3×C4—26no—
240C2×C3×C4—26no—
241C2×C3×C4—26no—
242C2×C3×C4—36no—
243C2×C3×C4—46no—
244C2×C3×C4—624no—
245C2×C3×C4—66no—
246C2×C3×C4—66no—
247C2×C3×C4—63no—
248C2×C3×C4D3×D416yes—
249C2×C3×C4C2×#6716yes—
250C2×Dic3—26no—
251C2×Dic3—23no—
252C2×Dic3—26no—
253C2×Dic3—63no—
254C2×Dic3—66no—
255C2×Dic3—66no—
256C2×Dic3—63no—
257C2×Dic3—123no—
258C2×Dic3—126no—
259C2×Dic3—1212no—
260C2×Dic3C2×#6716yes—
261C4×D3—224no—
262C4×D3—1212no—
263Dic6—224no—
264C2×C32C2×#12011yescharacteristic
265C2×C32C2×C22⋊Q813yes—
266C2×C32C2×#12413yes—
267C3⋊D3—42no—
268C3×D3—42no—
269C3×D3#39318yescomplemented
270C24—31no—
271C24—31no—
272C24—94no—
273C24—91no—
274C24—186no—
275C24—186no—
276C2×Q8—26no—
277C2×Q8—612no—
278C2×Q8—632no—
279C2×Q8—66no—
280C22×C4—33no—
281C22×C4—312no—
282C22×C4—33no—
283C22×C4—612no—
284C22×C4—93no—
285C22×C4—186no—
286C22×C4—1812no—
287C22×C4C2×D3213yes—
288C22⋊C4—66no—
289C22⋊C4—186no—
290C22⋊C4—186no—
291C22⋊C4—186no—
292C22×C3—21no—
293C22×C3—23no—
294C22×C3—23no—
295C22×C3—312no—
296C22×C3—34no—
297C22×C3—312no—
298C22×C3—66no—
299C22×C3—123no—
300C22×C3—121no—
301C22×C3C2×D3×D413yes—
302C22×C3C2×D3×Q811yescharacteristic
303C22×C3C2×D3×Q811yescharacteristic
304C22×C3C2×#23913yes—
305C22×C3D3×#4113yes—
306C22×C3C22×#6713yes—
307C2×D3—26no—
308C2×D3—43no—
309C2×D3—41no—
310C2×D3—66no—
311C2×D3—66no—
312C2×D3—126no—
313C2×D3—1216no—
314C2×D3—123no—
315C2×D3—123no—
316C2×D3—121no—
317C2×D3—121no—
318C2×D3—1216no—
319C2×D3—243no—
320C2×D3—241no—
321C2×D3#946112yes—
322C2×D3#947112yes—
323C2×D3#95314yes—
324C3×C4—26no—
325C3×C4—26no—
326C3×C4—46no—
327C3×C4—66no—
328C3×C4—123no—
329Dic3—26no—
330Dic3—43no—
331Dic3—123no—
332Dic3—123no—
333Dic3—243no—
334C32C2×#39311yescharacteristic, complemented, Sylow
335C23—32no—
336C23—36no—
337C23—36no—
338C23—32no—
339C23—63no—
340C23—63no—
341C23—92no—
342C23—1824no—
343C23—183no—
344C23—183no—
345C23—3612no—
346C23—364no—
347C23C22×D3211yescharacteristic
348Q8—28no—
349Q8—624no—
350C2×C4—26no—
351C2×C4—36no—
352C2×C4—624no—
353C2×C4—66no—
354C2×C4—66no—
355C2×C4—63no—
356C2×C4—186no—
357C2×C4—183no—
358C2×C4—3612no—
359C2×C4D3×#6716yes—
360C2×C3—23no—
361C2×C3—23no—
362C2×C3—21no—
363C2×C3—38no—
364C2×C3—122no—
365C2×C3D3×#12011yescharacteristic
366C2×C3D3×C22⋊Q813yes—
367C2×C3D3×#12413yes—
368C2×C3C2×#94613yes—
369C2×C3C2×#94713yes—
370C2×C3C2×#95311yescharacteristic
371D3—42no—
372D3—122no—
373D3—122no—
374D3—242no—
375D3#523118yesdirect product factor
376C22—312no—
377C22—312no—
378C22—34no—
379C22—66no—
380C22—123no—
381C22—121no—
382C22—186no—
383C22—3616no—
384C22—363no—
385C22—361no—
386C22D32×Q811yescharacteristic
387C22D3×#23913yes—
388C22C2×D3×#6713yes—
389C4—26no—
390C4—66no—
391C4—123no—
392C4—363no—
393C3—21no—
394C3D3×#39311yescharacteristic, complemented
395C3C2×#523111yescharacteristic, complemented
396C2—38no—
397C2—122no—
398C2—362no—
399C2D3×#94613yes—
400C2D3×#94713yes—
401C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC23×D32C22
hypercenterC22×Q8D32
hypocenterC32C2×#393
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
3. #10592930C2semidirect
4. C3×#5231C2semidirect
5. D3×C3⋊#95C2semidirect
6. #10591310C2semidirect
7. #10591304C2semidirect
11. C22×C32×Q8C22semidirect
14. C22×C3×Dic6C22semidirect
21. #63658C22semidirect
22. C3×C3⋊#95C22semidirect
23. #63579C22semidirect
25. C22×D3×Q8D3semidirect
34. #5231D3direct (N × H)
44. C22×D32Q8semidirect
67. C22×C3×Q8C2×D3semidirect
68. C22×C3×Q8C2×D3semidirect
74. C22×Dic6C2×D3semidirect
92. C3⋊#95C2×D3semidirect
96. C22×C3⋊D3C2×Q8semidirect
101. C22×C3×D3C2×Q8semidirect
194. C22×Q8D32semidirect
232. C22×D3D3×Q8semidirect
269. C3×D3#393semidirect
334. C32C2×#393semidirect
375. D3#5231direct (N × H)
394. C3D3×#393semidirect
395. C3C2×#5231semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×D3×(C2×D3)⋊C42
#105929302
C3×#52312
D3×C3⋊#952
#105913102
#105913042
C2×#52313
D3×#3933