Finite Group Databasebeta

← D3×#4676 #11808276

Subgroups — D3×#4676 #11808276

Order 1152.

1909 conjugacy classes of subgroups; only the 304 normal subgroups are shown.

normal subgroups only

This group has 1909 conjugacy classes of subgroups — too many to draw. Only its 304 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×(C2×D3)⋊C4C213yesmaximal
2C2×D3×Dic3⋊C4C213yesmaximal, complemented
3#10592375C211yesmaximal, characteristic, complemented
4C3×#4676C211yesmaximal, characteristic, complemented
5C3×D3×#95C211yesmaximal, characteristic, complemented
6#10591347C213yesmaximal, complemented
7#10591309C213yesmaximal, complemented
8D3×#396—31nomaximal
9C2×#4676—31nomaximal
10C23×D32C2211yescharacteristic
11C22×C3×C4×D3C2213yes—
12C22×D3×Dic3C2213yes—
13C2×#3752C2213yes—
14C2×#3750C2213yescomplemented
15C2×C3×(C2×D3)⋊C4C2213yes—
16C2×C3×Dic3⋊C4C2213yescomplemented
17C2×#3724C2213yescomplemented
18C2×Dic3⋊Dic3C2213yescomplemented
19C2×#3722C2213yes—
20C2×(C2×D3)⋊Dic3C2213yes—
21D3×(C2×D3)⋊C4—212no—
22D3×Dic3⋊C4—212no—
23C32×#95C2211yescharacteristic, complemented
24C3×C3⋊#95C2213yescomplemented
25C22×(C2×D3)⋊C4—33no—
26C22×Dic3⋊C4—33no—
27C2×D3×C4⋊C4—33no—
28C2×D3×C22⋊C4—33no—
29C3×#396—31no—
30C2×C3×#95—31no—
31#4994—33no—
32#4948—33no—
33#4676—33no—
34#4676—33no—
35#4676—31no—
36#4676—31no—
37#4676—61no—
38#4676D311yescharacteristic, direct product factor
39D3×#95D311yescharacteristic, complemented
40C23×C3⋊D3C2311yescharacteristic
41C23×C3×D3C2311yescharacteristic
42C23×C3×D3C2311yescharacteristic
43C22×D32—26no—
44C22×D32—26no—
45C22×D32Q814yes—
46C22×C32×C4C2313yes—
47C22×C3⋊Dic3C2313yes—
48C22×C3×Dic3C2313yes—
49C22×C3×Dic3C2313yes—
50C2×C3×C4×D3—26no—
51C2×C3×C4×D3—26no—
52C2×C3×C4×D3—26no—
53C2×D3×Dic3—26no—
54C2×D3×Dic3—26no—
55C2×D3×Dic3D4112yes—
56#3752—26no—
57#3750—26no—
58C3×(C2×D3)⋊C4—26no—
59C3×Dic3⋊C4—26no—
60#3724—26no—
61Dic3⋊Dic3—26no—
62#3722—26no—
63(C2×D3)⋊Dic3—26no—
64C2×#396—91noSylow
65C24×D3—31no—
66C24×D3—31no—
67C23×C3×C4—33no—
68C23×Dic3—33no—
69C22×C4×D3—33no—
70C22×C4×D3C2×D313yes—
71C2×C3×C4⋊C4—33no—
72C2×C3×C22⋊C4—33no—
73C2×#217—33no—
74C2×(C2×D3)⋊C4—33no—
75C2×(C2×D3)⋊C4—33no—
76C2×(C2×D3)⋊C4—33no—
77C2×(C2×D3)⋊C4—33no—
78C2×(C2×D3)⋊C4—33no—
79C2×(C2×D3)⋊C4—63no—
80C2×(C2×D3)⋊C4—612no—
81C2×(C2×D3)⋊C4C2×D313yes—
82C2×C4⋊Dic3—33no—
83C2×Dic3⋊C4—33no—
84C2×Dic3⋊C4—33no—
85C2×Dic3⋊C4—33no—
86C2×Dic3⋊C4—33no—
87C2×Dic3⋊C4—33no—
88C2×Dic3⋊C4—63no—
89C2×Dic3⋊C4—612no—
90C2×Dic3⋊C4C2×D313yescomplemented
91D3×C4⋊C4—612no—
92D3×C22⋊C4—612no—
93C3×#95—21no—
94C3×#95—33no—
95C3×#95C2×D311yescharacteristic, complemented
96C3×#95C2×D311yescharacteristic, complemented
97C3⋊#95C2×D313yescomplemented
98C23×C32C2411yescharacteristic
99C22×C3⋊D3—23no—
100C22×C3⋊D3—23no—
101C22×C3⋊D3C2×Q812yes—
102C22×C3×D3—23no—
103C22×C3×D3—23no—
104C22×C3×D3C2×D416yes—
105C22×C3×D3C2×Q812yes—
106C22×C3×D3C2×Q812yes—
107C22×C3×D3#4116yes—
108C2×D32—224no—
109C2×D32—412no—
110C2×D32—44no—
111C2×C32×C4—23no—
112C2×C32×C4—23no—
113C2×C32×C4—23no—
114C2×C3⋊Dic3—23no—
115C2×C3⋊Dic3—23no—
116C2×C3⋊Dic3C2×D416yes—
117C2×C3×Dic3—23no—
118C2×C3×Dic3—23no—
119C2×C3×Dic3—23no—
120C2×C3×Dic3—23no—
121C2×C3×Dic3—23no—
122C2×C3×Dic3C2×D416yes—
123C3×C4×D3—412no—
124D3×Dic3—224no—
125C22×C4⋊C4—93no—
126C22×C22⋊C4—93no—
127#396—31no—
128#396—93no—
129#396—93no—
130#396—91no—
131C2×#95—31no—
132C24×C3—31no—
133C24×C3—31no—
134C23×D3—31no—
135C23×D3—31no—
136C23×D3—34no—
137C23×D3—34no—
138C23×D3—61no—
139C23×D3—66no—
140C23×D3—66no—
141C23×D3—66no—
142C23×D3—66no—
143C23×D3C22×D311yescharacteristic
144C23×D3C22×D311yescharacteristic
145C22×C3×C4—23no—
146C22×C3×C4—33no—
147C22×C3×C4—33no—
148C22×C3×C4—66no—
149C22×C3×C4—66no—
150C22×C3×C4—66no—
151C22×C3×C4C22×D313yes—
152C22×C3×C4C22×D313yes—
153C22×Dic3—33no—
154C22×Dic3—33no—
155C22×Dic3—312no—
156C22×Dic3—63no—
157C22×Dic3—66no—
158C22×Dic3—66no—
159C22×Dic3C22×D313yes—
160C22×Dic3C22×D313yes—
161C2×C4×D3—26no—
162C2×C4×D3—26no—
163C2×C4×D3—26no—
164C2×C4×D3—312no—
165C2×C4×D3—66no—
166C2×C4×D3—66no—
167C3×C4⋊C4—66no—
168C3×C22⋊C4—66no—
169#217—66no—
170(C2×D3)⋊C4—26no—
171(C2×D3)⋊C4—66no—
172(C2×D3)⋊C4—66no—
173(C2×D3)⋊C4—66no—
174(C2×D3)⋊C4—66no—
175(C2×D3)⋊C4—66no—
176(C2×D3)⋊C4—126no—
177C4⋊Dic3—66no—
178Dic3⋊C4—26no—
179Dic3⋊C4—66no—
180Dic3⋊C4—66no—
181Dic3⋊C4—66no—
182Dic3⋊C4—66no—
183Dic3⋊C4—66no—
184Dic3⋊C4—126no—
185C22×C32C22×D413yes—
186C22×C32C22×Q811yescharacteristic
187C22×C32C2×#4113yes—
188C2×C3⋊D3—26no—
189C2×C3⋊D3—43no—
190C2×C3⋊D3—41no—
191C2×C3×D3—26no—
192C2×C3×D3—43no—
193C2×C3×D3—41no—
194C2×C3×D3#121112yes—
195C2×C3×D3C22⋊Q8112yes—
196C2×C3×D3#12614yes—
197D32—416no—
198C32×C4—43no—
199C3⋊Dic3—26no—
200C3×Dic3—26no—
201C3×Dic3—43no—
202C25—91no—
203C23×C4—33no—
204C23×C4—93no—
205C2×C4⋊C4—33no—
206C2×C4⋊C4—93no—
207C2×C4⋊C4—93no—
208C2×C4⋊C4—93no—
209C2×C4⋊C4—1812no—
210C2×C22⋊C4—33no—
211C2×C22⋊C4—93no—
212C2×C22⋊C4—93no—
213C2×C22⋊C4—93no—
214C2×C22⋊C4—1812no—
215#95—33no—
216#95D3211yescharacteristic, complemented
217C23×C3—21no—
218C23×C3—36no—
219C23×C3—32no—
220C23×C3—36no—
221C23×C3—32no—
222C23×C3—63no—
223C23×C3—63no—
224C23×C3C23×D311yescharacteristic
225C23×C3C23×D311yescharacteristic
226C22×D3—23no—
227C22×D3—23no—
228C22×D3—32no—
229C22×D3—32no—
230C22×D3—62no—
231C22×D3—624no—
232C22×D3—63no—
233C22×D3—63no—
234C22×D3—63no—
235C22×D3—63no—
236C22×D3—624no—
237C22×D3—123no—
238C22×D3—123no—
239C22×D3—124no—
240C22×D3—1212no—
241C22×D3—124no—
242C22×D3—1212no—
243C22×D3#23516yes—
244C22×D3D3×D416yes—
245C22×D3D3×Q812yes—
246C22×D3D3×Q812yes—
247C2×C3×C4—23no—
248C2×C3×C4—23no—
249C2×C3×C4—23no—
250C2×C3×C4—23no—
251C2×C3×C4—23no—
252C2×C3×C4—23no—
253C2×C3×C4—36no—
254C2×C3×C4—43no—
255C2×C3×C4—43no—
256C2×C3×C4—43no—
257C2×C3×C4—63no—
258C2×C3×C4—63no—
259C2×C3×C4—63no—
260C2×C3×C4—63no—
261C2×C3×C4—63no—
262C2×C3×C4—1212no—
263C2×Dic3—23no—
264C2×Dic3—23no—
265C2×Dic3—23no—
266C2×Dic3—23no—
267C2×Dic3—23no—
268C2×Dic3—36no—
269C2×Dic3—36no—
270C2×Dic3—66no—
271C2×Dic3—624no—
272C2×Dic3—63no—
273C2×Dic3—63no—
274C2×Dic3—63no—
275C2×Dic3—63no—
276C2×Dic3—123no—
277C2×Dic3—123no—
278C2×Dic3D3×D416yes—
279C4×D3—412no—
280C4×D3—624no—
281C2×C32C2×#12113yes—
282C2×C32C2×C22⋊Q813yes—
283C2×C32C2×#12611yescharacteristic
284C3⋊D3—42no—
285C3×D3—42no—
286C3×D3#39618yescomplemented
287C24—31no—
288C24—31no—
289C24—94no—
290C24—91no—
291C24—186no—
292C24—186no—
293C22×C4—33no—
294C22×C4—33no—
295C22×C4—66no—
296C22×C4—66no—
297C22×C4—66no—
298C22×C4—912no—
299C22×C4—93no—
300C22×C4—186no—
301C22×C4—186no—
302C22×C4C2×D3213yes—
303C4⋊C4—66no—
304C4⋊C4—186no—
305C4⋊C4—186no—
306C4⋊C4—186no—
307C22⋊C4—66no—
308C22⋊C4—186no—
309C22⋊C4—186no—
310C22⋊C4—186no—
311C22×C3—23no—
312C22×C3—23no—
313C22×C3—21no—
314C22×C3—34no—
315C22×C3—312no—
316C22×C3—312no—
317C22×C3—66no—
318C22×C3—121no—
319C22×C3—123no—
320C22×C3C2×#23513yes—
321C22×C3C2×D3×D413yes—
322C22×C3C2×D3×D413yes—
323C22×C3C2×D3×Q811yescharacteristic
324C22×C3C2×D3×Q811yescharacteristic
325C22×C3D3×#4113yes—
326C2×D3—26no—
327C2×D3—41no—
328C2×D3—43no—
329C2×D3—66no—
330C2×D3—66no—
331C2×D3—126no—
332C2×D3—1216no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—123no—
336C2×D3—123no—
337C2×D3—1216no—
338C2×D3—243no—
339C2×D3—241no—
340C2×D3#87614yes—
341C2×D3#884112yes—
342C2×D3#896112yes—
343C3×C4—43no—
344C3×C4—43no—
345C3×C4—66no—
346C3×C4—83no—
347C3×C4—123no—
348Dic3—26no—
349Dic3—43no—
350Dic3—66no—
351Dic3—66no—
352Dic3—126no—
353C32C2×#39611yescharacteristic, complemented, Sylow
354C23—36no—
355C23—36no—
356C23—32no—
357C23—32no—
358C23—63no—
359C23—63no—
360C23—92no—
361C23—1824no—
362C23—183no—
363C23—183no—
364C23—3612no—
365C23—364no—
366C23C22×D3211yescharacteristic
367C2×C4—23no—
368C2×C4—23no—
369C2×C4—23no—
370C2×C4—36no—
371C2×C4—63no—
372C2×C4—63no—
373C2×C4—63no—
374C2×C4—63no—
375C2×C4—63no—
376C2×C4—96no—
377C2×C4—1212no—
378C2×C4—1824no—
379C2×C4—183no—
380C2×C4—183no—
381C2×C3—23no—
382C2×C3—23no—
383C2×C3—21no—
384C2×C3—38no—
385C2×C3—122no—
386C2×C3C2×#87611yescharacteristic
387C2×C3C2×#88413yes—
388C2×C3C2×#89613yes—
389C2×C3D3×#12113yes—
390C2×C3D3×C22⋊Q813yes—
391C2×C3D3×#12611yescharacteristic
392D3—42no—
393D3—122no—
394D3—122no—
395D3—242no—
396D3#467618yesdirect product factor
397C22—312no—
398C22—312no—
399C22—34no—
400C22—66no—
401C22—123no—
402C22—121no—
403C22—186no—
404C22—3616no—
405C22—363no—
406C22—361no—
407C22D3×#23513yes—
408C22D32×D413yes—
409C22D32×Q811yescharacteristic
410C4—43no—
411C4—66no—
412C4—123no—
413C4—186no—
414C3—21no—
415C3C2×#467611yescharacteristic, complemented
416C3D3×#39611yescharacteristic, complemented
417C2—38no—
418C2—122no—
419C2—362no—
420C2D3×#87611yescharacteristic
421C2D3×#88413yes—
422C2D3×#89613yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×D32C22
hypercenter#95D32
hypocenterC32C2×#396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic3⋊C4C2semidirect
3. #10592375C2semidirect
4. C3×#4676C2semidirect
5. C3×D3×#95C2semidirect
6. #10591347C2semidirect
7. #10591309C2semidirect
14. C2×#3750C22semidirect
16. C2×C3×Dic3⋊C4C22semidirect
17. C2×#3724C22semidirect
18. C2×Dic3⋊Dic3C22semidirect
23. C32×#95C22semidirect
24. C3×C3⋊#95C22semidirect
38. #4676D3direct (N × H)
39. D3×#95D3semidirect
90. C2×Dic3⋊C4C2×D3semidirect
95. C3×#95C2×D3semidirect
96. C3×#95C2×D3semidirect
97. C3⋊#95C2×D3semidirect
216. #95D32semidirect
286. C3×D3#396semidirect
353. C32C2×#396semidirect
396. D3#4676direct (N × H)
415. C3C2×#4676semidirect
416. C3D3×#396semidirect

Maximal subgroups

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

subgroupindex
C2×D3×(C2×D3)⋊C42
C2×D3×Dic3⋊C42
#105923752
C3×#46762
C3×D3×#952
#105913472
#105913092
D3×#3963
C2×#46763