Finite Group Databasebeta

← C3⋊D3×#396 #11808254

Subgroups — C3⋊D3×#396 #11808254

Order 1152.

2724 conjugacy classes of subgroups; only the 359 normal subgroups are shown.

normal subgroups only

This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 359 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×C4⋊C4×C3⋊D3C213yesmaximal, complemented
2C2×C22⋊C4×C3⋊D3C213yesmaximal
3C32×#396C211yesmaximal, characteristic, complemented
4#10592693C213yesmaximal, complemented
5#10592647C213yesmaximal, complemented
6#10592375C211yesmaximal, characteristic, complemented
7C3⋊D3×#95C211yesmaximal, characteristic, complemented
8D3×#396—34nomaximal
9C24×C3⋊D3C2211yescharacteristic
10C22×C4×C3⋊D3C2213yes—
11C22×C4×C3⋊D3C2213yes—
12C2×C32×C4⋊C4C2213yescomplemented
13C2×C32×C22⋊C4C2213yes—
14C2×#3757C2213yes—
15C2×#3752C2213yes—
16C2×#3752C2213yes—
17C2×C4⋊(C3⋊Dic3)C2213yescomplemented
18C2×#3750C2213yescomplemented
19C2×#3750C2213yescomplemented
20C4⋊C4×C3⋊D3—212no—
21C22⋊C4×C3⋊D3—212no—
22C32×#95C2211yescharacteristic, complemented
23#63658C2213yescomplemented
24C2×D3×C4⋊C4—312no—
25C2×D3×C22⋊C4—312no—
26C3×#396D314yescomplemented
27#4994—312no—
28#4948—312no—
29#4676—34no—
30D3×#95—34no—
31C24×C32C2311yescharacteristic
32C23×C3⋊D3—26no—
33C23×C3⋊D3—26no—
34C23×C3⋊D3Q814yes—
35C23×C3⋊D3C2311yescharacteristic
36C23×C3⋊D3C2311yescharacteristic
37C22×C32×C4C2313yes—
38C22×C32×C4C2313yes—
39C22×C3⋊Dic3C2313yes—
40C22×C3⋊Dic3C2313yes—
41C2×C4×C3⋊D3—26no—
42C2×C4×C3⋊D3—26no—
43C2×C4×C3⋊D3—26no—
44C2×C4×C3⋊D3—26no—
45C2×C4×C3⋊D3—26no—
46C2×C4×C3⋊D3D4112yes—
47C32×C4⋊C4—26no—
48C32×C22⋊C4—26no—
49#3757—26no—
50#3752—26no—
51#3752—26no—
52C4⋊(C3⋊Dic3)—26no—
53#3750—26no—
54#3750—26no—
55C2×#396—91noSylow
56C24×D3—34no—
57C22×C4×D3—312no—
58C22×C4×D3—312no—
59C2×C3×C4⋊C4C2×D3112yescomplemented
60C2×C3×C22⋊C4C2×D3112yes—
61C2×#217—312no—
62C2×(C2×D3)⋊C4—312no—
63C2×(C2×D3)⋊C4—312no—
64C2×C4⋊Dic3—312no—
65C2×Dic3⋊C4—312no—
66C2×Dic3⋊C4—312no—
67D3×C4⋊C4—648no—
68D3×C22⋊C4—648no—
69C3×#95C2×D314yescomplemented
70C3⋊#95—312no—
71C23×C32—23no—
72C23×C32—23no—
73C23×C32C2×Q812yes—
74C23×C32C2411yescharacteristic
75C22×C3⋊D3—23no—
76C22×C3⋊D3—23no—
77C22×C3⋊D3—224no—
78C22×C3⋊D3—412no—
79C22×C3⋊D3—44no—
80C22×C3⋊D3C2×D416yes—
81C22×C3⋊D3C2×Q812yes—
82C22×C3⋊D3C2×Q812yes—
83C22×C3⋊D3#4116yes—
84C2×C32×C4—23no—
85C2×C32×C4—23no—
86C2×C32×C4—23no—
87C2×C32×C4—23no—
88C2×C32×C4—23no—
89C2×C32×C4C2×D416yes—
90C2×C3⋊Dic3—23no—
91C2×C3⋊Dic3—23no—
92C2×C3⋊Dic3—23no—
93C2×C3⋊Dic3—23no—
94C2×C3⋊Dic3—23no—
95C2×C3⋊Dic3C2×D416yes—
96C4×C3⋊D3—224no—
97C4×C3⋊D3—412no—
98C22×C4⋊C4—93no—
99C22×C22⋊C4—93no—
100#396—93no—
101#396—93no—
102#396—91no—
103#396C3⋊D311yescharacteristic, direct product factor
104C2×#95—91no—
105C24×C3C22×D314yes—
106C23×D3—34no—
107C23×D3—316no—
108C23×D3—34no—
109C23×D3—624no—
110C23×D3—624no—
111C22×C3×C4C22×D3112yes—
112C22×C3×C4C22×D3112yes—
113C22×Dic3—312no—
114C22×Dic3—312no—
115C2×C4×D3—348no—
116C2×C4×D3—624no—
117C2×C4×D3—624no—
118C2×C4×D3—624no—
119C2×C4×D3—624no—
120C2×C4×D3—624no—
121C3×C4⋊C4—224no—
122C3×C22⋊C4—224no—
123#217—624no—
124(C2×D3)⋊C4—624no—
125(C2×D3)⋊C4—624no—
126C4⋊Dic3—624no—
127Dic3⋊C4—624no—
128Dic3⋊C4—624no—
129C22×C32—26no—
130C22×C32—43no—
131C22×C32—41no—
132C22×C32C22×D413yes—
133C22×C32C22×Q811yescharacteristic
134C22×C32C2×#4113yes—
135C2×C3⋊D3—26no—
136C2×C3⋊D3—43no—
137C2×C3⋊D3—41no—
138C2×C3⋊D3—416no—
139C2×C3⋊D3#121112yes—
140C2×C3⋊D3C22⋊Q8112yes—
141C2×C3⋊D3#12614yes—
142C32×C4—26no—
143C32×C4—43no—
144C3⋊Dic3—26no—
145C3⋊Dic3—43no—
146C25—91no—
147C23×C4—93no—
148C23×C4—93no—
149C2×C4⋊C4—93no—
150C2×C4⋊C4—93no—
151C2×C4⋊C4—93no—
152C2×C4⋊C4—1812no—
153C2×C4⋊C4C2×C3⋊D313yescomplemented
154C2×C22⋊C4—93no—
155C2×C22⋊C4—93no—
156C2×C22⋊C4—93no—
157C2×C22⋊C4—1812no—
158C2×C22⋊C4C2×C3⋊D313yes—
159#95—93no—
160#95C2×C3⋊D311yescharacteristic, complemented
161C23×C3—212no—
162C23×C3—212no—
163C23×C3D3×Q818yes—
164C23×C3C23×D314yes—
165C22×D3—324no—
166C22×D3—38no—
167C22×D3—324no—
168C22×D3—38no—
169C22×D3—696no—
170C22×D3—612no—
171C22×D3—612no—
172C22×D3—1216no—
173C22×D3—1248no—
174C2×C3×C4—212no—
175C2×C3×C4—212no—
176C2×C3×C4—212no—
177C2×C3×C4—212no—
178C2×C3×C4—212no—
179C2×C3×C4D3×D4124yes—
180C2×Dic3—324no—
181C2×Dic3—612no—
182C2×Dic3—612no—
183C2×Dic3—612no—
184C2×Dic3—612no—
185C2×Dic3—612no—
186C4×D3—696no—
187C4×D3—1248no—
188C2×C32—42no—
189C2×C32C2×#12113yes—
190C2×C32C2×C22⋊Q813yes—
191C2×C32C2×#12611yescharacteristic
192C3⋊D3—42no—
193C3⋊D3#39618yesdirect product factor
194C24—91no—
195C24—91no—
196C24—94no—
197C24—186no—
198C24—186no—
199C24C22×C3⋊D311yescharacteristic
200C22×C4—93no—
201C22×C4—912no—
202C22×C4—93no—
203C22×C4—186no—
204C22×C4—186no—
205C22×C4—186no—
206C22×C4—186no—
207C22×C4—186no—
208C22×C4C22×C3⋊D313yes—
209C22×C4C22×C3⋊D313yes—
210C4⋊C4—26no—
211C4⋊C4—186no—
212C4⋊C4—186no—
213C4⋊C4—186no—
214C22⋊C4—26no—
215C22⋊C4—186no—
216C22⋊C4—186no—
217C22⋊C4—186no—
218C22×C3—224no—
219C22×C3—44no—
220C22×C3—412no—
221C22×C3C2×D3×D4112yes—
222C22×C3C2×D3×Q814yes—
223C22×C3D3×#41112yes—
224C2×D3—316no—
225C2×D3—348no—
226C2×D3—348no—
227C2×D3—624no—
228C2×D3—1264no—
229C2×D3—124no—
230C2×D3—1212no—
231C3×C4—224no—
232C3×C4—412no—
233Dic3—624no—
234Dic3—1212no—
235C32C2×#39611yescharacteristic, complemented, Sylow
236C23—23no—
237C23—23no—
238C23—96no—
239C23—92no—
240C23—96no—
241C23—92no—
242C23—1824no—
243C23—183no—
244C23—183no—
245C23—364no—
246C23—3612no—
247C23Q8×C3⋊D312yes—
248C23C23×C3⋊D311yescharacteristic
249C2×C4—23no—
250C2×C4—23no—
251C2×C4—23no—
252C2×C4—23no—
253C2×C4—23no—
254C2×C4—96no—
255C2×C4—1824no—
256C2×C4—183no—
257C2×C4—183no—
258C2×C4—183no—
259C2×C4—183no—
260C2×C4—183no—
261C2×C4—3612no—
262C2×C4D4×C3⋊D316yes—
263C2×C3—48no—
264C2×C3D3×#121112yes—
265C2×C3D3×C22⋊Q8112yes—
266C2×C3D3×#12614yes—
267D3—332no—
268D3—128no—
269C22—26no—
270C22—41no—
271C22—43no—
272C22—912no—
273C22—94no—
274C22—912no—
275C22—186no—
276C22—3616no—
277C22—361no—
278C22—363no—
279C22C2×D4×C3⋊D313yes—
280C22C2×Q8×C3⋊D311yescharacteristic
281C22#41×C3⋊D313yes—
282C4—26no—
283C4—43no—
284C4—186no—
285C4—363no—
286C3D3×#39614yescomplemented
287C2—42no—
288C2—98no—
289C2—362no—
290C2C3⋊D3×#12113yes—
291C2C3⋊D3×C22⋊Q813yes—
292C2C3⋊D3×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#396C2
prime radicalC24×C3⋊D3C22
hypercenter#396C3⋊D3
hypocenterC32C2×#396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
3. C32×#396C2semidirect
4. #10592693C2semidirect
5. #10592647C2semidirect
6. #10592375C2semidirect
7. C3⋊D3×#95C2semidirect
12. C2×C32×C4⋊C4C22semidirect
17. C2×C4⋊(C3⋊Dic3)C22semidirect
18. C2×#3750C22semidirect
19. C2×#3750C22semidirect
22. C32×#95C22semidirect
23. #63658C22semidirect
26. C3×#396D3semidirect
59. C2×C3×C4⋊C4C2×D3semidirect
69. C3×#95C2×D3semidirect
103. #396C3⋊D3direct (N × H)
153. C2×C4⋊C4C2×C3⋊D3semidirect
160. #95C2×C3⋊D3semidirect
193. C3⋊D3#396direct (N × H)
235. C32C2×#396semidirect
286. C3D3×#396semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C22⋊C4×C3⋊D32
C32×#3962
#105926932
#105926472
#105923752
C3⋊D3×#952
D3×#3963