Finite Group Databasebeta

← C4×#64266 #11922889

Subgroups — C4×#64266 #11922889

Order 1152.

736 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 97 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×#64266C211yesmaximal, characteristic
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3#10593658C211yesmaximal, characteristic, complemented
4C4×C3⋊GL(2,𝔽3)C212yesmaximal, complemented
5C4×C3⋊#226C212yesmaximal, complemented
6C4×#985—33nomaximal
7C4×#950—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64266C414yesdirect product factor
10C2×C3⋊GL(2,𝔽3)C2211yescharacteristic
11C2×C3⋊#226C2211yescharacteristic
12C42×C3⋊D3—41nomaximal
13C3×C4×SL(2,𝔽3)C2212yes—
14C3⋊#859C2212yes—
15C2×#985—33no—
16C3×C4×#41D311yescharacteristic, complemented
17C2×#950—31no—
18C4×#235—31no—
19C4×#41⋊C3D313yescomplemented
20#5424—33no—
21C4×GL(2,𝔽3)—36no—
22C4×#226—36no—
23#5233—31no—
24C4×#216—32no—
25C4×#215—32no—
26C4×#214—32no—
27C4×#213—32no—
28#5002—31no—
29#4998—31no—
30C2×C4×C3⋊C8—31no—
31C2×C4×C3⋊D3—42no—
32C2×C4×C3⋊D3—41no—
33C3×#41⋊C3C2×C412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊GL(2,𝔽3)C2×C412yescomplemented
36C3⋊#226C2×C412yescomplemented
37C32×C42—41no—
38C4×C3⋊Dic3—42no—
39C4×C3⋊Dic3—41no—
40C4×#135—91noSylow
41C2×C3×#41C2×D311yescharacteristic
42C2×#235—31no—
43C2×#41⋊C3C2×D313yes—
44#985—312no—
45C2×GL(2,𝔽3)—33no—
46C2×#226—33no—
47C3×C4×Q8C2×D312yes—
48C3×C4×D4—32no—
49C3×#117—31no—
50C2×C3×C42—31no—
51#950—34no—
52#950—34no—
53C2×#216—31no—
54C2×#215—31no—
55C2×#214—31no—
56C2×#213—31no—
57C4×#67—62no—
58#926—31no—
59C22×C3⋊C8—31no—
60C22×C3⋊C8—31no—
61C4×D12—32no—
62#872—61no—
63C42×D3—61no—
64C42×D3—123no—
65C4×Dic6—32no—
66C4×SL(2,𝔽3)C2×D316yes—
67#859—36no—
68#835—32no—
69#832—32no—
70#810—32no—
71#809—32no—
72#808—32no—
73#807—32no—
74C4×C3⋊C8—32no—
75C4×C3⋊C8—32no—
76C22×C3⋊D3—41no—
77C2×C32×C4—41no—
78C2×C32×C4—42no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—42no—
81C4×C3⋊D3—44no—
82C4×C3⋊D3—48no—
83C3×SL(2,𝔽3)C22×C411yescharacteristic
84C2×#135—91no—
85C4×#41—91no—
86C4×#41C3⋊D311yescharacteristic, complemented
87C4×Q16—92no—
88C4×SD16—92no—
89C4×SD16—92no—
90C4×D8—92no—
91#427—91no—
92#416—91no—
93#416—91no—
94C2×C4×C8—91no—
95C3×#41—32no—
96C3×#41C4×D312yescomplemented
97C2×C3×Q8C22×D311yescharacteristic
98C2×C3×D4—31no—
99C22×C3×C4—31no—
100C22×C3×C4—32no—
101C2×#67—61no—
102#235—34no—
103#235—62no—
104C2×D12—31no—
105C2×C4×D3—61no—
106C2×C4×D3—62no—
107C2×C4×D3—126no—
108C2×C4×D3—123no—
109C2×Dic6—31no—
110#41⋊C3C4×D316yescomplemented
111C2×SL(2,𝔽3)C22×D313yes—
112GL(2,𝔽3)—36no—
113#226—36no—
114C3×C4⋊C4—32no—
115C3×C22⋊C4—61no—
116C3×C42—32no—
117C3×C42—31no—
118C3×C42—43no—
119C3×C42S411yescharacteristic
120#217—61no—
121#216—32no—
122#216—32no—
123#215—32no—
124#215—32no—
125#214—34no—
126#213—34no—
127(C2×D3)⋊C4—62no—
128C4⋊Dic3—32no—
129Dic3⋊C4—62no—
130C4×Dic3—62no—
131C4×Dic3—61no—
132C4×Dic3—126no—
133C4×Dic3—123no—
134C2×C3⋊C8—31no—
135C2×C3⋊C8—31no—
136C2×C3⋊C8—34no—
137C2×C3⋊C8—32no—
138C2×C3⋊C8—62no—
139C22×C32—41no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3—44no—
142C32×C4—42no—
143C32×C4—44no—
144C3⋊Dic3—42no—
145C3⋊Dic3—44no—
146C2×#41—91no—
147C2×#41C2×C3⋊D311yescharacteristic
148#135—94no—
149#135—94no—
150C2×Q16—91no—
151C2×SD16—91no—
152C2×SD16—91no—
153C2×D8—91no—
154C22×C8—91no—
155C22×C8—91no—
156C4×Q8—92no—
157C4×Q8C2×C3⋊D312yes—
158C4×D4—32no—
159C4×D4—92no—
160C4×D4—182no—
161#117—31no—
162#117—91no—
163#117—181no—
164C2×C42—31no—
165C2×C42—181no—
166#107—92no—
167#106—92no—
168#103—92no—
169#103—92no—
170#102—92no—
171#102—92no—
172C4×C8—92no—
173C4×C8—92no—
174C23×C3—31no—
175C22×D3—61no—
176C22×D3—123no—
177C3×Q8—31no—
178C3×Q8C2×C4×D311yescharacteristic
179C3×D4—32no—
180C3×D4—61no—
181C2×C3×C4—31no—
182C2×C3×C4—32no—
183C2×C3×C4—32no—
184C2×C3×C4—32no—
185C2×C3×C4—46no—
186C2×C3×C4—43no—
187C2×C3×C4—64no—
188C2×C3×C4C2×S411yescharacteristic
189C2×C3×C4C2×S412yes—
190#67—64no—
191C2×Dic3—61no—
192C2×Dic3—62no—
193C2×Dic3—126no—
194C2×Dic3—123no—
195D12—32no—
196D12—61no—
197C4×D3—64no—
198C4×D3—1212no—
199C4×D3—1224no—
200C4×D3—124no—
201Dic6—32no—
202Dic6—61no—
203SL(2,𝔽3)C2×C4×D313yes—
204C3⋊C8—32no—
205C3⋊C8—32no—
206C3⋊C8—62no—
207C2×C32—41no—
208C2×C32—42no—
209C3⋊D3—44no—
210#41—32no—
211#41—94no—
212#41—182no—
213#41C4×C3⋊D312yescomplemented
214C2×Q8—91no—
215C2×Q8C22×C3⋊D311yescharacteristic
216C2×D4—31no—
217C2×D4—91no—
218C2×D4—181no—
219C22×C4—31no—
220C22×C4—32no—
221C22×C4—181no—
222C22×C4—182no—
223Q16—92no—
224Q16—92no—
225SD16—94no—
226SD16—92no—
227SD16—92no—
228D8—94no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—94no—
232C2×C8—92no—
233C2×C8—182no—
234C4⋊C4—32no—
235C4⋊C4—92no—
236C4⋊C4—182no—
237C22⋊C4—61no—
238C22⋊C4—182no—
239C22⋊C4—181no—
240C42—32no—
241C42—31no—
242C42—181no—
243C42—182no—
244C42C3⋊S411yescharacteristic
245C22×C3—32no—
246C22×C3—43no—
247C22×C3—62no—
248C22×C3C22×S411yescharacteristic
249C2×D3—62no—
250C2×D3—126no—
251C2×D3—1212no—
252C2×D3—122no—
253C3×C4—31no—
254C3×C4—31no—
255C3×C4—46no—
256C3×C4—412no—
257C3×C4—62no—
258C3×C4C4×S412yes—
259C3×C4#98514yescomplemented
260Dic3—62no—
261Dic3—126no—
262Dic3—1212no—
263Dic3—122no—
264C32—41noSylow
265C23—31no—
266C23—181no—
267Q8—31no—
268Q8—92no—
269Q8—181no—
270Q8C2×C4×C3⋊D311yescharacteristic
271D4—32no—
272D4—61no—
273D4—92no—
274D4—181no—
275D4—184no—
276C2×C4—31no—
277C2×C4—32no—
278C2×C4—32no—
279C2×C4—32no—
280C2×C4—64no—
281C2×C4—181no—
282C2×C4—184no—
283C2×C4—182no—
284C2×C4—364no—
285C2×C4C2×C3⋊S411yescharacteristic
286C2×C4C2×C3⋊S412yes—
287C8—92no—
288C8—92no—
289C8—182no—
290C2×C3—43no—
291C2×C3—46no—
292C2×C3—62no—
293C2×C3C2×C4×S411yescharacteristic
294C2×C3C2×#98512yes—
295D3—1212no—
296D3—122no—
297C22—32no—
298C22—62no—
299C22—182no—
300C22—362no—
301C22C22×C3⋊S411yescharacteristic
302C4—31no—
303C4—31no—
304C4—62no—
305C4—182no—
306C4—362no—
307C4C4×C3⋊S412yes—
308C4#6426614yesdirect product factor
309C3—43no—
310C3C4×#98511yescharacteristic, complemented
311C2—62no—
312C2—362no—
313C2C2×C4×C3⋊S411yescharacteristic
314C2C2×#6426612yes—
subgroupG/H
center, hypercenterC42C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C22×C3⋊S4
FittingC3×C4×#41D3
socleC22×C3C22×S4
prime radicalC2×#64266C2
cosocleC2×C3×SL(2,𝔽3)C23
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#41⋊C3C2semidirect
3. #10593658C2semidirect
4. C4×C3⋊GL(2,𝔽3)C2semidirect
5. C4×C3⋊#226C2semidirect
9. #64266C4direct (N × H)
16. C3×C4×#41D3semidirect
19. C4×#41⋊C3D3semidirect
33. C3×#41⋊C3C2×C4semidirect
35. C3⋊GL(2,𝔽3)C2×C4semidirect
36. C3⋊#226C2×C4semidirect
86. C4×#41C3⋊D3semidirect
96. C3×#41C4×D3semidirect
110. #41⋊C3C4×D3semidirect
213. #41C4×C3⋊D3semidirect
259. C3×C4#985semidirect
308. C4#64266direct (N × H)
310. C3C4×#985semidirect

Maximal subgroups

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

subgroupindex
C2×#642662
C3×C4×#41⋊C32
#105936582
C4×C3⋊GL(2,𝔽3)2
C4×C3⋊#2262
C4×#9853
C4×#9503
C42×C3⋊D34