Finite Group Databasebeta

← C4×#64267 #11922891

Subgroups — C4×#64267 #11922891

Order 1152.

756 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 93 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×#64267C211yesmaximal, characteristic
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3#10593660C211yesmaximal, characteristic, complemented
4#10593628C212yesmaximal, complemented
5C4×C3⋊GL(2,𝔽3)C212yesmaximal, complemented
6C4×#986—33nomaximal
7C4×#949—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64267C414yesdirect product factor
10C2×C3⋊GL(2,𝔽3)C2212yes—
11C4×C4⋊(C3⋊D3)—41nomaximal
12C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
13C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
14C3⋊#859C2212yescomplemented
15C2×#986—33no—
16C3×C4×#41D311yescharacteristic, complemented
17C2×#949—31no—
18C2×C4×D12—31no—
19C4×#41⋊C3D313yescomplemented
20#5426—33no—
21#5394—36no—
22C4×GL(2,𝔽3)—36no—
23#5232—31no—
24#5026—32no—
25C4×#215—32no—
26#5014—32no—
27C4×#213—32no—
28#5001—31no—
29#4995—31no—
30C4×#208—31no—
31C2×C4⋊(C3⋊D3)—41no—
32C2×C4×C3⋊D3—42no—
33C3×#41⋊C3C2×C412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊GL(2,𝔽3)C2×C414yescomplemented
36C32×C42—41no—
37#3752—42no—
38C4⋊(C3⋊Dic3)—41no—
39C4×AGL(1,ℤ/8)—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×D12—31no—
42C22×C4×D3—61no—
43C2×#41⋊C3C2×D313yes—
44#986—312no—
45C2×GL(2,𝔽3)—36no—
46C3×C4×Q8C2×D311yescharacteristic
47C3×C4×Q8C2×D311yescharacteristic
48C3×C4×D4—31no—
49C3×C4×D4—31no—
50C3×#117—31no—
51C2×C3×C42—31no—
52#949—34no—
53#949—34no—
54C2×#215—32no—
55C2×#213—32no—
56C2×(C2×D3)⋊C4—61no—
57C2×C4⋊Dic3—31no—
58C2×#208—31no—
59C2×#208—31no—
60C4×D12—32no—
61C4×D12—32no—
62C4×D12—61no—
63C4×D12—61no—
64C4×D12—123no—
65C4×SL(2,𝔽3)C2×D313yescomplemented
66C4×SL(2,𝔽3)C2×D313yescomplemented
67#859—36no—
68#835—32no—
69#832—32no—
70#809—32no—
71#809—32no—
72#808—32no—
73#807—32no—
74#803—32no—
75C4×C3⋊C8—32no—
76C22×C3⋊D3—42no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C3⋊Dic3—42no—
81C4⋊(C3⋊D3)—44no—
82C4×C3⋊D3—84no—
83C3×SL(2,𝔽3)C22×C411yescharacteristic, complemented
84C2×AGL(1,ℤ/8)—91no—
85C4×#41C3⋊D311yescharacteristic, complemented
86C2×C4×D4—91no—
87#442—92no—
88#440—92no—
89C4×SD16—92no—
90C4×D8—92no—
91#428—91no—
92#418—91no—
93#417—91no—
94C4×M16—91no—
95C23×D3—61no—
96C3×#41—32no—
97C3×#41C4×D312yescomplemented
98C2×C3×Q8C22×D311yescharacteristic
99C2×C3×D4—31no—
100C22×C3×C4—31no—
101C22×C3×C4—31no—
102C22×C3×C4—31no—
103C22×Dic3—61no—
104C2×D12—32no—
105C2×D12—34no—
106C2×D12—62no—
107C2×D12—61no—
108C2×D12—123no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—126no—
112C2×C4×D3—124no—
113#41⋊C3C4×D316yescomplemented
114C2×SL(2,𝔽3)C22×D313yes—
115GL(2,𝔽3)—312no—
116C3×C4⋊C4—31no—
117C3×C4⋊C4—31no—
118C3×C22⋊C4—61no—
119C3×C42—31no—
120C3×C42—31no—
121C3×C42—31no—
122C3×C42—43no—
123C3×C42S411yescharacteristic
124#215—34no—
125#215—34no—
126#213—38no—
127(C2×D3)⋊C4—62no—
128(C2×D3)⋊C4—62no—
129(C2×D3)⋊C4—126no—
130C4⋊Dic3—32no—
131C4⋊Dic3—61no—
132C4⋊Dic3—123no—
133#208—34no—
134#208—62no—
135C2×C3⋊C8—32no—
136C2×C3⋊C8—32no—
137C22×C32—41no—
138C2×C3⋊D3—44no—
139C2×C3⋊D3—82no—
140C2×C3⋊D3—82no—
141C32×C4—42no—
142C32×C4—42no—
143C32×C4—81no—
144C3⋊Dic3—82no—
145C2×#41C2×C3⋊D311yescharacteristic
146C22×D4—91no—
147C23×C4—181no—
148AGL(1,ℤ/8)—94no—
149AGL(1,ℤ/8)—94no—
150C2×SD16—92no—
151C2×D8—92no—
152C2×M16—91no—
153C2×M16—91no—
154C4×Q8C2×C3⋊D311yescharacteristic
155C4×Q8C2×C3⋊D311yescharacteristic
156C4×D4—31no—
157C4×D4—31no—
158C4×D4—92no—
159C4×D4—92no—
160C4×D4—181no—
161C4×D4—181no—
162#117—31no—
163C2×C4⋊C4—91no—
164C2×C22⋊C4—181no—
165C2×C42—31no—
166#107—92no—
167#106—92no—
168#103—92no—
169#102—92no—
170#102—92no—
171#102—92no—
172#97—92no—
173C4×C8—92no—
174C23×C3—31no—
175C22×D3—64no—
176C22×D3—62no—
177C22×D3—126no—
178C22×D3—122no—
179C22×D3—122no—
180C3×Q8—31no—
181C3×Q8C2×C4×D311yescharacteristic
182C3×D4—32no—
183C3×D4—61no—
184C2×C3×C4—31no—
185C2×C3×C4—32no—
186C2×C3×C4—32no—
187C2×C3×C4—31no—
188C2×C3×C4—31no—
189C2×C3×C4—43no—
190C2×C3×C4—43no—
191C2×C3×C4—43no—
192C2×C3×C4—62no—
193C2×C3×C4—121no—
194C2×C3×C4C2×S411yescharacteristic
195C2×C3×C4C2×S411yescharacteristic
196C2×C3×C4C2×S411yescharacteristic
197C2×Dic3—62no—
198C2×Dic3—126no—
199C2×Dic3—122no—
200D12—34no—
201D12—62no—
202D12—64no—
203D12—1212no—
204C4×D3—124no—
205C4×D3—124no—
206C4×D3—2412no—
207SL(2,𝔽3)C2×C4×D313yescomplemented
208C3⋊C8—34no—
209C3⋊C8—62no—
210C2×C32—41no—
211C2×C32—41no—
212C2×C32—41no—
213C3⋊D3—84no—
214C24—181no—
215#41—32no—
216#41C4×C3⋊D312yescomplemented
217C2×Q8C22×C3⋊D311yescharacteristic
218C2×D4—31no—
219C2×D4—92no—
220C2×D4—94no—
221C2×D4—182no—
222C2×D4—181no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—182no—
227C22×C4—181no—
228C22×C4—182no—
229C22×C4—364no—
230SD16—94no—
231SD16—94no—
232D8—98no—
233M16—94no—
234M16—182no—
235C2×C8—92no—
236C2×C8—92no—
237C4⋊C4—31no—
238C4⋊C4—31no—
239C4⋊C4—92no—
240C4⋊C4—181no—
241C22⋊C4—61no—
242C22⋊C4—182no—
243C22⋊C4—182no—
244C42—31no—
245C42—31no—
246C42—31no—
247C42C3⋊S411yescharacteristic
248C22×C3—32no—
249C22×C3—43no—
250C22×C3—61no—
251C22×C3—61no—
252C22×C3C22×S411yescharacteristic
253C2×D3—64no—
254C2×D3—1212no—
255C2×D3—128no—
256C2×D3—122no—
257C2×D3—122no—
258C2×D3—246no—
259C2×D3—246no—
260C3×C4—21no—
261C3×C4—31no—
262C3×C4—31no—
263C3×C4—46no—
264C3×C4—46no—
265C3×C4—61no—
266C3×C4—61no—
267C3×C4—83no—
268C3×C4C4×S412yes—
269C3×C4#98612yescomplemented
270Dic3—122no—
271Dic3—246no—
272C32—41noSylow
273C23—31no—
274C23—184no—
275C23—182no—
276C23—362no—
277C23—362no—
278Q8—31no—
279Q8C2×C4×C3⋊D311yescharacteristic
280D4—32no—
281D4—61no—
282D4—94no—
283D4—182no—
284D4—184no—
285C2×C4—31no—
286C2×C4—32no—
287C2×C4—32no—
288C2×C4—31no—
289C2×C4—31no—
290C2×C4—62no—
291C2×C4—121no—
292C2×C4—182no—
293C2×C4—364no—
294C2×C4—362no—
295C2×C4—364no—
296C2×C4C2×C3⋊S411yescharacteristic
297C2×C4C2×C3⋊S411yescharacteristic
298C2×C4C2×C3⋊S411yescharacteristic
299C8—94no—
300C8—182no—
301C2×C3—43no—
302C2×C3—43no—
303C2×C3—43no—
304C2×C3—62no—
305C2×C3C2×C4×S411yescharacteristic
306C2×C3C2×#98611yescharacteristic
307C2×C3#592311yescharacteristic
308D3—124no—
309D3—2412no—
310C22—32no—
311C22—61no—
312C22—61no—
313C22—184no—
314C22—368no—
315C22—362no—
316C22—362no—
317C22C22×C3⋊S411yescharacteristic
318C4—21no—
319C4—31no—
320C4—31no—
321C4—61no—
322C4—61no—
323C4—362no—
324C4C4×C3⋊S412yes—
325C4#6426712yesdirect product factor
326C3—43no—
327C3C4×#98611yescharacteristic, complemented
328C2—62no—
329C2—364no—
330C2C2×C4×C3⋊S411yescharacteristic
331C2C2×#6426711yescharacteristic
332C2#1059658611yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C22×C3⋊S4
FittingC3×C4×#41D3
socleC22×C3C22×S4
prime radicalC2×#64267C2
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC42C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#41⋊C3C2semidirect
3. #10593660C2semidirect
4. #10593628C2semidirect
5. C4×C3⋊GL(2,𝔽3)C2semidirect
9. #64267C4direct (N × H)
12. C3×C4×SL(2,𝔽3)C22semidirect
13. C3×C4×SL(2,𝔽3)C22semidirect
14. C3⋊#859C22semidirect
16. C3×C4×#41D3semidirect
19. C4×#41⋊C3D3semidirect
33. C3×#41⋊C3C2×C4semidirect
35. C3⋊GL(2,𝔽3)C2×C4semidirect
65. C4×SL(2,𝔽3)C2×D3semidirect
66. C4×SL(2,𝔽3)C2×D3semidirect
83. C3×SL(2,𝔽3)C22×C4semidirect
85. C4×#41C3⋊D3semidirect
97. C3×#41C4×D3semidirect
113. #41⋊C3C4×D3semidirect
207. SL(2,𝔽3)C2×C4×D3semidirect
216. #41C4×C3⋊D3semidirect
269. C3×C4#986semidirect
325. C4#64267direct (N × H)
327. C3C4×#986semidirect

Maximal subgroups

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

subgroupindex
C2×#642672
C3×C4×#41⋊C32
#105936602
#105936282
C4×C3⋊GL(2,𝔽3)2
C4×#9863
C4×#9493
C4×C4⋊(C3⋊D3)4