Finite Group Databasebeta

← C2×#5752⋊C3 #11923315

Subgroups — C2×#5752⋊C3 #11923315

Order 1152.

713 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 713 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3⋊#994C212yesmaximal, complemented
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3#5752⋊C3C214yesmaximal, direct product factor
4C2×#5752C311yesmaximal, characteristic, complemented
5C2×#576⋊C3—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3⋊#994—22no—
8C3⋊#994C2214yescomplemented
9C2×C3⋊(#41⋊C3)—22no—
10C2×C3×Dic12—41nomaximal
11C3×#131⋊C3C2212yescomplemented
12C2×#1009C2×C312yes—
13C2×#994—32no—
14C2×C3×#131C2×C311yescharacteristic
15#5752—34no—
16#5752C2×C314yescomplemented
17C2×#908—32no—
18C2×#904—31no—
19C22×D24—31no—
20#576⋊C3—34no—
21C2×#131⋊C3—21no—
22C2×#131⋊C3D311yescharacteristic, complemented
23C2×C3×Dic6—42no—
24C3×#41⋊C3D411yescharacteristic
25C3×#41⋊C3C2311yescharacteristic
26C2×C3×SL(2,𝔽3)D411yescharacteristic
27C3⋊(#41⋊C3)—24no—
28C2×C32×C8—41no—
29C3×Dic12—44no—
30C2×#576—31noSylow
31C2×C3×#41C22×C311yescharacteristic
32#1009—22no—
33#1009—34no—
34#1009—62no—
35#1009C22×C314yes—
36C2×#239—22no—
37C2×D3×D4—62no—
38C2×#235—32no—
39C22×D12—32no—
40#994—34no—
41#994—62no—
42C2×#41⋊C3—21no—
43C2×#41⋊C3—62no—
44C2×#41⋊C3C2×D311yescharacteristic
45C2×C3×Q16—121no—
46C3×#131—32no—
47C3×#131C22×C312yes—
48C2×C3×M16—31no—
49C22×C3×C8—31no—
50#908—38no—
51#908—38no—
52C2×Dic12A411yescharacteristic
53#904—34no—
54#904—34no—
55C2×D24—32no—
56C2×D24—34no—
57C2×D24—31no—
58C2×D24—34no—
59C2×#204—32no—
60#131⋊C3—22no—
61#131⋊C3C2×D312yescomplemented
62C2×C32×C4—41no—
63C2×C3×Dic3—82no—
64C3×Dic6—44no—
65C3×Dic6—82no—
66C3×SL(2,𝔽3)C2×D411yescharacteristic
67C32×C8—42no—
68C2×H(5,𝔽2)—32no—
69#576—34no—
70#576—94no—
71C2×AGL(1,ℤ/8)—92no—
72C2×#135—91no—
73C22×D8—91no—
74C2×#131C3×D311yescharacteristic
75C23×D3—62no—
76C3×#41—31no—
77C3×#41—31no—
78C3×#41C3×D411yescharacteristic
79C3×#41C23×C311yescharacteristic
80C2×C3×Q8—122no—
81C2×C3×Q8C3×D411yescharacteristic
82C2×C3×D4—31no—
83C22×C3×C4—31no—
84C2×#67—62no—
85#239—24no—
86#239—64no—
87D3×D4—68no—
88D3×D4—64no—
89D3×D4—64no—
90#235—34no—
91#235—34no—
92#235—62no—
93#235—62no—
94C2×D12—34no—
95C2×D12—32no—
96C2×D12—34no—
97C2×D12—62no—
98C2×D12—62no—
99C2×D12—62no—
100C2×C4×D3—62no—
101C2×Dic6C2×A412yes—
102#41⋊C3—21no—
103#41⋊C3—21no—
104#41⋊C3—64no—
105#41⋊C3D1211yescharacteristic
106#41⋊C3C22×D311yescharacteristic
107C2×SL(2,𝔽3)—21no—
108C2×SL(2,𝔽3)D1211yescharacteristic
109C3×Q16—124no—
110C3×M16—32no—
111C3×M16—32no—
112C2×C3×C8—31no—
113C2×C3×C8—32no—
114C2×C3×C8—32no—
115C2×C3×C8—41no—
116C2×C3×C8—81no—
117C2×C3×C8C2×A411yescharacteristic
118Dic12C2×A414yes—
119D24—38no—
120D24—34no—
121#204—38no—
122C22×C32—41no—
123C32×C4—41no—
124C32×C4—41no—
125C3×Dic3—84no—
126H(5,𝔽2)—34no—
127H(5,𝔽2)—62no—
128H(5,𝔽2)—94no—
129H(5,𝔽2)—182no—
130C2×#41—62no—
131C2×#41—92no—
132C2×#41C2×C3×D311yescharacteristic
133C22×D4—92no—
134C22×D4—182no—
135AGL(1,ℤ/8)—98no—
136AGL(1,ℤ/8)—98no—
137#135—94no—
138#135—94no—
139C2×Q16—31no—
140C2×SD16—92no—
141C2×D8—92no—
142C2×D8—94no—
143C2×D8—94no—
144C2×D8—91no—
145#131—32no—
146#131C2×C3×D312yes—
147C2×M16—31no—
148C22×C8—31no—
149C23×C3—31no—
150C22×D3—62no—
151C22×D3—64no—
152C22×D3—64no—
153C22×D3—244no—
154C3×Q8—31no—
155C3×Q8—124no—
156C3×Q8—242no—
157C3×Q8C2×C3×D411yescharacteristic
158C3×D4—31no—
159C3×D4—31no—
160C3×D4—32no—
161C2×C3×C4—31no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—41no—
167C2×C3×C4—81no—
168C2×C3×C4—242no—
169C2×C3×C4C22×A411yescharacteristic
170#67—64no—
171#67—64no—
172C2×Dic3—22no—
173D12—34no—
174D12—64no—
175D12—64no—
176D12—62no—
177C4×D3—64no—
178C4×D3—64no—
179Dic6—22no—
180Dic6C22×A414yes—
181SL(2,𝔽3)—21no—
182SL(2,𝔽3)C2×D1211yescharacteristic
183C3×C8—32no—
184C3×C8—42no—
185C3×C8—82no—
186C3×C8C22×A412yes—
187C2×C32—41no—
188C2×C32—42no—
189C24—182no—
190#41—31no—
191#41—31no—
192#41—64no—
193#41—94no—
194#41—94no—
195#41—182no—
196#41—182no—
197#41—184no—
198#41C3×D1211yescharacteristic
199#41C22×C3×D311yescharacteristic
200C2×Q8—32no—
201C2×Q8C3×D1211yescharacteristic
202C2×D4—31no—
203C2×D4—94no—
204C2×D4—94no—
205C2×D4—92no—
206C2×D4—182no—
207C2×D4—182no—
208C2×D4—182no—
209C2×D4—182no—
210C2×D4—188no—
211C2×D4—184no—
212C2×D4—184no—
213C22×C4—31no—
214C22×C4—182no—
215Q16—34no—
216SD16—98no—
217D8—98no—
218D8—94no—
219M16—32no—
220M16—32no—
221C2×C8—31no—
222C2×C8—32no—
223C2×C8—32no—
224C2×C8D3×A411yescharacteristic
225C22×C3—31no—
226C22×C3—31no—
227C22×C3—41no—
228C22×C3—62no—
229C22×C3—81no—
230C22×C3D4×A411yescharacteristic
231C2×D3—64no—
232C2×D3—124no—
233C2×D3—244no—
234C2×D3—244no—
235C3×C4—31no—
236C3×C4—31no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—81no—
240C3×C4—81no—
241C3×C4—244no—
242C3×C4D4×A411yescharacteristic
243C3×C4C23×A411yescharacteristic
244Dic3—24no—
245C32—41noSylow
246C23—31no—
247C23—184no—
248C23—184no—
249C23—182no—
250C23—724no—
251Q8—31no—
252Q8—34no—
253Q8—62no—
254Q8C2×C3×D1211yescharacteristic
255D4—31no—
256D4—31no—
257D4—32no—
258D4—94no—
259D4—184no—
260D4—184no—
261D4—184no—
262D4—184no—
263D4—182no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—62no—
270C2×C4—184no—
271C2×C4—184no—
272C2×C4C2×D3×A411yescharacteristic
273C8—32no—
274C8C2×D3×A412yes—
275C2×C3—41no—
276C2×C3—42no—
277C2×C3—61no—
278C2×C3—61no—
279C2×C3—81no—
280C2×C3—82no—
281C2×C3#576⋊C312yescomplemented
282C2×C3C2×D4×A411yescharacteristic
283D3—124no—
284C22—31no—
285C22—31no—
286C22—62no—
287C22—184no—
288C22—364no—
289C22—724no—
290C22—724no—
291C22A4×D1211yescharacteristic
292C4—31no—
293C4—31no—
294C4—64no—
295C4A4×D1211yescharacteristic
296C4C22×D3×A411yescharacteristic
297C3—41no—
298C3—81no—
299C3C2×#576⋊C311yescharacteristic, complemented
300C2—61no—
301C2—61no—
302C2—364no—
303C2#5752⋊C312yesdirect product factor
304C2C2×A4×D1211yescharacteristic
subgroupG/H
centerC22A4×D12
commutator, cosocleC3×#41C23×C3
FrattiniC4C22×D3×A4
FittingC2×C3×#131C2×C3
socleC22×C3D4×A4
hypercenterC2×C8D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C3×#41 ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#994C2semidirect
2. C2×C3×#131⋊C3C2semidirect
3. #5752⋊C3C2direct (N × H)
4. C2×#5752C3semidirect
8. C3⋊#994C22semidirect
11. C3×#131⋊C3C22semidirect
16. #5752C2×C3semidirect
22. C2×#131⋊C3D3semidirect
61. #131⋊C3C2×D3semidirect
281. C2×C3#576⋊C3semidirect
299. C3C2×#576⋊C3semidirect
303. C2#5752⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3⋊#9942
C2×C3×#131⋊C32
#5752⋊C32
C2×#57523
C2×#576⋊C33
C2×C3×Dic124