Finite Group Databasebeta

← #11920692

Subgroups — #11920692

Order 1152.

345 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 47 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×#984C211yesmaximal, characteristic
2#5827⋊C3C211yesmaximal, characteristic
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic
4#73077—31nomaximal
5#72100—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#984—21no—
8C3×#984C412yescomplemented
9C2×C3×#226—21no—
10Dic3×SL(2,𝔽3)—21no—
11C3⋊GU(2,𝔽3)—21no—
12#63565—41nomaximal
13C2×#984D311yescharacteristic
14C2×C3×#137—31no—
15#5827D311yescharacteristic
16#520⋊C3—31no—
17C2×GU(2,𝔽3)—31no—
18C2×GU(2,𝔽3)—61no—
19C2×#837—31no—
20#5229—31no—
21#5225—31no—
22#4555—31no—
23#4554—31no—
24C2×C3×Dic6—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3×#226—22no—
29C2×C3⋊(C3⋊C8)—41no—
30C3×C4⋊Dic3—41no—
31#1882—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×C3×Q8—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C2×D311yescharacteristic
36#984—21no—
37#984Dic312yescomplemented
38C2×#226—21no—
39C3×#137—32no—
40C3×#137—32no—
41C3×#137—61no—
42C3×#137—61no—
43C2×C3×Q16—61no—
44C2×C3×SD16—61no—
45C2×C3×M16—31no—
46Q8×Dic3—21no—
47D4×Dic3—61no—
48#926—31no—
49C2×C4⋊Dic3—31no—
50C2×C4×Dic3—31no—
51C2×#208—31no—
52C4×SL(2,𝔽3)—61no—
53GU(2,𝔽3)—62no—
54GU(2,𝔽3)—61no—
55#837—61no—
56#837—61no—
57#835—61no—
58#835—61no—
59C3⋊#95—62no—
60#810—121no—
61C2×C32×C4—41no—
62C2×C3×Dic3—81no—
63C2×C3×Dic3—81no—
64C3×Dic6—42no—
65C3×Dic6—81no—
66C3×SL(2,𝔽3)C22⋊C411yescharacteristic
67C3⋊(C3⋊C8)—81no—
68C2×#137—31no—
69#520—31no—
70C2×#104—91no—
71#419—91no—
72#391—91no—
73#343—91no—
74#339—91no—
75C3×#41—31no—
76C3×#41—31no—
77C3×#41C4×D311yescharacteristic
78C3×#41D1211yescharacteristic
79C2×C3×Q8—32no—
80C2×C3×Q8—61no—
81C2×C3×Q8—61no—
82C2×C3×Q8—61no—
83C2×C3×Q8—61no—
84C2×C3×Q8—61no—
85C2×C3×Q8#6711yescharacteristic
86C2×C3×D4—31no—
87C22×C3×C4—31no—
88C22×C3×C4—61no—
89C22×Dic3—32no—
90C22×Dic3—61no—
91C2×Dic6—41no—
92#41⋊C3—21no—
93#41⋊C3—21no—
94#41⋊C3C2×Dic311yescharacteristic
95#41⋊C3#6711yescharacteristic
96C2×SL(2,𝔽3)—21no—
97C2×SL(2,𝔽3)#6711yescharacteristic
98#226—22no—
99C3×Q16—62no—
100C3×Q16—62no—
101C3×SD16—62no—
102C3×SD16—62no—
103C3×M16—32no—
104C3×M16—61no—
105C2×C3×C8—61no—
106C3×C4⋊C4—121no—
107#217—61no—
108C4⋊Dic3—31no—
109C4⋊Dic3—61no—
110C4⋊Dic3S411yescharacteristic
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114#208—61no—
115#208—61no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—121no—
118C2×C3⋊C8—241no—
119C22×C32—41no—
120C32×C4—41no—
121C32×C4—41no—
122C3×Dic3—82no—
123C3×Dic3—161no—
124C2×#41D3211yescharacteristic
125C22×Q8—31no—
126#137—32no—
127#137—32no—
128#137—61no—
129#137—61no—
130C2×Q16—61no—
131C2×SD16—61no—
132C2×M16—31no—
133C2×M16—91no—
134C4×Q8—61no—
135C4×D4—181no—
136#117—91no—
137C2×C4⋊C4—91no—
138C2×C42—91no—
139#104—181no—
140#104—181no—
141#103—181no—
142#103—181no—
143#95—182no—
144C23×C3—31no—
145C3×Q8—31no—
146C3×Q8—62no—
147C3×Q8—62no—
148C3×Q8—121no—
149C3×Q8—121no—
150C3×Q8(C2×D3)⋊C411yescharacteristic
151C3×D4—31no—
152C3×D4—31no—
153C3×D4—61no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—31no—
159C2×C3×C4—41no—
160C2×C3×C4—62no—
161C2×C3×C4—81no—
162C2×C3×C4—121no—
163C2×C3×C4—121no—
164C2×C3×C4—241no—
165C2×C3×C4C2×S411yescharacteristic
166C2×Dic3—21no—
167C2×Dic3—62no—
168C2×Dic3—61no—
169C2×Dic3—81no—
170C2×Dic3—121no—
171C2×Dic3—121no—
172C2×Dic3—122no—
173Dic6—42no—
174Dic6—81no—
175SL(2,𝔽3)—21no—
176SL(2,𝔽3)#21711yescharacteristic
177C3×C8—62no—
178C3⋊C8—121no—
179C3⋊C8—241no—
180C3⋊C8—242no—
181C2×C32—41no—
182C2×C32—41no—
183C2×C32—41no—
184#41—31no—
185#41—31no—
186#41D3×Dic311yescharacteristic
187#41#62611yescharacteristic
188C2×Q8—32no—
189C2×Q8—61no—
190C2×Q8—61no—
191C2×Q8—61no—
192C2×Q8—61no—
193C2×Q8—61no—
194C2×Q8#62511yescharacteristic
195C2×D4—31no—
196C22×C4—31no—
197C22×C4—61no—
198C22×C4—92no—
199C22×C4—181no—
200Q16—62no—
201Q16—62no—
202SD16—62no—
203SD16—62no—
204M16—32no—
205M16—61no—
206M16—181no—
207M16—181no—
208C2×C8—61no—
209C2×C8—181no—
210C4⋊C4—31no—
211C4⋊C4—91no—
212C4⋊C4—181no—
213C22⋊C4—181no—
214C42—181no—
215C42—181no—
216C42—181no—
217C22×C3—31no—
218C22×C3—31no—
219C22×C3—41no—
220C22×C3—61no—
221C22×C3—61no—
222C22×C3—81no—
223C22×C3GL(2,ℤ/4)11yescharacteristic
224C3×C4—31no—
225C3×C4—31no—
226C3×C4—41no—
227C3×C4—41no—
228C3×C4—81no—
229C3×C4—81no—
230C3×C4—122no—
231C3×C4—481no—
232C3×C4C4×S411yescharacteristic
233C3×C4C4⋊S411yescharacteristic
234Dic3—41no—
235Dic3—82no—
236Dic3—122no—
237Dic3—121no—
238C32—41noSylow
239C23—31no—
240Q8—31no—
241Q8—62no—
242Q8—62no—
243Q8—121no—
244Q8—121no—
245Q8(C2×D3)⋊Dic311yescharacteristic
246D4—31no—
247D4—31no—
248D4—61no—
249C2×C4—31no—
250C2×C4—31no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—62no—
255C2×C4—61no—
256C2×C4—121no—
257C2×C4—121no—
258C2×C4—182no—
259C2×C4—181no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—362no—
263C2×C4D3×S411yescharacteristic
264C8—62no—
265C8—361no—
266C2×C3—41no—
267C2×C3—41no—
268C2×C3—41no—
269C2×C3—61no—
270C2×C3—61no—
271C2×C3—81no—
272C2×C3—81no—
273C2×C3—81no—
274C2×C3(C2×S4)⋊C411yescharacteristic
275C2×C3#542811yescharacteristic
276C2×C3#543011yescharacteristic
277C22—31no—
278C22—31no—
279C22—61no—
280C22—61no—
281C22#6420911yescharacteristic
282C4—31no—
283C4—31no—
284C4—121no—
285C4—122no—
286C4—362no—
287C4—361no—
288C4Dic3×S411yescharacteristic
289C4#6420711yescharacteristic
290C3—41no—
291C3—81no—
292C3#7307711yescharacteristic, complemented
293C2—61no—
294C2—61no—
295C2#1059323111yescharacteristic
296C2#1059323511yescharacteristic
297C2(C2×S4)⋊Dic311yescharacteristic
subgroupG/H
centerC22#64209
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3GL(2,ℤ/4)
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. C3×#984C4semidirect
37. #984Dic3semidirect
292. C3#73077semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9842
#5827⋊C32
C2×C3⋊GU(2,𝔽3)2
#730773
#721003
#635654