Finite Group Databasebeta

← #11920713

Subgroups — #11920713

Order 1152.

320 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 43 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#5819⋊C3C211yesmaximal, characteristic
3#10593657C211yesmaximal, characteristic
4#73130—31nomaximal
5#72102—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#984—21no—
8C3×#984—21no—
9C2×C3×#226C412yescomplemented
10C3⋊(#131⋊C3)—21no—
11C3⋊GU(2,𝔽3)—21no—
12#63560—41nomaximal
13C2×#984D311yescharacteristic
14C2×C3×#137—31no—
15#5819D311yescharacteristic
16#568⋊C3—31no—
17#5423—31no—
18#5423—61no—
19#5236—31no—
20C2×#836—31no—
21#5225—31no—
22C3⋊#338—31no—
23#4556—31no—
24C2×C3×Dic6—41no—
25C3×#41⋊C3D411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
28C3×#226—22no—
29#3748—41no—
30C3×#208—41no—
31#1902—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×C3×Q8—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C2×D311yescharacteristic
36#984—21no—
37#984—21no—
38C2×#226Dic312yescomplemented
39C3×#137—61no—
40C3×#137—61no—
41C3×#137—61no—
42C3×#137—61no—
43C2×C3×Q16—32no—
44C2×C3×SD16—32no—
45C2×C3×M16—31no—
46#948—21no—
47#948—61no—
48#926—31no—
49C2×#208—31no—
50C2×#208—31no—
51C2×#208—31no—
52#131⋊C3—61no—
53GU(2,𝔽3)—62no—
54GU(2,𝔽3)—61no—
55#837—61no—
56#837—61no—
57#836—61no—
58#836—61no—
59#835—62no—
60#824—121no—
61C2×C32×C4—41no—
62C2×C3×Dic3—42no—
63C3×Dic6—81no—
64C3×Dic6—81no—
65C3×SL(2,𝔽3)C22⋊C411yescharacteristic
66C3⋊(C3⋊C8)—81no—
67C3×C3⋊C8—81no—
68C2×#137—31no—
69#568—31no—
70#421—91no—
71#419—91no—
72C2×#101—91no—
73#344—91no—
74#338—91no—
75C3×#41—31no—
76C3×#41—31no—
77C3×#41D1211yescharacteristic
78C3×#41#6711yescharacteristic
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×Q8C4×D311yescharacteristic
86C2×C3×D4—31no—
87C22×C3×C4—31no—
88C22×C3×C4—61no—
89C2×Dic6—41no—
90#41⋊C3—21no—
91#41⋊C3—21no—
92#41⋊C3#6711yescharacteristic
93#41⋊C3#6711yescharacteristic
94C2×SL(2,𝔽3)—21no—
95C2×SL(2,𝔽3)C2×Dic311yescharacteristic
96#226—22no—
97C3×Q16—62no—
98C3×Q16—62no—
99C3×SD16—62no—
100C3×SD16—62no—
101C3×M16—61no—
102C3×M16—61no—
103C3×M16—121no—
104C2×C3×C8—32no—
105#217—61no—
106C4⋊Dic3—61no—
107C4×Dic3—61no—
108#208—31no—
109#208—61no—
110#208—61no—
111#208—61no—
112#208—61no—
113#208—121no—
114#208—241no—
115#208S411yescharacteristic
116C2×C3⋊C8—32no—
117C2×C3⋊C8—61no—
118C2×C3⋊C8—61no—
119C22×C32—41no—
120C32×C4—41no—
121C32×C4—41no—
122C3×Dic3—82no—
123C2×#41D3211yescharacteristic
124C22×Q8—31no—
125#137—61no—
126#137—61no—
127#137—61no—
128#137—61no—
129C2×Q16—32no—
130C2×SD16—32no—
131#131—61no—
132#131—181no—
133C2×M16—31no—
134C2×M16—91no—
135C2×M16—91no—
136C2×M16—91no—
137#117—91no—
138#104—181no—
139#104—181no—
140#103—182no—
141#101—181no—
142#101—181no—
143C23×C3—31no—
144C3×Q8—31no—
145C3×Q8—62no—
146C3×Q8—62no—
147C3×Q8—121no—
148C3×Q8—121no—
149C3×Q8(C2×D3)⋊C411yescharacteristic
150C3×D4—31no—
151C3×D4—31no—
152C3×D4—61no—
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—41no—
159C2×C3×C4—62no—
160C2×C3×C4—81no—
161C2×C3×C4—121no—
162C2×C3×C4—121no—
163C2×C3×C4C2×S411yescharacteristic
164C2×Dic3—42no—
165C2×Dic3—121no—
166Dic6—81no—
167Dic6—81no—
168SL(2,𝔽3)—21no—
169SL(2,𝔽3)#21711yescharacteristic
170C3×C8—62no—
171C3×C8—241no—
172C3⋊C8—21no—
173C3⋊C8—61no—
174C3⋊C8—121no—
175C3⋊C8—241no—
176C3⋊C8—242no—
177C2×C32—41no—
178C2×C32—81no—
179#41—31no—
180#41—31no—
181#41#62511yescharacteristic
182#41#62611yescharacteristic
183C2×Q8—32no—
184C2×Q8—61no—
185C2×Q8—61no—
186C2×Q8—61no—
187C2×Q8—61no—
188C2×Q8—61no—
189C2×Q8D3×Dic311yescharacteristic
190C2×D4—31no—
191C22×C4—31no—
192C22×C4—61no—
193Q16—62no—
194Q16—62no—
195SD16—62no—
196SD16—62no—
197M16—31no—
198M16—61no—
199M16—61no—
200M16—91no—
201M16—181no—
202M16—181no—
203M16—181no—
204M16—181no—
205C2×C8—32no—
206C2×C8—92no—
207C2×C8—181no—
208C2×C8—181no—
209C4⋊C4—181no—
210C22⋊C4—181no—
211C42—181no—
212C22×C3—31no—
213C22×C3—31no—
214C22×C3—41no—
215C22×C3—81no—
216C22×C3—121no—
217C22×C3C4×S411yescharacteristic
218C3×C4—31no—
219C3×C4—31no—
220C3×C4—41no—
221C3×C4—41no—
222C3×C4—81no—
223C3×C4—81no—
224C3×C4—122no—
225C3×C4C4⋊S411yescharacteristic
226C3×C4GL(2,ℤ/4)11yescharacteristic
227Dic3—82no—
228Dic3—241no—
229C32—41noSylow
230C23—31no—
231Q8—31no—
232Q8—62no—
233Q8—62no—
234Q8—121no—
235Q8—121no—
236Q8(C2×D3)⋊Dic311yescharacteristic
237D4—31no—
238D4—31no—
239D4—61no—
240C2×C4—31no—
241C2×C4—31no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—31no—
245C2×C4—62no—
246C2×C4—121no—
247C2×C4—121no—
248C2×C4—361no—
249C2×C4D3×S411yescharacteristic
250C8—62no—
251C8—61no—
252C8—181no—
253C8—361no—
254C2×C3—21no—
255C2×C3—41no—
256C2×C3—61no—
257C2×C3—61no—
258C2×C3—81no—
259C2×C3—81no—
260C2×C3—161no—
261C2×C3(C2×S4)⋊C411yescharacteristic
262C22—31no—
263C22—31no—
264C22—121no—
265C22Dic3×S411yescharacteristic
266C4—31no—
267C4—31no—
268C4—122no—
269C4—721no—
270C4#6420711yescharacteristic
271C4#6420911yescharacteristic
272C3—41no—
273C3—81no—
274C3#7313011yescharacteristic, complemented
275C2—21no—
276C2—61no—
277C2—61no—
278C2(C2×S4)⋊Dic311yescharacteristic
subgroupG/H
centerC2(C2×S4)⋊Dic3
commutatorC2×C3×SL(2,𝔽3)C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC2×C3(C2×S4)⋊C4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
9. C2×C3×#226C4semidirect
38. C2×#226Dic3semidirect
274. C3#73130semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9842
#5819⋊C32
#105936572
#731303
#721023
#635604