Finite Group Databasebeta

← #11920702

Subgroups — #11920702

Order 1152.

271 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 271 conjugacy classes of subgroups — too many to draw. Only its 49 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⋊(#131⋊C3)C211yesmaximal, characteristic
2#10593660C211yesmaximal, characteristic
3C3×#5426C211yesmaximal, characteristic
4#73125—31nomaximal
5#70299—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3⋊(#131⋊C3)C412yescomplemented
8C3⋊#859—21no—
9C3×#859—21no—
10#63573—41nomaximal
11C2×#948D311yescharacteristic
12C2×#131⋊C3—31no—
13#5426—31no—
14#5426—61no—
15#5426D311yescharacteristic
16C3×#417—31no—
17#5232—31no—
18C2×#822—31no—
19C2×#808—31no—
20#4554—31no—
21#4530—31no—
22C3×#41⋊C3C2×C411yescharacteristic
23C3×#41⋊C3Q811yescharacteristic
24C2×C3×SL(2,𝔽3)D411yescharacteristic
25C4⋊(C3⋊Dic3)—41no—
26C3×C4⋊Dic3—41no—
27C2×C3×C3⋊C8—41no—
28#1815—91noSylow
29C2×C3×#41C2×D311yescharacteristic
30C2×#41⋊C3—21no—
31C2×#41⋊C3C2×D311yescharacteristic
32C2×C3×M16—31no—
33C2×C3×C4⋊C4—31no—
34#948—32no—
35#948Dic312yescomplemented
36C2×C4⋊Dic3—31no—
37C2×#208—31no—
38C2×#208—31no—
39C22×C3⋊C8—31no—
40#131⋊C3—32no—
41#859—21no—
42#859—62no—
43#859—61no—
44C3×#103—61no—
45C3×#102—61no—
46#835—61no—
47#832—61no—
48#822—62no—
49#817—121no—
50#808—61no—
51#808—61no—
52C2×C32×C4—41no—
53C2×C3⋊Dic3—81no—
54C2×C3×Dic3—81no—
55C3×SL(2,𝔽3)C4⋊C411yescharacteristic
56C3×C3⋊C8—42no—
57C2×#131—31no—
58C2×#108—91no—
59C2×#106—91no—
60#417—31no—
61#417—91no—
62#343—91no—
63#343—91no—
64C3×#41—31no—
65C3×#41—31no—
66C3×#41Dic611yescharacteristic
67C3×#41C2×Dic311yescharacteristic
68C2×C3×Q8D1211yescharacteristic
69C2×C3×D4—31no—
70C22×C3×C4—31no—
71C22×C3×C4—61no—
72C22×Dic3—61no—
73#41⋊C3—21no—
74#41⋊C3—21no—
75#41⋊C3Dic611yescharacteristic
76#41⋊C3C4×D311yescharacteristic
77C2×SL(2,𝔽3)—21no—
78C2×SL(2,𝔽3)#6711yescharacteristic
79C3×M16—61no—
80C3×M16—61no—
81C2×C3×C8—61no—
82C2×C3×C8—121no—
83C3×C4⋊C4—61no—
84C3×C4⋊C4—61no—
85C4⋊Dic3—41no—
86C4⋊Dic3—61no—
87C4⋊Dic3—61no—
88C4⋊Dic3—121no—
89C4⋊Dic3—241no—
90#208—32no—
91#208—61no—
92#208—61no—
93#208—61no—
94C2×C3⋊C8—31no—
95C2×C3⋊C8—32no—
96C2×C3⋊C8—32no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8S411yescharacteristic
99C22×C32—41no—
100C32×C4—41no—
101C32×C4—41no—
102C3⋊Dic3—161no—
103C3×Dic3—161no—
104C2×#41D3211yescharacteristic
105#131—32no—
106#131—92no—
107C2×M16—31no—
108C2×M16—91no—
109C2×M16—91no—
110C22×C8—91no—
111C2×C4⋊C4—31no—
112C2×C4⋊C4—91no—
113#108—182no—
114#106—181no—
115#106—181no—
116#103—61no—
117#103—181no—
118#102—61no—
119#102—181no—
120C23×C3—31no—
121C3×Q8—31no—
122C3×Q8C4⋊Dic311yescharacteristic
123C3×D4—31no—
124C3×D4—31no—
125C3×D4—61no—
126C2×C3×C4—31no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—31no—
131C2×C3×C4—41no—
132C2×C3×C4—81no—
133C2×C3×C4—121no—
134C2×C3×C4—241no—
135C2×C3×C4C2×S411yescharacteristic
136C2×Dic3—81no—
137C2×Dic3—121no—
138C2×Dic3—241no—
139C2×Dic3—242no—
140C2×Dic3—241no—
141SL(2,𝔽3)—21no—
142SL(2,𝔽3)Dic3⋊C411yescharacteristic
143C3×C8—122no—
144C3×C8—121no—
145C3⋊C8—32no—
146C3⋊C8—121no—
147C3⋊C8SL(2,ℤ/4)12yes—
148C2×C32—41no—
149C2×C32—41no—
150C2×C32—41no—
151#41—31no—
152#41—31no—
153#41D3×Dic311yescharacteristic
154#41#62711yescharacteristic
155C2×Q8#62611yescharacteristic
156C2×D4—31no—
157C22×C4—31no—
158C22×C4—61no—
159C22×C4—181no—
160M16—61no—
161M16—61no—
162M16—92no—
163M16—181no—
164M16—181no—
165M16—181no—
166C2×C8—31no—
167C2×C8—61no—
168C2×C8—92no—
169C2×C8—92no—
170C2×C8—91no—
171C2×C8—181no—
172C4⋊C4—61no—
173C4⋊C4—61no—
174C4⋊C4—181no—
175C4⋊C4—181no—
176C22×C3—31no—
177C22×C3—31no—
178C22×C3—41no—
179C22×C3—61no—
180C22×C3—61no—
181C22×C3—81no—
182C22×C3C4⋊S411yescharacteristic
183C3×C4—31no—
184C3×C4—31no—
185C3×C4—41no—
186C3×C4—41no—
187C3×C4—81no—
188C3×C4—81no—
189C3×C4—241no—
190C3×C4A4⋊Q811yescharacteristic
191C3×C4C2×SL(2,ℤ/4)11yescharacteristic
192Dic3—161no—
193Dic3—241no—
194Dic3—481no—
195Dic3—482no—
196C32—41noSylow
197C23—31no—
198Q8—31no—
199Q8Dic3⋊Dic311yescharacteristic
200D4—31no—
201D4—31no—
202D4—61no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—121no—
209C2×C4—241no—
210C2×C4—361no—
211C2×C4—721no—
212C2×C4D3×S411yescharacteristic
213C8—32no—
214C8—92no—
215C8—121no—
216C8—361no—
217C2×C3—41no—
218C2×C3—41no—
219C2×C3—41no—
220C2×C3—61no—
221C2×C3—61no—
222C2×C3—81no—
223C2×C3—81no—
224C2×C3—81no—
225C2×C3#540611yescharacteristic
226C2×C3#540611yescharacteristic
227C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
228C22—31no—
229C22—31no—
230C22—61no—
231C22—61no—
232C22#6420711yescharacteristic
233C4—31no—
234C4—31no—
235C4—241no—
236C4—721no—
237C4#6420411yescharacteristic
238C4D3×SL(2,ℤ/4)11yescharacteristic
239C3—41no—
240C3—81no—
241C3#7312511yescharacteristic, complemented
242C2—61no—
243C2—61no—
244C2#1059322311yescharacteristic
245C2#1059322411yescharacteristic
246C2Dic3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC22#64207
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C4⋊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
7. C3⋊(#131⋊C3)C4semidirect
35. #948Dic3semidirect
241. C3#73125semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(#131⋊C3)2
#105936602
C3×#54262
#731253
#702993
#635734