Finite Group Databasebeta

← #11920704

Subgroups — #11920704

Order 1152.

254 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593657C211yesmaximal, characteristic
3C3×#5423C211yesmaximal, characteristic
4#73120—31nomaximal
5#70396—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3⋊(#131⋊C3)C411yescharacteristic, complemented
8C3⋊(#131⋊C3)C411yescharacteristic, complemented
9C3⋊GU(2,𝔽3)—21no—
10C3×GU(2,𝔽3)—21no—
11#63577—41nomaximal
12C2×#948D311yescharacteristic
13C2×#131⋊C3—31no—
14#5423—31no—
15#5423—61no—
16#5423D311yescharacteristic
17C3×#421—31no—
18#5236—31no—
19C2×#822—31no—
20#4998—31no—
21#4556—31no—
22#4533—31no—
23C3×#41⋊C3C2×C411yescharacteristic
24C3×#41⋊C3D411yescharacteristic
25C2×C3×SL(2,𝔽3)Q811yescharacteristic
26#3748—41no—
27C3×#208—41no—
28C2×C3×C3⋊C8—41no—
29#1814—91noSylow
30C2×C3×#41C2×D311yescharacteristic
31C2×#41⋊C3—21no—
32C2×#41⋊C3C2×D311yescharacteristic
33C2×C3×M16—31no—
34C3×#117—31no—
35#948—31no—
36#948—31no—
37#948Dic311yescharacteristic
38#948Dic311yescharacteristic
39#926—31no—
40C2×#208—31no—
41C2×#208—31no—
42C22×C3⋊C8—31no—
43#131⋊C3—31no—
44#131⋊C3—31no—
45GU(2,𝔽3)—21no—
46GU(2,𝔽3)—62no—
47GU(2,𝔽3)—61no—
48C3×#104—61no—
49C3×#104—61no—
50#837—61no—
51#837—61no—
52#822—61no—
53#822—61no—
54#819—121no—
55#808—61no—
56#807—61no—
57C2×C32×C4—41no—
58C3×SL(2,𝔽3)C4⋊C411yescharacteristic
59C3⋊(C3⋊C8)—81no—
60C3×C3⋊C8—41no—
61C3×C3⋊C8—41no—
62C3×C3⋊C8—81no—
63C2×#131—31no—
64C2×#108—91no—
65#427—91no—
66#421—31no—
67#421—91no—
68#344—91no—
69#344—91no—
70C3×#41—31no—
71C3×#41—31no—
72C3×#41D1211yescharacteristic
73C3×#41C2×Dic311yescharacteristic
74C2×C3×Q8Dic611yescharacteristic
75C2×C3×D4—31no—
76C22×C3×C4—31no—
77#41⋊C3—21no—
78#41⋊C3—21no—
79#41⋊C3C4×D311yescharacteristic
80#41⋊C3#6711yescharacteristic
81C2×SL(2,𝔽3)—21no—
82C2×SL(2,𝔽3)Dic611yescharacteristic
83C3×M16—61no—
84C3×M16—61no—
85C2×C3×C8—61no—
86C2×C3×C8—121no—
87C3×C4⋊C4—61no—
88C3×C22⋊C4—61no—
89C3×C42—61no—
90#217—61no—
91C4⋊Dic3—61no—
92C4×Dic3—61no—
93#208—31no—
94#208—31no—
95#208—41no—
96#208—61no—
97#208—61no—
98#208—61no—
99#208—121no—
100#208—241no—
101C2×C3⋊C8—31no—
102C2×C3⋊C8—31no—
103C2×C3⋊C8—31no—
104C2×C3⋊C8—31no—
105C2×C3⋊C8—31no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8S411yescharacteristic
108C22×C32—41no—
109C32×C4—41no—
110C32×C4—41no—
111C2×#41D3211yescharacteristic
112#131—31no—
113#131—31no—
114#131—91no—
115#131—91no—
116C2×M16—31no—
117C2×M16—91no—
118C2×M16—91no—
119C22×C8—91no—
120#117—31no—
121#117—91no—
122#108—181no—
123#108—181no—
124#107—181no—
125#106—181no—
126#104—61no—
127#104—61no—
128#104—181no—
129#104—181no—
130C23×C3—31no—
131C3×Q8—31no—
132C3×Q8C4⋊Dic311yescharacteristic
133C3×D4—31no—
134C3×D4—31no—
135C3×D4—61no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—41no—
142C2×C3×C4—81no—
143C2×C3×C4—121no—
144C2×C3×C4C2×S411yescharacteristic
145C2×Dic3—121no—
146SL(2,𝔽3)—21no—
147SL(2,𝔽3)Dic3⋊C411yescharacteristic
148C3×C8—121no—
149C3×C8—121no—
150C3×C8—121no—
151C3⋊C8—31no—
152C3⋊C8—31no—
153C3⋊C8—81no—
154C3⋊C8—121no—
155C3⋊C8—241no—
156C3⋊C8—242no—
157C3⋊C8SL(2,ℤ/4)11yescharacteristic
158C3⋊C8SL(2,ℤ/4)11yescharacteristic
159C2×C32—41no—
160C2×C32—81no—
161#41—31no—
162#41—31no—
163#41D3×Dic311yescharacteristic
164#41#62611yescharacteristic
165C2×Q8#62711yescharacteristic
166C2×D4—31no—
167C22×C4—31no—
168M16—61no—
169M16—61no—
170M16—91no—
171M16—91no—
172M16—181no—
173M16—181no—
174M16—181no—
175C2×C8—31no—
176C2×C8—61no—
177C2×C8—91no—
178C2×C8—91no—
179C2×C8—91no—
180C2×C8—91no—
181C2×C8—91no—
182C2×C8—181no—
183C4⋊C4—61no—
184C4⋊C4—181no—
185C22⋊C4—61no—
186C22⋊C4—181no—
187C42—61no—
188C42—181no—
189C22×C3—31no—
190C22×C3—31no—
191C22×C3—41no—
192C22×C3—81no—
193C22×C3—121no—
194C22×C3A4⋊Q811yescharacteristic
195C3×C4—31no—
196C3×C4—31no—
197C3×C4—41no—
198C3×C4—41no—
199C3×C4—81no—
200C3×C4—81no—
201C3×C4—241no—
202C3×C4C4⋊S411yescharacteristic
203C3×C4C2×SL(2,ℤ/4)11yescharacteristic
204Dic3—241no—
205C32—41noSylow
206C23—31no—
207Q8—31no—
208Q8Dic3⋊Dic311yescharacteristic
209D4—31no—
210D4—31no—
211D4—61no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—31no—
217C2×C4—121no—
218C2×C4—361no—
219C2×C4D3×S411yescharacteristic
220C8—31no—
221C8—31no—
222C8—91no—
223C8—91no—
224C8—121no—
225C8—361no—
226C2×C3—21no—
227C2×C3—41no—
228C2×C3—61no—
229C2×C3—61no—
230C2×C3—81no—
231C2×C3—81no—
232C2×C3—161no—
233C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
234C22—31no—
235C22—31no—
236C22—121no—
237C22#6420411yescharacteristic
238C4—31no—
239C4—31no—
240C4—241no—
241C4—721no—
242C4#6420711yescharacteristic
243C4D3×SL(2,ℤ/4)11yescharacteristic
244C3—41no—
245C3—81no—
246C3#7312011yescharacteristic, complemented
247C2—21no—
248C2—61no—
249C2—61no—
250C2Dic3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC4#64207
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC2×C3C4⋊SL(2,ℤ/4)
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C4⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
7. C3⋊(#131⋊C3)C4semidirect
8. C3⋊(#131⋊C3)C4semidirect
246. C3#73120semidirect

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
#105936572
C3×#54232
#731203
#703963
#635774