Finite Group Databasebeta

← #11771724

Subgroups — #11771724

Order 1152.

257 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 257 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C3×#5135C211yesmaximal, characteristic
2#10589419C211yesmaximal, characteristic, complemented
3C3×#4557C211yesmaximal, characteristic, complemented
4#67778—31nomaximal
5#67481—31nomaximal
6C2×C32×M16C2211yescharacteristic
7C3×#930—21no—
8C3×#926—21no—
9C2×C3×D24C411yescharacteristic, complemented
10#63639—21no—
11C3×#821—21no—
12C3×#817C411yescharacteristic, complemented
13C3×#469—31no—
14#5135D311yescharacteristic
15C3×H(3,ℤ/4)—31no—
16#4557D311yescharacteristic, complemented
17#4553—31no—
18#4553—31no—
19#4553—61no—
20C22×C32×C4D411yescharacteristic
21C2×C3×#67—41no—
22C2×C3×D12—21no—
23C32×M16—41no—
24C2×C32×C8C2×C411yescharacteristic
25C2×C32×C8D411yescharacteristic
26C3×#217—41no—
27C3×(C2×D3)⋊C4—41no—
28C3×C4⋊Dic3—21no—
29C3×C4⋊Dic3—41no—
30C3×C4×Dic3—22no—
31C3×D24—41no—
32C3⋊(C3⋊C16)—41no—
33#1339—91noSylow
34C2×C3×D8—31no—
35C2×C3×M16—21no—
36C2×C3×M16C2×D311yescharacteristic
37C2×C3×M16C2×D311yescharacteristic
38C3×#121—61no—
39C3×#117—61no—
40#930—21no—
41#926—21no—
42C2×D24Dic311yescharacteristic, complemented
43C3×#106—31no—
44C3×#102—61no—
45#821—21no—
46#817Dic311yescharacteristic, complemented
47#812—62no—
48#812—61no—
49#812—61no—
50C23×C32D811yescharacteristic
51C22×C3×D3—41no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4SD1611yescharacteristic
56C3×#67—82no—
57C2×C3×Dic3—42no—
58C2×C3×Dic3—41no—
59C3×D12—41no—
60C3×D12—41no—
61C32×C8—21no—
62C32×C8—21no—
63#469—31no—
64#349—91no—
65H(3,ℤ/4)—31no—
66C2×C3×D4—61no—
67C2×C3×D4—121no—
68C22×C3×C4—21no—
69C22×C3×C4#6711yescharacteristic
70C22×C3×C4#6711yescharacteristic
71C2×#67—41no—
72C2×D12—21no—
73C3×D8—121no—
74C3×M16—41no—
75C3×M16—41no—
76C3×M16—42no—
77C2×C3×C8—21no—
78C2×C3×C8—21no—
79C2×C3×C8C4×D311yescharacteristic
80C2×C3×C8D1211yescharacteristic
81C2×C3×C8C2×Dic311yescharacteristic
82C2×C3×C8#6711yescharacteristic
83C3×C4⋊C4—61no—
84C3×C4⋊C4—121no—
85C3×C22⋊C4—121no—
86C3×C22⋊C4—121no—
87C3×C42—62no—
88#217—41no—
89(C2×D3)⋊C4—41no—
90C4⋊Dic3—21no—
91C4⋊Dic3—41no—
92C4×Dic3—22no—
93D24—41no—
94C3⋊C16—122no—
95C3⋊C16—121no—
96C3⋊C16—121no—
97C22×C32—21no—
98C22×C32—41no—
99C22×C32#10211yescharacteristic
100C2×C3×D3—81no—
101C2×C3×D3—81no—
102C2×C3×D3—81no—
103C32×C4—21no—
104C32×C4#9911yescharacteristic
105C32×C4#10411yescharacteristic
106C3×Dic3—81no—
107C3×Dic3—82no—
108C2×D8—31no—
109C2×M16D3211yescharacteristic
110#121—61no—
111#117—61no—
112M32—181no—
113#106—31no—
114#102—61no—
115C23×C3—21no—
116C23×C3—121no—
117C23×C3#21311yescharacteristic
118C23×C3#21311yescharacteristic
119C22×D3—41no—
120C3×D4—121no—
121C3×D4—121no—
122C3×D4—242no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—41no—
130C2×C3×C4—41no—
131C2×C3×C4—122no—
132C2×C3×C4—121no—
133C2×C3×C4(C2×D3)⋊C411yescharacteristic
134C2×C3×C4#21411yescharacteristic
135C2×C3×C4#21511yescharacteristic
136C2×C3×C4#21711yescharacteristic
137#67—82no—
138C2×Dic3—42no—
139C2×Dic3—41no—
140D12—41no—
141D12—41no—
142C3×C8—22no—
143C3×C8—21no—
144C3×C8—21no—
145C3×C8—21no—
146C3×C8—21no—
147C3×C8—41no—
148C2×C32—21no—
149C2×C32—41no—
150C2×C32#32711yescharacteristic
151C3×D3—161no—
152C2×D4—61no—
153C2×D4—121no—
154C22×C4#62511yescharacteristic
155D8—121no—
156M16—41no—
157C2×C8D3×Dic311yescharacteristic
158C2×C8#62611yescharacteristic
159C4⋊C4—61no—
160C4⋊C4—121no—
161C22⋊C4—121no—
162C22⋊C4—121no—
163C42—62no—
164C16—361no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—21no—
168C22×C3—41no—
169C22×C3—41no—
170C22×C3—41no—
171C22×C3—81no—
172C22×C3—241no—
173C22×C3—241no—
174C22×C3—241no—
175C22×C3#80911yescharacteristic
176C22×C3#83211yescharacteristic
177C2×D3—81no—
178C2×D3—81no—
179C2×D3—81no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—41no—
185C3×C4—241no—
186C3×C4—242no—
187C3×C4#80511yescharacteristic
188C3×C4#80611yescharacteristic
189C3×C4#83411yescharacteristic
190C3×C4#83711yescharacteristic
191Dic3—81no—
192Dic3—82no—
193C32#133911yescharacteristic, complemented, Sylow
194C23—121no—
195C23#371311yescharacteristic
196D4—121no—
197D4—121no—
198D4—242no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—122no—
202C2×C4—121no—
203C2×C4#371511yescharacteristic
204C2×C4(C2×D3)⋊Dic311yescharacteristic
205C8—21no—
206C8—21no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—41no—
211C2×C3—41no—
212C2×C3—41no—
213C2×C3—81no—
214C2×C3—481no—
215C2×C3#445111yescharacteristic
216C2×C3#453711yescharacteristic
217D3—161no—
218C22—21no—
219C22—41no—
220C22—241no—
221C22—241no—
222C22—241no—
223C22#6356211yescharacteristic
224C4—21no—
225C4—241no—
226C4—242no—
227C4#6356911yescharacteristic
228C4#6358011yescharacteristic
229C3—21no—
230C3#6748111yescharacteristic, complemented
231C3#6777811yescharacteristic, complemented
232C2—21no—
233C2—41no—
234C2—481no—
235C2#1058914911yescharacteristic
subgroupG/H
centerC2#10589149
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#327
prime radicalC3×#5135C2
hypocenterC32#1339
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10589419C2semidirect
3. C3×#4557C2semidirect
9. C2×C3×D24C4semidirect
12. C3×#817C4semidirect
16. #4557D3semidirect
42. C2×D24Dic3semidirect
46. #817Dic3semidirect
193. C32#1339semidirect
230. C3#67481semidirect
231. C3#67778semidirect

Maximal subgroups

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

subgroupindex
C3×#51352
#105894192
C3×#45572
#677783
#674813