Finite Group Databasebeta

← #11771758

Subgroups — #11771758

Order 1152.

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

normal subgroups only

This group has 249 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×C3⋊#338C211yesmaximal, characteristic, complemented
4#67779—31nomaximal
5#67483—31nomaximal
6C2×C32×M16C2211yescharacteristic
7C3×#930—21no—
8C2×C3×#208—21no—
9C2×C3×D24C411yescharacteristic
10#63639—21no—
11C3×#821—21no—
12C3×#817C411yescharacteristic
13C3×#469—31no—
14#5135D311yescharacteristic
15C3×#338—31no—
16C3⋊#338D311yescharacteristic, 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×(C2×D3)⋊C4—41no—
27C3×C4⋊Dic3—21no—
28C3×#208—41no—
29C3×#208—41no—
30C2×C3×C3⋊C8—22no—
31C3×D24—41no—
32C3⋊(C3⋊C16)—41no—
33#1341—91noSylow
34C2×C3×D8—31no—
35C2×C3×M16—21no—
36C2×C3×M16—61no—
37C2×C3×M16C2×D311yescharacteristic
38C2×C3×M16C2×D311yescharacteristic
39C3×#121—61no—
40#930—21no—
41C2×#208—21no—
42C2×D24Dic311yescharacteristic
43C3×#106—31no—
44C3×#102—61no—
45#821—21no—
46#817Dic311yescharacteristic
47#812—62no—
48#812—61no—
49#812—61no—
50C23×C32SD1611yescharacteristic
51C22×C3×D3—41no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4D811yescharacteristic
56C3×#67—82no—
57C2×C3×Dic3—41no—
58C3×D12—41no—
59C3×D12—41no—
60C32×C8—21no—
61C32×C8—21no—
62C3×C3⋊C8—42no—
63#469—31no—
64#349—91no—
65#338—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—
77C3×M16—121no—
78C3×M16—121no—
79C2×C3×C8—21no—
80C2×C3×C8—21no—
81C2×C3×C8—62no—
82C2×C3×C8C4×D311yescharacteristic
83C2×C3×C8D1211yescharacteristic
84C2×C3×C8C2×Dic311yescharacteristic
85C2×C3×C8#6711yescharacteristic
86C3×C4⋊C4—61no—
87C3×C22⋊C4—121no—
88(C2×D3)⋊C4—41no—
89C4⋊Dic3—21no—
90#208—41no—
91#208—41no—
92C2×C3⋊C8—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—
107C2×D8—31no—
108C2×M16—61no—
109C2×M16D3211yescharacteristic
110#121—61no—
111M32—181no—
112#106—31no—
113#102—61no—
114C23×C3—21no—
115C23×C3—121no—
116C23×C3#21411yescharacteristic
117C23×C3#21511yescharacteristic
118C22×D3—41no—
119C3×D4—121no—
120C3×D4—121no—
121C3×D4—242no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—41no—
129C2×C3×C4—41no—
130C2×C3×C4—121no—
131C2×C3×C4(C2×D3)⋊C411yescharacteristic
132C2×C3×C4#21311yescharacteristic
133C2×C3×C4#21311yescharacteristic
134C2×C3×C4#21711yescharacteristic
135#67—82no—
136C2×Dic3—41no—
137D12—41no—
138D12—41no—
139C3×C8—22no—
140C3×C8—21no—
141C3×C8—21no—
142C3×C8—21no—
143C3×C8—21no—
144C3×C8—41no—
145C3×C8—122no—
146C3⋊C8—42no—
147C2×C32—21no—
148C2×C32—41no—
149C2×C32#32711yescharacteristic
150C3×D3—161no—
151C2×D4—61no—
152C2×D4—121no—
153C22×C4#62511yescharacteristic
154D8—121no—
155M16—41no—
156M16—121no—
157M16—121no—
158C2×C8—62no—
159C2×C8D3×Dic311yescharacteristic
160C2×C8#62611yescharacteristic
161C4⋊C4—61no—
162C22⋊C4—121no—
163C16—361no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—41no—
168C22×C3—41no—
169C22×C3—41no—
170C22×C3—81no—
171C22×C3—241no—
172C22×C3—241no—
173C22×C3—241no—
174C22×C3#80911yescharacteristic
175C22×C3#83211yescharacteristic
176C2×D3—81no—
177C2×D3—81no—
178C2×D3—81no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—41no—
184C3×C4—241no—
185C3×C4#80511yescharacteristic
186C3×C4#80611yescharacteristic
187C3×C4#83411yescharacteristic
188C3×C4#83711yescharacteristic
189Dic3—81no—
190C32#134111yescharacteristic, complemented, Sylow
191C23—121no—
192C23#371511yescharacteristic
193D4—121no—
194D4—121no—
195D4—242no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—121no—
199C2×C4#371311yescharacteristic
200C2×C4(C2×D3)⋊Dic311yescharacteristic
201C8—21no—
202C8—21no—
203C8—122no—
204C2×C3—21no—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—41no—
208C2×C3—41no—
209C2×C3—41no—
210C2×C3—81no—
211C2×C3—481no—
212C2×C3#445111yescharacteristic
213C2×C3#453711yescharacteristic
214D3—161no—
215C22—21no—
216C22—41no—
217C22—241no—
218C22—241no—
219C22—241no—
220C22#6356211yescharacteristic
221C4—21no—
222C4—241no—
223C4#6356911yescharacteristic
224C4#6358011yescharacteristic
225C3—21no—
226C3#6748311yescharacteristic, complemented
227C3#6777911yescharacteristic, complemented
228C2—21no—
229C2—41no—
230C2—481no—
231C2#1058914911yescharacteristic
subgroupG/H
centerC2#10589149
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#327
prime radicalC3×#5135C2
hypocenterC32#1341
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×C3⋊#338C2semidirect
16. C3⋊#338D3semidirect
190. C32#1341semidirect
226. C3#67483semidirect
227. C3#67779semidirect

Maximal subgroups

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

subgroupindex
C3×#51352
#105894192
C3×C3⋊#3382
#677793
#674833