Finite Group Databasebeta

← #11771756

Subgroups — #11771756

Order 1152.

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

normal subgroups only

This group has 263 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#10589426C211yesmaximal, characteristic, complemented
3C3×#4553C211yesmaximal, characteristic, complemented
4#67779—31nomaximal
5#67535—31nomaximal
6C2×C32×M16C2211yescharacteristic
7C2×#3748—21no—
8C3×#930—21no—
9C2×C3×D24C411yescharacteristic
10C3×#821—21no—
11C3×#817C411yescharacteristic
12C3×#812—21no—
13C3×#469—31no—
14#5135D311yescharacteristic
15C3×#349—31no—
16C3⋊#338—31no—
17C3⋊#338—31no—
18C3⋊#338—61no—
19#4553D311yescharacteristic, complemented
20C22×C32×C4D411yescharacteristic
21C2×C3×#67—41no—
22C2×C3×D12—21no—
23C32×M16—41no—
24C2×C32×C8C2×C411yescharacteristic
25C2×C32×C8D411yescharacteristic
26#3748—41no—
27#3748—41no—
28C2×C3⋊(C3⋊C8)—22no—
29C3×(C2×D3)⋊C4—41no—
30C3×C4⋊Dic3—21no—
31C3×D24—41no—
32C3×C3⋊C16—41no—
33#1341—91noSylow
34C2×C3×D8—31no—
35C2×C3×M16—21no—
36C2×C3×M16C2×D311yescharacteristic
37C2×C3×M16C2×D311yescharacteristic
38C3×#121—61no—
39#930—21no—
40C2×#208—62no—
41C2×#208—61no—
42C2×#208—61no—
43C2×D24Dic311yescharacteristic
44C3×M32—61no—
45C3×#106—31no—
46C3×#102—61no—
47#821—21no—
48#817Dic311yescharacteristic
49#812—21no—
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—31no—
65#338—91no—
66C2×C3×D4—61no—
67C2×C3×D4—121no—
68C22×C3×C4—21no—
69C22×C3×C4D1211yescharacteristic
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×C8C2×Dic311yescharacteristic
81C2×C3×C8#6711yescharacteristic
82C2×C3×C8#6711yescharacteristic
83C3×C4⋊C4—61no—
84C3×C22⋊C4—121no—
85(C2×D3)⋊C4—41no—
86C4⋊Dic3—21no—
87#208—122no—
88#208—121no—
89#208—121no—
90#208—122no—
91#208—121no—
92#208—121no—
93C2×C3⋊C8—64no—
94C2×C3⋊C8—62no—
95C2×C3⋊C8—62no—
96D24—41no—
97C3×C16—121no—
98C3⋊C16—41no—
99C22×C32—21no—
100C22×C32—41no—
101C22×C32#10211yescharacteristic
102C2×C3×D3—81no—
103C2×C3×D3—81no—
104C2×C3×D3—81no—
105C32×C4—21no—
106C32×C4#9911yescharacteristic
107C32×C4#10411yescharacteristic
108C3×Dic3—81no—
109C2×D8—31no—
110C2×M16—181no—
111C2×M16D3211yescharacteristic
112#121—61no—
113M32—61no—
114#106—31no—
115#102—61no—
116C23×C3—21no—
117C23×C3—121no—
118C23×C3#20411yescharacteristic
119C23×C3#21411yescharacteristic
120C22×D3—41no—
121C3×D4—121no—
122C3×D4—121no—
123C3×D4—242no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—121no—
133C2×C3×C4D2411yescharacteristic
134C2×C3×C4(C2×D3)⋊C411yescharacteristic
135C2×C3×C4#21311yescharacteristic
136C2×C3×C4#21711yescharacteristic
137#67—82no—
138C2×Dic3—41no—
139D12—41no—
140D12—41no—
141C3×C8—21no—
142C3×C8—21no—
143C3×C8—21no—
144C3×C8—21no—
145C3×C8—41no—
146C3×C8—41no—
147C3⋊C8—124no—
148C3⋊C8—122no—
149C3⋊C8—122no—
150C2×C32—21no—
151C2×C32—41no—
152C2×C32#32711yescharacteristic
153C3×D3—161no—
154C2×D4—61no—
155C2×D4—121no—
156C22×C4#62611yescharacteristic
157D8—121no—
158M16—41no—
159M16—361no—
160M16—361no—
161C2×C8—182no—
162C2×C8D3×Dic311yescharacteristic
163C2×C8#62511yescharacteristic
164C4⋊C4—61no—
165C22⋊C4—121no—
166C16—121no—
167C22×C3—22no—
168C22×C3—21no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—41no—
172C22×C3—41no—
173C22×C3—81no—
174C22×C3—241no—
175C22×C3—241no—
176C22×C3—241no—
177C22×C3#82111yescharacteristic
178C22×C3#83211yescharacteristic
179C2×D3—81no—
180C2×D3—81no—
181C2×D3—81no—
182C3×C4—22no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—241no—
188C3×C4#80611yescharacteristic
189C3×C4#82511yescharacteristic
190C3×C4#83411yescharacteristic
191C3×C4#83711yescharacteristic
192Dic3—81no—
193C32#134111yescharacteristic, complemented, Sylow
194C23—121no—
195C23#371611yescharacteristic
196D4—121no—
197D4—121no—
198D4—242no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—121no—
202C2×C4#371411yescharacteristic
203C2×C4(C2×D3)⋊Dic311yescharacteristic
204C8—21no—
205C8—21no—
206C8—362no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—41no—
211C2×C3—42no—
212C2×C3—41no—
213C2×C3—41no—
214C2×C3—481no—
215C2×C3#447011yescharacteristic
216C2×C3#453711yescharacteristic
217D3—161no—
218C22—21no—
219C22—41no—
220C22—241no—
221C22—241no—
222C22—241no—
223C22#6356311yescharacteristic
224C4—21no—
225C4—241no—
226C4#6356811yescharacteristic
227C4#6358011yescharacteristic
228C3—21no—
229C3#6753511yescharacteristic, complemented
230C3#6777911yescharacteristic, complemented
231C2—21no—
232C2—41no—
233C2—481no—
234C2#1058915011yescharacteristic
subgroupG/H
centerC2#10589150
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. #10589426C2semidirect
3. C3×#4553C2semidirect
19. #4553D3semidirect
193. C32#1341semidirect
229. C3#67535semidirect
230. C3#67779semidirect

Maximal subgroups

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

subgroupindex
C3×#51352
#105894262
C3×#45532
#677793
#675353