Finite Group Databasebeta

← #11771858

Subgroups — #11771858

Order 1152.

309 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 309 conjugacy classes of subgroups — too many to draw. Only its 74 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×#5115C211yesmaximal, characteristic
2#10589417C211yesmaximal, characteristic, complemented
3C3×#4549C211yesmaximal, characteristic, complemented
4#67774—31nomaximal
5#67526—31nomaximal
6C22×C32×C8C2211yescharacteristic
7C2×C4⋊(C3⋊Dic3)—21no—
8C3×#930—21no—
9C2×C3×D24C411yescharacteristic, complemented
10C3×#821—21no—
11C3×#818C411yescharacteristic, complemented
12C2×C3×C3⋊C16—21no—
13C3×#466—31no—
14#5115D311yescharacteristic
15C3×C22⋊C16—31no—
16#4551—31no—
17#4551—31no—
18#4551—61no—
19#4549D311yescharacteristic, complemented
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3—41no—
22C2×C3×#67—41no—
23C2×C3×D12—21no—
24C2×C32×C8—41no—
25C2×C32×C8C2×C411yescharacteristic
26C2×C32×C8D411yescharacteristic
27C4⋊(C3⋊Dic3)—22no—
28C4⋊(C3⋊Dic3)—41no—
29C3×(C2×D3)⋊C4—41no—
30C3×C4⋊Dic3—21no—
31C3×D24—41no—
32C3×C3⋊C16—41no—
33#1347—91noSylow
34C2×C3×D8—31no—
35C22×C3×C8—21no—
36C22×C3×C8C2×D311yescharacteristic
37C22×C3×C8C2×D311yescharacteristic
38C3×#121—61no—
39#930—21no—
40C2×C4⋊Dic3—62no—
41C2×C4⋊Dic3—61no—
42C2×C4⋊Dic3—61no—
43C2×D24Dic311yescharacteristic, complemented
44C2×C3×C16—61no—
45C3×#107—31no—
46C3×#102—61no—
47#821—21no—
48#818Dic311yescharacteristic, complemented
49C2×C3⋊C16—21no—
50C23×C32D811yescharacteristic
51C22×C3×D3—41no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4SD1611yescharacteristic
56C2×C3⋊Dic3—42no—
57C2×C3⋊Dic3—81no—
58C2×C3⋊Dic3—81no—
59C3×#67—81no—
60C3×#67—81no—
61C2×C3×Dic3—41no—
62C3×D12—41no—
63C3×D12—41no—
64C32×C8—21no—
65C32×C8—21no—
66#466—31no—
67C22⋊C16—31no—
68#340—91no—
69C2×C3×D4—61no—
70C2×C3×D4—121no—
71C22×C3×C4—21no—
72C22×C3×C4D1211yescharacteristic
73C22×C3×C4#6711yescharacteristic
74C2×#67—41no—
75C22×Dic3—122no—
76C22×Dic3—121no—
77C22×Dic3—121no—
78C2×D12—21no—
79C3×D8—121no—
80C2×C3×C8—21no—
81C2×C3×C8—21no—
82C2×C3×C8—41no—
83C2×C3×C8—41no—
84C2×C3×C8—42no—
85C2×C3×C8C4×D311yescharacteristic
86C2×C3×C8C2×Dic311yescharacteristic
87C2×C3×C8#6711yescharacteristic
88C2×C3×C8#6711yescharacteristic
89C3×C4⋊C4—61no—
90C3×C22⋊C4—121no—
91(C2×D3)⋊C4—41no—
92C4⋊Dic3—21no—
93C4⋊Dic3—64no—
94C4⋊Dic3—62no—
95C4⋊Dic3—62no—
96C4⋊Dic3—122no—
97C4⋊Dic3—121no—
98C4⋊Dic3—121no—
99D24—41no—
100C3×C16—121no—
101C3⋊C16—41no—
102C22×C32—21no—
103C22×C32—21no—
104C22×C32#10211yescharacteristic
105C22×C32D1611yescharacteristic
106C22×C32SD3211yescharacteristic
107C2×C3×D3—81no—
108C2×C3×D3—81no—
109C2×C3×D3—81no—
110C32×C4—21no—
111C32×C4#9911yescharacteristic
112C32×C4#10411yescharacteristic
113C3⋊Dic3—82no—
114C3×Dic3—81no—
115C2×D8—31no—
116C22×C8D3211yescharacteristic
117#121—61no—
118C2×C4⋊C4—181no—
119C2×C16—61no—
120#107—31no—
121#102—61no—
122C23×C3—21no—
123C23×C3—121no—
124C23×C3D2411yescharacteristic
125C23×C3#21311yescharacteristic
126C22×D3—41no—
127C3×D4—121no—
128C3×D4—121no—
129C3×D4—241no—
130C3×D4—241no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—121no—
140C2×C3×C4#20411yescharacteristic
141C2×C3×C4(C2×D3)⋊C411yescharacteristic
142C2×C3×C4#21411yescharacteristic
143C2×C3×C4#21711yescharacteristic
144#67—81no—
145#67—81no—
146C2×Dic3—41no—
147C2×Dic3—124no—
148C2×Dic3—122no—
149C2×Dic3—122no—
150C2×Dic3—242no—
151C2×Dic3—241no—
152C2×Dic3—241no—
153C2×Dic3—242no—
154C2×Dic3—241no—
155C2×Dic3—241no—
156D12—41no—
157D12—41no—
158C3×C8—21no—
159C3×C8—21no—
160C3×C8—21no—
161C3×C8—21no—
162C3×C8—41no—
163C3×C8—41no—
164C2×C32—21no—
165C2×C32—21no—
166C2×C32#32711yescharacteristic
167C2×C32#35711yescharacteristic
168C2×C32#36011yescharacteristic
169C3×D3—161no—
170C2×D4—61no—
171C2×D4—121no—
172C22×C4—361no—
173C22×C4#62611yescharacteristic
174D8—121no—
175C2×C8—41no—
176C2×C8D3×Dic311yescharacteristic
177C2×C8#62511yescharacteristic
178C4⋊C4—61no—
179C4⋊C4—182no—
180C4⋊C4—361no—
181C22⋊C4—121no—
182C16—121no—
183C22×C3—22no—
184C22×C3—22no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—241no—
193C22×C3—241no—
194C22×C3—241no—
195C22×C3D4811yescharacteristic
196C22×C3#80011yescharacteristic
197C22×C3#82111yescharacteristic
198C22×C3#82611yescharacteristic
199C22×C3#82711yescharacteristic
200C22×C3#83211yescharacteristic
201C2×D3—81no—
202C2×D3—81no—
203C2×D3—81no—
204C3×C4—22no—
205C3×C4—21no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—241no—
210C3×C4#80611yescharacteristic
211C3×C4#82511yescharacteristic
212C3×C4#83411yescharacteristic
213C3×C4#83711yescharacteristic
214Dic3—81no—
215Dic3—244no—
216Dic3—242no—
217Dic3—242no—
218C32#134711yescharacteristic, complemented, Sylow
219C23—121no—
220C23#371411yescharacteristic
221D4—121no—
222D4—121no—
223D4—241no—
224D4—241no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—121no—
228C2×C4—362no—
229C2×C4—721no—
230C2×C4—721no—
231C2×C4#371611yescharacteristic
232C2×C4(C2×D3)⋊Dic311yescharacteristic
233C8—21no—
234C8—21no—
235C2×C3—22no—
236C2×C3—22no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—481no—
245C2×C3#447011yescharacteristic
246C2×C3#450911yescharacteristic
247C2×C3#451811yescharacteristic
248C2×C3#453711yescharacteristic
249C2×C3#456211yescharacteristic
250C2×C3#456611yescharacteristic
251D3—161no—
252C22—21no—
253C22—21no—
254C22—241no—
255C22—241no—
256C22—241no—
257C22#6354611yescharacteristic
258C22#6354811yescharacteristic
259C22#6356311yescharacteristic
260C4—21no—
261C4—241no—
262C4—722no—
263C4#6356811yescharacteristic
264C4#6358011yescharacteristic
265C3—21no—
266C3#6752611yescharacteristic, complemented
267C3#6777411yescharacteristic, complemented
268C2—21no—
269C2—21no—
270C2—481no—
271C2#1058911511yescharacteristic
272C2#1058912411yescharacteristic
273C2#1058915011yescharacteristic
subgroupG/H
centerC22#63563
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC22×C8D32
Fitting, cosocleC22×C32×C8C22
socleC22×C32#102
prime radicalC3×#5115C2
hypocenterC32#1347
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10589417C2semidirect
3. C3×#4549C2semidirect
9. C2×C3×D24C4semidirect
11. C3×#818C4semidirect
19. #4549D3semidirect
43. C2×D24Dic3semidirect
48. #818Dic3semidirect
218. C32#1347semidirect
266. C3#67526semidirect
267. C3#67774semidirect

Maximal subgroups

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

subgroupindex
C3×#51152
#105894172
C3×#45492
#677743
#675263