Finite Group Databasebeta

← #11807584

Subgroups — #11807584

Order 1152.

2064 conjugacy classes of subgroups; only the 337 normal subgroups are shown.

normal subgroups only

This group has 2064 conjugacy classes of subgroups — too many to draw. Only its 337 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×#64162C211yesmaximal, characteristic
2C32×#379C211yesmaximal, characteristic, complemented
3#10592946C211yesmaximal, characteristic, complemented
4#10592656C213yesmaximal, complemented
5#10592655C213yesmaximal, complemented
6#10592644C213yesmaximal, complemented
7#10592643C213yesmaximal, complemented
8#73851—34nomaximal
9C25×C32C2211yescharacteristic
10C22×#638C2213yes—
11C22×C4×C3⋊D3C2211yescharacteristic, complemented
12C2×C32×C22⋊C4C2213yes—
13C2×C32×C22⋊C4C2213yes—
14#64162C418yescomplemented
15C2×#3757C2213yes—
16C2×#3757C2213yes—
17C2×#3757C2213yes—
18C2×#3752C2213yescomplemented
19C2×#3750C2213yescomplemented
20C2×C4×C3⋊Dic3C2213yescomplemented
21#63658C2213yescomplemented
22#63658C2213yescomplemented
23C2×#953—34no—
24C3×#379D314yescomplemented
25#5247—34no—
26#4957—312no—
27#4956—312no—
28#4945—312no—
29#4944—312no—
30C24×C32—43no—
31C24×C32—43no—
32C24×C32C2×C414yescomplemented
33C24×C32C2313yes—
34C23×C3⋊D3C2311yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C32×C4C2313yes—
37C2×#638—43no—
38C2×#638—43no—
39C2×#638C2×C4112yes—
40C22×C3⋊Dic3C2311yescharacteristic
41C22×C3⋊Dic3C2313yes—
42C22×C3⋊Dic3C2313yes—
43C2×C4×C3⋊D3—43no—
44C32×C22⋊C4—43no—
45C32×C22⋊C4—43no—
46#3757—43no—
47#3757—43no—
48#3757C2×C4112yescomplemented
49#3752—43no—
50#3750—43no—
51C4×C3⋊Dic3—43no—
52#2375—91noSylow
53C25×C3C2×D314yes—
54C22×#67—312no—
55C22×C4×D3—34no—
56C2×C3×C22⋊C4C2×D3112yes—
57C2×C3×C22⋊C4C2×D3112yes—
58#953—332no—
59C2×#217—312no—
60C2×#217—312no—
61C2×#217—312no—
62C2×(C2×D3)⋊C4—312no—
63C2×Dic3⋊C4—312no—
64C2×C4×Dic3—312no—
65C3⋊#95—312no—
66C3⋊#95—312no—
67C23×C32—23no—
68C23×C32—23no—
69C23×C32—23no—
70C23×C32—23no—
71C23×C32—23no—
72C23×C32—23no—
73C23×C32—412no—
74C23×C32—412no—
75C23×C32—44no—
76C23×C32C22×C416yes—
77C23×C32C2411yescharacteristic
78C22×C3⋊D3—23no—
79C22×C3⋊D3—23no—
80C22×C3⋊D3C22×C412yes—
81C2×C32×C4—23no—
82C2×C32×C4—23no—
83C2×C32×C4—23no—
84C2×C32×C4—23no—
85#638—412no—
86C2×C3⋊Dic3—23no—
87C2×C3⋊Dic3—23no—
88C2×C3⋊Dic3—23no—
89C2×C3⋊Dic3—23no—
90C2×C3⋊Dic3—23no—
91C2×C3⋊Dic3—23no—
92C2×C3⋊Dic3C22×C416yes—
93C4×C3⋊D3—44no—
94C2×#120—91no—
95#390—93no—
96#388—93no—
97#388—93no—
98#386—93no—
99#379—91no—
100#379C3⋊D311yescharacteristic, complemented
101C24×C3—412no—
102C24×C3—412no—
103C24×C3C4×D3116yescomplemented
104C24×C3C22×D3112yes—
105C23×D3—34no—
106C22×C3×C4C22×D314yes—
107C22×C3×C4C22×D3112yes—
108C2×#67—348no—
109C2×#67—1212no—
110C2×#67—1212no—
111C22×Dic3—312no—
112C22×Dic3—34no—
113C22×Dic3—312no—
114C2×C4×D3—1212no—
115C3×C22⋊C4—412no—
116C3×C22⋊C4—412no—
117#217—348no—
118#217—1212no—
119#217—1212no—
120(C2×D3)⋊C4—1212no—
121Dic3⋊C4—1212no—
122C4×Dic3—1212no—
123C22×C32—26no—
124C22×C32—26no—
125C22×C32—26no—
126C22×C32—416no—
127C22×C32—43no—
128C22×C32—43no—
129C22×C32—43no—
130C22×C32—43no—
131C22×C32C23×C411yescharacteristic
132C22×C32H(5,𝔽2)13yes—
133C22×C32H(5,𝔽2)13yes—
134C2×C3⋊D3—26no—
135C2×C3⋊D3—43no—
136C2×C3⋊D3—41no—
137C32×C4—43no—
138C32×C4—41no—
139C3⋊Dic3—26no—
140C3⋊Dic3—43no—
141C3⋊Dic3—41no—
142C25C2×C3⋊D311yescharacteristic
143C22×D4—93no—
144C23×C4—91no—
145#120—98no—
146C2×C4⋊C4—93no—
147C2×C22⋊C4—93no—
148C2×C22⋊C4—93no—
149C2×C22⋊C4—93no—
150C2×C22⋊C4—93no—
151C2×C22⋊C4C2×C3⋊D313yes—
152C2×C22⋊C4C2×C3⋊D313yes—
153C2×C42—93no—
154#95—93no—
155#95—93no—
156C23×C3—212no—
157C23×C3—212no—
158C23×C3—212no—
159C23×C3—212no—
160C23×C3—212no—
161C23×C3—212no—
162C23×C3—448no—
163C23×C3—416no—
164C23×C3—448no—
165C23×C3C2×C4×D3124yes—
166C23×C3C23×D314yes—
167C22×D3—38no—
168C22×D3—612no—
169C22×D3—612no—
170C2×C3×C4—212no—
171C2×C3×C4—212no—
172C2×C3×C4—212no—
173C2×C3×C4—212no—
174#67—1248no—
175C2×Dic3—324no—
176C2×Dic3—612no—
177C2×Dic3—612no—
178C2×Dic3—612no—
179C2×Dic3—612no—
180C2×Dic3—612no—
181C2×Dic3—612no—
182C4×D3—1216no—
183C2×C32—46no—
184C2×C32#51813yes—
185C2×C32#56013yes—
186C2×C32H(3,𝔽4)11yescharacteristic
187C3⋊D3—42no—
188C24—43no—
189C24—43no—
190C24—91no—
191C24C4×C3⋊D314yescomplemented
192C24C22×C3⋊D313yes—
193C2×D4—912no—
194C2×D4—363no—
195C2×D4—363no—
196C22×C4—93no—
197C22×C4—91no—
198C22×C4—93no—
199C22×C4—363no—
200C22×C4C22×C3⋊D311yescharacteristic
201C22×C4C22×C3⋊D313yes—
202C4⋊C4—363no—
203C22⋊C4—43no—
204C22⋊C4—43no—
205C22⋊C4—912no—
206C22⋊C4—363no—
207C22⋊C4—363no—
208C22⋊C4—363no—
209C42—363no—
210C22×C3—224no—
211C22×C3—224no—
212C22×C3—224no—
213C22×C3—464no—
214C22×C3—412no—
215C22×C3—412no—
216C22×C3—412no—
217C22×C3—412no—
218C22×C3C22×C4×D314yes—
219C22×C3#1004112yes—
220C22×C3#1004112yes—
221C2×D3—624no—
222C2×D3—124no—
223C2×D3—1212no—
224C3×C4—44no—
225C3×C4—412no—
226Dic3—624no—
227Dic3—124no—
228Dic3—1212no—
229C32#237511yescharacteristic, complemented, Sylow
230C23—23no—
231C23—23no—
232C23—23no—
233C23—23no—
234C23—23no—
235C23—23no—
236C23—412no—
237C23—44no—
238C23—412no—
239C23—92no—
240C23—183no—
241C23—183no—
242C23C2×C4×C3⋊D316yes—
243C23C23×C3⋊D311yescharacteristic
244D4—3612no—
245C2×C4—23no—
246C2×C4—23no—
247C2×C4—23no—
248C2×C4—23no—
249C2×C4—96no—
250C2×C4—183no—
251C2×C4—183no—
252C2×C4—183no—
253C2×C4—183no—
254C2×C4—183no—
255C2×C4—183no—
256C2×C4—364no—
257C2×C3—424no—
258C2×C3#5486112yes—
259C2×C3#559414yes—
260C2×C3#5595112yes—
261D3—128no—
262C22—26no—
263C22—26no—
264C22—26no—
265C22—416no—
266C22—43no—
267C22—43no—
268C22—43no—
269C22—43no—
270C22—186no—
271C22—361no—
272C22—363no—
273C22C22×C4×C3⋊D311yescharacteristic
274C22#6436113yes—
275C22#6436113yes—
276C4—41no—
277C4—43no—
278C4—186no—
279C4—361no—
280C4—363no—
281C3#7385114yescomplemented
282C2—46no—
283C2—362no—
284C2#1059595713yes—
285C2#1059606511yescharacteristic
286C2#1059606613yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#379C2
socle, cosocleC23×C32C24
prime radicalC2×#64162C2
hypercenter#379C3⋊D3
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C32×#379C2semidirect
3. #10592946C2semidirect
4. #10592656C2semidirect
5. #10592655C2semidirect
6. #10592644C2semidirect
7. #10592643C2semidirect
11. C22×C4×C3⋊D3C22semidirect
14. #64162C4semidirect
18. C2×#3752C22semidirect
19. C2×#3750C22semidirect
20. C2×C4×C3⋊Dic3C22semidirect
21. #63658C22semidirect
22. #63658C22semidirect
24. C3×#379D3semidirect
32. C24×C32C2×C4semidirect
48. #3757C2×C4semidirect
100. #379C3⋊D3semidirect
103. C24×C3C4×D3semidirect
191. C24C4×C3⋊D3semidirect
229. C32#2375semidirect
281. C3#73851semidirect

Maximal subgroups

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

subgroupindex
C2×#641622
C32×#3792
#105929462
#105926562
#105926552
#105926442
#105926432
#738513