Finite Group Databasebeta

← #157×C3⋊#157 #72228478

Subgroups — #157×C3⋊#157 #72228478

Order 3888.

600 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 36 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
1#14519511C211yesmaximal, characteristic
2C3⋊D3×C3⋊#157C211yesmaximal, characteristic
3C3×C3⋊D3×#157C211yesmaximal, characteristic
4#1572—31nomaximal
5C3×C3⋊D32C2211yescharacteristic
6C3⋊#66472C412yescomplemented
7C3⋊(C3⋊(C3⋊#157))C411yescharacteristic, complemented
8C3×C3⋊(C3⋊#157)C411yescharacteristic, complemented
9C32×C3⋊#157C411yescharacteristic, complemented
10C33×#157C411yescharacteristic, complemented
11#10620198—31no—
12C3⋊D3×#157—31no—
13C3⋊D3×#157D311yescharacteristic
14D3×C3⋊#157—62no—
15C3×D3×#157—62no—
16C3×C3⋊(C3⋊(C3⋊D3))C2×C411yescharacteristic
17C33×C3⋊D3C2×C411yescharacteristic
18C33×C3⋊D3C2×C411yescharacteristic
19C4×C3⋊#157—91nomaximal
20Dic3×#157—91nomaximal
21C3⋊D32C2×D311yescharacteristic
22C3×D3×C3⋊D3—62no—
23C3×D3×C3⋊D3—62no—
24#66472—32no—
25C3⋊(C3⋊#157)—31no—
26C3⋊(C3⋊#157)—62no—
27C3⋊(C3⋊#157)—122no—
28C3⋊(C3⋊#157)Dic311yescharacteristic, complemented
29C3×C3⋊#157—22no—
30C3×C3⋊#157—62no—
31C32×#157—22no—
32C32×#157—31no—
33C32×#157—42no—
34C32×#157Dic311yescharacteristic, complemented
35C35C4211yescharacteristic, complemented, Sylow
36C2×C3⋊#157—91no—
37C2×C3⋊#157—91no—
38C2×C3⋊#157—91no—
39C2×C3×#157—91no—
40D3×#157—62no—
41D3×#157—182no—
42C3×C4×C3⋊D3—91no—
43Dic3×C3⋊D3—91no—
44C3⋊(C3⋊(C3⋊D3))C4×D311yescharacteristic
45C3×C3⋊(C3⋊D3)—62no—
46C3×C3⋊(C3⋊D3)—62no—
47C3×C3⋊(C3⋊D3)—244no—
48C32×C3⋊D3—22no—
49C32×C3⋊D3—22no—
50C32×C3⋊D3—42no—
51C32×C3⋊D3—42no—
52C32×C3⋊D3C4×D311yescharacteristic
53C32×C3⋊D3C2×Dic311yescharacteristic
54C33×D3—62no—
55C33×D3—62no—
56C4×#157—271no—
57C4×#157—271no—
58C2×C3×C3⋊D3—91no—
59C2×C3×C3⋊D3—91no—
60D3×C3⋊D3—62no—
61D3×C3⋊D3—62no—
62C3×D32—364no—
63C3⋊#157—62no—
64C3⋊#157—92no—
65C3⋊#157—92no—
66C3⋊#157—91no—
67C3⋊#157—182no—
68C3⋊#157—362no—
69C3⋊#157—364no—
70C3⋊#157#15711yescharacteristic, direct product factor
71C3×#157—22no—
72C3×#157—42no—
73C3×#157—62no—
74C3×#157—91no—
75C3×#157#15711yescharacteristic, complemented
76C33×C4—91no—
77C3⋊(C3⋊Dic3)—91no—
78C3×C3⋊Dic3—91no—
79C32×Dic3—91no—
80C34—22no—
81C34—22no—
82C34—42no—
83C34—42no—
84C34—84no—
85C34—164no—
86C34C4×Dic311yescharacteristic, complemented
87C2×#157—91no—
88C2×#157—271no—
89C2×#157—271no—
90C2×#157—271no—
91C4×C3⋊D3—91no—
92C4×C3⋊D3—271no—
93C3×C4×D3—542no—
94D3×Dic3—542no—
95C2×C33—91no—
96C2×C33—91no—
97C3⋊(C3⋊D3)—62no—
98C3⋊(C3⋊D3)—62no—
99C3⋊(C3⋊D3)—244no—
100C3×C3⋊D3—22no—
101C3×C3⋊D3—22no—
102C3×C3⋊D3—42no—
103C3×C3⋊D3—42no—
104C3×C3⋊D3—91no—
105C3×C3⋊D3—91no—
106C3×C3⋊D3—364no—
107C3×C3⋊D3—364no—
108C3×C3⋊D3—724no—
109C3×C3⋊D3—724no—
110C3×C3⋊D3—724no—
111C3×C3⋊D3C2×#15711yescharacteristic
112C3×C3⋊D3C2×#15711yescharacteristic
113C32×D3—62no—
114C32×D3—62no—
115C32×D3—124no—
116C32×D3—124no—
117C32×D3—244no—
118C32×D3—244no—
119C4×Dic3—811no—
120C2×C3⋊D3—91no—
121C2×C3⋊D3—91no—
122C2×C3×D3—542no—
123C2×C3×D3—542no—
124D32—364no—
125#157—31no—
126#157—91no—
127#157—272no—
128#157—272no—
129#157—271no—
130#157—1084no—
131#157C3⋊#15711yescharacteristic, direct product factor
132C32×C4—91no—
133C32×C4—182no—
134C32×C4—271no—
135C32×C4—362no—
136C3⋊Dic3—91no—
137C3⋊Dic3—271no—
138C3⋊Dic3—542no—
139C3⋊Dic3—1082no—
140C3×Dic3—182no—
141C3×Dic3—542no—
142C33—22no—
143C33—22no—
144C33—44no—
145C33—44no—
146C33—42no—
147C33—42no—
148C33—84no—
149C33—84no—
150C33—84no—
151C33—84no—
152C33—84no—
153C33—84no—
154C33—164no—
155C33—164no—
156C33—164no—
157C33—168no—
158C33—164no—
159C33—164no—
160C33—168no—
161C33—168no—
162C33—1616no—
163C33C4×#15711yescharacteristic, complemented
164C33C4×#15711yescharacteristic, complemented
165C2×C3×C4—811no—
166C2×Dic3—811no—
167C2×Dic3—811no—
168C4×D3—542no—
169C4×D3—1622no—
170C2×C32—91no—
171C2×C32—91no—
172C2×C32—182no—
173C2×C32—182no—
174C2×C32—362no—
175C2×C32—362no—
176C3⋊D3—91no—
177C3⋊D3—91no—
178C3⋊D3—364no—
179C3⋊D3—364no—
180C3⋊D3—724no—
181C3⋊D3—724no—
182C3⋊D3—724no—
183C3⋊D3D3×#15711yescharacteristic
184C3⋊D3C2×C3⋊#15711yescharacteristic
185C3×D3—62no—
186C3×D3—62no—
187C3×D3—124no—
188C3×D3—124no—
189C3×D3—244no—
190C3×D3—244no—
191C3×D3—542no—
192C3×D3—542no—
193C3×D3—2164no—
194C42—2431noSylow
195C22×C3—811no—
196C2×D3—542no—
197C2×D3—542no—
198C3×C4—91no—
199C3×C4—182no—
200C3×C4—362no—
201C3×C4—542no—
202C3×C4—811no—
203Dic3—91no—
204Dic3—542no—
205Dic3—3242no—
206Dic3—811no—
207Dic3—812no—
208Dic3—1622no—
209C32—22no—
210C32—22no—
211C32—44no—
212C32—42no—
213C32—42no—
214C32—44no—
215C32—84no—
216C32—84no—
217C32—84no—
218C32—84no—
219C32—84no—
220C32—84no—
221C32—164no—
222C32—164no—
223C32—164no—
224C32—164no—
225C32—164no—
226C32—168no—
227C32—168no—
228C32—168no—
229C32—1616no—
230C32Dic3×#15711yescharacteristic, complemented
231C32C4×C3⋊#15711yescharacteristic, complemented
232C2×C4—811no—
233C2×C4—2431no—
234C2×C4—2431no—
235C2×C3—91no—
236C2×C3—91no—
237C2×C3—182no—
238C2×C3—182no—
239C2×C3—362no—
240C2×C3—362no—
241C2×C3—811no—
242D3—62no—
243D3—62no—
244D3—542no—
245D3—542no—
246D3—2164no—
247C22—811no—
248C4—91no—
249C4—271no—
250C4—811no—
251C4—2431no—
252C4—2432no—
253C3—22no—
254C3—22no—
255C3—42no—
256C3—42no—
257C3—84no—
258C3—164no—
259C3#157211yescharacteristic, complemented
260C2—91no—
261C2—91no—
262C2—811no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC35C42
prime radical, cosocleC3×C3⋊D32C22
LCSG ▷ C35
UCSC1

Complements

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

NH ≅ G/Ntype
6. C3⋊#66472C4semidirect
7. C3⋊(C3⋊(C3⋊#157))C4semidirect
8. C3×C3⋊(C3⋊#157)C4semidirect
9. C32×C3⋊#157C4semidirect
10. C33×#157C4semidirect
28. C3⋊(C3⋊#157)Dic3semidirect
34. C32×#157Dic3semidirect
35. C35C42semidirect
70. C3⋊#157#157direct (N × H)
75. C3×#157#157semidirect
86. C34C4×Dic3semidirect
131. #157C3⋊#157direct (N × H)
163. C33C4×#157semidirect
164. C33C4×#157semidirect
230. C32Dic3×#157semidirect
231. C32C4×C3⋊#157semidirect
259. C3#1572semidirect

Maximal subgroups

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

subgroupindex
#145195112
C3⋊D3×C3⋊#1572
C3×C3⋊D3×#1572
#15723
C4×C3⋊#1579
Dic3×#1579