Finite Group Databasebeta

← #125×#157 #11802478

Subgroups — #125×#157 #11802478

Order 1152.

710 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 182 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⋊D3×#125C211yesmaximal, characteristic
2#10593759C212yesmaximal
3#10593758C214yesmaximal
4C4⋊C4×#157C214yesmaximal
5C4⋊C4×#157C212yesmaximal
6#10593736C211yesmaximal, characteristic
7C42×#157C211yesmaximal, characteristic
8C2×C4⋊#157C2212yes—
9C2×C4⋊#157C2214yes—
10C2×C4×#157C2212yes—
11C2×C4×#157C2212yes—
12C2×C4×#157C2211yescharacteristic
13C2×C4×#157C2214yes—
14C2×C4×#157C2211yescharacteristic
15C32×#125C411yescharacteristic, complemented
16C4⋊C4×C3⋊D3C2214yes—
17C4⋊C4×C3⋊D3C2212yes—
18#64099C412yescomplemented
19#64098C414yescomplemented
20C42×C3⋊D3C2211yescharacteristic
21#64079C411yescharacteristic, complemented
22#63781C2214yes—
23#63781C2214yes—
24#63781C2214yes—
25D3×#125—62no—
26C22×#157C2314yes—
27C22×#157C2311yescharacteristic
28C22×#157C2312yes—
29C22×#157C2311yescharacteristic
30C2×C4×C3⋊D3C2312yes—
31C2×C4×C3⋊D3C2314yes—
32C2×C4×C3⋊D3C2311yescharacteristic
33C4⋊#157—28no—
34C4⋊#157—24no—
35C4×#157—24no—
36C4×#157—24no—
37C4×#157—28no—
38C4×#157—22no—
39C4×#157Q814yes—
40C32×C4⋊C4C2×C414yes—
41C32×C4⋊C4C2×C412yes—
42C32×C42C2×C411yescharacteristic
43C4⋊(C3⋊Dic3)C2×C412yes—
44C4⋊(C3⋊Dic3)C2×C414yes—
45#3750C2×C414yes—
46#3750C2×C414yes—
47#3750C2×C414yes—
48C4×C3⋊Dic3C2×C412yes—
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×#125—91nomaximal, Sylow
51C3×#125—22no—
52D3×C4⋊C4—68no—
53D3×C4⋊C4—64no—
54#890—64no—
55#889—68no—
56C42×D3—62no—
57#870—62no—
58C22×C3⋊D3C2411yescharacteristic
59C2×#157—22no—
60C2×#157—22no—
61C2×#157—22no—
62C2×#157—24no—
63C2×#157—24no—
64C2×#157—24no—
65C2×#157C2×Q812yes—
66C2×#157C2×Q812yes—
67C2×#157#4114yes—
68C2×#157#4114yes—
69C2×C32×C4C22×C412yes—
70C2×C32×C4C22×C414yes—
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3C22×C412yes—
73C2×C3⋊Dic3C22×C414yes—
74C2×C3⋊Dic3C22×C411yescharacteristic
75C4×C3⋊D3—22no—
76C4×C3⋊D3—24no—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—24no—
79C4×C3⋊D3C2×Q812yes—
80C4×C3⋊D3#4112yes—
81C2×#125—91no—
82#389—92no—
83#387—94no—
84#382—91no—
85C4×C4⋊C4—94no—
86C4×C4⋊C4—92no—
87C43—91no—
88C2×C4×D3—62no—
89C2×C4×D3—64no—
90C2×C4×D3—68no—
91C3×C4⋊C4—28no—
92C3×C4⋊C4—24no—
93C3×C42—22no—
94C4⋊Dic3—64no—
95C4⋊Dic3—68no—
96Dic3⋊C4—68no—
97Dic3⋊C4—68no—
98Dic3⋊C4—68no—
99C4×Dic3—64no—
100C4×Dic3—62no—
101C22×C32C23×C411yescharacteristic
102C2×C3⋊D3C22×Q811yescharacteristic
103C2×C3⋊D3C2×#4112yes—
104C2×C3⋊D3C2×#4111yescharacteristic
105C2×C3⋊D3C2×#4112yes—
106#157—24no—
107#157—22no—
108#157—44no—
109#157#12514yesdirect product factor
110C32×C4—22no—
111C32×C4—24no—
112C32×C4C4×Q812yes—
113C3⋊Dic3—22no—
114C3⋊Dic3—24no—
115C3⋊Dic3C4×Q812yes—
116#125—94no—
117#125—92no—
118#125—91no—
119#125#15711yescharacteristic, direct product factor
120C2×C4⋊C4—94no—
121C2×C4⋊C4—92no—
122C2×C4⋊C4—92no—
123C2×C4⋊C4—94no—
124C2×C42—91no—
125C2×C42—91no—
126C2×C42—92no—
127C2×C42—92no—
128C2×C42—91no—
129C2×C42—94no—
130#95—94no—
131#95—94no—
132#95—94no—
133C22×D3—62no—
134C2×C3×C4—22no—
135C2×C3×C4—24no—
136C2×C3×C4—28no—
137C2×Dic3—62no—
138C2×Dic3—64no—
139C2×Dic3—68no—
140C4×D3—64no—
141C4×D3—64no—
142C4×D3—124no—
143C4×D3—124no—
144C4×D3—128no—
145C4×D3—128no—
146C2×C32C2×C4×Q811yescharacteristic
147C2×C32C4×#4112yes—
148C3⋊D3C2×#12511yescharacteristic
149C3⋊D3#52912yes—
150C3⋊D3#53311yescharacteristic
151C22×C4—91no—
152C22×C4—91no—
153C22×C4—91no—
154C22×C4—92no—
155C22×C4—92no—
156C22×C4—94no—
157C22×C4—94no—
158C4⋊C4—94no—
159C4⋊C4—94no—
160C4⋊C4—94no—
161C4⋊C4—94no—
162C4⋊C4—92no—
163C4⋊C4—184no—
164C4⋊C4—188no—
165C4⋊C4C2×#15714yes—
166C4⋊C4C2×#15712yes—
167C42—94no—
168C42—92no—
169C42—91no—
170C42—184no—
171C42—188no—
172C42—182no—
173C42—184no—
174C42C2×#15711yescharacteristic
175C22×C3—22no—
176C2×D3—62no—
177C2×D3—62no—
178C2×D3—64no—
179C2×D3—64no—
180C3×C4—24no—
181C3×C4—44no—
182C3×C4—48no—
183Dic3—64no—
184Dic3—124no—
185Dic3—128no—
186C32C4×#12511yescharacteristic, complemented, Sylow
187C23—91no—
188C2×C4—92no—
189C2×C4—94no—
190C2×C4—91no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—92no—
194C2×C4—94no—
195C2×C4—92no—
196C2×C4—94no—
197C2×C4—182no—
198C2×C4—182no—
199C2×C4—184no—
200C2×C4—184no—
201C2×C4—182no—
202C2×C4—182no—
203C2×C4—182no—
204C2×C4—184no—
205C2×C4—184no—
206C2×C4—184no—
207C2×C4C22×#15712yes—
208C2×C4C22×#15714yes—
209C2×C4C22×#15711yescharacteristic
210C2×C3—22no—
211C2×C3—24no—
212D3—62no—
213D3—64no—
214D3—62no—
215C22—91no—
216C22—91no—
217C22—92no—
218C22—92no—
219C22C23×#15711yescharacteristic
220C4—22no—
221C4—24no—
222C4—94no—
223C4—92no—
224C4—184no—
225C4—182no—
226C4—182no—
227C4—184no—
228C4—364no—
229C4Q8×#15712yes—
230C3—22no—
231C2—91no—
232C2—92no—
233C2—91no—
234C2C2×Q8×#15711yescharacteristic
235C2#41×#15712yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#125C4
prime radical, cosocleC22×C3⋊D3C24
hypercenter#125#157
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
15. C32×#125C4semidirect
18. #64099C4semidirect
19. #64098C4semidirect
21. #64079C4semidirect
109. #157#125direct (N × H)
119. #125#157direct (N × H)
186. C32C4×#125semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
#105937592
#105937582
C4⋊C4×#1572
#105937362
C42×#1572
C4×#1259