Finite Group Databasebeta

← #11790757

Subgroups — #11790757

Order 1152.

910 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 78 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×#127C211yesmaximal, characteristic
2C2×#63782C214yesmaximal, complemented
3#10593736C211yesmaximal, characteristic, complemented
4#10593723C211yesmaximal, characteristic, complemented
5C2×D4×C3⋊D3—22no—
6C2×D4×C3⋊D3C2212yes—
7C2×C4⋊#157C2212yes—
8C2×#3787C2212yes—
9C32×#127C411yescharacteristic, complemented
10#64149—22no—
11#64149C412yescomplemented
12#64083C411yescharacteristic, complemented
13C42×C3⋊D3C2211yescharacteristic
14#63782—28no—
15#63781—22no—
16#63777—22no—
17D3×#127—62no—
18C23×C3⋊D3—22no—
19C22×#157—22no—
20C2×C32×D4—22no—
21C2×C32×D4C2×C412yes—
22C2×#638—24no—
23C2×#638—22no—
24D4×C3⋊D3—24no—
25D4×C3⋊D3—24no—
26D4×C3⋊D3—48no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)C2×C412yes—
29C2×C4×C3⋊D3D412yes—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#622—22no—
32C4⋊#157—24no—
33#3787—22no—
34#3787D414yescomplemented
35C32×C42C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D412yes—
38#1961—91nomaximal, Sylow
39C2×D3×D4—64no—
40C2×D3×D4—68no—
41C3×#127—22no—
42#940—64no—
43#940—68no—
44#874—62no—
45C42×D3—62no—
46C23×C32—22no—
47C22×C3⋊D3—22no—
48C22×C3⋊D3—42no—
49C22×C3⋊D3—42no—
50C22×C3⋊D3—48no—
51C22×C3⋊D3C2×D411yescharacteristic
52C2×#157—42no—
53C2×#157—44no—
54C32×D4—24no—
55C32×D4—44no—
56C2×C32×C4C22⋊C412yes—
57C2×C32×C4C22×C411yescharacteristic
58#638—48no—
59#638—44no—
60C2×C3⋊Dic3C22⋊C412yes—
61C2×C3⋊Dic3C2×D411yescharacteristic
62C4⋊(C3⋊D3)—24no—
63C4⋊(C3⋊D3)—44no—
64C4×C3⋊D3—24no—
65C4×C3⋊D3C2×D412yes—
66C4×C3⋊D3#4112yes—
67#622—24no—
68C2×#127—91no—
69C2×#102—94no—
70C2×#97—91no—
71#382—91no—
72C23×D3—68no—
73C2×C3×D4—28no—
74C2×C3×D4—24no—
75C2×#67—616no—
76C2×#67—68no—
77D3×D4—128no—
78D3×D4—128no—
79D3×D4—1232no—
80C2×D12—64no—
81C2×D12—68no—
82C2×C4×D3—64no—
83C2×C4×D3—62no—
84C3×C42—22no—
85C4×Dic3—62no—
86C4×Dic3—64no—
87C22×C32—42no—
88C22×C32—44no—
89C22×C32C2×C22⋊C411yescharacteristic
90C2×C3⋊D3—42no—
91C2×C3⋊D3—44no—
92C2×C3⋊D3—84no—
93C2×C3⋊D3—84no—
94C2×C3⋊D3#12411yescharacteristic
95C2×C3⋊D3#12711yescharacteristic
96C2×C3⋊D3AGL(1,ℤ/8)14yes—
97#157—82no—
98C32×C4—22no—
99C32×C4C4×D412yes—
100C3⋊Dic3—22no—
101C3⋊Dic3#12112yes—
102C22×D4—92no—
103C22×D4—182no—
104C22×C8—92no—
105#127—92no—
106#127—91no—
107#127—182no—
108#127#15711yescharacteristic, complemented
109C2×C4⋊C4—92no—
110C2×C42—91no—
111#102—188no—
112#97—182no—
113#95—182no—
114C23×C3—28no—
115C22×D3—62no—
116C22×D3—68no—
117C22×D3—128no—
118C22×D3—128no—
119C22×D3—1232no—
120C3×D4—48no—
121C3×D4—416no—
122C2×C3×C4—22no—
123C2×C3×C4—24no—
124#67—1216no—
125#67—1232no—
126C2×Dic3—64no—
127C2×Dic3—62no—
128D12—128no—
129D12—1216no—
130C4×D3—64no—
131C4×D3—64no—
132C4×D3—616no—
133C2×C32—82no—
134C2×C32#39011yescharacteristic
135C2×C32#41812yes—
136C3⋊D3—82no—
137C3⋊D3#49012yes—
138C3⋊D3#49612yes—
139C24—182no—
140C2×D4—22no—
141C2×D4—92no—
142C2×D4—184no—
143C2×D4—184no—
144C2×D4—184no—
145C2×D4—182no—
146C2×D4—182no—
147C2×D4—368no—
148C2×D4C2×#15712yes—
149C22×C4—91no—
150C22×C4—92no—
151C22×C4—182no—
152C2×C8—94no—
153C2×C8—182no—
154C2×C8—182no—
155C4⋊C4—184no—
156C42—91no—
157C42—92no—
158C42C2×#15711yescharacteristic
159C22×C3—22no—
160C22×C3—416no—
161C22×C3—48no—
162C2×D3—62no—
163C2×D3—62no—
164C2×D3—68no—
165C2×D3—1216no—
166C2×D3—128no—
167C2×D3—2416no—
168C2×D3—2416no—
169C3×C4—28no—
170C3×C4—24no—
171Dic3—64no—
172Dic3—68no—
173C32#196111yescharacteristic, complemented, Sylow
174C23—22no—
175C23—91no—
176C23—182no—
177C23—362no—
178C23—362no—
179C23—368no—
180D4—24no—
181D4—44no—
182D4—184no—
183D4—364no—
184D4—364no—
185D4—368no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—92no—
189C2×C4—92no—
190C2×C4—184no—
191C2×C4—362no—
192C2×C4—364no—
193C2×C4C22⋊#15712yes—
194C2×C4C22×#15711yescharacteristic
195C8—184no—
196C2×C3—24no—
197C2×C3—22no—
198C2×C3—88no—
199D3—64no—
200D3—64no—
201D3—248no—
202C22—44no—
203C22—42no—
204C22—94no—
205C22—91no—
206C22—91no—
207C22—364no—
208C22—362no—
209C22—724no—
210C22—724no—
211C22C2×C22⋊#15711yescharacteristic
212C4—22no—
213C4—92no—
214C4—182no—
215C4—722no—
216C4D4×#15712yes—
217C3—22no—
218C2—82no—
219C2—92no—
220C2—92no—
221C2—722no—
222C2#1059381412yes—
223C2#1059382711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#127C4
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#127C2
cosocleC2×C4×C3⋊D3C23
hypercenter#127#157
hypocenterC32#1961
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C2×#63782C2semidirect
3. #10593736C2semidirect
4. #10593723C2semidirect
9. C32×#127C4semidirect
11. #64149C4semidirect
12. #64083C4semidirect
34. #3787D4semidirect
108. #127#157semidirect
173. C32#1961semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1272
C2×#637822
#105937362
#105937232
#19619