Finite Group Databasebeta

← #11777345

Subgroups — #11777345

Order 1152.

326 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 64 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
1D4×#622C211yesmaximal, characteristic, complemented
2#10593749C211yesmaximal, characteristic, complemented
3#10592455C211yesmaximal, characteristic
4D4⋊#622C211yesmaximal, characteristic, complemented
5#10590172C211yesmaximal, characteristic, complemented
6#10590168C211yesmaximal, characteristic, complemented
7#10590160C211yesmaximal, characteristic, complemented
8C22×#622—21no—
9C2×#3787—21no—
10D4×C3⋊Dic3C2211yescharacteristic
11C2×#3753C411yescharacteristic
12#64102C2211yescharacteristic
13C22⋊#622—21no—
14#63778—21no—
15C4⋊#622C2211yescharacteristic
16C4⋊#622C2211yescharacteristic
17C4×#622C2211yescharacteristic
18C4×#622C2211yescharacteristic
19C32×#102C411yescharacteristic
20#63648C411yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22#63634C411yescharacteristic
23#4756—62no—
24C2×C32×D4C2×C411yescharacteristic
25C22×C3⋊Dic3—21no—
26C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—21no—
31C2×#622—42no—
32C2×#622D411yescharacteristic
33C2×#622D411yescharacteristic
34#3787—42no—
35C2×C32×C8C2×C411yescharacteristic
36C32×C4⋊C4C2×C411yescharacteristic
37#3757—21no—
38#3753C814yescomplemented
39#3752—21no—
40C4⋊(C3⋊Dic3)C2×C411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
43#1580—91nomaximal, Sylow
44D4×Dic3—62no—
45C2×#213—62no—
46#893—62no—
47C3×#102—22no—
48#821—62no—
49C8×Dic3—62no—
50#807—62no—
51C23×C32—21no—
52C22×C3⋊D3—21no—
53C32×D4—21no—
54C32×D4C2×C812yescomplemented
55C2×C32×C4—21no—
56C2×C32×C4C22×C411yescharacteristic
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4111yescharacteristic
62C4⋊(C3⋊D3)—21no—
63C4⋊(C3⋊D3)C2×C812yescomplemented
64C4×C3⋊D3—41no—
65C4×C3⋊D3—41no—
66#622—21no—
67#622—21no—
68#622—41no—
69#622—41no—
70#622—41no—
71C32×C8—21no—
72C3⋊(C3⋊C8)C2×C812yescomplemented
73C4×D8—91no—
74C8×D4—91no—
75C8×D4—91no—
76#334—91no—
77D4⋊C8—91no—
78D4⋊C8—91no—
79#322—91no—
80C2×C3×D4—22no—
81C22×Dic3—122no—
82C2×D12—62no—
83C2×C4×D3—122no—
84C2×C3×C8—22no—
85C3×C4⋊C4—22no—
86#217—122no—
87#213—68no—
88(C2×D3)⋊C4—122no—
89C4⋊Dic3—62no—
90C4×Dic3—62no—
91C2×C3⋊C8—62no—
92C22×C32—22no—
93C22×C32—41no—
94C22×C32—41no—
95C22×C32C4×D411yescharacteristic
96C2×C3⋊D3—22no—
97C2×C3⋊D3—41no—
98C2×C3⋊D3—41no—
99C32×C4—41no—
100C32×C4C22×C811yescharacteristic
101C32×C4#13111yescharacteristic
102C3⋊Dic3—21no—
103C3⋊Dic3—41no—
104C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
105C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
106C2×D8—91no—
107C22×C8—181no—
108C22×C8—181no—
109C4×D4—91no—
110C4×D4—91no—
111#107—91no—
112C4⋊C8—91no—
113C4⋊C8—91no—
114#102—91no—
115#102#15711yescharacteristic
116C22⋊C8—181no—
117C22⋊C8—181no—
118C4×C8—91no—
119C4×C8—91no—
120C4×C8—91no—
121C23×C3—42no—
122C22×D3—122no—
123C3×D4—24no—
124C3×D4—42no—
125C2×C3×C4—22no—
126C2×C3×C4—42no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129C2×Dic3—122no—
130C2×Dic3—242no—
131C2×Dic3—242no—
132D12—64no—
133D12—122no—
134C4×D3—242no—
135C4×D3—242no—
136C3×C8—42no—
137C3⋊C8—64no—
138C2×C32—42no—
139C2×C32C8×D411yescharacteristic
140C2×C32#44211yescharacteristic
141C2×C32#44411yescharacteristic
142C3⋊D3—42no—
143C2×D4—91no—
144C2×D4C2×#15711yescharacteristic
145C22×C4—181no—
146C22×C4—181no—
147D8—94no—
148C2×C8—91no—
149C2×C8—91no—
150C2×C8—91no—
151C2×C8—181no—
152C2×C8—181no—
153C2×C8—181no—
154C2×C8—362no—
155C2×C8—362no—
156C2×C8C2×#15711yescharacteristic
157C4⋊C4—91no—
158C4⋊C4C2×#15711yescharacteristic
159C22⋊C4—181no—
160C22⋊C4—181no—
161C42—91no—
162C22×C3—22no—
163C22×C3—44no—
164C22×C3—82no—
165C22×C3—82no—
166C2×D3—124no—
167C2×D3—242no—
168C2×D3—242no—
169C3×C4—22no—
170C3×C4—22no—
171C3×C4—82no—
172Dic3—62no—
173Dic3—62no—
174Dic3—122no—
175Dic3—242no—
176C32#158011yescharacteristic, complemented, Sylow
177C23—21no—
178C23—181no—
179D4—21no—
180D4—92no—
181D4—181no—
182D4#378712yescomplemented
183C2×C4—21no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—181no—
187C2×C4—361no—
188C2×C4—361no—
189C2×C4—361no—
190C2×C4—361no—
191C2×C4C22×#15711yescharacteristic
192C8—21no—
193C8—92no—
194C8—181no—
195C8—181no—
196C8—361no—
197C8—361no—
198C8—361no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202C2×C3—84no—
203D3—244no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—182no—
208C22—361no—
209C22—361no—
210C22D4×#15711yescharacteristic
211C4—41no—
212C4—91no—
213C4—91no—
214C4—181no—
215C4—361no—
216C4C2×#378711yescharacteristic
217C4#6428711yescharacteristic
218C3—22no—
219C2—42no—
220C2—362no—
221C2#1059373911yescharacteristic
222C2#1059377811yescharacteristic
223C2#1059378411yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×#102C4
socleC22×C32C4×D4
prime radicalC2×#3753C4
cosocleC4×C3⋊Dic3C23
hypercenter#102#157
hypocenterC32#1580
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#622C2semidirect
2. #10593749C2semidirect
4. D4⋊#622C2semidirect
5. #10590172C2semidirect
6. #10590168C2semidirect
7. #10590160C2semidirect
38. #3753C8semidirect
54. C32×D4C2×C8semidirect
63. C4⋊(C3⋊D3)C2×C8semidirect
72. C3⋊(C3⋊C8)C2×C8semidirect
176. C32#1580semidirect
182. D4#3787semidirect

Maximal subgroups

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

subgroupindex
D4×#6222
#105937492
#105924552
D4⋊#6222
#105901722
#105901682
#105901602
#15809