Finite Group Databasebeta

← #11777384

Subgroups — #11777384

Order 1152.

316 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 58 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#10593821C211yesmaximal, characteristic, complemented
2D4×#622C211yesmaximal, characteristic, complemented
3D8×C3⋊Dic3C211yesmaximal, characteristic
4D4⋊#622C211yesmaximal, characteristic, complemented
5D4⋊#622C211yesmaximal, characteristic, complemented
6#10590173C211yesmaximal, characteristic, complemented
7#10590169C211yesmaximal, characteristic, complemented
8C2×#3792—21no—
9C22×#622—21no—
10C2×C32×D8C411yescharacteristic
11D4×C3⋊Dic3C2211yescharacteristic
12D4×C3⋊Dic3C2211yescharacteristic
13C22⋊#622—21no—
14C22⋊#622—21no—
15C4⋊#622C2211yescharacteristic
16C4⋊#622C2211yescharacteristic
17C4×#622C2211yescharacteristic
18C4×#622C2211yescharacteristic
19#63659C411yescharacteristic
20#63659C411yescharacteristic
21#63645C411yescharacteristic
22C8×C3⋊Dic3C2211yescharacteristic
23Dic3×D8—62no—
24C2×C32×D4C2×C411yescharacteristic
25C2×C32×D4C2×C411yescharacteristic
26C22×C3⋊Dic3—21no—
27C22×C3⋊Dic3—21no—
28#3792—42no—
29C2×#622—21no—
30C2×#622—21no—
31C2×#622—21no—
32C2×#622—42no—
33C2×#622D411yescharacteristic
34C2×#622D411yescharacteristic
35C32×D8—22no—
36C2×C32×C8C2×C411yescharacteristic
37#3757—21no—
38#3757—21no—
39C4⋊(C3⋊Dic3)C2×C411yescharacteristic
40C4⋊(C3⋊Dic3)C2×C411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
43#1581—91nomaximal, Sylow
44C2×C3×D8—22no—
45D4×Dic3—62no—
46D4×Dic3—62no—
47#832—62no—
48#832—62no—
49#818—62no—
50C8×Dic3—62no—
51C23×C32—21no—
52C23×C32—21no—
53C32×D4—21no—
54C32×D4—21no—
55C32×D4—21no—
56C32×D4M1612yescomplemented
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3—21no—
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3—41no—
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3#4111yescharacteristic
66#622—21no—
67#622—41no—
68#622—41no—
69#622—41no—
70#622D812yescomplemented
71C32×C8—21no—
72C3⋊(C3⋊C8)—21no—
73C4×D8—91no—
74#436—91no—
75C8×D4—91no—
76#335—91no—
77D4⋊C8—91no—
78D4⋊C8—91no—
79#322—91no—
80C2×C3×D4—22no—
81C2×C3×D4—22no—
82C22×Dic3—122no—
83C22×Dic3—122no—
84C3×D8—28no—
85C2×C3×C8—22no—
86#217—122no—
87#217—122no—
88C4⋊Dic3—62no—
89C4⋊Dic3—62no—
90C4×Dic3—62no—
91C2×C3⋊C8—62no—
92C22×C32—22no—
93C22×C32—41no—
94C22×C32—41no—
95C22×C32—41no—
96C22×C32—41no—
97C22×C32—41no—
98C22×C32C4×D411yescharacteristic
99C32×C4C2×M1611yescharacteristic
100C32×C4#13111yescharacteristic
101C3⋊Dic3—21no—
102C3⋊Dic3—41no—
103C3⋊Dic3—41no—
104C3⋊Dic3C2×D811yescharacteristic
105C3⋊Dic3#13511yescharacteristic
106C2×D8#15711yescharacteristic
107C2×M16—181no—
108C22×C8—181no—
109C4×D4—91no—
110C4×D4—91no—
111#107—91no—
112C4⋊C8—91no—
113C4⋊C8—91no—
114#102—91no—
115#102—91no—
116C22⋊C8—181no—
117C22⋊C8—181no—
118C4×C8—91no—
119C4×C8—91no—
120C4×C8—91no—
121C23×C3—42no—
122C23×C3—42no—
123C3×D4—24no—
124C3×D4—24no—
125C3×D4—42no—
126C3×D4—42no—
127C2×C3×C4—22no—
128C2×Dic3—62no—
129C2×Dic3—62no—
130C2×Dic3—122no—
131C2×Dic3—122no—
132C2×Dic3—242no—
133C2×Dic3—242no—
134C2×Dic3—242no—
135C2×Dic3—242no—
136C3×C8—24no—
137C3⋊C8—122no—
138C2×C32—42no—
139C2×C32—81no—
140C2×C32#43511yescharacteristic
141C2×C32C4×D811yescharacteristic
142C2×C32#44411yescharacteristic
143C2×D4C2×#15711yescharacteristic
144C2×D4C2×#15711yescharacteristic
145C22×C4—181no—
146C22×C4—181no—
147D8—22no—
148M16—362no—
149C2×C8—91no—
150C2×C8—91no—
151C2×C8—91no—
152C2×C8—181no—
153C2×C8—181no—
154C2×C8—181no—
155C2×C8—362no—
156C2×C8C2×#15711yescharacteristic
157C4⋊C4—91no—
158C4⋊C4—91no—
159C22⋊C4—181no—
160C22⋊C4—181no—
161C42—91no—
162C22×C3—22no—
163C22×C3—44no—
164C22×C3—44no—
165C22×C3—82no—
166C22×C3—82no—
167C22×C3—82no—
168C22×C3—82no—
169C3×C4—22no—
170C3×C4—22no—
171Dic3—62no—
172Dic3—62no—
173Dic3—122no—
174Dic3—242no—
175Dic3—242no—
176C32#158111yescharacteristic, complemented, Sylow
177C23—21no—
178C23—21no—
179D4—21no—
180D4—21no—
181D4—21no—
182D4#379212yescomplemented
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—181no—
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—
203C2×C3—84no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22D4×#15711yescharacteristic
211C4—91no—
212C4—91no—
213C4—181no—
214C4—361no—
215C4—361no—
216C4#6428711yescharacteristic
217C4C2×#379211yescharacteristic
218C3—22no—
219C2—42no—
220C2—81no—
221C2D8×#15711yescharacteristic
222C2#1059378011yescharacteristic
223C2#1059382011yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
Fitting, prime radicalC2×C32×D8C4
socleC22×C32C4×D4
cosocleC4×C3⋊Dic3C23
hypercenterC2×D8#157
hypocenterC32#1581
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10593821C2semidirect
2. D4×#622C2semidirect
4. D4⋊#622C2semidirect
5. D4⋊#622C2semidirect
6. #10590173C2semidirect
7. #10590169C2semidirect
56. C32×D4M16semidirect
70. #622D8semidirect
176. C32#1581semidirect
182. D4#3792semidirect

Maximal subgroups

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

subgroupindex
#105938212
D4×#6222
D8×C3⋊Dic32
D4⋊#6222
#105901732
#105901692
#15819