Finite Group Databasebeta

← #11784195

Subgroups — #11784195

Order 1152.

550 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×#63779C212yesmaximal
2C2×#63777C212yesmaximal
3C42×C3⋊Dic3C211yesmaximal, characteristic
4#10590207C212yesmaximal
5C22×#622C2214yes—
6C2×C32×C42C411yescharacteristic
7C2×C4×C3⋊Dic3C411yescharacteristic
8C2×C4×C3⋊Dic3C411yescharacteristic
9C2×C4×C3⋊Dic3C411yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#63779C418yescomplemented
14#63777—24no—
15C42×Dic3—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C32×C4C2×C411yescharacteristic
18C22×C32×C4C2×C411yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C2×#622—24no—
24C2×#622—24no—
25C2×#622C2×C418yes—
26C32×C42—22no—
27C4×C3⋊Dic3—22no—
28C4×C3⋊Dic3—22no—
29C4×C3⋊Dic3—22no—
30C4×C3⋊Dic3—22no—
31C4×C3⋊Dic3C2×C414yes—
32C4×C3⋊Dic3D412yes—
33C4×C3⋊Dic3Q812yes—
34#1767—91nomaximal, Sylow
35C2×C3×C42—22no—
36C2×C4×Dic3—62no—
37C2×C4×Dic3—62no—
38C2×C4×Dic3—62no—
39C2×C4×Dic3—62no—
40C2×C4×Dic3—62no—
41C2×C4×Dic3—62no—
42C23×C32C22×C411yescharacteristic
43C2×C32×C4—21no—
44C2×C32×C4—21no—
45C2×C32×C4—21no—
46C2×C32×C4—21no—
47C2×C32×C4—21no—
48C2×C32×C4—21no—
49C2×C32×C4C4212yes—
50C2×C32×C4C4⋊C412yes—
51C2×C32×C4M1612yes—
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3C4212yes—
57C2×C3⋊Dic3C4⋊C412yes—
58C2×C3⋊Dic3M1612yes—
59C2×C3⋊Dic3M1612yes—
60C2×C3⋊Dic3M1612yes—
61C2×C3⋊Dic3C22×C412yes—
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3C2×Q811yescharacteristic
64C2×C3⋊Dic3#4112yes—
65#622—28no—
66C2×C4⋊C8—92no—
67C2×#97—92no—
68C43—91no—
69#336—92no—
70C22×C3×C4—22no—
71C22×C3×C4—22no—
72C22×C3×C4—22no—
73C22×Dic3—62no—
74C22×Dic3—62no—
75C22×Dic3—62no—
76C22×Dic3—62no—
77C3×C42—28no—
78C4×Dic3—68no—
79C4×Dic3—64no—
80C4×Dic3—64no—
81C4×Dic3—68no—
82C4×Dic3—68no—
83C4×Dic3—68no—
84C4×Dic3—68no—
85C22×C32C2×C4211yescharacteristic
86C22×C32C2×C4⋊C411yescharacteristic
87C22×C32#11711yescharacteristic
88C22×C32C2×M1611yescharacteristic
89C22×C32C2×M1611yescharacteristic
90C22×C32C2×M1611yescharacteristic
91C22×C32C2×M1611yescharacteristic
92C32×C4—22no—
93C32×C4—22no—
94C32×C4—22no—
95C3⋊Dic3—22no—
96C3⋊Dic3—22no—
97C3⋊Dic3#9714yescomplemented
98C3⋊Dic3C4×D412yes—
99C3⋊Dic3C4×Q812yes—
100C22×C8—94no—
101C2×C42—91no—
102C2×C42—91no—
103C2×C42—91no—
104C2×C42—91no—
105C2×C42—91no—
106C2×C42—91no—
107C2×C42#15711yescharacteristic
108C4⋊C8—98no—
109#97—184no—
110C23×C3—22no—
111C2×C3×C4—24no—
112C2×C3×C4—24no—
113C2×C3×C4—24no—
114C2×C3×C4—24no—
115C2×C3×C4—24no—
116C2×C3×C4—24no—
117C2×C3×C4—24no—
118C2×C3×C4—24no—
119C2×C3×C4—24no—
120C2×Dic3—64no—
121C2×Dic3—64no—
122C2×Dic3—64no—
123C2×Dic3—64no—
124C2×Dic3—64no—
125C2×Dic3—64no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—64no—
131C2×Dic3—64no—
132C2×Dic3—64no—
133C2×C32C4×C4⋊C411yescharacteristic
134C2×C32C2×#9711yescharacteristic
135C2×C32C4×M1611yescharacteristic
136C2×C32#42311yescharacteristic
137C2×C32#42311yescharacteristic
138C2×C32#43211yescharacteristic
139C2×C32#43211yescharacteristic
140C22×C4—91no—
141C22×C4—91no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4C2×#15711yescharacteristic
145C22×C4C2×#15711yescharacteristic
146C22×C4C2×#15711yescharacteristic
147C2×C8—98no—
148C2×C8—184no—
149C2×C8—184no—
150C42—22no—
151C42—94no—
152C42—92no—
153C42—92no—
154C42—182no—
155C42—182no—
156C42—182no—
157C42—182no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—22no—
165C3×C4—28no—
166C3×C4—28no—
167C3×C4—28no—
168Dic3—68no—
169Dic3—64no—
170Dic3—64no—
171Dic3—68no—
172Dic3—68no—
173C32#176711yescharacteristic, complemented, Sylow
174C23C22×#15711yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—92no—
182C2×C4—92no—
183C2×C4—92no—
184C2×C4—92no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—92no—
189C2×C4—92no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—181no—
193C2×C4—181no—
194C2×C4C4×#15712yes—
195C2×C4C4⋊#15712yes—
196C2×C4#379212yes—
197C8—188no—
198C2×C3—22no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202C2×C3—22no—
203C2×C3—22no—
204C2×C3—22no—
205C22#6428311yescharacteristic
206C22#6428311yescharacteristic
207C22#6428311yescharacteristic
208C22C2×C4×#15711yescharacteristic
209C22C2×C4⋊#15711yescharacteristic
210C22#6428611yescharacteristic
211C22C2×#379211yescharacteristic
212C4—22no—
213C4—22no—
214C4—22no—
215C4—94no—
216C4—92no—
217C4—92no—
218C4—182no—
219C4—182no—
220C3—22no—
221C2#1059372311yescharacteristic
222C2#1059372911yescharacteristic
223C2#1059373111yescharacteristic
224C2C4×C4⋊#15711yescharacteristic
225C2C4×#379211yescharacteristic
226C2#1059380411yescharacteristic
227C2#1059380511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C42C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32#1767
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
13. #63779C4semidirect
97. C3⋊Dic3#97semidirect
173. C32#1767semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C2×#637772
C42×C3⋊Dic32
#105902072
#17679