Finite Group Databasebeta

← #11784640

Subgroups — #11784640

Order 1152.

2182 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 2182 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C22×D4×C3⋊D3C211yesmaximal, characteristic
2C2×#63788C214yesmaximal, complemented
3#10593802C212yesmaximal, complemented
4C24×C3⋊D3C412yes—
5C22×C32×D4C411yescharacteristic
6C22×#638C2212yes—
7C2×D4×C3⋊D3—28no—
8C2×D4×C3⋊D3—24no—
9C22×C4⋊(C3⋊D3)C411yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×#3792C2214yescomplemented
12#63788—28no—
13#63778—24no—
14C22×D3×D4—62no—
15C24×C32C2×C412yes—
16C23×C3⋊D3—24no—
17C23×C3⋊D3—24no—
18C23×C3⋊D3—24no—
19C23×C3⋊D3—48no—
20C23×C3⋊D3C2×C411yescharacteristic
21C23×C3⋊D3C2×C412yes—
22C2×C32×D4—24no—
23C2×C32×D4—22no—
24C22×C32×C4C2×C411yescharacteristic
25C2×#638—24no—
26C2×#638—24no—
27C2×#638D418yes—
28C22×C3⋊Dic3C2311yescharacteristic
29D4×C3⋊D3—232no—
30C2×C4⋊(C3⋊D3)—24no—
31C2×C4⋊(C3⋊D3)—22no—
32C2×C4×C3⋊D3—24no—
33C2×C4×C3⋊D3D414yes—
34#3792—28no—
35C2×#622—24no—
36#1783—91nomaximal, Sylow
37C24×D3—64no—
38C22×C3×D4—22no—
39C22×#67—64no—
40C2×D3×D4—616no—
41C2×D3×D4—632no—
42C22×D12—62no—
43C22×C4×D3—62no—
44C23×C32—22no—
45C23×C32—22no—
46C23×C32—44no—
47C23×C32C22⋊C414yes—
48C23×C32C22×C411yescharacteristic
49C22×C3⋊D3—22no—
50C22×C3⋊D3—24no—
51C22×C3⋊D3—216no—
52C22×C3⋊D3—22no—
53C22×C3⋊D3—22no—
54C22×C3⋊D3—416no—
55C22×C3⋊D3—416no—
56C22×C3⋊D3—48no—
57C22×C3⋊D3—48no—
58C22×C3⋊D3—44no—
59C22×C3⋊D3C22⋊C412yes—
60C22×C3⋊D3C22⋊C414yes—
61C32×D4—28no—
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C412yes—
64#638—216no—
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3C2×D414yes—
67C4⋊(C3⋊D3)—28no—
68C4×C3⋊D3—28no—
69#622—44no—
70C23×D4—91no—
71C2×#100—94no—
72#407—92no—
73C24×C3—24no—
74C23×D3—62no—
75C23×D3—64no—
76C23×D3—616no—
77C23×D3—616no—
78C23×D3—616no—
79C23×D3—1232no—
80C2×C3×D4—216no—
81C2×C3×D4—28no—
82C22×C3×C4—22no—
83C2×#67—616no—
84C2×#67—616no—
85C2×#67—616no—
86C22×Dic3—62no—
87D3×D4—6128no—
88C2×D12—616no—
89C2×D12—68no—
90C2×C4×D3—68no—
91C2×C4×D3—616no—
92C22×C32—22no—
93C22×C32—24no—
94C22×C32—44no—
95C22×C32—44no—
96C22×C32—44no—
97C22×C32C2×C22⋊C412yes—
98C22×C32C2×C22⋊C411yescharacteristic
99C2×C3⋊D3—28no—
100C2×C3⋊D3—22no—
101C2×C3⋊D3—22no—
102C2×C3⋊D3—24no—
103C2×C3⋊D3—432no—
104C2×C3⋊D3—44no—
105C2×C3⋊D3—44no—
106C2×C3⋊D3—44no—
107C2×C3⋊D3#10014yescomplemented
108C32×C4—22no—
109C3⋊Dic3#12014yes—
110C25—92no—
111C22×D4—92no—
112C22×D4—91no—
113C22×D4—184no—
114C22×D4—188no—
115C22×D4#15711yescharacteristic
116C23×C4—91no—
117C2×M16—94no—
118#100—188no—
119C22⋊C8—184no—
120C23×C3—28no—
121C23×C3—28no—
122C23×C3—22no—
123C23×C3—28no—
124C23×C3—416no—
125C22×D3—64no—
126C22×D3—68no—
127C22×D3—68no—
128C22×D3—616no—
129C22×D3—68no—
130C22×D3—68no—
131C22×D3—664no—
132C22×D3—1232no—
133C22×D3—1264no—
134C22×D3—1264no—
135C22×D3—1232no—
136C22×D3—1216no—
137C3×D4—232no—
138C2×C3×C4—28no—
139C2×C3×C4—24no—
140#67—664no—
141C2×Dic3—68no—
142C2×Dic3—64no—
143D12—632no—
144C4×D3—632no—
145C2×C32—22no—
146C2×C32—44no—
147C2×C32#37911yescharacteristic
148C2×C32C2×#10012yes—
149C3⋊D3—24no—
150C3⋊D3—44no—
151C24—91no—
152C24—92no—
153C24—184no—
154C24—184no—
155C24—184no—
156C24—368no—
157C24C2×#15712yes—
158C2×D4—24no—
159C2×D4—22no—
160C2×D4—98no—
161C2×D4—184no—
162C2×D4—184no—
163C2×D4—184no—
164C2×D4—1832no—
165C2×D4—182no—
166C22×C4—91no—
167C22×C4—94no—
168C22×C4—184no—
169C22×C4C2×#15711yescharacteristic
170M16—188no—
171C2×C8—184no—
172C22×C3—28no—
173C22×C3—216no—
174C22×C3—24no—
175C22×C3—22no—
176C22×C3—416no—
177C22×C3—416no—
178C22×C3—416no—
179C2×D3—68no—
180C2×D3—68no—
181C2×D3—632no—
182C2×D3—68no—
183C2×D3—616no—
184C2×D3—12128no—
185C2×D3—1216no—
186C2×D3—1216no—
187C2×D3—1216no—
188C3×C4—28no—
189Dic3—68no—
190C32#178311yescharacteristic, complemented, Sylow
191C23—22no—
192C23—22no—
193C23—44no—
194C23—92no—
195C23—94no—
196C23—184no—
197C23—1816no—
198C23—182no—
199C23—182no—
200C23—182no—
201C23—364no—
202C23—368no—
203C23—3616no—
204C23—3616no—
205C23—368no—
206C23C22⋊#15714yes—
207C23C22×#15711yescharacteristic
208D4—28no—
209D4—188no—
210D4—1816no—
211C2×C4—22no—
212C2×C4—94no—
213C2×C4—92no—
214C2×C4—188no—
215C2×C4C22⋊#15712yes—
216C8—364no—
217C2×C3—28no—
218C2×C3—24no—
219C2×C3—22no—
220C2×C3—416no—
221D3—616no—
222D3—1216no—
223C22—22no—
224C22—24no—
225C22—44no—
226C22—44no—
227C22—44no—
228C22—94no—
229C22—188no—
230C22—182no—
231C22—182no—
232C22—184no—
233C22—364no—
234C22—364no—
235C22—3632no—
236C22—364no—
237C22C2×C22⋊#15712yes—
238C22C2×C22⋊#15711yescharacteristic
239C4—22no—
240C4—94no—
241C3—22no—
242C2—22no—
243C2—44no—
244C2—184no—
245C2—364no—
246C2#1059382512yes—
247C2#1059384711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC22×C32×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×D4×C3⋊D3C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×D4#157
hypocenterC32#1783
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63788C2semidirect
3. #10593802C2semidirect
11. C2×#3792C22semidirect
107. C2×C3⋊D3#100semidirect
190. C32#1783semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C2×#637882
#105938022
#17839