Finite Group Databasebeta

← #11773823

Subgroups — #11773823

Order 1152.

372 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 100 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×#63449C211yesmaximal, characteristic
2#10588398C212yesmaximal
3C9×#324C211yesmaximal, characteristic
4#10588205C211yesmaximal, characteristic
5#10588145C212yesmaximal
6#68125—31nomaximal
7C22×Dic18C411yescharacteristic
8C2×C9×C4⋊C4C2211yescharacteristic
9C2×Dic9⋊C4C411yescharacteristic
10C2×Dic9⋊C4C2211yescharacteristic
11C2×C4×Dic9C411yescharacteristic
12C2×C4×Dic9C411yescharacteristic
13C2×C4×Dic9C2211yescharacteristic
14#63449—22no—
15#63449—22no—
16C9×C22⋊C8C2212yes—
17#63389C2212yes—
18Dic9⋊C8—22no—
19C8×Dic9—22no—
20C2×#887—31no—
21#4718—32no—
22C3×#324D311yescharacteristic
23#4528—31no—
24#4469—32no—
25C22×C4×C9C2×C411yescharacteristic
26C22×C4×C9C2×C411yescharacteristic
27C22×C4×C9C2311yescharacteristic
28C22×Dic9C2×C411yescharacteristic
29C22×Dic9C2×C411yescharacteristic
30C22×Dic9C2×C411yescharacteristic
31C22×Dic9C2×C411yescharacteristic
32C2×Dic18—22no—
33C2×Dic18—22no—
34C2×Dic18C814yescomplemented
35C2×C8×C9—22no—
36C9×C4⋊C4—22no—
37Dic9⋊C4—22no—
38Dic9⋊C4—22no—
39C4×Dic9—21no—
40C4×Dic9—21no—
41C4×Dic9—21no—
42C4×Dic9—21no—
43C4×Dic9D412yes—
44C4×Dic9D412yes—
45C2×C9⋊C8—22no—
46#1461—91noSylow
47C22×Dic6—31no—
48C2×C3×C4⋊C4C2×D311yescharacteristic
49C2×Dic3⋊C4—31no—
50C2×Dic3⋊C4—31no—
51C2×C4×Dic3—31no—
52C2×C4×Dic3—31no—
53C2×C4×Dic3—31no—
54#887—62no—
55#887—62no—
56C3×C22⋊C8C2×D312yes—
57#830—32no—
58Dic3⋊C8—62no—
59C8×Dic3—62no—
60C23×C9C22×C411yescharacteristic
61C2×C4×C9—21no—
62C2×C4×C9—21no—
63C2×C4×C9—21no—
64C2×C4×C9—41no—
65C2×C4×C9—41no—
66C2×C4×C9C2×C812yes—
67C2×C4×C9C2×D412yes—
68C2×Dic9—21no—
69C2×Dic9—21no—
70C2×Dic9—22no—
71C2×Dic9—21no—
72C2×Dic9—41no—
73C2×Dic9C22⋊C411yescharacteristic
74C2×Dic9C22⋊C412yes—
75C2×Dic9C22⋊C411yescharacteristic
76C2×Dic9C2×C812yes—
77C2×Dic9C2×C812yes—
78C2×Dic9M1612yes—
79Dic18—28no—
80C8×C9—42no—
81C9⋊C8—42no—
82C2×C4×Q8—91no—
83#431—92no—
84#324—91no—
85#324—92no—
86#324D911yescharacteristic
87C22×C3×C4C4×D311yescharacteristic
88C22×C3×C4C4×D311yescharacteristic
89C22×C3×C4C22×D311yescharacteristic
90C22×Dic3—31no—
91C22×Dic3—31no—
92C22×Dic3—31no—
93C22×Dic3—31no—
94C2×Dic6—34no—
95C2×Dic6—62no—
96C2×Dic6—62no—
97C2×C3×C8—22no—
98C3×C4⋊C4—22no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101C4×Dic3—32no—
102C4×Dic3—32no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C2×C3⋊C8—62no—
108C22×C9—21no—
109C22×C9—21no—
110C22×C9C2×C22⋊C411yescharacteristic
111C22×C9C22×C811yescharacteristic
112C22×C9C2×M1611yescharacteristic
113C4×C9—22no—
114C4×C9—22no—
115C4×C9—41no—
116Dic9—22no—
117Dic9—21no—
118Dic9—41no—
119Dic9C22⋊C814yes—
120Dic9#10112yes—
121C22×Q8—91no—
122C4×Q8—182no—
123C4×Q8—182no—
124C2×C4⋊C4—91no—
125C2×C4⋊C4—91no—
126C2×C4⋊C4C2×D911yescharacteristic
127C2×C42—91no—
128C2×C42—91no—
129C2×C42—91no—
130C4⋊C8—182no—
131C22⋊C8—92no—
132C22⋊C8C2×D912yes—
133C4×C8—182no—
134C23×C3C2×C4×D311yescharacteristic
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×C3×C4D3×C812yes—
141C2×C3×C4D3×D412yes—
142C2×Dic3—31no—
143C2×Dic3—32no—
144C2×Dic3—32no—
145C2×Dic3—32no—
146C2×Dic3—31no—
147C2×Dic3—32no—
148C2×Dic3—62no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—121no—
153Dic6—68no—
154C3×C8—42no—
155C3⋊C8—122no—
156C2×C9—21no—
157C2×C9—21no—
158C2×C9C2×C22⋊C811yescharacteristic
159C2×C9#41011yescharacteristic
160C2×C9C2×#10111yescharacteristic
161C2×Q8—94no—
162C2×Q8—182no—
163C2×Q8—182no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4C4×D911yescharacteristic
169C22×C4C4×D911yescharacteristic
170C22×C4C22×D911yescharacteristic
171C2×C8—22no—
172C2×C8—182no—
173C4⋊C4—22no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C42—92no—
177C42—92no—
178C42—181no—
179C42—181no—
180C42—181no—
181C42—181no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3D3×C22⋊C411yescharacteristic
185C22×C3C2×D3×C811yescharacteristic
186C22×C3D3×M1611yescharacteristic
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—41no—
190Dic3—34no—
191Dic3—32no—
192Dic3—62no—
193Dic3—61no—
194Dic3—121no—
195C9#146111yescharacteristic, complemented, Sylow
196C23C2×C4×D911yescharacteristic
197Q8—188no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—91no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—92no—
207C2×C4—91no—
208C2×C4—92no—
209C2×C4—182no—
210C2×C4—181no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C4—361no—
214C2×C4C8×D912yes—
215C2×C4D4×D912yes—
216C8—42no—
217C8—362no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3D3×C22⋊C811yescharacteristic
221C2×C3#474011yescharacteristic
222C2×C3D3×#10111yescharacteristic
223C22—21no—
224C22—21no—
225C22C22⋊C4×D911yescharacteristic
226C22C2×C8×D911yescharacteristic
227C22M16×D911yescharacteristic
228C4—22no—
229C4—22no—
230C4—41no—
231C4—92no—
232C4—94no—
233C4—181no—
234C4—182no—
235C4—361no—
236C3#6812511yescharacteristic
237C2—21no—
238C2—21no—
239C2D9×C22⋊C811yescharacteristic
240C2#1058842011yescharacteristic
241C2D9×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC22×C9C22×C8
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3D3×C22⋊C4
prime radicalC23×C3C2×C4×D3
cosocleC22×C4×C9C23
hypercenter#324D9
hypocenterC9#1461
LCSG ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
34. C2×Dic18C8semidirect
195. C9#1461semidirect

Maximal subgroups

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

subgroupindex
C2×#634492
#105883982
C9×#3242
#105882052
#105881452
#681253