Finite Group Databasebeta

← #11796561

Subgroups — #11796561

Order 1152.

345 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 68 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#10589826C211yesmaximal, characteristic
2#10588431C212yesmaximal
3C9×#356C211yesmaximal, characteristic, complemented
4#10588225C211yesmaximal, characteristic, complemented
5#10588154C212yesmaximal, complemented
6#69173—31nomaximal
7C2×#3701C2211yescharacteristic
8C2×Q8×D9C411yescharacteristic
9C9×C4⋊Q8C2211yescharacteristic
10#63509C411yescharacteristic
11#63506C2211yescharacteristic
12M16×D9—22no—
13#63458—22no—
14#63456—22no—
15#63437C411yescharacteristic
16#63434C411yescharacteristic
17C9×#101C2212yes—
18#63394C2212yes—
19#63383—22no—
20#5724—31no—
21#4751—32no—
22C3×#356D311yescharacteristic
23#4548—31no—
24#4478—32no—
25C2×Q8×C9C2×C411yescharacteristic
26C2×Q8×C9C2311yescharacteristic
27#3701—42no—
28Q8×D9—42no—
29C2×D36C2×C411yescharacteristic
30C2×D36D412yes—
31C2×C4×D9—21no—
32C2×C4×D9C2×C411yescharacteristic
33C2×C4×D9D412yes—
34C2×Dic18—21no—
35C2×Dic18C2×C411yescharacteristic
36C9×M16—22no—
37C9×C4⋊C4—22no—
38C42×C9C2×C411yescharacteristic
39(C2×D9)⋊C4—22no—
40(C2×D9)⋊C4—21no—
41(C2×D9)⋊C4—22no—
42Dic9⋊C4—22no—
43Dic9⋊C4—21no—
44C4×Dic9C2×C411yescharacteristic
45#3667—22no—
46#3663—42no—
47C8×D9—42no—
48#2135—91noSylow
49C2×#239—31no—
50C2×D3×Q8—31no—
51C3×C4⋊Q8C2×D311yescharacteristic
52#947—31no—
53#944—31no—
54D3×M16—62no—
55#896—62no—
56#894—62no—
57#875—31no—
58#872—31no—
59C3×#101C2×D312yes—
60#836—32no—
61#823—62no—
62C22×D9C22⋊C412yes—
63C22×D9C22⋊C411yescharacteristic
64Q8×C9—41no—
65Q8×C9—41no—
66C2×C4×C9—21no—
67C2×C4×C9—21no—
68C2×C4×C9C22×C411yescharacteristic
69C2×C4×C9C2×D412yes—
70C2×Dic9—21no—
71C2×Dic9—21no—
72C2×Dic9C22⋊C411yescharacteristic
73D36—41no—
74D36—42no—
75C4×D9—22no—
76C4×D9—22no—
77C4×D9—22no—
78C4×D9—42no—
79Dic18—42no—
80Dic18—41no—
81C8×C9—42no—
82C9⋊C8—42no—
83#536—91no—
84#413—92no—
85#356—91no—
86#356—92no—
87#356D911yescharacteristic, complemented
88C2×C3×Q8C4×D311yescharacteristic
89C2×C3×Q8C22×D311yescharacteristic
90#239—122no—
91D3×Q8—122no—
92C2×D12—31no—
93C2×D12—32no—
94C2×C4×D3—31no—
95C2×C4×D3—32no—
96C2×C4×D3—61no—
97C2×Dic6—31no—
98C2×Dic6—61no—
99C3×M16—22no—
100C3×C4⋊C4—22no—
101C3×C42C4×D311yescharacteristic
102(C2×D3)⋊C4—61no—
103(C2×D3)⋊C4—62no—
104(C2×D3)⋊C4—62no—
105Dic3⋊C4—61no—
106Dic3⋊C4—62no—
107C4×Dic3—31no—
108#208—62no—
109ΓL(1,𝔽25)—122no—
110D3×C8—122no—
111C22×C9C2×C22⋊C411yescharacteristic
112C2×D9—21no—
113C2×D9—22no—
114C2×D9—42no—
115C2×D9—41no—
116C4×C9—22no—
117C4×C9—21no—
118C4×C9—41no—
119C4×C9—41no—
120Dic9—41no—
121Dic9—41no—
122Dic9#9912yes—
123C2×#41—91no—
124C22×Q8—91no—
125C2×M16—182no—
126C4⋊Q8—91no—
127C4⋊Q8C2×D911yescharacteristic
128#124—91no—
129#124—91no—
130#123—182no—
131C22⋊Q8—182no—
132#117—91no—
133#101—92no—
134#101C2×D912yes—
135#100—182no—
136C22×D3—32no—
137C22×D3—31no—
138C3×Q8—41no—
139C3×Q8—41no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4C2×C4×D311yescharacteristic
143C2×C3×C4D3×D412yes—
144C2×Dic3—31no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147D12—122no—
148D12—121no—
149C4×D3—62no—
150C4×D3—62no—
151C4×D3—62no—
152C4×D3—122no—
153Dic6—122no—
154Dic6—121no—
155C3×C8—42no—
156C3⋊C8—122no—
157C2×C9—21no—
158C2×C9C2×#9911yescharacteristic
159D9—41no—
160D9—42no—
161#41—362no—
162C2×Q8—91no—
163C2×Q8—181no—
164C2×Q8—362no—
165C2×Q8C4×D911yescharacteristic
166C2×Q8C22×D911yescharacteristic
167C2×D4—91no—
168C2×D4—92no—
169C22×C4—91no—
170C22×C4—92no—
171C22×C4—181no—
172M16—22no—
173M16—182no—
174M16—362no—
175C2×C8—362no—
176C4⋊C4—22no—
177C4⋊C4—181no—
178C4⋊C4—182no—
179C22⋊C4—181no—
180C22⋊C4—182no—
181C22⋊C4—182no—
182C42—91no—
183C42C4×D911yescharacteristic
184C22×C3D3×C22⋊C411yescharacteristic
185C2×D3—61no—
186C2×D3—62no—
187C2×D3—122no—
188C2×D3—121no—
189C3×C4—22no—
190C3×C4—21no—
191C3×C4—41no—
192C3×C4—41no—
193Dic3—32no—
194Dic3—121no—
195Dic3—121no—
196C9#213511yescharacteristic, complemented, Sylow
197C23—92no—
198C23—91no—
199Q8—41no—
200Q8—41no—
201Q8—361no—
202Q8—362no—
203D4—362no—
204D4—361no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—91no—
208C2×C4—182no—
209C2×C4—182no—
210C2×C4—182no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C4—362no—
214C2×C4C2×C4×D911yescharacteristic
215C2×C4D4×D912yes—
216C8—42no—
217C8—362no—
218C2×C3—21no—
219C2×C3D3×#9911yescharacteristic
220D3—121no—
221D3—122no—
222C22—181no—
223C22—182no—
224C22—362no—
225C22—361no—
226C22C22⋊C4×D911yescharacteristic
227C4—22no—
228C4—21no—
229C4—41no—
230C4—41no—
231C4—92no—
232C4—361no—
233C4—361no—
234C3#6917311yescharacteristic
235C2—21no—
236C2—361no—
237C2—362no—
238C2D9×#9911yescharacteristic
subgroupG/H
centerC2D9×#99
commutatorC2×C4×C9C22×C4
FrattiniC2×C3×Q8C22×D3
FittingC9×#356C2
socleC2×C3D3×#99
prime radicalC2×#3701C22
cosocleC2×Q8×C9C23
hypercenter#356D9
hypocenterC9#2135
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. C9×#356C2semidirect
4. #10588225C2semidirect
5. #10588154C2semidirect
87. #356D9semidirect
196. C9#2135semidirect

Maximal subgroups

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

subgroupindex
#105898262
#105884312
C9×#3562
#105882252
#105881542
#691733