Finite Group Databasebeta

← C9×#2189 #11766910

Subgroups — C9×#2189 #11766910

Order 1152.

330 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 102 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×C9×#135C211yesmaximal, characteristic
2C2×C9×Q32C211yesmaximal, characteristic, complemented
3C2×C9×SD32C211yesmaximal, characteristic, complemented
4C9×#467C211yesmaximal, characteristic, complemented
5C9×#358C211yesmaximal, characteristic, complemented
6C9×#357C211yesmaximal, characteristic, complemented
7C9×C22⋊C16C211yesmaximal, characteristic, complemented
8C3×#2189C311yesmaximal, characteristic
9C2×C9×#41—21no—
10C9×#135—22no—
11C9×#135—22no—
12C2×C9×Q16C2211yescharacteristic
13C2×C9×Q16C2211yescharacteristic
14C2×C9×SD16—21no—
15C2×C9×D8C2211yescharacteristic
16C22×C8×C9C2211yescharacteristic
17C9×C22⋊Q8—21no—
18C9×Q32—22no—
19C9×SD32—22no—
20C2×C9×C16C2211yescharacteristic
21C2×C9×C16C2211yescharacteristic
22C9×#107C2211yescharacteristic
23C9×#103—21no—
24C2×C3×#135C2×C311yescharacteristic
25C2×C3×Q32C2×C311yescharacteristic
26C2×C3×SD32C2×C311yescharacteristic
27C3×#467C2×C311yescharacteristic
28C3×#358C2×C311yescharacteristic
29C3×#357C2×C311yescharacteristic
30C3×C22⋊C16C2×C311yescharacteristic
31C9×#41—24no—
32C9×#41—42no—
33C2×Q8×C9—21no—
34C2×Q8×C9—21no—
35C2×D4×C9—21no—
36C2×D4×C9—41no—
37C22×C4×C9—41no—
38C22×C4×C9D411yescharacteristic
39C9×Q16—21no—
40C9×Q16—21no—
41C9×Q16—21no—
42C9×Q16D412yes—
43C9×SD16—24no—
44C9×D8—21no—
45C9×D8D412yes—
46C2×C8×C9—21no—
47C2×C8×C9—21no—
48C2×C8×C9D411yescharacteristic
49C2×C8×C9C2311yescharacteristic
50C9×C4⋊C4—21no—
51C9×C4⋊C4—41no—
52C9×C22⋊C4—41no—
53C9×C16—21no—
54C9×C16—21no—
55#2189C911yescharacteristic, direct product factor, Sylow
56C2×C3×#41—21no—
57C3×#135—22no—
58C3×#135—22no—
59C2×C3×Q16C22×C311yescharacteristic
60C2×C3×Q16C22×C311yescharacteristic
61C2×C3×SD16—21no—
62C2×C3×D8C22×C311yescharacteristic
63C22×C3×C8C22×C311yescharacteristic
64C3×C22⋊Q8—21no—
65C3×Q32—22no—
66C3×SD32—22no—
67C2×C3×C16C22×C311yescharacteristic
68C2×C3×C16C22×C311yescharacteristic
69C3×#107C22×C311yescharacteristic
70C3×#103—21no—
71C23×C9—41no—
72C23×C9D811yescharacteristic
73Q8×C9—22no—
74Q8×C9—41no—
75Q8×C9—41no—
76Q8×C9—41no—
77D4×C9—22no—
78D4×C9—44no—
79D4×C9—41no—
80C2×C4×C9—21no—
81C2×C4×C9—21no—
82C2×C4×C9—44no—
83C2×C4×C9—41no—
84C2×C4×C9—41no—
85C2×C4×C9—41no—
86C2×C4×C9D811yescharacteristic
87C2×C4×C9C2×D411yescharacteristic
88C8×C9—21no—
89C8×C9C2×D411yescharacteristic
90C8×C9C2×D411yescharacteristic
91C2×#135C2×C911yescharacteristic
92C2×Q32C2×C911yescharacteristic, complemented
93C2×SD32C2×C911yescharacteristic, complemented
94#467C2×C911yescharacteristic, complemented
95#358C2×C911yescharacteristic, complemented
96#357C2×C911yescharacteristic, complemented
97C22⋊C16C2×C911yescharacteristic, complemented
98C3×#41—24no—
99C3×#41—42no—
100C2×C3×Q8—21no—
101C2×C3×Q8—21no—
102C2×C3×D4—21no—
103C2×C3×D4—41no—
104C22×C3×C4—41no—
105C22×C3×C4C3×D411yescharacteristic
106C3×Q16—21no—
107C3×Q16—21no—
108C3×Q16—21no—
109C3×Q16C3×D412yes—
110C3×SD16—24no—
111C3×D8—21no—
112C3×D8C3×D412yes—
113C2×C3×C8—21no—
114C2×C3×C8—21no—
115C2×C3×C8C3×D411yescharacteristic
116C2×C3×C8C23×C311yescharacteristic
117C3×C4⋊C4—21no—
118C3×C4⋊C4—41no—
119C3×C22⋊C4—41no—
120C3×C16—21no—
121C3×C16—21no—
122C22×C9—21no—
123C22×C9—21no—
124C22×C9—21no—
125C22×C9—42no—
126C22×C9—81no—
127C22×C9—81no—
128C22×C9C2×D811yescharacteristic
129C4×C9—21no—
130C4×C9—42no—
131C4×C9—81no—
132C4×C9—81no—
133C4×C9#12011yescharacteristic
134C4×C9AGL(1,ℤ/8)11yescharacteristic
135C2×#41—21no—
136#135—22no—
137#135—22no—
138C2×Q16C22×C911yescharacteristic
139C2×Q16C22×C911yescharacteristic
140C2×SD16—21no—
141C2×D8C22×C911yescharacteristic
142C22×C8C22×C911yescharacteristic
143C22⋊Q8—21no—
144Q32—22no—
145SD32—22no—
146C2×C16C22×C911yescharacteristic
147C2×C16C22×C911yescharacteristic
148#107C22×C911yescharacteristic
149#103—21no—
150C23×C3—41no—
151C23×C3C3×D811yescharacteristic
152C3×Q8—22no—
153C3×Q8—41no—
154C3×Q8—41no—
155C3×Q8—41no—
156C3×D4—22no—
157C3×D4—44no—
158C3×D4—41no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—44no—
162C2×C3×C4—41no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4C3×D811yescharacteristic
166C2×C3×C4C2×C3×D411yescharacteristic
167C3×C8—21no—
168C3×C8C2×C3×D411yescharacteristic
169C3×C8C2×C3×D411yescharacteristic
170C2×C9—41no—
171C2×C9—82no—
172C2×C9#44711yescharacteristic
173C2×C9#50811yescharacteristic
174C2×C9#51011yescharacteristic
175#41—24no—
176#41—42no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×D4—21no—
180C2×D4—41no—
181C22×C4—41no—
182C22×C4D4×C911yescharacteristic
183Q16—21no—
184Q16—21no—
185Q16—21no—
186Q16D4×C912yes—
187SD16—24no—
188D8—21no—
189D8D4×C912yes—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8D4×C911yescharacteristic
193C2×C8C23×C911yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—41no—
196C22⋊C4—41no—
197C16—21no—
198C16—21no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—21no—
202C22×C3—42no—
203C22×C3—81no—
204C22×C3—81no—
205C22×C3C2×C3×D811yescharacteristic
206C3×C4—21no—
207C3×C4—42no—
208C3×C4—81no—
209C3×C4—81no—
210C3×C4C3×#12011yescharacteristic
211C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
212C9#218911yescharacteristic, direct product factor, Sylow
213C23—41no—
214C23C9×D811yescharacteristic
215Q8—22no—
216Q8—41no—
217Q8—41no—
218Q8—41no—
219D4—22no—
220D4—44no—
221D4—41no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4C9×D811yescharacteristic
229C2×C4C2×D4×C911yescharacteristic
230C8—21no—
231C8C2×D4×C911yescharacteristic
232C8C2×D4×C911yescharacteristic
233C2×C3—41no—
234C2×C3—82no—
235C2×C3C3×#44711yescharacteristic
236C2×C3C3×#50811yescharacteristic
237C2×C3C3×#51011yescharacteristic
238C22—21no—
239C22—21no—
240C22—21no—
241C22—42no—
242C22—81no—
243C22—81no—
244C22C2×C9×D811yescharacteristic
245C4—21no—
246C4—42no—
247C4—81no—
248C4—81no—
249C4C9×#12011yescharacteristic
250C4C9×AGL(1,ℤ/8)11yescharacteristic
251C3C3×#218911yescharacteristic
252C2—41no—
253C2—82no—
254C2C9×#44711yescharacteristic
255C2C9×#50811yescharacteristic
256C2C9×#51011yescharacteristic
subgroupG/H
centerC22×C9C2×D8
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC22×C3C2×C3×D8
prime radicalC2×C3×#135C2×C3
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ C22×C8×C9 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C9×Q32C2semidirect
3. C2×C9×SD32C2semidirect
4. C9×#467C2semidirect
5. C9×#358C2semidirect
6. C9×#357C2semidirect
7. C9×C22⋊C16C2semidirect
55. #2189C9direct (N × H)
92. C2×Q32C2×C9semidirect
93. C2×SD32C2×C9semidirect
94. #467C2×C9semidirect
95. #358C2×C9semidirect
96. #357C2×C9semidirect
97. C22⋊C16C2×C9semidirect
212. C9#2189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1352
C2×C9×Q322
C2×C9×SD322
C9×#4672
C9×#3582
C9×#3572
C9×C22⋊C162
C3×#21893