Finite Group Databasebeta

← #2884⋊C9 #11919531

Subgroups — #2884⋊C9 #11919531

Order 1152.

339 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×2−1+4⋊C9C211yesmaximal, characteristic
2#519⋊C9C212yesmaximal, complemented
3C3×#2884C311yesmaximal, characteristic
42−1+4⋊C9—22no—
5C2×#41⋊C9C411yescharacteristic, complemented
6C22×Q8⋊C9C411yescharacteristic, complemented
7C22×Q8⋊C9C2211yescharacteristic
8C4×Q8⋊C9—22no—
9C9×#99—41nomaximal
10C2×C3×2−1+4C2×C311yescharacteristic
11C3×#519C2×C312yes—
12C3×#410—31no—
13C3×#410—31no—
14C3×#410—32no—
15C2×D4×C9—41no—
16#41⋊C9—21no—
17C2×Q8⋊C9—21no—
18C2×Q8⋊C9C2×C411yescharacteristic
19C2×Q8⋊C9D412yes—
20C9×C22⋊C4—42no—
21#2884C911yescharacteristic, complemented, Sylow
22C3×2−1+4—22no—
23C3×2−1+4—62no—
24C2×C3×#41—31no—
25C2×C3×#41—31no—
26C2×C3×#41—31no—
27C2×C3×#41C3×C411yescharacteristic
28C22×C3×Q8—31no—
29C22×C3×Q8C3×C411yescharacteristic
30C22×C3×Q8C22×C311yescharacteristic
31C3×C4×Q8—22no—
32C3×C4×Q8—62no—
33C3×#117—32no—
34C3×#117—32no—
35C3×#99—32no—
36C3×#99—31no—
37C3×#99—32no—
38C3×#99A411yescharacteristic
39C23×C9—41no—
40C23×C9—41no—
41D4×C9—82no—
42C2×C4×C9—41no—
43C2×C4×C9—82no—
44Q8⋊C9C22⋊C411yescharacteristic
45C2×2−1+4C2×C911yescharacteristic
46#519C2×C912yescomplemented
47#410—31no—
48#410—31no—
49#410—32no—
50C3×#41—21no—
51C3×#41—62no—
52C3×#41—62no—
53C3×#41—62no—
54C3×#41—62no—
55C3×#41—62no—
56C3×#41—62no—
57C3×#41—61no—
58C2×C3×Q8—21no—
59C2×C3×Q8—31no—
60C2×C3×Q8—32no—
61C2×C3×Q8—31no—
62C2×C3×Q8—31no—
63C2×C3×Q8—62no—
64C2×C3×Q8—62no—
65C2×C3×Q8—61no—
66C2×C3×Q8C2×C3×C411yescharacteristic
67C2×C3×Q8C3×D412yes—
68C2×C3×D4—31no—
69C2×C3×D4—31no—
70C2×C3×D4—31no—
71C2×C3×D4C2×A411yescharacteristic
72C22×C3×C4—31no—
73C22×C3×C4—32no—
74C22×C3×C4—31no—
75C22×C3×C4—31no—
76C3×C4⋊C4—62no—
77C3×C4⋊C4—62no—
78C3×C22⋊C4—32no—
79C3×C22⋊C4C2×A412yes—
80C3×C42—62no—
81C3×C42—62no—
82C22×C9—41no—
83C22×C9—42no—
84C22×C9—81no—
85C22×C9—161no—
86C22×C9—161no—
87C4×C9—81no—
88C4×C9—162no—
892−1+4—22no—
902−1+4—62no—
91C2×#41—31no—
92C2×#41—31no—
93C2×#41—31no—
94C2×#41C4×C911yescharacteristic, complemented
95C22×Q8—31no—
96C22×Q8C4×C911yescharacteristic, complemented
97C22×Q8C22×C911yescharacteristic
98C4×Q8—22no—
99C4×Q8—62no—
100#117—32no—
101#117—32no—
102#99—32no—
103#99—31no—
104#99—32no—
105#99C22⋊C911yescharacteristic
106C23×C3—31no—
107C23×C3C4×A411yescharacteristic
108C23×C3C22×A411yescharacteristic
109C3×Q8—31no—
110C3×Q8—32no—
111C3×Q8—32no—
112C3×Q8—62no—
113C3×Q8—61no—
114C3×Q8—61no—
115C3×Q8C3×C22⋊C411yescharacteristic
116C3×D4—22no—
117C3×D4—62no—
118C3×D4—61no—
119C3×D4—61no—
120C3×D4—62no—
121C2×C3×C4—22no—
122C2×C3×C4—31no—
123C2×C3×C4—31no—
124C2×C3×C4—32no—
125C2×C3×C4—32no—
126C2×C3×C4—31no—
127C2×C3×C4—61no—
128C2×C3×C4—61no—
129C2×C3×C4—61no—
130C2×C3×C4—61no—
131C2×C3×C4—64no—
132C2×C3×C4—62no—
133C2×C3×C4C4×A411yescharacteristic
134C2×C9—41no—
135C2×C9—82no—
136C2×C9—81no—
137C2×C9—161no—
138#41—21no—
139#41—62no—
140#41—62no—
141#41—62no—
142#41—62no—
143#41—62no—
144#41—62no—
145#41—61no—
146C2×Q8—21no—
147C2×Q8—31no—
148C2×Q8—32no—
149C2×Q8—31no—
150C2×Q8—31no—
151C2×Q8—62no—
152C2×Q8—62no—
153C2×Q8—61no—
154C2×Q8C2×C4×C911yescharacteristic
155C2×Q8D4×C912yes—
156C2×D4—31no—
157C2×D4—31no—
158C2×D4—31no—
159C2×D4C2×C22⋊C911yescharacteristic
160C22×C4—31no—
161C22×C4—32no—
162C22×C4—31no—
163C22×C4—31no—
164C4⋊C4—62no—
165C4⋊C4—62no—
166C22⋊C4—32no—
167C22⋊C4C2×C22⋊C912yes—
168C42—62no—
169C42—62no—
170C22×C3—21no—
171C22×C3—41no—
172C22×C3—41no—
173C22×C3—61no—
174C22×C3—121no—
175C22×C3C2×C4×A411yescharacteristic
176C22×C3D4×A412yes—
177C3×C4—21no—
178C3×C4—32no—
179C3×C4—31no—
180C3×C4—31no—
181C3×C4—42no—
182C3×C4—61no—
183C3×C4—122no—
184C9—41noSylow
185C23—31no—
186C23C4×C22⋊C911yescharacteristic
187C23C22×C22⋊C911yescharacteristic
188Q8—31no—
189Q8—32no—
190Q8—32no—
191Q8—62no—
192Q8—61no—
193Q8—61no—
194Q8C9×C22⋊C411yescharacteristic
195D4—22no—
196D4—62no—
197D4—61no—
198D4—61no—
199D4—62no—
200C2×C4—22no—
201C2×C4—31no—
202C2×C4—31no—
203C2×C4—32no—
204C2×C4—32no—
205C2×C4—31no—
206C2×C4—61no—
207C2×C4—61no—
208C2×C4—61no—
209C2×C4—61no—
210C2×C4—64no—
211C2×C4—62no—
212C2×C4C4×C22⋊C911yescharacteristic
213C2×C3—22no—
214C2×C3—21no—
215C2×C3—41no—
216C2×C3—121no—
217C2×C3A4×C22⋊C411yescharacteristic
218C22—21no—
219C22—41no—
220C22—41no—
221C22—61no—
222C22—121no—
223C22C2×C4×C22⋊C911yescharacteristic
224C22D4×C22⋊C912yes—
225C4—21no—
226C4—31no—
227C4—31no—
228C4—32no—
229C4—42no—
230C4—61no—
231C4—122no—
232C3#2884⋊C311yescharacteristic
233C2—22no—
234C2—21no—
235C2—41no—
236C2—121no—
237C2C22⋊C4×C22⋊C911yescharacteristic
subgroupG/H
center, socleC2×C3A4×C22⋊C4
commutatorC2×Q8C2×C4×C9
FrattiniC23×C3C22×A4
FittingC3×#2884C3
prime radicalC2×C3×2−1+4C2×C3
cosocleC22×C3×Q8C22×C3
hypercenterC3×#99A4
hypocenterQ8C9×C22⋊C4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#99

Complements

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

NH ≅ G/Ntype
2. #519⋊C9C2semidirect
5. C2×#41⋊C9C4semidirect
6. C22×Q8⋊C9C4semidirect
21. #2884C9semidirect
46. #519C2×C9semidirect
94. C2×#41C4×C9semidirect
96. C22×Q8C4×C9semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
#519⋊C92
C3×#28843
C9×#994