Finite Group Databasebeta

← #3428⋊C9 #11919685

Subgroups — #3428⋊C9 #11919685

Order 1152.

665 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 665 conjugacy classes of subgroups — too many to draw. Only its 141 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×#41⋊C9C211yesmaximal, characteristic
2#520⋊C9C212yesmaximal, complemented
3#519⋊C9C212yesmaximal, complemented
4C4×#41⋊C9C212yesmaximal, complemented
5C3×#3428C311yesmaximal, characteristic
6C2×#41⋊C9C414yescomplemented
7C2×#41⋊C9C2211yescharacteristic
8C2×#41⋊C9C2211yescharacteristic
9C22×Q8⋊C9C2211yescharacteristic
10C9×#117—41nomaximal
11C4×Q8⋊C9C2214yescomplemented
12C22×C3×#41C2×C311yescharacteristic
13C3×#520—32no—
14C3×#520C2×C312yes—
15C3×#519C2×C312yes—
16C3×#518—32no—
17C3×C4×#41—32no—
18C3×C4×#41C2×C312yes—
19C2×C3×#117—31no—
20C2×C3×#117—31no—
21C22×C4×C9—41no—
22#41⋊C9C2×C412yescomplemented
23#41⋊C9C2×C412yescomplemented
24C2×Q8⋊C9C2×C412yescomplemented
25C2×Q8⋊C9C2311yescharacteristic
26C9×C4⋊C4—42no—
27C9×C22⋊C4—42no—
28C42×C9—42no—
29#3428C911yescharacteristic, complemented, Sylow
30C2×C3×#41—34no—
31C2×C3×#41—31no—
32C2×C3×#41—31no—
33C2×C3×#41C3×C414yes—
34C2×C3×#41C22×C311yescharacteristic
35C2×C3×#41C22×C311yescharacteristic
36C22×C3×Q8C22×C311yescharacteristic
37C22×C3×D4—31no—
38C23×C3×C4—31no—
39C3×C4×Q8—34no—
40C3×C4×Q8C22×C314yes—
41C3×C4×D4—38no—
42C3×C4×D4—34no—
43C3×C4×D4—34no—
44C3×#117—32no—
45C3×#117—31no—
46C3×#117—32no—
47C3×#117—32no—
48C3×#117—32no—
49C3×#117—32no—
50C3×#117—32no—
51C3×#117A411yescharacteristic
52C2×C3×C4⋊C4—32no—
53C2×C3×C4⋊C4—32no—
54C2×C3×C22⋊C4—32no—
55C2×C3×C22⋊C4—32no—
56C2×C3×C42—32no—
57C2×C3×C42—32no—
58C23×C9—41no—
59C2×C4×C9—44no—
60C2×C4×C9—41no—
61C2×C4×C9—44no—
62C2×C4×C9—41no—
63Q8⋊C9C22×C411yescharacteristic
64C22×#41C2×C911yescharacteristic
65#520—32no—
66#520C2×C912yescomplemented
67#519C2×C912yes—
68#518—32no—
69C4×#41—32no—
70C4×#41C2×C912yescomplemented
71C2×#117—31no—
72C2×#117—31no—
73C24×C3—31no—
74C3×#41—34no—
75C3×#41—34no—
76C3×#41—34no—
77C3×#41—34no—
78C3×#41—32no—
79C3×#41—32no—
80C3×#41C2×C3×C412yes—
81C3×#41C2×C3×C412yes—
82C2×C3×Q8—31no—
83C2×C3×Q8—32no—
84C2×C3×Q8C2×C3×C412yes—
85C2×C3×Q8C23×C311yescharacteristic
86C2×C3×D4—31no—
87C2×C3×D4—31no—
88C2×C3×D4—34no—
89C2×C3×D4—32no—
90C2×C3×D4—34no—
91C22×C3×C4—31no—
92C22×C3×C4—34no—
93C22×C3×C4—34no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—31no—
97C22×C3×C4—31no—
98C22×C3×C4—34no—
99C22×C3×C4—34no—
100C22×C3×C4C2×A411yescharacteristic
101C3×C4⋊C4—34no—
102C3×C4⋊C4—32no—
103C3×C4⋊C4—34no—
104C3×C4⋊C4C2×A412yes—
105C3×C22⋊C4—34no—
106C3×C22⋊C4—32no—
107C3×C22⋊C4—34no—
108C3×C22⋊C4C2×A412yes—
109C3×C42—34no—
110C3×C42—34no—
111C3×C42—32no—
112C3×C42C2×A412yes—
113C22×C9—42no—
114C22×C9—41no—
115C22×C9—82no—
116C4×C9—42no—
117C4×C9—42no—
118C4×C9—84no—
119C2×#41—31no—
120C2×#41—31no—
121C2×#41—34no—
122C2×#41C4×C914yescomplemented
123C2×#41C22×C911yescharacteristic
124C2×#41C22×C911yescharacteristic
125C22×Q8C22×C911yescharacteristic
126C22×D4—31no—
127C23×C4—31no—
128C4×Q8—34no—
129C4×Q8C22×C914yes—
130C4×D4—38no—
131C4×D4—34no—
132C4×D4—34no—
133#117—32no—
134#117—31no—
135#117—32no—
136#117—32no—
137#117—32no—
138#117—32no—
139#117—32no—
140#117C22⋊C911yescharacteristic
141C2×C4⋊C4—32no—
142C2×C4⋊C4—32no—
143C2×C22⋊C4—32no—
144C2×C22⋊C4—32no—
145C2×C42—32no—
146C2×C42—32no—
147C23×C3—31no—
148C23×C3—31no—
149C23×C3—34no—
150C23×C3—122no—
151C23×C3C22×A411yescharacteristic
152C3×Q8—32no—
153C3×Q8—31no—
154C3×Q8—32no—
155C3×Q8C22×C3×C411yescharacteristic
156C3×D4—32no—
157C3×D4—32no—
158C3×D4—32no—
159C3×D4—32no—
160C3×D4—38no—
161C2×C3×C4—32no—
162C2×C3×C4—32no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—32no—
166C2×C3×C4—34no—
167C2×C3×C4—32no—
168C2×C3×C4—34no—
169C2×C3×C4—32no—
170C2×C3×C4—32no—
171C2×C3×C4—34no—
172C2×C3×C4—124no—
173C2×C3×C4—124no—
174C2×C3×C4C4×A414yes—
175C2×C3×C4C22×A414yes—
176C2×C3×C4C22×A411yescharacteristic
177C2×C3×C4C22×A411yescharacteristic
178C2×C9—41no—
179C2×C9—42no—
180C2×C9—82no—
181C24—31no—
182#41—34no—
183#41—34no—
184#41—34no—
185#41—34no—
186#41—32no—
187#41—32no—
188#41C2×C4×C912yes—
189#41C2×C4×C912yes—
190C2×Q8—31no—
191C2×Q8—32no—
192C2×Q8C2×C4×C912yes—
193C2×Q8C23×C911yescharacteristic
194C2×D4—31no—
195C2×D4—31no—
196C2×D4—34no—
197C2×D4—32no—
198C2×D4—34no—
199C22×C4—31no—
200C22×C4—34no—
201C22×C4—34no—
202C22×C4—31no—
203C22×C4—31no—
204C22×C4—31no—
205C22×C4—31no—
206C22×C4—34no—
207C22×C4—34no—
208C22×C4C2×C22⋊C911yescharacteristic
209C4⋊C4—34no—
210C4⋊C4—32no—
211C4⋊C4—34no—
212C4⋊C4C2×C22⋊C912yes—
213C22⋊C4—34no—
214C22⋊C4—32no—
215C22⋊C4—34no—
216C22⋊C4C2×C22⋊C912yes—
217C42—34no—
218C42—32no—
219C42—34no—
220C42C2×C22⋊C912yes—
221C22×C3—22no—
222C22×C3—32no—
223C22×C3—32no—
224C22×C3—62no—
225C22×C3—62no—
226C22×C3—124no—
227C22×C3C2×C4×A412yes—
228C22×C3C23×A411yescharacteristic
229C3×C4—24no—
230C3×C4—31no—
231C3×C4—32no—
232C3×C4—31no—
233C3×C4—64no—
234C3×C4C2×C4×A412yes—
235C3×C4C2×C4×A412yes—
236C9—41noSylow
237C23—31no—
238C23—31no—
239C23—34no—
240C23—122no—
241C23C22×C22⋊C911yescharacteristic
242Q8—32no—
243Q8—31no—
244Q8—32no—
245Q8C22×C4×C911yescharacteristic
246D4—32no—
247D4—32no—
248D4—32no—
249D4—32no—
250D4—38no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—32no—
254C2×C4—32no—
255C2×C4—32no—
256C2×C4—32no—
257C2×C4—34no—
258C2×C4—34no—
259C2×C4—32no—
260C2×C4—32no—
261C2×C4—34no—
262C2×C4—124no—
263C2×C4—124no—
264C2×C4C4×C22⋊C914yes—
265C2×C4C22×C22⋊C914yes—
266C2×C4C22×C22⋊C911yescharacteristic
267C2×C4C22×C22⋊C911yescharacteristic
268C2×C3—22no—
269C2×C3—62no—
270C2×C3—62no—
271C2×C3C22×C4×A411yescharacteristic
272C2×C3#594512yes—
273C22—22no—
274C22—32no—
275C22—32no—
276C22—62no—
277C22—62no—
278C22—124no—
279C22C2×C4×C22⋊C912yes—
280C22C23×C22⋊C911yescharacteristic
281C4—24no—
282C4—31no—
283C4—31no—
284C4—32no—
285C4—64no—
286C4C2×C4×C22⋊C912yes—
287C4C2×C4×C22⋊C912yes—
288C3#3428⋊C311yescharacteristic
289C2—22no—
290C2—62no—
291C2—62no—
292C2C22×C4×C22⋊C911yescharacteristic
293C2#1059312012yes—
subgroupG/H
centerC2×C3×C4C22×A4
commutator, hypocenterQ8C22×C4×C9
Frattini, socleC22×C3C23×A4
FittingC3×#3428C3
prime radicalC22×C3×#41C2×C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×#117A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

Complements

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

NH ≅ G/Ntype
2. #520⋊C9C2semidirect
3. #519⋊C9C2semidirect
4. C4×#41⋊C9C2semidirect
6. C2×#41⋊C9C4semidirect
11. C4×Q8⋊C9C22semidirect
22. #41⋊C9C2×C4semidirect
23. #41⋊C9C2×C4semidirect
24. C2×Q8⋊C9C2×C4semidirect
29. #3428C9semidirect
66. #520C2×C9semidirect
70. C4×#41C2×C9semidirect
122. C2×#41C4×C9semidirect

Maximal subgroups

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

subgroupindex
C22×#41⋊C92
#520⋊C92
#519⋊C92
C4×#41⋊C92
C3×#34283
C9×#1174