Finite Group Databasebeta

← #3480⋊C9 #11919731

Subgroups — #3480⋊C9 #11919731

Order 1152.

506 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 111 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#557⋊C9C211yesmaximal, characteristic, complemented
2C4⋊(#41⋊C9)C211yesmaximal, characteristic, complemented
3#548⋊C9C212yesmaximal, complemented
4C4×#41⋊C9C212yesmaximal, complemented
5C2×C4×Q8⋊C9C211yesmaximal, characteristic, complemented
6C3×#3480C311yesmaximal, characteristic
7C2×#41⋊C9C2212yes—
8C22×Q8⋊C9C2211yescharacteristic
9C9×#117—41nomaximal
10C4×Q8⋊C9C2211yescharacteristic
11C4×Q8⋊C9C2211yescharacteristic
12C4×Q8⋊C9C2212yes—
13C3×#559—31no—
14C3×#557C2×C311yescharacteristic
15C3×#556—31no—
16C3×#553—32no—
17C3×#550C2×C311yescharacteristic
18C3×#548C2×C312yes—
19C3×#532—31no—
20C3×#529—32no—
21C3×C4×#41—31no—
22C3×C4×#41C2×C312yes—
23C2×C3×C4×Q8C2×C311yescharacteristic
24C22×C4×C9—41no—
25#41⋊C9—22no—
26C2×Q8⋊C9—21no—
27C2×Q8⋊C9C2311yescharacteristic
28C9×C4⋊C4—41no—
29C9×C4⋊C4—41no—
30C9×C22⋊C4—42no—
31C42×C9—42no—
32#3480C911yescharacteristic, complemented, Sylow
33C2×C3×#41—31no—
34C2×C3×#41C22×C312yes—
35C22×C3×Q8C22×C311yescharacteristic
36C3×C4⋊Q8—31no—
37C3×#127—31no—
38C3×#126—34no—
39C3×#125—32no—
40C3×#124—32no—
41C3×#124—32no—
42C3×#123—34no—
43C3×C22⋊Q8—32no—
44C3×#121—32no—
45C3×#121—32no—
46C3×#121—32no—
47C3×C4×Q8—31no—
48C3×C4×Q8—31no—
49C3×C4×Q8—31no—
50C3×C4×Q8—31no—
51C3×C4×Q8C22×C311yescharacteristic
52C3×C4×Q8C22×C311yescharacteristic
53C3×C4×Q8C22×C312yes—
54C3×C4×D4—32no—
55C3×C4×D4—32no—
56C3×C4×D4—32no—
57C3×C4×D4—31no—
58C3×C4×D4—31no—
59C3×C4×D4—32no—
60C3×C4×D4—32no—
61C3×#117—32no—
62C3×#117—32no—
63C3×#117A411yescharacteristic
64C2×C3×C4⋊C4—31no—
65C2×C3×C42—31no—
66C2×C3×C42—32no—
67C23×C9—41no—
68C2×C4×C9—44no—
69C2×C4×C9—41no—
70C2×C4×C9—42no—
71C2×C4×C9—42no—
72C2×C4×C9—41no—
73Q8⋊C9#4111yescharacteristic, complemented
74#559—31no—
75#557C2×C911yescharacteristic, complemented
76#556—31no—
77#553—32no—
78#550C2×C911yescharacteristic, complemented
79#548C2×C912yes—
80#532—31no—
81#529—32no—
82C4×#41—31no—
83C4×#41C2×C912yescomplemented
84C2×C4×Q8C2×C911yescharacteristic
85C3×#41—22no—
86C3×#41—64no—
87C3×#41—62no—
88C2×C3×Q8—21no—
89C2×C3×Q8—31no—
90C2×C3×Q8—31no—
91C2×C3×Q8—61no—
92C2×C3×Q8C23×C311yescharacteristic
93C2×C3×D4—32no—
94C2×C3×D4—32no—
95C2×C3×D4—32no—
96C2×C3×D4—31no—
97C22×C3×C4—31no—
98C22×C3×C4—31no—
99C22×C3×C4—32no—
100C22×C3×C4—32no—
101C22×C3×C4—32no—
102C22×C3×C4C2×A411yescharacteristic
103C3×C4⋊C4—31no—
104C3×C4⋊C4—31no—
105C3×C4⋊C4—32no—
106C3×C4⋊C4—32no—
107C3×C4⋊C4—32no—
108C3×C4⋊C4—32no—
109C3×C4⋊C4—32no—
110C3×C4⋊C4C2×A411yescharacteristic
111C3×C4⋊C4C2×A411yescharacteristic
112C3×C22⋊C4—34no—
113C3×C22⋊C4—34no—
114C3×C22⋊C4—32no—
115C3×C22⋊C4—32no—
116C3×C22⋊C4C2×A412yes—
117C3×C42—32no—
118C3×C42—32no—
119C3×C42—31no—
120C3×C42—31no—
121C3×C42—31no—
122C3×C42—31no—
123C3×C42C2×A412yes—
124C22×C9—42no—
125C22×C9—41no—
126C22×C9—81no—
127C22×C9—81no—
128C4×C9—42no—
129C4×C9—42no—
130C4×C9—82no—
131C4×C9—82no—
132C2×#41—31no—
133C2×#41C22×C912yes—
134C22×Q8C22×C911yescharacteristic
135C4⋊Q8—31no—
136#127—31no—
137#126—34no—
138#125—32no—
139#124—32no—
140#124—32no—
141#123—34no—
142C22⋊Q8—32no—
143#121—32no—
144#121—32no—
145#121—32no—
146C4×Q8—31no—
147C4×Q8—31no—
148C4×Q8—31no—
149C4×Q8—31no—
150C4×Q8C22×C911yescharacteristic
151C4×Q8C22×C911yescharacteristic
152C4×Q8C22×C912yes—
153C4×D4—32no—
154C4×D4—32no—
155C4×D4—32no—
156C4×D4—31no—
157C4×D4—31no—
158C4×D4—32no—
159C4×D4—32no—
160#117—32no—
161#117—32no—
162#117C22⋊C911yescharacteristic
163C2×C4⋊C4—31no—
164C2×C42—31no—
165C2×C42—32no—
166C23×C3—32no—
167C23×C3C22×A411yescharacteristic
168C3×Q8—31no—
169C3×Q8—61no—
170C3×Q8—61no—
171C3×Q8—62no—
172C3×Q8C3×#4111yescharacteristic
173C3×D4—62no—
174C3×D4—62no—
175C3×D4—64no—
176C3×D4—62no—
177C3×D4—122no—
178C2×C3×C4—31no—
179C2×C3×C4—31no—
180C2×C3×C4—31no—
181C2×C3×C4—32no—
182C2×C3×C4—31no—
183C2×C3×C4—62no—
184C2×C3×C4—62no—
185C2×C3×C4—61no—
186C2×C3×C4—61no—
187C2×C3×C4—64no—
188C2×C3×C4—122no—
189C2×C3×C4—121no—
190C2×C3×C4#41⋊C314yes—
191C2×C3×C4C22×A412yes—
192C2×C3×C4C22×A412yes—
193C2×C3×C4C22×A411yescharacteristic
194C2×C3×C4C22×A411yescharacteristic
195C2×C9—41no—
196C2×C9—41no—
197C2×C9—41no—
198C2×C9—82no—
199#41—22no—
200#41—64no—
201#41—62no—
202C2×Q8—21no—
203C2×Q8—31no—
204C2×Q8—31no—
205C2×Q8—61no—
206C2×Q8C23×C911yescharacteristic
207C2×D4—32no—
208C2×D4—32no—
209C2×D4—32no—
210C2×D4—31no—
211C22×C4—31no—
212C22×C4—31no—
213C22×C4—32no—
214C22×C4—32no—
215C22×C4—32no—
216C22×C4C2×C22⋊C911yescharacteristic
217C4⋊C4—31no—
218C4⋊C4—31no—
219C4⋊C4—32no—
220C4⋊C4—32no—
221C4⋊C4—32no—
222C4⋊C4—32no—
223C4⋊C4—32no—
224C4⋊C4C2×C22⋊C911yescharacteristic
225C4⋊C4C2×C22⋊C911yescharacteristic
226C22⋊C4—34no—
227C22⋊C4—34no—
228C22⋊C4—32no—
229C22⋊C4—32no—
230C22⋊C4C2×C22⋊C912yes—
231C42—31no—
232C42—31no—
233C42—32no—
234C42—32no—
235C42—31no—
236C42—31no—
237C42C2×C22⋊C912yes—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—62no—
241C22×C3—62no—
242C22×C3—62no—
243C22×C3C2×#41⋊C312yes—
244C22×C3C23×A411yescharacteristic
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—31no—
248C3×C4—31no—
249C3×C4—62no—
250C3×C4—61no—
251C3×C4—61no—
252C3×C4—61no—
253C3×C4C2×#41⋊C312yes—
254C3×C4C2×#41⋊C312yes—
255C9—41noSylow
256C23—32no—
257C23C22×C22⋊C911yescharacteristic
258Q8—31no—
259Q8—61no—
260Q8—61no—
261Q8—62no—
262Q8C9×#4111yescharacteristic
263D4—62no—
264D4—62no—
265D4—64no—
266D4—62no—
267D4—122no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—32no—
272C2×C4—31no—
273C2×C4—62no—
274C2×C4—62no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—64no—
278C2×C4—122no—
279C2×C4—121no—
280C2×C4#41⋊C914yescomplemented
281C2×C4C22×C22⋊C912yes—
282C2×C4C22×C22⋊C912yes—
283C2×C4C22×C22⋊C911yescharacteristic
284C2×C4C22×C22⋊C911yescharacteristic
285C2×C3—22no—
286C2×C3—122no—
287C2×C3C22×#41⋊C311yescharacteristic
288C2×C3A4×#4111yescharacteristic
289C2×C3#594511yescharacteristic
290C22—21no—
291C22—21no—
292C22—62no—
293C22—62no—
294C22—62no—
295C22C2×#41⋊C912yes—
296C22C23×C22⋊C911yescharacteristic
297C4—22no—
298C4—22no—
299C4—31no—
300C4—31no—
301C4—62no—
302C4—61no—
303C4—61no—
304C4—61no—
305C4C2×#41⋊C912yes—
306C4C2×#41⋊C912yes—
307C3#3480⋊C311yescharacteristic
308C2—22no—
309C2—122no—
310C2C22×#41⋊C911yescharacteristic
311C2#41×C22⋊C911yescharacteristic
312C2#1059312011yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutatorC2×Q8C23×C9
Frattini, socleC22×C3C23×A4
Fitting, prime radicalC3×#3480C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×#117A4
hypocenterQ8C9×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
2. C4⋊(#41⋊C9)C2semidirect
3. #548⋊C9C2semidirect
4. C4×#41⋊C9C2semidirect
5. C2×C4×Q8⋊C9C2semidirect
32. #3480C9semidirect
73. Q8⋊C9#41semidirect
75. #557C2×C9semidirect
78. #550C2×C9semidirect
83. C4×#41C2×C9semidirect
280. C2×C4#41⋊C9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
C4⋊(#41⋊C9)2
#548⋊C92
C4×#41⋊C92
C2×C4×Q8⋊C92
C3×#34803
C9×#1174