Finite Group Databasebeta

← #3482⋊C9 #11919733

Subgroups — #3482⋊C9 #11919733

Order 1152.

521 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 115 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
2D4×Q8⋊C9C211yesmaximal, characteristic, complemented
3#548⋊C9C212yesmaximal, complemented
4C4×#41⋊C9C211yesmaximal, characteristic, complemented
5C2×C4×Q8⋊C9C212yesmaximal, complemented
6C3×#3482C311yesmaximal, characteristic
7C2×#41⋊C9C2211yescharacteristic
8C22×Q8⋊C9C2212yes—
9C4×D4×C9—41nomaximal
10C4×Q8⋊C9C2211yescharacteristic
11C4×Q8⋊C9C2212yes—
12C4×Q8⋊C9C2211yescharacteristic
13C3×#557C2×C311yescharacteristic
14C3×#556—31no—
15C3×#552—32no—
16C3×D4×Q8C2×C311yescharacteristic
17C3×#548C2×C312yes—
18C3×#547—31no—
19C3×#533—31no—
20C3×#529—32no—
21C3×C4×#41—31no—
22C3×C4×#41C2×C311yescharacteristic
23C2×C3×C4×Q8C2×C312yes—
24C2×D4×C9—41no—
25C22×C4×C9—42no—
26#41⋊C9—21no—
27C2×Q8⋊C9—22no—
28C2×Q8⋊C9C2311yescharacteristic
29C9×C4⋊C4—41no—
30C9×C22⋊C4—42no—
31C42×C9—41no—
32#3482C911yescharacteristic, complemented, Sylow
33C2×C3×#41—31no—
34C2×C3×#41C22×C311yescharacteristic
35C22×C3×Q8C22×C312yes—
36C3×C4⋊Q8—31no—
37C3×C4⋊Q8—31no—
38C3×#126—34no—
39C3×#125—32no—
40C3×#125—32no—
41C3×#124—32no—
42C3×#123—34no—
43C3×C22⋊Q8—32no—
44C3×C22⋊Q8—32no—
45C3×C22⋊Q8—32no—
46C3×#121—32no—
47C3×C4×Q8—31no—
48C3×C4×Q8—31no—
49C3×C4×Q8—32no—
50C3×C4×Q8—32no—
51C3×C4×Q8C22×C311yescharacteristic
52C3×C4×Q8C22×C312yes—
53C3×C4×Q8C22×C311yescharacteristic
54C3×C4×D4—31no—
55C3×C4×D4—32no—
56C3×C4×D4—31no—
57C3×C4×D4—31no—
58C3×C4×D4—32no—
59C3×C4×D4A411yescharacteristic
60C3×#117—32no—
61C3×#117—31no—
62C3×#117—32no—
63C3×#117—31no—
64C2×C3×C4⋊C4—32no—
65C2×C3×C42—32no—
66C2×C3×C42—31no—
67C23×C9—42no—
68D4×C9—44no—
69C2×C4×C9—41no—
70C2×C4×C9—41no—
71C2×C4×C9—42no—
72C2×C4×C9—41no—
73C2×C4×C9—84no—
74Q8⋊C9#4111yescharacteristic, complemented
75#557C2×C911yescharacteristic, complemented
76#556—31no—
77#552—32no—
78D4×Q8C2×C911yescharacteristic
79#548C2×C912yescomplemented
80#547—31no—
81#533—31no—
82#529—32no—
83C4×#41—31no—
84C4×#41C2×C911yescharacteristic, complemented
85C2×C4×Q8C2×C912yescomplemented
86C3×#41—21no—
87C3×#41—64no—
88C3×#41—61no—
89C2×C3×Q8—22no—
90C2×C3×Q8—31no—
91C2×C3×Q8—32no—
92C2×C3×Q8—62no—
93C2×C3×Q8C23×C311yescharacteristic
94C2×C3×D4—31no—
95C2×C3×D4—32no—
96C2×C3×D4C2×A411yescharacteristic
97C22×C3×C4—32no—
98C22×C3×C4—32no—
99C22×C3×C4—31no—
100C22×C3×C4—31no—
101C22×C3×C4—31no—
102C22×C3×C4C2×A412yes—
103C3×C4⋊C4—31no—
104C3×C4⋊C4—32no—
105C3×C4⋊C4—31no—
106C3×C4⋊C4—34no—
107C3×C4⋊C4—32no—
108C3×C4⋊C4—32no—
109C3×C4⋊C4—31no—
110C3×C4⋊C4—32no—
111C3×C4⋊C4—32no—
112C3×C4⋊C4C2×A411yescharacteristic
113C3×C22⋊C4—32no—
114C3×C22⋊C4—34no—
115C3×C22⋊C4—32no—
116C3×C22⋊C4—32no—
117C3×C22⋊C4C2×A412yes—
118C3×C42—31no—
119C3×C42—32no—
120C3×C42—31no—
121C3×C42—32no—
122C3×C42—31no—
123C3×C42—32no—
124C3×C42C2×A411yescharacteristic
125C22×C9—44no—
126C22×C9—41no—
127C22×C9—82no—
128C22×C9—82no—
129C4×C9—42no—
130C4×C9—42no—
131C4×C9—82no—
132C4×C9—81no—
133C2×#41—31no—
134C2×#41C22×C911yescharacteristic
135C22×Q8C22×C912yes—
136C4⋊Q8—31no—
137C4⋊Q8—31no—
138#126—34no—
139#125—32no—
140#125—32no—
141#124—32no—
142#123—34no—
143C22⋊Q8—32no—
144C22⋊Q8—32no—
145C22⋊Q8—32no—
146#121—32no—
147C4×Q8—31no—
148C4×Q8—31no—
149C4×Q8—32no—
150C4×Q8—32no—
151C4×Q8C22×C911yescharacteristic
152C4×Q8C22×C912yes—
153C4×Q8C22×C911yescharacteristic
154C4×D4—31no—
155C4×D4—32no—
156C4×D4—31no—
157C4×D4—31no—
158C4×D4—32no—
159C4×D4C22⋊C911yescharacteristic
160#117—32no—
161#117—31no—
162#117—32no—
163#117—31no—
164C2×C4⋊C4—32no—
165C2×C42—32no—
166C2×C42—31no—
167C23×C3—31no—
168C23×C3C22×A412yes—
169C3×Q8—31no—
170C3×Q8—62no—
171C3×Q8—62no—
172C3×Q8—62no—
173C3×Q8C3×#4111yescharacteristic
174C3×D4—61no—
175C3×D4—61no—
176C3×D4—64no—
177C3×D4#41⋊C314yes—
178C2×C3×C4—24no—
179C2×C3×C4—31no—
180C2×C3×C4—31no—
181C2×C3×C4—31no—
182C2×C3×C4—32no—
183C2×C3×C4—32no—
184C2×C3×C4—61no—
185C2×C3×C4—61no—
186C2×C3×C4—62no—
187C2×C3×C4—62no—
188C2×C3×C4—64no—
189C2×C3×C4—62no—
190C2×C3×C4—62no—
191C2×C3×C4C22×A412yes—
192C2×C3×C4C22×A411yescharacteristic
193C2×C3×C4C22×A411yescharacteristic
194C2×C3×C4C22×A411yescharacteristic
195C2×C9—41no—
196C2×C9—41no—
197C2×C9—41no—
198C2×C9—84no—
199#41—21no—
200#41—64no—
201#41—61no—
202C2×Q8—22no—
203C2×Q8—31no—
204C2×Q8—32no—
205C2×Q8—62no—
206C2×Q8C23×C911yescharacteristic
207C2×D4—31no—
208C2×D4—32no—
209C2×D4C2×C22⋊C911yescharacteristic
210C22×C4—32no—
211C22×C4—32no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4C2×C22⋊C912yes—
216C4⋊C4—31no—
217C4⋊C4—32no—
218C4⋊C4—31no—
219C4⋊C4—34no—
220C4⋊C4—32no—
221C4⋊C4—32no—
222C4⋊C4—31no—
223C4⋊C4—32no—
224C4⋊C4—32no—
225C4⋊C4C2×C22⋊C911yescharacteristic
226C22⋊C4—32no—
227C22⋊C4—34no—
228C22⋊C4—32no—
229C22⋊C4—32no—
230C22⋊C4C2×C22⋊C912yes—
231C42—31no—
232C42—31no—
233C42—32no—
234C42—32no—
235C42—31no—
236C42—32no—
237C42C2×C22⋊C911yescharacteristic
238C22×C3—22no—
239C22×C3—22no—
240C22×C3—61no—
241C22×C3—61no—
242C22×C3—61no—
243C22×C3C2×#41⋊C314yes—
244C22×C3C23×A411yescharacteristic
245C3×C4—21no—
246C3×C4—22no—
247C3×C4—31no—
248C3×C4—31no—
249C3×C4—61no—
250C3×C4—62no—
251C3×C4—62no—
252C3×C4—61no—
253C3×C4C2×#41⋊C312yes—
254C3×C42−1+4⋊C312yes—
255C9—41noSylow
256C23—31no—
257C23C22×C22⋊C912yes—
258Q8—31no—
259Q8—62no—
260Q8—62no—
261Q8—62no—
262Q8C9×#4111yescharacteristic
263D4—61no—
264D4—61no—
265D4—64no—
266D4#41⋊C914yescomplemented
267C2×C4—24no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—32no—
272C2×C4—32no—
273C2×C4—61no—
274C2×C4—61no—
275C2×C4—62no—
276C2×C4—62no—
277C2×C4—64no—
278C2×C4—62no—
279C2×C4—62no—
280C2×C4C22×C22⋊C912yes—
281C2×C4C22×C22⋊C911yescharacteristic
282C2×C4C22×C22⋊C911yescharacteristic
283C2×C4C22×C22⋊C911yescharacteristic
284C2×C3—24no—
285C2×C3—121no—
286C2×C3C22×#41⋊C311yescharacteristic
287C2×C3A4×#4111yescharacteristic
288C2×C3C2×2−1+4⋊C311yescharacteristic
289C22—22no—
290C22—22no—
291C22—61no—
292C22—61no—
293C22—61no—
294C22C2×#41⋊C914yes—
295C22C23×C22⋊C911yescharacteristic
296C4—21no—
297C4—22no—
298C4—31no—
299C4—31no—
300C4—61no—
301C4—62no—
302C4—62no—
303C4—61no—
304C4C2×#41⋊C912yes—
305C42−1+4⋊C912yes—
306C3#3482⋊C311yescharacteristic
307C2—24no—
308C2—121no—
309C2C22×#41⋊C911yescharacteristic
310C2#41×C22⋊C911yescharacteristic
311C2C2×2−1+4⋊C911yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutatorC2×Q8C23×C9
Frattini, socleC22×C3C23×A4
Fitting, prime radicalC3×#3482C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×C4×D4A4
hypocenterQ8C9×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
2. D4×Q8⋊C9C2semidirect
3. #548⋊C9C2semidirect
4. C4×#41⋊C9C2semidirect
5. C2×C4×Q8⋊C9C2semidirect
32. #3482C9semidirect
74. Q8⋊C9#41semidirect
75. #557C2×C9semidirect
79. #548C2×C9semidirect
84. C4×#41C2×C9semidirect
85. C2×C4×Q8C2×C9semidirect
266. D4#41⋊C9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
D4×Q8⋊C92
#548⋊C92
C4×#41⋊C92
C2×C4×Q8⋊C92
C3×#34823
C4×D4×C94