Finite Group Databasebeta

← #10591334

Subgroups — #10591334

Order 576.

362 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 112 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×C4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×Dic3⋊Dic3C211yesmaximal, characteristic
4C3×C3⋊#95C211yesmaximal, characteristic
5#63579C211yesmaximal, characteristic
6#63579C211yesmaximal, characteristic
7#63579C211yesmaximal, characteristic
8#4978—31nomaximal
9#4653—31nomaximal
10C22×C32×C4C2211yescharacteristic
11C22×C3⋊Dic3C2211yescharacteristic
12C22×C3⋊Dic3C2211yescharacteristic
13C22×C3×Dic3C2211yescharacteristic
14C22×C3×Dic3C2211yescharacteristic
15C22×C3×Dic3C2211yescharacteristic
16C22×C3×Dic3C2211yescharacteristic
17C4×C3⋊Dic3—22no—
18C3×Dic3⋊C4—22no—
19Dic3⋊Dic3C414yescomplemented
20C2×C3×C4⋊C4—31no—
21C2×C4⋊Dic3—31no—
22C2×Dic3⋊C4—31no—
23C2×Dic3⋊C4D311yescharacteristic
24C2×C4×Dic3—31no—
25C2×C4×Dic3—31no—
26C2×C4×Dic3—61no—
27C3×#95—31no—
28C3⋊#95—31no—
29C3⋊#95—31no—
30C3⋊#95—31no—
31C3⋊#95—31no—
32C3⋊#95—31no—
33C3⋊#95—31no—
34C3⋊#95D311yescharacteristic
35C23×C32C2311yescharacteristic
36C2×C32×C4—21no—
37C2×C32×C4—21no—
38C2×C32×C4D412yes—
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3C2×C412yes—
44C2×C3⋊Dic3Q812yes—
45C2×C3×Dic3—21no—
46C2×C3×Dic3—21no—
47C2×C3×Dic3—21no—
48C2×C3×Dic3—21no—
49C2×C3×Dic3—21no—
50C2×C3×Dic3—21no—
51C2×C3×Dic3—21no—
52C2×C3×Dic3—21no—
53C2×C3×Dic3—21no—
54C2×C3×Dic3—21no—
55C2×C3×Dic3C2×C412yes—
56C2×C3×Dic3C2×C412yes—
57#387—91noSylow
58C22×C3×C4—21no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4—31no—
62C22×C3×C4—31no—
63C22×C3×C4C2×D311yescharacteristic
64C22×C3×C4C2×D311yescharacteristic
65C22×Dic3—31no—
66C22×Dic3—31no—
67C22×Dic3—31no—
68C22×Dic3—31no—
69C22×Dic3—61no—
70C22×Dic3—61no—
71C22×Dic3C2×D311yescharacteristic
72C22×Dic3C2×D311yescharacteristic
73C22×Dic3C2×D311yescharacteristic
74C22×Dic3C2×D311yescharacteristic
75C3×C4⋊C4—62no—
76C4⋊Dic3—34no—
77Dic3⋊C4—22no—
78Dic3⋊C4—34no—
79C4×Dic3—64no—
80C4×Dic3—62no—
81C4×Dic3—62no—
82C22×C32C22×C411yescharacteristic
83C22×C32C2×D411yescharacteristic
84C22×C32C2×Q811yescharacteristic
85C22×C32#4111yescharacteristic
86C22×C32#4111yescharacteristic
87C22×C32#4111yescharacteristic
88C22×C32#4111yescharacteristic
89C32×C4—22no—
90C3⋊Dic3—22no—
91C3⋊Dic3—22no—
92C3×Dic3—22no—
93C3×Dic3—22no—
94C3×Dic3—41no—
95C3×Dic3—41no—
96C2×C4⋊C4—31no—
97C2×C4⋊C4—91no—
98C2×C42—91no—
99#95—31no—
100#95—91no—
101#95—91no—
102#95—91no—
103C23×C3—21no—
104C23×C3C22×D311yescharacteristic
105C23×C3C22×D311yescharacteristic
106C2×C3×C4—22no—
107C2×C3×C4—22no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—22no—
113C2×C3×C4—32no—
114C2×C3×C4—32no—
115C2×C3×C4—61no—
116C2×C3×C4—61no—
117C2×C3×C4—61no—
118C2×C3×C4—61no—
119C2×C3×C4—61no—
120C2×C3×C4—61no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×C3×C4—61no—
125C2×C3×C4D1212yes—
126C2×C3×C4#6712yes—
127C2×Dic3—21no—
128C2×Dic3—21no—
129C2×Dic3—21no—
130C2×Dic3—21no—
131C2×Dic3—21no—
132C2×Dic3—21no—
133C2×Dic3—21no—
134C2×Dic3—21no—
135C2×Dic3—21no—
136C2×Dic3—21no—
137C2×Dic3—32no—
138C2×Dic3—32no—
139C2×Dic3—32no—
140C2×Dic3—32no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3C4×D312yes—
156C2×Dic3C4×D312yes—
157C2×C32#11711yescharacteristic
158C2×C32C4×D411yescharacteristic
159C2×C32C4×Q811yescharacteristic
160C2×C32C22⋊Q811yescharacteristic
161C2×C32#12311yescharacteristic
162C2×C32#12511yescharacteristic
163C2×C32#12611yescharacteristic
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—31no—
167C22×C4—31no—
168C22×C4—91no—
169C22×C4—91no—
170C22×C4D3211yescharacteristic
171C4⋊C4—62no—
172C4⋊C4—94no—
173C42—182no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3—21no—
181C22×C3C2×C4×D311yescharacteristic
182C22×C3C2×C4×D311yescharacteristic
183C22×C3C2×D1211yescharacteristic
184C22×C3#23511yescharacteristic
185C22×C3#23511yescharacteristic
186C22×C3#23711yescharacteristic
187C22×C3#23711yescharacteristic
188C22×C3#23711yescharacteristic
189C22×C3#23711yescharacteristic
190C22×C3#23711yescharacteristic
191C22×C3D3×Q811yescharacteristic
192C22×C3D3×Q811yescharacteristic
193C22×C3#23911yescharacteristic
194C22×C3C2×#6711yescharacteristic
195C3×C4—24no—
196C3×C4—22no—
197C3×C4—22no—
198C3×C4—62no—
199C3×C4—62no—
200C3×C4—121no—
201C3×C4—121no—
202Dic3—22no—
203Dic3—22no—
204Dic3—41no—
205Dic3—41no—
206Dic3—64no—
207Dic3—64no—
208Dic3—62no—
209Dic3—62no—
210Dic3—62no—
211Dic3—62no—
212C32#38711yescharacteristic, complemented, Sylow
213C23C2×D3211yescharacteristic
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—32no—
217C2×C4—32no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—61no—
221C2×C4—61no—
222C2×C4—61no—
223C2×C4—61no—
224C2×C4—61no—
225C2×C4—61no—
226C2×C4—61no—
227C2×C4—61no—
228C2×C4—92no—
229C2×C4—92no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4#62612yes—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3C4×D1211yescharacteristic
243C2×C3#87711yescharacteristic
244C2×C3#87911yescharacteristic
245C2×C3#88611yescharacteristic
246C2×C3#88711yescharacteristic
247C2×C3#88711yescharacteristic
248C2×C3#88911yescharacteristic
249C2×C3#88911yescharacteristic
250C2×C3#89211yescharacteristic
251C2×C3#89711yescharacteristic
252C2×C3#89811yescharacteristic
253C2×C3C4×#6711yescharacteristic
254C2×C3#93511yescharacteristic
255C2×C3#94611yescharacteristic
256C22#379611yescharacteristic
257C22#379711yescharacteristic
258C22#379811yescharacteristic
259C22C4×D3211yescharacteristic
260C22#380511yescharacteristic
261C22#380511yescharacteristic
262C22C2×#62611yescharacteristic
263C4—22no—
264C4—62no—
265C4—62no—
266C4—121no—
267C4—121no—
268C4—182no—
269C4—182no—
270C3—21no—
271C3#465311yescharacteristic, complemented
272C3#497811yescharacteristic, complemented
273C2#6383811yescharacteristic
274C2#6386211yescharacteristic
275C2#6387011yescharacteristic
276C2#6387111yescharacteristic
277C2#6387811yescharacteristic
278C2C4×#62611yescharacteristic
279C2#6396211yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutatorC22×C32C22×C4
FittingC22×C32×C4C22
socle, prime radical, cosocleC23×C32C23
hypercenterC22×C4D32
hypocenterC32#387
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
19. Dic3⋊Dic3C4semidirect
212. C32#387semidirect
271. C3#4653semidirect
272. C3#4978semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊Dic32
C2×C3×Dic3⋊C42
C2×Dic3⋊Dic32
C3×C3⋊#952
#635792
#49783
#46533