Finite Group Databasebeta

← C3×#4994 #10592091

Subgroups — C3×#4994 #10592091

Order 576.

418 conjugacy classes of subgroups.

The subgroup lattice has 337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
5C2×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#396—31nomaximal
9#4994C311yesmaximal, characteristic, direct product factor
10C23×C3×D3C2211yescharacteristic
11C22×C32×C4C2211yescharacteristic
12C22×C32×C4C2211yescharacteristic
13C22×C32×C4C2211yescharacteristic
14C22×C3×Dic3C2211yescharacteristic
15C22×C3×Dic3C2211yescharacteristic
16C22×C3×Dic3C2211yescharacteristic
17C32×C4⋊C4—22no—
18C3×(C2×D3)⋊C4—22no—
19C3×(C2×D3)⋊C4—22no—
20C3×(C2×D3)⋊C4—22no—
21C3×C4⋊Dic3—22no—
22C3×Dic3⋊C4—22no—
23C2×C3×C4⋊C4—21no—
24C2×C3×C4⋊C4—31no—
25C2×C3×C4⋊C4—31no—
26C2×C3×C4⋊C4D311yescharacteristic, complemented
27C2×C3×C4⋊C4C2×C311yescharacteristic, complemented
28C2×C3×C22⋊C4—31no—
29C2×C3×C22⋊C4—31no—
30C2×C3×C22⋊C4—31no—
31C2×(C2×D3)⋊C4C2×C311yescharacteristic
32C2×(C2×D3)⋊C4C2×C311yescharacteristic
33C2×(C2×D3)⋊C4C2×C311yescharacteristic
34C2×C4⋊Dic3C2×C311yescharacteristic, complemented
35C2×Dic3⋊C4C2×C311yescharacteristic, complemented
36C3×#95—31no—
37C3⋊#95C2×C311yescharacteristic, complemented
38C23×C32C2311yescharacteristic
39C22×C3×D3—21no—
40C22×C3×D3—21no—
41C22×C3×D3—21no—
42C22×C3×D3—21no—
43C22×C3×D3—21no—
44C22×C3×D3—21no—
45C22×C3×D3Q812yes—
46C2×C32×C4—21no—
47C2×C32×C4—21no—
48C2×C32×C4—21no—
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4D412yes—
54C2×C32×C4D412yes—
55C2×C3×Dic3—21no—
56C2×C3×Dic3—21no—
57C2×C3×Dic3—21no—
58C2×C3×Dic3—21no—
59C2×C3×Dic3—21no—
60C2×C3×Dic3—21no—
61C2×C3×Dic3—21no—
62C2×C3×Dic3—21no—
63C2×C3×Dic3D412yes—
64#396—31noSylow
65C24×C3—31no—
66C23×D3C22×C311yescharacteristic
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—21no—
70C22×C3×C4—31no—
71C22×C3×C4—31no—
72C22×C3×C4—31no—
73C22×C3×C4C2×D311yescharacteristic
74C22×C3×C4C2×D311yescharacteristic
75C22×C3×C4C2×D311yescharacteristic
76C22×C3×C4C22×C311yescharacteristic
77C22×C3×C4C22×C311yescharacteristic
78C22×C3×C4C22×C311yescharacteristic
79C22×Dic3C22×C311yescharacteristic
80C22×Dic3C22×C311yescharacteristic
81C22×Dic3C22×C311yescharacteristic
82C3×C4⋊C4—24no—
83C3×C4⋊C4—22no—
84C3×C4⋊C4—22no—
85C3×C4⋊C4—62no—
86C3×C4⋊C4—62no—
87C3×C22⋊C4—62no—
88C3×C22⋊C4—62no—
89C3×C22⋊C4—62no—
90(C2×D3)⋊C4—22no—
91(C2×D3)⋊C4—22no—
92(C2×D3)⋊C4—22no—
93C4⋊Dic3—22no—
94Dic3⋊C4—22no—
95C22×C32C2×D411yescharacteristic
96C22×C32C2×D411yescharacteristic
97C22×C32C2×D411yescharacteristic
98C22×C32C2×Q811yescharacteristic
99C22×C32#4111yescharacteristic
100C22×C32#4111yescharacteristic
101C22×C32#4111yescharacteristic
102C2×C3×D3—22no—
103C2×C3×D3—22no—
104C2×C3×D3—22no—
105C2×C3×D3—41no—
106C2×C3×D3—41no—
107C2×C3×D3—41no—
108C2×C3×D3—41no—
109C32×C4—22no—
110C32×C4—22no—
111C32×C4—41no—
112C3×Dic3—22no—
113C3×Dic3—41no—
114C3×Dic3—41no—
115C2×C4⋊C4—31no—
116C2×C4⋊C4—31no—
117C2×C4⋊C4C3×D311yescharacteristic, complemented
118C2×C22⋊C4—31no—
119C2×C22⋊C4—31no—
120C2×C22⋊C4—31no—
121#95—31no—
122C23×C3—21no—
123C23×C3—32no—
124C23×C3—61no—
125C23×C3—61no—
126C23×C3—61no—
127C23×C3—61no—
128C23×C3—61no—
129C23×C3—61no—
130C23×C3C22×D311yescharacteristic
131C23×C3C23×C311yescharacteristic
132C22×D3—21no—
133C22×D3—21no—
134C22×D3—21no—
135C22×D3—21no—
136C22×D3—21no—
137C22×D3—21no—
138C22×D3C3×Q812yes—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—22no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—32no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4—61no—
164C2×C3×C4—61no—
165C2×C3×C4—61no—
166C2×C3×C4—61no—
167C2×C3×C4—61no—
168C2×C3×C4—61no—
169C2×C3×C4—61no—
170C2×C3×C4—61no—
171C2×C3×C4D1212yes—
172C2×C3×C4#6712yes—
173C2×C3×C4C3×D412yes—
174C2×C3×C4C3×D412yes—
175C2×Dic3—21no—
176C2×Dic3—21no—
177C2×Dic3—21no—
178C2×Dic3—21no—
179C2×Dic3—21no—
180C2×Dic3—21no—
181C2×Dic3—21no—
182C2×Dic3—21no—
183C2×Dic3C3×D412yes—
184C2×C32#12111yescharacteristic
185C2×C32#12111yescharacteristic
186C2×C32#12111yescharacteristic
187C2×C32C22⋊Q811yescharacteristic
188C2×C32C22⋊Q811yescharacteristic
189C2×C32C22⋊Q811yescharacteristic
190C2×C32#12611yescharacteristic
191C3×D3—42no—
192C24—31no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—31no—
196C22×C4C2×C3×D311yescharacteristic
197C22×C4C2×C3×D311yescharacteristic
198C22×C4C2×C3×D311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—62no—
201C4⋊C4—62no—
202C22⋊C4—62no—
203C22⋊C4—62no—
204C22⋊C4—62no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—62no—
213C22×C3—62no—
214C22×C3—62no—
215C22×C3—121no—
216C22×C3—121no—
217C22×C3—121no—
218C22×C3—121no—
219C22×C3C2×D1211yescharacteristic
220C22×C3#23511yescharacteristic
221C22×C3D3×D411yescharacteristic
222C22×C3#23711yescharacteristic
223C22×C3D3×Q811yescharacteristic
224C22×C3#23911yescharacteristic
225C22×C3C2×#6711yescharacteristic
226C22×C3C2×C3×D411yescharacteristic
227C22×C3C2×C3×D411yescharacteristic
228C22×C3C2×C3×D411yescharacteristic
229C22×C3C2×C3×Q811yescharacteristic
230C22×C3C3×#4111yescharacteristic
231C22×C3C3×#4111yescharacteristic
232C22×C3C3×#4111yescharacteristic
233C2×D3—22no—
234C2×D3—22no—
235C2×D3—22no—
236C2×D3—41no—
237C2×D3—41no—
238C2×D3—41no—
239C2×D3—41no—
240C3×C4—24no—
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—22no—
245C3×C4—42no—
246C3×C4—42no—
247C3×C4—41no—
248C3×C4—41no—
249C3×C4—62no—
250C3×C4—121no—
251C3×C4—121no—
252Dic3—22no—
253Dic3—41no—
254Dic3—41no—
255C32#39611yescharacteristic, complemented, Sylow
256C23—32no—
257C23—61no—
258C23—61no—
259C23—61no—
260C23—61no—
261C23—61no—
262C23—61no—
263C23C22×C3×D311yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—32no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4C3×D1212yes—
281C2×C4C3×#6712yes—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—122no—
290C2×C3#89511yescharacteristic
291C2×C3#89611yescharacteristic
292C2×C3#89711yescharacteristic
293C2×C3#89811yescharacteristic
294C2×C3#93011yescharacteristic
295C2×C3#93911yescharacteristic
296C2×C3#94611yescharacteristic
297C2×C3C3×#12111yescharacteristic
298C2×C3C3×#12111yescharacteristic
299C2×C3C3×#12111yescharacteristic
300C2×C3C3×C22⋊Q811yescharacteristic
301C2×C3C3×C22⋊Q811yescharacteristic
302C2×C3C3×C22⋊Q811yescharacteristic
303C2×C3C3×#12611yescharacteristic
304D3—42no—
305C22—62no—
306C22—62no—
307C22—62no—
308C22—121no—
309C22—121no—
310C22—121no—
311C22—121no—
312C22C2×C3×D1211yescharacteristic
313C22C3×#23511yescharacteristic
314C22C3×D3×D411yescharacteristic
315C22C3×#23711yescharacteristic
316C22C3×D3×Q811yescharacteristic
317C22C3×#23911yescharacteristic
318C22C2×C3×#6711yescharacteristic
319C4—22no—
320C4—22no—
321C4—41no—
322C4—62no—
323C4—121no—
324C4—121no—
325C3—21no—
326C3#499411yescharacteristic, direct product factor
327C3C3×#39611yescharacteristic, complemented
328C2—122no—
329C2C3×#89511yescharacteristic
330C2C3×#89611yescharacteristic
331C2C3×#89711yescharacteristic
332C2C3×#89811yescharacteristic
333C2C3×#93011yescharacteristic
334C2C3×#93911yescharacteristic
335C2C3×#94611yescharacteristic
subgroupG/H
centerC23×C3C22×D3
commutator, cosocleC23×C3C23×C3
FrattiniC23C22×C3×D3
FittingC2×C32×C4⋊C4C2
socleC23×C32C23
prime radicalC23×C3×D3C22
hypercenterC2×C3×C4⋊C4D3
hypocenterC3C3×#396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4⋊C4C2semidirect
5. C2×C3×C4⋊Dic3C2semidirect
6. C2×C3×Dic3⋊C4C2semidirect
7. C3×C3⋊#95C2semidirect
9. #4994C3direct (N × H)
26. C2×C3×C4⋊C4D3semidirect
27. C2×C3×C4⋊C4C2×C3semidirect
34. C2×C4⋊Dic3C2×C3semidirect
35. C2×Dic3⋊C4C2×C3semidirect
37. C3⋊#95C2×C3semidirect
117. C2×C4⋊C4C3×D3semidirect
255. C32#396semidirect
326. C3#4994direct (N × H)
327. C3C3×#396semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊C42
C2×C3×(C2×D3)⋊C42
C2×C3×C4⋊Dic32
C2×C3×Dic3⋊C42
C3×C3⋊#952
C3×#3963
#49943