Finite Group Databasebeta

← C3×#74358 #11802841

Subgroups — C3×#74358 #11802841

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C32×#384C211yesmaximal, characteristic, complemented
3C3×#4990C214yesmaximal
4C3×#4987C212yesmaximal
5C3×#4978C214yesmaximal, complemented
6C3×Dic3×C4⋊C4C212yesmaximal, complemented
7C3×#4936C211yesmaximal, characteristic, complemented
8C3×#2314—31nomaximal
9#74358C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C4⋊C4C2212yes—
12C2×C32×C4⋊C4C2214yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2214yes—
15C2×C3×(C2×D3)⋊C4C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2214yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C3×#872C418yescomplemented
21C3×C3⋊#95C2214yes—
22C3×C3⋊#95C2214yes—
23C3×C3⋊#95C2214yes—
24C2×C3×#117—31no—
25C2×#872C2×C311yescharacteristic
26C3×#388—34no—
27C3×#387—34no—
28C3×#384—21no—
29C3×#384D311yescharacteristic, complemented
30C3×#384C2×C311yescharacteristic, complemented
31C3×#382—31no—
32C3×#380—32no—
33C3×C4×C4⋊C4—32no—
34#4990C2×C314yes—
35#4987C2×C312yes—
36#4978C2×C314yescomplemented
37Dic3×C4⋊C4C2×C312yescomplemented
38#4936C2×C311yescharacteristic, complemented
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2314yes—
41C22×C32×C4C2312yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2311yescharacteristic
46C2×C3×C4×D3—22no—
47C2×C3×C4×D3—22no—
48C2×C3×C4×D3C2×C414yes—
49C32×C4⋊C4—24no—
50C32×C4⋊C4—44no—
51C32×C42C2×C414yes—
52C3×(C2×D3)⋊C4—44no—
53C3×(C2×D3)⋊C4C2×C418yes—
54C3×C4⋊Dic3—24no—
55C3×Dic3⋊C4C2×C418yes—
56C3×C4×Dic3—44no—
57C3×C4×Dic3C2×C414yes—
58#2314—31noSylow
59C23×C3×C4—31no—
60C22×C4×D3C22×C311yescharacteristic
61C3×#117—38no—
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—24no—
64C2×C3×C4⋊C4—32no—
65C2×C3×C4⋊C4—32no—
66C2×C3×C4⋊C4C2×D312yes—
67C2×C3×C4⋊C4C2×D314yes—
68C2×C3×C4⋊C4C22×C312yes—
69C2×C3×C4⋊C4C22×C314yes—
70C2×C3×C22⋊C4—32no—
71C2×C3×C22⋊C4—34no—
72C2×C3×C42—21no—
73C2×C3×C42—31no—
74C2×C3×C42—34no—
75C2×C3×C42C2×D311yescharacteristic
76C2×C3×C42C22×C311yescharacteristic
77C2×(C2×D3)⋊C4C22×C314yes—
78C2×(C2×D3)⋊C4C22×C312yes—
79C2×C4⋊Dic3C22×C312yes—
80C2×Dic3⋊C4C22×C312yes—
81C2×C4×Dic3C22×C314yes—
82C2×C4×Dic3C22×C311yescharacteristic
83#872C3×C418yescomplemented
84C3×#95—34no—
85C3×#95—34no—
86C3×#95—34no—
87C3⋊#95C22×C314yes—
88C3⋊#95C22×C314yes—
89C3⋊#95C22×C314yes—
90C23×C32C2411yescharacteristic
91C22×C3×D3—21no—
92C22×C3×D3—21no—
93C22×C3×D3—22no—
94C22×C3×D3—22no—
95C22×C3×D3C22×C412yes—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—24no—
99C2×C32×C4—24no—
100C2×C32×C4—24no—
101C2×C32×C4C22×C414yes—
102C2×C32×C4C22×C412yes—
103C2×C32×C4#4112yes—
104C2×C32×C4#4112yes—
105C2×C3×Dic3—21no—
106C2×C3×Dic3—21no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3C22×C414yes—
113C2×C3×Dic3C22×C412yes—
114C3×C4×D3—28no—
115C2×#117—31no—
116#388—34no—
117#387—34no—
118#384C3×D311yescharacteristic, complemented
119#382—31no—
120#380—32no—
121C4×C4⋊C4—32no—
122C24×C3—31no—
123C23×D3C23×C311yescharacteristic
124C22×C3×C4—22no—
125C22×C3×C4—21no—
126C22×C3×C4—24no—
127C22×C3×C4—31no—
128C22×C3×C4—32no—
129C22×C3×C4—34no—
130C22×C3×C4—34no—
131C22×C3×C4—62no—
132C22×C3×C4—62no—
133C22×C3×C4C22×D314yes—
134C22×C3×C4C22×D312yes—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C23×C314yes—
137C22×C3×C4C23×C312yes—
138C22×C3×C4C23×C311yescharacteristic
139C22×Dic3C23×C314yes—
140C22×Dic3C23×C311yescharacteristic
141C22×Dic3C23×C312yes—
142C2×C4×D3—22no—
143C2×C4×D3—22no—
144C2×C4×D3C2×C3×C414yes—
145C3×C4⋊C4—24no—
146C3×C4⋊C4—24no—
147C3×C4⋊C4—38no—
148C3×C4⋊C4—44no—
149C3×C4⋊C4—44no—
150C3×C4⋊C4—44no—
151C3×C4⋊C4—48no—
152C3×C4⋊C4—64no—
153C3×C22⋊C4—38no—
154C3×C22⋊C4—124no—
155C3×C42—24no—
156C3×C42—34no—
157C3×C42—124no—
158C3×C42C4×D314yes—
159C3×C42C2×C3×C414yes—
160(C2×D3)⋊C4—44no—
161(C2×D3)⋊C4C2×C3×C418yes—
162C4⋊Dic3—24no—
163Dic3⋊C4C2×C3×C418yes—
164C4×Dic3—44no—
165C4×Dic3C2×C3×C414yes—
166C22×C32C23×C411yescharacteristic
167C22×C32C2×#4111yescharacteristic
168C22×C32C2×#4111yescharacteristic
169C22×C32H(5,𝔽2)12yes—
170C22×C322−1+412yes—
171C2×C3×D3—22no—
172C2×C3×D3—24no—
173C2×C3×D3—41no—
174C2×C3×D3—41no—
175C2×C3×D3—42no—
176C32×C4—24no—
177C32×C4—44no—
178C32×C4#11714yes—
179C3×Dic3—22no—
180C3×Dic3—24no—
181C3×Dic3—44no—
182C23×C4—31no—
183#117—38no—
184C2×C4⋊C4—32no—
185C2×C4⋊C4—32no—
186C2×C4⋊C4C2×C3×D312yes—
187C2×C4⋊C4C2×C3×D314yes—
188C2×C22⋊C4—32no—
189C2×C22⋊C4—34no—
190C2×C42—31no—
191C2×C42—34no—
192C2×C42C2×C3×D311yescharacteristic
193#95—34no—
194#95—34no—
195#95—34no—
196C23×C3—21no—
197C23×C3—32no—
198C23×C3—61no—
199C23×C3—62no—
200C23×C3—61no—
201C23×C3—62no—
202C23×C3C23×D311yescharacteristic
203C23×C3C24×C311yescharacteristic
204C22×D3—21no—
205C22×D3—21no—
206C22×D3—22no—
207C22×D3—22no—
208C22×D3C22×C3×C412yes—
209C2×C3×C4—24no—
210C2×C3×C4—24no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—34no—
226C2×C3×C4—32no—
227C2×C3×C4—44no—
228C2×C3×C4—44no—
229C2×C3×C4—44no—
230C2×C3×C4—61no—
231C2×C3×C4—62no—
232C2×C3×C4—61no—
233C2×C3×C4—62no—
234C2×C3×C4—68no—
235C2×C3×C4—64no—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4C2×C4×D314yes—
239C2×C3×C4C2×C4×D312yes—
240C2×C3×C4#23712yes—
241C2×C3×C4#23912yes—
242C2×C3×C4C22×C3×C414yes—
243C2×C3×C4C22×C3×C412yes—
244C2×C3×C4C3×#4112yes—
245C2×C3×C4C3×#4112yes—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—22no—
249C2×Dic3—22no—
250C2×Dic3—24no—
251C2×Dic3—24no—
252C2×Dic3—24no—
253C2×Dic3C22×C3×C414yes—
254C2×Dic3C22×C3×C412yes—
255C4×D3—28no—
256C2×C32C2×#11711yescharacteristic
257C2×C32#52012yes—
258C2×C32#54011yescharacteristic
259C2×C32#54111yescharacteristic
260C2×C32#54212yes—
261C3×D3—42no—
262C24—31no—
263C22×C4—31no—
264C22×C4—32no—
265C22×C4—34no—
266C22×C4—34no—
267C22×C4—62no—
268C22×C4—62no—
269C22×C4C22×C3×D314yes—
270C22×C4C22×C3×D312yes—
271C22×C4C22×C3×D311yescharacteristic
272C4⋊C4—24no—
273C4⋊C4—38no—
274C4⋊C4—44no—
275C4⋊C4—64no—
276C22⋊C4—38no—
277C22⋊C4—124no—
278C42—34no—
279C42—124no—
280C42C3×C4×D314yes—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—22no—
286C22×C3—62no—
287C22×C3—64no—
288C22×C3—121no—
289C22×C3—121no—
290C22×C3—122no—
291C22×C3C22×C4×D311yescharacteristic
292C22×C3C2×#23711yescharacteristic
293C22×C3#100412yes—
294C22×C3C2×#23911yescharacteristic
295C22×C3#100712yes—
296C22×C3C23×C3×C411yescharacteristic
297C22×C3C2×C3×#4111yescharacteristic
298C22×C3C2×C3×#4111yescharacteristic
299C22×C3C3×H(5,𝔽2)12yes—
300C22×C3C3×2−1+412yes—
301C2×D3—22no—
302C2×D3—24no—
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—42no—
306C3×C4—28no—
307C3×C4—24no—
308C3×C4—24no—
309C3×C4—24no—
310C3×C4—44no—
311C3×C4—44no—
312C3×C4—62no—
313C3×C4—64no—
314C3×C4—84no—
315C3×C4—124no—
316C3×C4#89214yes—
317C3×C4C3×#11714yes—
318Dic3—22no—
319Dic3—24no—
320Dic3—44no—
321C32#231411yescharacteristic, complemented, Sylow
322C23—32no—
323C23—61no—
324C23—62no—
325C23—61no—
326C23—62no—
327C23C23×C3×D311yescharacteristic
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—34no—
334C2×C4—32no—
335C2×C4—61no—
336C2×C4—62no—
337C2×C4—61no—
338C2×C4—62no—
339C2×C4—68no—
340C2×C4—64no—
341C2×C4—64no—
342C2×C4—64no—
343C2×C4C2×C3×C4×D314yes—
344C2×C4C2×C3×C4×D312yes—
345C2×C4C3×#23712yes—
346C2×C4C3×#23912yes—
347C2×C3—21no—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—22no—
352C2×C3—122no—
353C2×C3C2×#89211yescharacteristic
354C2×C3#550412yes—
355C2×C3#571911yescharacteristic
356C2×C3#573111yescharacteristic
357C2×C3#573312yes—
358C2×C3C2×C3×#11711yescharacteristic
359C2×C3C3×#52012yes—
360C2×C3C3×#54011yescharacteristic
361C2×C3C3×#54111yescharacteristic
362C2×C3C3×#54212yes—
363D3—42no—
364C22—62no—
365C22—64no—
366C22—121no—
367C22—121no—
368C22—122no—
369C22C22×C3×C4×D311yescharacteristic
370C22C2×C3×#23711yescharacteristic
371C22C3×#100412yes—
372C22C2×C3×#23911yescharacteristic
373C22C3×#100712yes—
374C4—24no—
375C4—44no—
376C4—62no—
377C4—64no—
378C4—124no—
379C4C3×#89214yes—
380C3—21no—
381C3#7435811yescharacteristic, direct product factor
382C3C3×#231411yescharacteristic, complemented
383C2—122no—
384C2C2×C3×#89211yescharacteristic
385C2C3×#550412yes—
386C2C3×#571911yescharacteristic
387C2C3×#573111yescharacteristic
388C2C3×#573312yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#384C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#384D3
hypocenterC3C3×#2314
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#384

Complements

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

NH ≅ G/Ntype
2. C32×#384C2semidirect
5. C3×#4978C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. C3×#4936C2semidirect
9. #74358C3direct (N × H)
20. C3×#872C4semidirect
29. C3×#384D3semidirect
30. C3×#384C2×C3semidirect
36. #4978C2×C3semidirect
37. Dic3×C4⋊C4C2×C3semidirect
38. #4936C2×C3semidirect
83. #872C3×C4semidirect
118. #384C3×D3semidirect
321. C32#2314semidirect
381. C3#74358direct (N × H)
382. C3C3×#2314semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C32×#3842
C3×#49902
C3×#49872
C3×#49782
C3×Dic3×C4⋊C42
C3×#49362
C3×#23143
#743583