Finite Group Databasebeta

← C3×#68124 #11773754

Subgroups — C3×#68124 #11773754

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C3×#4718C212yesmaximal, complemented
3C32×#324C211yesmaximal, characteristic, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5C3×#4468C212yesmaximal
6C3×#1458—31nomaximal
7#68124C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×D3C411yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C3×(C2×D3)⋊C4C411yescharacteristic
11C2×C3×(C2×D3)⋊C4C2211yescharacteristic
12C2×C3×C4⋊Dic3C411yescharacteristic
13C2×C3×C4×Dic3C411yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#892—22no—
16C3×#892—22no—
17C32×C22⋊C8C2212yes—
18C3×#830C2212yes—
19C3×Dic3⋊C8—22no—
20C3×C8×Dic3—22no—
21C2×C3×#117—31no—
22C2×#892C2×C311yescharacteristic
23C3×#431—32no—
24#4718C2×C312yescomplemented
25C3×#324—21no—
26C3×#324—31no—
27C3×#324D311yescharacteristic, complemented
28C3×#324C2×C311yescharacteristic, complemented
29C3×#323—32no—
30#4528C2×C311yescharacteristic, complemented
31#4468C2×C312yes—
32C23×C3×D3C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3C2×C411yescharacteristic
37C22×C3×Dic3C2×C411yescharacteristic
38C22×C3×Dic3C2×C411yescharacteristic
39C2×C3×C4×D3—21no—
40C2×C3×C4×D3—21no—
41C2×C3×C4×D3—22no—
42C2×C3×C4×D3C814yescomplemented
43C2×C32×C8—22no—
44C32×C4⋊C4—22no—
45C3×(C2×D3)⋊C4—22no—
46C3×(C2×D3)⋊C4—22no—
47C3×C4⋊Dic3—22no—
48C3×C4×Dic3—21no—
49C3×C4×Dic3—21no—
50C3×C4×Dic3D412yes—
51C3×C4×Dic3D412yes—
52C2×C3×C3⋊C8—22no—
53#1458—31noSylow
54C23×C3×C4—31no—
55C22×C4×D3C3×C411yescharacteristic
56C3×#117—62no—
57C3×#117—62no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C4⋊C4C2×D311yescharacteristic
61C2×C3×C4⋊C4C22×C311yescharacteristic
62C2×C3×C22⋊C4—31no—
63C2×C3×C22⋊C4—31no—
64C2×C3×C42—31no—
65C2×C3×C42—31no—
66C2×(C2×D3)⋊C4C3×C411yescharacteristic
67C2×(C2×D3)⋊C4C22×C311yescharacteristic
68C2×C4⋊Dic3C3×C411yescharacteristic
69C2×C4×Dic3C3×C411yescharacteristic
70C2×C4×Dic3C22×C311yescharacteristic
71#892—22no—
72#892—22no—
73C3×C4⋊C8—62no—
74C3×C22⋊C8—22no—
75C3×C22⋊C8—32no—
76C3×C22⋊C8C2×D312yes—
77C3×C22⋊C8C22×C312yes—
78C3×C4×C8—62no—
79#830C22×C312yes—
80Dic3⋊C8—22no—
81C8×Dic3—22no—
82C23×C32C22×C411yescharacteristic
83C22×C3×D3—21no—
84C22×C3×D3—21no—
85C22×C3×D3—41no—
86C22×C3×D3—41no—
87C22×C3×D3C2×C812yes—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C2×C812yes—
94C2×C32×C4C2×D412yes—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3C22⋊C412yes—
99C2×C3×Dic3C22⋊C411yescharacteristic
100C2×C3×Dic3C22⋊C411yescharacteristic
101C2×C3×Dic3C2×C812yes—
102C2×C3×Dic3M1612yes—
103C3×C4×D3—24no—
104C3×C4×D3—24no—
105C32×C8—42no—
106C3×C3⋊C8—42no—
107C2×#117—31no—
108#431—32no—
109#324—31no—
110#324C3×D311yescharacteristic, complemented
111#323—32no—
112C24×C3—31no—
113C23×D3C2×C3×C411yescharacteristic
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—34no—
120C22×C3×C4—31no—
121C22×C3×C4—61no—
122C22×C3×C4—61no—
123C22×C3×C4—62no—
124C22×C3×C4C4×D311yescharacteristic
125C22×C3×C4C4×D311yescharacteristic
126C22×C3×C4C2×C3×C411yescharacteristic
127C22×C3×C4C2×C3×C411yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C23×C311yescharacteristic
130C22×Dic3C2×C3×C411yescharacteristic
131C22×Dic3C2×C3×C411yescharacteristic
132C22×Dic3C2×C3×C411yescharacteristic
133C2×C4×D3—21no—
134C2×C4×D3—21no—
135C2×C4×D3—22no—
136C2×C4×D3C3×C814yescomplemented
137C2×C3×C8—22no—
138C2×C3×C8—22no—
139C2×C3×C8—42no—
140C2×C3×C8—62no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—42no—
144C3×C4⋊C4—62no—
145C3×C22⋊C4—62no—
146C3×C22⋊C4—62no—
147C3×C42—32no—
148C3×C42—32no—
149C3×C42—61no—
150C3×C42—61no—
151(C2×D3)⋊C4—22no—
152(C2×D3)⋊C4—22no—
153C4⋊Dic3—22no—
154C4×Dic3—21no—
155C4×Dic3—21no—
156C4×Dic3C3×D412yes—
157C4×Dic3C3×D412yes—
158C2×C3⋊C8—22no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32C22×C811yescharacteristic
163C22×C32C2×M1611yescharacteristic
164C2×C3×D3—22no—
165C2×C3×D3—42no—
166C2×C3×D3—41no—
167C2×C3×D3—41no—
168C2×C3×D3—42no—
169C32×C4—22no—
170C32×C4—22no—
171C32×C4—41no—
172C3×Dic3—22no—
173C3×Dic3—41no—
174C3×Dic3C22⋊C812yes—
175C3×Dic3C22⋊C812yes—
176C23×C4—31no—
177#117—62no—
178#117—62no—
179C2×C4⋊C4—31no—
180C2×C4⋊C4C2×C3×D311yescharacteristic
181C2×C22⋊C4—31no—
182C2×C22⋊C4—31no—
183C2×C42—31no—
184C2×C42—31no—
185C4⋊C8—62no—
186C22⋊C8—32no—
187C22⋊C8C2×C3×D312yes—
188C4×C8—62no—
189C23×C3—21no—
190C23×C3—32no—
191C23×C3—61no—
192C23×C3—61no—
193C23×C3—121no—
194C23×C3—121no—
195C23×C3C2×C4×D311yescharacteristic
196C23×C3C22×C3×C411yescharacteristic
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—41no—
200C22×D3—41no—
201C22×D3C2×C3×C812yes—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—32no—
213C2×C3×C4—32no—
214C2×C3×C4—32no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—64no—
223C2×C3×C4—64no—
224C2×C3×C4—61no—
225C2×C3×C4—81no—
226C2×C3×C4—81no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4D3×C812yes—
230C2×C3×C4C2×C3×C812yes—
231C2×C3×C4D3×D412yes—
232C2×C3×C4C2×C3×D412yes—
233C2×Dic3—21no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236C2×Dic3C3×C22⋊C412yes—
237C2×Dic3C3×C22⋊C411yescharacteristic
238C2×Dic3C3×C22⋊C411yescharacteristic
239C2×Dic3C2×C3×C812yes—
240C2×Dic3C3×M1612yes—
241C4×D3—24no—
242C4×D3—24no—
243C3×C8—42no—
244C3×C8—42no—
245C3×C8—82no—
246C3×C8—122no—
247C3⋊C8—42no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32C2×C22⋊C811yescharacteristic
251C2×C32#41011yescharacteristic
252C2×C32#41311yescharacteristic
253C3×D3—42no—
254C24—31no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—34no—
258C22×C4—31no—
259C22×C4—61no—
260C22×C4—61no—
261C22×C4—62no—
262C22×C4C3×C4×D311yescharacteristic
263C22×C4C3×C4×D311yescharacteristic
264C22×C4C22×C3×D311yescharacteristic
265C2×C8—22no—
266C2×C8—62no—
267C4⋊C4—22no—
268C4⋊C4—62no—
269C22⋊C4—62no—
270C22⋊C4—62no—
271C42—32no—
272C42—32no—
273C42—61no—
274C42—61no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—62no—
285C22×C3—122no—
286C22×C3—122no—
287C22×C3—121no—
288C22×C3—121no—
289C22×C3D3×C22⋊C411yescharacteristic
290C22×C3C2×D3×C811yescharacteristic
291C22×C3D3×M1611yescharacteristic
292C22×C3C2×C3×C22⋊C411yescharacteristic
293C22×C3C22×C3×C811yescharacteristic
294C22×C3C2×C3×M1611yescharacteristic
295C2×D3—22no—
296C2×D3—42no—
297C2×D3—41no—
298C2×D3—41no—
299C2×D3—42no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—32no—
305C3×C4—32no—
306C3×C4—42no—
307C3×C4—42no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—62no—
311C3×C4—81no—
312C3×C4—121no—
313Dic3—22no—
314Dic3—41no—
315Dic3C3×C22⋊C812yes—
316Dic3C3×C22⋊C812yes—
317C32#145811yescharacteristic, complemented, Sylow
318C23—32no—
319C23—61no—
320C23—61no—
321C23—121no—
322C23—121no—
323C23C2×C3×C4×D311yescharacteristic
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—31no—
328C2×C4—31no—
329C2×C4—32no—
330C2×C4—32no—
331C2×C4—32no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—64no—
335C2×C4—64no—
336C2×C4—61no—
337C2×C4—121no—
338C2×C4—121no—
339C2×C4C3×D3×C812yes—
340C2×C4C3×D3×D412yes—
341C8—42no—
342C8—122no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—122no—
353C2×C3D3×C22⋊C811yescharacteristic
354C2×C3#474011yescharacteristic
355C2×C3#475111yescharacteristic
356C2×C3C2×C3×C22⋊C811yescharacteristic
357C2×C3C3×#41011yescharacteristic
358C2×C3C3×#41311yescharacteristic
359D3—42no—
360C22—21no—
361C22—21no—
362C22—62no—
363C22—122no—
364C22—122no—
365C22—121no—
366C22—121no—
367C22C3×D3×C22⋊C411yescharacteristic
368C22C2×C3×D3×C811yescharacteristic
369C22C3×D3×M1611yescharacteristic
370C4—22no—
371C4—22no—
372C4—32no—
373C4—32no—
374C4—41no—
375C4—62no—
376C4—121no—
377C3—21no—
378C3#6812411yescharacteristic, direct product factor
379C3C3×#145811yescharacteristic, complemented
380C2—21no—
381C2—21no—
382C2—122no—
383C2C3×D3×C22⋊C811yescharacteristic
384C2C3×#474011yescharacteristic
385C2C3×#475111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#324D3
hypocenterC3C3×#1458
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
2. C3×#4718C2semidirect
3. C32×#324C2semidirect
4. C3×#4528C2semidirect
7. #68124C3direct (N × H)
24. #4718C2×C3semidirect
27. C3×#324D3semidirect
28. C3×#324C2×C3semidirect
30. #4528C2×C3semidirect
42. C2×C3×C4×D3C8semidirect
110. #324C3×D3semidirect
136. C2×C4×D3C3×C8semidirect
317. C32#1458semidirect
378. C3#68124direct (N × H)
379. C3C3×#1458semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C3×#47182
C32×#3242
C3×#45282
C3×#44682
C3×#14583
#681243