Finite Group Databasebeta

← C3×#68419 #11776234

Subgroups — C3×#68419 #11776234

Order 1152.

436 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic
3C3×#4833C211yesmaximal, characteristic
4C32×#332C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1544—31nomaximal
9#68419C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C3×#946—21no—
12C3×Q8×Dic3—21no—
13C3×#897—21no—
14C3×#892C412yes—
15C3×#890C412yes—
16C3×#887—21no—
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C3×(C2×D3)⋊C8—21no—
22C3×(C2×D3)⋊C8—21no—
23C3×C8×Dic3—21no—
24C3×C8×Dic3—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#533—31no—
28#5728C2×C311yescharacteristic
29C3×#431—31no—
30C3×#431—31no—
31#4833C2×C311yescharacteristic
32#4833C2×C311yescharacteristic
33C3×#332—21no—
34C3×#332—31no—
35C3×#332—31no—
36C3×#332—31no—
37C3×#332D311yescharacteristic, complemented
38C3×#332C2×C311yescharacteristic, complemented
39#4547C2×C311yescharacteristic, complemented
40#4486C2×C311yescharacteristic, complemented
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C3×C4×D3C2×C411yescharacteristic
44C2×C3×C4×D3D411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×C32×C8—21no—
48C2×C32×C8—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4C2×C412yes—
51C32×C42C2311yescharacteristic
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3C2×C412yes—
56C3×Dic3⋊C4—22no—
57C3×C4×Dic3—22no—
58C3×C4×Dic3C2×C411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63#1544—31noSylow
64C3×C4⋊Q8—21no—
65C3×C4⋊Q8—31no—
66C3×C4⋊Q8C2×D311yescharacteristic
67C3×C4⋊Q8C22×C311yescharacteristic
68C3×#125—32no—
69C3×C22⋊Q8—61no—
70C3×C22⋊Q8—61no—
71C3×C4×Q8—61no—
72C3×C4×Q8—61no—
73C3×#117—32no—
74C2×C3×C42—31no—
75#946—21no—
76Q8×Dic3—21no—
77#897—21no—
78#892C3×C412yes—
79#890C3×C412yes—
80#887—21no—
81C42×D3C22×C311yescharacteristic
82#869C22×C311yescharacteristic
83C3×C4⋊C8—21no—
84C3×C4⋊C8—21no—
85C3×C4⋊C8—31no—
86C3×C4⋊C8—31no—
87C3×C4⋊C8C2×D311yescharacteristic
88C3×C4⋊C8C2×D311yescharacteristic
89C3×C4⋊C8C22×C311yescharacteristic
90C3×C4⋊C8C22×C311yescharacteristic
91C3×C22⋊C8—61no—
92C3×C22⋊C8—61no—
93C3×C4×C8—61no—
94C3×C4×C8—61no—
95(C2×D3)⋊C8—21no—
96(C2×D3)⋊C8—21no—
97C8×Dic3—21no—
98C8×Dic3—21no—
99C4⋊(C3⋊C8)C22×C311yescharacteristic
100C4⋊(C3⋊C8)C22×C311yescharacteristic
101C22×C3×D3C22⋊C411yescharacteristic
102C32×Q8—41no—
103C32×Q8—41no—
104C2×C32×C4—22no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3×Dic3—22no—
109C2×C3×Dic3C22⋊C411yescharacteristic
110C2×C3×Dic3C22⋊C411yescharacteristic
111C2×C3×Dic3C22⋊C411yescharacteristic
112C3×C4×D3—21no—
113C3×C4×D3—21no—
114C3×C4×D3—21no—
115C3×C4×D3—21no—
116C3×C4×D3—22no—
117C3×Dic6—41no—
118C3×Dic6—41no—
119C32×C8—41no—
120C32×C8—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123#533—31no—
124#431—31no—
125#431—31no—
126#332—31no—
127#332—31no—
128#332—31no—
129#332C3×D311yescharacteristic, complemented
130C2×C3×Q8—21no—
131C2×C3×Q8—21no—
132C2×C3×Q8—41no—
133C2×C3×Q8—61no—
134C22×C3×C4—31no—
135C22×C3×C4—31no—
136C22×C3×C4—31no—
137C2×C4×D3C2×C3×C411yescharacteristic
138C2×C4×D3C3×D411yescharacteristic
139C2×C4×D3C3×D411yescharacteristic
140C2×Dic6—21no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—41no—
146C2×C3×C8—41no—
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—22no—
152C3×C4⋊C4—32no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4—62no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4C4×D312yes—
158C3×C4⋊C4C2×C3×C412yes—
159C3×C22⋊C4—62no—
160C3×C42—21no—
161C3×C42—31no—
162C3×C42—31no—
163C3×C42—31no—
164C3×C42—62no—
165C3×C42C22×D311yescharacteristic
166C3×C42C23×C311yescharacteristic
167(C2×D3)⋊C4—22no—
168C4⋊Dic3—21no—
169C4⋊Dic3—22no—
170C4⋊Dic3C2×C3×C412yes—
171Dic3⋊C4—22no—
172C4×Dic3—22no—
173C4×Dic3C2×C3×C411yescharacteristic
174C4×Dic3C3×D411yescharacteristic
175C4×Dic3C3×D411yescharacteristic
176C2×C3⋊C8—21no—
177C2×C3⋊C8—21no—
178C22×C32C2×C22⋊C411yescharacteristic
179C2×C3×D3—21no—
180C2×C3×D3—21no—
181C2×C3×D3—21no—
182C32×C4—21no—
183C32×C4—42no—
184C32×C4#13511yescharacteristic
185C32×C4#13511yescharacteristic
186C32×C4#13511yescharacteristic
187C32×C4#13511yescharacteristic
188C3×Dic3—21no—
189C3×Dic3—21no—
190C3×Dic3—42no—
191C3×Dic3#10112yes—
192C4⋊Q8—31no—
193C4⋊Q8C2×C3×D311yescharacteristic
194#125—32no—
195C22⋊Q8—61no—
196C22⋊Q8—61no—
197C4×Q8—61no—
198C4×Q8—61no—
199#117—32no—
200C2×C42—31no—
201C4⋊C8—31no—
202C4⋊C8—31no—
203C4⋊C8C2×C3×D311yescharacteristic
204C4⋊C8C2×C3×D311yescharacteristic
205C22⋊C8—61no—
206C22⋊C8—61no—
207C4×C8—61no—
208C4×C8—61no—
209C23×C3—31no—
210C22×D3C3×C22⋊C411yescharacteristic
211C3×Q8—41no—
212C3×Q8—41no—
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—81no—
216C3×Q8—81no—
217C3×Q8—121no—
218C3×Q8—121no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—42no—
228C2×C3×C4—62no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—62no—
234C2×C3×C4C2×C4×D311yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4C22×C3×C411yescharacteristic
238C2×C3×C4C2×C3×D411yescharacteristic
239C2×C3×C4C2×C3×D411yescharacteristic
240C2×Dic3—22no—
241C2×Dic3C3×C22⋊C411yescharacteristic
242C2×Dic3C3×C22⋊C411yescharacteristic
243C2×Dic3C3×C22⋊C411yescharacteristic
244C4×D3—21no—
245C4×D3—21no—
246C4×D3—21no—
247C4×D3—21no—
248C4×D3—22no—
249Dic6—41no—
250Dic6—41no—
251C3×C8—41no—
252C3×C8—41no—
253C3×C8—41no—
254C3×C8—41no—
255C3×C8—81no—
256C3×C8—81no—
257C3×C8—121no—
258C3×C8—121no—
259C3⋊C8—41no—
260C3⋊C8—41no—
261C2×C32C2×#10111yescharacteristic
262C2×C32#41611yescharacteristic
263C2×C32#41611yescharacteristic
264C3×D3—41no—
265C2×Q8—21no—
266C2×Q8—61no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—61no—
273C2×C8—61no—
274C4⋊C4—21no—
275C4⋊C4—32no—
276C4⋊C4—62no—
277C4⋊C4—62no—
278C4⋊C4—61no—
279C4⋊C4C3×C4×D312yes—
280C22⋊C4—62no—
281C42—31no—
282C42—31no—
283C42—31no—
284C42—62no—
285C42C22×C3×D311yescharacteristic
286C22×C3—21no—
287C22×C3—61no—
288C22×C3—61no—
289C22×C3—61no—
290C22×C3D3×C22⋊C411yescharacteristic
291C22×C3C2×C3×C22⋊C411yescharacteristic
292C2×D3—21no—
293C2×D3—21no—
294C2×D3—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—32no—
302C3×C4—41no—
303C3×C4—42no—
304C3×C4—42no—
305C3×C4—61no—
306C3×C4—61no—
307C3×C4—82no—
308C3×C4—122no—
309C3×C4#91211yescharacteristic
310C3×C4#91611yescharacteristic
311C3×C4#91611yescharacteristic
312C3×C4#91911yescharacteristic
313C3×C4C3×#13511yescharacteristic
314C3×C4C3×#13511yescharacteristic
315C3×C4C3×#13511yescharacteristic
316C3×C4C3×#13511yescharacteristic
317Dic3—21no—
318Dic3—21no—
319Dic3—42no—
320Dic3C3×#10112yes—
321C32#154411yescharacteristic, complemented, Sylow
322C23—31no—
323Q8—41no—
324Q8—41no—
325Q8—121no—
326Q8—121no—
327C2×C4—22no—
328C2×C4—31no—
329C2×C4—31no—
330C2×C4—31no—
331C2×C4—62no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—62no—
337C2×C4C2×C3×C4×D311yescharacteristic
338C2×C4C3×D3×D411yescharacteristic
339C2×C4C3×D3×D411yescharacteristic
340C8—41no—
341C8—41no—
342C8—121no—
343C8—121no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—121no—
348C2×C3D3×#10111yescharacteristic
349C2×C3#477211yescharacteristic
350C2×C3#480411yescharacteristic
351C2×C3C2×C3×#10111yescharacteristic
352C2×C3C3×#41611yescharacteristic
353C2×C3C3×#41611yescharacteristic
354D3—41no—
355C22—61no—
356C22—61no—
357C22—61no—
358C22C3×D3×C22⋊C411yescharacteristic
359C4—21no—
360C4—32no—
361C4—42no—
362C4—61no—
363C4—61no—
364C4—122no—
365C4C3×#91211yescharacteristic
366C4C3×#91611yescharacteristic
367C4C3×#91611yescharacteristic
368C4C3×#91911yescharacteristic
369C3—21no—
370C3#6841911yescharacteristic, direct product factor
371C3C3×#154411yescharacteristic, complemented
372C2—121no—
373C2C3×D3×#10111yescharacteristic
374C2C3×#477211yescharacteristic
375C2C3×#480411yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC3×C42C23×C3
hypercenterC3×#332D3
hypocenterC3C3×#1544
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
4. C32×#332C2semidirect
5. C3×#4547C2semidirect
6. C3×#4486C2semidirect
7. C3×#4482C2semidirect
9. #68419C3direct (N × H)
37. C3×#332D3semidirect
38. C3×#332C2×C3semidirect
39. #4547C2×C3semidirect
40. #4486C2×C3semidirect
41. #4482C2×C3semidirect
129. #332C3×D3semidirect
321. C32#1544semidirect
370. C3#68419direct (N × H)
371. C3C3×#1544semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×#48332
C32×#3322
C3×#45472
C3×#44862
C3×#44822
C3×#15443
#684193