Finite Group Databasebeta

← C3×#68506 #11779952

Subgroups — C3×#68506 #11779952

Order 1152.

448 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3C3×#4849C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic
5C32×#333C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic
8C3×#1644—31nomaximal
9#68506C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C3×#946—22no—
12C2×C3×Dic12—21no—
13C3×#897—21no—
14C3×#893—21no—
15C3×D3×C4⋊C4—21no—
16C3×#890—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C3×#835—22no—
23C3×#821—21no—
24C3×#818—21no—
25C3×#816—21no—
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#554—31no—
28#5730C2×C311yescharacteristic
29C3×#487—31no—
30C3×#474—31no—
31C3×#462—31no—
32#5079C2×C311yescharacteristic, complemented
33#4849C2×C311yescharacteristic, complemented
34#4846C2×C311yescharacteristic
35C3×#333—21no—
36C3×#333D311yescharacteristic, complemented
37C3×#333C2×C311yescharacteristic, complemented
38C3×Q8⋊C8—31no—
39C3×D4⋊C8—31no—
40#4484C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic
42C2×C32×Q8D412yes—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—22no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C42C2311yescharacteristic
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C3×Dic12—42no—
65#1644—31noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C22×C311yescharacteristic
71C3×#125—61no—
72C3×C22⋊Q8—61no—
73C3×C22⋊Q8—62no—
74C3×C4×Q8—31no—
75C3×C4×D4—31no—
76C3×C4×D4—61no—
77C2×C3×C4⋊C4—61no—
78#946—22no—
79C2×Dic12—21no—
80#897—21no—
81#893—21no—
82D3×C4⋊C4—21no—
83#890—21no—
84C4×D12C22×C311yescharacteristic
85#869C22×C311yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C22×C311yescharacteristic
93C3×C4⋊C8C22×C311yescharacteristic
94C3×#103—61no—
95C3×#103—62no—
96C3×#102—61no—
97C3×C4×C8—31no—
98#835—22no—
99#821—21no—
100#818—21no—
101#816—21no—
102C4×C3⋊C8C22×C311yescharacteristic
103C22×C3×D3—21no—
104C32×Q8—42no—
105C2×C32×C4—22no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×D12—21no—
114C3×D12Q1612yescomplemented
115C3×C4×D3—41no—
116C3×C4×D3—41no—
117C3×C4×D3—82no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—41no—
123C32×C8—41no—
124C3×C3⋊C8—41no—
125#554—31no—
126#487—31no—
127#474—31no—
128#462—31no—
129#333C3×D311yescharacteristic, complemented
130Q8⋊C8—31no—
131D4⋊C8—31no—
132C2×C3×Q8—22no—
133C2×C3×Q8—31no—
134C2×C3×Q8—61no—
135C2×C3×Q8D1212yes—
136C2×C3×Q8C3×D412yes—
137C2×C3×D4—31no—
138C22×C3×C4—62no—
139C22×C3×C4—61no—
140C2×D12C3×D411yescharacteristic
141C2×C4×D3—21no—
142C2×C4×D3—22no—
143C2×Dic6—21no—
144C2×Dic6C3×D411yescharacteristic
145C3×Q16—122no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—41no—
151C2×C3×C8—41no—
152C2×C3×C8—61no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—41no—
160C3×C4⋊C4—41no—
161C3×C4⋊C4—62no—
162C3×C4⋊C4—62no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—62no—
167C3×C22⋊C4—61no—
168C3×C42—21no—
169C3×C42—61no—
170C3×C42C22×D311yescharacteristic
171C3×C42C23×C311yescharacteristic
172(C2×D3)⋊C4—22no—
173(C2×D3)⋊C4—21no—
174C4⋊Dic3—22no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3C3×D411yescharacteristic
178C4⋊Dic3C3×D411yescharacteristic
179Dic3⋊C4—22no—
180Dic3⋊C4—21no—
181C4×Dic3—21no—
182C2×C3⋊C8—21no—
183Dic12—42no—
184C22×C32#12011yescharacteristic
185C2×C3×D3—22no—
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C32×C4—21no—
189C32×C4—42no—
190C32×C4C2×Q1611yescharacteristic
191C32×C4#13511yescharacteristic
192C32×C4AGL(1,ℤ/8)11yescharacteristic
193C32×C4#13711yescharacteristic
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—81no—
198C2×Q16—61no—
199C4⋊Q8—31no—
200C4⋊Q8C2×C3×D311yescharacteristic
201#125—61no—
202C22⋊Q8—61no—
203C22⋊Q8—62no—
204C4×Q8—31no—
205C4×D4—31no—
206C4×D4—61no—
207C2×C4⋊C4—61no—
208#107—61no—
209C4⋊C8C2×C3×D311yescharacteristic
210C4⋊C8C2×C3×D311yescharacteristic
211#103—61no—
212#103—62no—
213#102—61no—
214C4×C8—31no—
215C23×C3—61no—
216C22×D3—21no—
217C3×Q8—42no—
218C3×Q8—42no—
219C3×Q8—61no—
220C3×Q8—61no—
221C3×Q8—82no—
222C3×Q8—121no—
223C3×Q8—121no—
224C3×D4—32no—
225C3×D4—61no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—42no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4—121no—
238C2×C3×C4—242no—
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4C2×C3×D411yescharacteristic
243C2×C3×C4C2×C3×D411yescharacteristic
244C2×C3×C4C2×C3×D411yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—41no—
249D12—21no—
250D12C3×Q1612yescomplemented
251C4×D3—41no—
252C4×D3—41no—
253C4×D3—82no—
254Dic6—21no—
255Dic6—21no—
256Dic6—41no—
257Dic6—41no—
258C3×C8—41no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—41no—
262C3×C8—81no—
263C3×C8—81no—
264C3×C8—121no—
265C3⋊C8—41no—
266C2×C32#44911yescharacteristic
267C2×C32#45111yescharacteristic
268C2×C32#45511yescharacteristic
269C3×D3—42no—
270C2×Q8—31no—
271C2×Q8—61no—
272C2×Q8C3×D1212yes—
273C2×D4—31no—
274C22×C4—62no—
275C22×C4—61no—
276Q16—122no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—61no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—62no—
285C4⋊C4—62no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C22⋊C4—62no—
290C22⋊C4—61no—
291C42—61no—
292C42C22×C3×D311yescharacteristic
293C22×C3—21no—
294C22×C3—62no—
295C22×C3—121no—
296C22×C3—121no—
297C22×C3#88211yescharacteristic
298C22×C3C3×#12011yescharacteristic
299C2×D3—22no—
300C2×D3—41no—
301C2×D3—41no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—42no—
310C3×C4—42no—
311C3×C4—82no—
312C3×C4—121no—
313C3×C4—121no—
314C3×C4—121no—
315C3×C4—241no—
316C3×C4#91411yescharacteristic
317C3×C4#91511yescharacteristic
318C3×C4D3×Q1611yescharacteristic
319C3×C4#91911yescharacteristic
320C3×C4C2×C3×Q1611yescharacteristic
321C3×C4C3×#13511yescharacteristic
322C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
323C3×C4C3×#13711yescharacteristic
324Dic3—41no—
325Dic3—41no—
326Dic3—41no—
327Dic3—81no—
328C32#164411yescharacteristic, complemented, Sylow
329C23—61no—
330Q8—42no—
331Q8—61no—
332Q8—61no—
333Q8—121no—
334Q8—121no—
335D4—32no—
336D4—61no—
337C2×C4—22no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—121no—
342C2×C4—121no—
343C2×C4—121no—
344C2×C4—242no—
345C2×C4C2×C3×D1211yescharacteristic
346C2×C4C3×D3×D411yescharacteristic
347C2×C4C3×D3×D411yescharacteristic
348C8—41no—
349C8—41no—
350C8—121no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—122no—
355C2×C3#474611yescharacteristic
356C2×C3#480911yescharacteristic
357C2×C3#481011yescharacteristic
358C2×C3C3×#44911yescharacteristic
359C2×C3C3×#45111yescharacteristic
360C2×C3C3×#45511yescharacteristic
361D3—42no—
362C22—62no—
363C22—121no—
364C22—121no—
365C22C3×#88211yescharacteristic
366C4—21no—
367C4—42no—
368C4—121no—
369C4—121no—
370C4—121no—
371C4—241no—
372C4C3×#91411yescharacteristic
373C4C3×#91511yescharacteristic
374C4C3×D3×Q1611yescharacteristic
375C4C3×#91911yescharacteristic
376C3—21no—
377C3#6850611yescharacteristic, direct product factor
378C3C3×#164411yescharacteristic, complemented
379C2—122no—
380C2C3×#474611yescharacteristic
381C2C3×#480911yescharacteristic
382C2C3×#481011yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#333C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#333D3
hypocenterC3C3×#1644
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
2. C3×#5079C2semidirect
3. C3×#4849C2semidirect
5. C32×#333C2semidirect
6. C3×#4484C2semidirect
9. #68506C3direct (N × H)
32. #5079C2×C3semidirect
33. #4849C2×C3semidirect
36. C3×#333D3semidirect
37. C3×#333C2×C3semidirect
40. #4484C2×C3semidirect
114. C3×D12Q16semidirect
129. #333C3×D3semidirect
250. D12C3×Q16semidirect
328. C32#1644semidirect
377. C3#68506direct (N × H)
378. C3C3×#1644semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×#50792
C3×#48492
C3×#48462
C32×#3332
C3×#44842
C3×#44832
C3×#16443
#685063