Finite Group Databasebeta

← C3×#68262 #11779765

Subgroups — C3×#68262 #11779765

Order 1152.

459 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic, complemented
3C3×#4851C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1640—31nomaximal
9#68262C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×#947—21no—
12C2×C3×#216—21no—
13C3×#894—22no—
14C3×#893—21no—
15C3×#875—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12—21no—
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#821—22no—
23C3×#817—21no—
24C3×#816—21no—
25C3×#810—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#559—31no—
28#5585C2×C311yescharacteristic
29C3×#486—31no—
30C3×#475—31no—
31C3×#462—31no—
32#5031C2×C311yescharacteristic, complemented
33#4851C2×C311yescharacteristic, complemented
34#4694C2×C311yescharacteristic
35C3×#331—31no—
36C3×Q8⋊C8—21no—
37C3×Q8⋊C8—31no—
38C3×Q8⋊C8D311yescharacteristic, complemented
39C3×Q8⋊C8C2×C311yescharacteristic, complemented
40#4485C2×C311yescharacteristic
41#4456C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D412yes—
46C2×C3×C4×D3—22no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C42—21no—
54C32×C42C2311yescharacteristic
55C3×#216—42no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—22no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65#1640—31noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—31no—
68C3×#127—31no—
69C3×#124—61no—
70C3×#124—61no—
71C3×#123—62no—
72C3×C4×Q8—21no—
73C3×C4×Q8—31no—
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×Q8C22×C311yescharacteristic
76C3×C4×D4—61no—
77C3×C4×D4—61no—
78#947—21no—
79C2×#216—21no—
80#894—22no—
81#893—21no—
82#875—21no—
83#874C22×C311yescharacteristic
84C4×D12—21no—
85#869C22×C311yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C22×C311yescharacteristic
92C3×#103—61no—
93C3×#103—61no—
94C3×#102—62no—
95C3×C4×C8—21no—
96C3×C4×C8C2×D311yescharacteristic
97C3×C4×C8C22×C311yescharacteristic
98#821—22no—
99#817—21no—
100#816—21no—
101#810—21no—
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C22×C3×D3—22no—
104C32×Q8—21no—
105C32×Q8—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—42no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×C4×D3—82no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C32×C8—41no—
125C32×C8—41no—
126C3×C3⋊C8—41no—
127#559—31no—
128#486—31no—
129#475—31no—
130#462—31no—
131#331—31no—
132Q8⋊C8—31no—
133Q8⋊C8C3×D311yescharacteristic, complemented
134C2×C3×Q8—21no—
135C2×C3×Q8—31no—
136C2×C3×Q8—61no—
137C2×C3×Q8D1211yescharacteristic
138C2×C3×Q8C3×D411yescharacteristic
139C2×C3×D4—32no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C22×C3×C4—62no—
143C2×D12—21no—
144C2×D12—21no—
145C2×D12C3×D412yes—
146C2×C4×D3—22no—
147C2×Dic6—21no—
148C2×Dic6C3×D411yescharacteristic
149C3×Q16—122no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—41no—
155C2×C3×C8—41no—
156C2×C3×C8—61no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—41no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4D1211yescharacteristic
166C3×C4⋊C4C3×D411yescharacteristic
167C3×C22⋊C4—62no—
168C3×C22⋊C4—62no—
169C3×C22⋊C4—62no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—41no—
174C3×C42—61no—
175C3×C42C22×D311yescharacteristic
176C3×C42C23×C311yescharacteristic
177#216—42no—
178(C2×D3)⋊C4—22no—
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—22no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3C3×D411yescharacteristic
184Dic3⋊C4—21no—
185C4×Dic3—21no—
186C2×C3⋊C8—21no—
187C22×C32#12011yescharacteristic
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C2×C3×D3—42no—
191C32×C4—21no—
192C32×C4—41no—
193C32×C4—41no—
194C32×C4#13511yescharacteristic
195C32×C4#13511yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C32×C4#13711yescharacteristic
198C3×Dic3—41no—
199C3×Dic3—41no—
200C3×Dic3—81no—
201C2×Q16—61no—
202C4⋊Q8—31no—
203#127—31no—
204#124—61no—
205#124—61no—
206#123—62no—
207C4×Q8—31no—
208C4×Q8C2×C3×D311yescharacteristic
209C4×D4—61no—
210C4×D4—61no—
211#106—61no—
212C4⋊C8—31no—
213C4⋊C8C2×C3×D311yescharacteristic
214#103—61no—
215#103—61no—
216#102—62no—
217C4×C8C2×C3×D311yescharacteristic
218C23×C3—62no—
219C22×D3—22no—
220C3×Q8—22no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—21no—
224C3×Q8—21no—
225C3×Q8—41no—
226C3×Q8—61no—
227C3×Q8—61no—
228C3×Q8—121no—
229C3×Q8—121no—
230C3×D4—122no—
231C3×D4—121no—
232C3×D4—121no—
233C3×D4—121no—
234C3×D4—121no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—121no—
247C2×C3×C4—242no—
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4C2×C3×D411yescharacteristic
252C2×C3×C4C2×C3×D411yescharacteristic
253C2×C3×C4C2×C3×D411yescharacteristic
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—41no—
257D12—42no—
258D12—41no—
259D12—41no—
260D12—41no—
261D12—41no—
262C4×D3—82no—
263Dic6—21no—
264Dic6—21no—
265Dic6—41no—
266Dic6—41no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—42no—
270C3×C8—41no—
271C3×C8—41no—
272C3×C8—81no—
273C3×C8—121no—
274C3⋊C8—41no—
275C2×C32#44911yescharacteristic
276C2×C32#45211yescharacteristic
277C2×C32#45511yescharacteristic
278C3×D3—82no—
279C2×Q8—31no—
280C2×Q8—61no—
281C2×Q8C3×D1211yescharacteristic
282C2×D4—32no—
283C2×D4—61no—
284C2×D4—61no—
285C22×C4—62no—
286Q16—122no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—61no—
290C4⋊C4—21no—
291C4⋊C4—31no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4C3×D1211yescharacteristic
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C42—21no—
300C42—61no—
301C42C22×C3×D311yescharacteristic
302C22×C3—21no—
303C22×C3—122no—
304C22×C3—122no—
305C22×C3—122no—
306C22×C3#88211yescharacteristic
307C22×C3C3×#12011yescharacteristic
308C2×D3—42no—
309C2×D3—42no—
310C2×D3—42no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—42no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—81no—
324C3×C4—121no—
325C3×C4—121no—
326C3×C4—241no—
327C3×C4#90411yescharacteristic
328C3×C4#90811yescharacteristic
329C3×C4#91611yescharacteristic
330C3×C4#91811yescharacteristic
331C3×C4C3×#13511yescharacteristic
332C3×C4C3×#13511yescharacteristic
333C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
334C3×C4C3×#13711yescharacteristic
335Dic3—41no—
336Dic3—41no—
337Dic3—81no—
338C32#164011yescharacteristic, complemented, Sylow
339C23—62no—
340Q8—21no—
341Q8—21no—
342Q8—61no—
343Q8—61no—
344Q8—121no—
345Q8—121no—
346D4—122no—
347D4—121no—
348D4—121no—
349D4—121no—
350D4—121no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—121no—
356C2×C4—242no—
357C2×C4C2×C3×D1211yescharacteristic
358C2×C4C3×D3×D411yescharacteristic
359C2×C4C3×D3×D411yescharacteristic
360C8—41no—
361C8—41no—
362C8—121no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—242no—
367C2×C3#473411yescharacteristic
368C2×C3#480811yescharacteristic
369C2×C3#482511yescharacteristic
370C2×C3C3×#44911yescharacteristic
371C2×C3C3×#45211yescharacteristic
372C2×C3C3×#45511yescharacteristic
373D3—82no—
374C22—122no—
375C22—122no—
376C22—122no—
377C22C3×#88211yescharacteristic
378C4—21no—
379C4—41no—
380C4—41no—
381C4—121no—
382C4—121no—
383C4—241no—
384C4C3×#90411yescharacteristic
385C4C3×#90811yescharacteristic
386C4C3×#91611yescharacteristic
387C4C3×#91811yescharacteristic
388C3—21no—
389C3#6826211yescharacteristic, direct product factor
390C3C3×#164011yescharacteristic, complemented
391C2—242no—
392C2C3×#473411yescharacteristic
393C2C3×#480811yescharacteristic
394C2C3×#482511yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1640
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#5031C2semidirect
3. C3×#4851C2semidirect
5. C32×Q8⋊C8C2semidirect
7. C3×#4456C2semidirect
9. #68262C3direct (N × H)
32. #5031C2×C3semidirect
33. #4851C2×C3semidirect
38. C3×Q8⋊C8D3semidirect
39. C3×Q8⋊C8C2×C3semidirect
41. #4456C2×C3semidirect
133. Q8⋊C8C3×D3semidirect
338. C32#1640semidirect
389. C3#68262direct (N × H)
390. C3C3×#1640semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#50312
C3×#48512
C3×#46942
C32×Q8⋊C82
C3×#44852
C3×#44562
C3×#16403
#682623