Finite Group Databasebeta

← C3×#68248 #11779862

Subgroups — C3×#68248 #11779862

Order 1152.

535 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5577C211yesmaximal, characteristic
2C3×#5020C211yesmaximal, characteristic, complemented
3C3×#4841C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1642—31nomaximal
9#68248C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C32×C4×Q8C2211yescharacteristic
12C2×C3×#204—21no—
13C3×#895—22no—
14C3×#895—21no—
15C3×#874—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12—21no—
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#835—21no—
23C3×#821—22no—
24C3×#816—21no—
25C3×#808—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#550—31no—
28#5577C2×C311yescharacteristic
29C3×#486—31no—
30C3×#475—31no—
31C3×#461—31no—
32#5020C2×C311yescharacteristic, complemented
33#4841C2×C311yescharacteristic, complemented
34#4694C2×C311yescharacteristic, complemented
35C3×#331—31no—
36C3×Q8⋊C8—21no—
37C3×Q8⋊C8D311yescharacteristic, complemented
38C3×Q8⋊C8C2×C311yescharacteristic, complemented
39C3×D4⋊C8—31no—
40#4485C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
43C3×#239—42no—
44C3×#239—42no—
45C2×C3×D12—22no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—22no—
49C2×C3×D12D411yescharacteristic
50C2×C3×D12D412yes—
51C2×C3×C4×D3—22no—
52C2×C3×C4×D3—21no—
53C2×C3×Dic6—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C42—21no—
59C32×C42C2311yescharacteristic
60C3×(C2×D3)⋊C4—22no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C3×#204—42no—
67#1642—31noSylow
68C2×C3×#41—61no—
69C2×#239—21no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×#127—61no—
74C3×#121—62no—
75C3×#121—61no—
76C3×C4×Q8—21no—
77C3×C4×Q8C2×D311yescharacteristic
78C3×C4×Q8C22×C311yescharacteristic
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81C2×#204—21no—
82#895—22no—
83#895—21no—
84#874—21no—
85#874C22×C311yescharacteristic
86C4×D12—21no—
87C4×D12C22×C311yescharacteristic
88#869C22×C311yescharacteristic
89C3×#106—61no—
90C3×C4⋊C8—21no—
91C3×C4⋊C8—31no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C22×C311yescharacteristic
94C3×#103—61no—
95C3×#103—61no—
96C3×#102—62no—
97C3×C4×C8—21no—
98C3×C4×C8C2×D311yescharacteristic
99C3×C4×C8C22×C311yescharacteristic
100#835—21no—
101#821—22no—
102#816—21no—
103#808—21no—
104C4⋊(C3⋊C8)C22×C311yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—22no—
107C32×Q8—21no—
108C32×Q8SD1612yescomplemented
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—44no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—82no—
125C3×C4×D3—44no—
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C32×C8—41no—
131C32×C8—41no—
132C3×C3⋊C8—41no—
133#550—31no—
134#486—31no—
135#475—31no—
136#461—31no—
137#331—31no—
138Q8⋊C8C3×D311yescharacteristic, complemented
139D4⋊C8—31no—
140C3×#41—122no—
141C3×#41—122no—
142C2×C3×Q8—21no—
143C2×C3×Q8—61no—
144C2×C3×Q8D1211yescharacteristic
145C2×C3×Q8C3×D411yescharacteristic
146C2×C3×D4—31no—
147C2×C3×D4—32no—
148C2×C3×D4—62no—
149C2×C3×D4—62no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C22×C3×C4—62no—
153C22×C3×C4—61no—
154#239—42no—
155#239—42no—
156C2×D12—22no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—22no—
160C2×D12C3×D411yescharacteristic
161C2×D12C3×D412yes—
162C2×C4×D3—22no—
163C2×C4×D3—21no—
164C2×Dic6—21no—
165C3×SD16—122no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—41no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4D1211yescharacteristic
181C3×C4⋊C4C3×D411yescharacteristic
182C3×C22⋊C4—62no—
183C3×C22⋊C4—61no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—41no—
188C3×C42C22×D311yescharacteristic
189C3×C42C23×C311yescharacteristic
190(C2×D3)⋊C4—22no—
191(C2×D3)⋊C4—21no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3C3×D411yescharacteristic
195C2×C3⋊C8—21no—
196#204—42no—
197C22×C32#12011yescharacteristic
198C2×C3×D3—41no—
199C2×C3×D3—42no—
200C2×C3×D3—42no—
201C2×C3×D3—41no—
202C2×C3×D3—42no—
203C2×C3×D3—41no—
204C32×C4—22no—
205C32×C4—21no—
206C32×C4—41no—
207C32×C4C2×SD1611yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C3×Dic3—41no—
212C3×Dic3—81no—
213C2×#41—61no—
214C2×SD16—61no—
215C4⋊Q8—31no—
216#127—31no—
217#127—61no—
218#121—62no—
219#121—61no—
220C4×Q8C2×C3×D311yescharacteristic
221C4×D4—31no—
222C4×D4—61no—
223#106—61no—
224C4⋊C8—31no—
225C4⋊C8C2×C3×D311yescharacteristic
226#103—61no—
227#103—61no—
228#102—62no—
229C4×C8C2×C3×D311yescharacteristic
230C23×C3—61no—
231C23×C3—62no—
232C22×D3—21no—
233C22×D3—22no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—22no—
237C3×Q8—41no—
238C3×Q8—121no—
239C3×Q8—121no—
240C3×Q8#20412yescomplemented
241C3×Q8C3×SD1612yescomplemented
242C3×D4—61no—
243C3×D4—61no—
244C3×D4—122no—
245C3×D4—124no—
246C3×D4—121no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—242no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—61no—
261C2×C3×C4—124no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4C2×C3×D411yescharacteristic
269C2×C3×C4C2×C3×D411yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—41no—
273D12—21no—
274D12—21no—
275D12—42no—
276D12—44no—
277D12—41no—
278D12—41no—
279D12—41no—
280D12—41no—
281D12—82no—
282C4×D3—44no—
283C4×D3—41no—
284C4×D3—41no—
285Dic6—41no—
286Dic6—41no—
287C3×C8—41no—
288C3×C8—41no—
289C3×C8—42no—
290C3×C8—41no—
291C3×C8—41no—
292C3×C8—81no—
293C3×C8—121no—
294C3⋊C8—41no—
295C2×C32#44911yescharacteristic
296C2×C32#45011yescharacteristic
297C2×C32#45511yescharacteristic
298C3×D3—81no—
299C3×D3—82no—
300#41—122no—
301#41—122no—
302C2×Q8—61no—
303C2×Q8C3×D1211yescharacteristic
304C2×D4—31no—
305C2×D4—32no—
306C2×D4—62no—
307C2×D4—62no—
308C2×D4—61no—
309C2×D4—61no—
310C22×C4—62no—
311C22×C4—61no—
312SD16—122no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—61no—
316C4⋊C4—21no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4C3×D1211yescharacteristic
321C22⋊C4—62no—
322C22⋊C4—61no—
323C42—21no—
324C42C22×C3×D311yescharacteristic
325C22×C3—21no—
326C22×C3—122no—
327C22×C3—121no—
328C22×C3—121no—
329C22×C3—122no—
330C22×C3—122no—
331C22×C3—121no—
332C22×C3#88211yescharacteristic
333C22×C3C3×#12011yescharacteristic
334C2×D3—41no—
335C2×D3—42no—
336C2×D3—42no—
337C2×D3—41no—
338C2×D3—42no—
339C2×D3—41no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—41no—
349C3×C4—42no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—81no—
353C3×C4—121no—
354C3×C4—241no—
355C3×C4C2×#20411yescharacteristic
356C3×C4#90811yescharacteristic
357C3×C4#91411yescharacteristic
358C3×C4#91911yescharacteristic
359C3×C4C2×C3×SD1611yescharacteristic
360C3×C4C3×#13511yescharacteristic
361C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
362C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
363Dic3—41no—
364Dic3—81no—
365C32#164211yescharacteristic, complemented, Sylow
366C23—61no—
367C23—62no—
368Q8—21no—
369Q8—121no—
370Q8—121no—
371Q8C3×#20412yescomplemented
372D4—61no—
373D4—61no—
374D4—122no—
375D4—124no—
376D4—121no—
377D4—121no—
378D4—121no—
379D4—121no—
380D4—242no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—61no—
384C2×C4—124no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4C2×C3×D1211yescharacteristic
389C2×C4C3×D3×D411yescharacteristic
390C2×C4C3×D3×D411yescharacteristic
391C8—41no—
392C8—41no—
393C8—121no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—241no—
398C2×C3—242no—
399C2×C3#473111yescharacteristic
400C2×C3#481011yescharacteristic
401C2×C3#482511yescharacteristic
402C2×C3C3×#44911yescharacteristic
403C2×C3C3×#45011yescharacteristic
404C2×C3C3×#45511yescharacteristic
405D3—81no—
406D3—82no—
407C22—122no—
408C22—121no—
409C22—121no—
410C22—122no—
411C22—122no—
412C22—121no—
413C22C3×#88211yescharacteristic
414C4—22no—
415C4—21no—
416C4—41no—
417C4—121no—
418C4—241no—
419C4C2×C3×#20411yescharacteristic
420C4C3×#90811yescharacteristic
421C4C3×#91411yescharacteristic
422C4C3×#91911yescharacteristic
423C3—21no—
424C3#6824811yescharacteristic, direct product factor
425C3C3×#164211yescharacteristic, complemented
426C2—241no—
427C2—242no—
428C2C3×#473111yescharacteristic
429C2C3×#481011yescharacteristic
430C2C3×#482511yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC3×#5577C2
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1642
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×#5020C2semidirect
3. C3×#4841C2semidirect
4. C3×#4694C2semidirect
5. C32×Q8⋊C8C2semidirect
6. C3×#4485C2semidirect
7. C3×#4459C2semidirect
9. #68248C3direct (N × H)
32. #5020C2×C3semidirect
33. #4841C2×C3semidirect
34. #4694C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
40. #4485C2×C3semidirect
41. #4459C2×C3semidirect
108. C32×Q8SD16semidirect
138. Q8⋊C8C3×D3semidirect
240. C3×Q8#204semidirect
241. C3×Q8C3×SD16semidirect
365. C32#1642semidirect
371. Q8C3×#204semidirect
424. C3#68248direct (N × H)
425. C3C3×#1642semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C3×#50202
C3×#48412
C3×#46942
C32×Q8⋊C82
C3×#44852
C3×#44592
C3×#16423
#682483