Finite Group Databasebeta

← C3×#68259 #11778959

Subgroups — C3×#68259 #11778959

Order 1152.

591 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5577C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3C3×#4843C211yesmaximal, characteristic, complemented
4C3×#4695C211yesmaximal, characteristic, complemented
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1621—31nomaximal
9#68259C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C32×C4×Q8C2211yescharacteristic
12C2×C3×#215—21no—
13C2×C3×D24—22no—
14C2×C3×D24—21no—
15C3×#895—22no—
16C3×#895—21no—
17C3×#874—21no—
18C3×#874C2211yescharacteristic
19C3×#874C2211yescharacteristic
20C3×C4×D12—21no—
21C3×C4×D12C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24C3×#821—21no—
25C3×#809—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#550—31no—
28#5577C2×C311yescharacteristic, complemented
29C3×#493—31no—
30C3×#460—31no—
31C3×#459—31no—
32#5027C2×C311yescharacteristic, complemented
33#4843C2×C311yescharacteristic, complemented
34#4695C2×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—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—22no—
52C2×C3×D12D411yescharacteristic
53C2×C3×D12D412yes—
54C2×C3×C4×D3—22no—
55C2×C3×C4×D3—21no—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4D411yescharacteristic
60C32×C42—21no—
61C32×C42C2311yescharacteristic
62C3×#215—42no—
63C3×(C2×D3)⋊C4—22no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C3×D24—44no—
68C3×D24—42no—
69#1621—31noSylow
70C2×C3×#41—61no—
71C2×#239—21no—
72C2×C3×SD16—61no—
73C2×C3×D8—61no—
74C2×C3×D8—62no—
75C3×#127—31no—
76C3×#127—31no—
77C3×#127—61no—
78C3×#121—62no—
79C3×#121—61no—
80C3×C4×Q8—21no—
81C3×C4×Q8C2×D311yescharacteristic
82C3×C4×Q8C22×C311yescharacteristic
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85C2×#215—21no—
86C2×D24—22no—
87C2×D24—21no—
88#895—22no—
89#895—21no—
90#874—21no—
91#874C22×C311yescharacteristic
92#874C22×C311yescharacteristic
93C4×D12—21no—
94C4×D12C22×C311yescharacteristic
95C3×C4⋊C8—21no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8C2×D311yescharacteristic
98C3×C4⋊C8C22×C311yescharacteristic
99C3×#102—61no—
100C3×#102—61no—
101C3×C4×C8—21no—
102C3×C4×C8C2×D311yescharacteristic
103C3×C4×C8C22×C311yescharacteristic
104#821—21no—
105#809—21no—
106C4⋊(C3⋊C8)C22×C311yescharacteristic
107C22×C3×D3—21no—
108C22×C3×D3—22no—
109C22×C3×D3—41no—
110C32×Q8—21no—
111C32×Q8D812yescomplemented
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3×Dic3—21no—
118C3×D12—21no—
119C3×D12—21no—
120C3×D12—42no—
121C3×D12—44no—
122C3×D12—42no—
123C3×D12—41no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12—82no—
132C3×C4×D3—44no—
133C3×C4×D3—41no—
134C3×C4×D3—41no—
135C32×C8—22no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#550—31no—
139#493—31no—
140#460—31no—
141#459—31no—
142#331—31no—
143Q8⋊C8C3×D311yescharacteristic, complemented
144D4⋊C8—31no—
145C3×#41—122no—
146C3×#41—122no—
147C2×C3×Q8—21no—
148C2×C3×Q8D1211yescharacteristic
149C2×C3×Q8C3×D411yescharacteristic
150C2×C3×D4—31no—
151C2×C3×D4—32no—
152C2×C3×D4—62no—
153C2×C3×D4—62no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C22×C3×C4—62no—
160C22×C3×C4—61no—
161#239—42no—
162#239—42no—
163C2×D12—22no—
164C2×D12—21no—
165C2×D12—21no—
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12—22no—
170C2×D12C3×D411yescharacteristic
171C2×D12C3×D412yes—
172C2×C4×D3—22no—
173C2×C4×D3—21no—
174C3×SD16—122no—
175C3×D8—124no—
176C3×D8—122no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—41no—
182C2×C3×C8—41no—
183C2×C3×C8—61no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4D1211yescharacteristic
190C3×C4⋊C4C3×D411yescharacteristic
191C3×C22⋊C4—62no—
192C3×C22⋊C4—61no—
193C3×C42—21no—
194C3×C42—21no—
195C3×C42—21no—
196C3×C42—41no—
197C3×C42C22×D311yescharacteristic
198C3×C42C23×C311yescharacteristic
199#215—42no—
200(C2×D3)⋊C4—22no—
201(C2×D3)⋊C4—21no—
202C4⋊Dic3C3×D411yescharacteristic
203C2×C3⋊C8—21no—
204D24—44no—
205D24—42no—
206C22×C32#12011yescharacteristic
207C2×C3×D3—42no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C2×C3×D3—42no—
211C2×C3×D3—42no—
212C2×C3×D3—41no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C2×C3×D3—81no—
216C32×C4—22no—
217C32×C4—21no—
218C32×C4—41no—
219C32×C4C2×D811yescharacteristic
220C32×C4#13511yescharacteristic
221C32×C4AGL(1,ℤ/8)11yescharacteristic
222C32×C4AGL(1,ℤ/8)11yescharacteristic
223C3×Dic3—41no—
224C2×#41—61no—
225C2×SD16—61no—
226C2×D8—61no—
227C2×D8—62no—
228#127—31no—
229#127—31no—
230#127—61no—
231#121—62no—
232#121—61no—
233C4×Q8C2×C3×D311yescharacteristic
234C4×D4—31no—
235C4×D4—61no—
236C4⋊C8—31no—
237C4⋊C8C2×C3×D311yescharacteristic
238#102—61no—
239#102—61no—
240C4×C8C2×C3×D311yescharacteristic
241C23×C3—61no—
242C23×C3—62no—
243C23×C3—121no—
244C22×D3—21no—
245C22×D3—22no—
246C22×D3—41no—
247C3×Q8—21no—
248C3×Q8—21no—
249C3×Q8—22no—
250C3×Q8—41no—
251C3×Q8D2412yescomplemented
252C3×Q8C3×D812yescomplemented
253C3×D4—61no—
254C3×D4—61no—
255C3×D4—122no—
256C3×D4—124no—
257C3×D4—122no—
258C3×D4—121no—
259C3×D4—121no—
260C3×D4—121no—
261C3×D4—121no—
262C3×D4—121no—
263C3×D4—121no—
264C3×D4—121no—
265C3×D4—121no—
266C3×D4—242no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—61no—
277C2×C3×C4—124no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4C2×C3×D411yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286C2×Dic3—21no—
287D12—21no—
288D12—21no—
289D12—42no—
290D12—44no—
291D12—42no—
292D12—41no—
293D12—41no—
294D12—41no—
295D12—41no—
296D12—41no—
297D12—41no—
298D12—41no—
299D12—41no—
300D12—82no—
301C4×D3—44no—
302C4×D3—41no—
303C4×D3—41no—
304C3×C8—22no—
305C3×C8—22no—
306C3×C8—42no—
307C3×C8—41no—
308C3×C8—41no—
309C3×C8—81no—
310C3×C8—121no—
311C3⋊C8—41no—
312C2×C32#44711yescharacteristic
313C2×C32#44911yescharacteristic
314C2×C32#45311yescharacteristic
315C3×D3—81no—
316C3×D3—82no—
317C3×D3—161no—
318#41—122no—
319#41—122no—
320C2×Q8C3×D1211yescharacteristic
321C2×D4—31no—
322C2×D4—32no—
323C2×D4—62no—
324C2×D4—62no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—61no—
328C2×D4—61no—
329C2×D4—61no—
330C22×C4—62no—
331C22×C4—61no—
332SD16—122no—
333D8—124no—
334D8—122no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—61no—
338C4⋊C4—21no—
339C4⋊C4—31no—
340C4⋊C4C3×D1211yescharacteristic
341C22⋊C4—62no—
342C22⋊C4—61no—
343C42—21no—
344C42C22×C3×D311yescharacteristic
345C22×C3—21no—
346C22×C3—122no—
347C22×C3—121no—
348C22×C3—121no—
349C22×C3—122no—
350C22×C3—122no—
351C22×C3—121no—
352C22×C3—241no—
353C22×C3—241no—
354C22×C3—241no—
355C22×C3#88211yescharacteristic
356C22×C3C3×#12011yescharacteristic
357C2×D3—42no—
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—42no—
361C2×D3—42no—
362C2×D3—41no—
363C2×D3—81no—
364C2×D3—81no—
365C2×D3—81no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—41no—
375C3×C4—42no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—81no—
379C3×C4—121no—
380C3×C4C2×D2411yescharacteristic
381C3×C4#90811yescharacteristic
382C3×C4#91411yescharacteristic
383C3×C4#91911yescharacteristic
384C3×C4C2×C3×D811yescharacteristic
385C3×C4C3×#13511yescharacteristic
386C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
387C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
388Dic3—41no—
389C32#162111yescharacteristic, complemented, Sylow
390C23—61no—
391C23—62no—
392C23—121no—
393Q8—21no—
394Q8C3×D2412yescomplemented
395D4—61no—
396D4—61no—
397D4—122no—
398D4—124no—
399D4—122no—
400D4—121no—
401D4—121no—
402D4—121no—
403D4—121no—
404D4—121no—
405D4—121no—
406D4—121no—
407D4—121no—
408D4—242no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—61no—
412C2×C4—124no—
413C2×C4—121no—
414C2×C4—121no—
415C2×C4C2×C3×D1211yescharacteristic
416C2×C4C3×D3×D411yescharacteristic
417C2×C4C3×D3×D411yescharacteristic
418C8—22no—
419C8—41no—
420C8—121no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—241no—
425C2×C3—242no—
426C2×C3—481no—
427C2×C3#473211yescharacteristic
428C2×C3#481011yescharacteristic
429C2×C3#482211yescharacteristic
430C2×C3C3×#44711yescharacteristic
431C2×C3C3×#44911yescharacteristic
432C2×C3C3×#45311yescharacteristic
433D3—81no—
434D3—82no—
435D3—161no—
436C22—122no—
437C22—121no—
438C22—121no—
439C22—122no—
440C22—122no—
441C22—121no—
442C22—241no—
443C22—241no—
444C22—241no—
445C22C3×#88211yescharacteristic
446C4—22no—
447C4—21no—
448C4—41no—
449C4—121no—
450C4C2×C3×D2411yescharacteristic
451C4C3×#90811yescharacteristic
452C4C3×#91411yescharacteristic
453C4C3×#91911yescharacteristic
454C3—21no—
455C3#6825911yescharacteristic, direct product factor
456C3C3×#162111yescharacteristic, complemented
457C2—241no—
458C2—242no—
459C2—481no—
460C2C3×#473211yescharacteristic
461C2C3×#481011yescharacteristic
462C2C3×#482211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1621
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
1. C3×#5577C2semidirect
2. C3×#5027C2semidirect
3. C3×#4843C2semidirect
4. C3×#4695C2semidirect
5. C32×Q8⋊C8C2semidirect
6. C3×#4485C2semidirect
7. C3×#4459C2semidirect
9. #68259C3direct (N × H)
28. #5577C2×C3semidirect
32. #5027C2×C3semidirect
33. #4843C2×C3semidirect
34. #4695C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
40. #4485C2×C3semidirect
41. #4459C2×C3semidirect
111. C32×Q8D8semidirect
143. Q8⋊C8C3×D3semidirect
251. C3×Q8D24semidirect
252. C3×Q8C3×D8semidirect
389. C32#1621semidirect
394. Q8C3×D24semidirect
455. C3#68259direct (N × H)
456. C3C3×#1621semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C3×#50272
C3×#48432
C3×#46952
C32×Q8⋊C82
C3×#44852
C3×#44592
C3×#16213
#682593