Finite Group Databasebeta

← C3×#5662 #10595759

Subgroups — C3×#5662 #10595759

Order 576.

471 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#123C211yesmaximal, characteristic, complemented
2C3×#939C211yesmaximal, characteristic
3C3×#936C211yesmaximal, characteristic, complemented
4C3×C4×#67C211yesmaximal, characteristic, complemented
5C3×#924C211yesmaximal, characteristic, complemented
6C3×#898C211yesmaximal, characteristic, complemented
7C3×#896C211yesmaximal, characteristic, complemented
8C3×#888C211yesmaximal, characteristic, complemented
9C3×#887C211yesmaximal, characteristic, complemented
10C3×#885C211yesmaximal, characteristic, complemented
11C3×#885C211yesmaximal, characteristic, complemented
12C3×#883C211yesmaximal, characteristic, complemented
13C3×#879C211yesmaximal, characteristic, complemented
14C3×#878C211yesmaximal, characteristic, complemented
15C3×#877C211yesmaximal, characteristic, complemented
16C3×#542—31nomaximal
17#5662C311yesmaximal, characteristic, direct product factor
18C2×C32×D4C2211yescharacteristic
19C22×C32×C4C2211yescharacteristic
20C2×C3×#67C2211yescharacteristic
21C2×C3×#67C2211yescharacteristic
22C22×C3×Dic3C2211yescharacteristic
23C2×C3×C4×D3C2211yescharacteristic
24C2×C3×Dic6C2211yescharacteristic
25C2×C3×Dic6C2211yescharacteristic
26C2×C3×Dic6C2211yescharacteristic
27C32×C4⋊C4C2211yescharacteristic
28C32×C4⋊C4C2211yescharacteristic
29C32×C22⋊C4C2211yescharacteristic
30C32×C22⋊C4C2211yescharacteristic
31C32×C22⋊C4C2211yescharacteristic
32C3×#217C2211yescharacteristic
33C3×#217C2211yescharacteristic
34C3×#217C2211yescharacteristic
35C3×#217C2211yescharacteristic
36C3×#217C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D3)⋊C4C2211yescharacteristic
41C3×C4⋊Dic3C2211yescharacteristic
42C3×C4⋊Dic3C2211yescharacteristic
43C3×Dic3⋊C4C2211yescharacteristic
44C3×Dic3⋊C4C2211yescharacteristic
45C3×Dic3⋊C4C2211yescharacteristic
46C3×Dic3⋊C4C2211yescharacteristic
47C3×Dic3⋊C4C2211yescharacteristic
48C3×Dic3⋊C4C2211yescharacteristic
49C3×C4×Dic3C2211yescharacteristic
50C3×C4×Dic3C2211yescharacteristic
51C3×C4×Dic3C2211yescharacteristic
52C3×C4×Dic3C2211yescharacteristic
53C3×C4⋊Q8—31no—
54C3×#126—31no—
55C3×#126—31no—
56C3×#124—31no—
57C3×#124—31no—
58C3×#124—31no—
59C3×#123—21no—
60C3×#123—31no—
61C3×#123D311yescharacteristic, complemented
62C3×#123C2×C311yescharacteristic, complemented
63C3×C22⋊Q8—31no—
64C3×C22⋊Q8—31no—
65C3×C22⋊Q8—31no—
66C3×#121—31no—
67C3×C4×Q8—31no—
68C3×C4×D4—31no—
69C3×#117—31no—
70#939C2×C311yescharacteristic
71#936C2×C311yescharacteristic, complemented
72C4×#67C2×C311yescharacteristic, complemented
73#924C2×C311yescharacteristic, complemented
74#898C2×C311yescharacteristic, complemented
75#896C2×C311yescharacteristic, complemented
76#888C2×C311yescharacteristic, complemented
77#887C2×C311yescharacteristic, complemented
78#885C2×C311yescharacteristic, complemented
79#885C2×C311yescharacteristic, complemented
80#883C2×C311yescharacteristic, complemented
81#879C2×C311yescharacteristic, complemented
82#878C2×C311yescharacteristic, complemented
83#877C2×C311yescharacteristic, complemented
84C23×C32C2311yescharacteristic
85C23×C32C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C32×D4—41no—
88C2×C32×C4—41no—
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92C2×C32×C4C2311yescharacteristic
93C2×C32×C4C2311yescharacteristic
94C3×#67—22no—
95C3×#67—41no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C3×C4×D3—41no—
105C3×Dic6—22no—
106C3×Dic6—41no—
107C3×Dic6—41no—
108#542—31noSylow
109C2×C3×Q8—31no—
110C2×C3×Q8—31no—
111C2×C3×Q8—31no—
112C2×C3×D4—21no—
113C2×C3×D4—31no—
114C2×C3×D4—31no—
115C2×C3×D4C2×D311yescharacteristic
116C2×C3×D4C22×C311yescharacteristic
117C22×C3×C4—21no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4C2×D311yescharacteristic
121C22×C3×C4C22×C311yescharacteristic
122C2×#67C22×C311yescharacteristic
123C2×#67C22×C311yescharacteristic
124C22×Dic3C22×C311yescharacteristic
125C2×C4×D3C22×C311yescharacteristic
126C2×Dic6C22×C311yescharacteristic
127C2×Dic6C22×C311yescharacteristic
128C2×Dic6C22×C311yescharacteristic
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—31no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4C2×D311yescharacteristic
140C3×C4⋊C4C2×D311yescharacteristic
141C3×C4⋊C4C22×C311yescharacteristic
142C3×C4⋊C4C22×C311yescharacteristic
143C3×C22⋊C4—21no—
144C3×C22⋊C4—21no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4—31no—
147C3×C22⋊C4—31no—
148C3×C22⋊C4—31no—
149C3×C22⋊C4—31no—
150C3×C22⋊C4—31no—
151C3×C22⋊C4—31no—
152C3×C22⋊C4—31no—
153C3×C22⋊C4—31no—
154C3×C22⋊C4—31no—
155C3×C22⋊C4C2×D311yescharacteristic
156C3×C22⋊C4C2×D311yescharacteristic
157C3×C22⋊C4C2×D311yescharacteristic
158C3×C22⋊C4C22×C311yescharacteristic
159C3×C22⋊C4C22×C311yescharacteristic
160C3×C22⋊C4C22×C311yescharacteristic
161C3×C42—31no—
162C3×C42—31no—
163C3×C42—31no—
164C3×C42—31no—
165#217C22×C311yescharacteristic
166#217C22×C311yescharacteristic
167#217C22×C311yescharacteristic
168#217C22×C311yescharacteristic
169#217C22×C311yescharacteristic
170(C2×D3)⋊C4C22×C311yescharacteristic
171(C2×D3)⋊C4C22×C311yescharacteristic
172(C2×D3)⋊C4C22×C311yescharacteristic
173(C2×D3)⋊C4C22×C311yescharacteristic
174C4⋊Dic3C22×C311yescharacteristic
175C4⋊Dic3C22×C311yescharacteristic
176Dic3⋊C4C22×C311yescharacteristic
177Dic3⋊C4C22×C311yescharacteristic
178Dic3⋊C4C22×C311yescharacteristic
179Dic3⋊C4C22×C311yescharacteristic
180Dic3⋊C4C22×C311yescharacteristic
181Dic3⋊C4C22×C311yescharacteristic
182C4×Dic3C22×C311yescharacteristic
183C4×Dic3C22×C311yescharacteristic
184C4×Dic3C22×C311yescharacteristic
185C4×Dic3C22×C311yescharacteristic
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32C2411yescharacteristic
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3—21no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—21no—
201C3×Dic3—21no—
202C3×Dic3—21no—
203C3×Dic3—21no—
204C3×Dic3—21no—
205C3×Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3#4112yes—
208C4⋊Q8—31no—
209#126—31no—
210#126—31no—
211#124—31no—
212#124—31no—
213#124—31no—
214#123—31no—
215#123C3×D311yescharacteristic, complemented
216C22⋊Q8—31no—
217C22⋊Q8—31no—
218C22⋊Q8—31no—
219#121—31no—
220C4×Q8—31no—
221C4×D4—31no—
222#117—31no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—31no—
226C23×C3C22×D311yescharacteristic
227C23×C3C22×D311yescharacteristic
228C23×C3C23×C311yescharacteristic
229C23×C3C23×C311yescharacteristic
230C22×D3C23×C311yescharacteristic
231C3×Q8—62no—
232C3×Q8—121no—
233C3×Q8—121no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—42no—
237C3×D4—62no—
238C3×D4—121no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—42no—
254C2×C3×C4—62no—
255C2×C3×C4—121no—
256C2×C3×C4C22×D311yescharacteristic
257C2×C3×C4C22×D311yescharacteristic
258C2×C3×C4C22×D311yescharacteristic
259C2×C3×C4C22×D311yescharacteristic
260C2×C3×C4C22×D311yescharacteristic
261C2×C3×C4C23×C311yescharacteristic
262C2×C3×C4C23×C311yescharacteristic
263C2×C3×C4C23×C311yescharacteristic
264C2×C3×C4C23×C311yescharacteristic
265C2×C3×C4C23×C311yescharacteristic
266#67—22no—
267#67—41no—
268C2×Dic3—22no—
269C2×Dic3C23×C311yescharacteristic
270C2×Dic3C23×C311yescharacteristic
271C2×Dic3C23×C311yescharacteristic
272C2×Dic3C23×C311yescharacteristic
273C2×Dic3C23×C311yescharacteristic
274C2×Dic3C23×C311yescharacteristic
275C2×Dic3C23×C311yescharacteristic
276C4×D3—41no—
277Dic6—22no—
278Dic6—41no—
279Dic6—41no—
280C2×C32—41no—
281C2×C32—41no—
282C2×C32C2×#4111yescharacteristic
283C2×C32H(5,𝔽2)11yescharacteristic
284C2×C322−1+411yescharacteristic
285C3×D3—41no—
286C2×Q8—31no—
287C2×Q8—31no—
288C2×Q8—31no—
289C2×D4—31no—
290C2×D4—31no—
291C2×D4C2×C3×D311yescharacteristic
292C22×C4—31no—
293C22×C4—31no—
294C22×C4C2×C3×D311yescharacteristic
295C4⋊C4—31no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4C2×C3×D311yescharacteristic
304C4⋊C4C2×C3×D311yescharacteristic
305C22⋊C4—31no—
306C22⋊C4—31no—
307C22⋊C4—31no—
308C22⋊C4—31no—
309C22⋊C4—31no—
310C22⋊C4—31no—
311C22⋊C4—31no—
312C22⋊C4—31no—
313C22⋊C4—31no—
314C22⋊C4C2×C3×D311yescharacteristic
315C22⋊C4C2×C3×D311yescharacteristic
316C22⋊C4C2×C3×D311yescharacteristic
317C42—31no—
318C42—31no—
319C42—31no—
320C42—31no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—61no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3C23×D311yescharacteristic
344C22×C3C24×C311yescharacteristic
345C2×D3—21no—
346C2×D3—21no—
347C2×D3—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—32no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—61no—
365C3×C4—61no—
366C3×C4—61no—
367C3×C4—61no—
368C3×C4—61no—
369C3×C4—61no—
370Dic3—21no—
371Dic3—21no—
372Dic3—21no—
373Dic3—21no—
374Dic3—21no—
375Dic3—21no—
376Dic3C3×#4112yes—
377C32#54211yescharacteristic, complemented, Sylow
378C23—31no—
379C23C22×C3×D311yescharacteristic
380C23C22×C3×D311yescharacteristic
381Q8—62no—
382Q8—121no—
383Q8—121no—
384D4—41no—
385D4—62no—
386D4—121no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—41no—
395C2×C4—62no—
396C2×C4—121no—
397C2×C4C22×C3×D311yescharacteristic
398C2×C4C22×C3×D311yescharacteristic
399C2×C4C22×C3×D311yescharacteristic
400C2×C4C22×C3×D311yescharacteristic
401C2×C4C22×C3×D311yescharacteristic
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—42no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3—41no—
409C2×C3—41no—
410C2×C3—81no—
411C2×C3—121no—
412C2×C3#100411yescharacteristic
413C2×C3D3×#4111yescharacteristic
414C2×C3#101011yescharacteristic
415C2×C3C2×C3×#4111yescharacteristic
416C2×C3C3×H(5,𝔽2)11yescharacteristic
417C2×C3C3×2−1+411yescharacteristic
418D3—41no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—61no—
426C22—61no—
427C22—61no—
428C22C23×C3×D311yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—32no—
435C4—61no—
436C4—61no—
437C4—61no—
438C4—61no—
439C4—61no—
440C4—61no—
441C3—21no—
442C3#566211yescharacteristic, direct product factor
443C3C3×#54211yescharacteristic, complemented
444C2—41no—
445C2—41no—
446C2—121no—
447C2C3×#100411yescharacteristic
448C2C3×D3×#4111yescharacteristic
449C2C3×#101011yescharacteristic
subgroupG/H
centerC22×C3C23×D3
commutator, cosocleC22×C3C24×C3
FrattiniC22C23×C3×D3
FittingC32×#123C2
socleC22×C32C24
prime radicalC3×#939C2
hypercenterC3×#123D3
hypocenterC3C3×#542
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#123

Complements

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

NH ≅ G/Ntype
1. C32×#123C2semidirect
3. C3×#936C2semidirect
4. C3×C4×#67C2semidirect
5. C3×#924C2semidirect
6. C3×#898C2semidirect
7. C3×#896C2semidirect
8. C3×#888C2semidirect
9. C3×#887C2semidirect
10. C3×#885C2semidirect
11. C3×#885C2semidirect
12. C3×#883C2semidirect
13. C3×#879C2semidirect
14. C3×#878C2semidirect
15. C3×#877C2semidirect
17. #5662C3direct (N × H)
61. C3×#123D3semidirect
62. C3×#123C2×C3semidirect
71. #936C2×C3semidirect
72. C4×#67C2×C3semidirect
73. #924C2×C3semidirect
74. #898C2×C3semidirect
75. #896C2×C3semidirect
76. #888C2×C3semidirect
77. #887C2×C3semidirect
78. #885C2×C3semidirect
79. #885C2×C3semidirect
80. #883C2×C3semidirect
81. #879C2×C3semidirect
82. #878C2×C3semidirect
83. #877C2×C3semidirect
215. #123C3×D3semidirect
377. C32#542semidirect
442. C3#5662direct (N × H)
443. C3C3×#542semidirect

Maximal subgroups

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

subgroupindex
C32×#1232
C3×#9392
C3×#9362
C3×C4×#672
C3×#9242
C3×#8982
C3×#8962
C3×#8882
C3×#8872
C3×#8852
C3×#8832
C3×#8792
C3×#8782
C3×#8772
C3×#5423
#56623