Finite Group Databasebeta

← C3×#5693 #10595790

Subgroups — C3×#5693 #10595790

Order 576.

456 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#125C211yesmaximal, characteristic, complemented
2C3×#898C211yesmaximal, characteristic, complemented
3C3×#898C211yesmaximal, characteristic, complemented
4C3×#896C211yesmaximal, characteristic, complemented
5C3×#896C211yesmaximal, characteristic, complemented
6C3×#894C211yesmaximal, characteristic
7C3×#894C211yesmaximal, characteristic
8C3×#893C211yesmaximal, characteristic
9C3×#892C211yesmaximal, characteristic, complemented
10C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
11C3×#889C211yesmaximal, characteristic, complemented
12C3×#889C211yesmaximal, characteristic, complemented
13C3×#887C211yesmaximal, characteristic, complemented
14C3×#872C211yesmaximal, characteristic, complemented
15C3×#872C211yesmaximal, characteristic, complemented
16C3×#552—31nomaximal
17#5693C311yesmaximal, characteristic, direct product factor
18C2×C3×D12C2211yescharacteristic
19C2×C3×C4×D3C2211yescharacteristic
20C2×C3×C4×D3C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×C3×C4×D3C2211yescharacteristic
23C2×C3×Dic6C2211yescharacteristic
24C32×C4⋊C4C2211yescharacteristic
25C32×C4⋊C4C2211yescharacteristic
26C32×C4⋊C4C2211yescharacteristic
27C32×C4⋊C4C2211yescharacteristic
28C32×C4⋊C4C2211yescharacteristic
29C32×C4⋊C4C2211yescharacteristic
30C32×C42C2211yescharacteristic
31C3×(C2×D3)⋊C4C2211yescharacteristic
32C3×(C2×D3)⋊C4C2211yescharacteristic
33C3×(C2×D3)⋊C4C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×C4⋊Dic3C2211yescharacteristic
40C3×C4⋊Dic3C2211yescharacteristic
41C3×Dic3⋊C4C2211yescharacteristic
42C3×Dic3⋊C4C2211yescharacteristic
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×#126—31no—
54C3×#126—31no—
55C3×#125—21no—
56C3×#125—31no—
57C3×#125—31no—
58C3×#125D311yescharacteristic, complemented
59C3×#125C2×C311yescharacteristic, complemented
60C3×#123—31no—
61C3×#123—31no—
62C3×C22⋊Q8—31no—
63C3×C22⋊Q8—31no—
64C3×C4×Q8—31no—
65C3×C4×D4—31no—
66C3×#117—31no—
67C3×#117—31no—
68C3×#117—31no—
69C2×C3×C4⋊C4—31no—
70#898C2×C311yescharacteristic, complemented
71#898C2×C311yescharacteristic, complemented
72#896C2×C311yescharacteristic, complemented
73#896C2×C311yescharacteristic, complemented
74#894C2×C311yescharacteristic
75#894C2×C311yescharacteristic
76#893C2×C311yescharacteristic
77#892C2×C311yescharacteristic, complemented
78D3×C4⋊C4C2×C311yescharacteristic, complemented
79#889C2×C311yescharacteristic, complemented
80#889C2×C311yescharacteristic, complemented
81#887C2×C311yescharacteristic, complemented
82#872C2×C311yescharacteristic, complemented
83#872C2×C311yescharacteristic, complemented
84C22×C3×D3C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C2×C32×C4C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92C2×C32×C4C2311yescharacteristic
93C2×C3×Dic3C2311yescharacteristic
94C2×C3×Dic3C2311yescharacteristic
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C3×D12—22no—
100C3×C4×D3—22no—
101C3×C4×D3—22no—
102C3×C4×D3—22no—
103C3×C4×D3—22no—
104C3×Dic6—22no—
105#552—31noSylow
106C2×C3×Q8—31no—
107C2×C3×D4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—31no—
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C2×D12C22×C311yescharacteristic
113C2×C4×D3C22×C311yescharacteristic
114C2×C4×D3C22×C311yescharacteristic
115C2×C4×D3C22×C311yescharacteristic
116C2×C4×D3C22×C311yescharacteristic
117C2×Dic6C22×C311yescharacteristic
118C3×C4⋊C4—21no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4—31no—
125C3×C4⋊C4—31no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—31no—
129C3×C4⋊C4—31no—
130C3×C4⋊C4—31no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4C2×D311yescharacteristic
135C3×C4⋊C4C2×D311yescharacteristic
136C3×C4⋊C4C2×D311yescharacteristic
137C3×C4⋊C4C2×D311yescharacteristic
138C3×C4⋊C4C2×D311yescharacteristic
139C3×C4⋊C4C2×D311yescharacteristic
140C3×C4⋊C4C22×C311yescharacteristic
141C3×C4⋊C4C22×C311yescharacteristic
142C3×C4⋊C4C22×C311yescharacteristic
143C3×C4⋊C4C22×C311yescharacteristic
144C3×C4⋊C4C22×C311yescharacteristic
145C3×C4⋊C4C22×C311yescharacteristic
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×C42—21no—
155C3×C42—31no—
156C3×C42—31no—
157C3×C42—31no—
158C3×C42—31no—
159C3×C42C2×D311yescharacteristic
160C3×C42C22×C311yescharacteristic
161(C2×D3)⋊C4C22×C311yescharacteristic
162(C2×D3)⋊C4C22×C311yescharacteristic
163(C2×D3)⋊C4C22×C311yescharacteristic
164(C2×D3)⋊C4C22×C311yescharacteristic
165(C2×D3)⋊C4C22×C311yescharacteristic
166(C2×D3)⋊C4C22×C311yescharacteristic
167(C2×D3)⋊C4C22×C311yescharacteristic
168(C2×D3)⋊C4C22×C311yescharacteristic
169C4⋊Dic3C22×C311yescharacteristic
170C4⋊Dic3C22×C311yescharacteristic
171Dic3⋊C4C22×C311yescharacteristic
172Dic3⋊C4C22×C311yescharacteristic
173Dic3⋊C4C22×C311yescharacteristic
174Dic3⋊C4C22×C311yescharacteristic
175Dic3⋊C4C22×C311yescharacteristic
176Dic3⋊C4C22×C311yescharacteristic
177Dic3⋊C4C22×C311yescharacteristic
178Dic3⋊C4C22×C311yescharacteristic
179C4×Dic3C22×C311yescharacteristic
180C4×Dic3C22×C311yescharacteristic
181C4×Dic3C22×C311yescharacteristic
182C4×Dic3C22×C311yescharacteristic
183C22×C32C2411yescharacteristic
184C2×C3×D3—21no—
185C2×C3×D3—21no—
186C2×C3×D3—21no—
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3#4112yes—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—21no—
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—21no—
197C3×Dic3—21no—
198C3×Dic3—21no—
199C3×Dic3—21no—
200C3×Dic3—21no—
201C3×Dic3—21no—
202C3×Dic3#4112yes—
203#126—31no—
204#126—31no—
205#125—31no—
206#125—31no—
207#125C3×D311yescharacteristic, complemented
208#123—31no—
209#123—31no—
210C22⋊Q8—31no—
211C22⋊Q8—31no—
212C4×Q8—31no—
213C4×D4—31no—
214#117—31no—
215#117—31no—
216#117—31no—
217C2×C4⋊C4—31no—
218C23×C3—31no—
219C23×C3—31no—
220C22×D3C23×C311yescharacteristic
221C22×D3C23×C311yescharacteristic
222C3×Q8—62no—
223C3×D4—62no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—31no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—62no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—62no—
241C2×C3×C4C22×D311yescharacteristic
242C2×C3×C4C22×D311yescharacteristic
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245C2×C3×C4C22×D311yescharacteristic
246C2×C3×C4C22×D311yescharacteristic
247C2×C3×C4C22×D311yescharacteristic
248C2×C3×C4C23×C311yescharacteristic
249C2×C3×C4C23×C311yescharacteristic
250C2×C3×C4C23×C311yescharacteristic
251C2×C3×C4C23×C311yescharacteristic
252C2×C3×C4C23×C311yescharacteristic
253C2×C3×C4C23×C311yescharacteristic
254C2×C3×C4C23×C311yescharacteristic
255C2×Dic3C23×C311yescharacteristic
256C2×Dic3C23×C311yescharacteristic
257C2×Dic3C23×C311yescharacteristic
258C2×Dic3C23×C311yescharacteristic
259C2×Dic3C23×C311yescharacteristic
260C2×Dic3C23×C311yescharacteristic
261D12—22no—
262C4×D3—22no—
263C4×D3—22no—
264C4×D3—22no—
265C4×D3—22no—
266Dic6—22no—
267C2×C32C2×#4111yescharacteristic
268C2×C32C2×#4111yescharacteristic
269C2×C322−1+411yescharacteristic
270C3×D3—22no—
271C3×D3—41no—
272C2×Q8—31no—
273C2×D4—31no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—31no—
278C4⋊C4—31no—
279C4⋊C4—31no—
280C4⋊C4—31no—
281C4⋊C4—31no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—31no—
287C4⋊C4—31no—
288C4⋊C4C2×C3×D311yescharacteristic
289C4⋊C4C2×C3×D311yescharacteristic
290C4⋊C4C2×C3×D311yescharacteristic
291C4⋊C4C2×C3×D311yescharacteristic
292C4⋊C4C2×C3×D311yescharacteristic
293C4⋊C4C2×C3×D311yescharacteristic
294C22⋊C4—31no—
295C22⋊C4—31no—
296C22⋊C4—31no—
297C22⋊C4—31no—
298C22⋊C4—31no—
299C22⋊C4—31no—
300C22⋊C4—31no—
301C22⋊C4—31no—
302C42—31no—
303C42—31no—
304C42—31no—
305C42—31no—
306C42C2×C3×D311yescharacteristic
307C22×C3—21no—
308C22×C3—32no—
309C22×C3—61no—
310C22×C3—61no—
311C22×C3—61no—
312C22×C3—61no—
313C22×C3—61no—
314C22×C3C23×D311yescharacteristic
315C22×C3C24×C311yescharacteristic
316C2×D3—21no—
317C2×D3—21no—
318C2×D3—21no—
319C2×D3—21no—
320C2×D3—21no—
321C2×D3C3×#4112yes—
322C3×C4—22no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—32no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—61no—
345C3×C4—61no—
346C3×C4—61no—
347C3×C4—61no—
348C3×C4—61no—
349Dic3—21no—
350Dic3—21no—
351Dic3—21no—
352Dic3—21no—
353Dic3—21no—
354Dic3C3×#4112yes—
355C32#55211yescharacteristic, complemented, Sylow
356C23—31no—
357C23—31no—
358Q8—62no—
359D4—62no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—62no—
367C2×C4—62no—
368C2×C4—62no—
369C2×C4—62no—
370C2×C4C22×C3×D311yescharacteristic
371C2×C4C22×C3×D311yescharacteristic
372C2×C4C22×C3×D311yescharacteristic
373C2×C4C22×C3×D311yescharacteristic
374C2×C4C22×C3×D311yescharacteristic
375C2×C4C22×C3×D311yescharacteristic
376C2×C4C22×C3×D311yescharacteristic
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—62no—
381C2×C3—121no—
382C2×C3#100711yescharacteristic
383C2×C3D3×#4111yescharacteristic
384C2×C3D3×#4111yescharacteristic
385C2×C3C2×C3×#4111yescharacteristic
386C2×C3C2×C3×#4111yescharacteristic
387C2×C3C3×2−1+411yescharacteristic
388D3—22no—
389D3—41no—
390C22—32no—
391C22—61no—
392C22—61no—
393C22—61no—
394C22—61no—
395C22—61no—
396C22C23×C3×D311yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—32no—
405C4—61no—
406C4—61no—
407C4—61no—
408C4—61no—
409C4—61no—
410C3—21no—
411C3#569311yescharacteristic, direct product factor
412C3C3×#55211yescharacteristic, complemented
413C2—62no—
414C2—121no—
415C2C3×#100711yescharacteristic
416C2C3×D3×#4111yescharacteristic
417C2C3×D3×#4111yescharacteristic
subgroupG/H
centerC22×C3C23×D3
commutator, cosocleC22×C3C24×C3
FrattiniC22C23×C3×D3
FittingC32×#125C2
socleC22×C32C24
prime radicalC2×C3×D12C22
hypercenterC3×#125D3
hypocenterC3C3×#552
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
1. C32×#125C2semidirect
2. C3×#898C2semidirect
3. C3×#898C2semidirect
4. C3×#896C2semidirect
5. C3×#896C2semidirect
9. C3×#892C2semidirect
10. C3×D3×C4⋊C4C2semidirect
11. C3×#889C2semidirect
12. C3×#889C2semidirect
13. C3×#887C2semidirect
14. C3×#872C2semidirect
15. C3×#872C2semidirect
17. #5693C3direct (N × H)
58. C3×#125D3semidirect
59. C3×#125C2×C3semidirect
70. #898C2×C3semidirect
71. #898C2×C3semidirect
72. #896C2×C3semidirect
73. #896C2×C3semidirect
77. #892C2×C3semidirect
78. D3×C4⋊C4C2×C3semidirect
79. #889C2×C3semidirect
80. #889C2×C3semidirect
81. #887C2×C3semidirect
82. #872C2×C3semidirect
83. #872C2×C3semidirect
207. #125C3×D3semidirect
355. C32#552semidirect
411. C3#5693direct (N × H)
412. C3C3×#552semidirect

Maximal subgroups

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

subgroupindex
C32×#1252
C3×#8982
C3×#8962
C3×#8942
C3×#8932
C3×#8922
C3×D3×C4⋊C42
C3×#8892
C3×#8872
C3×#8722
C3×#5523
#56933