Finite Group Databasebeta

← C3×#5692 #10595789

Subgroups — C3×#5692 #10595789

Order 576.

464 conjugacy classes of subgroups.

The subgroup lattice has 443 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×#897C211yesmaximal, characteristic, complemented
4C3×#896C211yesmaximal, characteristic, complemented
5C3×#896C211yesmaximal, characteristic, complemented
6C3×#895C211yesmaximal, characteristic
7C3×#894C211yesmaximal, characteristic, complemented
8C3×#894C211yesmaximal, characteristic, complemented
9C3×#894C211yesmaximal, characteristic, complemented
10C3×#894C211yesmaximal, characteristic, complemented
11C3×#893C211yesmaximal, characteristic, complemented
12C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
13C3×#889C211yesmaximal, characteristic, complemented
14C3×#876C211yesmaximal, characteristic, complemented
15C3×C4×D12C211yesmaximal, characteristic, complemented
16C3×#539—31nomaximal
17#5692C311yesmaximal, characteristic, direct product factor
18C2×C3×D12C2211yescharacteristic
19C2×C3×D12C2211yescharacteristic
20C2×C3×D12C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×C3×C4×D3C2211yescharacteristic
23C2×C3×C4×D3C2211yescharacteristic
24C2×C3×C4×D3C2211yescharacteristic
25C2×C3×C4×D3C2211yescharacteristic
26C2×C3×Dic6C2211yescharacteristic
27C32×C4⋊C4C2211yescharacteristic
28C32×C4⋊C4C2211yescharacteristic
29C32×C4⋊C4C2211yescharacteristic
30C32×C4⋊C4C2211yescharacteristic
31C32×C4⋊C4C2211yescharacteristic
32C32×C4⋊C4C2211yescharacteristic
33C32×C42C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D3)⋊C4C2211yescharacteristic
41C3×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D3)⋊C4C2211yescharacteristic
44C3×C4⋊Dic3C2211yescharacteristic
45C3×C4⋊Dic3C2211yescharacteristic
46C3×Dic3⋊C4C2211yescharacteristic
47C3×Dic3⋊C4C2211yescharacteristic
48C3×Dic3⋊C4C2211yescharacteristic
49C3×Dic3⋊C4C2211yescharacteristic
50C3×Dic3⋊C4C2211yescharacteristic
51C3×Dic3⋊C4C2211yescharacteristic
52C3×C4×Dic3C2211yescharacteristic
53C3×#126—31no—
54C3×#126—31no—
55C3×#125—21no—
56C3×#125—31no—
57C3×#125D311yescharacteristic, complemented
58C3×#125C2×C311yescharacteristic, complemented
59C3×#123—31no—
60C3×#123—31no—
61C3×#123—31no—
62C3×#123—31no—
63C3×C22⋊Q8—31no—
64C3×C22⋊Q8—31no—
65C3×C22⋊Q8—31no—
66C3×#121—31no—
67C3×C4×D4—31no—
68C3×C4×D4—31no—
69C2×C3×C4⋊C4—31no—
70#898C2×C311yescharacteristic, complemented
71#897C2×C311yescharacteristic, complemented
72#896C2×C311yescharacteristic, complemented
73#896C2×C311yescharacteristic, complemented
74#895C2×C311yescharacteristic
75#894C2×C311yescharacteristic, complemented
76#894C2×C311yescharacteristic, complemented
77#894C2×C311yescharacteristic, complemented
78#894C2×C311yescharacteristic, complemented
79#893C2×C311yescharacteristic, complemented
80D3×C4⋊C4C2×C311yescharacteristic, complemented
81#889C2×C311yescharacteristic, complemented
82#876C2×C311yescharacteristic, complemented
83C4×D12C2×C311yescharacteristic, complemented
84C22×C3×D3C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92C2×C32×C4C2311yescharacteristic
93C2×C32×C4C2311yescharacteristic
94C2×C3×Dic3C2311yescharacteristic
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C3×D12—22no—
100C3×D12—22no—
101C3×D12—41no—
102C3×C4×D3—22no—
103C3×C4×D3—41no—
104C3×C4×D3—41no—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C3×Dic6—41no—
108#539—31noSylow
109C2×C3×Q8—31no—
110C2×C3×D4—31no—
111C2×C3×D4—31no—
112C2×C3×D4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—31no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C2×D12C22×C311yescharacteristic
119C2×D12C22×C311yescharacteristic
120C2×D12C22×C311yescharacteristic
121C2×C4×D3C22×C311yescharacteristic
122C2×C4×D3C22×C311yescharacteristic
123C2×C4×D3C22×C311yescharacteristic
124C2×C4×D3C22×C311yescharacteristic
125C2×C4×D3C22×C311yescharacteristic
126C2×Dic6C22×C311yescharacteristic
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
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⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4C2×D311yescharacteristic
142C3×C4⋊C4C2×D311yescharacteristic
143C3×C4⋊C4C2×D311yescharacteristic
144C3×C4⋊C4C2×D311yescharacteristic
145C3×C4⋊C4C2×D311yescharacteristic
146C3×C4⋊C4C2×D311yescharacteristic
147C3×C4⋊C4C22×C311yescharacteristic
148C3×C4⋊C4C22×C311yescharacteristic
149C3×C4⋊C4C22×C311yescharacteristic
150C3×C4⋊C4C22×C311yescharacteristic
151C3×C4⋊C4C22×C311yescharacteristic
152C3×C4⋊C4C22×C311yescharacteristic
153C3×C22⋊C4—31no—
154C3×C22⋊C4—31no—
155C3×C22⋊C4—31no—
156C3×C22⋊C4—31no—
157C3×C22⋊C4—31no—
158C3×C22⋊C4—31no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4—31no—
163C3×C42—21no—
164C3×C42—31no—
165C3×C42C2×D311yescharacteristic
166C3×C42C22×C311yescharacteristic
167(C2×D3)⋊C4C22×C311yescharacteristic
168(C2×D3)⋊C4C22×C311yescharacteristic
169(C2×D3)⋊C4C22×C311yescharacteristic
170(C2×D3)⋊C4C22×C311yescharacteristic
171(C2×D3)⋊C4C22×C311yescharacteristic
172(C2×D3)⋊C4C22×C311yescharacteristic
173(C2×D3)⋊C4C22×C311yescharacteristic
174(C2×D3)⋊C4C22×C311yescharacteristic
175(C2×D3)⋊C4C22×C311yescharacteristic
176(C2×D3)⋊C4C22×C311yescharacteristic
177C4⋊Dic3C22×C311yescharacteristic
178C4⋊Dic3C22×C311yescharacteristic
179Dic3⋊C4C22×C311yescharacteristic
180Dic3⋊C4C22×C311yescharacteristic
181Dic3⋊C4C22×C311yescharacteristic
182Dic3⋊C4C22×C311yescharacteristic
183Dic3⋊C4C22×C311yescharacteristic
184Dic3⋊C4C22×C311yescharacteristic
185C4×Dic3C22×C311yescharacteristic
186C22×C32C2411yescharacteristic
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3—21no—
190C2×C3×D3—21no—
191C2×C3×D3—21no—
192C2×C3×D3—21no—
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3#4112yes—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C3×Dic3—21no—
204C3×Dic3—21no—
205C3×Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3—21no—
208#126—31no—
209#126—31no—
210#125—31no—
211#125C3×D311yescharacteristic, complemented
212#123—31no—
213#123—31no—
214#123—31no—
215#123—31no—
216C22⋊Q8—31no—
217C22⋊Q8—31no—
218C22⋊Q8—31no—
219#121—31no—
220C4×D4—31no—
221C4×D4—31no—
222C2×C4⋊C4—31no—
223C23×C3—31no—
224C23×C3—31no—
225C23×C3—31no—
226C22×D3C23×C311yescharacteristic
227C22×D3C23×C311yescharacteristic
228C22×D3C23×C311yescharacteristic
229C3×Q8—121no—
230C3×D4—62no—
231C3×D4—62no—
232C3×D4—121no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—62no—
246C2×C3×C4—121no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×C3×C4C22×D311yescharacteristic
251C2×C3×C4C22×D311yescharacteristic
252C2×C3×C4C22×D311yescharacteristic
253C2×C3×C4C22×D311yescharacteristic
254C2×C3×C4C22×D311yescharacteristic
255C2×C3×C4C22×D311yescharacteristic
256C2×C3×C4C22×D311yescharacteristic
257C2×C3×C4C23×C311yescharacteristic
258C2×C3×C4C23×C311yescharacteristic
259C2×C3×C4C23×C311yescharacteristic
260C2×C3×C4C23×C311yescharacteristic
261C2×C3×C4C23×C311yescharacteristic
262C2×C3×C4C23×C311yescharacteristic
263C2×C3×C4C23×C311yescharacteristic
264C2×Dic3C23×C311yescharacteristic
265C2×Dic3C23×C311yescharacteristic
266C2×Dic3C23×C311yescharacteristic
267C2×Dic3C23×C311yescharacteristic
268C2×Dic3C23×C311yescharacteristic
269D12—22no—
270D12—22no—
271D12—41no—
272C4×D3—22no—
273C4×D3—41no—
274C4×D3—41no—
275C4×D3—41no—
276C4×D3—41no—
277Dic6—41no—
278C2×C32C2×#4111yescharacteristic
279C2×C32H(5,𝔽2)11yescharacteristic
280C2×C322−1+411yescharacteristic
281C3×D3—22no—
282C3×D3—41no—
283C3×D3—41no—
284C2×Q8—31no—
285C2×D4—31no—
286C2×D4—31no—
287C2×D4—31no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—31no—
293C4⋊C4—31no—
294C4⋊C4—31no—
295C4⋊C4—31no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4C2×C3×D311yescharacteristic
302C4⋊C4C2×C3×D311yescharacteristic
303C4⋊C4C2×C3×D311yescharacteristic
304C4⋊C4C2×C3×D311yescharacteristic
305C4⋊C4C2×C3×D311yescharacteristic
306C4⋊C4C2×C3×D311yescharacteristic
307C22⋊C4—31no—
308C22⋊C4—31no—
309C22⋊C4—31no—
310C22⋊C4—31no—
311C22⋊C4—31no—
312C22⋊C4—31no—
313C22⋊C4—31no—
314C22⋊C4—31no—
315C22⋊C4—31no—
316C22⋊C4—31no—
317C42—31no—
318C42C2×C3×D311yescharacteristic
319C22×C3—21no—
320C22×C3—32no—
321C22×C3—61no—
322C22×C3—61no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3—61no—
326C22×C3—61no—
327C22×C3—61no—
328C22×C3—61no—
329C22×C3C23×D311yescharacteristic
330C22×C3C24×C311yescharacteristic
331C2×D3—21no—
332C2×D3—21no—
333C2×D3—21no—
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—21no—
337C2×D3—21no—
338C2×D3—21no—
339C2×D3C3×#4112yes—
340C3×C4—22no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—61no—
362C3×C4—61no—
363C3×C4—61no—
364C3×C4—61no—
365C3×C4—61no—
366Dic3—21no—
367Dic3—21no—
368Dic3—21no—
369Dic3—21no—
370Dic3—21no—
371C32#53911yescharacteristic, complemented, Sylow
372C23—31no—
373C23—31no—
374C23—31no—
375Q8—121no—
376D4—62no—
377D4—62no—
378D4—121no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—62no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4C22×C3×D311yescharacteristic
390C2×C4C22×C3×D311yescharacteristic
391C2×C4C22×C3×D311yescharacteristic
392C2×C4C22×C3×D311yescharacteristic
393C2×C4C22×C3×D311yescharacteristic
394C2×C4C22×C3×D311yescharacteristic
395C2×C4C22×C3×D311yescharacteristic
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—62no—
400C2×C3—121no—
401C2×C3—121no—
402C2×C3#100711yescharacteristic
403C2×C3D3×#4111yescharacteristic
404C2×C3#100911yescharacteristic
405C2×C3C2×C3×#4111yescharacteristic
406C2×C3C3×H(5,𝔽2)11yescharacteristic
407C2×C3C3×2−1+411yescharacteristic
408D3—22no—
409D3—41no—
410D3—41no—
411C22—32no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—61no—
417C22—61no—
418C22—61no—
419C22—61no—
420C22C23×C3×D311yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—61no—
429C4—61no—
430C4—61no—
431C4—61no—
432C4—61no—
433C3—21no—
434C3#569211yescharacteristic, direct product factor
435C3C3×#53911yescharacteristic, complemented
436C2—62no—
437C2—121no—
438C2—121no—
439C2C3×#100711yescharacteristic
440C2C3×D3×#4111yescharacteristic
441C2C3×#100911yescharacteristic
subgroupG/H
centerC22×C3C23×D3
commutator, cosocleC22×C3C24×C3
FrattiniC22C23×C3×D3
FittingC32×#125C2
socleC22×C32C24
prime radicalC3×#895C2
hypercenterC3×#125D3
hypocenterC3C3×#539
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×#897C2semidirect
4. C3×#896C2semidirect
5. C3×#896C2semidirect
7. C3×#894C2semidirect
8. C3×#894C2semidirect
9. C3×#894C2semidirect
10. C3×#894C2semidirect
11. C3×#893C2semidirect
12. C3×D3×C4⋊C4C2semidirect
13. C3×#889C2semidirect
14. C3×#876C2semidirect
15. C3×C4×D12C2semidirect
17. #5692C3direct (N × H)
57. C3×#125D3semidirect
58. C3×#125C2×C3semidirect
70. #898C2×C3semidirect
71. #897C2×C3semidirect
72. #896C2×C3semidirect
73. #896C2×C3semidirect
75. #894C2×C3semidirect
76. #894C2×C3semidirect
77. #894C2×C3semidirect
78. #894C2×C3semidirect
79. #893C2×C3semidirect
80. D3×C4⋊C4C2×C3semidirect
81. #889C2×C3semidirect
82. #876C2×C3semidirect
83. C4×D12C2×C3semidirect
211. #125C3×D3semidirect
371. C32#539semidirect
434. C3#5692direct (N × H)
435. C3C3×#539semidirect

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×#8972
C3×#8962
C3×#8952
C3×#8942
C3×#8932
C3×D3×C4⋊C42
C3×#8892
C3×#8762
C3×C4×D122
C3×#5393
#56923