Finite Group Databasebeta

← C2×#5665 #85995

Subgroups — C2×#5665 #85995

Order 384.

1144 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#123C211yesmaximal, characteristic, complemented
2C2×#939C211yesmaximal, characteristic
3C2×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#929C211yesmaximal, characteristic, complemented
5C22×C4⋊Dic3C211yesmaximal, characteristic, complemented
6#5665C2116yesmaximal, direct product factor
7C2×#898C211yesmaximal, characteristic, complemented
8C2×#897C211yesmaximal, characteristic, complemented
9C2×#890C211yesmaximal, characteristic, complemented
10C2×#889C211yesmaximal, characteristic, complemented
11C2×#886C211yesmaximal, characteristic, complemented
12C2×#883C211yesmaximal, characteristic, complemented
13C2×#67⋊C4C211yesmaximal, characteristic, complemented
14C2×#879C211yesmaximal, characteristic, complemented
15C2×#878C211yesmaximal, characteristic, complemented
16C2×#878C211yesmaximal, characteristic, complemented
17C2×#539—31nomaximal, Sylow
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C23×Dic3C2211yescharacteristic
24C23×Dic3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C22×Dic6C2211yescharacteristic
27C3×#123C2218yescomplemented
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C22⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36#939C2218yes—
37D4×Dic3C2218yescomplemented
38#929C2218yescomplemented
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×C4⋊Dic3C2211yescharacteristic
45C2×C4⋊Dic3C2211yescharacteristic
46C2×C4⋊Dic3C2211yescharacteristic
47C2×C4⋊Dic3C2211yescharacteristic
48C2×C4⋊Dic3C2211yescharacteristic
49C2×C4⋊Dic3C2218yescomplemented
50C2×Dic3⋊C4C2211yescharacteristic
51C2×Dic3⋊C4C2211yescharacteristic
52C2×Dic3⋊C4C2211yescharacteristic
53C2×Dic3⋊C4C2211yescharacteristic
54C2×Dic3⋊C4C2211yescharacteristic
55C2×Dic3⋊C4C2211yescharacteristic
56C2×C4×Dic3C2211yescharacteristic
57C2×C4×Dic3C2211yescharacteristic
58#898C2218yescomplemented
59#897C2218yescomplemented
60#890C2218yescomplemented
61#889C2218yescomplemented
62#886C2218yescomplemented
63#883C2218yescomplemented
64#67⋊C4C2218yescomplemented
65#879C2218yescomplemented
66#878C2218yescomplemented
67#878C2218yescomplemented
68#539—316no—
69C2×#126—31no—
70C2×#126—31no—
71C2×#125—31no—
72C2×#125—31no—
73C2×#123—31no—
74C2×#123—31no—
75C2×#123—31no—
76C2×#123D311yescharacteristic, complemented
77C2×C22⋊Q8—31no—
78C2×C22⋊Q8—31no—
79C2×C22⋊Q8—31no—
80C2×#121—31no—
81C2×C4×D4—31no—
82C2×C4×D4—31no—
83C22×C4⋊C4—31no—
84C24×C3C2311yescharacteristic
85C24×C3C2311yescharacteristic
86C23×D3C2311yescharacteristic
87C2×C3×D4—24no—
88C2×C3×D4C2314yes—
89C22×C3×C4—24no—
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C22×C3×C4C2311yescharacteristic
95C22×C3×C4C2314yes—
96C2×#67—24no—
97C2×#67—42no—
98C2×#67C2314yes—
99C2×#67C2314yes—
100C22×Dic3—42no—
101C22×Dic3—42no—
102C22×Dic3—42no—
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2314yes—
111C22×Dic3C2314yes—
112C22×Dic3C2314yes—
113C2×C4×D3—42no—
114C2×C4×D3C2314yes—
115C2×Dic6—42no—
116C2×Dic6C2314yes—
117C3×C4⋊C4C2314yes—
118C3×C4⋊C4C2314yes—
119C3×C22⋊C4C2314yes—
120C3×C22⋊C4C2314yes—
121C3×C22⋊C4C2314yes—
122#217C2314yes—
123#217C2314yes—
124#217C2314yes—
125(C2×D3)⋊C4C2314yes—
126(C2×D3)⋊C4C2314yes—
127(C2×D3)⋊C4C2314yes—
128(C2×D3)⋊C4C2314yes—
129C4⋊Dic3C2314yes—
130C4⋊Dic3C2314yes—
131C4⋊Dic3C2314yes—
132C4⋊Dic3C2314yes—
133C4⋊Dic3C2314yes—
134C4⋊Dic3C2314yes—
135Dic3⋊C4C2314yes—
136Dic3⋊C4C2314yes—
137Dic3⋊C4C2314yes—
138Dic3⋊C4C2314yes—
139Dic3⋊C4C2314yes—
140Dic3⋊C4C2314yes—
141C4×Dic3C2314yes—
142C4×Dic3C2314yes—
143C22×Q8—31no—
144C22×D4—31no—
145C22×D4—31no—
146C22×D4C2×D311yescharacteristic
147C23×C4—31no—
148C23×C4—31no—
149C23×C4—31no—
150C23×C4—31no—
151C23×C4C2×D311yescharacteristic
152#126—38no—
153#126—38no—
154#125—38no—
155#125—38no—
156#123—38no—
157#123—38no—
158#123—38no—
159#123C2×D318yescomplemented
160C22⋊Q8—38no—
161C22⋊Q8—38no—
162C22⋊Q8—38no—
163#121—38no—
164C4×D4—38no—
165C4×D4—38no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—31no—
168C2×C4⋊C4—31no—
169C2×C4⋊C4—31no—
170C2×C4⋊C4—38no—
171C2×C4⋊C4—31no—
172C2×C4⋊C4—31no—
173C2×C4⋊C4—31no—
174C2×C4⋊C4—31no—
175C2×C4⋊C4—31no—
176C2×C4⋊C4—31no—
177C2×C4⋊C4—31no—
178C2×C4⋊C4—31no—
179C2×C4⋊C4C2×D311yescharacteristic
180C2×C4⋊C4C2×D311yescharacteristic
181C2×C22⋊C4—31no—
182C2×C22⋊C4—31no—
183C2×C22⋊C4—31no—
184C2×C22⋊C4—31no—
185C2×C22⋊C4—31no—
186C2×C22⋊C4—31no—
187C2×C22⋊C4—31no—
188C2×C22⋊C4C2×D311yescharacteristic
189C2×C22⋊C4C2×D311yescharacteristic
190C2×C22⋊C4C2×D311yescharacteristic
191C2×C42—31no—
192C2×C42—31no—
193C23×C3—22no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3#4114yes—
199C23×C3C2412yes—
200C23×C3C2412yes—
201C23×C3C2411yescharacteristic
202C22×D3—22no—
203C22×D3—22no—
204C22×D3—22no—
205C22×D3C2412yes—
206C3×D4—28no—
207C2×C3×C4—28no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4C2412yes—
214C2×C3×C4C2412yes—
215C2×C3×C4C2412yes—
216C2×C3×C4C2412yes—
217C2×C3×C4C2412yes—
218#67—28no—
219#67—44no—
220C2×Dic3—22no—
221C2×Dic3—22no—
222C2×Dic3—22no—
223C2×Dic3—22no—
224C2×Dic3—22no—
225C2×Dic3—22no—
226C2×Dic3—22no—
227C2×Dic3—44no—
228C2×Dic3—44no—
229C2×Dic3—44no—
230C2×Dic3C2412yes—
231C2×Dic3C2412yes—
232C2×Dic3C2412yes—
233C2×Dic3C2412yes—
234C2×Dic3C2412yes—
235C2×Dic3C2412yes—
236C2×Dic3C2412yes—
237C4×D3—44no—
238Dic6—44no—
239C24—31no—
240C24C22×D311yescharacteristic
241C24C22×D311yescharacteristic
242C2×Q8—34no—
243C2×Q8—122no—
244C2×D4—24no—
245C2×D4—34no—
246C2×D4—34no—
247C2×D4—64no—
248C2×D4—122no—
249C2×D4C22×D314yes—
250C22×C4—24no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—34no—
259C22×C4—34no—
260C22×C4—34no—
261C22×C4—34no—
262C22×C4—122no—
263C22×C4—122no—
264C22×C4—122no—
265C22×C4—122no—
266C22×C4C22×D314yes—
267C22×C4C22×D311yescharacteristic
268C22×C4C22×D311yescharacteristic
269C22×C4C22×D311yescharacteristic
270C22×C4C22×D311yescharacteristic
271C22×C4C22×D311yescharacteristic
272C4⋊C4—34no—
273C4⋊C4—34no—
274C4⋊C4—34no—
275C4⋊C4—34no—
276C4⋊C4—34no—
277C4⋊C4—34no—
278C4⋊C4—34no—
279C4⋊C4—34no—
280C4⋊C4—34no—
281C4⋊C4—34no—
282C4⋊C4—34no—
283C4⋊C4—34no—
284C4⋊C4C22×D314yes—
285C4⋊C4C22×D314yes—
286C22⋊C4—34no—
287C22⋊C4—34no—
288C22⋊C4—34no—
289C22⋊C4—34no—
290C22⋊C4—34no—
291C22⋊C4—34no—
292C22⋊C4—34no—
293C22⋊C4C22×D314yes—
294C22⋊C4C22×D314yes—
295C22⋊C4C22×D314yes—
296C42—34no—
297C42—34no—
298C22×C3—28no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—44no—
305C22×C3C2×#4114yes—
306C22×C3C2×#4112yes—
307C22×C3H(5,𝔽2)12yes—
308C22×C32−1+412yes—
309C22×C3C2511yescharacteristic
310C2×D3—22no—
311C2×D3—22no—
312C2×D3—22no—
313C2×D3—44no—
314C3×C4—22no—
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—22no—
318C3×C4—22no—
319Dic3—22no—
320Dic3—22no—
321Dic3—22no—
322Dic3—22no—
323Dic3—22no—
324Dic3—22no—
325Dic3—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—32no—
332C23—62no—
333C23—62no—
334C23—62no—
335C23#23714yes—
336C23C23×D312yes—
337C23C23×D312yes—
338C23C23×D311yescharacteristic
339Q8—124no—
340D4—28no—
341D4—68no—
342D4—124no—
343C2×C4—28no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—32no—
350C2×C4—32no—
351C2×C4—32no—
352C2×C4—32no—
353C2×C4—32no—
354C2×C4—32no—
355C2×C4—32no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—124no—
364C2×C4—124no—
365C2×C4—124no—
366C2×C4—124no—
367C2×C4C23×D312yes—
368C2×C4C23×D312yes—
369C2×C4C23×D312yes—
370C2×C4C23×D312yes—
371C2×C4C23×D312yes—
372C2×C3—24no—
373C2×C3—42no—
374C2×C3#53914yescomplemented
375C2×C3C22×#4111yescharacteristic
376C2×C3C2×H(5,𝔽2)11yescharacteristic
377C2×C3C2×2−1+411yescharacteristic
378D3—42no—
379C22—28no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—44no—
386C22—62no—
387C22—62no—
388C22—62no—
389C22—124no—
390C22C2×#23714yes—
391C22C2×#23712yes—
392C22#100912yes—
393C22#101012yes—
394C22C24×D311yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—62no—
401C4—62no—
402C4—62no—
403C4—62no—
404C4—62no—
405C4—62no—
406C4—62no—
407C3C2×#53911yescharacteristic, complemented, Sylow
408C2—24no—
409C2—42no—
410C2—122no—
411C2#566514yesdirect product factor
412C2C22×#23711yescharacteristic
413C2C2×#100911yescharacteristic
414C2C2×#101011yescharacteristic
subgroupG/H
centerC23C23×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC2×C3×#123C2
socleC23×C3C24
prime radicalC2×#939C2
hypercenterC2×#123D3
hypocenterC3C2×#539
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×#123C2semidirect
3. C2×D4×Dic3C2semidirect
4. C2×#929C2semidirect
5. C22×C4⋊Dic3C2semidirect
6. #5665C2direct (N × H)
7. C2×#898C2semidirect
8. C2×#897C2semidirect
9. C2×#890C2semidirect
10. C2×#889C2semidirect
11. C2×#886C2semidirect
12. C2×#883C2semidirect
13. C2×#67⋊C4C2semidirect
14. C2×#879C2semidirect
15. C2×#878C2semidirect
16. C2×#878C2semidirect
27. C3×#123C22semidirect
37. D4×Dic3C22semidirect
38. #929C22semidirect
49. C2×C4⋊Dic3C22semidirect
58. #898C22semidirect
59. #897C22semidirect
60. #890C22semidirect
61. #889C22semidirect
62. #886C22semidirect
63. #883C22semidirect
64. #67⋊C4C22semidirect
65. #879C22semidirect
66. #878C22semidirect
67. #878C22semidirect
76. C2×#123D3semidirect
159. #123C2×D3semidirect
374. C2×C3#539semidirect
407. C3C2×#539semidirect
411. C2#5665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C2×#9392
C2×D4×Dic32
C2×#9292
C22×C4⋊Dic32
#56652
C2×#8982
C2×#8972
C2×#8902
C2×#8892
C2×#8862
C2×#8832
C2×#67⋊C42
C2×#8792
C2×#8782
C2×#5393