Finite Group Databasebeta

← C2×#11746946 #14430040

Subgroups — C2×#11746946 #14430040

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic30C211yesmaximal, characteristic
2C2×C5×#869C211yesmaximal, characteristic
3C2×C3×C4⋊#168C211yesmaximal, characteristic
4C2×#90985C212yesmaximal
5C2×#90975C212yesmaximal
6#11746946C218yesmaximal, direct product factor
7C2×#65383—31nomaximal, Hall
8C22×Dic30C2211yescharacteristic
9C22×C5×Dic6—21no—
10C2×C3×C42×C5C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C2×#6712—21no—
13C2×C4×Dic15—21no—
14C4×Dic30—22no—
15C4×Dic30C2214yes—
16C2×C5×C4⋊Dic3—21no—
17C2×C5×C4⋊Dic3C2212yes—
18C5×#869—22no—
19C5×#869C2214yes—
20C22×C3×#168C2212yes—
21C3×C4⋊#168C2214yes—
22#90985C2218yes—
23#90975C2218yes—
24C2×#4851—51nomaximal, Hall
25C2×C5×C4⋊Q8—31no—
26C2×C4×Dic10—31no—
27#65383—38no—
28C2×#3942—32no—
29C2×#3940—32no—
30C2×C4⋊#168D311yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15—21no—
35C22×Dic15—21no—
36C2×Dic30—21no—
37C2×Dic30—22no—
38C2×Dic30Q814yescomplemented
39C2×Dic30C2312yes—
40C22×C5×Dic3—22no—
41C2×C5×Dic6—24no—
42C2×C5×Dic6—44no—
43C3×C42×C5D412yes—
44C3×C42×C5C2312yes—
45C4⋊Dic15—21no—
46C4⋊Dic15C2312yes—
47#6712—24no—
48C4×Dic15—24no—
49C5×C4⋊Dic3—22no—
50C5×C4⋊Dic3—24no—
51C5×C4⋊Dic3C2314yes—
52C2×C3×#168—24no—
53C2×C3×#168C2314yes—
54C2×#869D511yescharacteristic
55C2×C4×Dic6—51no—
56C2×C3×C4⋊C8—51no—
57C2×#817—52no—
58C2×#816—52no—
59#4851—58no—
60C22×C5×Q8—61no—
61C22×Dic10—31no—
62C5×C4⋊Q8—34no—
63C5×C4⋊Q8—62no—
64C2×C5×C4⋊C4—32no—
65C2×C5×C4⋊C4—61no—
66C2×C42×C5C2×D311yescharacteristic
67C2×C4⋊Dic5—31no—
68C2×#683—61no—
69C2×C4×Dic5—61no—
70C22×#168C2×D312yes—
71C4×Dic10—34no—
72C4×Dic10—62no—
73#3942—38no—
74#3940—38no—
75C4⋊#168C2×D314yes—
76C2×#475—151noSylow
77C23×C3×C5C2×D411yescharacteristic
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5SD1614yes—
80C2×C3×C4×C5C2×D412yes—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D412yes—
83C2×C3×C4×C5C2×Q812yes—
84C2×C3×C4×C5#4112yes—
85C2×C3×C4×C5C2411yescharacteristic
86C2×Dic15—24no—
87C2×Dic15—22no—
88C2×Dic15—22no—
89C2×Dic15—42no—
90Dic30—24no—
91Dic30—22no—
92Dic30C2×Q814yescomplemented
93C2×C5×Dic3—24no—
94C2×C5×Dic3—44no—
95C5×Dic6—48no—
96C3×#168—24no—
97C22×Dic6—21no—
98C22×Dic6—51no—
99C22×C3×C8—52no—
100C2×C3×C42C2×D511yescharacteristic
101C2×C4⋊Dic3—21no—
102C2×C4⋊Dic3—51no—
103C2×C4⋊Dic3C2×D512yes—
104C2×Dic3⋊C4—101no—
105C2×C4×Dic3—101no—
106#869—22no—
107#869C2×D514yes—
108C4×Dic6—54no—
109C4×Dic6—102no—
110C3×C4⋊C8—54no—
111#817—58no—
112#816—58no—
113C2×C5×Q8—64no—
114C2×C5×Q8—124no—
115C22×C4×C5—62no—
116C22×C4×C5D1211yescharacteristic
117C22×C4×C5D1211yescharacteristic
118C22×C4×C5C22×D311yescharacteristic
119C22×Dic5—61no—
120C22×Dic5—61no—
121C2×Dic10—34no—
122C2×Dic10—32no—
123C2×Dic10—61no—
124C2×Dic10—62no—
125C5×C4⋊C4—34no—
126C5×C4⋊C4—62no—
127C5×C4⋊C4—64no—
128C42×C5D1212yes—
129C42×C5C22×D312yes—
130C4⋊Dic5—32no—
131C4⋊Dic5—61no—
132#683—64no—
133C4×Dic5—64no—
134C2×#168—24no—
135C2×#168C22×D314yes—
136C2×C4⋊Q8—31no—
137C2×C4×Q8—151no—
138#475—158no—
139C2×#106—152no—
140C2×C4⋊C8—51no—
141C2×#103—152no—
142C22×C3×C5C22⋊Q812yes—
143C22×C3×C5C2×SD1612yes—
144C22×C3×C5#13712yes—
145C22×C3×C5C22×D411yescharacteristic
146C3×C4×C5—22no—
147C3×C4×C5C22⋊Q812yes—
148C3×C4×C5C2×SD1614yes—
149C3×C4×C5C22×Q811yescharacteristic
150C3×C4×C5C2×#4111yescharacteristic
151Dic15—24no—
152Dic15—42no—
153C5×Dic3—44no—
154C22×C3×C4C22⋊D511yescharacteristic
155C22×C3×C4C22⋊D511yescharacteristic
156C22×C3×C4C22×D511yescharacteristic
157C22×Dic3—22no—
158C22×Dic3—101no—
159C22×Dic3—101no—
160C2×Dic6—24no—
161C2×Dic6—44no—
162C2×Dic6—54no—
163C2×Dic6—52no—
164C2×Dic6—102no—
165C2×Dic6—101no—
166C2×C3×C8—54no—
167C2×C3×C8—104no—
168C3×C42C22⋊D512yes—
169C3×C42C22×D512yes—
170C4⋊Dic3—22no—
171C4⋊Dic3—24no—
172C4⋊Dic3—52no—
173C4⋊Dic3—101no—
174C4⋊Dic3C22×D514yes—
175Dic3⋊C4—104no—
176C4×Dic3—104no—
177C23×C5C2×D1211yescharacteristic
178C5×Q8—128no—
179C2×C4×C5—22no—
180C2×C4×C5—64no—
181C2×C4×C5—124no—
182C2×C4×C5#20414yes—
183C2×C4×C5C2×D1212yes—
184C2×C4×C5C2×D1211yescharacteristic
185C2×C4×C5C2×D1212yes—
186C2×C4×C5#23712yes—
187C2×C4×C5D3×Q812yes—
188C2×C4×C5C23×D311yescharacteristic
189C2×Dic5—64no—
190C2×Dic5—62no—
191C2×Dic5—62no—
192C2×Dic5—122no—
193Dic10—34no—
194Dic10—64no—
195Dic10—62no—
196#168—24no—
197C22×Q8—61no—
198C22×Q8—151no—
199C22×C8—52no—
200C4⋊Q8—34no—
201C4⋊Q8—62no—
202C4×Q8—154no—
203C4×Q8—302no—
204C2×C4⋊C4—32no—
205C2×C4⋊C4—61no—
206C2×C4⋊C4—151no—
207C2×C4⋊C4—301no—
208C2×C42—301no—
209C2×C42D3×D511yescharacteristic
210#106—158no—
211C4⋊C8—54no—
212#103—158no—
213C2×C3×C5#47514yescomplemented
214C2×C3×C5C2×C22⋊Q811yescharacteristic
215C2×C3×C5C22×SD1611yescharacteristic
216C2×C3×C5C2×#13711yescharacteristic
217C23×C3C2×C22⋊D511yescharacteristic
218C2×C3×C4—22no—
219C2×C3×C4#68714yes—
220C2×C3×C4Q8×D512yes—
221C2×C3×C4#71312yes—
222C2×C3×C4C2×C22⋊D512yes—
223C2×C3×C4C2×C22⋊D512yes—
224C2×C3×C4C2×C22⋊D511yescharacteristic
225C2×C3×C4C23×D511yescharacteristic
226C2×Dic3—24no—
227C2×Dic3—44no—
228C2×Dic3—102no—
229C2×Dic3—104no—
230C2×Dic3—102no—
231C2×Dic3—202no—
232Dic6—48no—
233Dic6—54no—
234Dic6—102no—
235Dic6—104no—
236C3×C8—104no—
237C22×C5#89712yes—
238C22×C5C2×#20412yes—
239C22×C5#90912yes—
240C22×C5C22×D1211yescharacteristic
241C4×C5—22no—
242C4×C5—124no—
243C4×C5#89712yes—
244C4×C5C2×#20414yes—
245C4×C5C2×#23711yescharacteristic
246C4×C5C2×D3×Q811yescharacteristic
247Dic5—64no—
248Dic5—122no—
249C2×Q8—64no—
250C2×Q8—124no—
251C2×Q8—154no—
252C2×Q8—152no—
253C2×Q8—302no—
254C2×Q8—301no—
255C22×C4—62no—
256C22×C4—301no—
257C22×C4—301no—
258C22×C4#120311yescharacteristic
259C22×C4#120311yescharacteristic
260C22×C4C2×D3×D511yescharacteristic
261C2×C8—54no—
262C2×C8—104no—
263C4⋊C4—34no—
264C4⋊C4—62no—
265C4⋊C4—64no—
266C4⋊C4—152no—
267C4⋊C4—301no—
268C4⋊C4—304no—
269C42—304no—
270C42#120312yes—
271C42C2×D3×D512yes—
272C3×C5C2×#47511yescharacteristic, complemented, Hall
273C22×C3C2×#68712yes—
274C22×C3#408812yes—
275C22×C3#409212yes—
276C22×C3C22×C22⋊D511yescharacteristic
277C3×C4—22no—
278C3×C4C2×#68714yes—
279C3×C4#409212yes—
280C3×C4C2×Q8×D511yescharacteristic
281C3×C4C2×#71311yescharacteristic
282Dic3—44no—
283Dic3—104no—
284Dic3—202no—
285C2×C5#485114yescomplemented
286C2×C5C2×#89711yescharacteristic
287C2×C5C22×#20411yescharacteristic
288C2×C5C2×#90911yescharacteristic
289C23C2×#120311yescharacteristic
290Q8—128no—
291Q8—154no—
292Q8—302no—
293Q8—304no—
294C2×C4—22no—
295C2×C4—64no—
296C2×C4—124no—
297C2×C4—302no—
298C2×C4—304no—
299C2×C4—302no—
300C2×C4—602no—
301C2×C4#665914yes—
302C2×C4#676612yes—
303C2×C4D15⋊Q812yes—
304C2×C4C2×#120312yes—
305C2×C4C2×#120312yes—
306C2×C4C2×#120311yescharacteristic
307C2×C4C22×D3×D511yescharacteristic
308C8—104no—
309C2×C3#6538314yescomplemented
310C2×C3C22×#68711yescharacteristic
311C2×C3C2×#408811yescharacteristic
312C2×C3C2×#409211yescharacteristic
313C5C2×#485111yescharacteristic, complemented, Sylow
314C22C2×#665912yes—
315C22#9132112yes—
316C22#9138312yes—
317C22C22×#120311yescharacteristic
318C4—22no—
319C4—124no—
320C4—304no—
321C4—602no—
322C4C2×#665914yes—
323C4#9138312yes—
324C4C2×#676611yescharacteristic
325C4C2×D15⋊Q811yescharacteristic
326C3C2×#6538311yescharacteristic, complemented, Sylow
327C2#1174694614yesdirect product factor
328C2C22×#665911yescharacteristic
329C2C2×#9132111yescharacteristic
330C2C2×#9138311yescharacteristic
subgroupG/H
centerC23C2×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socle, prime radicalC23×C3×C5C2×D4
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#475
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
6. #11746946C2direct (N × H)
38. C2×Dic30Q8semidirect
92. Dic30C2×Q8semidirect
213. C2×C3×C5#475semidirect
272. C3×C5C2×#475semidirect
285. C2×C5#4851semidirect
309. C2×C3#65383semidirect
313. C5C2×#4851semidirect
326. C3C2×#65383semidirect
327. C2#11746946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C2×C5×#8692
C2×C3×C4⋊#1682
C2×#909852
C2×#909752
#117469462
C2×#653833
C2×#48515