Finite Group Databasebeta

← C2×#11750951 #14430077

Subgroups — C2×#11750951 #14430077

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×#91758C211yesmaximal, characteristic
2C2×C4×Dic30C211yesmaximal, characteristic
3C2×C3×C5×C4⋊C8C211yesmaximal, characteristic
4C2×#91102C212yesmaximal
5C2×#91100C212yesmaximal
6#11750951C218yesmaximal, direct product factor
7C2×#65139—31nomaximal, Hall
8C22×Dic30—21no—
9C22×Dic30C2211yescharacteristic
10C22×C3×C5×C8C2212yes—
11C2×C3×C42×C5C2211yescharacteristic
12C2×C4⋊Dic15—21no—
13C2×C4⋊Dic15C2212yes—
14C2×C4⋊Dic15C2211yescharacteristic
15C2×#6712—21no—
16C2×C4×Dic15—21no—
17#91758—22no—
18#91758C2214yes—
19C4×Dic30—22no—
20C4×Dic30C2214yes—
21C3×C5×C4⋊C8C2214yes—
22#91102C2218yes—
23#91100C2218yes—
24C2×#4850—51nomaximal, Hall
25C2×#4015—31no—
26C2×C4×Dic10—31no—
27C2×C5×C4⋊C8D311yescharacteristic
28C2×#3950—32no—
29C2×#3948—32no—
30#65139—38no—
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15—21no—
35C22×Dic15—21no—
36C22×Dic15—22no—
37C2×Dic30—21no—
38C2×Dic30—22no—
39C2×Dic30—24no—
40C2×Dic30—44no—
41C2×Dic30Q814yescomplemented
42C2×Dic30C2312yes—
43C2×C3×C5×C8—24no—
44C2×C3×C5×C8C2314yes—
45C3×C42×C5D412yes—
46C3×C42×C5C2312yes—
47C4⋊Dic15—21no—
48C4⋊Dic15—22no—
49C4⋊Dic15—24no—
50C4⋊Dic15C2312yes—
51C4⋊Dic15C2314yes—
52#6712—24no—
53C4×Dic15—24no—
54C2×#869—51no—
55C2×C4×Dic6—51no—
56C2×C3×C4⋊C8D511yescharacteristic
57C2×#818—52no—
58C2×#816—52no—
59#4850—58no—
60C22×Dic10—31no—
61C22×Dic10—61no—
62C22×C5×C8C2×D312yes—
63C2×C42×C5C2×D311yescharacteristic
64C2×C4⋊Dic5—31no—
65C2×C4⋊Dic5—32no—
66C2×C4⋊Dic5—61no—
67C2×#683—61no—
68C2×C4×Dic5—61no—
69#4015—34no—
70#4015—62no—
71C4×Dic10—34no—
72C4×Dic10—62no—
73C5×C4⋊C8C2×D314yes—
74#3950—38no—
75#3948—38no—
76C2×#477—151noSylow
77C23×C3×C5C2×D411yescharacteristic
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5Q1614yes—
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—24no—
90C2×Dic15—44no—
91C2×Dic15—42no—
92Dic30—24no—
93Dic30—22no—
94Dic30—48no—
95Dic30C2×Q814yescomplemented
96C3×C5×C8—24no—
97C22×Dic6—51no—
98C22×Dic6—101no—
99C22×C3×C8C2×D512yes—
100C2×C3×C42C2×D511yescharacteristic
101C2×C4⋊Dic3—51no—
102C2×C4⋊Dic3—52no—
103C2×C4⋊Dic3—101no—
104C2×Dic3⋊C4—101no—
105C2×C4×Dic3—101no—
106#869—54no—
107#869—102no—
108C4×Dic6—54no—
109C4×Dic6—102no—
110C3×C4⋊C8C2×D514yes—
111#818—58no—
112#816—58no—
113C22×C4×C5D1211yescharacteristic
114C22×C4×C5D1211yescharacteristic
115C22×C4×C5C22×D311yescharacteristic
116C22×Dic5—61no—
117C22×Dic5—62no—
118C22×Dic5—61no—
119C2×Dic10—34no—
120C2×Dic10—32no—
121C2×Dic10—61no—
122C2×Dic10—62no—
123C2×Dic10—64no—
124C2×Dic10—124no—
125C2×C5×C8—24no—
126C2×C5×C8C22×D314yes—
127C42×C5D1212yes—
128C42×C5C22×D312yes—
129C4⋊Dic5—34no—
130C4⋊Dic5—32no—
131C4⋊Dic5—61no—
132C4⋊Dic5—64no—
133C4⋊Dic5—62no—
134#683—64no—
135C4×Dic5—64no—
136C2×C4⋊Q8—151no—
137C2×C4×Q8—151no—
138#477—158no—
139C2×#107—152no—
140C2×C4⋊C8D1511yescharacteristic
141C2×#103—152no—
142C22×C3×C5C22⋊Q812yes—
143C22×C3×C5C2×Q1612yes—
144C22×C3×C5AGL(1,ℤ/8)12yes—
145C22×C3×C5C22×D411yescharacteristic
146C3×C4×C5—22no—
147C3×C4×C5C22⋊Q812yes—
148C3×C4×C5C2×Q1614yes—
149C3×C4×C5C22×Q811yescharacteristic
150C3×C4×C5C2×#4111yescharacteristic
151Dic15—24no—
152Dic15—44no—
153Dic15—42no—
154C22×C3×C4D2011yescharacteristic
155C22×C3×C4D2011yescharacteristic
156C22×C3×C4C22×D511yescharacteristic
157C22×Dic3—101no—
158C22×Dic3—101no—
159C22×Dic3—102no—
160C2×Dic6—54no—
161C2×Dic6—52no—
162C2×Dic6—101no—
163C2×Dic6—102no—
164C2×Dic6—104no—
165C2×Dic6—204no—
166C2×C3×C8—24no—
167C2×C3×C8C22×D514yes—
168C3×C42D2012yes—
169C3×C42C22×D512yes—
170C4⋊Dic3—54no—
171C4⋊Dic3—52no—
172C4⋊Dic3—101no—
173C4⋊Dic3—104no—
174C4⋊Dic3—102no—
175Dic3⋊C4—104no—
176C4×Dic3—104no—
177C23×C5C2×D1211yescharacteristic
178C2×C4×C5—22no—
179C2×C4×C5Dic1214yes—
180C2×C4×C5C2×D1212yes—
181C2×C4×C5C2×D1211yescharacteristic
182C2×C4×C5C2×D1212yes—
183C2×C4×C5#23712yes—
184C2×C4×C5D3×Q812yes—
185C2×C4×C5C23×D311yescharacteristic
186C2×Dic5—64no—
187C2×Dic5—62no—
188C2×Dic5—62no—
189C2×Dic5—64no—
190C2×Dic5—124no—
191C2×Dic5—122no—
192Dic10—34no—
193Dic10—64no—
194Dic10—62no—
195Dic10—128no—
196C5×C8—24no—
197C22×Q8—151no—
198C22×Q8—301no—
199C22×C8C2×D1512yes—
200C4⋊Q8—154no—
201C4⋊Q8—302no—
202C4×Q8—154no—
203C4×Q8—302no—
204C2×C4⋊C4—151no—
205C2×C4⋊C4—152no—
206C2×C4⋊C4—301no—
207C2×C4⋊C4—301no—
208C2×C42—301no—
209C2×C42C2×D1511yescharacteristic
210#107—158no—
211C4⋊C8C2×D1514yes—
212#103—158no—
213C2×C3×C5#47714yescomplemented
214C2×C3×C5C2×C22⋊Q811yescharacteristic
215C2×C3×C5C22×Q1611yescharacteristic
216C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
217C23×C3C2×D2011yescharacteristic
218C2×C3×C4—22no—
219C2×C3×C4Dic2014yes—
220C2×C3×C4C2×D2012yes—
221C2×C3×C4C2×D2011yescharacteristic
222C2×C3×C4C2×D2012yes—
223C2×C3×C4#71112yes—
224C2×C3×C4Q8×D512yes—
225C2×C3×C4C23×D511yescharacteristic
226C2×Dic3—102no—
227C2×Dic3—104no—
228C2×Dic3—102no—
229C2×Dic3—104no—
230C2×Dic3—204no—
231C2×Dic3—202no—
232Dic6—54no—
233Dic6—102no—
234Dic6—104no—
235Dic6—208no—
236C3×C8—24no—
237C22×C5#89712yes—
238C22×C5C2×Dic1212yes—
239C22×C5#90812yes—
240C22×C5C22×D1211yescharacteristic
241C4×C5—22no—
242C4×C5#89712yes—
243C4×C5C2×Dic1214yes—
244C4×C5C2×#23711yescharacteristic
245C4×C5C2×D3×Q811yescharacteristic
246Dic5—64no—
247Dic5—124no—
248Dic5—122no—
249C2×Q8—154no—
250C2×Q8—152no—
251C2×Q8—301no—
252C2×Q8—304no—
253C2×Q8—302no—
254C2×Q8—604no—
255C22×C4—301no—
256C22×C4—301no—
257C22×C4—302no—
258C22×C4D6011yescharacteristic
259C22×C4D6011yescharacteristic
260C22×C4C22×D1511yescharacteristic
261C2×C8—24no—
262C2×C8C22×D1514yes—
263C4⋊C4—154no—
264C4⋊C4—152no—
265C4⋊C4—301no—
266C4⋊C4—302no—
267C4⋊C4—304no—
268C4⋊C4—304no—
269C42—304no—
270C42D6012yes—
271C42C22×D1512yes—
272C3×C5C2×#47711yescharacteristic, complemented, Hall
273C22×C3#404312yes—
274C22×C3C2×Dic2012yes—
275C22×C3#405412yes—
276C22×C3C22×D2011yescharacteristic
277C3×C4—22no—
278C3×C4#404312yes—
279C3×C4C2×Dic2014yes—
280C3×C4C2×#71111yescharacteristic
281C3×C4C2×Q8×D511yescharacteristic
282Dic3—104no—
283Dic3—204no—
284Dic3—202no—
285C2×C5#485014yescomplemented
286C2×C5C2×#89711yescharacteristic
287C2×C5C22×Dic1211yescharacteristic
288C2×C5C2×#90811yescharacteristic
289C23C2×D6011yescharacteristic
290Q8—154no—
291Q8—304no—
292Q8—302no—
293Q8—608no—
294C2×C4—22no—
295C2×C4—304no—
296C2×C4—302no—
297C2×C4—302no—
298C2×C4—304no—
299C2×C4—604no—
300C2×C4—602no—
301C2×C4Dic6014yes—
302C2×C4C2×D6012yes—
303C2×C4C2×D6011yescharacteristic
304C2×C4C2×D6012yes—
305C2×C4#681912yes—
306C2×C4Q8×D1512yes—
307C2×C4C23×D1511yescharacteristic
308C8—24no—
309C2×C3#6513914yescomplemented
310C2×C3C2×#404311yescharacteristic
311C2×C3C22×Dic2011yescharacteristic
312C2×C3C2×#405411yescharacteristic
313C5C2×#485011yescharacteristic, complemented, Sylow
314C22#9178612yes—
315C22C2×Dic6012yes—
316C22#9179712yes—
317C22C22×D6011yescharacteristic
318C4—22no—
319C4—304no—
320C4—604no—
321C4—602no—
322C4#9178612yes—
323C4C2×Dic6014yes—
324C4C2×#681911yescharacteristic
325C4C2×Q8×D1511yescharacteristic
326C3C2×#6513911yescharacteristic, complemented, Sylow
327C2#1175095114yesdirect product factor
328C2C2×#9178611yescharacteristic
329C2C22×Dic6011yescharacteristic
330C2C2×#9179711yescharacteristic
subgroupG/H
centerC23C2×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×C4⋊C8C2
socle, prime radicalC23×C3×C5C2×D4
hypercenterC2×C4⋊C8D15
hypocenterC3×C5C2×#477
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
6. #11750951C2direct (N × H)
41. C2×Dic30Q8semidirect
95. Dic30C2×Q8semidirect
213. C2×C3×C5#477semidirect
272. C3×C5C2×#477semidirect
285. C2×C5#4850semidirect
309. C2×C3#65139semidirect
313. C5C2×#4850semidirect
326. C3C2×#65139semidirect
327. C2#11750951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917582
C2×C4×Dic302
C2×C3×C5×C4⋊C82
C2×#911022
C2×#911002
#117509512
C2×#651393
C2×#48505