Finite Group Databasebeta

← C2×#11756576 #14482813

Subgroups — C2×#11756576 #14482813

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×Q8C211yesmaximal, characteristic, complemented
2C22×#6821C211yesmaximal, characteristic, complemented
3#11756576C2116yesmaximal, direct product factor
4C2×#91836C213yesmaximal, complemented
5C2×#91835C213yesmaximal, complemented
6C2×Q8×Dic15C211yesmaximal, characteristic, complemented
7C2×#91819C213yesmaximal, complemented
8C2×C4×#1220C213yesmaximal, complemented
9C2×#66151—31nomaximal, Hall
10C22×C3×C5×Q8—28no—
11C22×C3×C5×Q8C2213yes—
12C22×C3×C5×Q8C2211yescharacteristic
13C22×C3×C5×Q8C2218yescomplemented
14C23×C3×C4×C5C2213yes—
15C22×#1220C2213yes—
16C2×#6821—28no—
17C2×#6821C2218yescomplemented
18C22×D60C2213yes—
19C22×C4×D15C2213yes—
20C2×#6719C2211yescharacteristic
21#91836C22124yescomplemented
22#91835C22124yescomplemented
23Q8×Dic15C2218yescomplemented
24#91819C22124yescomplemented
25C4×#1220C22124yescomplemented
26C2×#6714C2213yes—
27C2×#6714C2216yes—
28C2×C4⋊Dic15C2213yes—
29C2×#6712C2213yes—
30C2×C4×Dic15C2213yes—
31C2×#5817—51nomaximal, Hall
32C23×C5×Q8D311yescharacteristic, complemented
33C22×#713—31no—
34#66151—316no—
35C2×#4093—33no—
36C2×#4092—33no—
37C2×Q8×Dic5—31no—
38C2×#4076—33no—
39C2×C4×C22⋊D5—33no—
40C24×C3×C5C2311yescharacteristic
41C23×D15C2313yes—
42C2×C3×C5×Q8—232no—
43C2×C3×C5×Q8—212no—
44C2×C3×C5×Q8D418yescomplemented
45C2×C3×C5×Q8C23112yes—
46C2×C3×C5×Q8C2314yes—
47C22×C3×C4×C5—212no—
48C22×C3×C4×C5C2313yes—
49C22×C3×C4×C5C23112yes—
50C22×C3×C4×C5C2313yes—
51C2×#1220—212no—
52C2×#1220C23112yes—
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2313yes—
55C22×Dic15C2311yescharacteristic
56#6821—232no—
57C2×D60—212no—
58C2×D60C23112yes—
59C2×C4×D15—212no—
60C2×C4×D15C23112yes—
61#6719C2314yes—
62#6714C23112yes—
63#6714C23124yes—
64C4⋊Dic15C23112yes—
65#6712C23112yes—
66C4×Dic15C23112yes—
67C23×C3×Q8D511yescharacteristic, complemented
68C22×#239—51no—
69#5817—516no—
70C2×#947—53no—
71C2×#946—53no—
72C2×Q8×Dic3—51no—
73C2×#930—53no—
74C2×C4×#67—53no—
75C22×C5×Q8—28no—
76C22×C5×Q8C2×D313yes—
77C22×C5×Q8C2×D311yescharacteristic
78C22×C5×Q8C2×D318yescomplemented
79C23×C4×C5C2×D313yes—
80C22×C22⋊D5—33no—
81C2×#713—38no—
82C2×#713—68no—
83C22×D20—33no—
84C22×C4×D5—33no—
85C2×C22⋊Dic5—31no—
86#4093—324no—
87#4092—324no—
88Q8×Dic5—38no—
89#4076—324no—
90C4×C22⋊D5—324no—
91C2×#685—33no—
92C2×#685—36no—
93C2×C4⋊Dic5—33no—
94C2×#683—33no—
95C2×C4×Dic5—33no—
96C2×#548—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—22no—
99C23×C3×C5#4114yescomplemented
100C23×C3×C5C2412yes—
101C23×C3×C5C2411yescharacteristic
102C22×D15—26no—
103C22×D15—26no—
104C22×D15—26no—
105C22×D15C2416yes—
106C3×C5×Q8—224no—
107C3×C5×Q8C2×D4116yescomplemented
108C2×C3×C4×C5—26no—
109C2×C3×C4×C5—224no—
110C2×C3×C4×C5C2×D4112yes—
111C2×C3×C4×C5C2416yes—
112C2×C3×C4×C5C2416yes—
113#1220—224no—
114C2×Dic15—22no—
115C2×Dic15—26no—
116C2×Dic15—22no—
117C2×Dic15C2412yes—
118C2×Dic15C2416yes—
119C2×Dic15C2412yes—
120D60—224no—
121C4×D15—224no—
122C22×C3×Q8—28no—
123C22×C3×Q8C2×D513yes—
124C22×C3×Q8C2×D511yescharacteristic
125C22×C3×Q8C2×D518yescomplemented
126C23×C3×C4C2×D513yes—
127C22×#67—53no—
128C2×#239—58no—
129C2×#239—108no—
130C22×D12—53no—
131C22×C4×D3—53no—
132C2×#217—51no—
133#947—524no—
134#946—524no—
135Q8×Dic3—58no—
136#930—524no—
137C4×#67—524no—
138C2×(C2×D3)⋊C4—53no—
139C2×(C2×D3)⋊C4—56no—
140C2×C4⋊Dic3—53no—
141C2×Dic3⋊C4—53no—
142C2×C4×Dic3—53no—
143C24×C5C22×D311yescharacteristic
144C23×D5—33no—
145C2×C5×Q8—232no—
146C2×C5×Q8—212no—
147C2×C5×Q8#6718yescomplemented
148C2×C5×Q8C22×D3112yes—
149C2×C5×Q8C22×D314yes—
150C22×C4×C5—212no—
151C22×C4×C5C22×D313yes—
152C22×C4×C5C22×D3112yes—
153C22×C4×C5C22×D313yes—
154C2×C22⋊D5—312no—
155C2×C22⋊D5—612no—
156C22×Dic5—31no—
157C22×Dic5—31no—
158C22×Dic5—33no—
159#713—632no—
160C2×D20—312no—
161C2×D20—612no—
162C2×C4×D5—312no—
163C2×C4×D5—612no—
164C22⋊Dic5—34no—
165#685—312no—
166#685—324no—
167C4⋊Dic5—312no—
168#683—312no—
169C4×Dic5—312no—
170C22×#41—151no—
171C23×Q8D1511yescharacteristic, complemented
172#548—1516no—
173C2×#124—153no—
174C2×C22⋊Q8—153no—
175C2×#121—153no—
176C2×C4×Q8—151no—
177C2×C4×D4—153no—
178C22×C3×C5—28no—
179C22×C3×C5—22no—
180C22×C3×C5—22no—
181C22×C3×C5C22×D412yes—
182C22×C3×C5C2×#4112yes—
183C22×C3×C5C2×#4114yescomplemented
184C22×C3×C52−1+412yes—
185C22×C3×C5C2511yescharacteristic
186C2×D15—26no—
187C2×D15—26no—
188C2×D15—26no—
189C2×D15—412no—
190C3×C4×C5—26no—
191C3×C4×C5C22×D4112yes—
192Dic15—22no—
193Dic15—26no—
194Dic15—22no—
195C24×C3C22×D511yescharacteristic
196C23×D3—53no—
197C2×C3×Q8—232no—
198C2×C3×Q8—212no—
199C2×C3×Q8C22⋊D518yescomplemented
200C2×C3×Q8C22×D5112yes—
201C2×C3×Q8C22×D514yes—
202C22×C3×C4—212no—
203C22×C3×C4C22×D513yes—
204C22×C3×C4C22×D5112yes—
205C22×C3×C4C22×D513yes—
206C2×#67—512no—
207C2×#67—1012no—
208C22×Dic3—51no—
209C22×Dic3—53no—
210C22×Dic3—51no—
211#239—1032no—
212C2×D12—512no—
213C2×D12—1012no—
214C2×C4×D3—512no—
215C2×C4×D3—1012no—
216#217—54no—
217(C2×D3)⋊C4—512no—
218(C2×D3)⋊C4—524no—
219C4⋊Dic3—512no—
220Dic3⋊C4—512no—
221C4×Dic3—512no—
222C23×C5—22no—
223C23×C5—22no—
224C23×C5#23914yescomplemented
225C23×C5C23×D312yes—
226C23×C5C23×D311yescharacteristic
227C22×D5—36no—
228C22×D5—66no—
229C22×D5—66no—
230C22×D5—66no—
231C5×Q8—224no—
232C5×Q8C2×#67116yescomplemented
233C2×C4×C5—26no—
234C2×C4×C5—224no—
235C2×C4×C5C2×#67112yes—
236C2×C4×C5C23×D316yes—
237C2×C4×C5C23×D316yes—
238C22⋊D5—624no—
239C2×Dic5—32no—
240C2×Dic5—36no—
241C2×Dic5—32no—
242C2×Dic5—66no—
243C2×Dic5—62no—
244C2×Dic5—62no—
245D20—624no—
246C4×D5—624no—
247C2×#41—158no—
248C2×#41—308no—
249C22×Q8—28no—
250C22×Q8C2×D1513yes—
251C22×Q8C2×D1511yescharacteristic
252C22×Q8C2×D1518yescomplemented
253C22×D4—153no—
254C22×D4—153no—
255C23×C4—153no—
256C23×C4C2×D1513yes—
257#124—1524no—
258C22⋊Q8—1524no—
259#121—1524no—
260C4×Q8—158no—
261C4×D4—1524no—
262C2×C4⋊C4—153no—
263C2×C4⋊C4—153no—
264C2×C22⋊C4—151no—
265C2×C22⋊C4—153no—
266C2×C22⋊C4—156no—
267C2×C42—153no—
268C2×C3×C5—24no—
269C2×C3×C5#54814yescomplemented
270C2×C3×C5C23×D411yescharacteristic
271C2×C3×C5C22×#4111yescharacteristic
272C2×C3×C5C2×2−1+411yescharacteristic
273D15—46no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3#71314yescomplemented
277C23×C3C23×D512yes—
278C23×C3C23×D511yescharacteristic
279C22×D3—56no—
280C22×D3—106no—
281C22×D3—106no—
282C22×D3—106no—
283C3×Q8—224no—
284C3×Q8C2×C22⋊D5116yescomplemented
285C2×C3×C4—26no—
286C2×C3×C4—224no—
287C2×C3×C4C2×C22⋊D5112yes—
288C2×C3×C4C23×D516yes—
289C2×C3×C4C23×D516yes—
290#67—1024no—
291C2×Dic3—52no—
292C2×Dic3—56no—
293C2×Dic3—52no—
294C2×Dic3—106no—
295C2×Dic3—102no—
296C2×Dic3—102no—
297D12—1024no—
298C4×D3—1024no—
299C22×C5—22no—
300C22×C5—22no—
301C22×C5—28no—
302C22×C5C2×#23912yes—
303C22×C5C2×#23914yescomplemented
304C22×C5#100712yes—
305C22×C5C22×#6712yes—
306C22×C5C24×D311yescharacteristic
307C2×D5—66no—
308C2×D5—66no—
309C2×D5—66no—
310C2×D5—1212no—
311C4×C5—26no—
312C4×C5C22×#67112yes—
313Dic5—66no—
314Dic5—62no—
315Dic5—62no—
316C24—153no—
317C24C22×D1511yescharacteristic
318#41—3032no—
319C2×Q8—232no—
320C2×Q8—212no—
321C2×Q8#122018yescomplemented
322C2×Q8C22×D15112yes—
323C2×Q8C22×D1514yes—
324C2×D4—1512no—
325C2×D4—1512no—
326C2×D4—3012no—
327C2×D4—3012no—
328C22×C4—212no—
329C22×C4—151no—
330C22×C4—153no—
331C22×C4—151no—
332C22×C4—1512no—
333C22×C4—3012no—
334C22×C4C22×D15112yes—
335C22×C4C22×D1513yes—
336C22×C4C22×D1513yes—
337C4⋊C4—1512no—
338C4⋊C4—1512no—
339C22⋊C4—154no—
340C22⋊C4—1512no—
341C22⋊C4—1524no—
342C42—1512no—
343C3×C5C2×#54811yescharacteristic, complemented, Hall
344C22×C3—28no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3C2×#71312yes—
348C22×C3C2×#71314yescomplemented
349C22×C3#414712yes—
350C22×C3C22×C22⋊D512yes—
351C22×C3C24×D511yescharacteristic
352C2×D3—106no—
353C2×D3—106no—
354C2×D3—106no—
355C2×D3—2012no—
356C3×C4—26no—
357C3×C4C22×C22⋊D5112yes—
358Dic3—106no—
359Dic3—102no—
360Dic3—102no—
361C2×C5—24no—
362C2×C5#581714yescomplemented
363C2×C5C22×#23911yescharacteristic
364C2×C5C2×#100711yescharacteristic
365C2×C5C23×#6711yescharacteristic
366D5—126no—
367C23—22no—
368C23—22no—
369C23—156no—
370C23—306no—
371C23—306no—
372C23—306no—
373C23#682114yescomplemented
374C23C23×D1512yes—
375C23C23×D1511yescharacteristic
376Q8—224no—
377Q8C2×#1220116yescomplemented
378D4—3024no—
379D4—3024no—
380C2×C4—26no—
381C2×C4—224no—
382C2×C4—152no—
383C2×C4—156no—
384C2×C4—152no—
385C2×C4—306no—
386C2×C4—302no—
387C2×C4—302no—
388C2×C4—3024no—
389C2×C4C2×#1220112yes—
390C2×C4C23×D1516yes—
391C2×C4C23×D1516yes—
392C2×C3—24no—
393C2×C3#6615114yescomplemented
394C2×C3C22×#71311yescharacteristic
395C2×C3C2×#414711yescharacteristic
396C2×C3C23×C22⋊D511yescharacteristic
397D3—206no—
398C5C2×#581711yescharacteristic, complemented, Sylow
399C22—28no—
400C22—22no—
401C22—22no—
402C22—306no—
403C22—306no—
404C22—306no—
405C22—6012no—
406C22C2×#682112yes—
407C22C2×#682114yescomplemented
408C22#9209812yes—
409C22C22×#122012yes—
410C22C24×D1511yescharacteristic
411C4—26no—
412C4—306no—
413C4—302no—
414C4—302no—
415C4C22×#1220112yes—
416C3C2×#6615111yescharacteristic, complemented, Sylow
417C2—24no—
418C2—606no—
419C2#1175657614yesdirect product factor
420C2C22×#682111yescharacteristic
421C2C2×#9209811yescharacteristic
422C2C23×#122011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC23×C3×C5×Q8C2
socleC23×C3×C5C24
hypercenterC23×Q8D15
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C23×C3×C5×Q8C2semidirect
2. C22×#6821C2semidirect
3. #11756576C2direct (N × H)
4. C2×#91836C2semidirect
5. C2×#91835C2semidirect
6. C2×Q8×Dic15C2semidirect
7. C2×#91819C2semidirect
8. C2×C4×#1220C2semidirect
13. C22×C3×C5×Q8C22semidirect
17. C2×#6821C22semidirect
21. #91836C22semidirect
22. #91835C22semidirect
23. Q8×Dic15C22semidirect
24. #91819C22semidirect
25. C4×#1220C22semidirect
32. C23×C5×Q8D3semidirect
44. C2×C3×C5×Q8D4semidirect
67. C23×C3×Q8D5semidirect
78. C22×C5×Q8C2×D3semidirect
99. C23×C3×C5#41semidirect
107. C3×C5×Q8C2×D4semidirect
125. C22×C3×Q8C2×D5semidirect
147. C2×C5×Q8#67semidirect
171. C23×Q8D15semidirect
183. C22×C3×C5C2×#41semidirect
199. C2×C3×Q8C22⋊D5semidirect
224. C23×C5#239semidirect
232. C5×Q8C2×#67semidirect
252. C22×Q8C2×D15semidirect
269. C2×C3×C5#548semidirect
276. C23×C3#713semidirect
284. C3×Q8C2×C22⋊D5semidirect
303. C22×C5C2×#239semidirect
321. C2×Q8#1220semidirect
343. C3×C5C2×#548semidirect
348. C22×C3C2×#713semidirect
362. C2×C5#5817semidirect
373. C23#6821semidirect
377. Q8C2×#1220semidirect
393. C2×C3#66151semidirect
398. C5C2×#5817semidirect
407. C22C2×#6821semidirect
416. C3C2×#66151semidirect
419. C2#11756576direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C5×Q82
C22×#68212
#117565762
C2×#918362
C2×#918352
C2×Q8×Dic152
C2×#918192
C2×C4×#12202
C2×#661513
C2×#58175