Finite Group Databasebeta

← C2×#11747932 #14427712

Subgroups — C2×#11747932 #14427712

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×D15C211yesmaximal, characteristic, complemented
2C22×C3×D40C211yesmaximal, characteristic, complemented
3C2×#91465C212yesmaximal, complemented
4C2×C5×#818C211yesmaximal, characteristic, complemented
5C2×#90964C212yesmaximal, complemented
6#11747932C218yesmaximal, direct product factor
7C2×#65172—31nomaximal, Hall
8C22×C4×D15C2211yescharacteristic
9C22×C3×D20C2212yes—
10C22×#1202—22no—
11C22×C3×C5×C8C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C8×D15—24no—
14C2×C8×D15C2214yescomplemented
15C2×C5×C4⋊Dic3C2212yes—
16C2×C3×D40—24no—
17C2×C3×D40C2214yescomplemented
18C2×#6665—22no—
19#91465—24no—
20#91465C2218yescomplemented
21C5×#818C2214yescomplemented
22#90964C2218yescomplemented
23C2×#5157—51nomaximal, Hall
24C22×D40D311yescharacteristic, complemented
25C22×C8×D5—31no—
26C2×#4041—32no—
27C2×C5×#107—31no—
28C2×#3941—32no—
29#65172—38no—
30C23×D15D411yescharacteristic
31C23×C3×D5—22no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15D411yescharacteristic
34C2×C4×D15—22no—
35C2×C4×D15—22no—
36C2×C4×D15D412yes—
37C2×C4×D15C2312yes—
38C22×C5×Dic3—22no—
39C2×C3×D20—24no—
40C2×C3×D20—24no—
41C2×C3×D20—22no—
42C2×C3×D20C2314yes—
43C2×#1202—28no—
44C2×#1202—48no—
45C2×C3×C5×C8D414yescomplemented
46C2×C3×C5×C8C2312yes—
47C2×C3⋊#168—22no—
48C2×C3⋊#168C2312yes—
49C8×D15—28no—
50C5×C4⋊Dic3—22no—
51C5×C4⋊Dic3C2314yes—
52C3×D40—28no—
53#6665—28no—
54C22×C3×D8—51no—
55C2×#938—52no—
56C22×D3×C8—51no—
57C2×#832—52no—
58#5157—58no—
59C2×#818D511yescharacteristic, complemented
60C22×D20—62no—
61C22×D20C2×D312yes—
62C22×C4×D5—31no—
63C22×C5×C8C2×D311yescharacteristic
64C2×C5×C4⋊C4—32no—
65C2×#685—62no—
66C22×#168—31no—
67C2×D40—24no—
68C2×D40C2×D314yescomplemented
69C2×C8×D5—34no—
70C2×C8×D5—64no—
71#4041—38no—
72#4041—64no—
73C5×#107—34no—
74#3941—38no—
75C2×#466—151noSylow
76C23×C3×C5C2×D411yescharacteristic
77C22×D15—22no—
78C22×D15—22no—
79C22×D15D814yescomplemented
80C22×D15C2×D412yes—
81C22×C3×D5—24no—
82C22×C3×D5—44no—
83C22×C3×D5—44no—
84C22×C3×D5—44no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D412yes—
87C2×C3×C4×C5#4112yes—
88C2×C3×C4×C5C2411yescharacteristic
89C2×Dic15—22no—
90C2×Dic15C2×D412yes—
91C4×D15—24no—
92C4×D15—22no—
93C4×D15—22no—
94C2×C5×Dic3—24no—
95C2×C5×Dic3—44no—
96C3×D20—24no—
97C3×D20—24no—
98C3×D20—44no—
99#1202—416no—
100C3×C5×C8C2×D414yescomplemented
101C3⋊#168—22no—
102C22×C3×D4—52no—
103C22×#67—102no—
104C22×C4×D3—51no—
105C2×C3×D8—54no—
106C2×C3×D8—104no—
107C22×C3×C8C2×D511yescharacteristic
108C2×#217—102no—
109#938—58no—
110#938—104no—
111C2×C4⋊Dic3C2×D512yes—
112C22×C3⋊C8—51no—
113C2×D3×C8—54no—
114C2×D3×C8—104no—
115#832—58no—
116#818C2×D514yescomplemented
117C23×D5—22no—
118C23×D5—31no—
119C22×C4×C5—62no—
120C22×C4×C5C22×D311yescharacteristic
121C22×Dic5—31no—
122C2×D20—24no—
123C2×D20—24no—
124C2×D20—22no—
125C2×D20—68no—
126C2×D20—128no—
127C2×D20C22×D314yes—
128C2×C4×D5—32no—
129C2×C4×D5—32no—
130C2×C4×D5—62no—
131C2×C4×D5—62no—
132C2×C5×C8#6714yescomplemented
133C2×C5×C8C22×D312yes—
134C5×C4⋊C4—34no—
135C5×C4⋊C4—62no—
136#685—68no—
137C2×#168—32no—
138C2×#168—62no—
139D40—28no—
140C8×D5—68no—
141C22×D8—51no—
142C23×C8—151no—
143C2×#121—152no—
144#466—158no—
145C2×#107—31no—
146C2×#102—152no—
147C22×C3×C5#12112yes—
148C22×C3×C5C2×D812yes—
149C22×C3×C5#13512yes—
150C22×C3×C5C22×D411yescharacteristic
151C2×D15—22no—
152C2×D15—22no—
153C2×D15—28no—
154C2×D15C2×D814yescomplemented
155C2×C3×D5—44no—
156C2×C3×D5—44no—
157C2×C3×D5—44no—
158C2×C3×D5—88no—
159C3×C4×C5#12112yes—
160C3×C4×C5C22×D411yescharacteristic
161C3×C4×C5C2×#4111yescharacteristic
162Dic15—22no—
163C5×Dic3—44no—
164C24×C3—102no—
165C23×D3—51no—
166C2×C3×D4—54no—
167C2×C3×D4—104no—
168C2×C3×D4—102no—
169C2×C3×D4—104no—
170C22×C3×C4C22×D511yescharacteristic
171C2×#67—108no—
172C2×#67—208no—
173C22×Dic3—22no—
174C22×Dic3—51no—
175C2×C4×D3—52no—
176C2×C4×D3—52no—
177C2×C4×D3—102no—
178C2×C4×D3—102no—
179C3×D8—108no—
180C2×C3×C8D2014yescomplemented
181C2×C3×C8C22×D512yes—
182#217—108no—
183C4⋊Dic3—22no—
184C4⋊Dic3C22×D514yes—
185C2×C3⋊C8—52no—
186C2×C3⋊C8—102no—
187D3×C8—108no—
188C23×C5D3×D411yescharacteristic
189C22×D5—24no—
190C22×D5—34no—
191C22×D5—32no—
192C22×D5—44no—
193C22×D5—44no—
194C22×D5—44no—
195C22×D5—62no—
196C22×D5—62no—
197C2×C4×C5—64no—
198C2×C4×C5—124no—
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5#23712yes—
201C2×C4×C5C2×#6712yes—
202C2×C4×C5C23×D311yescharacteristic
203C2×Dic5—32no—
204C2×Dic5—62no—
205D20—24no—
206D20—24no—
207D20—44no—
208D20—1216no—
209C4×D5—64no—
210C4×D5—62no—
211C4×D5—62no—
212C5×C8C2×#6714yescomplemented
213#168—62no—
214C22×D4—52no—
215C22×D4—302no—
216C23×C4—151no—
217C2×D8—54no—
218C2×D8—104no—
219C22×C8—151no—
220C22×C8—154no—
221C22×C8—304no—
222C22×C8D3×D511yescharacteristic
223#121—158no—
224#121—304no—
225C2×C4⋊C4—32no—
226C2×C22⋊C4—302no—
227#107—34no—
228#102—158no—
229C2×C3×C5#46614yescomplemented
230C2×C3×C5C2×#12111yescharacteristic
231C2×C3×C5C22×D811yescharacteristic
232C2×C3×C5C2×#13511yescharacteristic
233D15—24no—
234C3×D5—84no—
235C23×C3—104no—
236C23×C3—204no—
237C23×C3—204no—
238C23×C3—204no—
239C23×C3D4×D511yescharacteristic
240C22×D3—52no—
241C22×D3—54no—
242C22×D3—102no—
243C22×D3—102no—
244C3×D4—104no—
245C3×D4—104no—
246C3×D4—204no—
247C2×C3×C4C2×D2012yes—
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4#71312yes—
250C2×C3×C4C23×D511yescharacteristic
251#67—2016no—
252C2×Dic3—24no—
253C2×Dic3—44no—
254C2×Dic3—52no—
255C2×Dic3—102no—
256C4×D3—102no—
257C4×D3—102no—
258C4×D3—104no—
259C3×C8C2×D2014yescomplemented
260C3⋊C8—102no—
261C22×C5D3×D812yes—
262C22×C5#91212yes—
263C22×C5#93812yes—
264C22×C5C2×D3×D411yescharacteristic
265C2×D5—34no—
266C2×D5—44no—
267C2×D5—44no—
268C2×D5—44no—
269C2×D5—68no—
270C2×D5—62no—
271C2×D5—62no—
272C2×D5—88no—
273C4×C5—124no—
274C4×C5#93812yes—
275C4×C5C2×#23711yescharacteristic
276C4×C5C22×#6711yescharacteristic
277Dic5—62no—
278C24—102no—
279C24—151no—
280C2×D4—54no—
281C2×D4—104no—
282C2×D4—102no—
283C2×D4—104no—
284C2×D4—308no—
285C2×D4—608no—
286C22×C4—62no—
287C22×C4—151no—
288C22×C4—152no—
289C22×C4—152no—
290C22×C4—302no—
291C22×C4—302no—
292C22×C4C2×D3×D511yescharacteristic
293D8—108no—
294C2×C8—152no—
295C2×C8—302no—
296C2×C8—308no—
297C2×C8#120214yescomplemented
298C2×C8C2×D3×D512yes—
299C4⋊C4—34no—
300C4⋊C4—62no—
301C22⋊C4—308no—
302C3×C5C2×#46611yescharacteristic, complemented, Hall
303C22×C3—204no—
304C22×C3—204no—
305C22×C3—204no—
306C22×C3—408no—
307C22×C3#404112yes—
308C22×C3D5×D812yes—
309C22×C3#406512yes—
310C22×C3C2×D4×D511yescharacteristic
311C2×D3—54no—
312C2×D3—102no—
313C2×D3—102no—
314C2×D3—108no—
315C3×C4#404112yes—
316C3×C4C22×D2011yescharacteristic
317C3×C4C2×#71311yescharacteristic
318Dic3—44no—
319Dic3—102no—
320C2×C5#515714yescomplemented
321C2×C5C2×D3×D811yescharacteristic
322C2×C5C2×#91211yescharacteristic
323C2×C5C2×#93811yescharacteristic
324D5—64no—
325D5—84no—
326C23—104no—
327C23—152no—
328C23—154no—
329C23—204no—
330C23—204no—
331C23—204no—
332C23—302no—
333C23—302no—
334C23#677711yescharacteristic
335D4—104no—
336D4—104no—
337D4—204no—
338D4—6016no—
339C2×C4—64no—
340C2×C4—124no—
341C2×C4—152no—
342C2×C4—302no—
343C2×C4—304no—
344C2×C4—302no—
345C2×C4—302no—
346C2×C4#676612yes—
347C2×C4#677711yescharacteristic
348C2×C4C2×#120212yes—
349C2×C4C22×D3×D511yescharacteristic
350C8—302no—
351C8C2×#120214yescomplemented
352C2×C3—404no—
353C2×C3#6517214yescomplemented
354C2×C3C2×#404111yescharacteristic
355C2×C3C2×D5×D811yescharacteristic
356C2×C3C2×#406511yescharacteristic
357D3—104no—
358C5C2×#515711yescharacteristic, complemented, Sylow
359C22—154no—
360C22—204no—
361C22—204no—
362C22—204no—
363C22—302no—
364C22—302no—
365C22—308no—
366C22—408no—
367C22#9125612yes—
368C22#9127712yes—
369C22#9146512yes—
370C22C2×#677711yescharacteristic
371C4—124no—
372C4—302no—
373C4#9146512yes—
374C4C2×#676611yescharacteristic
375C4C22×#120211yescharacteristic
376C3C2×#6517211yescharacteristic, complemented, Sylow
377C2—304no—
378C2—404no—
379C2#1174793214yesdirect product factor
380C2C2×#9125611yescharacteristic
381C2C2×#9127711yescharacteristic
382C2C2×#9146511yescharacteristic
subgroupG/H
centerC23#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#466
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C8×D15C2semidirect
2. C22×C3×D40C2semidirect
3. C2×#91465C2semidirect
4. C2×C5×#818C2semidirect
5. C2×#90964C2semidirect
6. #11747932C2direct (N × H)
14. C2×C8×D15C22semidirect
17. C2×C3×D40C22semidirect
20. #91465C22semidirect
21. C5×#818C22semidirect
22. #90964C22semidirect
24. C22×D40D3semidirect
45. C2×C3×C5×C8D4semidirect
59. C2×#818D5semidirect
68. C2×D40C2×D3semidirect
79. C22×D15D8semidirect
100. C3×C5×C8C2×D4semidirect
116. #818C2×D5semidirect
132. C2×C5×C8#67semidirect
154. C2×D15C2×D8semidirect
180. C2×C3×C8D20semidirect
212. C5×C8C2×#67semidirect
229. C2×C3×C5#466semidirect
259. C3×C8C2×D20semidirect
297. C2×C8#1202semidirect
302. C3×C5C2×#466semidirect
320. C2×C5#5157semidirect
351. C8C2×#1202semidirect
353. C2×C3#65172semidirect
358. C5C2×#5157semidirect
376. C3C2×#65172semidirect
379. C2#11747932direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×D152
C22×C3×D402
C2×#914652
C2×C5×#8182
C2×#909642
#117479322
C2×#651723
C2×#51575