Finite Group Databasebeta

← C2×#11746836 #14478313

Subgroups — C2×#11746836 #14478313

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91275C211yesmaximal, characteristic, complemented
2C2×#91273C211yesmaximal, characteristic, complemented
3C2×#91084C211yesmaximal, characteristic, complemented
4C2×C5×D3×C16C211yesmaximal, characteristic, complemented
5C2×C3×#3932C211yesmaximal, characteristic, complemented
6C2×#90947C211yesmaximal, characteristic, complemented
7C2×#90938C211yesmaximal, characteristic, complemented
8#11746836C218yesmaximal, direct product factor
9C2×#65193—31nomaximal, Hall
10C2×#6769—21no—
11C2×#6765—21no—
12C2×Dic60C2211yescharacteristic
13C2×D120C2211yescharacteristic
14C2×C5×D3×C8C2211yescharacteristic
15C2×C3×Dic20C2211yescharacteristic
16C2×C3×D40C2211yescharacteristic
17C2×#6658—21no—
18C2×#6657—21no—
19#91275—22no—
20#91275C2214yescomplemented
21#91273—22no—
22#91273C2214yescomplemented
23C2×C3×C5×C16C2211yescharacteristic
24#91084C2214yescomplemented
25C2×C5×C3⋊C16C2211yescharacteristic
26C5×D3×C16C2214yescomplemented
27C3×#3932C2214yescomplemented
28#90947C2214yescomplemented
29#90938C2214yescomplemented
30C2×#4916—51nomaximal, Hall
31C2×#4050—31no—
32C2×#4050—31no—
33C22×C5×C16—31no—
34C2×Dic40—31no—
35#65193—38no—
36C2×#3932—31no—
37C2×#3932D311yescharacteristic, complemented
38C2×D80—31no—
39C2×D60—21no—
40C2×Dic30—21no—
41C2×C4×C5×D3D411yescharacteristic
42C2×C3×D20—21no—
43C2×C3×Dic10—21no—
44C2×#1203—41no—
45C2×#1201—41no—
46C2×#1200—41no—
47C2×D5×Dic3—41no—
48#6769—24no—
49#6769—42no—
50#6765—24no—
51#6765—42no—
52C2×C3×C5×C8C2311yescharacteristic
53Dic60—21no—
54Dic60C2312yes—
55D120—21no—
56D120C2312yes—
57C2×C5×C3⋊C8D411yescharacteristic
58C5×D3×C8D412yes—
59C5×D3×C8C2312yes—
60C3×Dic20—21no—
61C3×Dic20C2312yes—
62C3×D40—21no—
63C3×D40C2312yes—
64#6658—24no—
65#6657—24no—
66C3×C5×C16C2312yes—
67C5×C3⋊C16C2312yes—
68C2×#919—51no—
69C2×#912—51no—
70C2×C3×SD32—51no—
71C2×#829—51no—
72C2×#826—51no—
73#4916—58no—
74C2×#800—51no—
75C2×D3×C16D511yescharacteristic, complemented
76C2×#709—61no—
77C2×#709—61no—
78C22×C5×C8—31no—
79C2×Dic20—31no—
80C2×Dic20C2×D311yescharacteristic
81#4050—34no—
82#4050—34no—
83#4050—62no—
84#4050—62no—
85C2×D40—31no—
86C2×D40C2×D311yescharacteristic
87C2×#677—61no—
88C2×#677—61no—
89C2×C5×C16—31no—
90C2×C5×C16—34no—
91C2×C5×C16C2×D311yescharacteristic
92Dic40—34no—
93#3932—34no—
94#3932C2×D314yescomplemented
95D80—34no—
96C2×#508—151noSylow
97C22×D15—41no—
98C22×C5×D3D811yescharacteristic
99C22×C3×D5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—41no—
102D60—22no—
103D60—41no—
104Dic30—22no—
105Dic30—41no—
106C2×C5×Dic3D811yescharacteristic
107C4×C5×D3D812yes—
108C4×C5×D3C2×D412yes—
109C2×C3×Dic5—41no—
110C3×D20—22no—
111C3×D20—41no—
112C3×Dic10—22no—
113C3×Dic10—41no—
114#1203—44no—
115#1201—44no—
116#1200—44no—
117D5×Dic3—44no—
118C3×C5×C8C2×D411yescharacteristic
119C3×C5×C8C2411yescharacteristic
120C5×C3⋊C8C2×D412yes—
121C2×#239—101no—
122C2×#237—101no—
123C2×C3×Q16—51no—
124C2×C3×D8—51no—
125C2×#215—101no—
126C2×#214—101no—
127#919—54no—
128#919—102no—
129#912—54no—
130#912—102no—
131C2×Dic12—51no—
132C2×D24—51no—
133C2×D3×C8C2×D511yescharacteristic
134C3×SD32—54no—
135C2×C3×C16C2×D511yescharacteristic
136#829—54no—
137#826—54no—
138C2×C3⋊C16C2×D511yescharacteristic
139#800—54no—
140D3×C16C2×D514yescomplemented
141C22×C4×C5—31no—
142C2×C22⋊D5—121no—
143C2×C22⋊D5—121no—
144#709—64no—
145#709—64no—
146#709—122no—
147#709—122no—
148C2×D20—21no—
149C2×D20—61no—
150C2×C4×D5—121no—
151C2×C4×D5—121no—
152C2×Dic10—21no—
153C2×Dic10—61no—
154C2×C5×C8—31no—
155C2×C5×C8—32no—
156C2×C5×C8—32no—
157C2×C5×C8C22×D311yescharacteristic
158Dic20—21no—
159Dic20—32no—
160Dic20—61no—
161Dic20C22×D312yes—
162D40—21no—
163D40—32no—
164D40—61no—
165D40C22×D312yes—
166#677—64no—
167#677—64no—
168C5×C16—32no—
169C5×C16C22×D312yes—
170C2×#135—151no—
171C2×#135—151no—
172#508—158no—
173C2×Q32—151no—
174C2×SD32—51no—
175C2×SD32—151no—
176C2×D16—151no—
177C22×C16—31no—
178C22×C3×C5C2×D811yescharacteristic
179C2×D15—42no—
180C2×D15—82no—
181C2×C5×D3—22no—
182C2×C5×D3C2×D812yes—
183C2×C3×D5—42no—
184C2×C3×D5—82no—
185C3×C4×C5C2×D811yescharacteristic
186C3×C4×C5C22×D411yescharacteristic
187Dic15—42no—
188C3×Dic5—42no—
189C5×Dic3C2×D812yes—
190C2×C3×Q8—101no—
191C2×C3×D4—101no—
192C2×#67—201no—
193C22×Dic3—201no—
194#239—104no—
195#239—202no—
196#237—104no—
197#237—202no—
198C2×D12—101no—
199C2×D12—201no—
200C2×C4×D3—201no—
201C2×C4×D3D2011yescharacteristic
202C2×Dic6—101no—
203C3×Q16—52no—
204C3×Q16—101no—
205C3×D8—52no—
206C3×D8—101no—
207C2×C3×C8C22×D511yescharacteristic
208#215—104no—
209#214—104no—
210C2×C3⋊C8D2011yescharacteristic
211Dic12—52no—
212Dic12—101no—
213D24—52no—
214D24—101no—
215D3×C8D2012yes—
216D3×C8C22×D512yes—
217C3×C16C22×D512yes—
218C3⋊C16C22×D512yes—
219C23×C5—31no—
220C22×D5—41no—
221C22×D5—121no—
222C2×C4×C5—31no—
223C2×C4×C5—32no—
224C2×C4×C5—32no—
225C2×C4×C5D3×D411yescharacteristic
226C22⋊D5—124no—
227C22⋊D5—124no—
228C2×Dic5—41no—
229C2×Dic5—121no—
230D20—22no—
231D20—41no—
232D20—62no—
233D20—121no—
234C4×D5—124no—
235C4×D5—124no—
236Dic10—22no—
237Dic10—41no—
238Dic10—62no—
239Dic10—121no—
240C5×C8—32no—
241C5×C8D3×D411yescharacteristic
242C5×C8C23×D311yescharacteristic
243C2×#41—301no—
244C2×#41—301no—
245#135—154no—
246#135—154no—
247#135—302no—
248#135—302no—
249C2×Q16—51no—
250C2×Q16—151no—
251C2×SD16—301no—
252C2×SD16—301no—
253C2×D8—51no—
254C2×D8—151no—
255C22×C8—31no—
256Q32—154no—
257SD32—54no—
258SD32—154no—
259D16—154no—
260C2×C16—31no—
261C2×C16—34no—
262C2×C16D3×D511yescharacteristic
263C2×C3×C5#50812yescomplemented
264C2×C3×C5C22×D811yescharacteristic
265D15—82no—
266C3×D5—82no—
267C5×D3—22no—
268C23×C3—201no—
269C22×D3—201no—
270C22×D3D4011yescharacteristic
271C3×Q8—102no—
272C3×Q8—201no—
273C3×D4—102no—
274C3×D4—201no—
275C2×C3×C4—201no—
276C2×C3×C4C2×D2011yescharacteristic
277#67—204no—
278C2×Dic3—201no—
279C2×Dic3—204no—
280C2×Dic3D4011yescharacteristic
281D12—102no—
282D12—204no—
283D12—201no—
284C4×D3—204no—
285C4×D3D4012yes—
286C4×D3C2×D2012yes—
287Dic6—102no—
288Dic6—201no—
289C3×C8C2×D2011yescharacteristic
290C3×C8C23×D511yescharacteristic
291C3⋊C8C2×D2012yes—
292C22×C5—32no—
293C22×C5—62no—
294C22×C5D3×D811yescharacteristic
295C2×D5—42no—
296C2×D5—82no—
297C2×D5—122no—
298C2×D5—242no—
299C4×C5—32no—
300C4×C5D3×D811yescharacteristic
301C4×C5C2×D3×D411yescharacteristic
302Dic5—42no—
303Dic5—122no—
304#41—304no—
305#41—304no—
306#41—602no—
307#41—602no—
308C2×Q8—101no—
309C2×Q8—301no—
310C2×D4—101no—
311C2×D4—301no—
312C2×D4—601no—
313C2×D4—601no—
314C22×C4—31no—
315C22×C4—601no—
316C22×C4—601no—
317Q16—52no—
318Q16—101no—
319Q16—152no—
320Q16—301no—
321SD16—304no—
322SD16—304no—
323D8—52no—
324D8—101no—
325D8—152no—
326D8—301no—
327C2×C8—31no—
328C2×C8—32no—
329C2×C8—32no—
330C2×C8C2×D3×D511yescharacteristic
331C16—32no—
332C16C2×D3×D512yes—
333C3×C5C2×#50811yescharacteristic, complemented, Hall
334C22×C3—202no—
335C22×C3—402no—
336C22×C3C2×D4011yescharacteristic
337C2×D3—22no—
338C2×D3—202no—
339C2×D3—402no—
340C2×D3C2×D4012yes—
341C3×C4—202no—
342C3×C4C2×D4011yescharacteristic
343C3×C4C22×D2011yescharacteristic
344Dic3—202no—
345Dic3C2×D4012yes—
346C2×C5—62no—
347C2×C5#491612yescomplemented
348C2×C5C2×D3×D811yescharacteristic
349D5—82no—
350D5—242no—
351C23—31no—
352C23—201no—
353C23—601no—
354Q8—102no—
355Q8—201no—
356Q8—302no—
357Q8—601no—
358D4—102no—
359D4—201no—
360D4—302no—
361D4—604no—
362D4—604no—
363D4—601no—
364C2×C4—31no—
365C2×C4—32no—
366C2×C4—32no—
367C2×C4—201no—
368C2×C4—604no—
369C2×C4—604no—
370C2×C4—601no—
371C2×C4D3×D2011yescharacteristic
372C8—32no—
373C8D3×D2011yescharacteristic
374C8C22×D3×D511yescharacteristic
375C2×C3—402no—
376C2×C3#6519312yescomplemented
377C2×C3C22×D4011yescharacteristic
378D3—22no—
379D3—402no—
380C5C2×#491611yescharacteristic, complemented, Sylow
381C22—32no—
382C22—62no—
383C22—202no—
384C22—402no—
385C22—602no—
386C22—1202no—
387C22D3×D4011yescharacteristic
388C4—32no—
389C4—202no—
390C4—602no—
391C4D3×D4011yescharacteristic
392C4C2×D3×D2011yescharacteristic
393C3C2×#6519311yescharacteristic, complemented, Sylow
394C2—62no—
395C2—402no—
396C2—1202no—
397C2#1174683612yesdirect product factor
398C2C2×D3×D4011yescharacteristic
subgroupG/H
centerC22D3×D40
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5C2×#508
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×#91275C2semidirect
2. C2×#91273C2semidirect
3. C2×#91084C2semidirect
4. C2×C5×D3×C16C2semidirect
5. C2×C3×#3932C2semidirect
6. C2×#90947C2semidirect
7. C2×#90938C2semidirect
8. #11746836C2direct (N × H)
20. #91275C22semidirect
22. #91273C22semidirect
24. #91084C22semidirect
26. C5×D3×C16C22semidirect
27. C3×#3932C22semidirect
28. #90947C22semidirect
29. #90938C22semidirect
37. C2×#3932D3semidirect
75. C2×D3×C16D5semidirect
94. #3932C2×D3semidirect
140. D3×C16C2×D5semidirect
263. C2×C3×C5#508semidirect
333. C3×C5C2×#508semidirect
347. C2×C5#4916semidirect
376. C2×C3#65193semidirect
380. C5C2×#4916semidirect
393. C3C2×#65193semidirect
397. C2#11746836direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#912752
C2×#912732
C2×#910842
C2×C5×D3×C162
C2×C3×#39322
C2×#909472
C2×#909382
#117468362
C2×#651933
C2×#49165