Finite Group Databasebeta

← C2×#11747498 #14412499

Subgroups — C2×#11747498 #14412499

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6772C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×#6649C211yesmaximal, characteristic, complemented
4C2×#91094C211yesmaximal, characteristic, complemented
5C2×C5×#809C211yesmaximal, characteristic, complemented
6C2×#90974C211yesmaximal, characteristic, complemented
7C2×#90966C211yesmaximal, characteristic, complemented
8#11747498C218yesmaximal, direct product factor
9C2×#65060—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×C5×D12C2211yescharacteristic
12C22×C3×C4×D5—21no—
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1201—21no—
15C22×D3×Dic5—21no—
16C2×#6772—24no—
17C2×#6772—22no—
18C2×#6772C418yescomplemented
19C2×#6772C2214yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#683—21no—
25C3×D5×C4⋊C4—22no—
26C3×D5×C4⋊C4C2214yescomplemented
27C2×#6649—24no—
28C2×#6649C2214yescomplemented
29#91094C2214yescomplemented
30C5×#809C2214yescomplemented
31#90974C2214yescomplemented
32#90966C2214yescomplemented
33C2×#4966—51nomaximal, Hall
34C22×#711—31no—
35C22×#676—31no—
36C2×D5×C4⋊C4D311yescharacteristic, complemented
37C2×C5×#102—31no—
38C2×#3964—31no—
39C2×#3948—31no—
40C2×#3942—31no—
41#65060—38no—
42C23×C5×D3—21no—
43C23×C3×D5D411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C2×Dic30—21no—
48C2×Dic30—22no—
49C2×Dic30C2×C414yescomplemented
50C2×Dic30C2312yes—
51C2×C5×D12—21no—
52C2×C5×D12—22no—
53C2×C5×D12C2×C414yescomplemented
54C2×C5×D12C2312yes—
55C22×C3×Dic5—21no—
56C22×C3×Dic5D411yescharacteristic
57C2×C3×C4×D5—24no—
58C2×C3×C4×D5—44no—
59C2×C3×C4×D5C2×C414yes—
60C2×C3×C4×D5D412yes—
61C2×C3×C4×D5D414yes—
62C2×C3×C4×D5C2312yes—
63C2×#1201—28no—
64C2×#1201—24no—
65C2×D3×Dic5—28no—
66C2×D3×Dic5—24no—
67#6772—216no—
68#6772—28no—
69#6772C2×C4116yescomplemented
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C2×C3⋊#168—22no—
73C2×C3⋊#168C2312yes—
74C2×C5×C3⋊C8—22no—
75C2×C5×C3⋊C8C2312yes—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5C2312yes—
78C3×#683—24no—
79#6649—28no—
80C22×#235—51no—
81C22×C3×C4⋊C4—51no—
82C22×#208—51no—
83C2×#810—51no—
84C2×#810—51no—
85#4966—58no—
86C2×#809—51no—
87C2×#809D511yescharacteristic, complemented
88C22×C5×D4—31no—
89C22×C22⋊D5—61no—
90C23×Dic5—61no—
91C2×#711—38no—
92C2×#711—34no—
93C2×#711—64no—
94C2×#711—62no—
95C22×C4×D5—21no—
96C22×C4×D5C2×D311yescharacteristic
97C22×Dic10—31no—
98C22×C5×C8—31no—
99C2×C5×C4⋊C4C2×D311yescharacteristic
100C2×C4⋊Dic5C2×D311yescharacteristic
101C2×#683—21no—
102C22×#168—31no—
103C2×#676—34no—
104C2×#676—64no—
105D5×C4⋊C4—22no—
106D5×C4⋊C4C2×D314yescomplemented
107C5×#102—34no—
108#3964—34no—
109#3948—34no—
110#3942—34no—
111C2×#417—151noSylow
112C23×C3×C5C2×D411yescharacteristic
113C22×C5×D3—24no—
114C22×C5×D3—22no—
115C22×C5×D3—42no—
116C22×C5×D3—42no—
117C22×C3×D5—22no—
118C22×C3×D5—22no—
119C22×C3×D5C22⋊C414yes—
120C22×C3×D5C2×D412yes—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—42no—
123C2×C3×C4×C5C22×C412yes—
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2411yescharacteristic
127C2×Dic15—24no—
128C2×Dic15—22no—
129Dic30—24no—
130Dic30—22no—
131Dic30C22×C414yescomplemented
132C5×D12—24no—
133C5×D12—22no—
134C5×D12C22×C414yescomplemented
135C2×C3×Dic5—22no—
136C2×C3×Dic5—42no—
137C2×C3×Dic5C22⋊C414yes—
138C2×C3×Dic5C2×D412yes—
139C3×C4×D5—48no—
140C3×C4×D5C22⋊C418yes—
141C3×C4×D5C22×C414yes—
142C3×C4×D5C2×D414yes—
143#1201—216no—
144D3×Dic5—216no—
145C3⋊#168—22no—
146C5×C3⋊C8—22no—
147C23×C3×C4—51no—
148C23×C3×C4—101no—
149C22×#67—101no—
150C2×#235—58no—
151C2×#235—54no—
152C2×#235—104no—
153C2×#235—102no—
154C22×D12C2×D511yescharacteristic
155C22×C4×D3—101no—
156C22×Dic6—51no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C4⋊C4—54no—
159C2×C3×C4⋊C4—102no—
160C2×C3×C4⋊C4—101no—
161C2×C3×C4⋊C4C2×D511yescharacteristic
162C2×#208—54no—
163C2×#208—104no—
164C22×C3⋊C8—51no—
165C22×C3⋊C8C2×D511yescharacteristic
166#810—54no—
167#810—54no—
168#809—54no—
169#809C2×D514yescomplemented
170C24×C5—61no—
171C23×D5#6711yescharacteristic
172C2×C5×D4—34no—
173C2×C5×D4—32no—
174C2×C5×D4—62no—
175C2×C5×D4—61no—
176C22×C4×C5—21no—
177C22×C4×C5C22×D311yescharacteristic
178C2×C22⋊D5—68no—
179C2×C22⋊D5—64no—
180C22×Dic5—21no—
181C22×Dic5—61no—
182C22×Dic5—68no—
183C22×Dic5—64no—
184C22×Dic5#6711yescharacteristic
185#711—316no—
186#711—616no—
187#711—68no—
188C2×C4×D5—24no—
189C2×C4×D5—44no—
190C2×C4×D5C4×D314yes—
191C2×C4×D5D1214yes—
192C2×C4×D5#6712yes—
193C2×C4×D5C22×D312yes—
194C2×Dic10—34no—
195C2×Dic10—32no—
196C2×Dic10—62no—
197C2×Dic10—61no—
198C2×C5×C8—32no—
199C2×C5×C8—62no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4C22×D312yes—
202C4⋊Dic5—21no—
203C4⋊Dic5C22×D312yes—
204#683—24no—
205C2×#168—32no—
206C2×#168—62no—
207#676—68no—
208C22×#41—151no—
209C22×M16—151no—
210C22×C4⋊C4—51no—
211#417—158no—
212C2×#103—151no—
213C2×#103—151no—
214C2×#102—31no—
215C2×#102—151no—
216C22×C3×C5C2×C22⋊C412yes—
217C22×C3×C5AGL(1,ℤ/8)12yes—
218C22×C3×C5#13712yes—
219C22×C3×C5C22×D411yescharacteristic
220C2×C5×D3—24no—
221C2×C5×D3—42no—
222C2×C5×D3—42no—
223C2×C5×D3—48no—
224C2×C3×D5—22no—
225C2×C3×D5—22no—
226C2×C3×D5—28no—
227C2×C3×D5C2×C22⋊C414yes—
228C3×C4×C5—42no—
229C3×C4×C5C2×C22⋊C412yes—
230C3×C4×C5C23×C411yescharacteristic
231C3×C4×C5C22×D411yescharacteristic
232Dic15—24no—
233C3×Dic5—42no—
234C3×Dic5C2×C22⋊C414yes—
235C24×C3—51no—
236C23×D3—21no—
237C22×C3×C4—21no—
238C22×C3×C4—51no—
239C22×C3×C4—54no—
240C22×C3×C4—54no—
241C22×C3×C4—52no—
242C22×C3×C4—52no—
243C22×C3×C4—104no—
244C22×C3×C4—101no—
245C22×C3×C4—204no—
246C22×C3×C4C22×D511yescharacteristic
247C2×#67—104no—
248C2×#67—108no—
249C22×Dic3—101no—
250#235—516no—
251#235—108no—
252#235—1016no—
253C2×D12—22no—
254C2×D12—21no—
255C2×D12C4×D514yescomplemented
256C2×D12C22×D512yes—
257C2×C4×D3—104no—
258C2×C4×D3—108no—
259C2×Dic6—54no—
260C2×Dic6—52no—
261C2×Dic6—102no—
262C2×Dic6—101no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—52no—
265C3×C4⋊C4—104no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4C22×D512yes—
268#208—108no—
269C2×C3⋊C8—22no—
270C2×C3⋊C8—52no—
271C2×C3⋊C8—102no—
272C2×C3⋊C8C22×D512yes—
273C23×C5—64no—
274C23×C5—62no—
275C23×C5—122no—
276C23×C5—122no—
277C23×C5C2×#6711yescharacteristic
278C22×D5—22no—
279C22×D5—22no—
280C22×D5(C2×D3)⋊C414yes—
281C22×D5C2×#6712yes—
282C5×D4—34no—
283C5×D4—64no—
284C5×D4—62no—
285C2×C4×C5—22no—
286C2×C4×C5—42no—
287C2×C4×C5C2×C4×D312yes—
288C2×C4×C5C2×D1212yes—
289C2×C4×C5C2×#6711yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—616no—
292C2×Dic5—22no—
293C2×Dic5—42no—
294C2×Dic5—64no—
295C2×Dic5—62no—
296C2×Dic5—616no—
297C2×Dic5(C2×D3)⋊C414yes—
298C2×Dic5C2×#6712yes—
299C4×D5—48no—
300C4×D5(C2×D3)⋊C418yes—
301C4×D5C2×C4×D314yes—
302C4×D5C2×D1214yes—
303Dic10—34no—
304Dic10—64no—
305Dic10—62no—
306C5×C8—62no—
307#168—62no—
308C2×#41—154no—
309C2×#41—158no—
310C2×#41—304no—
311C2×#41—302no—
312C22×Q8—151no—
313C22×D4—31no—
314C22×D4—301no—
315C23×C4—51no—
316C23×C4—101no—
317C23×C4—301no—
318C2×M16—154no—
319C2×M16—304no—
320C22×C8—31no—
321C22×C8—151no—
322C2×C4⋊C4—51no—
323C2×C4⋊C4—54no—
324C2×C4⋊C4—102no—
325C2×C4⋊C4—101no—
326C2×C4⋊C4D3×D511yescharacteristic
327#103—154no—
328#103—154no—
329#102—34no—
330#102—154no—
331C2×C3×C5#41714yescomplemented
332C2×C3×C5C22×C22⋊C411yescharacteristic
333C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
334C2×C3×C5C2×#13711yescharacteristic
335C3×D5—24no—
336C5×D3—44no—
337C23×C3—52no—
338C23×C3—54no—
339C23×C3—102no—
340C23×C3—102no—
341C23×C3D4×D511yescharacteristic
342C22×D3—22no—
343C22×D3—24no—
344C22×D3—42no—
345C22×D3—42no—
346C2×C3×C4—22no—
347C2×C3×C4—42no—
348C2×C3×C4—52no—
349C2×C3×C4—54no—
350C2×C3×C4—54no—
351C2×C3×C4—54no—
352C2×C3×C4—58no—
353C2×C3×C4—102no—
354C2×C3×C4—208no—
355C2×C3×C4—202no—
356C2×C3×C4C2×C4×D512yes—
357C2×C3×C4D4×D512yes—
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4C23×D511yescharacteristic
360#67—1016no—
361C2×Dic3—102no—
362C2×Dic3—104no—
363D12—22no—
364D12—24no—
365D12C2×C4×D514yescomplemented
366C4×D3—1016no—
367Dic6—54no—
368Dic6—102no—
369Dic6—104no—
370C3⋊C8—22no—
371C3⋊C8—102no—
372C22×C5—64no—
373C22×C5—128no—
374C22×C5—122no—
375C22×C5—122no—
376C22×C5C2×(C2×D3)⋊C412yes—
377C22×C5#93212yes—
378C22×C5#94212yes—
379C22×C5C22×#6711yescharacteristic
380C2×D5—28no—
381C2×D5—22no—
382C2×D5—22no—
383C2×D5C2×(C2×D3)⋊C414yes—
384C4×C5—42no—
385C4×C5C2×(C2×D3)⋊C412yes—
386C4×C5C22×C4×D311yescharacteristic
387C4×C5C22×D1211yescharacteristic
388Dic5—42no—
389Dic5—64no—
390Dic5C2×(C2×D3)⋊C414yes—
391C24—51no—
392C24—61no—
393#41—1516no—
394#41—3016no—
395#41—308no—
396C2×Q8—154no—
397C2×Q8—152no—
398C2×Q8—302no—
399C2×Q8—301no—
400C2×D4—34no—
401C2×D4—32no—
402C2×D4—62no—
403C2×D4—61no—
404C2×D4—308no—
405C2×D4—304no—
406C22×C4—21no—
407C22×C4—51no—
408C22×C4—54no—
409C22×C4—54no—
410C22×C4—52no—
411C22×C4—52no—
412C22×C4—104no—
413C22×C4—101no—
414C22×C4—204no—
415C22×C4—308no—
416C22×C4—304no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419M16—308no—
420C2×C8—32no—
421C2×C8—62no—
422C2×C8—152no—
423C2×C8—302no—
424C4⋊C4—21no—
425C4⋊C4—52no—
426C4⋊C4—104no—
427C4⋊C4—101no—
428C4⋊C4C2×D3×D512yes—
429C3×C5C2×#41711yescharacteristic, complemented, Hall
430C22×C3—54no—
431C22×C3—108no—
432C22×C3—102no—
433C22×C3—102no—
434C22×C3D5×C22⋊C412yes—
435C22×C3#405712yes—
436C22×C3#406112yes—
437C22×C3C2×D4×D511yescharacteristic
438C2×D3—24no—
439C2×D3—48no—
440C2×D3—42no—
441C2×D3—42no—
442C3×C4—42no—
443C3×C4—54no—
444C3×C4—202no—
445C3×C4D5×C22⋊C412yes—
446C3×C4C22×C4×D511yescharacteristic
447C3×C4C2×D4×D511yescharacteristic
448Dic3—104no—
449C2×C5—124no—
450C2×C5#496614yescomplemented
451C2×C5C22×(C2×D3)⋊C411yescharacteristic
452C2×C5C2×#93211yescharacteristic
453C2×C5C2×#94211yescharacteristic
454D5—24no—
455C23—54no—
456C23—52no—
457C23—64no—
458C23—62no—
459C23—102no—
460C23—102no—
461C23—122no—
462C23—122no—
463C23D5×#6711yescharacteristic
464Q8—154no—
465Q8—304no—
466Q8—302no—
467D4—34no—
468D4—64no—
469D4—62no—
470D4—3016no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—54no—
474C2×C4—52no—
475C2×C4—58no—
476C2×C4—54no—
477C2×C4—54no—
478C2×C4—102no—
479C2×C4—208no—
480C2×C4—202no—
481C2×C4—3016no—
482C2×C4—304no—
483C2×C4—302no—
484C2×C4C4×D3×D512yes—
485C2×C4D5×D1212yes—
486C2×C4D5×#6711yescharacteristic
487C2×C4C22×D3×D511yescharacteristic
488C8—62no—
489C8—302no—
490C2×C3—104no—
491C2×C3#6506014yescomplemented
492C2×C3C2×D5×C22⋊C411yescharacteristic
493C2×C3C2×#405711yescharacteristic
494C2×C3C2×#406111yescharacteristic
495D3—44no—
496C5C2×#496611yescharacteristic, complemented, Sylow
497C22—54no—
498C22—64no—
499C22—102no—
500C22—108no—
501C22—102no—
502C22—122no—
503C22—128no—
504C22—122no—
505C22D5×(C2×D3)⋊C412yes—
506C22#9148912yes—
507C22#9151312yes—
508C22C2×D5×#6711yescharacteristic
509C4—42no—
510C4—54no—
511C4—202no—
512C4—304no—
513C4D5×(C2×D3)⋊C412yes—
514C4C2×C4×D3×D511yescharacteristic
515C4C2×D5×D1211yescharacteristic
516C3C2×#6506011yescharacteristic, complemented, Sylow
517C2—104no—
518C2—124no—
519C2#1174749814yesdirect product factor
520C2C2×D5×(C2×D3)⋊C411yescharacteristic
521C2C2×#9148911yescharacteristic
522C2C2×#9151311yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6772C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#417
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×C4⋊C4C2semidirect
3. C22×#6649C2semidirect
4. C2×#91094C2semidirect
5. C2×C5×#809C2semidirect
6. C2×#90974C2semidirect
7. C2×#90966C2semidirect
8. #11747498C2direct (N × H)
18. C2×#6772C4semidirect
26. C3×D5×C4⋊C4C22semidirect
28. C2×#6649C22semidirect
29. #91094C22semidirect
30. C5×#809C22semidirect
31. #90974C22semidirect
32. #90966C22semidirect
36. C2×D5×C4⋊C4D3semidirect
49. C2×Dic30C2×C4semidirect
53. C2×C5×D12C2×C4semidirect
69. #6772C2×C4semidirect
87. C2×#809D5semidirect
106. D5×C4⋊C4C2×D3semidirect
131. Dic30C22×C4semidirect
134. C5×D12C22×C4semidirect
169. #809C2×D5semidirect
255. C2×D12C4×D5semidirect
331. C2×C3×C5#417semidirect
365. D12C2×C4×D5semidirect
429. C3×C5C2×#417semidirect
450. C2×C5#4966semidirect
491. C2×C3#65060semidirect
496. C5C2×#4966semidirect
516. C3C2×#65060semidirect
519. C2#11747498direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67722
C2×C3×D5×C4⋊C42
C22×#66492
C2×#910942
C2×C5×#8092
C2×#909742
C2×#909662
#117474982
C2×#650603
C2×#49665