Finite Group Databasebeta

← C2×#11748142 #14412518

Subgroups — C2×#11748142 #14412518

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×#6766C211yesmaximal, characteristic
2C22×#6705C211yesmaximal, characteristic, complemented
3C2×#91437C211yesmaximal, characteristic, complemented
4C2×C5×#816C211yesmaximal, characteristic, complemented
5C2×C3×#3953C211yesmaximal, characteristic, complemented
6C2×#90972C211yesmaximal, characteristic, complemented
7C2×#90964C211yesmaximal, characteristic, complemented
8#11748142C218yesmaximal, direct product factor
9C2×#65092—31nomaximal, Hall
10C22×C4×D15C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×D20C2211yescharacteristic
13C22×#1202—21no—
14C22×#1200—21no—
15C22×D5×Dic3—21no—
16C2×#6766—22no—
17C2×#6766—24no—
18C2×#6766C418yescomplemented
19C2×#6766C2214yes—
20C22×C3×C5×C8C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C2×#6705—24no—
23C2×#6705C2214yescomplemented
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×#6669—21no—
27#91437—22no—
28#91437C2214yescomplemented
29C5×#816C2214yescomplemented
30C3×#3953C2214yescomplemented
31#90972C2214yescomplemented
32#90964C2214yescomplemented
33C2×#4771—51nomaximal, Hall
34C22×#713—31no—
35C22×#676—31no—
36C2×D5×C4⋊C4—31no—
37C2×C5×#103—31no—
38C2×#3967—31no—
39C2×#3953D311yescharacteristic, complemented
40C2×#3941—31no—
41#65092—38no—
42C23×D15D411yescharacteristic
43C23×C3×D5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15D411yescharacteristic
46C2×C4×D15C2×C414yes—
47C2×C4×D15D412yes—
48C2×C4×D15D414yes—
49C2×C4×D15C2312yes—
50C22×C5×Dic3—21no—
51C22×C5×Dic3—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6—22no—
54C2×C5×Dic6C2×C414yescomplemented
55C2×C5×Dic6C2312yes—
56C22×C3×Dic5—21no—
57C2×C3×D20—21no—
58C2×C3×D20—22no—
59C2×C3×D20C2×C414yescomplemented
60C2×C3×D20C2312yes—
61C2×#1202—28no—
62C2×#1202—24no—
63C2×#1200—24no—
64C2×#1200—44no—
65C2×D5×Dic3—28no—
66C2×D5×Dic3—24no—
67#6766—216no—
68#6766—28no—
69#6766C2×C4116yescomplemented
70C2×C3×C5×C8—22no—
71C2×C3×C5×C8C2312yes—
72C2×C3⋊#168—22no—
73C2×C3⋊#168C2312yes—
74#6705—28no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yes—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5C2312yes—
79#6669—24no—
80C22×#237—51no—
81C22×ΓL(1,𝔽25)—51no—
82C2×D3×C4⋊C4—51no—
83C2×C3×#102—51no—
84C2×#832—51no—
85C2×#816D511yescharacteristic, complemented
86C2×#810—51no—
87#4771—58no—
88C22×C5×Q8—31no—
89C2×#713—38no—
90C2×#713—34no—
91C2×#713—62no—
92C2×#713—64no—
93C22×D20—61no—
94C22×D20C2×D311yescharacteristic
95C22×C4×D5—31no—
96C22×C4×D5—61no—
97C22×C4×D5—61no—
98C22×C5×C8C2×D311yescharacteristic
99C2×C5×C4⋊C4—31no—
100C2×C4⋊Dic5C2×D311yescharacteristic
101C2×#683—61no—
102C22×#168—31no—
103C2×#676—34no—
104C2×#676—64no—
105D5×C4⋊C4—34no—
106D5×C4⋊C4—62no—
107C5×#103—34no—
108#3967—34no—
109#3953C2×D314yescomplemented
110#3941—34no—
111C2×#417—151noSylow
112C23×C3×C5C2×D411yescharacteristic
113C22×D15—22no—
114C22×D15—22no—
115C22×D15C22⋊C414yes—
116C22×D15C2×D412yes—
117C22×C3×D5—24no—
118C22×C3×D5—22no—
119C22×C3×D5—42no—
120C22×C3×D5—42no—
121C2×C3×C4×C5C22×C412yes—
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D412yes—
124C2×C3×C4×C5C2411yescharacteristic
125C2×Dic15C22⋊C414yes—
126C2×Dic15C2×D412yes—
127C4×D15C22⋊C418yes—
128C4×D15C22×C414yes—
129C4×D15C2×D414yes—
130C2×C5×Dic3—24no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—42no—
134C5×Dic6—24no—
135C5×Dic6—22no—
136C5×Dic6C22×C414yescomplemented
137C2×C3×Dic5—22no—
138C2×C3×Dic5—42no—
139C3×D20—24no—
140C3×D20—22no—
141C3×D20C22×C414yescomplemented
142#1202—216no—
143#1200—48no—
144D5×Dic3—216no—
145C3×C5×C8—22no—
146C3⋊#168—22no—
147C22×C3×D4—51no—
148C22×#67—101no—
149C23×Dic3—101no—
150C2×#237—58no—
151C2×#237—54no—
152C2×#237—102no—
153C2×#237—104no—
154C22×C4×D3—51no—
155C22×C4×D3—101no—
156C22×Dic6C2×D511yescharacteristic
157C22×C3×C8C2×D511yescharacteristic
158C2×C3×C4⋊C4—51no—
159C2×C4⋊Dic3C2×D511yescharacteristic
160C2×Dic3⋊C4—101no—
161C22×C3⋊C8—51no—
162C2×ΓL(1,𝔽25)—54no—
163C2×ΓL(1,𝔽25)—104no—
164D3×C4⋊C4—54no—
165D3×C4⋊C4—102no—
166C3×#102—54no—
167#832—54no—
168#816C2×D514yescomplemented
169#810—54no—
170C23×D5—21no—
171C23×D5—31no—
172C2×C5×Q8—34no—
173C2×C5×Q8—32no—
174C2×C5×Q8—61no—
175C2×C5×Q8—62no—
176C22×C4×C5—61no—
177C22×C4×C5—61no—
178C22×C4×C5C22×D311yescharacteristic
179C22×Dic5—21no—
180C22×Dic5—31no—
181#713—316no—
182#713—616no—
183#713—68no—
184C2×D20—21no—
185C2×D20—22no—
186C2×D20—68no—
187C2×D20—64no—
188C2×D20C4×D314yescomplemented
189C2×D20C22×D312yes—
190C2×C4×D5—34no—
191C2×C4×D5—32no—
192C2×C4×D5—34no—
193C2×C4×D5—32no—
194C2×C4×D5—68no—
195C2×C4×D5—64no—
196C2×C4×D5—64no—
197C2×C4×D5—124no—
198C2×C5×C8—22no—
199C2×C5×C8C22×D312yes—
200C5×C4⋊C4—32no—
201C5×C4⋊C4—61no—
202C4⋊Dic5—21no—
203C4⋊Dic5C22×D312yes—
204#683—64no—
205C2×#168—32no—
206C2×#168—62no—
207#676—68no—
208C22×#41—151no—
209C22×M16—151no—
210C22×C4⋊C4—151no—
211#417—158no—
212C2×#103—31no—
213C2×#103—151no—
214C2×#102—51no—
215C2×#102—151no—
216C22×C3×C5C2×C22⋊C412yes—
217C22×C3×C5AGL(1,ℤ/8)12yes—
218C22×C3×C5#13712yes—
219C22×C3×C5C22×D411yescharacteristic
220C2×D15—22no—
221C2×D15—22no—
222C2×D15—28no—
223C2×D15C2×C22⋊C414yes—
224C2×C3×D5—24no—
225C2×C3×D5—42no—
226C2×C3×D5—42no—
227C2×C3×D5—48no—
228C3×C4×C5C2×C22⋊C412yes—
229C3×C4×C5C23×C411yescharacteristic
230C3×C4×C5C22×D411yescharacteristic
231Dic15C2×C22⋊C414yes—
232C3×Dic5—42no—
233C5×Dic3—24no—
234C5×Dic3—42no—
235C24×C3—101no—
236C23×D3—51no—
237C2×C3×D4—54no—
238C2×C3×D4—52no—
239C2×C3×D4—101no—
240C2×C3×D4—102no—
241C22×C3×C4—101no—
242C22×C3×C4C22×D511yescharacteristic
243C2×#67—104no—
244C2×#67—108no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—51no—
248C22×Dic3—104no—
249C22×Dic3—108no—
250#237—516no—
251#237—108no—
252#237—1016no—
253C2×C4×D3—54no—
254C2×C4×D3—52no—
255C2×C4×D3—54no—
256C2×C4×D3—52no—
257C2×C4×D3—104no—
258C2×C4×D3—204no—
259C2×Dic6—21no—
260C2×Dic6—22no—
261C2×Dic6C4×D514yescomplemented
262C2×Dic6C22×D512yes—
263C2×C3×C8—22no—
264C2×C3×C8C22×D512yes—
265C3×C4⋊C4—52no—
266C3×C4⋊C4—101no—
267C4⋊Dic3—21no—
268C4⋊Dic3C22×D512yes—
269Dic3⋊C4—104no—
270C2×C3⋊C8—52no—
271C2×C3⋊C8—102no—
272ΓL(1,𝔽25)—108no—
273C23×C5D3×D411yescharacteristic
274C22×D5—24no—
275C22×D5—22no—
276C22×D5—34no—
277C22×D5—32no—
278C22×D5—42no—
279C22×D5—42no—
280C22×D5—62no—
281C22×D5—62no—
282C5×Q8—34no—
283C5×Q8—64no—
284C5×Q8—62no—
285C2×C4×C5—64no—
286C2×C4×C5—62no—
287C2×C4×C5—62no—
288C2×C4×C5—122no—
289C2×C4×C5C2×C4×D312yes—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D412yes—
292C2×C4×C5C23×D311yescharacteristic
293C2×Dic5—22no—
294C2×Dic5—34no—
295C2×Dic5—32no—
296C2×Dic5—42no—
297D20—24no—
298D20—22no—
299D20—616no—
300D20C2×C4×D314yescomplemented
301C4×D5—38no—
302C4×D5—34no—
303C4×D5—34no—
304C4×D5—616no—
305C4×D5—128no—
306C5×C8—22no—
307#168—62no—
308C2×#41—154no—
309C2×#41—158no—
310C2×#41—302no—
311C2×#41—304no—
312C22×Q8—31no—
313C22×D4—51no—
314C22×D4—301no—
315C23×C4—151no—
316C23×C4—301no—
317C23×C4—301no—
318C2×M16—154no—
319C2×M16—304no—
320C22×C8—151no—
321C22×C8D3×D511yescharacteristic
322C2×C4⋊C4—31no—
323C2×C4⋊C4—51no—
324C2×C4⋊C4—154no—
325C2×C4⋊C4—302no—
326C2×C4⋊C4—301no—
327#103—34no—
328#103—154no—
329#102—54no—
330#102—154no—
331C2×C3×C5#41714yescomplemented
332C2×C3×C5C22×C22⋊C411yescharacteristic
333C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
334C2×C3×C5C2×#13711yescharacteristic
335D15—24no—
336C3×D5—44no—
337C23×C3—102no—
338C23×C3—104no—
339C23×C3—202no—
340C23×C3—202no—
341C23×C3D4×D511yescharacteristic
342C22×D3—52no—
343C22×D3—54no—
344C22×D3—102no—
345C22×D3—102no—
346C3×D4—54no—
347C3×D4—102no—
348C3×D4—104no—
349C2×C3×C4—102no—
350C2×C3×C4—202no—
351C2×C3×C4C2×C4×D512yes—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4D4×D512yes—
354C2×C3×C4C23×D511yescharacteristic
355#67—1016no—
356C2×Dic3—22no—
357C2×Dic3—24no—
358C2×Dic3—22no—
359C2×Dic3—42no—
360C2×Dic3—52no—
361C2×Dic3—54no—
362C2×Dic3—1016no—
363C4×D3—54no—
364C4×D3—54no—
365C4×D3—58no—
366C4×D3—208no—
367Dic6—22no—
368Dic6—24no—
369Dic6C2×C4×D514yescomplemented
370C3×C8—22no—
371C3⋊C8—102no—
372C22×C5D3×C22⋊C412yes—
373C22×C5#91112yes—
374C22×C5#91512yes—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—24no—
377C2×D5—34no—
378C2×D5—42no—
379C2×D5—42no—
380C2×D5—48no—
381C2×D5—62no—
382C2×D5—62no—
383C2×D5—68no—
384C4×C5—64no—
385C4×C5—122no—
386C4×C5D3×C22⋊C412yes—
387C4×C5C22×C4×D311yescharacteristic
388C4×C5C2×D3×D411yescharacteristic
389Dic5—34no—
390Dic5—42no—
391C24—101no—
392C24—151no—
393#41—1516no—
394#41—3016no—
395#41—308no—
396C2×Q8—34no—
397C2×Q8—32no—
398C2×Q8—61no—
399C2×Q8—62no—
400C2×D4—54no—
401C2×D4—52no—
402C2×D4—101no—
403C2×D4—102no—
404C2×D4—308no—
405C2×D4—304no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—101no—
409C22×C4—151no—
410C22×C4—154no—
411C22×C4—152no—
412C22×C4—154no—
413C22×C4—152no—
414C22×C4—304no—
415C22×C4—308no—
416C22×C4—304no—
417C22×C4—604no—
418C22×C4C2×D3×D511yescharacteristic
419M16—308no—
420C2×C8—22no—
421C2×C8—152no—
422C2×C8—302no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—32no—
425C4⋊C4—52no—
426C4⋊C4—61no—
427C4⋊C4—101no—
428C4⋊C4—304no—
429C3×C5C2×#41711yescharacteristic, complemented, Hall
430C22×C3—104no—
431C22×C3—202no—
432C22×C3—202no—
433C22×C3—208no—
434C22×C3D5×C22⋊C412yes—
435C22×C3#406012yes—
436C22×C3#406412yes—
437C22×C3C2×D4×D511yescharacteristic
438C2×D3—54no—
439C2×D3—102no—
440C2×D3—102no—
441C2×D3—108no—
442C3×C4—202no—
443C3×C4D5×C22⋊C412yes—
444C3×C4C22×C4×D511yescharacteristic
445C3×C4C2×D4×D511yescharacteristic
446Dic3—24no—
447Dic3—42no—
448Dic3—54no—
449C2×C5#477114yescomplemented
450C2×C5C2×D3×C22⋊C411yescharacteristic
451C2×C5C2×#91111yescharacteristic
452C2×C5C2×#91511yescharacteristic
453D5—44no—
454D5—64no—
455C23—104no—
456C23—102no—
457C23—154no—
458C23—152no—
459C23—202no—
460C23—202no—
461C23—302no—
462C23—302no—
463C23#677711yescharacteristic
464Q8—34no—
465Q8—64no—
466Q8—62no—
467D4—54no—
468D4—104no—
469D4—102no—
470D4—3016no—
471C2×C4—64no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—102no—
475C2×C4—122no—
476C2×C4—154no—
477C2×C4—152no—
478C2×C4—158no—
479C2×C4—154no—
480C2×C4—154no—
481C2×C4—202no—
482C2×C4—3016no—
483C2×C4—608no—
484C2×C4C4×D3×D512yes—
485C2×C4#677711yescharacteristic
486C2×C4#679012yes—
487C2×C4C22×D3×D511yescharacteristic
488C8—22no—
489C8—302no—
490C2×C3—204no—
491C2×C3#6509214yescomplemented
492C2×C3C2×D5×C22⋊C411yescharacteristic
493C2×C3C2×#406011yescharacteristic
494C2×C3C2×#406411yescharacteristic
495D3—104no—
496C5C2×#477111yescharacteristic, complemented, Sylow
497C22—104no—
498C22—154no—
499C22—202no—
500C22—208no—
501C22—202no—
502C22—302no—
503C22—308no—
504C22—302no—
505C22#9125812yes—
506C22#9127812yes—
507C22#9147312yes—
508C22C2×#677711yescharacteristic
509C4—64no—
510C4—122no—
511C4—154no—
512C4—202no—
513C4#9147312yes—
514C4C2×C4×D3×D511yescharacteristic
515C4C2×#679011yescharacteristic
516C3C2×#6509211yescharacteristic, complemented, Sylow
517C2—204no—
518C2—304no—
519C2#1174814214yesdirect product factor
520C2C2×#9125811yescharacteristic
521C2C2×#9127811yescharacteristic
522C2C2×#9147311yescharacteristic
subgroupG/H
centerC23#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×#6766C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#417
LCSG ▷ 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
2. C22×#6705C2semidirect
3. C2×#91437C2semidirect
4. C2×C5×#816C2semidirect
5. C2×C3×#3953C2semidirect
6. C2×#90972C2semidirect
7. C2×#90964C2semidirect
8. #11748142C2direct (N × H)
18. C2×#6766C4semidirect
23. C2×#6705C22semidirect
28. #91437C22semidirect
29. C5×#816C22semidirect
30. C3×#3953C22semidirect
31. #90972C22semidirect
32. #90964C22semidirect
39. C2×#3953D3semidirect
54. C2×C5×Dic6C2×C4semidirect
59. C2×C3×D20C2×C4semidirect
69. #6766C2×C4semidirect
85. C2×#816D5semidirect
109. #3953C2×D3semidirect
136. C5×Dic6C22×C4semidirect
141. C3×D20C22×C4semidirect
168. #816C2×D5semidirect
188. C2×D20C4×D3semidirect
261. C2×Dic6C4×D5semidirect
300. D20C2×C4×D3semidirect
331. C2×C3×C5#417semidirect
369. Dic6C2×C4×D5semidirect
429. C3×C5C2×#417semidirect
449. C2×C5#4771semidirect
491. C2×C3#65092semidirect
496. C5C2×#4771semidirect
516. C3C2×#65092semidirect
519. C2#11748142direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67662
C22×#67052
C2×#914372
C2×C5×#8162
C2×C3×#39532
C2×#909722
C2×#909642
#117481422
C2×#650923
C2×#47715