Finite Group Databasebeta

← C2×#11749121 #14427625

Subgroups — C2×#11749121 #14427625

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91827C211yesmaximal, characteristic
2C22×C5×#214C211yesmaximal, characteristic, complemented
3C2×#91383C211yesmaximal, characteristic, complemented
4C22×#6648C211yesmaximal, characteristic, complemented
5C2×C3×#3964C211yesmaximal, characteristic, complemented
6#11749121C218yesmaximal, direct product factor
7C2×#90987C211yesmaximal, characteristic, complemented
8C2×#90973C211yesmaximal, characteristic, complemented
9C2×#65460—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×#1220—21no—
12C22×C4×D15C2211yescharacteristic
13C22×C5×Dic6C2211yescharacteristic
14C2×#6719—21no—
15#91827—22no—
16#91827C2214yes—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C5×#214—24no—
19C2×C5×#214C2214yescomplemented
20C22×C5×C3⋊C8C2211yescharacteristic
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C22×C3×#168C2211yescharacteristic
23C2×#6668—21no—
24C2×#6667—21no—
25#91383—22no—
26#91383C2214yescomplemented
27C2×#6648—24no—
28C2×#6648C2214yescomplemented
29C3×#3964C2214yescomplemented
30#90987C2214yescomplemented
31#90973C2214yescomplemented
32C2×#4778—51nomaximal, Hall
33C22×C5×SD16—31no—
34C2×#4092—31no—
35C2×#4084—31no—
36C22×C8×D5—31no—
37C2×#3967—31no—
38C2×#3964D311yescharacteristic, complemented
39#65460—38no—
40C2×#3949—31no—
41C24×C3×C5—21no—
42C23×D15D411yescharacteristic
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—22no—
46C2×C3×C5×D4C2312yes—
47C22×C3×C4×C5C2311yescharacteristic
48C2×#1220—24no—
49C2×#1220—44no—
50C22×Dic15—21no—
51C22×Dic15D411yescharacteristic
52C2×C4×D15—22no—
53C2×C4×D15—22no—
54C2×C4×D15D412yes—
55C2×C4×D15C2312yes—
56C22×C5×Dic3—21no—
57C2×C5×Dic6—22no—
58C2×C5×Dic6—22no—
59C2×C5×Dic6—21no—
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5—21no—
62#6719—24no—
63C4⋊Dic15—21no—
64C4⋊Dic15C2312yes—
65C5×#214—28no—
66C2×C5×C3⋊C8D414yescomplemented
67C2×C5×C3⋊C8C2312yes—
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5C2312yes—
70C2×C3×#168—22no—
71C2×C3×#168C2312yes—
72#6668—24no—
73#6667—24no—
74#6648—28no—
75C2×#938—51no—
76C22×#214D511yescharacteristic, complemented
77C22×D3×C8—51no—
78C2×#897—51no—
79C2×C3×#102—51no—
80C2×#816—51no—
81C2×#808—51no—
82#4778—58no—
83C22×C5×Q8—31no—
84C22×C5×D4C2×D311yescharacteristic
85C22×C22⋊D5—61no—
86C22×C4×D5—31no—
87C2×C5×SD16—34no—
88C2×C5×SD16—64no—
89C22×C5×C8—31no—
90C2×C22⋊Dic5—61no—
91#4092—34no—
92#4092—62no—
93#4084—34no—
94#4084—62no—
95C2×#685—61no—
96C2×C4⋊Dic5—31no—
97C2×C4⋊Dic5C2×D311yescharacteristic
98C2×#683—61no—
99C22×#168C2×D311yescharacteristic
100C2×C8×D5—34no—
101C2×C8×D5—64no—
102#3967—34no—
103#3964C2×D314yescomplemented
104#3949—34no—
105C2×#465—151noSylow
106C23×C3×C5—22no—
107C23×C3×C5—42no—
108C23×C3×C5—42no—
109C23×C3×C5—42no—
110C23×C3×C5C2×D411yescharacteristic
111C22×D15—22no—
112C22×D15—22no—
113C22×D15SD1614yescomplemented
114C22×D15C2×D412yes—
115C3×C5×D4—22no—
116C3×C5×D4—22no—
117C3×C5×D4—42no—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D412yes—
120C2×C3×C4×C5#4112yes—
121C2×C3×C4×C5C2411yescharacteristic
122#1220—48no—
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15—42no—
126C2×Dic15C2×D412yes—
127C4×D15—24no—
128C4×D15—22no—
129C4×D15—22no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—42no—
132C5×Dic6—22no—
133C5×Dic6—22no—
134C5×Dic6—42no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—42no—
137C3×#168—22no—
138C5×C3⋊C8C2×D414yescomplemented
139C22×C3×D4C2×D511yescharacteristic
140C22×#67—101no—
141C22×C4×D3—51no—
142C22×Dic6C2×D511yescharacteristic
143C22×C3×C8—51no—
144C2×C3×C4⋊C4—51no—
145C2×#217—101no—
146#938—54no—
147#938—102no—
148C2×#214—24no—
149C2×#214C2×D514yescomplemented
150C2×(C2×D3)⋊C4—101no—
151C2×C4⋊Dic3—51no—
152C2×C4⋊Dic3—101no—
153C22×C3⋊C8C2×D511yescharacteristic
154C2×D3×C8—54no—
155C2×D3×C8—104no—
156#897—54no—
157#897—102no—
158C3×#102—54no—
159#816—54no—
160#808—54no—
161C24×C5—21no—
162C23×D5—31no—
163C2×C5×Q8—32no—
164C2×C5×Q8—61no—
165C2×C5×Q8—62no—
166C2×C5×Q8—62no—
167C2×C5×D4—22no—
168C2×C5×D4—22no—
169C2×C5×D4—21no—
170C2×C5×D4C22×D312yes—
171C22×C4×C5—61no—
172C22×C4×C5C22×D311yescharacteristic
173C2×C22⋊D5—64no—
174C2×C22⋊D5—124no—
175C22×Dic5—21no—
176C22×Dic5—31no—
177C22×Dic5—61no—
178C2×C4×D5—32no—
179C2×C4×D5—32no—
180C2×C4×D5—62no—
181C2×C4×D5—62no—
182C5×SD16—68no—
183C2×C5×C8—34no—
184C2×C5×C8—32no—
185C22⋊Dic5—64no—
186#685—64no—
187C4⋊Dic5—21no—
188C4⋊Dic5—32no—
189C4⋊Dic5—61no—
190C4⋊Dic5C22×D312yes—
191#683—64no—
192C2×#168—22no—
193C2×#168C22×D312yes—
194C8×D5—68no—
195C22×SD16—31no—
196C23×C8—151no—
197C2×C22⋊Q8—151no—
198C2×#121—151no—
199#465—158no—
200C2×#106—151no—
201C2×#103—151no—
202C2×#102—51no—
203C22×C3×C5—42no—
204C22×C3×C5—42no—
205C22×C3×C5—42no—
206C22×C3×C5—84no—
207C22×C3×C5#12112yes—
208C22×C3×C5C2×SD1612yes—
209C22×C3×C5#13512yes—
210C22×C3×C5C22×D411yescharacteristic
211C2×D15—22no—
212C2×D15—22no—
213C2×D15—28no—
214C2×D15C2×SD1614yescomplemented
215C3×C4×C5#12112yes—
216C3×C4×C5C22×D411yescharacteristic
217C3×C4×C5C2×#4111yescharacteristic
218Dic15—22no—
219Dic15—42no—
220C3×Dic5—42no—
221C5×Dic3—42no—
222C24×C3—21no—
223C23×D3—51no—
224C2×C3×D4—21no—
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4C22×D512yes—
228C22×C3×C4—101no—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—104no—
231C2×#67—204no—
232C22×Dic3—21no—
233C22×Dic3—51no—
234C22×Dic3—101no—
235C2×C4×D3—52no—
236C2×C4×D3—52no—
237C2×C4×D3—102no—
238C2×C4×D3—102no—
239C2×Dic6—22no—
240C2×Dic6—22no—
241C2×Dic6—21no—
242C2×Dic6C22×D512yes—
243C2×C3×C8—52no—
244C2×C3×C8—102no—
245C3×C4⋊C4—52no—
246C3×C4⋊C4—101no—
247#217—104no—
248#214—28no—
249(C2×D3)⋊C4—104no—
250C4⋊Dic3—52no—
251C4⋊Dic3—104no—
252C4⋊Dic3—101no—
253C2×C3⋊C8C22⋊D514yescomplemented
254C2×C3⋊C8C22×D512yes—
255D3×C8—108no—
256C23×C5—22no—
257C23×C5—42no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5D3×D411yescharacteristic
261C22×D5—34no—
262C22×D5—32no—
263C22×D5—62no—
264C22×D5—62no—
265C5×Q8—62no—
266C5×Q8—62no—
267C5×Q8—122no—
268C5×D4—22no—
269C5×D4—22no—
270C5×D4—42no—
271C2×C4×C5—62no—
272C2×C4×C5—122no—
273C2×C4×C5#23512yes—
274C2×C4×C5D3×D412yes—
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5C23×D311yescharacteristic
277C22⋊D5—128no—
278C2×Dic5—22no—
279C2×Dic5—32no—
280C2×Dic5—42no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5—122no—
284C4×D5—64no—
285C4×D5—62no—
286C4×D5—62no—
287C5×C8—34no—
288#168—22no—
289C22×Q8—31no—
290C22×D4—301no—
291C22×D4D3×D511yescharacteristic
292C23×C4—151no—
293C2×SD16—34no—
294C2×SD16—64no—
295C22×C8—31no—
296C22×C8—51no—
297C22×C8—154no—
298C22×C8—304no—
299C22⋊Q8—154no—
300C22⋊Q8—302no—
301#121—154no—
302#121—302no—
303C2×C4⋊C4—51no—
304C2×C4⋊C4—151no—
305C2×C4⋊C4—301no—
306C2×C22⋊C4—301no—
307C2×C22⋊C4—301no—
308#106—154no—
309#103—154no—
310#102—54no—
311C2×C3×C5—82no—
312C2×C3×C5#46514yescomplemented
313C2×C3×C5C2×#12111yescharacteristic
314C2×C3×C5C22×SD1611yescharacteristic
315C2×C3×C5C2×#13511yescharacteristic
316D15—24no—
317C23×C3—22no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3D4×D511yescharacteristic
322C22×D3—52no—
323C22×D3—54no—
324C22×D3—102no—
325C22×D3—102no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—42no—
329C2×C3×C4—102no—
330C2×C3×C4—202no—
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4#71112yes—
333C2×C3×C4C2×C22⋊D512yes—
334C2×C3×C4C23×D511yescharacteristic
335#67—208no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3—52no—
339C2×Dic3—102no—
340C2×Dic3—102no—
341C2×Dic3—202no—
342C4×D3—102no—
343C4×D3—102no—
344C4×D3—104no—
345Dic6—22no—
346Dic6—22no—
347Dic6—42no—
348C3×C8—102no—
349C3⋊C8C2×C22⋊D514yescomplemented
350C22×C5—42no—
351C22×C5—42no—
352C22×C5—42no—
353C22×C5—84no—
354C22×C5#88412yes—
355C22×C5#91212yes—
356C22×C5D3×SD1612yes—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—34no—
359C2×D5—62no—
360C2×D5—62no—
361C2×D5—68no—
362C4×C5—122no—
363C4×C5#88412yes—
364C4×C5C2×#23511yescharacteristic
365C4×C5C2×D3×D411yescharacteristic
366Dic5—42no—
367Dic5—62no—
368Dic5—122no—
369C24—21no—
370C24—151no—
371C2×Q8—32no—
372C2×Q8—61no—
373C2×Q8—62no—
374C2×Q8—62no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—304no—
379C2×D4—604no—
380C2×D4C2×D3×D512yes—
381C22×C4—61no—
382C22×C4—101no—
383C22×C4—151no—
384C22×C4—152no—
385C22×C4—152no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—301no—
389C22×C4C2×D3×D511yescharacteristic
390SD16—68no—
391C2×C8—34no—
392C2×C8—32no—
393C2×C8—52no—
394C2×C8—102no—
395C2×C8—308no—
396C4⋊C4—52no—
397C4⋊C4—101no—
398C4⋊C4—152no—
399C4⋊C4—304no—
400C4⋊C4—301no—
401C22⋊C4—304no—
402C22⋊C4—304no—
403C3×C5C2×#46511yescharacteristic, complemented, Hall
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—84no—
408C22×C3D5×SD1612yes—
409C22×C3#406212yes—
410C22×C3#408412yes—
411C22×C3C2×D4×D511yescharacteristic
412C2×D3—54no—
413C2×D3—102no—
414C2×D3—102no—
415C2×D3—108no—
416C3×C4—202no—
417C3×C4#408412yes—
418C3×C4C2×#71111yescharacteristic
419C3×C4C22×C22⋊D511yescharacteristic
420Dic3—42no—
421Dic3—102no—
422Dic3—202no—
423C2×C5—82no—
424C2×C5#477814yescomplemented
425C2×C5C2×#88411yescharacteristic
426C2×C5C2×#91211yescharacteristic
427C2×C5C2×D3×SD1611yescharacteristic
428D5—64no—
429C23—22no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—154no—
434C23—152no—
435C23—302no—
436C23—302no—
437C23#679011yescharacteristic
438Q8—62no—
439Q8—62no—
440Q8—122no—
441D4—22no—
442D4—22no—
443D4—42no—
444D4—608no—
445C2×C4—62no—
446C2×C4—102no—
447C2×C4—122no—
448C2×C4—152no—
449C2×C4—202no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—304no—
454C2×C4—302no—
455C2×C4—602no—
456C2×C4#678212yes—
457C2×C4D3×C22⋊D512yes—
458C2×C4#679011yescharacteristic
459C2×C4C22×D3×D511yescharacteristic
460C8—34no—
461C8—102no—
462C2×C3—82no—
463C2×C3#6546014yescomplemented
464C2×C3C2×D5×SD1611yescharacteristic
465C2×C3C2×#406211yescharacteristic
466C2×C3C2×#408411yescharacteristic
467D3—104no—
468C5C2×#477811yescharacteristic, complemented, Sylow
469C22—42no—
470C22—42no—
471C22—42no—
472C22—84no—
473C22—154no—
474C22—308no—
475C22—302no—
476C22—302no—
477C22#9148712yes—
478C22#9149712yes—
479C22#9155712yes—
480C22C2×#679011yescharacteristic
481C4—122no—
482C4—202no—
483C4—302no—
484C4—602no—
485C4#9155712yes—
486C4C2×#678211yescharacteristic
487C4C2×D3×C22⋊D511yescharacteristic
488C3C2×#6546011yescharacteristic, complemented, Sylow
489C2—82no—
490C2—304no—
491C2#1174912114yesdirect product factor
492C2C2×#9148711yescharacteristic
493C2C2×#9149711yescharacteristic
494C2C2×#9155711yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC2×#91827C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#465
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C5×#214C2semidirect
3. C2×#91383C2semidirect
4. C22×#6648C2semidirect
5. C2×C3×#3964C2semidirect
6. #11749121C2direct (N × H)
7. C2×#90987C2semidirect
8. C2×#90973C2semidirect
19. C2×C5×#214C22semidirect
26. #91383C22semidirect
28. C2×#6648C22semidirect
29. C3×#3964C22semidirect
30. #90987C22semidirect
31. #90973C22semidirect
38. C2×#3964D3semidirect
66. C2×C5×C3⋊C8D4semidirect
76. C22×#214D5semidirect
103. #3964C2×D3semidirect
113. C22×D15SD16semidirect
138. C5×C3⋊C8C2×D4semidirect
149. C2×#214C2×D5semidirect
214. C2×D15C2×SD16semidirect
253. C2×C3⋊C8C22⋊D5semidirect
312. C2×C3×C5#465semidirect
349. C3⋊C8C2×C22⋊D5semidirect
403. C3×C5C2×#465semidirect
424. C2×C5#4778semidirect
463. C2×C3#65460semidirect
468. C5C2×#4778semidirect
488. C3C2×#65460semidirect
491. C2#11749121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918272
C22×C5×#2142
C2×#913832
C22×#66482
C2×C3×#39642
#117491212
C2×#909872
C2×#909732
C2×#654603
C2×#47785