Finite Group Databasebeta

← C2×#11748158 #14423545

Subgroups — C2×#11748158 #14423545

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6768C211yesmaximal, characteristic
2C22×C5×#204C211yesmaximal, characteristic, complemented
3C2×#91383C211yesmaximal, characteristic, complemented
4C22×#6661C211yesmaximal, characteristic, complemented
5C2×#91104C211yesmaximal, characteristic, complemented
6C2×C3×#3948C211yesmaximal, characteristic, complemented
7C2×#90966C211yesmaximal, characteristic, complemented
8#11748158C218yesmaximal, direct product factor
9C2×#65462—31nomaximal, Hall
10C22×C4×D15C2211yescharacteristic
11C22×C5×D12C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×#1203—21no—
15C22×D3×Dic5—21no—
16C2×#6768—22no—
17C2×#6768—24no—
18C2×#6768—24no—
19C2×#6768C2214yes—
20C22×C3×C5×C8C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C2×C5×#204—24no—
23C2×C5×#204C2214yescomplemented
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×#6668—21no—
26C2×#6667—21no—
27#91383—22no—
28#91383C2214yescomplemented
29C2×#6661—24no—
30C2×#6661C2214yescomplemented
31#91104C2214yescomplemented
32C3×#3948C2214yescomplemented
33#90966C2214yescomplemented
34C2×#4808—51nomaximal, Hall
35C22×#711—31no—
36C22×C5×SD16—31no—
37C2×#4092—31no—
38C22×#689—31no—
39C2×#3964—31no—
40#65462—38no—
41C2×#3952—31no—
42C2×#3948D311yescharacteristic, complemented
43C23×D15D411yescharacteristic
44C23×C5×D3—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15D411yescharacteristic
47C2×C4×D15—22no—
48C2×C4×D15—22no—
49C2×C4×D15D412yes—
50C2×C4×D15C2312yes—
51C22×C5×Dic3—21no—
52C2×C5×D12—21no—
53C2×C5×D12—22no—
54C2×C5×D12D414yes—
55C2×C5×D12C2312yes—
56C2×C5×Dic6—22no—
57C2×C5×Dic6—22no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6C2312yes—
60C22×C3×Dic5—21no—
61C22×C3×Dic5—21no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—22no—
64C2×C3×Dic10D414yes—
65C2×C3×Dic10C2312yes—
66C2×#1203—28no—
67C2×#1203—24no—
68C2×D3×Dic5—28no—
69C2×D3×Dic5—24no—
70#6768—216no—
71#6768—28no—
72#6768—28no—
73C2×C3×C5×C8—22no—
74C2×C3×C5×C8C2312yes—
75C2×C3⋊#168—22no—
76C2×C3⋊#168C2312yes—
77C5×#204—28no—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80#6668—24no—
81#6667—24no—
82#6661—28no—
83C22×#239—51no—
84C22×#216—51no—
85C22×#204D511yescharacteristic, complemented
86C2×#897—51no—
87C2×C3×#103—51no—
88C2×(C2×D3)⋊C8—51no—
89C2×#809—51no—
90#4808—58no—
91C22×C5×Q8—31no—
92C22×C5×D4—31no—
93C22×C22⋊D5—61no—
94C23×Dic5—61no—
95C2×#711—34no—
96C2×#711—62no—
97C2×#711—64no—
98C2×#711—64no—
99C22×C4×D5—31no—
100C22×Dic10C2×D311yescharacteristic
101C2×C5×SD16—34no—
102C2×C5×SD16—64no—
103C22×C5×C8C2×D311yescharacteristic
104#4092—34no—
105#4092—62no—
106C2×#689—34no—
107C2×#689—64no—
108C2×#685—61no—
109C2×C4⋊Dic5C2×D311yescharacteristic
110C2×#683—61no—
111C22×#168—31no—
112#3964—34no—
113#3952—34no—
114#3948C2×D314yescomplemented
115C2×#452—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15—22no—
120C22×D15C2×D412yes—
121C22×C5×D3—24no—
122C22×C5×D3—22no—
123C22×C5×D3—42no—
124C22×C5×D3—42no—
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15—22no—
130C2×Dic15C2×D412yes—
131C4×D15—24no—
132C4×D15—22no—
133C4×D15—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—42no—
136C5×D12—24no—
137C5×D12—22no—
138C5×D12C2×D414yes—
139C5×Dic6—22no—
140C5×Dic6—22no—
141C5×Dic6—42no—
142C2×C3×Dic5—24no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—42no—
146C3×Dic10—24no—
147C3×Dic10—22no—
148C3×Dic10C2×D414yes—
149#1203—216no—
150D3×Dic5—216no—
151C3×C5×C8—22no—
152C3⋊#168—22no—
153C22×C3×Q8—51no—
154C2×#239—54no—
155C2×#239—102no—
156C2×#239—104no—
157C2×#239—104no—
158C22×D12—101no—
159C22×D12C2×D511yescharacteristic
160C22×C4×D3—51no—
161C22×C4×D3—101no—
162C22×Dic6C2×D511yescharacteristic
163C22×C3×C8C2×D511yescharacteristic
164C2×C3×C4⋊C4—51no—
165C2×#216—54no—
166C2×#216—104no—
167C2×(C2×D3)⋊C4—101no—
168C2×C4⋊Dic3—101no—
169C22×C3⋊C8—51no—
170C2×#204—24no—
171C2×#204C2×D514yescomplemented
172#897—54no—
173#897—102no—
174C3×#103—54no—
175(C2×D3)⋊C8—54no—
176#809—54no—
177C24×C5—61no—
178C23×D5—31no—
179C2×C5×Q8—32no—
180C2×C5×Q8—61no—
181C2×C5×Q8—62no—
182C2×C5×Q8—62no—
183C2×C5×D4—34no—
184C2×C5×D4—32no—
185C2×C5×D4—62no—
186C2×C5×D4—61no—
187C22×C4×C5—61no—
188C22×C4×C5C22×D311yescharacteristic
189C2×C22⋊D5—64no—
190C2×C22⋊D5—68no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—31no—
194C22×Dic5—64no—
195C22×Dic5—68no—
196#711—68no—
197#711—616no—
198#711—68no—
199C2×C4×D5—32no—
200C2×C4×D5—32no—
201C2×C4×D5—62no—
202C2×C4×D5—62no—
203C2×Dic10—21no—
204C2×Dic10—22no—
205C2×Dic10D1214yes—
206C2×Dic10C22×D312yes—
207C5×SD16—68no—
208C2×C5×C8—22no—
209C2×C5×C8C22×D312yes—
210#689—68no—
211#685—64no—
212C4⋊Dic5—21no—
213C4⋊Dic5C22×D312yes—
214#683—64no—
215C2×#168—32no—
216C2×#168—62no—
217C22×#41—151no—
218C22×Q16—151no—
219C22×SD16—31no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—51no—
223C2×#102—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5#12012yes—
226C22×C3×C5#13512yes—
227C22×C3×C5#13712yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×D15—22no—
230C2×D15—22no—
231C2×D15—22no—
232C2×D15—44no—
233C2×C5×D3—24no—
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C2×C5×D3—48no—
237C3×C4×C5#12012yes—
238C3×C4×C5C22×D411yescharacteristic
239C3×C4×C5C22×D411yescharacteristic
240Dic15—22no—
241C3×Dic5—24no—
242C3×Dic5—42no—
243C5×Dic3—42no—
244C23×D3—21no—
245C23×D3—51no—
246C2×C3×Q8—54no—
247C2×C3×Q8—52no—
248C2×C3×Q8—101no—
249C2×C3×Q8—102no—
250C22×C3×C4—101no—
251C22×C3×C4—101no—
252C22×C3×C4C22×D511yescharacteristic
253C22×Dic3—21no—
254C22×Dic3—51no—
255#239—108no—
256#239—1016no—
257#239—108no—
258C2×D12—22no—
259C2×D12—21no—
260C2×D12—104no—
261C2×D12—108no—
262C2×D12C22⋊D514yes—
263C2×D12C22×D512yes—
264C2×C4×D3—52no—
265C2×C4×D3—52no—
266C2×C4×D3—104no—
267C2×C4×D3—108no—
268C2×C4×D3—102no—
269C2×C4×D3—102no—
270C2×Dic6—22no—
271C2×Dic6—22no—
272C2×Dic6—21no—
273C2×Dic6C22×D512yes—
274C2×C3×C8—22no—
275C2×C3×C8C22×D512yes—
276C3×C4⋊C4—52no—
277C3×C4⋊C4—101no—
278#216—108no—
279(C2×D3)⋊C4—104no—
280C4⋊Dic3—104no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—102no—
283#204—28no—
284C23×C5—64no—
285C23×C5—62no—
286C23×C5—122no—
287C23×C5—122no—
288C23×C5D3×D411yescharacteristic
289C22×D5—32no—
290C22×D5—62no—
291C22×D5—62no—
292C22×D5—62no—
293C5×Q8—62no—
294C5×Q8—62no—
295C5×Q8—122no—
296C5×D4—34no—
297C5×D4—64no—
298C5×D4—62no—
299C2×C4×C5—62no—
300C2×C4×C5—122no—
301C2×C4×C5C2×D1212yes—
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5D3×D412yes—
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—616no—
306C2×Dic5—24no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—32no—
310C2×Dic5—42no—
311C2×Dic5—616no—
312C2×Dic5—62no—
313C4×D5—64no—
314C4×D5—62no—
315C4×D5—62no—
316Dic10—24no—
317Dic10—22no—
318Dic10C2×D1214yes—
319C5×C8—22no—
320#168—62no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8—31no—
326C22×Q8—51no—
327C22×D4—31no—
328C22×D4—301no—
329C23×C4—151no—
330C23×C4—301no—
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—34no—
334C2×SD16—64no—
335C22×C8—151no—
336C22×C8D3×D511yescharacteristic
337C22⋊Q8—154no—
338C22⋊Q8—302no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—301no—
341C2×C22⋊C4—301no—
342#103—54no—
343#102—154no—
344C22⋊C8—154no—
345C2×C3×C5#45214yescomplemented
346C2×C3×C5C2×#12011yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5C2×#13711yescharacteristic
349D15—42no—
350C5×D3—44no—
351C23×C3D4×D511yescharacteristic
352C22×D3—22no—
353C22×D3—24no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—52no—
357C22×D3—102no—
358C22×D3—102no—
359C22×D3—102no—
360C3×Q8—54no—
361C3×Q8—102no—
362C3×Q8—104no—
363C2×C3×C4—102no—
364C2×C3×C4—104no—
365C2×C3×C4—102no—
366C2×C3×C4—202no—
367C2×C3×C4D4×D512yes—
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4C2×C22⋊D512yes—
370C2×C3×C4C23×D511yescharacteristic
371C2×Dic3—22no—
372C2×Dic3—42no—
373C2×Dic3—52no—
374C2×Dic3—102no—
375D12—22no—
376D12—24no—
377D12—1016no—
378D12C2×C22⋊D514yes—
379C4×D3—1016no—
380C4×D3—102no—
381C4×D3—102no—
382C4×D3—104no—
383Dic6—22no—
384Dic6—22no—
385Dic6—42no—
386C3×C8—22no—
387C3⋊C8—102no—
388C22×C5—64no—
389C22×C5—122no—
390C22×C5—122no—
391C22×C5—128no—
392C22×C5#88212yes—
393C22×C5#91612yes—
394C22×C5#91812yes—
395C22×C5C2×D3×D411yescharacteristic
396C2×D5—62no—
397C2×D5—62no—
398C2×D5—62no—
399C2×D5—124no—
400C4×C5—122no—
401C4×C5#88212yes—
402C4×C5C22×D1211yescharacteristic
403C4×C5C2×D3×D411yescharacteristic
404Dic5—24no—
405Dic5—42no—
406Dic5—62no—
407C24—61no—
408C24—151no—
409#41—308no—
410#41—308no—
411#41—3016no—
412C2×Q8—32no—
413C2×Q8—54no—
414C2×Q8—52no—
415C2×Q8—61no—
416C2×Q8—62no—
417C2×Q8—62no—
418C2×Q8—101no—
419C2×Q8—102no—
420C2×D4—34no—
421C2×D4—32no—
422C2×D4—62no—
423C2×D4—61no—
424C2×D4—304no—
425C2×D4—308no—
426C22×C4—61no—
427C22×C4—101no—
428C22×C4—101no—
429C22×C4—151no—
430C22×C4—152no—
431C22×C4—152no—
432C22×C4—304no—
433C22×C4—308no—
434C22×C4—302no—
435C22×C4—302no—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—68no—
439C2×C8—22no—
440C2×C8—152no—
441C2×C8—302no—
442C2×C8C2×D3×D512yes—
443C4⋊C4—52no—
444C4⋊C4—101no—
445C4⋊C4—304no—
446C22⋊C4—304no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3#406112yes—
449C22×C3#406212yes—
450C22×C3#408312yes—
451C22×C3C2×D4×D511yescharacteristic
452C2×D3—24no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—48no—
456C2×D3—102no—
457C2×D3—102no—
458C2×D3—102no—
459C2×D3—204no—
460C3×C4—104no—
461C3×C4—202no—
462C3×C4#408312yes—
463C3×C4C2×D4×D511yescharacteristic
464C3×C4C22×C22⋊D511yescharacteristic
465Dic3—42no—
466Dic3—102no—
467C2×C5—124no—
468C2×C5#480814yescomplemented
469C2×C5C2×#88211yescharacteristic
470C2×C5C2×#91611yescharacteristic
471C2×C5C2×#91811yescharacteristic
472D5—122no—
473C23—64no—
474C23—62no—
475C23—122no—
476C23—122no—
477C23—152no—
478C23—302no—
479C23—302no—
480C23—302no—
481C23#677711yescharacteristic
482Q8—54no—
483Q8—62no—
484Q8—62no—
485Q8—104no—
486Q8—102no—
487Q8—122no—
488D4—34no—
489D4—64no—
490D4—62no—
491D4—3016no—
492C2×C4—62no—
493C2×C4—104no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—122no—
497C2×C4—152no—
498C2×C4—202no—
499C2×C4—3016no—
500C2×C4—302no—
501C2×C4—304no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4D5×D1212yes—
505C2×C4#677711yescharacteristic
506C2×C4D3×C22⋊D512yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—22no—
509C8—302no—
510C2×C3#6546214yescomplemented
511C2×C3C2×#406111yescharacteristic
512C2×C3C2×#406211yescharacteristic
513C2×C3C2×#408311yescharacteristic
514D3—44no—
515D3—202no—
516C5C2×#480811yescharacteristic, complemented, Sylow
517C22—64no—
518C22—122no—
519C22—122no—
520C22—128no—
521C22—302no—
522C22—302no—
523C22—302no—
524C22—604no—
525C22#9127612yes—
526C22#9128012yes—
527C22#9147512yes—
528C22C2×#677711yescharacteristic
529C4—104no—
530C4—122no—
531C4—202no—
532C4—302no—
533C4#9147512yes—
534C4C2×D5×D1211yescharacteristic
535C4C2×D3×C22⋊D511yescharacteristic
536C3C2×#6546211yescharacteristic, complemented, Sylow
537C2—124no—
538C2—602no—
539C2#1174815814yesdirect product factor
540C2C2×#9127611yescharacteristic
541C2C2×#9128011yescharacteristic
542C2C2×#9147511yescharacteristic
subgroupG/H
centerC23#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×#6768C2
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#452
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
2. C22×C5×#204C2semidirect
3. C2×#91383C2semidirect
4. C22×#6661C2semidirect
5. C2×#91104C2semidirect
6. C2×C3×#3948C2semidirect
7. C2×#90966C2semidirect
8. #11748158C2direct (N × H)
23. C2×C5×#204C22semidirect
28. #91383C22semidirect
30. C2×#6661C22semidirect
31. #91104C22semidirect
32. C3×#3948C22semidirect
33. #90966C22semidirect
42. C2×#3948D3semidirect
85. C22×#204D5semidirect
114. #3948C2×D3semidirect
171. C2×#204C2×D5semidirect
345. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
468. C2×C5#4808semidirect
510. C2×C3#65462semidirect
516. C5C2×#4808semidirect
536. C3C2×#65462semidirect
539. C2#11748158direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67682
C22×C5×#2042
C2×#913832
C22×#66612
C2×#911042
C2×C3×#39482
C2×#909662
#117481582
C2×#654623
C2×#48085