Finite Group Databasebeta

← C2×#11755198 #14484101

Subgroups — C2×#11755198 #14484101

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#947C211yesmaximal, characteristic
3C2×C3×#4090C211yesmaximal, characteristic, complemented
4#11755198C2116yesmaximal, direct product factor
5C2×C4×#1204C211yesmaximal, characteristic, complemented
6C2×#91417C212yesmaximal, complemented
7C2×Dic5×D12C211yesmaximal, characteristic
8C2×#91400C212yesmaximal, complemented
9C2×#91370C211yesmaximal, characteristic
10C2×#91367C212yesmaximal, complemented
11C2×#91342C212yesmaximal, complemented
12C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
13C2×#66005—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C22×#1204C2211yescharacteristic
18C22×D3×Dic5C2212yes—
19Q8×Dic15C2218yescomplemented
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2212yes—
22C2×C4×Dic15C2212yes—
23C2×C4×Dic15C2211yescharacteristic
24C5×#947C2218yes—
25C2×C5×(C2×D3)⋊C4C2212yes—
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C4×C5×Dic3C2211yescharacteristic
28C3×#4090C2218yescomplemented
29C2×C3×#683C2212yes—
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6668C2212yes—
35C2×#6668C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40C4×#1204C2218yescomplemented
41#91417C22116yescomplemented
42Dic5×D12C2218yes—
43#91400C22116yescomplemented
44#91370C2218yes—
45#91367C22116yescomplemented
46#91342C22116yescomplemented
47Dic3×Dic10C2218yescomplemented
48C2×#5732—51nomaximal, Hall
49C2×C5×#124—31no—
50C2×Q8×Dic5—31no—
51C2×#4090D311yescharacteristic, complemented
52C2×#4082—31no—
53C2×D4×Dic5—31no—
54#66005—316no—
55C2×#4025—32no—
56C2×#4025—32no—
57C2×#4024—32no—
58C2×#4023—32no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10—31no—
61C23×C5×D3C2312yes—
62C2×C3×C5×Q8—24no—
63C2×C3×C5×Q8C2314yes—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2311yescharacteristic
71C2×C5×D12—24no—
72C2×C5×D12C2314yes—
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×Dic10—24no—
77C2×C3×Dic10C2314yes—
78C2×#1204—24no—
79C2×#1204C2314yes—
80C2×D3×Dic5—28no—
81C2×D3×Dic5C2318yes—
82C4⋊Dic15C2314yes—
83C4⋊Dic15C2318yes—
84C4×Dic15C2318yes—
85C4×Dic15C2314yes—
86C5×(C2×D3)⋊C4C2318yes—
87C5×(C2×D3)⋊C4C2318yes—
88C4×C5×Dic3C2314yes—
89C3×#683C2318yes—
90C3×#683C2318yes—
91C3×C4×Dic5C2314yes—
92Dic3⋊Dic5C2314yes—
93#6669C2314yes—
94#6668C2314yes—
95#6668C2318yes—
96(C2×D3)⋊Dic5C2318yes—
97(C2×D3)⋊Dic5C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C4⋊Q8—51no—
101C2×#947—51no—
102C2×#947D511yescharacteristic
103C2×Q8×Dic3—51no—
104C2×Q8×Dic3—51no—
105#5732—516no—
106C2×#898—52no—
107C2×#898—52no—
108C2×#897—52no—
109C2×#892—52no—
110C2×C4×D12—51no—
111C2×C4×Dic6—51no—
112C22×C5×Q8C2×D311yescharacteristic
113C22×C5×D4—31no—
114C23×Dic5—32no—
115C22×Dic10—31no—
116C22×Dic10C2×D311yescharacteristic
117C5×#124—38no—
118C2×C5×C22⋊C4—32no—
119C2×C5×C22⋊C4—32no—
120C2×C42×C5—31no—
121C2×C22⋊Dic5—32no—
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124Q8×Dic5—38no—
125#4090C2×D318yescomplemented
126#4082—38no—
127D4×Dic5—38no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—31no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683—31no—
134C2×#683C2×D312yes—
135C2×#683C2×D312yes—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—32no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5C2×D311yescharacteristic
140#4025—316no—
141#4025—316no—
142#4024—316no—
143#4023—316no—
144C4×Dic10—38no—
145C4×Dic10—38no—
146C2×#556—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C5×D3—24no—
149C22×C5×D3—24no—
150C22×C5×D3—24no—
151C22×C5×D3C2414yes—
152C3×C5×Q8—28no—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5#4114yes—
155C2×C3×C4×C5C2414yes—
156C2×C3×C4×C5C2412yes—
157C2×Dic15—24no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15C2414yes—
161C2×Dic15C2412yes—
162C2×Dic15C2412yes—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3C2412yes—
166C2×C5×Dic3C2412yes—
167C5×D12—28no—
168C2×C3×Dic5—24no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5#4114yes—
171C2×C3×Dic5C2414yes—
172C2×C3×Dic5C2412yes—
173C2×C3×Dic5C2412yes—
174C3×Dic10—28no—
175#1204—28no—
176D3×Dic5—216no—
177C22×C3×Q8—51no—
178C22×C3×Q8C2×D511yescharacteristic
179C22×D12C2×D511yescharacteristic
180C22×C4×D3—52no—
181C22×Dic6—51no—
182C3×C4⋊Q8—58no—
183C2×C3×C4⋊C4—52no—
184C2×C3×C4⋊C4—52no—
185C2×C3×C42—51no—
186#947—58no—
187#947C2×D518yes—
188Q8×Dic3—58no—
189Q8×Dic3—58no—
190C2×(C2×D3)⋊C4—52no—
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D512yes—
194C2×(C2×D3)⋊C4C2×D512yes—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—51no—
198C2×C4⋊Dic3—52no—
199C2×Dic3⋊C4—51no—
200C2×Dic3⋊C4—51no—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3C2×D511yescharacteristic
205#898—516no—
206#898—516no—
207#897—516no—
208#892—516no—
209C4×D12—58no—
210C4×Dic6—58no—
211C24×C5—32no—
212C2×C5×Q8—24no—
213C2×C5×Q8C22×D314yes—
214C2×C5×D4—34no—
215C2×C5×D4—64no—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—31no—
221C22×Dic5—31no—
222C22×Dic5—32no—
223C22×Dic5—38no—
224C22×Dic5—68no—
225C22×Dic5C22×D312yes—
226C22×Dic5C22×D311yescharacteristic
227C22×Dic5C22×D311yescharacteristic
228C2×Dic10—24no—
229C2×Dic10—34no—
230C2×Dic10—64no—
231C2×Dic10C22×D314yes—
232C5×C22⋊C4—38no—
233C5×C22⋊C4—38no—
234C42×C5—34no—
235C22⋊Dic5—38no—
236C22⋊Dic5—38no—
237C22⋊Dic5—38no—
238C4⋊Dic5—34no—
239C4⋊Dic5—38no—
240C4⋊Dic5—34no—
241#683—34no—
242#683—38no—
243#683—34no—
244#683C22×D318yes—
245#683C22×D318yes—
246C4×Dic5—34no—
247C4×Dic5—38no—
248C4×Dic5—38no—
249C4×Dic5C22×D314yes—
250#556—1516no—
251C2×C4⋊Q8—51no—
252C2×#126—152no—
253C2×#126—152no—
254C2×#124—31no—
255C2×#124—151no—
256C2×C22⋊Q8—152no—
257C2×C4×Q8—151no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C22×C3×C5C2×#4112yes—
263C22×C3×C5C2×#4112yes—
264C22×C3×C52−1+412yes—
265C22×C3×C5C2511yescharacteristic
266C2×C5×D3—24no—
267C2×C5×D3—24no—
268C2×C5×D3—24no—
269C2×C5×D3—48no—
270C3×C4×C5—24no—
271C3×C4×C5C2×#4114yes—
272Dic15—24no—
273Dic15—22no—
274Dic15—22no—
275C3×Dic5—24no—
276C3×Dic5—22no—
277C3×Dic5C2×#4114yes—
278C5×Dic3—22no—
279C5×Dic3—22no—
280C23×D3C22×D512yes—
281C2×C3×Q8—24no—
282C2×C3×Q8—54no—
283C2×C3×Q8—104no—
284C2×C3×Q8C22×D514yes—
285C22×C3×C4—51no—
286C22×C3×C4—52no—
287C22×C3×C4—51no—
288C22×C3×C4C22×D512yes—
289C22×C3×C4C22×D511yescharacteristic
290C22×Dic3—51no—
291C22×Dic3—52no—
292C22×Dic3—51no—
293C22×Dic3C22×D511yescharacteristic
294C22×Dic3C22×D511yescharacteristic
295C2×D12—24no—
296C2×D12C22×D514yes—
297C2×C4×D3—58no—
298C2×C4×D3—108no—
299C2×Dic6—54no—
300C2×Dic6—104no—
301C3×C4⋊C4—58no—
302C3×C4⋊C4—58no—
303C3×C42—54no—
304(C2×D3)⋊C4—58no—
305(C2×D3)⋊C4—58no—
306(C2×D3)⋊C4—58no—
307(C2×D3)⋊C4C22×D518yes—
308(C2×D3)⋊C4C22×D518yes—
309C4⋊Dic3—54no—
310C4⋊Dic3—58no—
311C4⋊Dic3—54no—
312C4⋊Dic3—58no—
313Dic3⋊C4—54no—
314Dic3⋊C4—54no—
315C4×Dic3—54no—
316C4×Dic3—58no—
317C4×Dic3—58no—
318C4×Dic3C22×D514yes—
319C23×C5—34no—
320C23×C5—64no—
321C23×C5—64no—
322C23×C5—64no—
323C23×C5C23×D311yescharacteristic
324C5×Q8—28no—
325C5×D4—68no—
326C2×C4×C5—24no—
327C2×C4×C5—32no—
328C2×C4×C5—32no—
329C2×C4×C5—62no—
330C2×C4×C5—62no—
331C2×C4×C5#23714yes—
332C2×C4×C5C23×D314yes—
333C2×C4×C5C23×D312yes—
334C2×Dic5—24no—
335C2×Dic5—22no—
336C2×Dic5—32no—
337C2×Dic5—34no—
338C2×Dic5—32no—
339C2×Dic5—62no—
340C2×Dic5—64no—
341C2×Dic5—62no—
342C2×Dic5—616no—
343C2×Dic5#23914yes—
344C2×Dic5C23×D314yes—
345C2×Dic5C23×D312yes—
346C2×Dic5C23×D312yes—
347Dic10—28no—
348Dic10—68no—
349C22×Q8—51no—
350C22×Q8—151no—
351C22×Q8D3×D511yescharacteristic
352C22×D4—31no—
353C23×C4—152no—
354C4⋊Q8—58no—
355#126—1516no—
356#126—1516no—
357#124—38no—
358#124—158no—
359C22⋊Q8—1516no—
360C4×Q8—158no—
361C4×Q8—158no—
362C4×Q8—158no—
363C4×D4—158no—
364#117—1516no—
365C2×C4⋊C4—52no—
366C2×C4⋊C4—52no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—152no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—152no—
377C2×C22⋊C4—152no—
378C2×C42—31no—
379C2×C42—51no—
380C2×C42—152no—
381C2×C42—152no—
382C2×C42—151no—
383C2×C3×C5#55614yescomplemented
384C2×C3×C5C22×#4111yescharacteristic
385C2×C3×C5C22×#4111yescharacteristic
386C2×C3×C5C2×2−1+411yescharacteristic
387C5×D3—44no—
388C23×C3C23×D511yescharacteristic
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3C23×D514yes—
393C3×Q8—28no—
394C3×Q8—108no—
395C2×C3×C4—24no—
396C2×C3×C4—54no—
397C2×C3×C4—52no—
398C2×C3×C4—54no—
399C2×C3×C4—52no—
400C2×C3×C4—104no—
401C2×C3×C4—102no—
402C2×C3×C4#71114yes—
403C2×C3×C4C23×D514yes—
404C2×C3×C4C23×D512yes—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—52no—
408C2×Dic3—54no—
409C2×Dic3—52no—
410C2×Dic3—102no—
411C2×Dic3—104no—
412C2×Dic3—102no—
413C2×Dic3C23×D512yes—
414C2×Dic3C23×D512yes—
415D12—28no—
416C4×D3—1016no—
417Dic6—108no—
418C22×C5—64no—
419C22×C5—64no—
420C22×C5—64no—
421C22×C5—128no—
422C22×C5C2×#23712yes—
423C22×C5C2×#23912yes—
424C22×C5#100712yes—
425C22×C5C24×D311yescharacteristic
426C4×C5—24no—
427C4×C5—62no—
428C4×C5—62no—
429C4×C5C2×#23714yes—
430Dic5—24no—
431Dic5—22no—
432Dic5—62no—
433Dic5—64no—
434Dic5—62no—
435Dic5C2×#23914yes—
436C24—32no—
437C2×Q8—24no—
438C2×Q8—54no—
439C2×Q8—104no—
440C2×Q8—154no—
441C2×Q8—304no—
442C2×Q8C2×D3×D514yes—
443C2×D4—34no—
444C2×D4—64no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—52no—
450C22×C4—158no—
451C22×C4—151no—
452C22×C4—152no—
453C22×C4—151no—
454C22×C4—308no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—58no—
458C4⋊C4—58no—
459C4⋊C4—154no—
460C4⋊C4—158no—
461C4⋊C4—154no—
462C4⋊C4—154no—
463C4⋊C4—154no—
464C4⋊C4—158no—
465C22⋊C4—38no—
466C22⋊C4—38no—
467C22⋊C4—158no—
468C22⋊C4—158no—
469C22⋊C4—158no—
470C42—34no—
471C42—54no—
472C42—158no—
473C42—158no—
474C42—154no—
475C3×C5C2×#55611yescharacteristic, complemented, Hall
476C22×C3C2×#71112yes—
477C22×C3D5×#4112yes—
478C22×C3#415012yes—
479C22×C3C24×D511yescharacteristic
480C2×D3—24no—
481C2×D3—24no—
482C2×D3—24no—
483C2×D3—48no—
484C3×C4—24no—
485C3×C4—54no—
486C3×C4—104no—
487C3×C4—102no—
488C3×C4C2×#71114yes—
489Dic3—22no—
490Dic3—22no—
491Dic3—102no—
492Dic3—104no—
493Dic3—102no—
494C2×C5—124no—
495C2×C5#573214yescomplemented
496C2×C5C22×#23711yescharacteristic
497C2×C5C22×#23911yescharacteristic
498C2×C5C2×#100711yescharacteristic
499C23—34no—
500C23—64no—
501C23—64no—
502C23—64no—
503C23C22×D3×D511yescharacteristic
504Q8—28no—
505Q8—108no—
506Q8—308no—
507D4—68no—
508C2×C4—24no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—54no—
512C2×C4—52no—
513C2×C4—52no—
514C2×C4—54no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—102no—
518C2×C4—104no—
519C2×C4—152no—
520C2×C4—154no—
521C2×C4—152no—
522C2×C4—3016no—
523C2×C4—302no—
524C2×C4—304no—
525C2×C4—302no—
526C2×C4#678014yes—
527C2×C4C22×D3×D514yes—
528C2×C4C22×D3×D512yes—
529C2×C3#6600514yescomplemented
530C2×C3C22×#71111yescharacteristic
531C2×C3C2×D5×#4111yescharacteristic
532C2×C3C2×#415011yescharacteristic
533D3—44no—
534C5C2×#573211yescharacteristic, complemented, Sylow
535C22—64no—
536C22—64no—
537C22—64no—
538C22—128no—
539C22#9203012yes—
540C22D5×#23912yes—
541C22C2×#678012yes—
542C22C23×D3×D511yescharacteristic
543C4—24no—
544C4—54no—
545C4—62no—
546C4—62no—
547C4—104no—
548C4—102no—
549C4—302no—
550C4—304no—
551C4—302no—
552C4C2×#678014yes—
553C3C2×#6600511yescharacteristic, complemented, Sylow
554C2—124no—
555C2#1175519814yesdirect product factor
556C2C2×#9203011yescharacteristic
557C2C2×D5×#23911yescharacteristic
558C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic15C2semidirect
3. C2×C3×#4090C2semidirect
4. #11755198C2direct (N × H)
5. C2×C4×#1204C2semidirect
6. C2×#91417C2semidirect
8. C2×#91400C2semidirect
10. C2×#91367C2semidirect
11. C2×#91342C2semidirect
12. C2×Dic3×Dic10C2semidirect
19. Q8×Dic15C22semidirect
28. C3×#4090C22semidirect
40. C4×#1204C22semidirect
41. #91417C22semidirect
43. #91400C22semidirect
45. #91367C22semidirect
46. #91342C22semidirect
47. Dic3×Dic10C22semidirect
51. C2×#4090D3semidirect
125. #4090C2×D3semidirect
383. C2×C3×C5#556semidirect
475. C3×C5C2×#556semidirect
495. C2×C5#5732semidirect
529. C2×C3#66005semidirect
534. C5C2×#5732semidirect
553. C3C2×#66005semidirect
555. C2#11755198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic152
C2×C5×#9472
C2×C3×#40902
#117551982
C2×C4×#12042
C2×#914172
C2×Dic5×D122
C2×#914002
C2×#913702
C2×#913672
C2×#913422
C2×Dic3×Dic102
C2×#660053
C2×#57325