Finite Group Databasebeta

← C2×#11756298 #14483804

Subgroups — C2×#11756298 #14483804

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×D4×Dic15C211yesmaximal, characteristic
3C2×D4×Dic15C211yesmaximal, characteristic
4C2×#91813C212yesmaximal, complemented
5C22×#6712C212yesmaximal, complemented
6#11756298C2116yesmaximal, direct product factor
7C2×#91779C211yesmaximal, characteristic, complemented
8C2×#91777C211yesmaximal, characteristic, complemented
9C2×#91767C212yesmaximal, complemented
10C2×#91767C212yesmaximal, complemented
11C2×#91759C211yesmaximal, characteristic, complemented
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#65873—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2212yes—
16C23×Dic15C2212yes—
17C23×Dic15C2212yes—
18C22×Dic30C2211yescharacteristic
19C22×Dic30C2212yes—
20C3×C4×C5×D4C2218yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2212yes—
23C2×C3×C42×C5C2211yescharacteristic
24C2×#6719C2212yes—
25C2×#6719C2212yes—
26D4×Dic15C2218yes—
27D4×Dic15C2218yes—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
31C2×C4⋊Dic15C2212yes—
32#91813C22116yescomplemented
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2212yes—
36C2×#6712C2212yes—
37C2×#6712C2212yes—
38C2×#6712C2212yes—
39C2×#6712C22116yescomplemented
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42#91779C2218yescomplemented
43#91777C2218yescomplemented
44#91767C22116yescomplemented
45#91767C22116yescomplemented
46#91759C2218yescomplemented
47C4×Dic30C2218yescomplemented
48C2×#5539—51nomaximal, Hall
49C2×C4×C5×D4D311yescharacteristic
50C2×D4×Dic5—31no—
51C2×D4×Dic5—31no—
52C2×#4070—32no—
53C22×#683—32no—
54#65873—316no—
55C2×#4036—31no—
56C2×#4034—31no—
57C2×#4024—32no—
58C2×#4024—32no—
59C2×#4016—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2312yes—
62C2×C3×C5×D4Q818yescomplemented
63C2×C3×C5×D4C2314yes—
64C22×C3×C4×C5—44no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2318yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×Dic15—28no—
71C22×Dic15—44no—
72C22×Dic15C2318yes—
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2312yes—
77C22×Dic15C2312yes—
78C22×Dic15C2318yes—
79C22×Dic15C2311yescharacteristic
80C2×Dic30—24no—
81C2×Dic30—44no—
82C2×Dic30C2314yes—
83C2×Dic30C2318yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C22⋊C4C2318yes—
86C3×C42×C5C2314yes—
87#6719C2318yes—
88#6719C2318yes—
89C4⋊Dic15C2314yes—
90C4⋊Dic15C2314yes—
91C4⋊Dic15C2314yes—
92C4⋊Dic15C2318yes—
93#6712C2314yes—
94#6712C2314yes—
95#6712C2318yes—
96#6712C2318yes—
97#6712C2318yes—
98#6712C2318yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C2×C3×C4×D4D511yescharacteristic
102C2×D4×Dic3—51no—
103C2×D4×Dic3—51no—
104C2×#924—52no—
105C22×Dic3⋊C4—52no—
106#5539—516no—
107C2×#890—51no—
108C2×#888—51no—
109C2×#878—52no—
110C2×#878—52no—
111C2×#870—51no—
112C2×C4×Dic6—51no—
113C22×C5×D4C2×D311yescharacteristic
114C23×C4×C5C2×D312yes—
115C23×Dic5—32no—
116C23×Dic5—32no—
117C22×Dic10—31no—
118C22×Dic10—32no—
119C4×C5×D4C2×D318yes—
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C22⋊C4C2×D312yes—
122C2×C42×C5C2×D311yescharacteristic
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5—32no—
125D4×Dic5—38no—
126D4×Dic5—38no—
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131#4070—316no—
132C2×#683—31no—
133C2×#683—31no—
134C2×#683—32no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×#683—316no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141#4036—38no—
142#4034—38no—
143#4024—316no—
144#4024—316no—
145#4016—38no—
146C4×Dic10—38no—
147C2×#554—151noSylow
148C23×C3×C5—24no—
149C23×C3×C5—24no—
150C23×C3×C5C2×Q818yes—
151C23×C3×C5C2414yes—
152C23×C3×C5C2411yescharacteristic
153C3×C5×D4C2×Q8116yescomplemented
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—24no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—48no—
158C2×C3×C4×C5C2×Q814yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2414yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—22no—
164C2×Dic15—24no—
165C2×Dic15—22no—
166C2×Dic15—24no—
167C2×Dic15—22no—
168C2×Dic15—216no—
169C2×Dic15—48no—
170C2×Dic15#4114yes—
171C2×Dic15C2412yes—
172C2×Dic15C2412yes—
173C2×Dic15C2412yes—
174C2×Dic15C2414yes—
175C2×Dic15C2414yes—
176C2×Dic15C2412yes—
177Dic30—28no—
178Dic30—48no—
179C22×C3×D4C2×D511yescharacteristic
180C23×C3×C4C2×D512yes—
181C23×Dic3—52no—
182C23×Dic3—52no—
183C22×Dic6—51no—
184C22×Dic6—52no—
185C3×C4×D4C2×D518yes—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4C2×D512yes—
188C2×C3×C42C2×D511yescharacteristic
189C2×#217—52no—
190C2×#217—52no—
191D4×Dic3—58no—
192D4×Dic3—58no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197#924—516no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—51no—
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204C2×Dic3⋊C4—516no—
205C2×C4×Dic3—51no—
206C2×C4×Dic3—51no—
207#890—58no—
208#888—58no—
209#878—516no—
210#878—516no—
211#870—58no—
212C4×Dic6—58no—
213C24×C5C22×D312yes—
214C2×C5×D4Dic618yescomplemented
215C2×C5×D4C22×D314yes—
216C22×C4×C5—44no—
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D312yes—
220C22×C4×C5C22×D318yes—
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—31no—
223C22×Dic5—31no—
224C22×Dic5—31no—
225C22×Dic5—32no—
226C22×Dic5—32no—
227C22×Dic5—31no—
228C22×Dic5—38no—
229C22×Dic5—38no—
230C22×Dic5—68no—
231C22×Dic5—124no—
232C2×Dic10—34no—
233C2×Dic10—38no—
234C2×Dic10—64no—
235C2×Dic10—124no—
236C5×C4⋊C4C22×D314yes—
237C5×C22⋊C4C22×D318yes—
238C42×C5C22×D314yes—
239C22⋊Dic5—38no—
240C22⋊Dic5—38no—
241C4⋊Dic5—34no—
242C4⋊Dic5—34no—
243C4⋊Dic5—34no—
244C4⋊Dic5—38no—
245#683—34no—
246#683—34no—
247#683—38no—
248#683—38no—
249#683—38no—
250#683—38no—
251C4×Dic5—34no—
252C4×Dic5—34no—
253#554—1516no—
254C2×C4⋊Q8—151no—
255C2×#125—151no—
256C2×#125—151no—
257C2×C22⋊Q8—152no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—152no—
260C2×C4×Q8—151no—
261C2×C4×D4—151no—
262C2×C4×D4—151no—
263C2×C4×D4D1511yescharacteristic
264C22×C4⋊C4—152no—
265C22×C3×C5—216no—
266C22×C3×C5—24no—
267C22×C3×C5—24no—
268C22×C3×C5C22×Q818yes—
269C22×C3×C5C22×Q812yes—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5H(5,𝔽2)12yes—
272C22×C3×C5C2511yescharacteristic
273C3×C4×C5—22no—
274C3×C4×C5—24no—
275C3×C4×C5—22no—
276C3×C4×C5C22×Q814yes—
277Dic15—22no—
278Dic15—24no—
279Dic15—22no—
280Dic15—24no—
281Dic15—22no—
282Dic15C2×#4114yes—
283C24×C3C22×D512yes—
284C2×C3×D4Dic1018yescomplemented
285C2×C3×D4C22×D514yes—
286C22×C3×C4—44no—
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C22×C3×C4C22×D512yes—
290C22×C3×C4C22×D518yes—
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—51no—
293C22×Dic3—58no—
294C22×Dic3—51no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3—52no—
298C22×Dic3—52no—
299C22×Dic3—58no—
300C22×Dic3—108no—
301C22×Dic3—204no—
302C2×Dic6—54no—
303C2×Dic6—58no—
304C2×Dic6—104no—
305C2×Dic6—204no—
306C3×C4⋊C4C22×D514yes—
307C3×C22⋊C4C22×D518yes—
308C3×C42C22×D514yes—
309#217—58no—
310#217—58no—
311C4⋊Dic3—54no—
312C4⋊Dic3—54no—
313C4⋊Dic3—54no—
314C4⋊Dic3—58no—
315Dic3⋊C4—54no—
316Dic3⋊C4—54no—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321C4×Dic3—54no—
322C4×Dic3—54no—
323C23×C5—24no—
324C23×C5—24no—
325C23×C5C2×Dic618yes—
326C23×C5C23×D314yes—
327C23×C5C23×D311yescharacteristic
328C5×D4C2×Dic6116yescomplemented
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—48no—
333C2×C4×C5C2×Dic614yes—
334C2×C4×C5C23×D312yes—
335C2×C4×C5C23×D312yes—
336C2×C4×C5C23×D314yes—
337C2×C4×C5C23×D312yes—
338C2×Dic5—34no—
339C2×Dic5—32no—
340C2×Dic5—32no—
341C2×Dic5—32no—
342C2×Dic5—32no—
343C2×Dic5—34no—
344C2×Dic5—34no—
345C2×Dic5—616no—
346C2×Dic5—62no—
347C2×Dic5—64no—
348C2×Dic5—62no—
349C2×Dic5—62no—
350C2×Dic5—64no—
351C2×Dic5—128no—
352Dic10—68no—
353Dic10—128no—
354C22×Q8—151no—
355C22×Q8—152no—
356C22×D4C2×D1511yescharacteristic
357C23×C4—152no—
358C23×C4—152no—
359C23×C4C2×D1512yes—
360C4⋊Q8—158no—
361#125—158no—
362#125—158no—
363C22⋊Q8—1516no—
364C22⋊Q8—1516no—
365C22⋊Q8—1516no—
366C4×Q8—158no—
367C4×D4—158no—
368C4×D4—158no—
369C4×D4C2×D1518yes—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—1516no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—151no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4C2×D1511yescharacteristic
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4C2×D1512yes—
385C2×C42—151no—
386C2×C42—151no—
387C2×C42C2×D1511yescharacteristic
388C2×C3×C5—28no—
389C2×C3×C5#55414yescomplemented
390C2×C3×C5C23×Q811yescharacteristic
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
393C23×C3—24no—
394C23×C3—24no—
395C23×C3C2×Dic1018yes—
396C23×C3C23×D514yes—
397C23×C3C23×D511yescharacteristic
398C3×D4C2×Dic10116yescomplemented
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—48no—
403C2×C3×C4C2×Dic1014yes—
404C2×C3×C4C23×D512yes—
405C2×C3×C4C23×D512yes—
406C2×C3×C4C23×D514yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—54no—
409C2×Dic3—52no—
410C2×Dic3—52no—
411C2×Dic3—52no—
412C2×Dic3—52no—
413C2×Dic3—54no—
414C2×Dic3—54no—
415C2×Dic3—1016no—
416C2×Dic3—102no—
417C2×Dic3—104no—
418C2×Dic3—102no—
419C2×Dic3—102no—
420C2×Dic3—104no—
421C2×Dic3—208no—
422Dic6—108no—
423Dic6—208no—
424C22×C5—24no—
425C22×C5—24no—
426C22×C5—216no—
427C22×C5C22×Dic618yes—
428C22×C5C22×Dic612yes—
429C22×C5#100412yes—
430C22×C5D3×#4112yes—
431C22×C5C24×D311yescharacteristic
432C4×C5—24no—
433C4×C5—22no—
434C4×C5—22no—
435C4×C5C22×Dic614yes—
436Dic5—34no—
437Dic5—62no—
438Dic5—64no—
439Dic5—62no—
440Dic5—62no—
441Dic5—64no—
442C24C22×D1512yes—
443C2×Q8—154no—
444C2×Q8—158no—
445C2×Q8—304no—
446C2×Q8—604no—
447C2×D4Dic3018yescomplemented
448C2×D4C22×D1514yes—
449C22×C4—44no—
450C22×C4—151no—
451C22×C4—158no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—151no—
455C22×C4—152no—
456C22×C4—152no—
457C22×C4—158no—
458C22×C4—308no—
459C22×C4—604no—
460C22×C4C22×D1511yescharacteristic
461C22×C4C22×D1511yescharacteristic
462C22×C4C22×D1512yes—
463C22×C4C22×D1518yes—
464C22×C4C22×D1511yescharacteristic
465C4⋊C4—154no—
466C4⋊C4—158no—
467C4⋊C4—158no—
468C4⋊C4—158no—
469C4⋊C4—154no—
470C4⋊C4—154no—
471C4⋊C4—154no—
472C4⋊C4—154no—
473C4⋊C4—158no—
474C4⋊C4—158no—
475C4⋊C4C22×D1514yes—
476C22⋊C4—158no—
477C22⋊C4—158no—
478C22⋊C4C22×D1518yes—
479C42—154no—
480C42—154no—
481C42C22×D1514yes—
482C3×C5C2×#55411yescharacteristic, complemented, Hall
483C22×C3—216no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3C22×Dic1018yes—
487C22×C3C22×Dic1012yes—
488C22×C3#414412yes—
489C22×C3D5×#4112yes—
490C22×C3C24×D511yescharacteristic
491C3×C4—24no—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4C22×Dic1014yes—
495Dic3—54no—
496Dic3—102no—
497Dic3—104no—
498Dic3—102no—
499Dic3—102no—
500Dic3—104no—
501C2×C5—28no—
502C2×C5#553914yescomplemented
503C2×C5C23×Dic611yescharacteristic
504C2×C5C2×#100411yescharacteristic
505C2×C5C2×D3×#4111yescharacteristic
506C23—24no—
507C23—24no—
508C23C2×Dic3018yes—
509C23C23×D1514yes—
510C23C23×D1511yescharacteristic
511Q8—308no—
512Q8—608no—
513D4C2×Dic30116yescomplemented
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—48no—
518C2×C4—154no—
519C2×C4—152no—
520C2×C4—152no—
521C2×C4—152no—
522C2×C4—152no—
523C2×C4—154no—
524C2×C4—154no—
525C2×C4—3016no—
526C2×C4—302no—
527C2×C4—304no—
528C2×C4—302no—
529C2×C4—304no—
530C2×C4—302no—
531C2×C4—608no—
532C2×C4C2×Dic3014yes—
533C2×C4C23×D1512yes—
534C2×C4C23×D1512yes—
535C2×C4C23×D1514yes—
536C2×C4C23×D1512yes—
537C2×C3—28no—
538C2×C3#6587314yescomplemented
539C2×C3C23×Dic1011yescharacteristic
540C2×C3C2×#414411yescharacteristic
541C2×C3C2×D5×#4111yescharacteristic
542C5C2×#553911yescharacteristic, complemented, Sylow
543C22—216no—
544C22—24no—
545C22—24no—
546C22C22×Dic3018yes—
547C22C22×Dic3012yes—
548C22#9209512yes—
549C22#41×D1512yes—
550C22C24×D1511yescharacteristic
551C4—22no—
552C4—24no—
553C4—22no—
554C4—154no—
555C4—302no—
556C4—304no—
557C4—302no—
558C4—304no—
559C4—302no—
560C4C22×Dic3014yes—
561C3C2×#6587311yescharacteristic, complemented, Sylow
562C2—28no—
563C2#1175629814yesdirect product factor
564C2C23×Dic3011yescharacteristic
565C2C2×#9209511yescharacteristic
566C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×C4×D4D15
hypocenterC3×C5C2×#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×#91813C2semidirect
5. C22×#6712C2semidirect
6. #11756298C2direct (N × H)
7. C2×#91779C2semidirect
8. C2×#91777C2semidirect
9. C2×#91767C2semidirect
10. C2×#91767C2semidirect
11. C2×#91759C2semidirect
12. C2×C4×Dic30C2semidirect
32. #91813C22semidirect
39. C2×#6712C22semidirect
42. #91779C22semidirect
43. #91777C22semidirect
44. #91767C22semidirect
45. #91767C22semidirect
46. #91759C22semidirect
47. C4×Dic30C22semidirect
62. C2×C3×C5×D4Q8semidirect
153. C3×C5×D4C2×Q8semidirect
214. C2×C5×D4Dic6semidirect
284. C2×C3×D4Dic10semidirect
328. C5×D4C2×Dic6semidirect
389. C2×C3×C5#554semidirect
398. C3×D4C2×Dic10semidirect
447. C2×D4Dic30semidirect
482. C3×C5C2×#554semidirect
502. C2×C5#5539semidirect
513. D4C2×Dic30semidirect
538. C2×C3#65873semidirect
542. C5C2×#5539semidirect
561. C3C2×#65873semidirect
563. C2#11756298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×D4×Dic152
C2×#918132
C22×#67122
#117562982
C2×#917792
C2×#917772
C2×#917672
C2×#917592
C2×C4×Dic302
C2×#658733
C2×#55395