Finite Group Databasebeta

← C2×#11748574 #14332016

Subgroups — C2×#11748574 #14332016

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6714C211yesmaximal, characteristic
2C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×#683C211yesmaximal, characteristic, complemented
4C22×#6669C211yesmaximal, characteristic, complemented
5C22×#6667C211yesmaximal, characteristic
6C22×#6667C211yesmaximal, characteristic
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748574C218yesmaximal, direct product factor
9C2×#65281—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C2×#6714—24no—
18C2×#6714C2214yes—
19C2×C5×Dic3⋊C4—24no—
20C2×C5×Dic3⋊C4C2214yescomplemented
21C2×C3×#683—24no—
22C2×C3×#683C2214yescomplemented
23C2×#6669—24no—
24C2×#6669C2214yescomplemented
25C2×#6667—24no—
26C2×#6667—24no—
27C2×#6667C2214yes—
28C2×#6667C2214yes—
29#90994C2214yescomplemented
30C2×#4993—51nomaximal, Hall
31C22×C5×C4⋊C4—31no—
32C22×#685—31no—
33C22×#685—31no—
34C22×#685—31no—
35C22×#683—31no—
36C22×#683D311yescharacteristic, complemented
37C2×#3963—31no—
38#65281—38no—
39C24×C3×C5C2311yescharacteristic
40C23×D15—22no—
41C23×D15—22no—
42C23×D15—22no—
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15Q814yes—
47C23×D15C2312yes—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5C2312yes—
52C22×Dic15—22no—
53C22×Dic15—22no—
54C22×Dic15D414yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3—22no—
57C22×C5×Dic3—22no—
58C22×C5×Dic3—22no—
59C22×C5×Dic3—22no—
60C22×C5×Dic3—22no—
61C22×C5×Dic3D414yes—
62C22×C5×Dic3C2312yes—
63C22×C5×Dic3C2312yes—
64C22×C3×Dic5—22no—
65C22×C3×Dic5—22no—
66C22×C3×Dic5—22no—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5D414yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2312yes—
72#6714—28no—
73C5×Dic3⋊C4—28no—
74C3×#683—28no—
75#6669—28no—
76#6667—28no—
77#6667—28no—
78C22×C3×C4⋊C4—51no—
79C22×(C2×D3)⋊C4—51no—
80C22×(C2×D3)⋊C4—51no—
81C22×(C2×D3)⋊C4—51no—
82C22×Dic3⋊C4—51no—
83C22×Dic3⋊C4D511yescharacteristic, complemented
84C2×C3⋊#95—51no—
85#4993—58no—
86C24×D5—31no—
87C23×C4×C5—31no—
88C23×C4×C5—31no—
89C23×C4×C5C2×D311yescharacteristic
90C23×Dic5—31no—
91C23×Dic5C2×D311yescharacteristic
92C23×Dic5C2×D311yescharacteristic
93C2×C5×C4⋊C4—34no—
94C2×C5×C4⋊C4—64no—
95C2×#685—34no—
96C2×#685—34no—
97C2×#685—34no—
98C2×#685—64no—
99C2×#685—64no—
100C2×#685—64no—
101C2×#683—24no—
102C2×#683—34no—
103C2×#683—64no—
104C2×#683C2×D314yescomplemented
105#3963—34no—
106C2×#399—151noSylow
107C23×C3×C5C2×D412yes—
108C23×C3×C5C2×D412yes—
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2×Q812yes—
111C23×C3×C5#4112yes—
112C23×C3×C5#4112yes—
113C23×C3×C5#4112yes—
114C23×C3×C5C2411yescharacteristic
115C22×D15—28no—
116C22×D15—28no—
117C22×D15—28no—
118C22×D15—22no—
119C22×D15—22no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—22no—
124C22×D15—44no—
125C22×D15—44no—
126C22×D15—44no—
127C22×D15—44no—
128C22×D15C2×Q814yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—44no—
133C2×Dic15—28no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15C2×D414yes—
137C2×C5×Dic3—28no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—44no—
144C2×C5×Dic3C2×D414yes—
145C2×C3×Dic5—28no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—44no—
152C2×C3×Dic5C2×D414yes—
153C24×D3—51no—
154C23×C3×C4—51no—
155C23×C3×C4—51no—
156C23×C3×C4C2×D511yescharacteristic
157C23×Dic3—51no—
158C23×Dic3C2×D511yescharacteristic
159C23×Dic3C2×D511yescharacteristic
160C2×C3×C4⋊C4—54no—
161C2×C3×C4⋊C4—104no—
162C2×(C2×D3)⋊C4—54no—
163C2×(C2×D3)⋊C4—54no—
164C2×(C2×D3)⋊C4—54no—
165C2×(C2×D3)⋊C4—104no—
166C2×(C2×D3)⋊C4—104no—
167C2×(C2×D3)⋊C4—104no—
168C2×Dic3⋊C4—24no—
169C2×Dic3⋊C4—54no—
170C2×Dic3⋊C4—104no—
171C2×Dic3⋊C4C2×D514yescomplemented
172C3⋊#95—54no—
173C24×C5C22×D311yescharacteristic
174C23×D5—34no—
175C23×D5—32no—
176C23×D5—62no—
177C23×D5—62no—
178C23×D5—62no—
179C23×D5—62no—
180C23×D5—62no—
181C23×D5—62no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—34no—
186C22×C4×C5—32no—
187C22×C4×C5—32no—
188C22×C4×C5—62no—
189C22×C4×C5—62no—
190C22×C4×C5—62no—
191C22×C4×C5—62no—
192C22×C4×C5—62no—
193C22×C4×C5C22×D312yes—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—34no—
200C22×Dic5—32no—
201C22×Dic5—62no—
202C22×Dic5—62no—
203C22×Dic5#6714yes—
204C22×Dic5C22×D312yes—
205C22×Dic5C22×D312yes—
206C5×C4⋊C4—68no—
207#685—68no—
208#685—68no—
209#685—68no—
210#683—28no—
211#683—68no—
212C22×C4⋊C4—31no—
213C22×C4⋊C4—51no—
214C22×C4⋊C4—151no—
215C22×C22⋊C4—151no—
216C22×C22⋊C4—151no—
217C22×C22⋊C4—151no—
218#399—158no—
219C2×#95—151no—
220C22×C3×C5C22⋊Q814yes—
221C22×C3×C5C22⋊Q814yes—
222C22×C3×C5C22⋊Q814yes—
223C22×C3×C5#12314yes—
224C22×C3×C5#12314yes—
225C22×C3×C5#12314yes—
226C22×C3×C5#12714yes—
227C22×C3×C5C22×D411yescharacteristic
228C22×C3×C5C22×D411yescharacteristic
229C22×C3×C5C22×D411yescharacteristic
230C22×C3×C5C22×Q811yescharacteristic
231C22×C3×C5C2×#4111yescharacteristic
232C22×C3×C5C2×#4111yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C2×D15—24no—
235C2×D15—24no—
236C2×D15—24no—
237C2×D15—42no—
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—42no—
241C2×D15—416no—
242C3×C4×C5—42no—
243Dic15—24no—
244C3×Dic5—24no—
245C3×Dic5—42no—
246C5×Dic3—24no—
247C5×Dic3—42no—
248C24×C3C22×D511yescharacteristic
249C23×D3—54no—
250C23×D3—52no—
251C23×D3—102no—
252C23×D3—102no—
253C23×D3—102no—
254C23×D3—102no—
255C23×D3—102no—
256C23×D3—102no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—54no—
261C22×C3×C4—52no—
262C22×C3×C4—52no—
263C22×C3×C4—102no—
264C22×C3×C4—102no—
265C22×C3×C4—102no—
266C22×C3×C4—102no—
267C22×C3×C4—102no—
268C22×C3×C4C22×D512yes—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—54no—
275C22×Dic3—52no—
276C22×Dic3—102no—
277C22×Dic3—102no—
278C22×Dic3C22⋊D514yes—
279C22×Dic3C22×D512yes—
280C22×Dic3C22×D512yes—
281C3×C4⋊C4—108no—
282(C2×D3)⋊C4—108no—
283(C2×D3)⋊C4—108no—
284(C2×D3)⋊C4—108no—
285Dic3⋊C4—28no—
286Dic3⋊C4—108no—
287C23×C5#23512yes—
288C23×C5#23512yes—
289C23×C5D3×D412yes—
290C23×C5D3×D412yes—
291C23×C5D3×Q812yes—
292C23×C5#23912yes—
293C23×C5C2×#6712yes—
294C23×C5C23×D311yescharacteristic
295C22×D5—34no—
296C22×D5—68no—
297C22×D5—68no—
298C22×D5—68no—
299C22×D5—62no—
300C22×D5—62no—
301C22×D5—62no—
302C22×D5—62no—
303C22×D5—62no—
304C22×D5—62no—
305C22×D5—124no—
306C22×D5—124no—
307C22×D5—124no—
308C22×D5—124no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—34no—
313C2×C4×C5—44no—
314C2×C4×C5—68no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5—62no—
319C2×C4×C5—62no—
320C2×C4×C5—124no—
321C2×Dic5—28no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—34no—
328C2×Dic5—44no—
329C2×Dic5—68no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5C2×#6714yes—
333C25—151no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—51no—
337C23×C4—51no—
338C23×C4—151no—
339C23×C4D3×D511yescharacteristic
340C2×C4⋊C4—34no—
341C2×C4⋊C4—54no—
342C2×C4⋊C4—64no—
343C2×C4⋊C4—104no—
344C2×C4⋊C4—154no—
345C2×C4⋊C4—304no—
346C2×C22⋊C4—154no—
347C2×C22⋊C4—154no—
348C2×C22⋊C4—154no—
349C2×C22⋊C4—304no—
350C2×C22⋊C4—304no—
351C2×C22⋊C4—304no—
352#95—154no—
353C2×C3×C5#39918yescomplemented
354C2×C3×C5C2×C22⋊Q811yescharacteristic
355C2×C3×C5C2×C22⋊Q811yescharacteristic
356C2×C3×C5C2×C22⋊Q811yescharacteristic
357C2×C3×C5C2×#12311yescharacteristic
358C2×C3×C5C2×#12311yescharacteristic
359C2×C3×C5C2×#12311yescharacteristic
360C2×C3×C5C2×#12711yescharacteristic
361D15—44no—
362C23×C3#70912yes—
363C23×C3#70912yes—
364C23×C3D4×D512yes—
365C23×C3D4×D512yes—
366C23×C3Q8×D512yes—
367C23×C3#71312yes—
368C23×C3C2×C22⋊D512yes—
369C23×C3C23×D511yescharacteristic
370C22×D3—54no—
371C22×D3—102no—
372C22×D3—102no—
373C22×D3—102no—
374C22×D3—102no—
375C22×D3—102no—
376C22×D3—102no—
377C22×D3—108no—
378C22×D3—108no—
379C22×D3—108no—
380C22×D3—204no—
381C22×D3—204no—
382C22×D3—204no—
383C22×D3—204no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—44no—
388C2×C3×C4—54no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—108no—
392C2×C3×C4—102no—
393C2×C3×C4—102no—
394C2×C3×C4—102no—
395C2×C3×C4—204no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—28no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—44no—
403C2×Dic3—54no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—108no—
407C2×Dic3C2×C22⋊D514yes—
408C22×C5#89414yes—
409C22×C5#89414yes—
410C22×C5#89614yes—
411C22×C5#89614yes—
412C22×C5#92914yes—
413C22×C5#94014yes—
414C22×C5#94614yes—
415C22×C5C2×#23511yescharacteristic
416C22×C5C2×#23511yescharacteristic
417C22×C5C2×D3×D411yescharacteristic
418C22×C5C2×D3×D411yescharacteristic
419C22×C5C2×D3×Q811yescharacteristic
420C22×C5C2×#23911yescharacteristic
421C22×C5C22×#6711yescharacteristic
422C2×D5—64no—
423C2×D5—64no—
424C2×D5—64no—
425C2×D5—1216no—
426C2×D5—122no—
427C2×D5—122no—
428C2×D5—122no—
429C2×D5—122no—
430C4×C5—42no—
431C4×C5—64no—
432C4×C5—122no—
433Dic5—24no—
434Dic5—42no—
435Dic5—64no—
436C24—154no—
437C24—152no—
438C24—302no—
439C24—302no—
440C24—302no—
441C24—302no—
442C24—302no—
443C24—302no—
444C24C2×D3×D511yescharacteristic
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—34no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—54no—
452C22×C4—52no—
453C22×C4—52no—
454C22×C4—62no—
455C22×C4—62no—
456C22×C4—62no—
457C22×C4—62no—
458C22×C4—62no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—154no—
465C22×C4—152no—
466C22×C4—302no—
467C22×C4—302no—
468C22×C4C2×D3×D512yes—
469C4⋊C4—68no—
470C4⋊C4—108no—
471C4⋊C4—308no—
472C22⋊C4—308no—
473C22⋊C4—308no—
474C22⋊C4—308no—
475C3×C5C2×#39911yescharacteristic, complemented, Hall
476C22×C3#404014yes—
477C22×C3#404014yes—
478C22×C3#404214yes—
479C22×C3#404214yes—
480C22×C3#407514yes—
481C22×C3#408614yes—
482C22×C3#409214yes—
483C22×C3C2×#70911yescharacteristic
484C22×C3C2×#70911yescharacteristic
485C22×C3C2×D4×D511yescharacteristic
486C22×C3C2×D4×D511yescharacteristic
487C22×C3C2×Q8×D511yescharacteristic
488C22×C3C2×#71311yescharacteristic
489C22×C3C22×C22⋊D511yescharacteristic
490C2×D3—104no—
491C2×D3—104no—
492C2×D3—104no—
493C2×D3—2016no—
494C2×D3—202no—
495C2×D3—202no—
496C2×D3—202no—
497C2×D3—202no—
498C3×C4—42no—
499C3×C4—104no—
500C3×C4—202no—
501Dic3—24no—
502Dic3—42no—
503Dic3—104no—
504C2×C5#499318yescomplemented
505C2×C5C2×#89411yescharacteristic
506C2×C5C2×#89411yescharacteristic
507C2×C5C2×#89611yescharacteristic
508C2×C5C2×#89611yescharacteristic
509C2×C5C2×#92911yescharacteristic
510C2×C5C2×#94011yescharacteristic
511C2×C5C2×#94611yescharacteristic
512D5—124no—
513C23—154no—
514C23—308no—
515C23—308no—
516C23—302no—
517C23—302no—
518C23—302no—
519C23—302no—
520C23—302no—
521C23—302no—
522C23—308no—
523C23—604no—
524C23—604no—
525C23—604no—
526C23—604no—
527C23#676912yes—
528C23D15⋊Q812yes—
529C23#677112yes—
530C23#677312yes—
531C23D5×#6712yes—
532C23D3×C22⋊D512yes—
533C23#679012yes—
534C23C22×D3×D511yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—34no—
539C2×C4—44no—
540C2×C4—54no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—68no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—102no—
548C2×C4—102no—
549C2×C4—108no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—124no—
554C2×C4—154no—
555C2×C4—204no—
556C2×C4—308no—
557C2×C4—302no—
558C2×C4—302no—
559C2×C3#6528118yescomplemented
560C2×C3C2×#404011yescharacteristic
561C2×C3C2×#404011yescharacteristic
562C2×C3C2×#404211yescharacteristic
563C2×C3C2×#404211yescharacteristic
564C2×C3C2×#407511yescharacteristic
565C2×C3C2×#408611yescharacteristic
566C2×C3C2×#409211yescharacteristic
567D3—204no—
568C5C2×#499311yescharacteristic, complemented, Sylow
569C22—304no—
570C22—304no—
571C22—304no—
572C22—602no—
573C22—602no—
574C22—6016no—
575C22—602no—
576C22—602no—
577C22#9134814yes—
578C22#9135114yes—
579C22#9137714yes—
580C22#9141114yes—
581C22#9142414yes—
582C22#9143314yes—
583C22#9156714yes—
584C22C2×#676911yescharacteristic
585C22C2×D15⋊Q811yescharacteristic
586C22C2×#677111yescharacteristic
587C22C2×#677311yescharacteristic
588C22C2×D5×#6711yescharacteristic
589C22C2×D3×C22⋊D511yescharacteristic
590C22C2×#679011yescharacteristic
591C4—42no—
592C4—64no—
593C4—104no—
594C4—122no—
595C4—202no—
596C4—304no—
597C3C2×#6528111yescharacteristic, complemented, Sylow
598C2—604no—
599C2#1174857418yesdirect product factor
600C2C2×#9134811yescharacteristic
601C2C2×#9135111yescharacteristic
602C2C2×#9137711yescharacteristic
603C2C2×#9141111yescharacteristic
604C2C2×#9142411yescharacteristic
605C2C2×#9143311yescharacteristic
606C2C2×#9156711yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC24×D15C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#399
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C5×Dic3⋊C4C2semidirect
3. C22×C3×#683C2semidirect
4. C22×#6669C2semidirect
7. C2×#90994C2semidirect
8. #11748574C2direct (N × H)
20. C2×C5×Dic3⋊C4C22semidirect
22. C2×C3×#683C22semidirect
24. C2×#6669C22semidirect
29. #90994C22semidirect
36. C22×#683D3semidirect
83. C22×Dic3⋊C4D5semidirect
104. C2×#683C2×D3semidirect
171. C2×Dic3⋊C4C2×D5semidirect
353. C2×C3×C5#399semidirect
475. C3×C5C2×#399semidirect
504. C2×C5#4993semidirect
559. C2×C3#65281semidirect
568. C5C2×#4993semidirect
597. C3C2×#65281semidirect
599. C2#11748574direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67142
C22×C5×Dic3⋊C42
C22×C3×#6832
C22×#66692
C22×#66672
C2×#909942
#117485742
C2×#652813
C2×#49935