Finite Group Databasebeta

← C2×#21450743 #29851786

Subgroups — C2×#21450743 #29851786

Order 15616.

3614 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519757C211yesmaximal, characteristic, complemented
2C22×#14519756C211yesmaximal, characteristic, complemented
3C22×#14519742C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D61C211yesmaximal, characteristic
5#21450743C2116yesmaximal, direct product factor
6C2×#16839686C212yesmaximal, complemented
7C2×#16839685C212yesmaximal, complemented
8C2×#16839662C212yesmaximal
9C2×#16839659C212yesmaximal, complemented
10C2×#16839631C211yesmaximal, characteristic, complemented
11C2×#16839619C211yesmaximal, characteristic, complemented
12C2×C61×#380C211yesmaximal, characteristic, complemented
13C23×Dic122C2211yescharacteristic
14C23×C22⋊D61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×#14519757—28no—
17C2×#14519757C2218yescomplemented
18C2×#14519756—28no—
19C2×#14519756C2218yescomplemented
20C2×#14519742—28no—
21C2×#14519742C2218yescomplemented
22C2×C4×C22⋊D61—28no—
23C2×C4×C22⋊D61C2218yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2212yes—
26C22×#11758196C2212yes—
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2212yes—
29C22×#11758196C2212yes—
30C22×#11758196C2212yes—
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2212yes—
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2212yes—
35C22×#11758198C2212yes—
36C22×C4×Dic61C2212yes—
37C22×C4×Dic61C2211yescharacteristic
38#16839686C22116yescomplemented
39#16839685C22116yescomplemented
40#16839662C22116yes—
41#16839659C22116yescomplemented
42#16839631C2218yescomplemented
43#16839619C2218yescomplemented
44C2×#14519684C2212yes—
45C24×C4×C61C2211yescharacteristic
46C22×C4⋊C4×C61C2211yescharacteristic
47C22×C4⋊C4×C61C2211yescharacteristic
48C22×C22⋊C4×C61C2212yes—
49C61×#380C2218yescomplemented
50C2×#95×C61C2212yes—
51C24×D61C2311yescharacteristic
52C22×Dic122—24no—
53C22×Dic122—24no—
54C22×Dic122D418yescomplemented
55C22×Dic122C2314yes—
56C22×C22⋊D61—24no—
57C22×C22⋊D61—24no—
58C22×C22⋊D61Q818yescomplemented
59C22×C22⋊D61C2314yes—
60C23×Dic61C2312yes—
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2312yes—
64C23×Dic61C2311yescharacteristic
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61C2314yes—
69#14519757—232no—
70#14519756—232no—
71#14519742—232no—
72C4×C22⋊D61—232no—
73C2×C4⋊Dic61—24no—
74C2×C4⋊Dic61—28no—
75C2×C4⋊Dic61C2318yes—
76C2×C4⋊Dic61C2314yes—
77C2×#11758196—24no—
78C2×#11758196—28no—
79C2×#11758196—28no—
80C2×#11758196—28no—
81C2×#11758196—44no—
82C2×#11758196C2318yes—
83C2×#11758196C2318yes—
84C2×#11758196C2314yes—
85C2×#11758196C2318yes—
86C2×#11758196C2318yes—
87C2×C22⋊Dic61—24no—
88C2×C22⋊Dic61—28no—
89C2×C22⋊Dic61C2314yes—
90C2×C22⋊Dic61C2318yes—
91C2×#11758198—24no—
92C2×#11758198—28no—
93C2×#11758198—44no—
94C2×#11758198C2314yes—
95C2×#11758198C2318yes—
96C2×#11758198C2318yes—
97C2×C4×Dic61—28no—
98C2×C4×Dic61D418yes—
99C2×C4×Dic61C2318yes—
100C2×C4×Dic61C2314yes—
101#14519684C2318yes—
102C25×C61C2311yescharacteristic
103C23×C4×C61—24no—
104C23×C4×C61—24no—
105C23×C4×C61—24no—
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2312yes—
109C23×C4×C61C2314yes—
110C23×C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61—24no—
112C2×C4⋊C4×C61—24no—
113C2×C4⋊C4×C61C2314yes—
114C2×C4⋊C4×C61C2314yes—
115C2×C22⋊C4×C61—44no—
116C2×C22⋊C4×C61C2318yes—
117#95×C61C2318yes—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61C2×Q814yes—
125C24×C61C2412yes—
126C24×C61C2411yescharacteristic
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61C2×Q814yes—
134C23×D61C2412yes—
135C22×C4×C61—24no—
136C22×C4×C61—24no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—24no—
141C22×C4×C61—24no—
142C22×C4×C61—24no—
143C22×C4×C61—24no—
144C22×C4×C61—28no—
145C22×C4×C61—28no—
146C22×C4×C61—28no—
147C22×C4×C61—416no—
148C22×C4×C61C2×D414yes—
149C22×C4×C61C2×D414yes—
150C22×C4×C61#4114yes—
151C22×C4×C61C2412yes—
152C22×C4×C61C2414yes—
153C22×C4×C61C2414yes—
154C22×C4×C61C2412yes—
155C2×C22⋊D61—232no—
156C2×C22⋊D61—28no—
157C2×C22⋊D61—28no—
158C2×C22⋊D61C2×Q8116yescomplemented
159C22×Dic61—24no—
160C22×Dic61—24no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—24no—
166C22×Dic61—22no—
167C22×Dic61—24no—
168C22×Dic61—24no—
169C22×Dic61C2×D418yes—
170C22×Dic61C2×D414yes—
171C22×Dic61C2×D414yes—
172C22×Dic61C2×Q814yes—
173C22×Dic61#4114yes—
174C22×Dic61C2412yes—
175C22×Dic61C2414yes—
176C22×Dic61C2414yes—
177C22×Dic61C2412yes—
178C22×Dic61C2412yes—
179C2×C4×D61—28no—
180C2×C4×D61—28no—
181C2×C4×D61—28no—
182C2×C4×D61—416no—
183C2×Dic122—232no—
184C2×Dic122—28no—
185C2×Dic122—28no—
186C2×Dic122C2×D4116yescomplemented
187C4⋊C4×C61—28no—
188C4⋊C4×C61—28no—
189C22⋊C4×C61—48no—
190C22⋊Dic61—28no—
191C22⋊Dic61—216no—
192#11758198—28no—
193#11758198—216no—
194#11758198—48no—
195C4⋊Dic61—28no—
196C4⋊Dic61—216no—
197#11758196—28no—
198#11758196—216no—
199#11758196—216no—
200#11758196—216no—
201#11758196—48no—
202C4×Dic61—216no—
203C4×Dic61C2×D4116yes—
204C23×C61—28no—
205C23×C61—28no—
206C23×C61—28no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—44no—
214C23×C61—44no—
215C23×C61—44no—
216C23×C61—44no—
217C23×C61C22×D412yes—
218C23×C61C22×D412yes—
219C23×C61C22×Q814yes—
220C23×C61C22×Q812yes—
221C23×C61C2×#4112yes—
222C23×C61C2×#4112yes—
223C23×C61H(5,𝔽2)12yes—
224C23×C612−1+412yes—
225C23×C61C2511yescharacteristic
226C22×D61—28no—
227C22×D61—28no—
228C22×D61—28no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—44no—
236C22×D61—44no—
237C22×D61—44no—
238C22×D61—44no—
239C22×D61C22×Q814yes—
240C2×C4×C61—24no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—22no—
246C2×C4×C61—24no—
247C2×C4×C61—24no—
248C2×C4×C61—24no—
249C2×C4×C61—44no—
250C2×C4×C61—48no—
251C2×C4×C61—48no—
252C2×C4×C61—416no—
253C2×C4×C61#121116yes—
254C2×C4×C61C22×D414yes—
255C2×C4×C61C22×D414yes—
256C2×C4×C61C2×#4114yes—
257C22⋊D61—232no—
258C2×Dic61—216no—
259C2×Dic61—28no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—24no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—24no—
268C2×Dic61—22no—
269C2×Dic61—24no—
270C2×Dic61—44no—
271C2×Dic61—48no—
272C2×Dic61C22⋊Q8116yescomplemented
273C2×Dic61C22×D414yes—
274C2×Dic61C22×D418yes—
275C2×Dic61C22×D414yes—
276C2×Dic61C22×Q814yes—
277C2×Dic61C2×#4114yes—
278C4×D61—416no—
279Dic122—232no—
280C2×#2538—611nomaximal, Sylow
281C22×C61—24no—
282C22×C61—24no—
283C22×C61—24no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—416no—
289C22×C61C2×#12114yes—
290C22×C61C2×C22⋊Q814yes—
291C22×C61#53714yes—
292C22×C61D4×Q814yes—
293C22×C61#55014yes—
294C22×C61#55414yes—
295C22×C61#55614yes—
296C22×C61C23×D411yescharacteristic
297C22×C61C23×D411yescharacteristic
298C22×C61C23×Q811yescharacteristic
299C22×C61C22×#4111yescharacteristic
300C22×C61C22×#4111yescharacteristic
301C22×C61C2×H(5,𝔽2)11yescharacteristic
302C22×C61C2×2−1+411yescharacteristic
303C2×D61—24no—
304C2×D61—24no—
305C2×D61—24no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—416no—
311C4×C61—42no—
312C4×C61—44no—
313C4×C61—44no—
314C4×C61C2×#12118yes—
315Dic61—28no—
316Dic61—24no—
317Dic61—42no—
318Dic61—44no—
319Dic61C2×C22⋊Q818yescomplemented
320C22×C22⋊Q8—611no—
321C22×C22⋊Q8—611no—
322C22×C4×Q8—611no—
323C22×C4×D4—611no—
324#2538—6116no—
325C2×#396—612no—
326C2×#396—612no—
327C2×#390—612no—
328C2×#389—612no—
329C2×#384—611no—
330C2×#380—611no—
331C2×#380D6111yescharacteristic, complemented
332C2×C61—44no—
333C2×C61#253818yescomplemented
334C2×C61C22×#12111yescharacteristic
335C2×C61C22×C22⋊Q811yescharacteristic
336C2×C61C2×#53711yescharacteristic
337C2×C61C2×D4×Q811yescharacteristic
338C2×C61C2×#55011yescharacteristic
339C2×C61C2×#55411yescharacteristic
340C2×C61C2×#55611yescharacteristic
341D61—44no—
342C23×Q8—611no—
343C23×D4—611no—
344C24×C4—611no—
345C24×C4C2×D6111yescharacteristic
346C2×C22⋊Q8—618no—
347C2×C22⋊Q8—618no—
348C2×C22⋊Q8—1228no—
349C2×C22⋊Q8—1228no—
350C2×C4×Q8—618no—
351C2×C4×Q8—1228no—
352C2×C4×D4—618no—
353C2×C4×D4—1228no—
354C22×C4⋊C4—612no—
355C22×C4⋊C4—612no—
356C22×C4⋊C4—611no—
357C22×C4⋊C4—612no—
358C22×C4⋊C4—612no—
359C22×C4⋊C4—611no—
360C22×C4⋊C4—612no—
361C22×C4⋊C4C2×D6111yescharacteristic
362C22×C4⋊C4C2×D6111yescharacteristic
363C22×C22⋊C4—611no—
364C22×C22⋊C4—612no—
365C22×C22⋊C4—611no—
366C22×C22⋊C4—612no—
367C22×C22⋊C4—612no—
368C22×C22⋊C4C2×D6112yes—
369C22×C42—611no—
370C22×C42—612no—
371#396—6116no—
372#396—6116no—
373#390—6116no—
374#389—6116no—
375#384—618no—
376#380—618no—
377#380C2×D6118yescomplemented
378C2×#95—612no—
379C2×#95C2×D6112yes—
380C61C2×#253811yescharacteristic, complemented, Sylow
381C25—611no—
382C25C22×D6111yescharacteristic
383C22×Q8—618no—
384C22×Q8—614no—
385C22×Q8—1224no—
386C22×Q8—1224no—
387C22×D4—618no—
388C22×D4—614no—
389C22×D4—1224no—
390C22×D4—1224no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—612no—
397C23×C4—612no—
398C23×C4—611no—
399C23×C4—614no—
400C23×C4—1224no—
401C23×C4—1224no—
402C23×C4—1224no—
403C23×C4C22×D6114yes—
404C23×C4C22×D6112yes—
405C23×C4C22×D6112yes—
406C23×C4C22×D6111yescharacteristic
407C23×C4C22×D6111yescharacteristic
408C22⋊Q8—12232no—
409C22⋊Q8—12232no—
410C4×Q8—12232no—
411C4×D4—12232no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—614no—
415C2×C4⋊C4—618no—
416C2×C4⋊C4—614no—
417C2×C4⋊C4—618no—
418C2×C4⋊C4—618no—
419C2×C4⋊C4—618no—
420C2×C4⋊C4—618no—
421C2×C4⋊C4—1224no—
422C2×C4⋊C4—1228no—
423C2×C4⋊C4—1228no—
424C2×C4⋊C4—1228no—
425C2×C4⋊C4—1228no—
426C2×C4⋊C4—1224no—
427C2×C4⋊C4—2444no—
428C2×C4⋊C4C22×D6114yes—
429C2×C4⋊C4C22×D6114yes—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—614no—
432C2×C22⋊C4—618no—
433C2×C22⋊C4—614no—
434C2×C22⋊C4—618no—
435C2×C22⋊C4—618no—
436C2×C22⋊C4—1224no—
437C2×C22⋊C4—1228no—
438C2×C22⋊C4—1224no—
439C2×C22⋊C4—1228no—
440C2×C22⋊C4—2444no—
441C2×C22⋊C4C22×D6118yes—
442C2×C42—618no—
443C2×C42—614no—
444C2×C42—618no—
445C2×C42—1228no—
446#95—618no—
447#95C22×D6118yes—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—614no—
455C24—612no—
456C24—1222no—
457C24—1222no—
458C24—1222no—
459C24—1222no—
460C24—1222no—
461C24—1222no—
462C24Q8×D6114yes—
463C24C23×D6112yes—
464C24C23×D6111yescharacteristic
465C2×Q8—6116no—
466C2×Q8—1228no—
467C2×Q8—1228no—
468C2×Q8—12232no—
469C2×D4—6116no—
470C2×D4—1228no—
471C2×D4—12232no—
472C2×D4—1228no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—416no—
486C22×C4—614no—
487C22×C4—614no—
488C22×C4—614no—
489C22×C4—612no—
490C22×C4—614no—
491C22×C4—618no—
492C22×C4—612no—
493C22×C4—614no—
494C22×C4—612no—
495C22×C4—614no—
496C22×C4—1224no—
497C22×C4—1224no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1224no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1224no—
504C22×C4—1222no—
505C22×C4—1224no—
506C22×C4—1228no—
507C22×C4—1228no—
508C22×C4—1228no—
509C22×C4—24416no—
510C22×C4#1175822214yes—
511C22×C4D4×D6114yes—
512C22×C4D4×D6114yes—
513C22×C4C23×D6114yes—
514C22×C4C23×D6112yes—
515C22×C4C23×D6114yes—
516C22×C4C23×D6112yes—
517C4⋊C4—28no—
518C4⋊C4—28no—
519C4⋊C4—12216no—
520C4⋊C4—1228no—
521C4⋊C4—12216no—
522C4⋊C4—12216no—
523C4⋊C4—12216no—
524C4⋊C4—1228no—
525C4⋊C4—2448no—
526C22⋊C4—48no—
527C22⋊C4—1228no—
528C22⋊C4—12216no—
529C22⋊C4—1228no—
530C22⋊C4—12216no—
531C22⋊C4—2448no—
532C42—6116no—
533C42—12216no—
534C23—28no—
535C23—28no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—28no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23—614no—
548C23—1228no—
549C23—1228no—
550C23—1222no—
551C23—1222no—
552C23—1222no—
553C23—1222no—
554C23—1222no—
555C23—1222no—
556C23—1228no—
557C23—2444no—
558C23—2444no—
559C23—2444no—
560C23—2444no—
561C23C2×D4×D6112yes—
562C23C2×D4×D6112yes—
563C23C2×Q8×D6114yes—
564C23C2×Q8×D6112yes—
565C23#41×D6112yes—
566C23C2×#1175822212yes—
567C23#1451982212yes—
568C23#1451982412yes—
569C23C24×D6111yescharacteristic
570Q8—12232no—
571D4—12232no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—44no—
582C2×C4—48no—
583C2×C4—48no—
584C2×C4—416no—
585C2×C4—6116no—
586C2×C4—614no—
587C2×C4—614no—
588C2×C4—614no—
589C2×C4—614no—
590C2×C4—618no—
591C2×C4—12216no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1228no—
597C2×C4—1224no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1224no—
601C2×C4—1222no—
602C2×C4—1224no—
603C2×C4—2444no—
604C2×C4—2448no—
605C2×C4—24416no—
606C2×C4#14519750116yes—
607C2×C4C2×D4×D6114yes—
608C2×C4C2×D4×D6114yes—
609C2×C4C2×#1175822214yes—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—416no—
618C22—1224no—
619C22—1224no—
620C22—1224no—
621C22—2442no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22—24416no—
626C22C2×#1451975014yes—
627C22C22⋊Q8×D6114yes—
628C22#1684034114yes—
629C22#1684042514yes—
630C22#1684043014yes—
631C22#1684046714yes—
632C22#1684048014yes—
633C22C22×D4×D6111yescharacteristic
634C22C22×D4×D6111yescharacteristic
635C22C22×Q8×D6111yescharacteristic
636C22C2×#41×D6111yescharacteristic
637C22C22×#1175822211yescharacteristic
638C22C2×#1451982211yescharacteristic
639C22C2×#1451982411yescharacteristic
640C4—42no—
641C4—44no—
642C4—44no—
643C4—618no—
644C4—1228no—
645C4—1224no—
646C4—2442no—
647C4—2444no—
648C4C2×#1451975018yes—
649C2—44no—
650C2—2444no—
651C2#2145074318yesdirect product factor
652C2C22×#1451975011yescharacteristic
653C2C2×C22⋊Q8×D6111yescharacteristic
654C2C2×#1684034111yescharacteristic
655C2C2×#1684042511yescharacteristic
656C2C2×#1684043011yescharacteristic
657C2C2×#1684046711yescharacteristic
658C2C2×#1684048011yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#380C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#380D61
hypocenterC61C2×#2538
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#14519757C2semidirect
2. C22×#14519756C2semidirect
3. C22×#14519742C2semidirect
5. #21450743C2direct (N × H)
6. C2×#16839686C2semidirect
7. C2×#16839685C2semidirect
9. C2×#16839659C2semidirect
10. C2×#16839631C2semidirect
11. C2×#16839619C2semidirect
12. C2×C61×#380C2semidirect
17. C2×#14519757C22semidirect
19. C2×#14519756C22semidirect
21. C2×#14519742C22semidirect
38. #16839686C22semidirect
39. #16839685C22semidirect
41. #16839659C22semidirect
42. #16839631C22semidirect
43. #16839619C22semidirect
49. C61×#380C22semidirect
54. C22×Dic122D4semidirect
58. C22×C22⋊D61Q8semidirect
158. C2×C22⋊D61C2×Q8semidirect
186. C2×Dic122C2×D4semidirect
272. C2×Dic61C22⋊Q8semidirect
319. Dic61C2×C22⋊Q8semidirect
331. C2×#380D61semidirect
333. C2×C61#2538semidirect
377. #380C2×D61semidirect
380. C61C2×#2538semidirect
651. C2#21450743direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197572
C22×#145197562
C22×#145197422
C22×C4×C22⋊D612
#214507432
C2×#168396862
C2×#168396852
C2×#168396622
C2×#168396592
C2×#168396312
C2×#168396192
C2×C61×#3802
C2×#253861