Finite Group Databasebeta

← C2×#21449273 #29847972

Subgroups — C2×#21449273 #29847972

Order 15616.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519753C211yesmaximal, characteristic, complemented
2C22×#14519753C211yesmaximal, characteristic, complemented
3C22×C4×D244C211yesmaximal, characteristic
4C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
5#21449273C2116yesmaximal, direct product factor
6C2×#16839696C212yesmaximal, complemented
7C2×#16839686C212yesmaximal, complemented
8C2×#16839660C211yesmaximal, characteristic, complemented
9C2×#16839640C212yesmaximal
10C2×#16839621C212yesmaximal, complemented
11C2×#16839619C211yesmaximal, characteristic, complemented
12C2×C61×#391C211yesmaximal, characteristic, complemented
13C23×D244C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C23×C4×D61C2212yes—
16C23×C4×D61C2211yescharacteristic
17C2×#14519753—28no—
18C2×#14519753—28no—
19C2×#14519753C2218yescomplemented
20C2×#14519753C2218yescomplemented
21C2×C4×D244—28no—
22C2×C4×D244C2218yes—
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196C2212yes—
27C22×#11758196C2212yes—
28C22×#11758196C2212yes—
29C22×#11758196C2212yes—
30C2×C4⋊C4×D61—28no—
31C2×C4⋊C4×D61C2218yescomplemented
32C22×#11758198C2212yes—
33C22×#11758198C2212yes—
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2212yes—
37#16839696C22116yescomplemented
38#16839686C22116yescomplemented
39#16839660C2218yescomplemented
40#16839640C22116yes—
41#16839621C22116yescomplemented
42#16839619C2218yescomplemented
43C2×#14519684C2212yes—
44C2×#14519684C2212yes—
45C23×Q8×C61C2211yescharacteristic
46C22×C4⋊C4×C61C2211yescharacteristic
47C22×C42×C61C2211yescharacteristic
48C61×#391C2218yescomplemented
49C2×#95×C61C2212yes—
50C2×#95×C61C2212yes—
51C24×D61C2311yescharacteristic
52C24×D61C2311yescharacteristic
53C22×D244—24no—
54C22×D244—24no—
55C22×D244Q818yescomplemented
56C22×D244C2314yes—
57C23×Dic61C2312yes—
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2312yes—
61C22×C4×D61—24no—
62C22×C4×D61—24no—
63C22×C4×D61—28no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61—28no—
68C22×C4×D61—44no—
69C22×C4×D61D418yes—
70C22×C4×D61C2314yes—
71C22×C4×D61C2318yes—
72C22×C4×D61C2314yes—
73#14519753—232no—
74#14519753—232no—
75C4×D244—232no—
76C2×C4⋊Dic61—24no—
77C2×C4⋊Dic61—24no—
78C2×C4⋊Dic61D418yescomplemented
79C2×C4⋊Dic61C2314yes—
80C2×C4⋊Dic61C2314yes—
81C2×C4⋊Dic61C2314yes—
82C2×#11758196—28no—
83C2×#11758196—28no—
84C2×#11758196—28no—
85C2×#11758196—44no—
86C2×#11758196C2318yes—
87C2×#11758196C2318yes—
88C2×#11758196C2318yes—
89C2×#11758196C2318yes—
90C4⋊C4×D61—232no—
91C2×#11758198—24no—
92C2×#11758198—28no—
93C2×#11758198—24no—
94C2×#11758198—28no—
95C2×#11758198—44no—
96C2×#11758198C2314yes—
97C2×#11758198C2318yes—
98C2×#11758198C2314yes—
99C2×#11758198C2318yes—
100C2×#11758198C2318yes—
101#14519684C2318yes—
102#14519684C2318yes—
103C22×Q8×C61—24no—
104C22×Q8×C61—24no—
105C22×Q8×C61—24no—
106C22×Q8×C61C2314yes—
107C23×C4×C61C2312yes—
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2312yes—
110C23×C4×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61—24no—
113C2×C4⋊C4×C61C2314yes—
114C2×C42×C61—24no—
115C2×C42×C61C2314yes—
116#95×C61C2318yes—
117#95×C61C2318yes—
118C24×C61C2411yescharacteristic
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61C2×D414yes—
130C23×D61C2×Q814yes—
131C23×D61C2×Q814yes—
132C23×D61#4114yes—
133C23×D61C2412yes—
134C23×D61C2412yes—
135C2×Q8×C61—28no—
136C2×Q8×C61—28no—
137C2×Q8×C61—28no—
138C2×Q8×C61—416no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—24no—
142C22×C4×C61—22no—
143C22×C4×C61—24no—
144C22×C4×C61—24no—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—24no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61C2×D414yes—
151C22×C4×C61C2×D414yes—
152C22×C4×C61C2×Q814yes—
153C22×C4×C61#4114yes—
154C22×C4×C61C2414yes—
155C22×C4×C61C2412yes—
156C22×C4×C61C2414yes—
157C22×C4×C61C2412yes—
158C22×C4×C61C2412yes—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—24no—
162C22×Dic61—24no—
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×Dic61C2412yes—
172C22×Dic61C2414yes—
173C22×Dic61C2414yes—
174C22×Dic61C2412yes—
175C2×D244—232no—
176C2×D244—28no—
177C2×D244—28no—
178C2×D244C2×Q8116yescomplemented
179C2×C4×D61—232no—
180C2×C4×D61—28no—
181C2×C4×D61—28no—
182C2×C4×D61—216no—
183C2×C4×D61—28no—
184C2×C4×D61—28no—
185C2×C4×D61—28no—
186C2×C4×D61—216no—
187C2×C4×D61—48no—
188C2×C4×D61—432no—
189C2×C4×D61—416no—
190C2×C4×D61C2×D4116yes—
191C4⋊C4×C61—28no—
192C42×C61—28no—
193#11758198—28no—
194#11758198—216no—
195#11758198—28no—
196#11758198—216no—
197#11758198—48no—
198C4⋊Dic61—28no—
199C4⋊Dic61—28no—
200C4⋊Dic61C2×D4116yescomplemented
201#11758196—216no—
202#11758196—216no—
203#11758196—216no—
204#11758196—48no—
205C23×C61C22×D412yes—
206C23×C61C22×D412yes—
207C23×C61C22×Q812yes—
208C23×C61C2×#4112yes—
209C23×C61C2×#4112yes—
210C23×C61H(5,𝔽2)12yes—
211C23×C612−1+412yes—
212C23×C61C2511yescharacteristic
213C22×D61—28no—
214C22×D61—28no—
215C22×D61—28no—
216C22×D61—28no—
217C22×D61—28no—
218C22×D61—28no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—28no—
224C22×D61—28no—
225C22×D61—28no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—44no—
233C22×D61—44no—
234C22×D61—44no—
235C22×D61—44no—
236C22×D61C22⋊Q8116yescomplemented
237C22×D61C22×D414yes—
238C22×D61C22×Q814yes—
239C22×D61C22×Q814yes—
240C22×D61C2×#4114yes—
241Q8×C61—416no—
242C2×C4×C61—28no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—24no—
246C2×C4×C61—24no—
247C2×C4×C61—24no—
248C2×C4×C61—22no—
249C2×C4×C61—24no—
250C2×C4×C61—24no—
251C2×C4×C61—22no—
252C2×C4×C61—24no—
253C2×C4×C61—22no—
254C2×C4×C61—48no—
255C2×C4×C61—44no—
256C2×C4×C61—48no—
257C2×C4×C61#121116yes—
258C2×C4×C61C22×D414yes—
259C2×C4×C61C22×D414yes—
260C2×C4×C61C22×Q814yes—
261C2×C4×C61C2×#4114yes—
262C2×Dic61—28no—
263C2×Dic61—216no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—22no—
269C2×Dic61—24no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—24no—
273C2×Dic61—24no—
274C2×Dic61—44no—
275C2×Dic61—48no—
276C2×Dic61C22×D414yes—
277C2×Dic61C22×D418yes—
278D244—232no—
279C4×D61—232no—
280C4×D61—432no—
281C4×D61—416no—
282C2×#2417—611nomaximal, Sylow
283C22×C61C2×#12114yes—
284C22×C61C2×C22⋊Q814yes—
285C22×C61#53714yes—
286C22×C61#54614yes—
287C22×C61D4×Q814yes—
288C22×C61#55214yes—
289C22×C61#55414yes—
290C22×C61C23×D411yescharacteristic
291C22×C61C23×D411yescharacteristic
292C22×C61C23×Q811yescharacteristic
293C22×C61C22×#4111yescharacteristic
294C22×C61C22×#4111yescharacteristic
295C22×C61C2×H(5,𝔽2)11yescharacteristic
296C22×C61C2×2−1+411yescharacteristic
297C2×D61—24no—
298C2×D61—232no—
299C2×D61—24no—
300C2×D61—24no—
301C2×D61—24no—
302C2×D61—24no—
303C2×D61—24no—
304C2×D61—24no—
305C2×D61—24no—
306C2×D61—24no—
307C2×D61—42no—
308C2×D61—416no—
309C2×D61—42no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61C2×C22⋊Q818yescomplemented
313C4×C61—24no—
314C4×C61—44no—
315C4×C61—42no—
316C4×C61—44no—
317C4×C61C2×#12118yes—
318Dic61—24no—
319Dic61—28no—
320Dic61—42no—
321Dic61—44no—
322C22×C22⋊Q8—611no—
323C22×C22⋊Q8—611no—
324C22×C4×D4—611no—
325C23×C4⋊C4—611no—
326#2417—6116no—
327C2×#398—612no—
328C2×#396—612no—
329C2×#391D6111yescharacteristic, complemented
330C2×#389—611no—
331C2×#386—612no—
332C2×#380—612no—
333C2×#380—611no—
334C2×C61#241718yescomplemented
335C2×C61C22×#12111yescharacteristic
336C2×C61C22×C22⋊Q811yescharacteristic
337C2×C61C2×#53711yescharacteristic
338C2×C61C2×#54611yescharacteristic
339C2×C61C2×D4×Q811yescharacteristic
340C2×C61C2×#55211yescharacteristic
341C2×C61C2×#55411yescharacteristic
342D61—28no—
343D61—44no—
344C23×Q8C2×D6111yescharacteristic
345C23×D4—611no—
346C24×C4—611no—
347C24×C4—611no—
348C24×C4—612no—
349C2×C22⋊Q8—618no—
350C2×C22⋊Q8—618no—
351C2×C22⋊Q8—1228no—
352C2×C22⋊Q8—1228no—
353C2×C4×D4—618no—
354C2×C4×D4—1228no—
355C22×C4⋊C4—611no—
356C22×C4⋊C4—612no—
357C22×C4⋊C4—612no—
358C22×C4⋊C4—612no—
359C22×C4⋊C4—611no—
360C22×C4⋊C4—611no—
361C22×C4⋊C4—612no—
362C22×C4⋊C4—618no—
363C22×C4⋊C4—1228no—
364C22×C4⋊C4C2×D6111yescharacteristic
365C22×C22⋊C4—611no—
366C22×C22⋊C4—612no—
367C22×C22⋊C4—611no—
368C22×C22⋊C4—612no—
369C22×C22⋊C4—612no—
370C22×C42C2×D6111yescharacteristic
371#398—6116no—
372#396—6116no—
373#391C2×D6118yescomplemented
374#389—618no—
375#386—6116no—
376#380—618no—
377#380—6116no—
378C2×#95—612no—
379C2×#95—612no—
380C2×#95C2×D6112yes—
381C2×#95C2×D6112yes—
382C61C2×#241711yescharacteristic, complemented, Sylow
383C25—611no—
384C25—611no—
385C22×Q8—24no—
386C22×Q8—24no—
387C22×Q8—24no—
388C22×Q8C22×D6114yes—
389C22×D4—618no—
390C22×D4—614no—
391C22×D4—1224no—
392C22×D4—1224no—
393C23×C4—611no—
394C23×C4—612no—
395C23×C4—618no—
396C23×C4—614no—
397C23×C4—612no—
398C23×C4—611no—
399C23×C4—614no—
400C23×C4—618no—
401C23×C4—1228no—
402C23×C4—1228no—
403C23×C4—1224no—
404C23×C4—1224no—
405C23×C4—1224no—
406C23×C4—1224no—
407C23×C4—1224no—
408C23×C4—2444no—
409C23×C4C22×D6112yes—
410C23×C4C22×D6111yescharacteristic
411C23×C4C22×D6112yes—
412C23×C4C22×D6111yescharacteristic
413C23×C4C22×D6111yescharacteristic
414C22⋊Q8—12232no—
415C22⋊Q8—12232no—
416C4×D4—12232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—618no—
419C2×C4⋊C4—614no—
420C2×C4⋊C4—618no—
421C2×C4⋊C4—614no—
422C2×C4⋊C4—614no—
423C2×C4⋊C4—618no—
424C2×C4⋊C4—618no—
425C2×C4⋊C4—618no—
426C2×C4⋊C4—12232no—
427C2×C4⋊C4—1228no—
428C2×C4⋊C4—1224no—
429C2×C4⋊C4—1228no—
430C2×C4⋊C4—1228no—
431C2×C4⋊C4—1224no—
432C2×C4⋊C4—2444no—
433C2×C4⋊C4C22×D6114yes—
434C2×C22⋊C4—614no—
435C2×C22⋊C4—614no—
436C2×C22⋊C4—618no—
437C2×C22⋊C4—618no—
438C2×C22⋊C4—618no—
439C2×C22⋊C4—1224no—
440C2×C22⋊C4—1228no—
441C2×C22⋊C4—1224no—
442C2×C22⋊C4—1228no—
443C2×C22⋊C4—2444no—
444C2×C42—24no—
445C2×C42C22×D6114yes—
446#95—618no—
447#95—618no—
448#95C22×D6118yes—
449#95C22×D6118yes—
450C24—614no—
451C24—614no—
452C24—614no—
453C24—612no—
454C24—614no—
455C24—612no—
456C24—1222no—
457C24—1222no—
458C24—1222no—
459C24—1222no—
460C24—1222no—
461C24—1222no—
462C24—1222no—
463C24—1222no—
464C24—1222no—
465C24—1222no—
466C24C23×D6111yescharacteristic
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—416no—
471C2×D4—6116no—
472C2×D4—1228no—
473C2×D4—12232no—
474C2×D4—1228no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—618no—
487C22×C4—614no—
488C22×C4—614no—
489C22×C4—612no—
490C22×C4—6116no—
491C22×C4—614no—
492C22×C4—612no—
493C22×C4—12216no—
494C22×C4—12216no—
495C22×C4—1222no—
496C22×C4—1224no—
497C22×C4—1222no—
498C22×C4—1224no—
499C22×C4—1228no—
500C22×C4—1228no—
501C22×C4—12232no—
502C22×C4—1224no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1224no—
507C22×C4—1224no—
508C22×C4—1228no—
509C22×C4—1228no—
510C22×C4—1228no—
511C22×C4—2448no—
512C22×C4—24432no—
513C22×C4—24416no—
514C22×C4#1175822214yes—
515C22×C4D4×D6114yes—
516C22×C4D4×D6114yes—
517C22×C4Q8×D6114yes—
518C22×C4C23×D6114yes—
519C22×C4C23×D6112yes—
520C22×C4C23×D6114yes—
521C22×C4C23×D6112yes—
522C22×C4C23×D6112yes—
523C4⋊C4—28no—
524C4⋊C4—6116no—
525C4⋊C4—12216no—
526C4⋊C4—12216no—
527C4⋊C4—12216no—
528C4⋊C4—1228no—
529C4⋊C4—1228no—
530C4⋊C4—2448no—
531C22⋊C4—1228no—
532C22⋊C4—12216no—
533C22⋊C4—1228no—
534C22⋊C4—12216no—
535C22⋊C4—2448no—
536C42—28no—
537C23—6116no—
538C23—614no—
539C23—614no—
540C23—614no—
541C23—614no—
542C23—1228no—
543C23—1228no—
544C23—1228no—
545C23—1222no—
546C23—1222no—
547C23—1222no—
548C23—1222no—
549C23—1228no—
550C23—1228no—
551C23—1228no—
552C23—1228no—
553C23—1228no—
554C23—1222no—
555C23—1222no—
556C23—1222no—
557C23—1222no—
558C23—1222no—
559C23—1222no—
560C23—1228no—
561C23—2444no—
562C23—2444no—
563C23—2444no—
564C23—2444no—
565C23C2×D4×D6112yes—
566C23C2×D4×D6112yes—
567C23C2×Q8×D6112yes—
568C23#41×D6112yes—
569C23C2×#1175822212yes—
570C23#1451982312yes—
571C23#1451982512yes—
572C23C24×D6111yescharacteristic
573Q8—416no—
574D4—12232no—
575C2×C4—28no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—48no—
588C2×C4—44no—
589C2×C4—48no—
590C2×C4—618no—
591C2×C4—614no—
592C2×C4—1228no—
593C2×C4—1222no—
594C2×C4—1224no—
595C2×C4—1222no—
596C2×C4—1224no—
597C2×C4—12216no—
598C2×C4—12232no—
599C2×C4—1224no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—24432no—
606C2×C4—2444no—
607C2×C4—2448no—
608C2×C4—24416no—
609C2×C4#14519750116yes—
610C2×C4C2×D4×D6114yes—
611C2×C4C2×D4×D6114yes—
612C2×C4C2×Q8×D6114yes—
613C2×C4C2×#1175822214yes—
614C22—618no—
615C22—12232no—
616C22—1224no—
617C22—1224no—
618C22—1224no—
619C22—1224no—
620C22—1224no—
621C22—1224no—
622C22—1224no—
623C22—1224no—
624C22—1224no—
625C22—24416no—
626C22—2442no—
627C22—2442no—
628C22—2442no—
629C22—2442no—
630C22C2×#1451975014yes—
631C22C22⋊Q8×D6114yes—
632C22#1684034214yes—
633C22#1684040514yes—
634C22#1684042714yes—
635C22#1684045314yes—
636C22#1684047214yes—
637C22C22×D4×D6111yescharacteristic
638C22C22×D4×D6111yescharacteristic
639C22C22×Q8×D6111yescharacteristic
640C22C2×#41×D6111yescharacteristic
641C22C22×#1175822211yescharacteristic
642C22C2×#1451982311yescharacteristic
643C22C2×#1451982511yescharacteristic
644C4—24no—
645C4—44no—
646C4—44no—
647C4—42no—
648C4—1228no—
649C4—1224no—
650C4—2442no—
651C4—2444no—
652C4C2×#1451975018yes—
653C2—1228no—
654C2—2444no—
655C2#2144927318yesdirect product factor
656C2C22×#1451975011yescharacteristic
657C2C2×C22⋊Q8×D6111yescharacteristic
658C2C2×#1684034211yescharacteristic
659C2C2×#1684040511yescharacteristic
660C2C2×#1684042711yescharacteristic
661C2C2×#1684045311yescharacteristic
662C2C2×#1684047211yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#391C2
socleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#391D61
hypocenterC61C2×#2417
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C22×#14519753C2semidirect
2. C22×#14519753C2semidirect
4. C22×C4⋊C4×D61C2semidirect
5. #21449273C2direct (N × H)
6. C2×#16839696C2semidirect
7. C2×#16839686C2semidirect
8. C2×#16839660C2semidirect
10. C2×#16839621C2semidirect
11. C2×#16839619C2semidirect
12. C2×C61×#391C2semidirect
19. C2×#14519753C22semidirect
20. C2×#14519753C22semidirect
31. C2×C4⋊C4×D61C22semidirect
37. #16839696C22semidirect
38. #16839686C22semidirect
39. #16839660C22semidirect
41. #16839621C22semidirect
42. #16839619C22semidirect
48. C61×#391C22semidirect
55. C22×D244Q8semidirect
78. C2×C4⋊Dic61D4semidirect
178. C2×D244C2×Q8semidirect
200. C4⋊Dic61C2×D4semidirect
236. C22×D61C22⋊Q8semidirect
312. C2×D61C2×C22⋊Q8semidirect
329. C2×#391D61semidirect
334. C2×C61#2417semidirect
373. #391C2×D61semidirect
382. C61C2×#2417semidirect
655. C2#21449273direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197532
C22×C4×D2442
C22×C4⋊C4×D612
#214492732
C2×#168396962
C2×#168396862
C2×#168396602
C2×#168396402
C2×#168396212
C2×#168396192
C2×C61×#3912
C2×#241761