Finite Group Databasebeta

← C2×#21446216 #29681570

Subgroups — C2×#21446216 #29681570

Order 15616.

2526 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519774C211yesmaximal, characteristic
2C2×#16840236C211yesmaximal, characteristic, complemented
3C2×#16839768C211yesmaximal, characteristic, complemented
4C2×#16839766C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446216C218yesmaximal, direct product factor
7C2×#16839522C211yesmaximal, characteristic, complemented
8C2×C61×#339C211yesmaximal, characteristic, complemented
9C23×D244—22no—
10C23×D244C2211yescharacteristic
11C23×D244C2211yescharacteristic
12C22×#11758194C2211yescharacteristic
13C2×#14519774—24no—
14C2×#14519774—22no—
15C2×#14519774C418yescomplemented
16C2×#14519774C2214yes—
17#16840236—22no—
18#16840236—22no—
19#16840236—22no—
20#16840236C2214yescomplemented
21C2×C4×D244—22no—
22C2×#14519739—22no—
23C2×#14519736C2211yescharacteristic
24C2×C22⋊C4×D61—22no—
25#16839768—22no—
26#16839768C2214yescomplemented
27#16839766—22no—
28#16839766C2214yescomplemented
29C2×#14519699—22no—
30C2×#14519697—22no—
31C2×#14519693—24no—
32C2×#14519693C2214yescomplemented
33#16839522C2214yescomplemented
34C22×M16×C61C2211yescharacteristic
35C2×#117×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C61×#339C2214yescomplemented
38C24×D61—21no—
39C24×D61D412yes—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244—21no—
49C22×D244—21no—
50C22×D244—22no—
51C22×D244—22no—
52C22×D244—216no—
53C22×D244—28no—
54C22×D244—21no—
55C22×D244—22no—
56C22×D244—416no—
57C22×D244C2×C414yes—
58C22×D244C2×C414yescomplemented
59C22×D244D412yes—
60C22×D244D414yes—
61C22×D244C2312yes—
62C22×D244C2312yes—
63C22×C4×D61—24no—
64C2×#11758194—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194C2312yes—
68C22×#92418—21no—
69#14519774—216no—
70#14519774—28no—
71#14519774C2×C4116yescomplemented
72C4×D244—28no—
73C4×D244—28no—
74#14519739—28no—
75#14519739—28no—
76#14519736—21no—
77#14519736—21no—
78#14519736D412yescomplemented
79#14519736C2312yes—
80C2×C4⋊Dic61D412yescomplemented
81C2×C22⋊Dic61—21no—
82C2×#11758198—24no—
83C22⋊C4×D61—28no—
84C22⋊C4×D61—28no—
85C2×C4×Dic61—21no—
86#14519699—28no—
87#14519697—28no—
88#14519693—28no—
89C23×C4×C61—21no—
90C23×C4×C61C2311yescharacteristic
91C2×M16×C61—21no—
92C2×M16×C61—22no—
93C2×M16×C61—22no—
94C2×M16×C61C2312yes—
95C22×C8×C61—21no—
96#117×C61—21no—
97#117×C61—21no—
98#117×C61D412yescomplemented
99#117×C61C2312yes—
100C2×C4⋊C4×C61D412yescomplemented
101C2×C22⋊C4×C61—21no—
102C2×C42×C61—21no—
103C2×C42×C61—21no—
104C2×C42×C61—22no—
105C2×C42×C61C2×C414yescomplemented
106C2×C42×C61C2312yes—
107C24×C61C2×D411yescharacteristic
108C23×D61—22no—
109C23×D61—22no—
110C23×D61—24no—
111C23×D61—24no—
112C23×D61—22no—
113C23×D61—48no—
114C23×D61—48no—
115C23×D61—41no—
116C23×D61—41no—
117C23×D61—42no—
118C23×D61C22⋊C418yes—
119C23×D61C2×D414yes—
120C22×C4×C61—28no—
121C22×C4×C61—24no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D412yes—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61#4112yes—
132C22×C4×C61#4112yes—
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—22no—
135C2×D244—24no—
136C2×D244—24no—
137C2×D244—24no—
138C2×D244—24no—
139C2×D244—22no—
140C2×D244—22no—
141C2×D244—24no—
142C2×D244—24no—
143C2×D244—24no—
144C2×D244—24no—
145C2×D244—24no—
146C2×D244—22no—
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—24no—
151C2×D244—24no—
152C2×D244—24no—
153C2×D244—24no—
154C2×D244—22no—
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—232no—
159C2×D244—24no—
160C2×D244—22no—
161C2×D244—464no—
162C2×D244—432no—
163C2×D244—41no—
164C2×D244—41no—
165C2×D244—42no—
166C2×D244—42no—
167C2×D244—42no—
168C2×D244—42no—
169C2×D244—42no—
170C2×D244C22⋊C418yes—
171C2×D244C22×C414yes—
172C2×D244C22×C414yescomplemented
173C2×D244C2×D414yes—
174C2×C4×D61—216no—
175C2×C4×D61—88no—
176M16×C61—22no—
177M16×C61—22no—
178M16×C61—42no—
179C2×C8×C61—22no—
180C2×C8×C61—42no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61C2×D414yescomplemented
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C42×C61—24no—
186C42×C61—22no—
187C42×C61—22no—
188C42×C61—22no—
189C42×C61C22×C414yescomplemented
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192#11758198—216no—
193C4⋊Dic61—22no—
194C4⋊Dic61C2×D414yescomplemented
195C4×Dic61—22no—
196C4×Dic61—22no—
197#11758194—22no—
198#11758194—22no—
199#11758194—42no—
200C2×#92418—22no—
201C2×#92418—42no—
202C23×C61—24no—
203C23×C61C2×C22⋊C412yes—
204C23×C61#12011yescharacteristic
205C23×C61#12011yescharacteristic
206C23×C61#12312yes—
207C23×C61C22×D411yescharacteristic
208C22×D61—24no—
209C22×D61—28no—
210C22×D61—24no—
211C22×D61—28no—
212C22×D61—24no—
213C22×D61—48no—
214C22×D61—416no—
215C22×D61—48no—
216C22×D61—416no—
217C22×D61—48no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—44no—
221C22×D61—44no—
222C22×D61—88no—
223C22×D61—84no—
224C22×D61—88no—
225C22×D61—84no—
226C22×D61—84no—
227C22×D61C2×C22⋊C418yes—
228C2×C4×C61—216no—
229C2×C4×C61—28no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—44no—
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C4×D412yes—
235C2×C4×C61C4×D412yes—
236C2×C4×C61C4×D412yes—
237C2×C4×C61C4×D412yes—
238C2×C4×C61#12011yescharacteristic
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12112yes—
241C2×C4×C61#12112yes—
242C2×C4×C61#12112yes—
243C2×C4×C61#12112yes—
244C2×C4×C61#12312yes—
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×Dic61—24no—
252C2×Dic61—44no—
253D244—24no—
254D244—24no—
255D244—24no—
256D244—24no—
257D244—24no—
258D244—24no—
259D244—28no—
260D244—28no—
261D244—464no—
262D244—42no—
263D244—42no—
264D244—44no—
265D244—44no—
266C4×D61—816no—
267C8×C61—42no—
268#92418—42no—
269C2×#1887—611nomaximal, Sylow
270C22×C61—24no—
271C22×C61—24no—
272C22×C61—22no—
273C22×C61—22no—
274C22×C61#38612yes—
275C22×C61#38612yes—
276C22×C61#45314yes—
277C22×C61C22×C22⋊C411yescharacteristic
278C22×C61C2×#12011yescharacteristic
279C22×C61C2×#12311yescharacteristic
280C2×D61—28no—
281C2×D61—416no—
282C2×D61—48no—
283C2×D61—48no—
284C2×D61—48no—
285C2×D61—44no—
286C2×D61—84no—
287C2×D61—88no—
288C2×D61—84no—
289C2×D61—88no—
290C2×D61—88no—
291C2×D61—84no—
292C4×C61—28no—
293C4×C61—44no—
294C4×C61#38612yes—
295C4×C61#38612yes—
296C4×C61C2×C4×D411yescharacteristic
297C4×C61C2×C4×D411yescharacteristic
298C4×C61C2×#12111yescharacteristic
299C4×C61C2×#12111yescharacteristic
300Dic61—44no—
301C22×#127—611no—
302C2×#518—611no—
303C2×#418—611no—
304C2×#418—611no—
305C22×#100—611no—
306#1887—618no—
307C2×#339—611no—
308C2×#339D6111yescharacteristic, complemented
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—22no—
312C2×C61#188714yescomplemented
313C2×C61C2×#38611yescharacteristic
314C2×C61C2×#45312yes—
315D61—48no—
316D61—84no—
317C23×D4—611no—
318C23×D4—611no—
319C23×D4—1222no—
320C22×M16—611no—
321C22×M16C2×D6111yescharacteristic
322C2×#127—618no—
323C2×#127—614no—
324C2×#127—1222no—
325C2×#127—1224no—
326#518—614no—
327#518—1222no—
328#518—1222no—
329#518—1222no—
330C2×C4×D4—1222no—
331C2×C4×D4—1222no—
332C2×#117—611no—
333C2×#117C2×D6111yescharacteristic
334C22×C22⋊C4—1222no—
335C22×C42C2×D6111yescharacteristic
336#418—614no—
337#418—614no—
338#418—1222no—
339#418—1222no—
340C2×#102—1222no—
341C2×#102—1222no—
342C2×#100—614no—
343C2×#100—1224no—
344#339—614no—
345#339C2×D6114yescomplemented
346C61C2×#188711yescharacteristic, complemented, Sylow
347C25—612no—
348C25—1221no—
349C22×D4—614no—
350C22×D4—614no—
351C22×D4—612no—
352C22×D4—614no—
353C22×D4—612no—
354C22×D4—612no—
355C22×D4—1228no—
356C22×D4—12216no—
357C22×D4—1221no—
358C22×D4—1221no—
359C22×D4—1221no—
360C22×D4—1221no—
361C22×D4—1222no—
362C22×D4—1222no—
363C22×D4—1221no—
364C22×D4—1221no—
365C22×D4—1221no—
366C22×D4—1221no—
367C22×D4—1222no—
368C22×D4—1221no—
369C22×D4—1222no—
370C22×D4—1222no—
371C22×D4—24416no—
372C23×C4—21no—
373C23×C4—1224no—
374C23×C4C22×D6111yescharacteristic
375C2×M16—21no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—612no—
379C2×M16—1221no—
380C2×M16—1222no—
381C2×M16—1222no—
382C2×M16C22×D6112yes—
383C22×C8—21no—
384C22×C8—1221no—
385#127—6116no—
386#127—1228no—
387#127—12216no—
388C4×D4—1228no—
389C4×D4—1228no—
390C4×D4—1228no—
391C4×D4—1228no—
392#117—21no—
393#117—21no—
394#117—612no—
395#117—612no—
396#117—1221no—
397#117—1221no—
398#117D24412yescomplemented
399#117C22×D6112yes—
400C2×C4⋊C4—612no—
401C2×C4⋊C4D24412yescomplemented
402C2×C22⋊C4—21no—
403C2×C22⋊C4—1228no—
404C2×C22⋊C4—1228no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—1221no—
407C2×C42—21no—
408C2×C42—22no—
409C2×C42—21no—
410C2×C42—1221no—
411C2×C42C4×D6114yescomplemented
412C2×C42C22×D6112yes—
413#102—1228no—
414#102—1228no—
415#100—1228no—
416C24—614no—
417C24—618no—
418C24—1222no—
419C24—1224no—
420C24—1222no—
421C24—1222no—
422C24—1224no—
423C24—2448no—
424C24—2448no—
425C24—2441no—
426C24—2441no—
427C24—2442no—
428C24D4×D6111yescharacteristic
429C2×D4—614no—
430C2×D4—614no—
431C2×D4—614no—
432C2×D4—618no—
433C2×D4—12232no—
434C2×D4—1222no—
435C2×D4—1222no—
436C2×D4—1222no—
437C2×D4—1222no—
438C2×D4—1222no—
439C2×D4—1222no—
440C2×D4—1222no—
441C2×D4—1222no—
442C2×D4—1222no—
443C2×D4—1224no—
444C2×D4—1224no—
445C2×D4—1224no—
446C2×D4—1224no—
447C2×D4—1224no—
448C2×D4—1224no—
449C2×D4—1224no—
450C2×D4—1224no—
451C2×D4—1224no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1224no—
455C2×D4—1224no—
456C2×D4—1224no—
457C2×D4—1224no—
458C2×D4—1224no—
459C2×D4—24432no—
460C2×D4—24464no—
461C2×D4—2441no—
462C2×D4—2441no—
463C2×D4—2442no—
464C2×D4—2442no—
465C2×D4—2442no—
466C2×D4—2442no—
467C2×D4—2442no—
468C22×C4—28no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—12216no—
473C22×C4—1222no—
474C22×C4—4888no—
475C22×C4C2×C4×D6112yes—
476C22×C4C2×D24411yescharacteristic
477C22×C4C2×D24411yescharacteristic
478C22×C4#1175822212yes—
479C22×C4D4×D6112yes—
480C22×C4D4×D6111yescharacteristic
481C22×C4D4×D6111yescharacteristic
482C22×C4D4×D6111yescharacteristic
483C22×C4#1175822612yes—
484C22×C4C23×D6111yescharacteristic
485M16—22no—
486M16—22no—
487M16—42no—
488M16—1222no—
489M16—1222no—
490M16—2442no—
491C2×C8—22no—
492C2×C8—42no—
493C2×C8—1222no—
494C2×C8—2442no—
495C4⋊C4—22no—
496C4⋊C4—614no—
497C4⋊C4—1222no—
498C4⋊C4C2×D24414yescomplemented
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—12216no—
502C22⋊C4—1222no—
503C22⋊C4—1222no—
504C42—22no—
505C42—22no—
506C42—24no—
507C42—22no—
508C42—1222no—
509C42—1222no—
510C42C2×C4×D6114yescomplemented
511C23—24no—
512C23—618no—
513C23—1224no—
514C23—1228no—
515C23—1224no—
516C23—1228no—
517C23—1224no—
518C23—4884no—
519C23—4888no—
520C23—4884no—
521C23—4888no—
522C23—4884no—
523C23—2448no—
524C23—24416no—
525C23—2448no—
526C23—24416no—
527C23—2442no—
528C23—2442no—
529C23—2444no—
530C23—2444no—
531C23—2448no—
532C23C22⋊C4×D6112yes—
533C23#1451974711yescharacteristic
534C23#1451974711yescharacteristic
535C23#1451976212yes—
536C23C2×D4×D6111yescharacteristic
537D4—1224no—
538D4—1224no—
539D4—1224no—
540D4—1224no—
541D4—1224no—
542D4—1224no—
543D4—1228no—
544D4—1228no—
545D4—24464no—
546D4—2442no—
547D4—2442no—
548D4—2444no—
549D4—2444no—
550C2×C4—28no—
551C2×C4—216no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—1224no—
556C2×C4—48816no—
557C2×C4—2444no—
558C2×C4C22⋊C4×D6112yes—
559C2×C4#1451973912yes—
560C2×C4#1451973912yes—
561C2×C4C4×D24412yes—
562C2×C4C4×D24412yes—
563C2×C4#1451974711yescharacteristic
564C2×C4#1451974711yescharacteristic
565C2×C4#1451975012yes—
566C2×C4#1451975012yes—
567C2×C4#1451975212yes—
568C2×C4#1451975212yes—
569C2×C4#1451976212yes—
570C2×C4C22×C4×D6111yescharacteristic
571C2×C4C2×D4×D6111yescharacteristic
572C2×C4C2×D4×D6111yescharacteristic
573C2×C4C22×D24411yescharacteristic
574C2×C4C2×#1175822211yescharacteristic
575C2×C4C2×#1175822611yescharacteristic
576C8—42no—
577C8—2442no—
578C22—22no—
579C22—22no—
580C22—24no—
581C22—24no—
582C22—1228no—
583C22—4884no—
584C22—4888no—
585C22—4884no—
586C22—4888no—
587C22—4884no—
588C22—4888no—
589C22—2448no—
590C22—2448no—
591C22—2444no—
592C22—2448no—
593C22—24416no—
594C22#1683964012yes—
595C22#1683964012yes—
596C22#1683993114yes—
597C22C2×C22⋊C4×D6111yescharacteristic
598C22C2×#1451974711yescharacteristic
599C22C2×#1451976211yescharacteristic
600C4—28no—
601C4—44no—
602C4—2444no—
603C4#1683964012yes—
604C4#1683964012yes—
605C4C2×#1451973911yescharacteristic
606C4C2×C4×D24411yescharacteristic
607C4C2×#1451975011yescharacteristic
608C4C2×#1451975211yescharacteristic
609C2—21no—
610C2—21no—
611C2—22no—
612C2—4884no—
613C2—2448no—
614C2#2144621614yesdirect product factor
615C2C2×#1683964011yescharacteristic
616C2C2×#1683993112yes—
subgroupG/H
centerC23#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#339C2
socleC23×C61#120
prime radicalC22×#14519774C2
cosocleC22×C4×C61C24
hypercenterC2×#339D61
hypocenterC61C2×#1887
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
2. C2×#16840236C2semidirect
3. C2×#16839768C2semidirect
4. C2×#16839766C2semidirect
5. C22×#14519693C2semidirect
6. #21446216C2direct (N × H)
7. C2×#16839522C2semidirect
8. C2×C61×#339C2semidirect
15. C2×#14519774C4semidirect
20. #16840236C22semidirect
26. #16839768C22semidirect
28. #16839766C22semidirect
32. C2×#14519693C22semidirect
33. #16839522C22semidirect
37. C61×#339C22semidirect
58. C22×D244C2×C4semidirect
71. #14519774C2×C4semidirect
78. #14519736D4semidirect
80. C2×C4⋊Dic61D4semidirect
98. #117×C61D4semidirect
100. C2×C4⋊C4×C61D4semidirect
105. C2×C42×C61C2×C4semidirect
172. C2×D244C22×C4semidirect
182. C4⋊C4×C61C2×D4semidirect
189. C42×C61C22×C4semidirect
194. C4⋊Dic61C2×D4semidirect
308. C2×#339D61semidirect
312. C2×C61#1887semidirect
345. #339C2×D61semidirect
346. C61C2×#1887semidirect
398. #117D244semidirect
401. C2×C4⋊C4D244semidirect
411. C2×C42C4×D61semidirect
498. C4⋊C4C2×D244semidirect
510. C42C2×C4×D61semidirect
614. C2#21446216direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197742
C2×#168402362
C2×#168397682
C2×#168397662
C22×#145196932
#214462162
C2×#168395222
C2×C61×#3392
C2×#188761