Finite Group Databasebeta

← #29730741

Subgroups — #29730741

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839988C212yesmaximal, complemented
2C2×#16839827C211yesmaximal, characteristic, complemented
3#21450773C211yesmaximal, characteristic, complemented
4#21450732C211yesmaximal, characteristic
5#21447014C212yesmaximal, complemented
6#21446819C212yesmaximal, complemented
7#21446622C211yesmaximal, characteristic, complemented
8#21446583C211yesmaximal, characteristic, complemented
9#21446239C212yesmaximal, complemented
10C4×#14519698C211yesmaximal, characteristic, complemented
11C2×C61×#461C211yesmaximal, characteristic, complemented
12C22×C8×D61C2212yes—
13C2×#14519753C2212yes—
14C2×#14519753C2212yes—
15C2×#14519751—21no—
16C2×#14519748C2212yes—
17C2×C4×D244C2211yescharacteristic
18#16839988—28no—
19#16839827—24no—
20C2×#14519709C2212yes—
21C2×#14519701C2212yes—
22C2×#14519701C2212yes—
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519689C2212yes—
26C2×C4×#92418C2211yescharacteristic
27#16839697—22no—
28#16839678—22no—
29#16839663—21no—
30#16839632C2211yescharacteristic
31#16839631—21no—
32#16839622—21no—
33#16839619C2212yes—
34C4×C4⋊Dic61C2211yescharacteristic
35#16839525C2212yes—
36#16839524C2211yescharacteristic
37#16839524C2211yescharacteristic
38C22×SD16×C61C2212yes—
39C2×C4⋊Q8×C61C2211yescharacteristic
40C2×C4×D4×C61C2211yescharacteristic
41C61×#461—24no—
42C2×C4⋊C8×C61C2211yescharacteristic
43C2×#103×C61C2212yes—
44C22×D244D411yescharacteristic
45C22×C22⋊D61—22no—
46C22×C4×D61C2312yes—
47C22×#92418C2311yescharacteristic
48C22×#92418C2311yescharacteristic
49C2×C8×D61—24no—
50C2×C8×D61—24no—
51C2×C8×D61—42no—
52#14519753—24no—
53#14519753—24no—
54#14519753—42no—
55#14519753—42no—
56#14519751—44no—
57#14519748—24no—
58#14519748—42no—
59C4×D244—22no—
60C4×D244—22no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61D411yescharacteristic
64C2×C4⋊Dic61C2312yes—
65C2×C4⋊Dic61C2311yescharacteristic
66C2×C4⋊Dic61C2311yescharacteristic
67C2×#11758196—22no—
68C2×#11758196—22no—
69C2×C22⋊Dic61—22no—
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×#11758198—22no—
73C2×#11758198D412yes—
74C2×C4×Dic61—21no—
75#14519709—24no—
76#14519701—24no—
77#14519701—42no—
78#14519698—22no—
79#14519698D414yescomplemented
80#14519689—24no—
81C4×#92418—22no—
82#14519684—21no—
83#14519684—22no—
84C22×Q8×C61C2312yes—
85C22×D4×C61C2311yescharacteristic
86C23×C4×C61—21no—
87C2×SD16×C61—24no—
88C2×SD16×C61—24no—
89C2×SD16×C61—42no—
90C22×C8×C61C2312yes—
91C4⋊Q8×C61—22no—
92C4⋊Q8×C61—22no—
93C4×D4×C61—22no—
94C4×D4×C61—22no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C22⋊C4×C61—21no—
99C2×C42×C61C2311yescharacteristic
100C4⋊C8×C61D414yescomplemented
101#103×C61—24no—
102C24×C61—21no—
103C23×D61C2×D412yes—
104C2×Q8×C61—22no—
105C2×Q8×C61—22no—
106C2×Q8×C61—22no—
107C2×Q8×C61—22no—
108C2×Q8×C61—22no—
109C2×Q8×C61—22no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61C2×D412yes—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—42no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2411yescharacteristic
124C2×C22⋊D61—44no—
125C2×C22⋊D61—44no—
126C2×C22⋊D61—82no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—22no—
130C22×Dic61C2×D412yes—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244SD1614yescomplemented
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140SD16×C61—48no—
141C2×C8×C61—22no—
142C2×C8×C61—22no—
143C2×C8×C61C2×D414yes—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—42no—
147C4⋊C4×C61—42no—
148C22⋊C4×C61—42no—
149C42×C61C2×D412yes—
150C42×C61#4112yes—
151C22⋊Dic61—44no—
152#11758198—24no—
153#11758198—44no—
154#11758198—44no—
155#11758198—44no—
156C4⋊Dic61—22no—
157C4⋊Dic61—21no—
158C4⋊Dic61—21no—
159C4⋊Dic61—22no—
160C4⋊Dic61—22no—
161C4⋊Dic61—42no—
162C4⋊Dic61—81no—
163C4⋊Dic61C2×D412yes—
164C4⋊Dic61#4112yes—
165#11758196—44no—
166#11758196—44no—
167C4×Dic61—42no—
168C2×#92418—21no—
169C2×#92418—21no—
170C2×#92418—21no—
171C2×#92418—21no—
172C2×#92418—21no—
173C2×#92418C2×D412yes—
174C8×D61—48no—
175C23×C61—22no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61C22×D411yescharacteristic
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—22no—
189C22×D61C2×SD1614yes—
190Q8×C61—42no—
191Q8×C61—42no—
192Q8×C61—42no—
193Q8×C61—42no—
194D4×C61—22no—
195D4×C61—22no—
196D4×C61—41no—
197D4×C61—41no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—41no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—84no—
207C2×C4×C61#12112yes—
208C2×C4×C61#12112yes—
209C2×C4×C61C2×SD1612yes—
210C2×C4×C61#13512yes—
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×C4×C61C2×#4111yescharacteristic
214C2×C4×C61C2×#4111yescharacteristic
215C2×C4×C61H(5,𝔽2)11yescharacteristic
216C2×C4×C61H(5,𝔽2)11yescharacteristic
217C22⋊D61—88no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230D244—28no—
231C4×D61—42no—
232C4×D61—42no—
233C4×D61—42no—
234C4×D61—42no—
235C8×C61—24no—
236#92418—22no—
237#92418—41no—
238#25385—611nomaximal, Sylow
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—81no—
243C22×C61—81no—
244C22×C61—81no—
245C22×C61—81no—
246C22×C61C2×#12111yescharacteristic
247C22×C61D4211yescharacteristic
248C22×C61#54611yescharacteristic
249C22×C61C22×SD1611yescharacteristic
250C22×C61C2×#13511yescharacteristic
251C22×C61#57711yescharacteristic
252C22×C61#57811yescharacteristic
253C2×D61—24no—
254C2×D61—24no—
255C2×D61—24no—
256C2×D61—42no—
257C2×D61—42no—
258C2×D61—42no—
259C2×D61—42no—
260C4×C61—22no—
261C4×C61—82no—
262C4×C61—81no—
263C4×C61#46514yescomplemented
264C4×C61#53211yescharacteristic
265C4×C61#54011yescharacteristic
266C4×C61D4211yescharacteristic
267C4×C61#55011yescharacteristic
268Dic61—42no—
269Dic61—42no—
270Dic61—42no—
271Dic61—82no—
272C2×#465—612no—
273C2×#461D6111yescharacteristic, complemented
274C2×C8×D4—611no—
275#2542—611no—
276#2537—611no—
277#2035—612no—
278#2000—612no—
279#1956—611no—
280#1948—611no—
281#1892—612no—
282C4×#102—611no—
283C2×C61—82no—
284C2×C61#242811yescharacteristic
285C2×C61C2×#46511yescharacteristic
286C2×C61#306311yescharacteristic
287C2×C61D4×SD1611yescharacteristic
288C2×C61#328311yescharacteristic
289C2×C61#329811yescharacteristic
290C2×C61#330311yescharacteristic
291D61—44no—
292C22×SD16C2×D6112yes—
293C23×C8—612no—
294C2×C4⋊Q8C2×D6111yescharacteristic
295C2×C22⋊Q8—612no—
296C2×C22⋊Q8—612no—
297C2×#121—612no—
298C2×#121—1221no—
299C2×C4×D4—611no—
300C2×C4×D4C2×D6111yescharacteristic
301#465—1228no—
302#461—24no—
303C8×D4—1224no—
304C2×#106—612no—
305C2×C4⋊C8C2×D6111yescharacteristic
306C2×#103—612no—
307C2×#103—612no—
308C2×#103C2×D6112yes—
309C2×#102—611no—
310C2×#102—611no—
311C2×C22⋊C8—612no—
312C2×C4×C8—611no—
313#399—1222no—
314#394—1222no—
315#390—1221no—
316#384—611no—
317#384—1221no—
318#380—612no—
319#380—1221no—
320C4×C4⋊C4—611no—
321#340—612no—
322#340—611no—
323#340—611no—
324C61#2538511yescharacteristic, complemented, Sylow
325C22×Q8C22×D6112yes—
326C22×D4—611no—
327C22×D4—1222no—
328C22×D4C22×D6111yescharacteristic
329C23×C4—21no—
330C23×C4—612no—
331C2×SD16—24no—
332C2×SD16—24no—
333C2×SD16—42no—
334C22×C8—611no—
335C22×C8—611no—
336C22×C8—1224no—
337C22×C8—1224no—
338C22×C8—2442no—
339C22×C8C22×D6112yes—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C22⋊Q8—1224no—
343C22⋊Q8—1224no—
344C22⋊Q8—2442no—
345C22⋊Q8—2442no—
346#121—1224no—
347#121—2442no—
348#121—2444no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—1222no—
352C4×D4—1222no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—611no—
356C2×C4⋊C4—611no—
357C2×C4⋊C4—611no—
358C2×C4⋊C4—612no—
359C2×C4⋊C4—1221no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4C22×D6111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—612no—
366C2×C22⋊C4—1222no—
367C2×C22⋊C4—1222no—
368C2×C22⋊C4—1222no—
369C2×C22⋊C4—1222no—
370C2×C42—1221no—
371C2×C42C22×D6111yescharacteristic
372#106—1224no—
373C4⋊C8C22⋊D6114yescomplemented
374#103—24no—
375#103—1224no—
376#103—2442no—
377#102—614no—
378#102—1222no—
379C22⋊C8—1224no—
380C4×C8—1222no—
381#95—1222no—
382#95—1221no—
383C24—21no—
384C24—612no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—614no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—4882no—
400C2×D4—2444no—
401C2×D4—2444no—
402C2×D4D4×D6112yes—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—612no—
409C22×C4—1221no—
410C22×C4—1221no—
411C22×C4—1222no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1222no—
417C22×C4—1222no—
418C22×C4D4×D6111yescharacteristic
419C22×C4D4×D6111yescharacteristic
420C22×C4C23×D6111yescharacteristic
421SD16—48no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—612no—
425C2×C8—1221no—
426C2×C8—1221no—
427C2×C8—1221no—
428C2×C8—1221no—
429C2×C8—1221no—
430C2×C8—2448no—
431C2×C8C2×C22⋊D6114yes—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—42no—
435C4⋊C4—42no—
436C4⋊C4—612no—
437C4⋊C4—612no—
438C4⋊C4—1221no—
439C4⋊C4—1221no—
440C4⋊C4—1222no—
441C4⋊C4—1222no—
442C4⋊C4—1222no—
443C4⋊C4—4881no—
444C4⋊C4—2444no—
445C4⋊C4—2444no—
446C4⋊C4—2442no—
447C22⋊C4—42no—
448C22⋊C4—1224no—
449C22⋊C4—2444no—
450C22⋊C4—2444no—
451C22⋊C4—2444no—
452C22⋊C4—2444no—
453C42—2442no—
454C42#1175822412yes—
455C42C2×C22⋊D6112yes—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—614no—
464C23—1222no—
465C23—1222no—
466C23—1222no—
467C23—1222no—
468C23—1222no—
469C23—1222no—
470C23C2×D4×D6111yescharacteristic
471Q8—42no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475D4—22no—
476D4—22no—
477D4—41no—
478D4—41no—
479D4—1228no—
480D4—4888no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—84no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—1222no—
494C2×C4—1222no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4#1451974812yes—
507C2×C4#1451974812yes—
508C2×C4SD16×D6112yes—
509C2×C4#1451979812yes—
510C2×C4C2×D4×D6111yescharacteristic
511C2×C4C22×C22⋊D6111yescharacteristic
512C2×C4#41×D6111yescharacteristic
513C2×C4C2×#1175822411yescharacteristic
514C2×C4#1451982211yescharacteristic
515C2×C4#1451982311yescharacteristic
516C8—24no—
517C8—1222no—
518C8—2441no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—1224no—
527C22—1224no—
528C22—1224no—
529C22—2442no—
530C22—2442no—
531C22—2442no—
532C22—2442no—
533C22C2×#1451974811yescharacteristic
534C22#1684039611yescharacteristic
535C22#1684040911yescharacteristic
536C22C2×SD16×D6111yescharacteristic
537C22C2×#1451979811yescharacteristic
538C22#1684057111yescharacteristic
539C22#1684057811yescharacteristic
540C4—22no—
541C4—81no—
542C4—82no—
543C4—4882no—
544C4—2442no—
545C4—2442no—
546C4—2442no—
547C4#1683998814yescomplemented
548C4#1684030711yescharacteristic
549C4#1684036511yescharacteristic
550C4D4×C22⋊D6111yescharacteristic
551C4#1684043111yescharacteristic
552C2—82no—
553C2—2444no—
554C2#2144940311yescharacteristic
555C2C2×#1683998811yescharacteristic
556C2#2145550411yescharacteristic
557C2#2145751811yescharacteristic
558C2#2145753611yescharacteristic
559C2#2145768711yescharacteristic
560C2#2145775011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#461C2
socleC23×C61C22×D4
prime radical#21450732C2
hypercenterC2×#461D61
hypocenterC61#25385
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#16839988C2semidirect
2. C2×#16839827C2semidirect
3. #21450773C2semidirect
5. #21447014C2semidirect
6. #21446819C2semidirect
7. #21446622C2semidirect
8. #21446583C2semidirect
9. #21446239C2semidirect
10. C4×#14519698C2semidirect
11. C2×C61×#461C2semidirect
79. #14519698D4semidirect
100. C4⋊C8×C61D4semidirect
133. C2×D244SD16semidirect
263. C4×C61#465semidirect
273. C2×#461D61semidirect
324. C61#25385semidirect
373. C4⋊C8C22⋊D61semidirect
547. C4#16839988semidirect

Maximal subgroups

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

subgroupindex
C2×#168399882
C2×#168398272
#214507732
#214507322
#214470142
#214468192
#214466222
#214465832
#214462392
C4×#145196982
C2×C61×#4612
#2538561