Finite Group Databasebeta

← #29689336

Subgroups — #29689336

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D61C211yesmaximal, characteristic
2C2×#16839814C211yesmaximal, characteristic, complemented
3#21448215C211yesmaximal, characteristic, complemented
4#21446752C211yesmaximal, characteristic, complemented
5#21446751C211yesmaximal, characteristic, complemented
6#21446749C211yesmaximal, characteristic, complemented
7#21446629C212yesmaximal, complemented
8#21446627C212yesmaximal, complemented
9#21445752C212yesmaximal, complemented
10#21445748C212yesmaximal
11C61×#1983C211yesmaximal, characteristic, complemented
12C22×Q8×D61C2211yescharacteristic
13C22×D4×D61C2211yescharacteristic
14C2×#14519766C2211yescharacteristic
15C2×#14519765C2211yescharacteristic
16C2×#14519764C2211yescharacteristic
17C2×#14519763—21no—
18C2×#14519763—21no—
19#124×D61—24no—
20#124×D61C418yescomplemented
21C2×C22⋊C4×D61—21no—
22C2×C22⋊C4×D61—21no—
23C2×C42×D61C2211yescharacteristic
24#16839814—24no—
25C2×C4⋊#92418C2211yescharacteristic, complemented
26C2×#14519702C2212yescomplemented
27C2×#14519701C2212yescomplemented
28C2×#14519700C2212yescomplemented
29C2×#14519699C2212yes—
30C2×#14519698C2212yes—
31C2×#14519697C2212yes—
32C2×#14519689C2212yes—
33C2×C8×Dic61C2212yescomplemented
34#16839629—21no—
35#16839627C2212yescomplemented
36#16839624—21no—
37#16839619C2212yes—
38C4×C4⋊Dic61C2211yescharacteristic, complemented
39C4×#11758198—21no—
40#16839608—21no—
41C2×#124×C61C2211yescharacteristic
42C2×C4⋊C8×C61C2211yescharacteristic, complemented
43C2×#103×C61C2212yescomplemented
44C2×#102×C61C2212yes—
45C4×C4⋊C4×C61C2211yescharacteristic, complemented
46C24×D61—21no—
47C22×Dic122—21no—
48C22×Dic122C2311yescharacteristic
49C2×Q8×D61—22no—
50C2×Q8×D61—42no—
51C2×Q8×D61—42no—
52C2×Q8×D61C2×C414yes—
53C22×D244C2311yescharacteristic
54C22×C22⋊D61—21no—
55C2×D4×D61—22no—
56C2×D4×D61—42no—
57C2×D4×D61—42no—
58C2×D4×D61C2×C414yes—
59C22×C4×D61—21no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2312yes—
64#14519766—22no—
65#14519766C2×C414yes—
66#14519765—22no—
67#14519765C2×C414yes—
68#14519764—22no—
69#14519764C2×C414yes—
70#14519763—28no—
71#14519763—28no—
72C2×C4⋊Dic61C2312yes—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—22no—
80C22⋊C4×D61—28no—
81C22⋊C4×D61—28no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C42×D61C2×C414yes—
87C42×D61D414yes—
88C4⋊#92418—22no—
89#14519702—42no—
90#14519701—42no—
91#14519700—42no—
92#14519699—42no—
93#14519698—42no—
94#14519697—42no—
95#14519689—24no—
96C8×Dic61—24no—
97#14519684—21no—
98#14519684—22no—
99#14519684—22no—
100#14519684—22no—
101C22×Q8×C61C2311yescharacteristic
102C22×D4×C61C2311yescharacteristic
103C22×C8×C61C2312yes—
104#124×C61—22no—
105#124×C61C2×C414yes—
106C2×C4⋊C4×C61C2312yes—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C42×C61—21no—
110C2×C42×C61C2311yescharacteristic
111C4⋊C8×C61—22no—
112#103×C61—42no—
113#102×C61—42no—
114#95×C61—21no—
115C24×C61—21no—
116C23×D61—21no—
117C23×D61—24no—
118C23×D61—44no—
119C23×D61—42no—
120C23×D61—42no—
121C23×D61—44no—
122C23×D61C2×D411yescharacteristic
123C2×Q8×C61—21no—
124C2×Q8×C61—22no—
125C2×Q8×C61—22no—
126C2×Q8×C61C22×C412yes—
127C2×D4×C61—21no—
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61C22×C412yes—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—24no—
137C2×C22⋊D61—44no—
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143Q8×D61—48no—
144Q8×D61—44no—
145Q8×D61—44no—
146D4×D61—48no—
147D4×D61—44no—
148D4×D61—44no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—21no—
152C2×D244C22×C412yes—
153C2×C4×D61—24no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—24no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×C4×D61—44no—
160C2×C4×D61C22⋊C414yes—
161C2×C4×D61C22⋊C414yes—
162C2×C4×D61C22×C412yes—
163C2×C4×D61C2×D412yes—
164C2×Dic122—22no—
165C2×Dic122—22no—
166C2×Dic122—21no—
167C2×Dic122—24no—
168C2×Dic122—44no—
169C2×Dic122C22×C412yes—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C22⋊C4×C61—24no—
176C22⋊C4×C61—24no—
177C42×C61—42no—
178C42×C61C22×C412yes—
179C42×C61C2×D412yes—
180C22⋊Dic61—24no—
181C22⋊Dic61—24no—
182#11758198—24no—
183#11758198—24no—
184#11758198—24no—
185#11758198—24no—
186#11758198—44no—
187C4⋊Dic61—22no—
188C4⋊Dic61—22no—
189C4×Dic61—42no—
190C4×Dic61C22⋊C414yes—
191C4×Dic61C22⋊C414yes—
192C4×Dic61C22×C412yes—
193C4×Dic61C2×D412yes—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—22no—
197C23×C61—22no—
198C23×C61—42no—
199C23×C61—42no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61C22×D411yescharacteristic
203C22×D61—22no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—22no—
207C22×D61—48no—
208C22×D61—48no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—48no—
214C22×D61—88no—
215C22×D61—88no—
216C22×D61C2×C22⋊C412yes—
217C22×D61#13514yes—
218Q8×C61—24no—
219Q8×C61—41no—
220Q8×C61—41no—
221D4×C61—24no—
222D4×C61—41no—
223D4×C61—41no—
224C2×C4×C61—22no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61C2×C22⋊C412yes—
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C23×C411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61H(5,𝔽2)12yes—
237C2×C4×C61H(5,𝔽2)12yes—
238C22⋊D61—48no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—22no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C412yes—
250C2×Dic61C2×C22⋊C412yes—
251D244—24no—
252D244—41no—
253D244—41no—
254C4×D61—28no—
255C4×D61—24no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—44no—
259C4×D61—48no—
260Dic122—24no—
261Dic122—48no—
262Dic122—41no—
263Dic122—41no—
264C8×C61—42no—
265#92418—42no—
266#21806—611nomaximal, Sylow
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—82no—
271C22×C61—82no—
272C22×C61C22×C22⋊C411yescharacteristic
273C22×C61#53512yes—
274C22×C61C2×#13512yes—
275C22×C61#57511yescharacteristic
276C22×C61#57511yescharacteristic
277C2×D61—22no—
278C2×D61—22no—
279C2×D61—24no—
280C2×D61—24no—
281C2×D61—42no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—816no—
285C2×D61—82no—
286C2×D61—82no—
287C2×D61#41614yes—
288C4×C61—22no—
289C4×C61—22no—
290C4×C61—42no—
291C4×C61—82no—
292C4×C61#51812yes—
293C4×C61#53511yescharacteristic
294C4×C61#53511yescharacteristic
295Dic61—22no—
296Dic61—22no—
297Dic61—22no—
298Dic61—42no—
299Dic61—82no—
300C22×#124—611no—
301C2×#431—611no—
302#2283—611no—
303#1983—611no—
304#1983—611no—
305#1983—611no—
306#1983D6111yescharacteristic, complemented
307#1958—612no—
308#1958—612no—
309#1787—612no—
310#1786—612no—
311C2×C61—82no—
312C2×C61#230911yescharacteristic
313C2×C61C2×#41611yescharacteristic
314C2×C61#289611yescharacteristic
315C2×C61#321112yes—
316C2×C61#321112yes—
317D61—24no—
318D61—82no—
319C23×Q8—611no—
320C23×D4—611no—
321C2×#124—611no—
322C2×#124—611no—
323C2×#124—618no—
324C2×#124—611no—
325C2×#124—1221no—
326C2×#124—1221no—
327C2×#124—1224no—
328C2×#124C2×D6111yescharacteristic
329C22×C22⋊C4—1221no—
330C22×C22⋊C4—1221no—
331C22×C42—611no—
332#431—1224no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8C2×D6111yescharacteristic, complemented
335C2×#103—612no—
336C2×#103—612no—
337C2×#103—612no—
338C2×#103C2×D6112yescomplemented
339C2×#102—612no—
340C2×#102—612no—
341C2×#102—612no—
342C2×#102C2×D6112yes—
343C2×C22⋊C8—612no—
344C2×C4×C8—612no—
345#383—1221no—
346#382—612no—
347#381—1221no—
348#380—612no—
349C4×C4⋊C4—611no—
350C4×C4⋊C4C2×D6111yescharacteristic, complemented
351C4×C22⋊C4—1221no—
352#376—1221no—
353C61#2180611yescharacteristic, complemented, Sylow
354C25—1221no—
355C22×Q8—614no—
356C22×Q8—611no—
357C22×Q8—1221no—
358C22×Q8—1222no—
359C22×Q8—2442no—
360C22×Q8—2442no—
361C22×Q8C22×D6111yescharacteristic
362C22×D4—614no—
363C22×D4—611no—
364C22×D4—1222no—
365C22×D4—1221no—
366C22×D4—2442no—
367C22×D4—2442no—
368C22×D4C22×D6111yescharacteristic
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1221no—
373C22×C8—612no—
374C22×C8C22×D6112yes—
375#124—22no—
376#124—614no—
377#124—614no—
378#124—614no—
379#124—1228no—
380#124—1228no—
381#124—1222no—
382#124—1222no—
383#124—1222no—
384#124C4×D6114yes—
385C2×C4⋊C4—612no—
386C2×C4⋊C4C22×D6112yes—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—1228no—
390C2×C22⋊C4—1228no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C22⋊C4—1221no—
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1222no—
398C2×C42—21no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—614no—
403C2×C42—614no—
404C2×C42—1221no—
405C2×C42C22×D6111yescharacteristic
406C4⋊C8—22no—
407C4⋊C8—1222no—
408#103—42no—
409#103—2442no—
410#103—2442no—
411#103—2442no—
412#102—42no—
413#102—2442no—
414#102—2442no—
415#102—2442no—
416C22⋊C8—1224no—
417C4×C8—1224no—
418#95—21no—
419#95—1222no—
420#95—1222no—
421#95—1222no—
422#95—1221no—
423C24—21no—
424C24—611no—
425C24—1224no—
426C24—1221no—
427C24—2444no—
428C24—2444no—
429C24—2442no—
430C24—2442no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—612no—
435C2×Q8—1224no—
436C2×Q8—1221no—
437C2×Q8—1222no—
438C2×Q8—1222no—
439C2×Q8—2444no—
440C2×Q8—2448no—
441C2×Q8—2444no—
442C2×Q8—2444no—
443C2×Q8C2×C4×D6112yes—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—612no—
448C2×D4—1224no—
449C2×D4—1221no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4—2448no—
453C2×D4—2444no—
454C2×D4—2444no—
455C2×D4—2444no—
456C2×D4C2×C4×D6112yes—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—614no—
465C22×C4—614no—
466C22×C4—1224no—
467C22×C4—1224no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1221no—
471C22×C4—1222no—
472C22×C4—2441no—
473C22×C4—2441no—
474C22×C4—2444no—
475C22×C4D4×D6111yescharacteristic
476C22×C4D4×D6111yescharacteristic
477C22×C4C23×D6111yescharacteristic
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—1222no—
482C2×C8—1222no—
483C2×C8—1222no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—1224no—
491C22⋊C4—1224no—
492C22⋊C4—1224no—
493C22⋊C4—1224no—
494C22⋊C4—1224no—
495C22⋊C4—1224no—
496C22⋊C4—2444no—
497C42—42no—
498C42—612no—
499C42—612no—
500C42—614no—
501C42—614no—
502C42—2442no—
503C42C2×C4×D6112yes—
504C42D4×D6112yes—
505C23—22no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—612no—
511C23—614no—
512C23—1221no—
513C23—1221no—
514C23—1222no—
515C23—1222no—
516C23—4888no—
517C23—4888no—
518C23—2448no—
519C23—2448no—
520C23—2448no—
521C23—2442no—
522C23—2441no—
523C23—2441no—
524C23—2442no—
525C23C2×D4×D6111yescharacteristic
526Q8—24no—
527Q8—41no—
528Q8—41no—
529Q8—1224no—
530Q8—2448no—
531Q8—2441no—
532Q8—2441no—
533D4—24no—
534D4—41no—
535D4—41no—
536D4—1224no—
537D4—2448no—
538D4—2441no—
539D4—2441no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—1228no—
552C2×C4—1222no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1222no—
556C2×C4—1224no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—2444no—
561C2×C4—2448no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4C22⋊C4×D6112yes—
567C2×C4C22⋊C4×D6112yes—
568C2×C4C22×C4×D6111yescharacteristic
569C2×C4C2×D4×D6111yescharacteristic
570C2×C4#1451982212yes—
571C2×C4#1451982312yes—
572C8—42no—
573C8—2442no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—614no—
580C22—1224no—
581C22—1224no—
582C22—1222no—
583C22—1222no—
584C22—48816no—
585C22—4882no—
586C22—4882no—
587C22—2442no—
588C22—2442no—
589C22—2442no—
590C22C2×C22⋊C4×D6111yescharacteristic
591C22#1684032812yes—
592C22#135×D6112yes—
593C22#1684055811yescharacteristic
594C22#1684056111yescharacteristic
595C4—22no—
596C4—22no—
597C4—42no—
598C4—82no—
599C4—1222no—
600C4—1222no—
601C4—1222no—
602C4—4882no—
603C4—2442no—
604C4#1684023412yes—
605C4#1684032511yescharacteristic
606C4#1684033011yescharacteristic
607C2—82no—
608C2—1224no—
609C2—4882no—
610C2#2144839811yescharacteristic
611C2#416×D6111yescharacteristic
612C2#2145433511yescharacteristic
613C2#2145678212yes—
614C2#2145678812yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1983C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1983D61
hypocenterC61#21806
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#16839814C2semidirect
3. #21448215C2semidirect
4. #21446752C2semidirect
5. #21446751C2semidirect
6. #21446749C2semidirect
7. #21446629C2semidirect
8. #21446627C2semidirect
9. #21445752C2semidirect
11. C61×#1983C2semidirect
20. #124×D61C4semidirect
25. C2×C4⋊#92418C22semidirect
26. C2×#14519702C22semidirect
27. C2×#14519701C22semidirect
28. C2×#14519700C22semidirect
33. C2×C8×Dic61C22semidirect
35. #16839627C22semidirect
38. C4×C4⋊Dic61C22semidirect
42. C2×C4⋊C8×C61C22semidirect
43. C2×#103×C61C22semidirect
45. C4×C4⋊C4×C61C22semidirect
306. #1983D61semidirect
334. C2×C4⋊C8C2×D61semidirect
338. C2×#103C2×D61semidirect
350. C4×C4⋊C4C2×D61semidirect
353. C61#21806semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D612
C2×#168398142
#214482152
#214467522
#214467512
#214467492
#214466292
#214466272
#214457522
#214457482
C61×#19832
#2180661