Finite Group Databasebeta

← #30610545

Subgroups — #30610545

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462496C211yesmaximal, characteristic, complemented
2C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#21461135C214yesmaximal, complemented
4#21461128C212yesmaximal, complemented
5#21461125C212yesmaximal, complemented
6#21461114C214yesmaximal, complemented
7#21459114C211yesmaximal, characteristic
8C22×D61⋊C8—21no—
9#16840784—21no—
10#16840783—21no—
11#16840781C2212yes—
12#16840778C2212yes—
13#16840766—21no—
14C2×#14519844—21no—
15D61⋊(C4⋊C8)—21no—
16D61⋊(C4⋊C8)—21no—
17D61⋊(C4⋊C8)C2212yes—
18D61⋊(C4⋊C8)C2212yes—
19C2×C4⋊#92420C2212yes—
20#16840733—21no—
21C4×#11758213C2212yes—
22Q8⋊#92420C2218yescomplemented
23D4⋊#92420C2218yescomplemented
24#16840319C411yescharacteristic
25#16840317C411yescharacteristic
26#16840317C2211yescharacteristic
27#16840310C411yescharacteristic
28#16840310C2211yescharacteristic
29#16840294—21no—
30#16840294—21no—
31#16840293—21no—
32#16840293—21no—
33#16840291C412yes—
34#16840291C2212yes—
35#16840272—21no—
36#16840272—21no—
37#16840269C412yes—
38#41×Dic61C2212yes—
39C4×#11758224—21no—
40C4×#11758224—21no—
41C2×C42×D61C2211yescharacteristic
42C61×#532C411yescharacteristic
43C2×#11758213—22no—
44C2×D61⋊C8—22no—
45C2×D61⋊C8—22no—
46C2×D61⋊C8—44no—
47C22×#92420—22no—
48#14519844—22no—
49#14519844—22no—
50C4⋊#92420—22no—
51C4⋊#92420—22no—
52C4⋊#92420—22no—
53C4⋊#92420C2314yes—
54#14519834—22no—
55C22⋊#92420—22no—
56#14519832—22no—
57C4×#92420C2314yes—
58C2×#11758224—21no—
59C2×#11758224—21no—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63#14519777C2×C411yescharacteristic
64#14519777C2×C411yescharacteristic
65#14519770—22no—
66#14519770—22no—
67#14519769C2×C412yes—
68#14519768—21no—
69#14519768—21no—
70#14519764—21no—
71#14519764—21no—
72#14519759—22no—
73#14519759—22no—
74#14519758—22no—
75#14519757—21no—
76#14519757—21no—
77#14519756—21no—
78#14519756—21no—
79#14519753C2×C412yes—
80#14519753C2×C412yes—
81#14519748—21no—
82#14519748—21no—
83#14519748C2×C412yes—
84#14519748C2×C412yes—
85#14519745—22no—
86Q8×Dic61C2×C412yes—
87Q8×Dic61C2312yes—
88C4×Dic122—21no—
89C4×Dic122—21no—
90#14519742—21no—
91#14519742—21no—
92D4×Dic61—22no—
93D4×Dic61—22no—
94D4×Dic61—21no—
95D4×Dic61—21no—
96D4×Dic61C2×C412yes—
97D4×Dic61C2312yes—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100#14519737—22no—
101#14519737—22no—
102#14519736—22no—
103#14519736C2×C412yes—
104#14519735—21no—
105#14519735—21no—
106#14519733—22no—
107#14519733—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C2×#41×C61C2×C412yes—
121C4⋊Q8×C61C2×C411yescharacteristic
122#127×C61C2×C411yescharacteristic
123#124×C61C2×C412yes—
124#121×C61—21no—
125#121×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C23×D61C22⋊C411yescharacteristic
130#41×C61—28no—
131C2×Q8×C61C22×C412yes—
132C2×D4×C61—22no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61C22×C412yes—
136C22×C4×C61—22no—
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61C22⋊C411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147#11758224—44no—
148#11758224—42no—
149#11758224—42no—
150C2×C4×D61—24no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—42no—
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×#92420—24no—
169C2×#92420—24no—
170C2×#92420—44no—
171#11758213—44no—
172D61⋊C8—44no—
173D61⋊C8—44no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C42×C61C22⋊C411yescharacteristic
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22×C411yescharacteristic
181C42×C61C22×C411yescharacteristic
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187#11758198—22no—
188#11758198—22no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61C22×C412yes—
194C4⋊Dic61C22×C412yes—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22×C411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2411yescharacteristic
214C23×C61—22no—
215C23×C61C2×C22⋊C411yescharacteristic
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61C2×C22⋊C411yescharacteristic
220C22×D61C2×C22⋊C411yescharacteristic
221Q8×C61—24no—
222D4×C61—24no—
223D4×C61—42no—
224D4×C61—44no—
225D4×C61—42no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—41no—
229C2×C4×C61—44no—
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61#13114yes—
236C2×C4×C61C23×C411yescharacteristic
237C22⋊D61—44no—
238C22⋊D61—44no—
239C2×Dic61—22no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—41no—
245C2×Dic61—44no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C22×D411yescharacteristic
253C2×Dic61C22×D411yescharacteristic
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—21no—
263C4×D61—21no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61AGL(1,ℤ/8)12yes—
267C4×D61#13712yes—
268Dic122—42no—
269Dic122—42no—
270#92420—44no—
271#92420—44no—
272#17466—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61#40812yes—
279C22×C61C22×C22⋊C411yescharacteristic
280C2×D61—28no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61#41712yes—
286C2×D61#42112yes—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—42no—
291C4×C61#40812yes—
292C4×C61#41712yes—
293C4×C61C2×#13112yes—
294Dic61—21no—
295Dic61—21no—
296Dic61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—42no—
300Dic61—42no—
301Dic61C2×AGL(1,ℤ/8)11yescharacteristic
302Dic61C2×#13711yescharacteristic
303#3444—611no—
304#2920—611no—
305C22×C4⋊C8—611no—
306#1483—614no—
307#1481—612no—
308#1480—612no—
309#1477—614no—
310C2×C61—22no—
311C2×C61—82no—
312C2×C61C2×#40811yescharacteristic
313C2×C61C2×#41711yescharacteristic
314C2×C61C2×#42111yescharacteristic
315D61—22no—
316D61—22no—
317C23×C8—1221no—
318#533—611no—
319#533—611no—
320#533—611no—
321#532—611no—
322#532—611no—
323#532#692311yescharacteristic
324#529—612no—
325#529—612no—
326#529—1221no—
327#529—1221no—
328#529—1221no—
329#529—1221no—
330#525—612no—
331#525—1221no—
332#525—1221no—
333C4×#41—612no—
334C4×#41—1221no—
335C4×#41—1221no—
336C22×C42—611no—
337#432—1221no—
338#432—1221no—
339#431—612no—
340#431—612no—
341#423—1221no—
342C2×C4⋊C8—612no—
343C2×C4⋊C8—612no—
344C2×C4⋊C8—612no—
345C2×C4⋊C8—1221no—
346C2×C4⋊C8—1221no—
347C2×C4⋊C8—1221no—
348#407—1221no—
349C4×M16—612no—
350Q8⋊C8—618no—
351D4⋊C8—618no—
352C61#1746611yescharacteristic, complemented, Sylow
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41C2×#692312yes—
356C23×C4—611no—
357C23×C4—611no—
358C23×C4—611no—
359C2×M16—1222no—
360C22×C8—1222no—
361C22×C8—1222no—
362C22×C8—1222no—
363C22×C8—2444no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366C4⋊Q8C2×#692311yescharacteristic
367#127C2×#692311yescharacteristic
368#126—1222no—
369#126—1222no—
370#125—612no—
371#125—1221no—
372#125—1221no—
373#124—1221no—
374#124—1221no—
375#124C2×#692312yes—
376#123—1222no—
377#123—1222no—
378#123—1222no—
379C22⋊Q8—612no—
380C22⋊Q8—612no—
381C22⋊Q8—1221no—
382C22⋊Q8—1221no—
383C22⋊Q8—1221no—
384C22⋊Q8—1221no—
385#121—21no—
386#121—21no—
387#121—612no—
388#121—612no—
389#121—1221no—
390#121—1221no—
391#120—1222no—
392C4×Q8—612no—
393C4×Q8—612no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×Q8—1221no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—612no—
401C4×D4—612no—
402C4×D4—1221no—
403C4×D4—1221no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410#117—612no—
411#117—1222no—
412#117—1222no—
413#117—1222no—
414#117—1221no—
415#117—1221no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—1222no—
428C2×C42C2×#692311yescharacteristic
429C4⋊C8—614no—
430C4⋊C8—1222no—
431C4⋊C8—1222no—
432C4⋊C8—1222no—
433C4⋊C8—1222no—
434C4⋊C8—1222no—
435C22⋊C8—1222no—
436C22⋊C8—1222no—
437#97—1222no—
438C4×C8—614no—
439C24—611no—
440#41—28no—
441#41—2442no—
442#41—2442no—
443#41—2444no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×Q8C22×#692312yes—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4C22×#692312yes—
453C22×C4—22no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1224no—
474C22×C4—2442no—
475C22×C4C22⋊#692311yescharacteristic
476C22×C4C22⋊#692311yescharacteristic
477C22×C4C22×#692311yescharacteristic
478M16—2444no—
479C2×C8—1224no—
480C2×C8—1224no—
481C2×C8—2444no—
482C2×C8—2444no—
483C2×C8—2444no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—612no—
487C4⋊C4—612no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—1222no—
504C22⋊C4—1222no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—1222no—
518C42—1222no—
519C42—1222no—
520C42C22⋊#692311yescharacteristic
521C42C22⋊#692311yescharacteristic
522C42C22×#692311yescharacteristic
523C42C22×#692311yescharacteristic
524C23—22no—
525C23—611no—
526C23—611no—
527C23—1222no—
528C23—1222no—
529C23—1222no—
530C23C2×C22⋊#692311yescharacteristic
531Q8—24no—
532Q8—2442no—
533Q8—2442no—
534D4—24no—
535D4—42no—
536D4—44no—
537D4—42no—
538D4—2444no—
539D4—2444no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—44no—
544C2×C4—611no—
545C2×C4—612no—
546C2×C4—612no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2441no—
572C2×C4—2444no—
573C2×C4C2×C22⋊#692311yescharacteristic
574C2×C4C2×C22⋊#692311yescharacteristic
575C2×C4C2×C22⋊#692311yescharacteristic
576C2×C4C2×C22⋊#692311yescharacteristic
577C2×C4C2×C22⋊#692311yescharacteristic
578C2×C4#1451986414yes—
579C2×C4C23×#692311yescharacteristic
580C8—2444no—
581C8—2444no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—612no—
588C22—612no—
589C22—1228no—
590C22—1221no—
591C22—1221no—
592C22—1221no—
593C22—1221no—
594C22#1684073612yes—
595C22C22×C22⋊#692311yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—42no—
600C4—611no—
601C4—611no—
602C4—1221no—
603C4—1221no—
604C4—1221no—
605C4—1221no—
606C4—1221no—
607C4—2442no—
608C4—2442no—
609C4#1684073612yes—
610C4#1684075312yes—
611C4C2×#1451986412yes—
612C2—22no—
613C2—82no—
614C2—1222no—
615C2—1222no—
616C2C2×#1684073611yescharacteristic
617C2C2×#1684075311yescharacteristic
618C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#532C4
socleC22×C61C22×C22⋊C4
prime radical#21459114C2
cosocleC4×Dic61C24
hypercenter#532#6923
hypocenterC61#17466
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21462496C2semidirect
2. C2×D61⋊(C4⋊C8)C2semidirect
3. #21461135C2semidirect
4. #21461128C2semidirect
5. #21461125C2semidirect
6. #21461114C2semidirect
22. Q8⋊#92420C22semidirect
23. D4⋊#92420C22semidirect
352. C61#17466semidirect

Maximal subgroups

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

subgroupindex
#214624962
C2×D61⋊(C4⋊C8)2
#214611352
#214611282
#214611252
#214611142
#214591142
#1746661