Finite Group Databasebeta

← #29838703

Subgroups — #29838703

Order 15616.

2250 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic
2#21448471C211yesmaximal, characteristic, complemented
3#21448470C211yesmaximal, characteristic, complemented
4#21448469C212yesmaximal, complemented
5#21448467C212yesmaximal, complemented
6#21448465C211yesmaximal, characteristic, complemented
7#21448434C212yesmaximal
8#21448418C214yesmaximal
9#21448402C212yesmaximal
10#21448294C212yesmaximal, complemented
11#21448292C214yesmaximal, complemented
12#21448290C212yesmaximal, complemented
13#21448216C212yesmaximal
14#21448212C212yesmaximal
15C4×#14519735C211yesmaximal, characteristic
16#21448158C211yesmaximal, characteristic
17C61×#2320C211yesmaximal, characteristic, complemented
18C22×Q8×D61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×Dic122C2212yes—
22C2×#14519742C2211yescharacteristic
23C2×#14519742C2212yes—
24C4×Q8×D61C4116yescomplemented
25C2×#14519735C2212yes—
26C2×#14519734C2212yes—
27C2×C4⋊C4×D61C2212yes—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C42×D61C2212yes—
30C2×C42×D61C2211yescharacteristic
31#16839669C2212yes—
32#16839668C2212yes—
33#16839667C2212yes—
34#16839666C2214yes—
35#16839666C2214yes—
36#16839661C2212yes—
37#16839660C2212yes—
38#16839659C2214yes—
39#16839658C2212yes—
40#16839657C2214yes—
41#16839649C2214yes—
42#16839648C2214yes—
43#16839647C2214yes—
44#16839646C2214yes—
45#16839645C2214yes—
46#16839644C2214yes—
47#16839643C2214yes—
48#16839630C2212yes—
49#16839629C2212yes—
50#16839629C2212yes—
51#16839628C2212yes—
52#16839626C2212yes—
53#16839626C2212yes—
54#16839624C2214yes—
55#16839624C2214yes—
56#16839621C2214yes—
57#16839619C2214yes—
58C4⋊C4×Dic61C2214yes—
59C4⋊C4×Dic61C2212yes—
60C4×C4⋊Dic61C2211yescharacteristic
61#16839613C2211yescharacteristic
62#16839613C2211yescharacteristic
63#16839613C2214yes—
64#16839613C2212yes—
65C4×#11758198C2212yes—
66#16839609C2211yescharacteristic
67#16839609C2212yes—
68#16839609C2211yescharacteristic
69#16839609C2212yes—
70#16839608C2211yescharacteristic
71#16839607C2212yes—
72#16839607C2214yes—
73#16839607C2214yes—
74C42×Dic61C2212yes—
75C42×Dic61C2212yes—
76C2×C4×Q8×C61C2211yescharacteristic
77C61×#391C2212yes—
78C61×#389C2212yes—
79C61×#387C2214yes—
80C61×#383C2212yes—
81C61×#382C2212yes—
82C4×C4⋊C4×C61C2211yescharacteristic
83C61×#376C2211yescharacteristic
84C22×Dic122C2312yes—
85C22×Dic122C2311yescharacteristic
86C2×Q8×D61—28no—
87C2×Q8×D61C2×C418yes—
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2312yes—
90C22×C4×D61C2311yescharacteristic
91C22×C4×D61C2312yes—
92C22×C4×D61C2311yescharacteristic
93Q8×Dic61C2×C418yes—
94C4×Dic122C2×C418yes—
95C4×Dic122C2×C4116yes—
96#14519742C2×C418yes—
97#14519742C2×C4116yes—
98#14519735—28no—
99#14519734—28no—
100C2×C4⋊Dic61C2312yes—
101C2×C4⋊Dic61C2314yes—
102C2×C4⋊Dic61C2312yes—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196C2312yes—
105C2×#11758196C2312yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2312yes—
109C2×#11758196C2312yes—
110C2×#11758196C2312yes—
111C4⋊C4×D61C2×C4116yes—
112C4⋊C4×D61C2×C418yes—
113C2×#11758198C2312yes—
114C2×#11758198C2312yes—
115C2×#11758198C2314yes—
116C2×C4×Dic61C2312yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2312yes—
119C2×C4×Dic61C2312yes—
120C2×C4×Dic61C2314yes—
121C2×C4×Dic61C2312yes—
122C2×C4×Dic61C2312yes—
123C2×C4×Dic61C2312yes—
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2312yes—
126C2×C4×Dic61C2311yescharacteristic
127C2×C4×Dic61C2312yes—
128C2×C4×Dic61C2311yescharacteristic
129C2×C4×Dic61C2312yes—
130C42×D61C2×C4116yes—
131C42×D61C2×C418yes—
132#14519684C2312yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139#14519684C2314yes—
140#14519684C2311yescharacteristic
141#14519684C2311yescharacteristic
142#14519684C2312yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146C22×Q8×C61C2311yescharacteristic
147C4×Q8×C61C2×C418yes—
148C2×C4⋊C4×C61C2312yes—
149C2×C4⋊C4×C61C2314yes—
150C2×C4⋊C4×C61C2312yes—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C42×C61C2312yes—
153C2×C42×C61C2312yes—
154C2×C42×C61C2311yescharacteristic
155C2×C42×C61C2312yes—
156#95×C61C2311yescharacteristic
157#95×C61C2311yescharacteristic
158#95×C61C2312yes—
159#95×C61C2312yes—
160#95×C61C2314yes—
161#95×C61C2314yes—
162#95×C61C2314yes—
163C23×D61C2411yescharacteristic
164C2×Q8×C61—24no—
165C2×Q8×C61C22×C414yes—
166C22×C4×C61C2412yes—
167C22×C4×C61C2414yes—
168C22×C4×C61C2412yes—
169C22×C4×C61C2412yes—
170C22×C4×C61C2411yescharacteristic
171C22×C4×C61C2411yescharacteristic
172C22×C4×C61C2412yes—
173C22×C4×C61C2411yescharacteristic
174C22×Dic61C2412yes—
175C22×Dic61C2412yes—
176C22×Dic61C2414yes—
177C22×Dic61C2412yes—
178C22×Dic61C2411yescharacteristic
179C22×Dic61C2412yes—
180C22×Dic61C2411yescharacteristic
181C22×Dic61C2411yescharacteristic
182Q8×D61—232no—
183C2×C4×D61—28no—
184C2×C4×D61—24no—
185C2×C4×D61—41no—
186C2×C4×D61—41no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61C22×C418yes—
190C2×C4×D61C22×C414yes—
191C2×C4×D61C22×C414yes—
192C2×C4×D61C22×C418yes—
193C2×C4×D61C22×C414yes—
194C2×C4×D61#4118yes—
195C2×Dic122—24no—
196C2×Dic122—28no—
197C2×Dic122C22×C414yes—
198C2×Dic122C22×C418yes—
199C4⋊C4×C61—24no—
200C4⋊C4×C61—44no—
201C4⋊C4×C61C22×C418yes—
202C4⋊C4×C61C22×C414yes—
203C42×C61—24no—
204C42×C61—42no—
205C42×C61C22×C418yes—
206C42×C61C22×C414yes—
207#11758198—24no—
208#11758198—24no—
209#11758198—28no—
210C4⋊Dic61—24no—
211C4⋊Dic61—44no—
212C4⋊Dic61C22×C418yes—
213C4⋊Dic61C22×C414yes—
214#11758196—24no—
215#11758196—24no—
216#11758196—44no—
217#11758196—44no—
218#11758196C22×C418yes—
219#11758196C22×C418yes—
220#11758196C22×C418yes—
221C4×Dic61—24no—
222C4×Dic61—28no—
223C4×Dic61—24no—
224C4×Dic61—24no—
225C4×Dic61—28no—
226C4×Dic61—42no—
227C4×Dic61—42no—
228C4×Dic61—42no—
229C4×Dic61C22×C418yes—
230C4×Dic61C22×C414yes—
231C4×Dic61C22×C418yes—
232C4×Dic61C22×C414yes—
233C4×Dic61C22×C418yes—
234C4×Dic61C22×C414yes—
235C23×C61C2511yescharacteristic
236C22×D61—22no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61C23×C412yes—
240C22×D61C2×#4114yes—
241Q8×C61—28no—
242C2×C4×C61—24no—
243C2×C4×C61—22no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—21no—
247C2×C4×C61—22no—
248C2×C4×C61—24no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—24no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—24no—
257C2×C4×C61C23×C412yes—
258C2×C4×C61C23×C412yes—
259C2×C4×C61C23×C414yes—
260C2×C4×C61C23×C414yes—
261C2×C4×C61C23×C412yes—
262C2×C4×C61C2×#4114yes—
263C2×Dic61—24no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—24no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—24no—
274C2×Dic61—22no—
275C2×Dic61—24no—
276C2×Dic61—22no—
277C2×Dic61C23×C412yes—
278C2×Dic61C23×C414yes—
279C2×Dic61C23×C414yes—
280C2×Dic61C23×C412yes—
281C2×Dic61C23×C412yes—
282C2×Dic61C2×#4114yes—
283C2×Dic612−1+414yes—
284C4×D61—216no—
285C4×D61—28no—
286C4×D61—44no—
287C4×D61—48no—
288C4×D61#117116yes—
289Dic122—28no—
290Dic122—216no—
291#34059—611nomaximal, Sylow
292C22×C61C24×C411yescharacteristic
293C22×C61C22×#4112yes—
294C22×C61C2×2−1+412yes—
295C22×C61#58511yescharacteristic
296C22×C61#58511yescharacteristic
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—24no—
300C2×D61—24no—
301C2×D61C2×#11714yes—
302C4×C61—24no—
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—24no—
306C4×C61—44no—
307C4×C61—42no—
308C4×C61—42no—
309C4×C61C2×#11714yes—
310Dic61—24no—
311Dic61—22no—
312Dic61—24no—
313Dic61—42no—
314Dic61—42no—
315Dic61—44no—
316Dic61C2×#11714yes—
317Dic61#51914yes—
318C22×C4×Q8—611no—
319#2320—612no—
320#2320—612no—
321#2320—611no—
322#2320—611no—
323#2320—611no—
324#2320D6111yescharacteristic, complemented
325#2316—612no—
326#2313—614no—
327#2310—612no—
328#2295—612no—
329#2295—612no—
330#2295—614no—
331#2283—612no—
332#2283—612no—
333C4×#117—611no—
334C4×#117—611no—
335C2×C61C22×#11711yescharacteristic
336C2×C61C2×#51911yescharacteristic
337C2×C61#342811yescharacteristic
338C2×C61#346112yes—
339C2×C61#346112yes—
340D61—24no—
341C23×Q8—611no—
342C2×C4×Q8—611no—
343C2×C4×Q8—6116no—
344C2×C4×Q8—611no—
345C2×C4×Q8—612no—
346C2×C4×Q8—612no—
347C2×C4×Q8—611no—
348C2×C4×Q8C2×D6111yescharacteristic
349C2×#117—612no—
350C2×#117—612no—
351C22×C4⋊C4—612no—
352C22×C4⋊C4—611no—
353C22×C42—611no—
354C22×C42—612no—
355#391—612no—
356#391—612no—
357#391—612no—
358#391—614no—
359#391—614no—
360#391C2×D6112yes—
361#389—614no—
362#389—612no—
363#389—612no—
364#389—612no—
365#389—614no—
366#389C2×D6112yes—
367#387—614no—
368#387—614no—
369#387—614no—
370#387—614no—
371#387—614no—
372#387—614no—
373#387—614no—
374#387C2×D6114yes—
375#383—612no—
376#383—612no—
377#383—612no—
378#383C2×D6112yes—
379#382—612no—
380#382—612no—
381#382—612no—
382#382C2×D6112yes—
383#381—614no—
384#381—614no—
385#380—614no—
386#380—614no—
387C4×C4⋊C4—612no—
388C4×C4⋊C4—614no—
389C4×C4⋊C4—611no—
390C4×C4⋊C4—611no—
391C4×C4⋊C4—611no—
392C4×C4⋊C4—612no—
393C4×C4⋊C4—614no—
394C4×C4⋊C4C2×D6111yescharacteristic
395C4×C22⋊C4—612no—
396C4×C22⋊C4—612no—
397C4×C22⋊C4—612no—
398C4×C22⋊C4—611no—
399C4×C22⋊C4—611no—
400#376—611no—
401#376—612no—
402#376—614no—
403#376—614no—
404#376C2×D6111yescharacteristic
405C43—612no—
406C43—612no—
407C61#3405911yescharacteristic, complemented, Sylow
408C22×Q8—618no—
409C22×Q8—612no—
410C22×Q8—611no—
411C22×Q8—1228no—
412C22×Q8C22×D6111yescharacteristic
413C23×C4—611no—
414C23×C4—612no—
415C23×C4—611no—
416C23×C4—611no—
417C23×C4—612no—
418C4×Q8—618no—
419C4×Q8—6116no—
420C4×Q8—618no—
421C4×Q8—6116no—
422C4×Q8—618no—
423C4×Q8C4×D6118yes—
424#117—1228no—
425#117—1228no—
426C2×C4⋊C4—612no—
427C2×C4⋊C4—612no—
428C2×C4⋊C4—612no—
429C2×C4⋊C4—612no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—618no—
432C2×C4⋊C4—6116no—
433C2×C4⋊C4—612no—
434C2×C4⋊C4—612no—
435C2×C4⋊C4—612no—
436C2×C4⋊C4—614no—
437C2×C4⋊C4—614no—
438C2×C4⋊C4—614no—
439C2×C4⋊C4C22×D6112yes—
440C2×C4⋊C4C22×D6114yes—
441C2×C4⋊C4C22×D6112yes—
442C2×C4⋊C4C22×D6111yescharacteristic
443C2×C22⋊C4—614no—
444C2×C22⋊C4—612no—
445C2×C22⋊C4—612no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—612no—
449C2×C42—612no—
450C2×C42—611no—
451C2×C42—612no—
452C2×C42—618no—
453C2×C42—6116no—
454C2×C42—614no—
455C2×C42—612no—
456C2×C42—614no—
457C2×C42—612no—
458C2×C42—612no—
459C2×C42—612no—
460C2×C42—612no—
461C2×C42—612no—
462C2×C42C22×D6112yes—
463C2×C42C22×D6112yes—
464C2×C42C22×D6111yescharacteristic
465C2×C42C22×D6112yes—
466#95—611no—
467#95—611no—
468#95—612no—
469#95—614no—
470#95—612no—
471#95—614no—
472#95—614no—
473#95—614no—
474#95—614no—
475#95—614no—
476#95—614no—
477#95—614no—
478#95—614no—
479#95—614no—
480#95C22×D6112yes—
481#95C22×D6114yes—
482#95C22×D6114yes—
483#95C22×D6111yescharacteristic
484#95C22×D6111yescharacteristic
485#95C22×D6112yes—
486#95C22×D6114yes—
487C24—611no—
488C2×Q8—24no—
489C2×Q8—618no—
490C2×Q8—614no—
491C2×Q8—1228no—
492C2×Q8—12232no—
493C2×Q8—1224no—
494C2×Q8C2×C4×D6114yes—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—614no—
498C22×C4—618no—
499C22×C4—612no—
500C22×C4—611no—
501C22×C4—612no—
502C22×C4—614no—
503C22×C4—618no—
504C22×C4—614no—
505C22×C4—618no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—614no—
509C22×C4—1224no—
510C22×C4—1228no—
511C22×C4—2441no—
512C22×C4—2442no—
513C22×C4—2441no—
514C22×C4—2442no—
515C22×C4C23×D6112yes—
516C22×C4C23×D6114yes—
517C22×C4C23×D6112yes—
518C22×C4C23×D6111yescharacteristic
519C22×C4C23×D6112yes—
520C22×C4C23×D6111yescharacteristic
521C22×C4C23×D6112yes—
522C22×C4C23×D6111yescharacteristic
523C4⋊C4—24no—
524C4⋊C4—44no—
525C4⋊C4—618no—
526C4⋊C4—618no—
527C4⋊C4—618no—
528C4⋊C4—618no—
529C4⋊C4—614no—
530C4⋊C4—1224no—
531C4⋊C4—1224no—
532C4⋊C4—1224no—
533C4⋊C4—2444no—
534C4⋊C4—2444no—
535C4⋊C4—2444no—
536C4⋊C4C2×C4×D6118yes—
537C4⋊C4C2×C4×D6114yes—
538C22⋊C4—1224no—
539C22⋊C4—1224no—
540C22⋊C4—1228no—
541C42—24no—
542C42—42no—
543C42—614no—
544C42—618no—
545C42—614no—
546C42—618no—
547C42—614no—
548C42—618no—
549C42—1228no—
550C42—1224no—
551C42—1224no—
552C42—1228no—
553C42—1224no—
554C42—2442no—
555C42—2442no—
556C42—2442no—
557C42C2×C4×D6118yes—
558C42C2×C4×D6114yes—
559C23—612no—
560C23—614no—
561C23—1222no—
562C23—1221no—
563C23—1221no—
564C23C24×D6111yescharacteristic
565Q8—28no—
566Q8—12216no—
567Q8—1228no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—612no—
584C2×C4—612no—
585C2×C4—614no—
586C2×C4—614no—
587C2×C4—6116no—
588C2×C4—612no—
589C2×C4—614no—
590C2×C4—614no—
591C2×C4—1228no—
592C2×C4—12216no—
593C2×C4—1224no—
594C2×C4—1221no—
595C2×C4—1222no—
596C2×C4—1221no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1224no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1224no—
604C2×C4—1222no—
605C2×C4—1224no—
606C2×C4—1222no—
607C2×C4—2444no—
608C2×C4—2448no—
609C2×C4C22×C4×D6112yes—
610C2×C4C22×C4×D6112yes—
611C2×C4C22×C4×D6114yes—
612C2×C4C22×C4×D6114yes—
613C2×C4C22×C4×D6112yes—
614C2×C4#41×D6114yes—
615C22—614no—
616C22—1224no—
617C22—1224no—
618C22—1222no—
619C22—1222no—
620C22C23×C4×D6111yescharacteristic
621C22C2×#41×D6112yes—
622C222−1+4×D6112yes—
623C22#1684059711yescharacteristic
624C22#1684059911yescharacteristic
625C4—24no—
626C4—22no—
627C4—22no—
628C4—24no—
629C4—42no—
630C4—44no—
631C4—42no—
632C4—614no—
633C4—614no—
634C4—1224no—
635C4—1222no—
636C4—1224no—
637C4—2442no—
638C4—2442no—
639C4—2444no—
640C4#117×D6114yes—
641C2—1224no—
642C2C2×#117×D6111yescharacteristic
643C2#519×D6111yescharacteristic
644C2#2145901911yescharacteristic
645C2#2145924512yes—
646C2#2145925112yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2320C2
socle, cosocleC23×C61C25
prime radicalC23×D61C24
hypercenter#2320D61
hypocenterC61#34059
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #21448471C2semidirect
3. #21448470C2semidirect
4. #21448469C2semidirect
5. #21448467C2semidirect
6. #21448465C2semidirect
10. #21448294C2semidirect
11. #21448292C2semidirect
12. #21448290C2semidirect
17. C61×#2320C2semidirect
24. C4×Q8×D61C4semidirect
324. #2320D61semidirect
407. C61#34059semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
#214484712
#214484702
#214484692
#214484672
#214484652
#214484342
#214484182
#214484022
#214482942
#214482922
#214482902
#214482162
#214482122
C4×#145197352
#214481582
C61×#23202
#3405961