Finite Group Databasebeta

← #29840698

Subgroups — #29840698

Order 15616.

2094 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic
2#21448908C211yesmaximal, characteristic, complemented
3#21448908C211yesmaximal, characteristic, complemented
4#21448879C211yesmaximal, characteristic, complemented
5#21448851C212yesmaximal
6#21448842C212yesmaximal
7#21448781C214yesmaximal, complemented
8#21448711C212yesmaximal
9#21448700C212yesmaximal
10#21448571C214yesmaximal
11#21448464C212yesmaximal, complemented
12#21448378C212yesmaximal, complemented
13C4×#14519768C212yesmaximal, complemented
14#21448215C211yesmaximal, characteristic
15#21448184C212yesmaximal, complemented
16C4×#14519735C211yesmaximal, characteristic
17C61×#2365C211yesmaximal, characteristic, complemented
18#16840317C4116yescomplemented
19C2×#14519777C2211yescharacteristic
20C2×#14519768C2212yes—
21C2×#14519757C2212yes—
22C2×#14519753C2212yes—
23C2×Q8×Dic61C2212yes—
24C2×Q8×Dic61C2212yes—
25C2×#14519742C2212yes—
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519735C2212yes—
29C2×C42×D61C2211yescharacteristic
30#16839669C2212yes—
31#16839666C2214yes—
32#16839666C2214yes—
33#16839661C2212yes—
34#16839660C2212yes—
35#16839660C2212yes—
36#16839658C2212yes—
37#16839658C2212yes—
38#16839654C2214yes—
39#16839653C2214yes—
40#16839652C2214yes—
41#16839651C2214yes—
42#16839649C2214yes—
43#16839648C2214yes—
44#16839647C2214yes—
45#16839645C2214yes—
46#16839643C2214yes—
47#16839629C2214yes—
48#16839629C2212yes—
49#16839627C2211yescharacteristic
50#16839627C2211yescharacteristic
51#16839626C2214yes—
52#16839624C2212yes—
53#16839619C2211yescharacteristic
54#16839619C2211yescharacteristic
55C4⋊C4×Dic61C2214yes—
56C4⋊C4×Dic61C2212yes—
57C4⋊C4×Dic61C2211yescharacteristic
58C4⋊C4×Dic61C2214yes—
59C4⋊C4×Dic61C2212yes—
60C4⋊C4×Dic61C2212yes—
61C4⋊C4×Dic61C2211yescharacteristic
62C4×#11758196C2214yes—
63C4×C4⋊Dic61C2212yes—
64C4×C4⋊Dic61C2211yescharacteristic
65C4×C4⋊Dic61C2214yes—
66C4×C4⋊Dic61C2212yes—
67C4×C4⋊Dic61C2211yescharacteristic
68#16839613C2214yes—
69C4×#11758198C2212yes—
70C4×#11758198C2212yes—
71#16839609C2212yes—
72#16839608C2212yes—
73#16839608C2214yes—
74#16839607C2212yes—
75C42×Dic61C2212yes—
76C2×C4⋊Q8×C61C2211yescharacteristic
77C2×C4×Q8×C61C2212yes—
78C61×#391C2212yes—
79C61×#389C2212yes—
80C61×#387C2214yes—
81C4×C4⋊C4×C61C2211yescharacteristic
82C4×C4⋊C4×C61C2212yes—
83C4×C4⋊C4×C61C2211yescharacteristic
84C22×Dic122C2312yes—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88#14519777C2×C418yes—
89#14519768C2×C4116yes—
90#14519757C2×C4116yes—
91#14519753C2×C4116yes—
92Q8×Dic61—28no—
93Q8×Dic61C2×C4116yes—
94#14519742C2×C4116yes—
95#14519735—24no—
96#14519735—24no—
97#14519735C2×C4116yes—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2314yes—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2312yes—
103C2×C4⋊Dic61C2312yes—
104C2×C4⋊Dic61C2314yes—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758198C2312yes—
110C2×#11758198C2312yes—
111C2×#11758198C2312yes—
112C2×#11758198C2312yes—
113C2×#11758198C2314yes—
114C2×C4×Dic61C2312yes—
115C2×C4×Dic61C2312yes—
116C2×C4×Dic61C2312yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2312yes—
119C2×C4×Dic61C2312yes—
120C2×C4×Dic61C2312yes—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2311yescharacteristic
126C2×C4×Dic61C2314yes—
127C42×D61C2×C418yes—
128#14519684C2312yes—
129#14519684C2312yes—
130#14519684C2312yes—
131#14519684C2312yes—
132#14519684C2312yes—
133#14519684C2314yes—
134#14519684C2312yes—
135#14519684C2312yes—
136#14519684C2314yes—
137#14519684C2312yes—
138#14519684C2312yes—
139#14519684C2312yes—
140#14519684C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143#14519684C2314yes—
144C22×Q8×C61C2312yes—
145C4⋊Q8×C61C2×C418yes—
146C4×Q8×C61—28no—
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2314yes—
151C2×C4⋊C4×C61C2312yes—
152C2×C4⋊C4×C61C2312yes—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C42×C61C2312yes—
155C2×C42×C61C2314yes—
156C2×C42×C61C2312yes—
157C2×C42×C61C2311yescharacteristic
158#95×C61C2312yes—
159#95×C61C2312yes—
160#95×C61C2314yes—
161#95×C61C2314yes—
162C23×D61C2411yescharacteristic
163C2×Q8×C61—24no—
164C2×Q8×C61—24no—
165C2×Q8×C61C22×C418yes—
166C22×C4×C61C2412yes—
167C22×C4×C61C2412yes—
168C22×C4×C61C2412yes—
169C22×C4×C61C2411yescharacteristic
170C22×C4×C61C2414yes—
171C22×C4×C61C2412yes—
172C22×C4×C61C2411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61C2412yes—
175C22×Dic61C2412yes—
176C22×Dic61C2412yes—
177C22×Dic61C2411yescharacteristic
178C22×Dic61C2411yescharacteristic
179C22×Dic61C2411yescharacteristic
180C22×Dic61C2414yes—
181C22×Dic61C2412yes—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—41no—
187C2×C4×D61—41no—
188C2×C4×D61C22×C414yes—
189C2×C4×D61C22×C414yes—
190C2×C4×D61C22×C414yes—
191C2×Dic122—42no—
192C2×Dic122—42no—
193C2×Dic122C22×C418yes—
194C4⋊C4×C61—28no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61C22×C418yes—
199C4⋊C4×C61C22×C418yes—
200C4⋊C4×C61#4114yes—
201C42×C61—28no—
202C42×C61—24no—
203C42×C61—24no—
204C42×C61C22×C414yes—
205#11758198—24no—
206#11758198—24no—
207#11758198—42no—
208#11758198—42no—
209#11758198C22×C4116yes—
210C4⋊Dic61—22no—
211C4⋊Dic61—22no—
212C4⋊Dic61—22no—
213C4⋊Dic61—28no—
214C4⋊Dic61C22×C418yes—
215C4⋊Dic61C22×C418yes—
216C4⋊Dic61C22×C4116yes—
217C4⋊Dic61#4114yes—
218#11758196—44no—
219#11758196—44no—
220#11758196C22×C4116yes—
221C4×Dic61—24no—
222C4×Dic61—24no—
223C4×Dic61—24no—
224C4×Dic61—24no—
225C4×Dic61—28no—
226C4×Dic61—44no—
227C4×Dic61—42no—
228C4×Dic61—44no—
229C4×Dic61—42no—
230C4×Dic61C22×C414yes—
231C4×Dic61C22×C414yes—
232C4×Dic61C22×C414yes—
233C4×Dic61C22×C4116yes—
234C23×C61C2511yescharacteristic
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61C23×C412yes—
242Q8×C61—216no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61C23×C418yes—
259C2×C4×C61C23×C412yes—
260C2×C4×C61C23×C412yes—
261C2×C4×C61C23×C412yes—
262C2×C4×C61C2×#4114yes—
263C2×C4×C61C2×#4112yes—
264C2×C4×C61C2×#4112yes—
265C2×C4×C612−1+412yes—
266C2×C4×C612−1+412yes—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—22no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—22no—
273C2×Dic61—24no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—24no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61C23×C412yes—
287C2×Dic61C23×C412yes—
288C2×Dic61C23×C412yes—
289C2×Dic61C23×C418yes—
290C2×Dic61C2×#4114yes—
291C4×D61—28no—
292C4×D61—28no—
293C4×D61—44no—
294Dic122—48no—
295#34231—611nomaximal, Sylow
296C22×C61C24×C411yescharacteristic
297C22×C61C22×#4111yescharacteristic
298C22×C61C22×#4111yescharacteristic
299C22×C61C2×2−1+411yescharacteristic
300C22×C61C2×2−1+411yescharacteristic
301C22×C61#58511yescharacteristic
302C22×C61#58511yescharacteristic
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C4×C61—28no—
311C4×C61—22no—
312C4×C61—24no—
313C4×C61—42no—
314C4×C61—42no—
315C4×C61—42no—
316C4×C61C4×#4114yes—
317C4×C61#51914yes—
318Dic61—22no—
319Dic61—22no—
320Dic61—28no—
321Dic61—22no—
322Dic61—24no—
323Dic61—42no—
324Dic61—42no—
325Dic61—42no—
326C2×#533—611no—
327#2369—611no—
328#2369—611no—
329#2365—611no—
330#2365D6111yescharacteristic, complemented
331#2362—612no—
332#2362—612no—
333#2356—614no—
334#2347—612no—
335#2346—612no—
336#2332—614no—
337#2320—612no—
338C4×#125—612no—
339C4×#125—612no—
340#2283—611no—
341#2276—612no—
342C4×#117—611no—
343C2×C61C2×C4×#4111yescharacteristic
344C2×C61C2×#51911yescharacteristic
345C2×C61#342811yescharacteristic
346C2×C61#351511yescharacteristic
347C2×C61#351511yescharacteristic
348C2×C61#351811yescharacteristic
349C2×C61#351811yescharacteristic
350D61—42no—
351#533—6116no—
352C2×C4⋊Q8—611no—
353C2×C4⋊Q8C2×D6111yescharacteristic
354C2×#125—612no—
355C2×C22⋊Q8—612no—
356C2×C22⋊Q8—612no—
357C2×C4×Q8—612no—
358C2×C4×Q8—612no—
359C2×C4×Q8—612no—
360C2×C4×Q8C2×D6112yes—
361C2×#117—612no—
362C2×#117—611no—
363C2×#117—611no—
364C22×C42—611no—
365#391—612no—
366#391—614no—
367#391—614no—
368#391C2×D6112yes—
369#389—612no—
370#389—612no—
371#389—612no—
372#389—612no—
373#389—612no—
374#389C2×D6112yes—
375#388—614no—
376#388—614no—
377#388—614no—
378#388—614no—
379#387—614no—
380#387—614no—
381#387—614no—
382#387—614no—
383#387—614no—
384#387C2×D6114yes—
385#383—614no—
386#383—612no—
387#382—611no—
388#382—611no—
389#382—614no—
390#381—612no—
391#380—611no—
392#380—611no—
393C4×C4⋊C4—614no—
394C4×C4⋊C4—612no—
395C4×C4⋊C4—612no—
396C4×C4⋊C4—611no—
397C4×C4⋊C4—614no—
398C4×C4⋊C4—612no—
399C4×C4⋊C4—611no—
400C4×C4⋊C4—614no—
401C4×C4⋊C4—612no—
402C4×C4⋊C4—614no—
403C4×C4⋊C4—612no—
404C4×C4⋊C4—611no—
405C4×C4⋊C4—611no—
406C4×C4⋊C4—614no—
407C4×C4⋊C4C2×D6112yes—
408C4×C4⋊C4C2×D6111yescharacteristic
409C4×C4⋊C4C2×D6111yescharacteristic
410C4×C22⋊C4—612no—
411C4×C22⋊C4—612no—
412C4×C22⋊C4—612no—
413#376—612no—
414#376—614no—
415#376—612no—
416C43—612no—
417C61#3423111yescharacteristic, complemented, Sylow
418C22×Q8—612no—
419C22×Q8C22×D6112yes—
420C23×C4—611no—
421C23×C4—611no—
422C23×C4—611no—
423C4⋊Q8—618no—
424C4⋊Q8C4×D6118yes—
425#125—6116no—
426C22⋊Q8—6116no—
427C22⋊Q8—6116no—
428C4×Q8—28no—
429C4×Q8—6116no—
430C4×Q8—6116no—
431C4×Q8—1228no—
432#117—6116no—
433#117—1224no—
434#117—1224no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—612no—
437C2×C4⋊C4—614no—
438C2×C4⋊C4—614no—
439C2×C4⋊C4—612no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—614no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—614no—
445C2×C4⋊C4—614no—
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C4⋊C4C22×D6114yes—
448C2×C4⋊C4C22×D6111yescharacteristic
449C2×C4⋊C4C22×D6111yescharacteristic
450C2×C4⋊C4C22×D6112yes—
451C2×C4⋊C4C22×D6112yes—
452C2×C4⋊C4C22×D6111yescharacteristic
453C2×C22⋊C4—614no—
454C2×C22⋊C4—612no—
455C2×C22⋊C4—612no—
456C2×C22⋊C4—612no—
457C2×C22⋊C4—612no—
458C2×C42—614no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—618no—
463C2×C42—612no—
464C2×C42—612no—
465C2×C42—612no—
466C2×C42—614no—
467C2×C42—612no—
468C2×C42—612no—
469C2×C42—612no—
470C2×C42—614no—
471C2×C42—614no—
472C2×C42C22×D6112yes—
473C2×C42C22×D6114yes—
474C2×C42C22×D6112yes—
475C2×C42C22×D6111yescharacteristic
476#95—612no—
477#95—612no—
478#95—612no—
479#95—612no—
480#95—612no—
481#95—612no—
482#95—612no—
483#95—614no—
484#95—614no—
485#95—612no—
486#95—612no—
487#95—612no—
488#95—614no—
489#95—614no—
490#95—614no—
491#95—614no—
492#95C22×D6112yes—
493#95C22×D6114yes—
494#95C22×D6112yes—
495#95C22×D6114yes—
496C24—611no—
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—618no—
500C2×Q8—2442no—
501C2×Q8—2442no—
502C2×Q8C2×C4×D6118yes—
503C22×C4—611no—
504C22×C4—612no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—614no—
508C22×C4—614no—
509C22×C4—614no—
510C22×C4—614no—
511C22×C4—612no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—2441no—
519C22×C4—2441no—
520C22×C4C23×D6112yes—
521C22×C4C23×D6112yes—
522C22×C4C23×D6112yes—
523C22×C4C23×D6111yescharacteristic
524C22×C4C23×D6114yes—
525C22×C4C23×D6112yes—
526C22×C4C23×D6111yescharacteristic
527C22×C4C23×D6111yescharacteristic
528C4⋊C4—22no—
529C4⋊C4—28no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—6116no—
533C4⋊C4—618no—
534C4⋊C4—6116no—
535C4⋊C4—618no—
536C4⋊C4—614no—
537C4⋊C4—1228no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—1222no—
541C4⋊C4—2444no—
542C4⋊C4—2444no—
543C4⋊C4C2×C4×D6118yes—
544C4⋊C4C2×C4×D6118yes—
545C4⋊C4#1175822414yes—
546C22⋊C4—6116no—
547C22⋊C4—1224no—
548C22⋊C4—1224no—
549C22⋊C4—2442no—
550C22⋊C4—2442no—
551C42—28no—
552C42—24no—
553C42—24no—
554C42—614no—
555C42—614no—
556C42—614no—
557C42—6116no—
558C42—1224no—
559C42—1228no—
560C42—1224no—
561C42—1224no—
562C42—1224no—
563C42—2442no—
564C42—2444no—
565C42—2444no—
566C42—2442no—
567C42C2×C4×D6114yes—
568C23—612no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23—1221no—
573C23—1221no—
574C23—1221no—
575C23C24×D6111yescharacteristic
576Q8—216no—
577Q8—2448no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—612no—
594C2×C4—612no—
595C2×C4—612no—
596C2×C4—618no—
597C2×C4—614no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1222no—
602C2×C4—1221no—
603C2×C4—1222no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1224no—
607C2×C4—1224no—
608C2×C4—1228no—
609C2×C4—1228no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—2444no—
620C2×C4C22×C4×D6112yes—
621C2×C4C22×C4×D6118yes—
622C2×C4C22×C4×D6112yes—
623C2×C4C22×C4×D6112yes—
624C2×C4#41×D6112yes—
625C2×C4C2×#1175822414yes—
626C2×C4C2×#1175822412yes—
627C2×C4#1451982412yes—
628C2×C4#1451982512yes—
629C22—1222no—
630C22—1222no—
631C22—1222no—
632C22—2441no—
633C22—2441no—
634C22—2441no—
635C22—2441no—
636C22C23×C4×D6111yescharacteristic
637C22C2×#41×D6111yescharacteristic
638C22C22×#1175822411yescharacteristic
639C22C2×#1451982411yescharacteristic
640C22C2×#1451982511yescharacteristic
641C22#1684059911yescharacteristic
642C22#1684059911yescharacteristic
643C4—28no—
644C4—24no—
645C4—22no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—1222no—
650C4—1222no—
651C4—1222no—
652C4—1228no—
653C4—1224no—
654C4—2442no—
655C4—2442no—
656C4—2442no—
657C4C4×#1175822414yes—
658C4#1684023814yes—
659C2—2442no—
660C2C2×C4×#1175822411yescharacteristic
661C2C2×#1684023811yescharacteristic
662C2#2145902111yescharacteristic
663C2#2145978811yescharacteristic
664C2#2145979611yescharacteristic
665C2#2145983111yescharacteristic
666C2#2145983311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2365C2
socle, cosocleC23×C61C25
prime radicalC23×D61C24
hypercenter#2365D61
hypocenterC61#34231
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #21448908C2semidirect
3. #21448908C2semidirect
4. #21448879C2semidirect
7. #21448781C2semidirect
11. #21448464C2semidirect
12. #21448378C2semidirect
13. C4×#14519768C2semidirect
15. #21448184C2semidirect
17. C61×#2365C2semidirect
18. #16840317C4semidirect
330. #2365D61semidirect
417. C61#34231semidirect

Maximal subgroups

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

subgroupindex
C2×#168403172
#214489082
#214488792
#214488512
#214488422
#214487812
#214487112
#214487002
#214485712
#214484642
#214483782
C4×#145197682
#214482152
#214481842
C4×#145197352
C61×#23652
#3423161