Finite Group Databasebeta

← #29646313

Subgroups — #29646313

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic
2#21454850C212yesmaximal
3#21444182C212yesmaximal, complemented
4#21444181C212yesmaximal, complemented
5#21444173C212yesmaximal, complemented
6#21444161C211yesmaximal, characteristic, complemented
7#21444149C211yesmaximal, characteristic, complemented
8#21444147C211yesmaximal, characteristic, complemented
9#21444141C211yesmaximal, characteristic, complemented
10#324×D61C211yesmaximal, characteristic, complemented
11C2×C61×#324C211yesmaximal, characteristic, complemented
12#16840467—22no—
13#16840467—22no—
14#16840467—22no—
15#16840467—22no—
16C2×#14519776C411yescharacteristic
17C2×#14519767C411yescharacteristic
18C2×#14519767C2211yescharacteristic
19C2×#14519757C411yescharacteristic
20C2×#14519756C411yescharacteristic
21C2×#14519756C411yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519755C411yescharacteristic
24C2×#14519755C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×C4×C22⋊D61C411yescharacteristic
27C2×C4×C22⋊D61C411yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16839837—22no—
31#16839836—22no—
32#16839833—22no—
33C8×C22⋊D61—22no—
34#16839816C2212yes—
35#16839812C2212yes—
36#16839726C2212yes—
37#16839724C2212yes—
38C22⋊C8×D61C2212yes—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839488C2212yes—
42#16839487C2212yes—
43#16839487C2212yes—
44#16839487C2212yes—
45#16839487C2212yes—
46C22×C4⋊C4×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#324C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×Dic122C2×C411yescharacteristic
53C22×Dic122C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2311yescharacteristic
58C2×#11758194—22no—
59C2×#11758189—22no—
60C2×C8×D61—22no—
61#14519776—22no—
62#14519776—22no—
63#14519767—22no—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519757—22no—
68#14519757—22no—
69#14519756—22no—
70#14519756—22no—
71#14519756—22no—
72#14519756—22no—
73#14519756—22no—
74#14519756—22no—
75#14519755—22no—
76#14519755—22no—
77#14519755—22no—
78#14519755—22no—
79#14519742—22no—
80#14519742—22no—
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84C4×C22⋊D61—21no—
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61D412yes—
90C4×C22⋊D61D412yes—
91C4×C22⋊D61D412yes—
92C4×C22⋊D61D412yes—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2311yescharacteristic
104C2×#11758196C2311yescharacteristic
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—22no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C23×C4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—22no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C22⋊C8×C61—22no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—41no—
146C22×C4×C61—81no—
147C22×C4×C61—81no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—24no—
157C2×C22⋊D61C22⋊C411yescharacteristic
158C2×C22⋊D61C22⋊C411yescharacteristic
159C2×C22⋊D61C22⋊C411yescharacteristic
160C2×C22⋊D61C22⋊C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—41no—
174C2×C4×D61—81no—
175C2×C4×D61—81no—
176C2×C4×D61C2×D412yes—
177C2×C4×D61C2×D412yes—
178C2×Dic122—22no—
179C2×Dic122—22no—
180C2×Dic122—22no—
181C2×Dic122—22no—
182C2×Dic122—41no—
183C2×Dic122—81no—
184C2×Dic122—81no—
185C2×C8×C61—22no—
186C2×C8×C61—22no—
187C2×C8×C61—82no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—22no—
192C22⋊Dic61—21no—
193C22⋊Dic61—21no—
194C22⋊Dic61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61C22⋊C412yes—
197C22⋊Dic61C22⋊C412yes—
198#11758198—21no—
199#11758198—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198C22⋊C412yes—
203#11758198C22⋊C412yes—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—21no—
211#11758196—21no—
212#11758196—21no—
213#11758196—21no—
214#11758196—22no—
215#11758196—22no—
216#11758196—22no—
217#11758196C22⋊C412yes—
218#11758196C22⋊C412yes—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61C2×D412yes—
224C4×Dic61C2×D412yes—
225#11758194—82no—
226C2×#92418—22no—
227C2×#92418—22no—
228#11758189—82no—
229C8×D61—82no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—22no—
233C23×C61—41no—
234C23×C61C2×C22⋊C411yescharacteristic
235C23×C61C2×C22⋊C411yescharacteristic
236C23×C61C23×C411yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—22no—
240C22×D61—41no—
241C22×D61C2×C22⋊C411yescharacteristic
242C22×D61C2×C22⋊C411yescharacteristic
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—81no—
259C2×C4×C61—81no—
260C2×C4×C61C2×C22⋊C412yes—
261C2×C4×C61#13112yes—
262C2×C4×C61C22×D412yes—
263C22⋊D61—22no—
264C22⋊D61—22no—
265C22⋊D61—22no—
266C22⋊D61#10114yes—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—22no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C412yes—
283C2×Dic61C2×C22⋊C412yes—
284C2×Dic61C2×C22⋊C411yescharacteristic
285C4×D61—42no—
286C4×D61—42no—
287C4×D61—42no—
288C4×D61—42no—
289C4×D61—81no—
290C4×D61—81no—
291Dic122—44no—
292Dic122—82no—
293Dic122—82no—
294C8×C61—42no—
295C8×C61—42no—
296#92418—42no—
297#92418—42no—
298#17426—611nomaximal, Sylow
299C22×C61—21no—
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61C2×#10112yes—
309C22×C61C22×C22⋊C411yescharacteristic
310C22×C61C2×#13111yescharacteristic
311C22×C61#56811yescharacteristic
312C2×D61—21no—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—42no—
318C2×D61—42no—
319C2×D61C2×#10112yes—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—22no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61—41no—
326Dic61—22no—
327Dic61—22no—
328Dic61—21no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61—41no—
333Dic61C2×#10112yes—
334C2×#554—611no—
335#2974—612no—
336#1472—612no—
337#1472—612no—
338#1470—612no—
339#1467—611no—
340#1463—611no—
341#1463—611no—
342#1461—611no—
343C2×#324—611no—
344C2×#324D6111yescharacteristic, complemented
345C2×C61—21no—
346C2×C61—21no—
347C2×C61—22no—
348C2×C61—41no—
349C2×C61#288011yescharacteristic
350C2×C61#288311yescharacteristic
351C2×C61C22×#10111yescharacteristic
352D61—22no—
353D61—41no—
354#554—1222no—
355#554—1222no—
356#554—1222no—
357#554—1222no—
358C2×C4⋊Q8—611no—
359C2×#125—611no—
360C2×#125—611no—
361C2×C22⋊Q8—611no—
362C2×C22⋊Q8—611no—
363C2×C22⋊Q8—611no—
364C2×C22⋊Q8—611no—
365C2×C22⋊Q8—611no—
366C2×C22⋊Q8—611no—
367C2×C4×Q8—611no—
368C2×C4×D4—611no—
369C2×C4×D4—611no—
370C2×C4×D4—611no—
371C22×C4⋊C4—611no—
372C22×C4⋊C4C2×D6111yescharacteristic
373#436—1222no—
374#435—1222no—
375#435—1222no—
376C8×D4—1222no—
377#432—612no—
378#431—612no—
379#407—612no—
380#407—612no—
381C2×C22⋊C8—612no—
382C2×C22⋊C8C2×D6112yes—
383#324—611no—
384#324—611no—
385#324—612no—
386#324—612no—
387#324—612no—
388#324—612no—
389#324—612no—
390#324C2×D6111yescharacteristic
391#324C2×D6111yescharacteristic
392#324C2×D6112yes—
393C61#1742611yescharacteristic, complemented, Sylow
394C22×Q8—611no—
395C22×Q8—611no—
396C22×Q8—611no—
397C22×D4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—611no—
401C23×C4C4×D6111yescharacteristic
402C23×C4C4×D6111yescharacteristic
403C23×C4C22×D6111yescharacteristic
404C2×M16—1222no—
405C2×M16—1222no—
406C22×C8—22no—
407C22×C8—1222no—
408C4⋊Q8—1222no—
409C4⋊Q8—1222no—
410#125—1222no—
411#125—1222no—
412#125—1222no—
413#125—1222no—
414C22⋊Q8—1222no—
415C22⋊Q8—1222no—
416C22⋊Q8—1222no—
417C22⋊Q8—1222no—
418C22⋊Q8—1222no—
419C22⋊Q8—1222no—
420C22⋊Q8—1222no—
421C22⋊Q8—1222no—
422C22⋊Q8—1222no—
423C22⋊Q8—1222no—
424C22⋊Q8—1222no—
425C22⋊Q8—1222no—
426C4×Q8—1222no—
427C4×Q8—1222no—
428C4×D4—612no—
429C4×D4—612no—
430C4×D4—612no—
431C4×D4—612no—
432C4×D4—1221no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1221no—
437C4×D4—1221no—
438C4×D4—1221no—
439C4×D4—1221no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—1222no—
455C2×C4⋊C4—1222no—
456C2×C4⋊C4C4×D6111yescharacteristic
457C2×C4⋊C4C4×D6111yescharacteristic
458C2×C4⋊C4C22×D6111yescharacteristic
459C2×C4⋊C4C22×D6111yescharacteristic
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C4⋊C8—1222no—
470C4⋊C8—1222no—
471C22⋊C8—22no—
472C22⋊C8—612no—
473C22⋊C8—612no—
474C22⋊C8—1222no—
475C22⋊C8—1222no—
476C22⋊C8—1222no—
477C22⋊C8C22×D6112yes—
478C22⋊C8C22×D6112yes—
479#97—1222no—
480C4×C8—1222no—
481C24—611no—
482C24C2×C4×D6111yescharacteristic
483C2×Q8—1222no—
484C2×Q8—1222no—
485C2×Q8—1222no—
486C2×Q8—1222no—
487C2×Q8—4881no—
488C2×Q8—4881no—
489C2×Q8—2441no—
490C2×D4—611no—
491C2×D4—611no—
492C2×D4—611no—
493C2×D4—611no—
494C2×D4—1224no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—41no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1222no—
517C22×C4—4881no—
518C22×C4—4881no—
519C22×C4—2441no—
520C22×C4C2×C4×D6111yescharacteristic
521C22×C4C2×C4×D6111yescharacteristic
522C22×C4C2×C4×D6111yescharacteristic
523C22×C4C2×C4×D6111yescharacteristic
524C22×C4C2×C4×D6111yescharacteristic
525C22×C4D4×D6112yes—
526C22×C4D4×D6112yes—
527C22×C4C23×D6111yescharacteristic
528M16—4882no—
529M16—4882no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—82no—
533C2×C8—1222no—
534C2×C8—1222no—
535C2×C8—4882no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—612no—
541C4⋊C4—612no—
542C4⋊C4—1222no—
543C4⋊C4—1222no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1222no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C4⋊C4—1222no—
553C4⋊C4—1222no—
554C4⋊C4—1222no—
555C22⋊C4—612no—
556C22⋊C4—612no—
557C22⋊C4—612no—
558C22⋊C4—612no—
559C22⋊C4—1221no—
560C22⋊C4—1221no—
561C22⋊C4—1221no—
562C22⋊C4—1221no—
563C22⋊C4—1221no—
564C22⋊C4—1221no—
565C22⋊C4—1221no—
566C22⋊C4—1221no—
567C42—612no—
568C42—612no—
569C42—1221no—
570C42—1221no—
571C42—1221no—
572C42—1221no—
573C23—22no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—611no—
578C23—611no—
579C23—1222no—
580C23—1221no—
581C23—1221no—
582C23—2441no—
583C23C22⋊C4×D6111yescharacteristic
584C23C22⋊C4×D6111yescharacteristic
585C23C22×C4×D6111yescharacteristic
586Q8—4882no—
587Q8—4882no—
588Q8—2444no—
589D4—614no—
590D4—1222no—
591D4—1222no—
592D4—1222no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—81no—
609C2×C4—81no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—612no—
613C2×C4—612no—
614C2×C4—1222no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—4881no—
626C2×C4—4881no—
627C2×C4—2442no—
628C2×C4—2442no—
629C2×C4—2442no—
630C2×C4—2442no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4C22⋊C4×D6112yes—
635C2×C4#1451978312yes—
636C2×C4C2×D4×D6112yes—
637C8—42no—
638C8—42no—
639C8—2442no—
640C8—2442no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—42no—
649C22—42no—
650C22—612no—
651C22—1221no—
652C22—1221no—
653C22—1221no—
654C22—1221no—
655C22—1221no—
656C22—2442no—
657C22—2442no—
658C22#101×D6112yes—
659C22C2×C22⋊C4×D6111yescharacteristic
660C22C2×#1451978311yescharacteristic
661C22#1684052811yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—612no—
669C4—1222no—
670C4—1222no—
671C4—1221no—
672C4—2441no—
673C4—2441no—
674C4—2441no—
675C4—2441no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—41no—
680C2—1222no—
681C2—2441no—
682C2#2145426511yescharacteristic
683C2#2145427711yescharacteristic
684C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#324D61
hypocenterC61#17426
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #21444182C2semidirect
4. #21444181C2semidirect
5. #21444173C2semidirect
6. #21444161C2semidirect
7. #21444149C2semidirect
8. #21444147C2semidirect
9. #21444141C2semidirect
10. #324×D61C2semidirect
11. C2×C61×#324C2semidirect
344. C2×#324D61semidirect
393. C61#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#168404672
#214548502
#214441822
#214441812
#214441732
#214441612
#214441492
#214441472
#214441412
#324×D612
C2×C61×#3242
#1742661