Finite Group Databasebeta

← #29679963

Subgroups — #29679963

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840241C211yesmaximal, characteristic
2#21448419C212yesmaximal, complemented
3#21445895C212yesmaximal, complemented
4#21445806C212yesmaximal, complemented
5#21445805C212yesmaximal, complemented
6#21445735C212yesmaximal
7C4×#14519691C212yesmaximal, complemented
8C4×#14519692C211yesmaximal, characteristic, complemented
9C4×#99×C61C211yesmaximal, characteristic, complemented
10C22×#11758224C2211yescharacteristic
11#16840241—24no—
12#16840241—24no—
13C2×C4×Dic122C411yescharacteristic, complemented
14C2×#14519742C411yescharacteristic, complemented
15C2×D4×Dic61C2211yescharacteristic
16C2×C4×C22⋊D61C411yescharacteristic, complemented
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519737C411yescharacteristic, complemented
19C2×#14519737C2211yescharacteristic
20C2×#14519734C411yescharacteristic, complemented
21C2×#14519733C411yescharacteristic, complemented
22C2×#14519733C2211yescharacteristic
23C22×#11758196C411yescharacteristic, complemented
24C22×#11758196C2211yescharacteristic
25C2×C4⋊C4×D61C411yescharacteristic, complemented
26C2×#14519692C2212yes—
27C2×#14519691C2214yes—
28#16839646—24no—
29#16839644—24no—
30#16839623C2214yes—
31#16839620C2214yes—
32C4×C22⋊Dic61C2212yes—
33#16839529C2212yes—
34#16839528C2214yes—
35C2×C4×D4×C61C2211yescharacteristic
36C2×#99×C61C2212yes—
37C4×C22⋊C4×C61C2212yes—
38C61×#342C2212yes—
39C2×#11758224—24no—
40C2×#11758224—24no—
41C2×#11758224—24no—
42C22×Dic122C2×C411yescharacteristic
43C22×C22⋊D61C2×C411yescharacteristic
44C22×C22⋊D61C2311yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C4×Dic122—22no—
53C4×Dic122—22no—
54#14519742—24no—
55D4×Dic61—24no—
56C4×C22⋊D61—22no—
57C4×C22⋊D61—22no—
58C4×C22⋊D61—22no—
59C4×C22⋊D61—22no—
60#14519737—24no—
61#14519737—24no—
62#14519734—22no—
63#14519734—22no—
64#14519733—24no—
65#14519733—24no—
66C2×C4⋊Dic61C2×C411yescharacteristic
67C2×#11758196—22no—
68C2×#11758196—22no—
69C2×#11758196—24no—
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2×C411yescharacteristic
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196D414yes—
79C2×#11758196D414yes—
80C4⋊C4×D61—24no—
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×C22⋊Dic61C2314yes—
83C2×C22⋊Dic61C2311yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×C4×Dic61—22no—
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92#14519692—24no—
93#14519691—28no—
94#14519684—22no—
95#14519684—24no—
96#14519684—28no—
97C22×D4×C61C2311yescharacteristic
98C23×C4×C61C2×C411yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C2×C4⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2314yes—
105C2×C22⋊C4×C61C2311yescharacteristic
106C2×C42×C61—22no—
107C2×C42×C61C2×C411yescharacteristic
108#99×C61—24no—
109#95×C61—22no—
110C24×C61C22×C411yescharacteristic
111C24×C61C2411yescharacteristic
112C23×D61C22×C411yescharacteristic
113C2×D4×C61—22no—
114C2×D4×C61—22no—
115C2×D4×C61#4114yes—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—24no—
119C22×C4×C61—81no—
120C22×C4×C61—81no—
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C2×D412yes—
127C22×C4×C61C2×D412yes—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61#4114yes—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—24no—
141C22×Dic61—81no—
142C22×Dic61—81no—
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C2×D414yes—
151C22×Dic61C2×D414yes—
152#11758224—232no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—81no—
159C2×C4×D61—81no—
160C2×Dic122—22no—
161C2×Dic122—22no—
162C2×Dic122—22no—
163C4⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—24no—
167C22⋊C4×C61—24no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—82no—
171C22⋊Dic61—22no—
172C22⋊Dic61—22no—
173C22⋊Dic61—24no—
174C22⋊Dic61—24no—
175#11758198—21no—
176#11758198—21no—
177#11758198—22no—
178C4⋊Dic61—22no—
179#11758196—21no—
180#11758196—21no—
181#11758196—22no—
182#11758196—22no—
183#11758196—22no—
184#11758196—84no—
185#11758196C22⋊C414yes—
186#11758196C22⋊C412yes—
187#11758196C22⋊C412yes—
188#11758196C22⋊C414yes—
189#11758196C22⋊C412yes—
190#11758196C22⋊C412yes—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61—22no—
195C4×Dic61—22no—
196C4×Dic61—82no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61#11712yes—
204C23×C61C23×C411yescharacteristic
205C23×C61C22×D412yes—
206C23×C61C2×#4112yes—
207C23×C61C2×#4112yes—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61#11712yes—
213D4×C61—28no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—44no—
225C2×C4×C61—44no—
226C2×C4×C61—44no—
227C2×C4×C61—81no—
228C2×C4×C61—81no—
229C2×C4×C61C2×C22⋊C412yes—
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61#11712yes—
233C22⋊D61—28no—
234C22⋊D61—28no—
235C2×Dic61—28no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—28no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—44no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—44no—
251C2×Dic61—44no—
252C2×Dic61—44no—
253C2×Dic61—82no—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61C2×C22⋊C412yes—
258C2×Dic61#11712yes—
259C4×D61—28no—
260C4×D61—82no—
261C4×D61—82no—
262Dic122—28no—
263#20725—611nomaximal, Sylow
264C22×C61—22no—
265C22×C61—21no—
266C22×C61—22no—
267C22×C61—21no—
268C22×C61—22no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61C22×C22⋊C411yescharacteristic
276C22×C61C2×#11711yescharacteristic
277C22×C61C2×#11711yescharacteristic
278C22×C61#52514yes—
279C2×D61—22no—
280C2×D61—42no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—42no—
284C4×C61—22no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—22no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—84no—
291Dic61—22no—
292Dic61—22no—
293Dic61—22no—
294Dic61—22no—
295Dic61—22no—
296Dic61—41no—
297Dic61—41no—
298Dic61—84no—
299C2×#520—611no—
300#2313—612no—
301#1820—612no—
302#1799—612no—
303#1799—612no—
304#1782—612no—
305C4×#99—612no—
306C4×#99—611no—
307C4×#99D6111yescharacteristic, complemented
308C2×C61—24no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—42no—
312C2×C61#228011yescharacteristic
313C2×C61#288311yescharacteristic
314C2×C61#288411yescharacteristic
315D61—42no—
316C22×#41—611no—
317#520—1224no—
318#520—1224no—
319C2×C4×Q8—611no—
320C2×C4×Q8—611no—
321C2×C4×D4—611no—
322C2×C4×D4—611no—
323C2×C4×D4—611no—
324C2×C4×D4—611no—
325C2×C4×D4—611no—
326C2×C4×D4C2×D6111yescharacteristic
327C2×#117—611no—
328C2×#117—611no—
329C2×#117—611no—
330C22×C4⋊C4—611no—
331C22×C4⋊C4—611no—
332C22×C4⋊C4—611no—
333C2×#99—612no—
334C2×#99—614no—
335C2×#99C2×D6112yes—
336#387—1224no—
337#387—1224no—
338#381—614no—
339#380—614no—
340C4×C22⋊C4—612no—
341C4×C22⋊C4C2×D6112yes—
342#342—614no—
343#342—612no—
344#342C2×D6112yes—
345C61#2072511yescharacteristic, complemented, Sylow
346C2×#41—1224no—
347C2×#41—1224no—
348C2×#41—1224no—
349C22×Q8—611no—
350C22×D4—611no—
351C22×D4—611no—
352C22×D4C22×D6111yescharacteristic
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—611no—
357C23×C4—611no—
358C23×C4—611no—
359C23×C4—611no—
360C23×C4C4×D6111yescharacteristic
361C23×C4C22×D6111yescharacteristic
362C4×Q8—1222no—
363C4×Q8—1222no—
364C4×Q8—1224no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—1224no—
368C4×D4—1224no—
369C4×D4—1222no—
370C4×D4—1222no—
371C4×D4—1224no—
372C4×D4—1222no—
373C4×D4—1222no—
374#117—1222no—
375#117—1222no—
376#117—1224no—
377#117—1224no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—614no—
383C2×C4⋊C4—614no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1224no—
390C2×C4⋊C4—1222no—
391C2×C4⋊C4—1222no—
392C2×C4⋊C4—1224no—
393C2×C4⋊C4C4×D6111yescharacteristic
394C2×C22⋊C4—611no—
395C2×C22⋊C4—611no—
396C2×C22⋊C4—611no—
397C2×C22⋊C4—611no—
398C2×C22⋊C4—614no—
399C2×C22⋊C4C4×D6111yescharacteristic
400C2×C22⋊C4C22×D6114yes—
401C2×C22⋊C4C22×D6111yescharacteristic
402C2×C42—22no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—1222no—
409C2×C42C4×D6111yescharacteristic
410#99—24no—
411#99—1228no—
412#99—1224no—
413#95—22no—
414#95—1224no—
415#95—1228no—
416#95—1222no—
417C24—611no—
418C24C2×C4×D6111yescharacteristic
419C24C23×D6111yescharacteristic
420#41—12232no—
421C2×Q8—1222no—
422C2×Q8—1222no—
423C2×Q8—1222no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—614no—
427C2×D4—1222no—
428C2×D4—1222no—
429C2×D4—1222no—
430C2×D4—1222no—
431C2×D4—1222no—
432C2×D4#1175822214yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—614no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—614no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1224no—
459C22×C4—4881no—
460C22×C4—4881no—
461C22×C4—4881no—
462C22×C4—4881no—
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4C2×C4×D6111yescharacteristic
467C22×C4C2×C4×D6111yescharacteristic
468C22×C4D4×D6112yes—
469C22×C4D4×D6112yes—
470C4⋊C4—22no—
471C4⋊C4—612no—
472C4⋊C4—612no—
473C4⋊C4—614no—
474C4⋊C4—612no—
475C4⋊C4—612no—
476C4⋊C4—614no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—4884no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—1222no—
489C22⋊C4—1222no—
490C22⋊C4—1222no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C22⋊C4—1224no—
494C22⋊C4—1224no—
495C42—21no—
496C42—21no—
497C42—82no—
498C42—1222no—
499C42—1222no—
500C42—1222no—
501C42—1222no—
502C42—1222no—
503C42—4882no—
504C23—21no—
505C23—21no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—612no—
511C23—1221no—
512C23—1221no—
513C23—2441no—
514C23—2441no—
515C23#1451973412yes—
516C23C22×C4×D6111yescharacteristic
517C23C2×D4×D6112yes—
518C23#41×D6112yes—
519C23C2×#1175822212yes—
520Q8—1228no—
521D4—28no—
522D4—1228no—
523D4—1228no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—1228no—
545C2×C4—1228no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1228no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—4882no—
556C2×C4—4882no—
557C2×C4—4882no—
558C2×C4—2444no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2444no—
562C2×C4—2444no—
563C2×C4—2444no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4C22⋊C4×D6111yescharacteristic
567C2×C4C22⋊C4×D6111yescharacteristic
568C2×C4C22⋊C4×D6112yes—
569C2×C4#1451973412yes—
570C22—22no—
571C22—21no—
572C22—22no—
573C22—21no—
574C22—22no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—41no—
581C22—1222no—
582C22—2442no—
583C22—2442no—
584C22—2441no—
585C22—2441no—
586C22C2×C22⋊C4×D6111yescharacteristic
587C22#117×D6111yescharacteristic
588C22C2×#1451973411yescharacteristic
589C22#1684027114yes—
590C4—22no—
591C4—21no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—84no—
597C4—1222no—
598C4—1222no—
599C4—1222no—
600C4—1222no—
601C4—1222no—
602C4—4884no—
603C4—2441no—
604C4—2441no—
605C2—24no—
606C2—21no—
607C2—21no—
608C2—42no—
609C2—2442no—
610C2#2144820011yescharacteristic
611C2#2145427711yescharacteristic
612C2#2145428111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C22
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#20725
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21448419C2semidirect
3. #21445895C2semidirect
4. #21445806C2semidirect
5. #21445805C2semidirect
7. C4×#14519691C2semidirect
8. C4×#14519692C2semidirect
9. C4×#99×C61C2semidirect
13. C2×C4×Dic122C4semidirect
14. C2×#14519742C4semidirect
16. C2×C4×C22⋊D61C4semidirect
18. C2×#14519737C4semidirect
20. C2×#14519734C4semidirect
21. C2×#14519733C4semidirect
23. C22×#11758196C4semidirect
25. C2×C4⋊C4×D61C4semidirect
307. C4×#99D61semidirect
345. C61#20725semidirect

Maximal subgroups

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

subgroupindex
C2×#168402412
#214484192
#214458952
#214458062
#214458052
#214457352
C4×#145196912
C4×#145196922
C4×#99×C612
#2072561