Finite Group Databasebeta

← #30610452

Subgroups — #30610452

Order 15616.

1646 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic, complemented
2#21462496C211yesmaximal, characteristic, complemented
3#21461160C212yesmaximal, complemented
4#21461158C212yesmaximal, complemented
5#21461145C214yesmaximal, complemented
6#21461119C214yesmaximal, complemented
7C2×C4×D4×D61C211yesmaximal, characteristic
8#16840785—21no—
9#16840784—21no—
10#16840784—21no—
11#16840783C2212yescomplemented
12#16840781C2212yescomplemented
13#16840781C2212yescomplemented
14#16840780C2212yescomplemented
15#16840778—21no—
16#16840766C2212yescomplemented
17#16840765—21no—
18#16840734—21no—
19#16840733—21no—
20C4×#11758213—21no—
21C4×#11758217C2212yescomplemented
22#16840610C2218yescomplemented
23D4⋊#92420C2218yescomplemented
24C22×D4×D61C411yescharacteristic
25C23×C4×D61—21no—
26C2×C4×D244C411yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519739C2211yescharacteristic
29C2×C4×C22⋊D61—21no—
30C2×#14519737—21no—
31C4×D4×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34C4×D4×D61—21no—
35C4×D4×D61C412yes—
36C4×D4×D61C412yes—
37C4×D4×D61C2212yes—
38C4×D4×D61C2212yes—
39C2×C4⋊C4×D61C411yescharacteristic
40C2×C22⋊C4×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×D4×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×#11758217—22no—
45#14519844—22no—
46C4⋊#92420—22no—
47C4⋊#92420—22no—
48C4⋊#92420C2314yescomplemented
49#14519834—22no—
50#14519834—22no—
51#14519834—22no—
52C22⋊#92420—22no—
53#14519832—22no—
54#14519832—22no—
55C4×#92420—22no—
56C4×#92420C2314yescomplemented
57C24×D61—21no—
58C22×D244C2×C411yescharacteristic
59C22×C22⋊D61—21no—
60C2×D4×D61—28no—
61C2×D4×D61—21no—
62C2×D4×D61—21no—
63C2×D4×D61C2×C412yes—
64C2×D4×D61C2×C412yes—
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—48no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C4×D244—21no—
78C4×D244—21no—
79C4×D244C2×C412yes—
80C4×D244C2×C412yes—
81D4×Dic61—21no—
82D4×Dic61—21no—
83D4×Dic61C2×C412yes—
84D4×Dic61C2312yes—
85#14519739—21no—
86#14519739—21no—
87#14519739C2×C412yes—
88#14519739C2312yes—
89C4×C22⋊D61—22no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96#14519737—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758196—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61C2×C412yes—
102C4⋊C4×D61C2×C412yes—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C22⋊C4×D61—22no—
107C22⋊C4×D61—22no—
108C22⋊C4×D61—22no—
109C22⋊C4×D61—22no—
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C22×D4×C61C2×C411yescharacteristic
122C23×C4×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61—21no—
125C4×D4×C61C2×C412yes—
126C4×D4×C61C2×C412yes—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C24×C61—21no—
131C23×D61—28no—
132C23×D61—21no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—44no—
136C23×D61—44no—
137C23×D61C22⋊C411yescharacteristic
138C2×D4×C61—24no—
139C2×D4×C61—21no—
140C2×D4×C61C22×C412yes—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—44no—
145C22×C4×C61C22⋊C411yescharacteristic
146C22×C4×C61C22⋊C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—28no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—44no—
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158D4×D61—28no—
159D4×D61—28no—
160D4×D61—24no—
161D4×D61—24no—
162D4×D61—24no—
163D4×D61M1618yescomplemented
164C2×D244—21no—
165C2×D244—24no—
166C2×D244C22×C412yes—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—48no—
176C2×C4×D61—48no—
177C2×C4×D61—48no—
178C2×C4×D61—42no—
179C2×C4×D61—44no—
180C2×C4×D61—44no—
181C2×C4×D61—44no—
182C2×C4×D61—48no—
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22×C411yescharacteristic
190C2×C4×D61C22×C411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195#11758217—44no—
196C2×#92420—24no—
197C2×#92420—24no—
198#11758213—44no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61C22×C412yes—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C42×C61C22⋊C411yescharacteristic
204C42×C61C22⋊C411yescharacteristic
205C42×C61C22×C411yescharacteristic
206C42×C61C22×C411yescharacteristic
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213C4⋊Dic61—21no—
214C4⋊Dic61C22×C412yes—
215#11758196—22no—
216#11758196—22no—
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22×C411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2411yescharacteristic
229C23×C61—24no—
230C23×C61—22no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61C2×C22⋊C411yescharacteristic
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—24no—
238C22×D61—28no—
239C22×D61—22no—
240C22×D61—28no—
241C22×D61—44no—
242C22×D61—432no—
243C22×D61—44no—
244C22×D61—44no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—44no—
248C22×D61C2×C22⋊C411yescharacteristic
249C22×D61C2×C22⋊C411yescharacteristic
250D4×C61—24no—
251D4×C61—22no—
252D4×C61C2×M1614yes—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—44no—
258C2×C4×C61—42no—
259C2×C4×C61—44no—
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C23×C411yescharacteristic
266C22⋊D61—28no—
267C22⋊D61—28no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—44no—
273C2×Dic61—42no—
274C2×Dic61—44no—
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C411yescharacteristic
277C2×Dic61C2×C22⋊C411yescharacteristic
278C2×Dic61C2×C22⋊C411yescharacteristic
279C2×Dic61C22×D411yescharacteristic
280C2×Dic61C22×D411yescharacteristic
281D244—24no—
282D244—22no—
283D244C2×M1614yes—
284C4×D61—22no—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—41no—
291C4×D61—41no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—44no—
295C4×D61—44no—
296C4×D61—44no—
297C4×D61—44no—
298C4×D61—44no—
299C4×D61—44no—
300C4×D61C2×M1614yes—
301C4×D61AGL(1,ℤ/8)14yes—
302#92420—44no—
303#92420—44no—
304#17448—611nomaximal, Sylow
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—24no—
308C22×C61—48no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61#42112yes—
312C22×C61C22×C22⋊C411yescharacteristic
313C2×D61—28no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—24no—
319C2×D61—416no—
320C2×D61—416no—
321C2×D61—48no—
322C2×D61—42no—
323C2×D61—42no—
324C2×D61#40712yes—
325C2×D61#41812yes—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—21no—
330C4×C61—42no—
331C4×C61#41812yes—
332C4×C61C22×M1612yes—
333Dic61—21no—
334Dic61—21no—
335Dic61—21no—
336Dic61—21no—
337Dic61—42no—
338Dic61#40712yes—
339Dic61C2×AGL(1,ℤ/8)12yes—
340C22×C4×D4—611no—
341#2920—611no—
342#2920—611no—
343#1490—612no—
344#1490—612no—
345#1486—614no—
346#1478—614no—
347C2×C61—22no—
348C2×C61—44no—
349C2×C61C2×#40711yescharacteristic
350C2×C61C2×#41811yescharacteristic
351C2×C61C2×#42111yescharacteristic
352D61—22no—
353D61—22no—
354D61—44no—
355C23×D4—611no—
356C24×C4—1221no—
357C2×C4×D4—611no—
358C2×C4×D4—612no—
359C2×C4×D4—612no—
360C2×C4×D4—612no—
361C2×C4×D4—612no—
362C2×C4×D4—611no—
363C2×C4×D4—611no—
364C2×C4×D4—1221no—
365C2×C4×D4—1221no—
366C2×C4×D4—1221no—
367C2×C4×D4—1221no—
368C2×C4×D4—1221no—
369C2×C4×D4—1221no—
370C2×C4×D4#692311yescharacteristic
371C22×C4⋊C4—611no—
372C22×C22⋊C4—1221no—
373C22×C42—611no—
374#432—612no—
375#432—1221no—
376#432—1221no—
377#432—1221no—
378#431—612no—
379#431—612no—
380#431—612no—
381#431—1221no—
382#423—612no—
383#423—1221no—
384#407—1221no—
385#407—1221no—
386C4×M16—612no—
387C4×M16—1221no—
388D4⋊C8—618no—
389D4⋊C8—618no—
390C61#1744811yescharacteristic, complemented, Sylow
391C25—1221no—
392C22×D4—612no—
393C22×D4—612no—
394C22×D4—611no—
395C22×D4—1221no—
396C22×D4—1221no—
397C22×D4—1221no—
398C22×D4—1228no—
399C22×D4C2×#692311yescharacteristic
400C23×C4—21no—
401C23×C4—611no—
402C23×C4—611no—
403C23×C4—611no—
404C23×C4—1221no—
405C23×C4—1222no—
406C23×C4—1222no—
407C23×C4—1222no—
408C23×C4—1222no—
409C23×C4—1221no—
410C23×C4—1221no—
411C23×C4—1221no—
412C23×C4—2448no—
413C2×M16—1222no—
414C2×M16—1222no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—612no—
418C4×D4—612no—
419C4×D4—612no—
420C4×D4—612no—
421C4×D4—612no—
422C4×D4—612no—
423C4×D4—1222no—
424C4×D4—1222no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1221no—
428C4×D4—1221no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1221no—
437C4×D4C2×#692312yes—
438C4×D4C2×#692312yes—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—612no—
441C2×C4⋊C4—612no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4C2×#692311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—1222no—
448C2×C22⋊C4—1222no—
449C2×C22⋊C4—1222no—
450C2×C22⋊C4—1222no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42C2×#692311yescharacteristic
466C4⋊C8—614no—
467C4⋊C8—1222no—
468C4⋊C8—1222no—
469C4⋊C8—1222no—
470C22⋊C8—1222no—
471C22⋊C8—1222no—
472C22⋊C8—1222no—
473C22⋊C8—1222no—
474#97—1222no—
475#97—1222no—
476C4×C8—614no—
477C4×C8—1222no—
478C24—21no—
479C24—611no—
480C24—1222no—
481C24—1222no—
482C24—1228no—
483C24—1221no—
484C24—2444no—
485C24—2444no—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—618no—
489C2×D4—612no—
490C2×D4—1224no—
491C2×D4—1224no—
492C2×D4—1222no—
493C2×D4—1222no—
494C2×D4—1224no—
495C2×D4—1228no—
496C2×D4—1228no—
497C2×D4—1228no—
498C2×D4—1224no—
499C2×D4—1221no—
500C2×D4C22×#692312yes—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—44no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—1224no—
521C22×C4—1224no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1222no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1221no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—2442no—
532C22×C4—2444no—
533C22×C4—2448no—
534C22×C4—2448no—
535C22×C4—2448no—
536C22×C4—2444no—
537C22×C4—2448no—
538C22×C4—2444no—
539C22×C4—2444no—
540C22×C4C22⋊#692311yescharacteristic
541C22×C4C22⋊#692311yescharacteristic
542C22×C4C22×#692311yescharacteristic
543M16—2444no—
544M16—2444no—
545C2×C8—1224no—
546C2×C8—1224no—
547C4⋊C4—21no—
548C4⋊C4—612no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C4⋊C4—1221no—
552C4⋊C4C22×#692312yes—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—1222no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C42—611no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42C22⋊#692311yescharacteristic
574C42C22⋊#692311yescharacteristic
575C42C22×#692311yescharacteristic
576C42C22×#692311yescharacteristic
577C23—24no—
578C23—22no—
579C23—42no—
580C23—42no—
581C23—611no—
582C23—611no—
583C23—1222no—
584C23—1222no—
585C23—1228no—
586C23—1224no—
587C23—1228no—
588C23—1222no—
589C23—1222no—
590C23—2442no—
591C23—2444no—
592C23—2444no—
593C23—24432no—
594C23—2444no—
595C23—2444no—
596C23—2442no—
597C23C2×C22⋊#692311yescharacteristic
598D4—24no—
599D4—22no—
600D4—614no—
601D4—1224no—
602D4—1228no—
603D4—1228no—
604D4—1222no—
605D4D61⋊M1614yes—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—44no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—614no—
616C2×C4—614no—
617C2×C4—611no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2444no—
636C2×C4—2444no—
637C2×C4—2444no—
638C2×C4—2444no—
639C2×C4—2444no—
640C2×C4—2444no—
641C2×C4—2444no—
642C2×C4—2442no—
643C2×C4—2444no—
644C2×C4C2×C22⋊#692311yescharacteristic
645C2×C4C2×C22⋊#692311yescharacteristic
646C2×C4C2×C22⋊#692311yescharacteristic
647C2×C4C2×C22⋊#692311yescharacteristic
648C2×C4C2×C22⋊#692311yescharacteristic
649C2×C4C23×#692311yescharacteristic
650C8—2444no—
651C8—2444no—
652C22—21no—
653C22—21no—
654C22—24no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22—612no—
659C22—612no—
660C22—1228no—
661C22—1221no—
662C22—1221no—
663C22—1221no—
664C22—1221no—
665C22—1224no—
666C22—2448no—
667C22—24416no—
668C22—24416no—
669C22—2442no—
670C22—2442no—
671C22#1684075912yes—
672C22C22×C22⋊#692311yescharacteristic
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—42no—
678C4—612no—
679C4—612no—
680C4—1221no—
681C4—1221no—
682C4—1221no—
683C4—1221no—
684C4—2442no—
685C4#1684075412yes—
686C4C2×D61⋊M1612yes—
687C2—22no—
688C2—44no—
689C2—1222no—
690C2—1222no—
691C2—2444no—
692C2D61⋊#40711yescharacteristic
693C2C2×#1684075411yescharacteristic
694C2C2×#1684075911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC4×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#17448
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462497C2semidirect
2. #21462496C2semidirect
3. #21461160C2semidirect
4. #21461158C2semidirect
5. #21461145C2semidirect
6. #21461119C2semidirect
11. #16840783C22semidirect
12. #16840781C22semidirect
13. #16840781C22semidirect
14. #16840780C22semidirect
16. #16840766C22semidirect
21. C4×#11758217C22semidirect
22. #16840610C22semidirect
23. D4⋊#92420C22semidirect
48. C4⋊#92420C23semidirect
56. C4×#92420C23semidirect
163. D4×D61M16semidirect
390. C61#17448semidirect

Maximal subgroups

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

subgroupindex
#214624972
#214624962
#214611602
#214611582
#214611452
#214611192
C2×C4×D4×D612
#1744861