Finite Group Databasebeta

← #30610973

Subgroups — #30610973

Order 15616.

1364 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461216C212yesmaximal, complemented
4#21461215C212yesmaximal, complemented
5#21461209C214yesmaximal, complemented
6#21461198C214yesmaximal, complemented
7C2×#16840309C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840785C2212yescomplemented
10#16840782—21no—
11#16840780C2212yescomplemented
12#16840779—21no—
13#16840767—21no—
14#16840733C2212yes—
15C4×#11758213—21no—
16C4×C4⋊#6923—21no—
17C4×C4⋊#6923C2212yescomplemented
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20#16840698C2212yescomplemented
21C42×#6923—21no—
22#16840614C2218yescomplemented
23#16840613C2218yescomplemented
24C22×#11758222—21no—
25#16840309—21no—
26#16840309—21no—
27#16840309—21no—
28#16840309—21no—
29#16840309C412yescomplemented
30#16840309C412yescomplemented
31#16840309C2212yes—
32#16840309C2212yes—
33C2×#14519776C411yescharacteristic, complemented
34C2×#14519773C411yescharacteristic, complemented
35C2×#14519763—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519748C2211yescharacteristic
39C2×C4×D244C411yescharacteristic, complemented
40C2×C4×C22⋊D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×D4×C61C411yescharacteristic, complemented
43C2×#11758213—22no—
44#14519856—28no—
45C2×C4⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923—22no—
50#14519844—22no—
51#14519844—22no—
52#14519834C2314yes—
53C22⋊#92420—22no—
54#14519832—22no—
55C4×#92420—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4C2314yes—
58C2×#11758222—22no—
59C2×#11758222—22no—
60C2×#11758222—22no—
61C2×#11758222—22no—
62C2×#11758222—48no—
63C22×Dic122—21no—
64C22×D244—21no—
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73#14519776—21no—
74#14519776—21no—
75#14519776C2×C412yes—
76#14519776C2×C412yes—
77#14519773—21no—
78#14519773—21no—
79#14519773C2×C412yes—
80#14519773C2×C412yes—
81#14519763—22no—
82#14519763—22no—
83#14519763—22no—
84#14519763—22no—
85#14519752—21no—
86#14519752—21no—
87#14519752C2×C412yes—
88#14519752C2312yes—
89#14519750—22no—
90#14519750—22no—
91#14519750—22no—
92#14519750—22no—
93#14519748—21no—
94#14519748—21no—
95#14519748C2×C412yes—
96#14519748C2312yes—
97C4×D244—21no—
98C4×D244—21no—
99C4×D244C2×C412yes—
100C4×D244C2×C412yes—
101C4×C22⋊D61—22no—
102C4×C22⋊D61—22no—
103C4×C22⋊D61—22no—
104C4×C22⋊D61—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×#11758196—21no—
107C2×C22⋊Dic61—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
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—21no—
132C23×D61C2×D411yescharacteristic
133C22×#6923—24no—
134C2×D4×C61—21no—
135C2×D4×C61—42no—
136C2×D4×C61C22×C412yes—
137C22×C4×C61—21no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—44no—
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22⋊C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—44no—
151C2×C22⋊D61—44no—
152C2×C22⋊D61—44no—
153C22×Dic61—21no—
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157#11758222—48no—
158#11758222—48no—
159#11758222—48no—
160#11758222—48no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—21no—
164C2×D244—44no—
165C2×D244—42no—
166C2×D244C22×C412yes—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—42no—
172C2×C4×D61—44no—
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22⋊C411yescharacteristic
177C2×C4×D61C22×C411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2×D411yescharacteristic
184C2×C4×D61C2411yescharacteristic
185C2×Dic122—22no—
186C2×Dic122—22no—
187C2×Dic122—44no—
188C22⋊#6923—28no—
189C2×#92420—24no—
190C4⋊#6923—28no—
191C4×#6923—28no—
192C4×#6923—44no—
193C4×#6923—44no—
194#11758213—44no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61C22×C412yes—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C42×C61C22⋊C411yescharacteristic
200C42×C61C22⋊C411yescharacteristic
201C42×C61C22×C411yescharacteristic
202C42×C61C22×C411yescharacteristic
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209C4⋊Dic61—21no—
210C4⋊Dic61C22×C412yes—
211#11758196—22no—
212#11758196—22no—
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C23×C61—22no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61C2×C22⋊C411yescharacteristic
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—41no—
234C22×D61—42no—
235C22×D61—42no—
236C22×D61—42no—
237C22×D61C2×C22⋊C411yescharacteristic
238C22×D61C22×D411yescharacteristic
239C2×#6923—28no—
240C2×#6923—44no—
241C2×#6923—44no—
242D4×C61—42no—
243D4×C61—42no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—44no—
249C2×C4×C61—42no—
250C2×C4×C61—44no—
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C23×C411yescharacteristic
257C22⋊D61—44no—
258C22⋊D61—44no—
259C22⋊D61—44no—
260C22⋊D61—44no—
261C22⋊D61—44no—
262C22⋊D61—44no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—41no—
266C2×Dic61—42no—
267C2×Dic61#10414yes—
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C22×D411yescharacteristic
274D244—42no—
275D244—44no—
276D244—44no—
277D244—42no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—44no—
290C4×D61—44no—
291C4×D61AGL(1,ℤ/8)14yes—
292Dic122—44no—
293Dic122—44no—
294#92420—44no—
295#17544—611nomaximal, Sylow
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—42no—
301C22×C61—84no—
302C22×C61C2×#10412yes—
303C22×C61C22×C22⋊C411yescharacteristic
304C2×D61—21no—
305C2×D61—21no—
306C2×D61—21no—
307C2×D61—21no—
308C2×D61—21no—
309C2×D61—44no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—84no—
314C2×D61C2×AGL(1,ℤ/8)12yes—
315#6923—48no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—42no—
321C4×C61#41012yes—
322C4×C61#41812yes—
323Dic61—21no—
324Dic61—21no—
325Dic61—21no—
326Dic61—42no—
327Dic61#41812yes—
328Dic61C2×#10412yes—
329Dic61C2×#10412yes—
330C2×#532—611no—
331#2920—611no—
332C4×#117—611no—
333#1507—612no—
334#1507—612no—
335#1505—614no—
336#1502—614no—
337C2×C61—22no—
338C2×C61—82no—
339C2×C61C2×#41011yescharacteristic
340C2×C61C2×#41811yescharacteristic
341C2×C61C22×#10411yescharacteristic
342D61—22no—
343D61—41no—
344D61—82no—
345C22×#41—1221no—
346#532—612no—
347#532—612no—
348#532—612no—
349#532—612no—
350#532—1221no—
351#532—1221no—
352#532—1221no—
353#532—1221no—
354C2×C4⋊Q8—611no—
355C2×#127—611no—
356C2×#124—1221no—
357C2×#121—611no—
358C2×#121—611no—
359C2×#121—1221no—
360C2×C4×D4—611no—
361C2×C4×D4—1221no—
362C2×C4×D4#692311yescharacteristic, complemented
363C2×#117—1221no—
364C22×C42—611no—
365#432—612no—
366#432—1221no—
367#431—612no—
368#431—1221no—
369#423—1221no—
370#407—612no—
371C4×M16—1221no—
372C4×C4⋊C4—612no—
373C4×C4⋊C4—1221no—
374C4×C22⋊C4—612no—
375C4×C22⋊C4—1221no—
376#376—612no—
377C43—1221no—
378#327—618no—
379#327—618no—
380C61#1754411yescharacteristic, complemented, Sylow
381C2×#41—1222no—
382C2×#41—1222no—
383C2×#41—1222no—
384C2×#41—1222no—
385C2×#41—2448no—
386C22×Q8—1221no—
387C22×D4—611no—
388C22×D4—1221no—
389C22×D4—1221no—
390C22×D4—1221no—
391C22×D4—1221no—
392C22×D4C2×#692311yescharacteristic
393C23×C4—21no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—1221no—
398C2×M16—1222no—
399C4⋊Q8—612no—
400C4⋊Q8—612no—
401C4⋊Q8—1221no—
402C4⋊Q8—1221no—
403#127—612no—
404#127—612no—
405#127—1221no—
406#127—1221no—
407#124—1222no—
408#124—1222no—
409#124—1222no—
410#124—1222no—
411#121—612no—
412#121—612no—
413#121—612no—
414#121—612no—
415#121—1222no—
416#121—1222no—
417#121—1222no—
418#121—1222no—
419#121—1221no—
420#121—1221no—
421#121—1221no—
422#121—1221no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—612no—
426C4×D4—612no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1221no—
432C4×D4—1221no—
433C4×D4C2×#692312yes—
434C4×D4C2×#692312yes—
435#117—1228no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1222no—
439C2×C4⋊C4C2×#692311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1222no—
444C2×C22⋊C4—1221no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—1222no—
457C2×C42—1222no—
458C2×C42—1222no—
459C2×C42C2×#692311yescharacteristic
460C4⋊C8—1222no—
461C4⋊C8—1222no—
462C22⋊C8—614no—
463C22⋊C8—1222no—
464#97—1222no—
465C4×C8—1222no—
466#95—614no—
467#95—1222no—
468C24—21no—
469C24—611no—
470C24—1221no—
471#41—2448no—
472#41—2448no—
473#41—2448no—
474#41—2448no—
475C2×Q8—1222no—
476C2×Q8—1222no—
477C2×Q8—2444no—
478C2×D4—21no—
479C2×D4—42no—
480C2×D4—612no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—1222no—
484C2×D4—1222no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1222no—
488C2×D4—1222no—
489C2×D4—1221no—
490C2×D4—2442no—
491C2×D4—2444no—
492C2×D4—2444no—
493C2×D4—2444no—
494C2×D4—2444no—
495C2×D4C22×#692312yes—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—44no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
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—1224no—
516C22×C4—1224no—
517C22×C4—1224no—
518C22×C4—1221no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—2442no—
522C22×C4—2444no—
523C22×C4C22⋊#692311yescharacteristic
524C22×C4C22⋊#692311yescharacteristic
525C22×C4C22×#692311yescharacteristic
526M16—2444no—
527C2×C8—1224no—
528C4⋊C4—21no—
529C4⋊C4—612no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1228no—
533C4⋊C4—1221no—
534C4⋊C4C22×#692312yes—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1228no—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—611no—
556C42—1228no—
557C42—2444no—
558C42—2444no—
559C42C22⋊#692311yescharacteristic
560C42C22⋊#692311yescharacteristic
561C42C22×#692311yescharacteristic
562C42C22×#692311yescharacteristic
563C23—22no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—611no—
568C23—611no—
569C23—1222no—
570C23—1222no—
571C23—1222no—
572C23—2441no—
573C23—2442no—
574C23—2442no—
575C23—2442no—
576C23C2×C22⋊#692311yescharacteristic
577Q8—2444no—
578Q8—2444no—
579D4—42no—
580D4—42no—
581D4—2442no—
582D4—2444no—
583D4—2444no—
584D4—2444no—
585D4—2444no—
586D4—2444no—
587D4—2444no—
588D4—2444no—
589D4—2444no—
590D4—2442no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—614no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—614no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1228no—
617C2×C4—1222no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2444no—
621C2×C4—2441no—
622C2×C4—2442no—
623C2×C4—2444no—
624C2×C4—2444no—
625C2×C4—2444no—
626C2×C4C2×C22⋊#692311yescharacteristic
627C2×C4C2×C22⋊#692311yescharacteristic
628C2×C4C2×C22⋊#692311yescharacteristic
629C2×C4C2×C22⋊#692311yescharacteristic
630C2×C4C2×C22⋊#692311yescharacteristic
631C2×C4C23×#692311yescharacteristic
632C8—2444no—
633C22—21no—
634C22—21no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—84no—
639C22—612no—
640C22—1221no—
641C22—1221no—
642C22—1221no—
643C22—1221no—
644C22—1221no—
645C22—4884no—
646C22—2444no—
647C22—2442no—
648C22—2442no—
649C22—2442no—
650C22D61⋊#10412yes—
651C22C22×C22⋊#692311yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—612no—
658C4—612no—
659C4—612no—
660C4—1221no—
661C4—1221no—
662C4—1221no—
663C4—2448no—
664C4—2442no—
665C4#1684074112yes—
666C4#1684075412yes—
667C2—22no—
668C2—82no—
669C2—1222no—
670C2—4882no—
671C2—2441no—
672C2C2×#1684074111yescharacteristic
673C2C2×#1684075411yescharacteristic
674C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840309C2
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#17544
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462498C2semidirect
2. C4×#14519856C2semidirect
3. #21461216C2semidirect
4. #21461215C2semidirect
5. #21461209C2semidirect
6. #21461198C2semidirect
9. #16840785C22semidirect
11. #16840780C22semidirect
17. C4×C4⋊#6923C22semidirect
20. #16840698C22semidirect
22. #16840614C22semidirect
23. #16840613C22semidirect
29. #16840309C4semidirect
30. #16840309C4semidirect
33. C2×#14519776C4semidirect
34. C2×#14519773C4semidirect
39. C2×C4×D244C4semidirect
42. C2×C4×D4×C61C4semidirect
362. C2×C4×D4#6923semidirect
380. C61#17544semidirect

Maximal subgroups

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

subgroupindex
#214624982
C4×#145198562
#214612162
#214612152
#214612092
#214611982
C2×#168403092
#1754461