Finite Group Databasebeta

← #30602413

Subgroups — #30602413

Order 15616.

1550 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic
2D61⋊#407C211yesmaximal, characteristic
3C2×#16840633C214yesmaximal, complemented
4C4×C22⋊C4×D61C211yesmaximal, characteristic
5C2×D61⋊M16C2212yes—
6C2×#14519856—28no—
7C2×#14519856—21no—
8C2×#14519856—21no—
9C2×#14519856C412yescomplemented
10C2×#14519856C2212yes—
11C22×C4⋊#6923C412yescomplemented
12C22×C22⋊#6923—21no—
13C22×C4×#6923—21no—
14#16840734—21no—
15#16840733C412yescomplemented
16#16840733C412yescomplemented
17#16840732—21no—
18D61⋊(C22⋊C8)—21no—
19D61⋊(C22⋊C8)—21no—
20#16840633—28no—
21C23×C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×C42×D61C2212yes—
24C22⋊C4×Dic61—21no—
25C4×#11758198C412yescomplemented
26C4×C22⋊Dic61C411yescharacteristic, complemented
27#16839609—21no—
28#95×D61—21no—
29C4×C22⋊C4×C61C411yescharacteristic, complemented
30C23×#6923—22no—
31C2×#11758213C2×C414yescomplemented
32D61⋊M16—24no—
33D61⋊M16—24no—
34C2×#11758217—22no—
35C2×D61⋊C8—22no—
36#14519856—28no—
37#14519856—28no—
38#14519856—24no—
39#14519856—28no—
40#14519856D418yes—
41C2×C4⋊#6923—22no—
42C2×C4⋊#6923—28no—
43C2×C4⋊#6923C2×C414yes—
44C2×C22⋊#6923—28no—
45C2×C22⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—28no—
48C2×C4×#6923—22no—
49C2×C4×#6923—22no—
50#14519834—22no—
51#14519834—22no—
52C22⋊#92420—22no—
53C22⋊#92420—22no—
54C24×D61D411yescharacteristic
55C23×Dic61D411yescharacteristic
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—22no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61Q811yescharacteristic
69C22×C4×D61Q811yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×C22⋊Dic61—21no—
72C2×#11758198—22no—
73C22⋊C4×D61—28no—
74C2×C4×Dic61—22no—
75C2×C4×Dic61C2×C412yescomplemented
76C42×D61—24no—
77C42×D61—24no—
78#14519684—21no—
79#14519684—22no—
80C23×C4×C61C2×C411yescharacteristic
81C2×C22⋊C4×C61—21no—
82C2×C42×C61C2×C412yescomplemented
83#95×C61—21no—
84C24×C61C22⋊C411yescharacteristic
85C23×D61—24no—
86C23×D61—22no—
87C23×D61—22no—
88C23×D61—42no—
89C23×D61C22⋊C411yescharacteristic
90C23×D61C22⋊C411yescharacteristic
91C23×D61C22⋊C411yescharacteristic
92C23×D61C4⋊C411yescharacteristic
93C23×D61C4⋊C411yescharacteristic
94C23×D61C2×D411yescharacteristic
95C22×#6923—28no—
96C22×#6923—24no—
97C22×#6923—44no—
98C22×#6923—44no—
99C22×C4×C61—24no—
100C22×C4×C61—22no—
101C22×C4×C61C4211yescharacteristic
102C22×C4×C61C4211yescharacteristic
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C4⋊C411yescharacteristic
105C22×C4×C61C4⋊C411yescharacteristic
106C22×C4×C61C22×C411yescharacteristic
107C22×Dic61—24no—
108C22×Dic61—22no—
109C22×Dic61C22⋊C411yescharacteristic
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C4⋊C411yescharacteristic
113C22×Dic61C4⋊C411yescharacteristic
114C22×Dic61C2×D411yescharacteristic
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—24no—
118C2×C4×D61—24no—
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—24no—
124C2×C4×D61—24no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—24no—
128C2×C4×D61—24no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—28no—
132C2×C4×D61—44no—
133C2×C4×D61—42no—
134C2×C4×D61—42no—
135C2×C4×D61C4211yescharacteristic
136C2×C4×D61C4211yescharacteristic
137C2×C4×D61C22⋊C411yescharacteristic
138C2×C4×D61C22⋊C411yescharacteristic
139C2×C4×D61C22⋊C411yescharacteristic
140C2×C4×D61C22⋊C411yescharacteristic
141C2×C4×D61C4⋊C411yescharacteristic
142C2×C4×D61C4⋊C411yescharacteristic
143C2×C4×D61C4⋊C411yescharacteristic
144C2×C4×D61C4⋊C411yescharacteristic
145C2×C4×D61C4⋊C411yescharacteristic
146C2×C4×D61C4⋊C411yescharacteristic
147C2×C4×D61C22×C411yescharacteristic
148C2×C4×D61C22×C411yescharacteristic
149C2×C4×D61C2×D414yes—
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61C2×Q811yescharacteristic
152C2×C4×D61#4114yes—
153C22⋊#6923—28no—
154C22⋊#6923—28no—
155#11758217—44no—
156C2×#92420—24no—
157C4⋊#6923—28no—
158C4⋊#6923—24no—
159C4⋊#6923C22⋊C418yescomplemented
160C4×#6923—28no—
161C4×#6923—28no—
162#11758213—28no—
163D61⋊C8—42no—
164D61⋊C8—42no—
165C22⋊C4×C61—24no—
166C42×C61—24no—
167C22⋊Dic61—24no—
168#11758198—28no—
169C4×Dic61—24no—
170C4×Dic61—44no—
171C23×C61—22no—
172C23×C61—22no—
173C23×C61—41no—
174C23×C61#9511yescharacteristic
175C23×C61#9511yescharacteristic
176C23×C61C2×C22⋊C411yescharacteristic
177C22×D61—21no—
178C22×D61—21no—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—22no—
189C22×D61—22no—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—41no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—48no—
196C22×D61—48no—
197C22×D61#9511yescharacteristic
198C22×D61#9511yescharacteristic
199C22×D61#10414yes—
200C22×D61C2×C22⋊C411yescharacteristic
201C22×D61C2×C4⋊C411yescharacteristic
202C22×D61#12012yes—
203C22×D61#12312yes—
204C2×#6923—28no—
205C2×#6923—416no—
206C2×#6923—44no—
207C2×#6923—44no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—24no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61#9511yescharacteristic
217C2×C4×C61#9511yescharacteristic
218C2×C4×C61C2×C4211yescharacteristic
219C2×C4×C61C2×C4⋊C411yescharacteristic
220C2×C4×C61C4×D414yes—
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—24no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61#9511yescharacteristic
230C2×Dic61#9511yescharacteristic
231C2×Dic61C2×C22⋊C411yescharacteristic
232C2×Dic61C2×C4⋊C411yescharacteristic
233C2×Dic61#12114yes—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—22no—
239C4×D61—22no—
240C4×D61—22no—
241C4×D61—22no—
242C4×D61—22no—
243C4×D61—22no—
244C4×D61—22no—
245C4×D61—22no—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—48no—
249C4×D61—48no—
250C4×D61C2×C22⋊C412yes—
251C4×D61#11712yes—
252C4×D61C4×D414yes—
253C4×D61#12012yes—
254C4×D61C22⋊Q814yes—
255C4×D61#12312yes—
256#92420—44no—
257#10733—611nomaximal, Sylow
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—44no—
266C22×C61#33912yescomplemented
267C22×C61C2×#9511yescharacteristic
268C22×C61#38612yes—
269C2×D61—21no—
270C2×D61—21no—
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—24no—
274C2×D61—24no—
275C2×D61—24no—
276C2×D61—24no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—44no—
281C2×D61—44no—
282C2×D61—44no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61#33912yescomplemented
286C2×D61#37911yescharacteristic
287C2×D61#38111yescharacteristic
288C2×D61#38512yes—
289C2×D61C2×#10412yes—
290C2×D61#42112yes—
291#6923—48no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—44no—
295C4×C61C4×C22⋊C412yes—
296C4×C61#38512yes—
297Dic61—21no—
298Dic61—21no—
299Dic61—44no—
300Dic61#38012yes—
301Dic61#38612yes—
302C22×#117—611no—
303C2×#407—611no—
304C2×C4×C22⋊C4—611no—
305C2×#339—614no—
306C2×C61—22no—
307C2×C61—22no—
308C2×C61—41no—
309C2×C61C22⋊#9511yescharacteristic
310C2×C61C2×#33911yescharacteristic
311C2×C61#173311yescharacteristic
312D61—22no—
313D61—22no—
314D61—41no—
315D61#178912yes—
316D61#182612yes—
317C24×C4—611no—
318C22×M16—612no—
319C2×#117—612no—
320C2×#117—612no—
321C2×#117—1228no—
322C2×#117—1221no—
323C2×#117—1221no—
324C22×C4⋊C4—612no—
325C22×C22⋊C4—1221no—
326C22×C22⋊C4—1221no—
327C22×C42—612no—
328C22×C42—1221no—
329#407—612no—
330#407—612no—
331#407—1221no—
332#407—1221no—
333C2×C22⋊C8—1221no—
334C2×C22⋊C8—1221no—
335C4×C22⋊C4—611no—
336C4×C22⋊C4—612no—
337C4×C22⋊C4—1221no—
338C4×C22⋊C4—1221no—
339C4×C22⋊C4#692311yescharacteristic, complemented
340C2×#95—1221no—
341#339—1228no—
342C61#1073311yescharacteristic, complemented, Sylow
343C25—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—611no—
357C23×C4—1224no—
358C23×C4—1224no—
359C23×C4—1222no—
360C23×C4—1222no—
361C23×C4C2×#692311yescharacteristic
362C2×M16—614no—
363C2×M16—1222no—
364C2×M16—1224no—
365C2×M16—1224no—
366C22×C8—1222no—
367#117—618no—
368#117—1228no—
369#117—1224no—
370#117—1228no—
371#117—1228no—
372C2×C4⋊C4—614no—
373C2×C4⋊C4—1228no—
374C2×C4⋊C4—1222no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—1228no—
377C2×C22⋊C4—1222no—
378C2×C22⋊C4—1222no—
379C2×C22⋊C4—1222no—
380C2×C22⋊C4—1228no—
381C2×C22⋊C4—1221no—
382C2×C42—612no—
383C2×C42—1224no—
384C2×C42—1224no—
385C2×C42—1222no—
386C2×C42—1222no—
387C2×C42—1228no—
388C2×C42—1222no—
389C2×C42C2×#692312yescomplemented
390C22⋊C8—1222no—
391C22⋊C8—1222no—
392C22⋊C8—1222no—
393C22⋊C8—1222no—
394#95—21no—
395#95—1222no—
396#95—1221no—
397C24—611no—
398C24—611no—
399C24—611no—
400C24—611no—
401C24—611no—
402C24—611no—
403C24—1222no—
404C24—1224no—
405C24—1222no—
406C24—2442no—
407C24C22⋊#692311yescharacteristic
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—614no—
416C22×C4—614no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1224no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—1224no—
446C22×C4—1224no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1228no—
450C22×C4—1224no—
451C22×C4—1224no—
452C22×C4—1224no—
453C22×C4—1228no—
454C22×C4—1222no—
455C22×C4—2442no—
456C22×C4—2442no—
457C22×C4—2444no—
458C22×C4—2444no—
459C22×C4—2444no—
460C22×C4C4×#692311yescharacteristic
461C22×C4C4×#692311yescharacteristic
462C22×C4C4⋊#692311yescharacteristic
463C22×C4C4⋊#692311yescharacteristic
464C22×C4C22⋊#692311yescharacteristic
465C22×C4C22×#692311yescharacteristic
466M16—1228no—
467M16—2444no—
468C2×C8—1224no—
469C2×C8—2442no—
470C2×C8—2442no—
471C4⋊C4—618no—
472C4⋊C4—1224no—
473C4⋊C4—1228no—
474C22⋊C4—24no—
475C22⋊C4—1228no—
476C22⋊C4—1224no—
477C22⋊C4—1228no—
478C22⋊C4—1228no—
479C42—24no—
480C42—1228no—
481C42—1228no—
482C42—1224no—
483C42—2444no—
484C23—22no—
485C23—22no—
486C23—41no—
487C23—611no—
488C23—612no—
489C23—612no—
490C23—614no—
491C23—611no—
492C23—611no—
493C23—611no—
494C23—1221no—
495C23—1221no—
496C23—1222no—
497C23—1222no—
498C23—1222no—
499C23—1221no—
500C23—1222no—
501C23—1222no—
502C23—1221no—
503C23—1222no—
504C23—1222no—
505C23—1222no—
506C23—1222no—
507C23—1222no—
508C23—1222no—
509C23—2441no—
510C23—2441no—
511C23—2441no—
512C23—2448no—
513C23—2448no—
514C23(C2×#6923)⋊C411yescharacteristic
515C23(C2×#6923)⋊C411yescharacteristic
516C23C2×C22⋊#692311yescharacteristic
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—614no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—612no—
529C2×C4—614no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—614no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1224no—
556C2×C4—1228no—
557C2×C4—2448no—
558C2×C4—2448no—
559C2×C4—2442no—
560C2×C4—2444no—
561C2×C4—2444no—
562C2×C4—24416no—
563C2×C4—2442no—
564C2×C4(C2×#6923)⋊C411yescharacteristic
565C2×C4(C2×#6923)⋊C411yescharacteristic
566C2×C4C2×C4×#692311yescharacteristic
567C2×C4C2×C4⋊#692311yescharacteristic
568C2×C4D4×#692314yes—
569C8—2444no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—44no—
578C22—611no—
579C22—611no—
580C22—612no—
581C22—612no—
582C22—612no—
583C22—612no—
584C22—1224no—
585C22—1224no—
586C22—1224no—
587C22—1224no—
588C22—1221no—
589C22—1221no—
590C22—1221no—
591C22—1221no—
592C22—1221no—
593C22—1221no—
594C22—1221no—
595C22—2444no—
596C22—2444no—
597C22—2442no—
598C22—2442no—
599C22—2444no—
600C22#1684063312yescomplemented
601C22C2×(C2×#6923)⋊C411yescharacteristic
602C22#1684071012yes—
603C4—21no—
604C4—21no—
605C4—44no—
606C4—612no—
607C4—612no—
608C4—1221no—
609C4—1221no—
610C4—2444no—
611C4—2448no—
612C4C22⋊C4×#692312yes—
613C4#1684070912yes—
614C2—22no—
615C2—22no—
616C2—41no—
617C2—612no—
618C2—612no—
619C2—1222no—
620C2—1222no—
621C2—2441no—
622C2#2146099211yescharacteristic
623C2C2×#1684063311yescharacteristic
624C2#2146150011yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#10733
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16840633C2semidirect
9. C2×#14519856C4semidirect
11. C22×C4⋊#6923C4semidirect
15. #16840733C4semidirect
16. #16840733C4semidirect
25. C4×#11758198C4semidirect
26. C4×C22⋊Dic61C4semidirect
29. C4×C22⋊C4×C61C4semidirect
31. C2×#11758213C2×C4semidirect
75. C2×C4×Dic61C2×C4semidirect
82. C2×C42×C61C2×C4semidirect
159. C4⋊#6923C22⋊C4semidirect
266. C22×C61#339semidirect
285. C2×D61#339semidirect
339. C4×C22⋊C4#6923semidirect
342. C61#10733semidirect
389. C2×C42C2×#6923semidirect
600. C22#16840633semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
D61⋊#4072
C2×#168406332
C4×C22⋊C4×D612
#1073361