Finite Group Databasebeta

← #30610469

Subgroups — #30610469

Order 15616.

1292 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic, complemented
2C2×#16840765C211yesmaximal, characteristic, complemented
3#21461156C214yesmaximal, complemented
4#21461149C212yesmaximal, complemented
5#21461146C212yesmaximal, complemented
6#21461116C214yesmaximal, complemented
7C2×#16840230C211yesmaximal, characteristic
8C22×#11758217—21no—
9#16840783—21no—
10#16840782—21no—
11#16840779C2212yes—
12#16840778C2212yescomplemented
13#16840765—21no—
14#16840765—21no—
15#16840765—21no—
16#16840765C2212yes—
17#16840765C2212yescomplemented
18C2×#14519844—21no—
19C2×C4⋊#92420C2212yescomplemented
20#16840732—21no—
21C4×#11758217C2212yescomplemented
22#16840612C2218yescomplemented
23#16840610C2218yescomplemented
24C22×#11758222C411yescharacteristic
25#16840230—21no—
26#16840230—21no—
27#16840230—21no—
28#16840230—21no—
29#16840230C412yes—
30#16840230C412yes—
31#16840230C2212yes—
32#16840230C2212yes—
33C2×#14519742C411yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×#14519739C411yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519737—21no—
38C2×#14519737—21no—
39C2×#14519734—21no—
40C22×C4×Dic61C2211yescharacteristic
41C2×C42×D61—21no—
42C2×#117×C61C411yescharacteristic
43C2×#11758217—22no—
44C2×#11758217—22no—
45C2×#11758217—22no—
46C2×#11758217—44no—
47C22×#92420—22no—
48#14519844—22no—
49#14519844—22no—
50#14519844—22no—
51C4⋊#92420—22no—
52C4⋊#92420—22no—
53C4⋊#92420C2314yes—
54C22⋊#92420—22no—
55C22⋊#92420—22no—
56#14519832—22no—
57C4×#92420C2314yes—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—28no—
61C2×#11758222C2×C412yes—
62C2×#11758222C2×C412yes—
63C22×Dic122C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×C22⋊D61—21no—
66C23×Dic61D411yescharacteristic
67C23×Dic61D411yescharacteristic
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71#14519742—21no—
72#14519742—21no—
73#14519742—21no—
74#14519742—21no—
75#14519742C2×C412yes—
76#14519742C2×C412yes—
77#14519742C2×C412yes—
78#14519742C2312yes—
79#14519739—21no—
80#14519739—21no—
81#14519739—21no—
82#14519739—21no—
83#14519739C2×C412yes—
84#14519739C2×C412yes—
85#14519739C2×C412yes—
86#14519739C2312yes—
87#14519737—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91#14519737—22no—
92#14519737—22no—
93#14519737—22no—
94#14519737—22no—
95#14519734—22no—
96#14519734—22no—
97#14519734—22no—
98#14519734—22no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C42×D61—22no—
118C42×D61—22no—
119C42×D61—22no—
120C42×D61—22no—
121C23×C4×C61C2×C411yescharacteristic
122#117×C61—21no—
123#117×C61—21no—
124#117×C61C2×C412yes—
125#117×C61C2×C412yes—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C42×C61—21no—
130C24×C61C22⋊C411yescharacteristic
131C23×D61—21no—
132C22×C4×C61—24no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C2×C22⋊D61—28no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—42no—
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160#11758222—28no—
161#11758222—28no—
162#11758222—24no—
163#11758222—24no—
164#11758222—24no—
165#11758222M1618yescomplemented
166C2×D244—21no—
167C2×D244—24no—
168C2×D244C22×C412yes—
169C2×C4×D61—28no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—44no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×Dic122—21no—
180C2×Dic122—24no—
181C2×Dic122C22×C412yes—
182#11758217—44no—
183#11758217—44no—
184#11758217—44no—
185C2×#92420—24no—
186C2×#92420—24no—
187C2×#92420—44no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61C22×C412yes—
191C4⋊C4×C61C22×C412yes—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—22no—
194C42×C61—22no—
195C42×C61—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2411yescharacteristic
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—41no—
227C23×C61C2×C22⋊C411yescharacteristic
228C23×C61C2×C22⋊C411yescharacteristic
229C23×C61C2×C22⋊C411yescharacteristic
230C22×D61—24no—
231C22×D61—22no—
232C22×D61—42no—
233C22×D61—42no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×M1614yes—
247C2×C4×C61C23×C411yescharacteristic
248C22⋊D61—28no—
249C22⋊D61—28no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61AGL(1,ℤ/8)12yes—
272C2×Dic61#13712yes—
273C2×Dic61C22×D411yescharacteristic
274C2×Dic61C22×D411yescharacteristic
275D244—24no—
276D244—22no—
277D244C2×M1614yescomplemented
278C4×D61—28no—
279C4×D61—28no—
280C4×D61—44no—
281C4×D61—42no—
282C4×D61—42no—
283C4×D61—44no—
284C4×D61—44no—
285Dic122—24no—
286Dic122—22no—
287Dic122C2×M1614yescomplemented
288#92420—44no—
289#92420—44no—
290#17451—611nomaximal, Sylow
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—44no—
299C22×C61#40712yes—
300C22×C61#41712yes—
301C22×C61C22×C22⋊C411yescharacteristic
302C2×D61—24no—
303C2×D61—48no—
304C2×D61—42no—
305C2×D61—42no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—42no—
309C4×C61—42no—
310C4×C61#40712yes—
311C4×C61C22×M1612yes—
312Dic61—24no—
313Dic61—21no—
314Dic61—21no—
315Dic61—21no—
316Dic61—21no—
317Dic61—21no—
318Dic61#41712yes—
319Dic61#42112yes—
320Dic61C2×AGL(1,ℤ/8)11yescharacteristic
321Dic61C2×#13711yescharacteristic
322C2×C4×#41—611no—
323#2920—611no—
324C2×#423—611no—
325#1489—614no—
326#1487—612no—
327#1486—612no—
328#1477—614no—
329C2×C61—22no—
330C2×C61—22no—
331C2×C61—41no—
332C2×C61C2×#40711yescharacteristic
333C2×C61C2×#41711yescharacteristic
334C2×C61C2×#42111yescharacteristic
335D61—44no—
336C22×#41—611no—
337C22×M16—1221no—
338C4×#41—612no—
339C4×#41—612no—
340C4×#41—612no—
341C4×#41—612no—
342C4×#41—1221no—
343C4×#41—1221no—
344C4×#41—1221no—
345C4×#41—1221no—
346C2×C4×Q8—611no—
347C2×C4×Q8—611no—
348C2×C4×D4—611no—
349C2×C4×D4—611no—
350C2×C4×D4—1221no—
351C2×C4×D4—1221no—
352C2×#117—1221no—
353C2×#117#692311yescharacteristic
354C22×C42—611no—
355C22×C42—1221no—
356#432—1221no—
357#432—1221no—
358#431—612no—
359#431—612no—
360#423—612no—
361#423—612no—
362#423—1221no—
363#423—1221no—
364#423—1221no—
365C2×C4⋊C8—612no—
366C2×C4⋊C8—1221no—
367#407—1221no—
368C4×M16—612no—
369Q8⋊C8—618no—
370D4⋊C8—618no—
371C61#1745111yescharacteristic, complemented, Sylow
372C2×#41—612no—
373C2×#41—612no—
374C2×#41—1228no—
375C2×#41—1221no—
376C2×#41—1221no—
377C22×Q8—611no—
378C22×D4—611no—
379C22×D4—1221no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—1221no—
383C23×C4—1221no—
384C23×C4—1221no—
385C23×C4C2×#692311yescharacteristic
386C2×M16—1222no—
387C2×M16—1222no—
388C2×M16—1222no—
389C2×M16—2444no—
390C22×C8—1222no—
391C4×Q8—612no—
392C4×Q8—612no—
393C4×Q8—612no—
394C4×Q8—612no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×Q8—1221no—
398C4×Q8—1221no—
399C4×D4—612no—
400C4×D4—612no—
401C4×D4—612no—
402C4×D4—612no—
403C4×D4—1221no—
404C4×D4—1221no—
405C4×D4—1221no—
406C4×D4—1221no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410C4×D4—1222no—
411C4×D4—1222no—
412C4×D4—1222no—
413C4×D4—1222no—
414C4×D4—1222no—
415#117—21no—
416#117—21no—
417#117—1222no—
418#117—1222no—
419#117—1222no—
420#117—1222no—
421#117C2×#692312yes—
422#117C2×#692312yes—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4C2×#692311yescharacteristic
426C2×C4⋊C4C2×#692311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C42—21no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—1222no—
444C2×C42—1222no—
445C2×C42—1222no—
446C2×C42—1222no—
447C2×C42—1221no—
448C2×C42—1221no—
449C4⋊C8—614no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C4⋊C8—1222no—
455C22⋊C8—1222no—
456C22⋊C8—1222no—
457#97—1222no—
458C4×C8—614no—
459C24—1221no—
460C24C22⋊#692311yescharacteristic
461#41—618no—
462#41—1224no—
463#41—1224no—
464#41—1228no—
465#41—1228no—
466#41—1224no—
467C2×Q8—612no—
468C2×Q8—1224no—
469C2×Q8—1221no—
470C2×D4—612no—
471C2×D4—1224no—
472C2×D4—1228no—
473C2×D4—1222no—
474C2×D4—1222no—
475C2×D4—1221no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1228no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1221no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—2442no—
502C22×C4—2442no—
503C22×C4—2444no—
504C22×C4—2442no—
505C22×C4C22⋊#692311yescharacteristic
506C22×C4C22⋊#692311yescharacteristic
507C22×C4C22⋊#692311yescharacteristic
508C22×C4C22×#692311yescharacteristic
509C22×C4C22×#692311yescharacteristic
510C22×C4C22×#692311yescharacteristic
511M16—2444no—
512M16—2444no—
513M16—2444no—
514C2×C8—1224no—
515C2×C8—1224no—
516C2×C8—2444no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4C22×#692312yes—
524C4⋊C4C22×#692312yes—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C42—22no—
532C42—22no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—1222no—
550C42—1222no—
551C42—1222no—
552C42—1222no—
553C23—22no—
554C23—22no—
555C23—41no—
556C23—1224no—
557C23—1222no—
558C23—2442no—
559C23—2442no—
560C23C2×C22⋊#692311yescharacteristic
561C23C2×C22⋊#692311yescharacteristic
562C23C2×C22⋊#692311yescharacteristic
563Q8—614no—
564Q8—1224no—
565Q8—1222no—
566D4—614no—
567D4—1224no—
568D4—1228no—
569D4—1228no—
570D4—1222no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—1228no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1222no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1224no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1228no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2444no—
607C2×C4—2444no—
608C2×C4—2444no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4C2×C22⋊#692311yescharacteristic
613C2×C4C2×C22⋊#692311yescharacteristic
614C2×C4C2×C22⋊#692311yescharacteristic
615C2×C4D61⋊M1614yes—
616C2×C4C23×#692311yescharacteristic
617C8—2444no—
618C8—2444no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—44no—
627C22—1224no—
628C22—2448no—
629C22—2442no—
630C22—2442no—
631C22#1684073412yes—
632C22#1684075312yes—
633C22C22×C22⋊#692311yescharacteristic
634C4—21no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—611no—
639C4—611no—
640C4—612no—
641C4—612no—
642C4—1224no—
643C4—1221no—
644C4—1221no—
645C4—1221no—
646C4—1221no—
647C4—1221no—
648C4#1684073412yes—
649C4C2×D61⋊M1612yes—
650C2—22no—
651C2—22no—
652C2—41no—
653C2—2444no—
654C2C2×#1684073411yescharacteristic
655C2C2×#1684075311yescharacteristic
656C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758222C4
cosocleC4×Dic61C24
hypercenterC2×#117#6923
hypocenterC61#17451
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. C2×#16840765C2semidirect
3. #21461156C2semidirect
4. #21461149C2semidirect
5. #21461146C2semidirect
6. #21461116C2semidirect
12. #16840778C22semidirect
17. #16840765C22semidirect
19. C2×C4⋊#92420C22semidirect
21. C4×#11758217C22semidirect
22. #16840612C22semidirect
23. #16840610C22semidirect
165. #11758222M16semidirect
277. D244C2×M16semidirect
287. Dic122C2×M16semidirect
371. C61#17451semidirect

Maximal subgroups

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

subgroupindex
#214624952
C2×#168407652
#214611562
#214611492
#214611462
#214611162
C2×#168402302
#1745161