Finite Group Databasebeta

← #29645822

Subgroups — #29645822

Order 15616.

1314 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840230C211yesmaximal, characteristic
2#431×D61C212yesmaximal, complemented
3#21444141C212yesmaximal, complemented
4#21444138C212yesmaximal, complemented
5#21444136C212yesmaximal, complemented
6#21444134C212yesmaximal, complemented
7#21444133C211yesmaximal, characteristic, complemented
8#21444131C212yesmaximal, complemented
9C61×#1458C211yesmaximal, characteristic, complemented
10C22×#11758222C411yescharacteristic
11#16840230—22no—
12#16840230—22no—
13#16840230—22no—
14#16840230—22no—
15C2×#14519742C411yescharacteristic
16C2×#14519742C2211yescharacteristic
17C2×#14519739C411yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519737C411yescharacteristic
20C2×#14519737C411yescharacteristic
21C2×#14519737C2211yescharacteristic
22C2×#14519737C2211yescharacteristic
23C2×#14519734C411yescharacteristic
24C2×#14519734C2211yescharacteristic
25C22×C4×Dic61C411yescharacteristic
26C2×C42×D61C411yescharacteristic
27C2×C42×D61C2211yescharacteristic
28#16839815C2212yes—
29#16839814—22no—
30#16839813—22no—
31#16839812C2214yes—
32C4⋊C8×D61—22no—
33C22⋊C8×D61C2214yes—
34C4×C8×D61—22no—
35#16839488C2212yes—
36#16839487C2214yes—
37#16839486C2212yes—
38#16839485C2214yes—
39C2×#117×C61C2211yescharacteristic
40C61×#431C2212yes—
41C61×#324C2212yes—
42C61×#323C2212yes—
43C2×#11758222—22no—
44C2×#11758222—22no—
45C2×#11758222—24no—
46C2×#11758222C818yescomplemented
47C22×Dic122C2×C411yescharacteristic
48C22×D244C2×C411yescharacteristic
49C22×C22⋊D61C2×C411yescharacteristic
50C22×C22⋊D61C2×C411yescharacteristic
51C23×Dic61C2×C411yescharacteristic
52C23×Dic61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×C8×D61—24no—
60#14519742—22no—
61#14519742—22no—
62#14519742—22no—
63#14519742—22no—
64#14519739—22no—
65#14519739—22no—
66#14519739—22no—
67#14519739—22no—
68#14519737—22no—
69#14519737—22no—
70#14519737—22no—
71#14519737—22no—
72#14519737—22no—
73#14519737—22no—
74#14519737—22no—
75#14519737—22no—
76#14519734—22no—
77#14519734—22no—
78#14519734—22no—
79#14519734—22no—
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2311yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2311yescharacteristic
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C42×D61—21no—
101C42×D61—21no—
102C42×D61—21no—
103C42×D61—21no—
104C42×D61D412yes—
105C42×D61D412yes—
106C42×D61D412yes—
107C42×D61D412yes—
108C4⋊#92418—22no—
109#14519706—24no—
110C22⋊#92418C2314yes—
111#14519689—24no—
112C4×#92418—22no—
113C8×Dic61—24no—
114C23×C4×C61C2×C411yescharacteristic
115#117×C61—22no—
116#117×C61—22no—
117C2×C4⋊C4×C61C2×C411yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2311yescharacteristic
121C2×C42×C61C2×C411yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C4⋊C8×C61—22no—
124C22⋊C8×C61C2314yes—
125C4×C8×C61—22no—
126C24×C61C22×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C23×D61C22×C411yescharacteristic
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61C2×C814yescomplemented
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61C2×C814yes—
144C2×C22⋊D61C2×C814yescomplemented
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—42no—
150C22×Dic61—42no—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157#11758222—216no—
158#11758222—216no—
159C2×D244—22no—
160C2×D244—22no—
161C2×D244C2×C814yes—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—22no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×C4×D61C22⋊C412yes—
174C2×C4×D61C22⋊C412yes—
175C2×C4×D61C22⋊C412yes—
176C2×C4×D61C22⋊C412yes—
177C2×C4×D61C2×C814yes—
178C2×C4×D61C2×C814yescomplemented
179C2×C4×D61M1614yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2×D412yes—
182C2×Dic122—22no—
183C2×Dic122—22no—
184C2×Dic122C2×C814yescomplemented
185C2×C8×C61—24no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61C2×D412yes—
193C42×C61C2×D412yes—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C412yes—
217C4×Dic61C22⋊C412yes—
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C2×#92418—24no—
221C8×D61—48no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61C22×C812yes—
227C23×C61C23×C411yescharacteristic
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61C2×C22⋊C412yes—
235C22×D61C22×C812yes—
236C22×D61C22×C812yes—
237C22×D61C2×M1612yes—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C22×C812yes—
252C2×C4×C61C22×C812yes—
253C2×C4×C61C2×M1612yes—
254C2×C4×C61C22×D412yes—
255C22⋊D61—28no—
256C22⋊D61—28no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C412yes—
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C22×C812yes—
275C2×Dic61C22×C812yes—
276C2×Dic61C2×M1612yes—
277D244—28no—
278C4×D61—24no—
279C4×D61—24no—
280C4×D61—24no—
281C4×D61—24no—
282C4×D61—42no—
283C4×D61—42no—
284C4×D61—42no—
285C4×D61—42no—
286C4×D61—42no—
287C4×D61—42no—
288C4×D61C22⋊C818yes—
289C4×D61C22⋊C818yes—
290Dic122—28no—
291C8×C61—44no—
292#92418—44no—
293#17349—611nomaximal, Sylow
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—22no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61C22×C22⋊C411yescharacteristic
302C22×C61C23×C811yescharacteristic
303C22×C61C22×M1611yescharacteristic
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—42no—
313C2×D61C2×C22⋊C814yes—
314C4×C61—22no—
315C4×C61—22no—
316C4×C61—22no—
317C4×C61—41no—
318C4×C61—41no—
319C4×C61C2×C22⋊C812yes—
320C4×C61C2×C22⋊C812yes—
321Dic61—22no—
322Dic61—21no—
323Dic61—21no—
324Dic61—41no—
325Dic61—41no—
326Dic61C2×C22⋊C814yes—
327Dic61#41012yes—
328Dic61#41312yes—
329C2×C4×#41—611no—
330C2×#431—612no—
331#1461—612no—
332#1460—612no—
333#1459—612no—
334#1459—612no—
335#1458—612no—
336#1458—611no—
337#1458D6111yescharacteristic, complemented
338C2×C61—21no—
339C2×C61—21no—
340C2×C61—42no—
341C2×C61C22×C22⋊C811yescharacteristic
342C2×C61C2×#41011yescharacteristic
343C2×C61C2×#41311yescharacteristic
344D61—24no—
345D61—42no—
346C22×#41—611no—
347C4×#41—1222no—
348C4×#41—1222no—
349C4×#41—1222no—
350C4×#41—1222no—
351C2×C4×Q8—611no—
352C2×C4×Q8—611no—
353C2×C4×D4—611no—
354C2×C4×D4—611no—
355C2×C4×D4—611no—
356C2×C4×D4—611no—
357C2×C4×D4—611no—
358C2×C4×D4—611no—
359C2×#117—611no—
360C2×#117—611no—
361C2×#117C2×D6111yescharacteristic
362C22×C42—611no—
363C22×C42—611no—
364C22×C42—611no—
365#431—612no—
366#431—614no—
367#431—1222no—
368#431—1222no—
369#431C2×D6112yes—
370C2×C4⋊C8—1222no—
371C2×C22⋊C8—614no—
372C2×C4×C8—1222no—
373#324—612no—
374#324—614no—
375#324C2×D6112yes—
376#323—612no—
377#323—614no—
378#323C2×D6112yes—
379C61#1734911yescharacteristic, complemented, Sylow
380C2×#41—618no—
381C2×#41—1222no—
382C2×#41—1222no—
383C2×#41—1224no—
384C22×Q8—611no—
385C22×D4—611no—
386C22×D4—611no—
387C22×D4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4C4×D6111yescharacteristic
397C22×C8—1224no—
398C4×Q8—1222no—
399C4×Q8—1222no—
400C4×Q8—1222no—
401C4×Q8—1222no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410C4×D4—1222no—
411C4×D4—1222no—
412C4×D4—1222no—
413C4×D4—1222no—
414#117—22no—
415#117—22no—
416#117—1222no—
417#117—1222no—
418#117—1222no—
419#117—1222no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4C4×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4C4×D6111yescharacteristic
431C2×C22⋊C4C22×D6111yescharacteristic
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—612no—
436C2×C42—612no—
437C2×C42—612no—
438C2×C42—612no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—1221no—
445C2×C42—1221no—
446C2×C42—1221no—
447C2×C42—1221no—
448C2×C42—1221no—
449C2×C42—1221no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42C4×D6111yescharacteristic
453C2×C42C22×D6111yescharacteristic
454C4⋊C8—22no—
455C4⋊C8—1224no—
456C4⋊C8—1222no—
457C22⋊C8—614no—
458C22⋊C8—1224no—
459C22⋊C8C22×D6114yes—
460C4×C8—22no—
461C4×C8—1224no—
462C4×C8—1222no—
463C24—611no—
464C24—611no—
465C24C2×C4×D6111yescharacteristic
466#41—12216no—
467#41—12216no—
468C2×Q8—614no—
469C2×Q8—1222no—
470C2×Q8—1222no—
471C2×D4—614no—
472C2×D4—614no—
473C2×D4—614no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1222no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—1222no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—611no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—614no—
487C22×C4—614no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—612no—
492C22×C4—612no—
493C22×C4—614no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1222no—
509C22×C4—2442no—
510C22×C4—2442no—
511C22×C4—2442no—
512C22×C4—2442no—
513C22×C4—2442no—
514C22×C4—2442no—
515C22×C4C8×D6114yescomplemented
516C22×C4C2×C4×D6111yescharacteristic
517C22×C4C2×C4×D6111yescharacteristic
518C22×C4C2×C4×D6111yescharacteristic
519C22×C4C2×C4×D6111yescharacteristic
520C22×C4C2×C4×D6111yescharacteristic
521C22×C4C23×D6111yescharacteristic
522C2×C8—24no—
523C2×C8—1224no—
524C2×C8—2448no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C42—21no—
538C42—21no—
539C42—612no—
540C42—612no—
541C42—611no—
542C42—611no—
543C42—612no—
544C42—612no—
545C42—611no—
546C42—611no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42—1221no—
553C42—1221no—
554C42—1221no—
555C42—1221no—
556C42—1221no—
557C42D4×D6112yes—
558C42D4×D6112yes—
559C23—21no—
560C23—21no—
561C23—41no—
562C23—41no—
563C23—612no—
564C23—612no—
565C23—612no—
566C23—612no—
567C23—1221no—
568C23—1221no—
569C23—2441no—
570C23—2441no—
571C23—2441no—
572C23—2441no—
573C23C2×C8×D6112yes—
574C23C22×C4×D6111yescharacteristic
575Q8—1228no—
576D4—1228no—
577D4—1228no—
578D4—1228no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—612no—
592C2×C4—612no—
593C2×C4—612no—
594C2×C4—618no—
595C2×C4—618no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—612no—
599C2×C4—1224no—
600C2×C4—1224no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4C22⋊C4×D6112yes—
622C2×C4C22⋊C4×D6111yescharacteristic
623C2×C4C22⋊C4×D6111yescharacteristic
624C2×C4C2×C8×D6112yes—
625C2×C4C2×C8×D6112yes—
626C2×C4M16×D6112yes—
627C2×C4C2×D4×D6112yes—
628C8—44no—
629C8—2444no—
630C22—21no—
631C22—21no—
632C22—22no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—41no—
637C22—614no—
638C22—1222no—
639C22—1222no—
640C22—1222no—
641C22—2442no—
642C22—2442no—
643C22—2442no—
644C22—2442no—
645C22—2441no—
646C22—2441no—
647C22C2×C22⋊C4×D6111yescharacteristic
648C22C22×C8×D6111yescharacteristic
649C22C2×M16×D6111yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—41no—
655C4—614no—
656C4—612no—
657C4—612no—
658C4—1222no—
659C4—1221no—
660C4—1221no—
661C4—2441no—
662C4—2441no—
663C4C22⋊C8×D6112yes—
664C4C22⋊C8×D6112yes—
665C2—21no—
666C2—21no—
667C2—42no—
668C2—1224no—
669C2—2442no—
670C2C2×C22⋊C8×D6111yescharacteristic
671C2#410×D6111yescharacteristic
672C2#413×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC22×C61C23×C8
FrattiniC22×C4C23×D61
FittingC61×#1458C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758222C4
cosocleC22×C4×C61C24
hypercenter#1458D61
hypocenterC61#17349
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. #21444141C2semidirect
4. #21444138C2semidirect
5. #21444136C2semidirect
6. #21444134C2semidirect
7. #21444133C2semidirect
8. #21444131C2semidirect
9. C61×#1458C2semidirect
46. C2×#11758222C8semidirect
132. C22×C4×C61C2×C8semidirect
144. C2×C22⋊D61C2×C8semidirect
178. C2×C4×D61C2×C8semidirect
184. C2×Dic122C2×C8semidirect
337. #1458D61semidirect
379. C61#17349semidirect
515. C22×C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402302
#431×D612
#214441412
#214441382
#214441362
#214441342
#214441332
#214441312
C61×#14582
#1734961