Finite Group Databasebeta

← #29601710

Subgroups — #29601710

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758196C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic61C211yesmaximal, characteristic
3C2×C4×C22⋊Dic61C211yesmaximal, characteristic
4C2×#16839608C211yesmaximal, characteristic, complemented
5#21444080C212yesmaximal, complemented
6#21444074C212yesmaximal, complemented
7#21444066C212yesmaximal
8#21444062C212yesmaximal
9C4×#14519684C211yesmaximal, characteristic, complemented
10C4×#14519684C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
12C22×#11758196C2212yes—
13C22×C22⋊Dic61C2212yes—
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C4×Dic61C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20C4×#11758196—24no—
21C4×C22⋊Dic61—24no—
22C4×C22⋊Dic61C418yescomplemented
23#16839608—24no—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C24×C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2212yes—
36C22×C42×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C4×C22⋊C4×C61—24no—
39C2×#95×C61C2212yes—
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2311yescharacteristic
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C23×Dic61C2312yes—
45C23×Dic61C2311yescharacteristic
46C2×#11758196—24no—
47C2×#11758196—24no—
48C2×#11758196—24no—
49C2×C22⋊Dic61—24no—
50C2×C22⋊Dic61—24no—
51C2×C22⋊Dic61—24no—
52C2×C22⋊Dic61—24no—
53C2×C22⋊Dic61—24no—
54C2×C22⋊Dic61C2×C414yes—
55C2×C22⋊Dic61C2×C414yes—
56C2×C4×Dic61—22no—
57C2×C4×Dic61—22no—
58C2×C4×Dic61—22no—
59C2×C4×Dic61—22no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61—22no—
64C2×C4×Dic61—22no—
65C2×C4×Dic61C2×C414yes—
66C2×C4×Dic61C2×C414yes—
67C2×C4×Dic61D414yes—
68#14519684—24no—
69#14519684—24no—
70#14519684—24no—
71#14519684—24no—
72#14519684—24no—
73#14519684—24no—
74#14519684—24no—
75#14519684—24no—
76#14519684C2×C414yes—
77#14519684C2×C414yes—
78C25×C61C2311yescharacteristic
79C23×C4×C61—22no—
80C23×C4×C61—22no—
81C23×C4×C61—22no—
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61C2×C414yes—
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2312yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2311yescharacteristic
90C2×C22⋊C4×C61—24no—
91C2×C22⋊C4×C61—24no—
92C2×C22⋊C4×C61—24no—
93C2×C42×C61—22no—
94C2×C42×C61—22no—
95C2×C42×C61—22no—
96C2×C42×C61—22no—
97C2×C42×C61—22no—
98C2×C42×C61D414yes—
99#95×C61—24no—
100C24×C61—21no—
101C24×C61—21no—
102C24×C61—22no—
103C24×C61—21no—
104C24×C61—21no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61C22×C412yes—
110C24×C61#4114yes—
111C24×C61C2411yescharacteristic
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—28no—
131C22×C4×C61—28no—
132C22×C4×C61—28no—
133C22×C4×C61—44no—
134C22×C4×C61—44no—
135C22×C4×C61—44no—
136C22×C4×C61—44no—
137C22×C4×C61C22×C412yes—
138C22×C4×C61C22×C412yes—
139C22×C4×C61C2×D414yes—
140C22×C4×C61C2×D412yes—
141C22×C4×C61C2×D412yes—
142C22×C4×C61#4114yes—
143C22×C4×C61#4112yes—
144C22×C4×C61#4112yes—
145C22×C4×C61#4112yes—
146C22×C4×C61#4112yes—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61C22×C412yes—
175C22×Dic61C22×C412yes—
176C22×Dic61C22×C412yes—
177C22×Dic61C22×C412yes—
178C22×Dic61C2×D414yes—
179C22×Dic61#4114yes—
180C22×Dic61#4114yes—
181C22⋊C4×C61—216no—
182C42×C61—28no—
183C42×C61—44no—
184C22⋊Dic61—216no—
185C22⋊Dic61—28no—
186C22⋊Dic61—28no—
187#11758196—216no—
188C4×Dic61—28no—
189C4×Dic61—28no—
190C4×Dic61—28no—
191C4×Dic61—44no—
192C23×C61—22no—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61—22no—
198C23×C61—24no—
199C23×C61—24no—
200C23×C61—24no—
201C23×C61—24no—
202C23×C61—24no—
203C23×C61—24no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—42no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—42no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61—42no—
213C23×C61—42no—
214C23×C61#11714yes—
215C23×C61C23×C411yescharacteristic
216C23×C61C22×D411yescharacteristic
217C23×C61C22×D411yescharacteristic
218C23×C61C2×#4111yescharacteristic
219C23×C61C2×#4111yescharacteristic
220C23×C61C2×#4112yes—
221C23×C61C2×#4112yes—
222C23×C61C2×#4111yescharacteristic
223C23×C61C2×#4111yescharacteristic
224C23×C61C2×#4112yes—
225C23×C61C2×#4112yes—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—42no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—42no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—416no—
248C2×C4×C61#11714yes—
249C2×C4×C61C4×D414yes—
250C2×C4×C61C4×D414yes—
251C2×C4×C61#12114yes—
252C2×C4×C61#12314yes—
253C2×C4×C61#12414yes—
254C2×C4×C61#12614yes—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—24no—
271C2×Dic61—24no—
272C2×Dic61—24no—
273C2×Dic61—24no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—42no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288C2×Dic61#11714yes—
289#13842—611nomaximal, Sylow
290C22×C61—24no—
291C22×C61—24no—
292C22×C61—24no—
293C22×C61—44no—
294C22×C61—44no—
295C22×C61—44no—
296C22×C61—44no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—42no—
301C22×C61C2×#11711yescharacteristic
302C22×C61C2×#11711yescharacteristic
303C22×C61C2×#11711yescharacteristic
304C22×C61C2×C4×D411yescharacteristic
305C22×C61C2×C4×D411yescharacteristic
306C22×C61C4×#4111yescharacteristic
307C22×C61C4×#4111yescharacteristic
308C22×C61C2×#12111yescharacteristic
309C22×C61C2×#12311yescharacteristic
310C22×C61#52512yes—
311C22×C61#52512yes—
312C22×C61#52512yes—
313C22×C61C2×#12411yescharacteristic
314C22×C61C2×#12611yescharacteristic
315C22×C61#52912yes—
316C22×C61#52912yes—
317C22×C61#52912yes—
318C22×C61#52912yes—
319C22×C61#52912yes—
320C22×C61#52912yes—
321C22×C61#52912yes—
322C22×C61#52912yes—
323C22×C61#53212yes—
324C4×C61—44no—
325C4×C61—44no—
326C4×C61—42no—
327C4×C61#38818yes—
328Dic61—24no—
329Dic61—44no—
330Dic61—44no—
331Dic61—42no—
332Dic61—42no—
333Dic61—42no—
334C2×C4×C4⋊C4—611no—
335C2×C4×C22⋊C4—611no—
336C2×C4×C22⋊C4—611no—
337C2×C4×C22⋊C4D6111yescharacteristic
338C2×#376—611no—
339#1443—612no—
340#1442—612no—
341#1440—612no—
342#1439—612no—
343C4×#95—611no—
344C4×#95—611no—
345C2×C61—44no—
346C2×C61#228311yescharacteristic
347C2×C61C2×#38811yescharacteristic
348C2×C61#229011yescharacteristic
349C2×C61#229011yescharacteristic
350C2×C61#229011yescharacteristic
351C2×C61#229311yescharacteristic
352C2×C61#229811yescharacteristic
353C2×C61#239212yes—
354C2×C61#239512yes—
355C2×C61#239812yes—
356C2×C61#240112yes—
357C24×C4C2×D6111yescharacteristic
358C22×C4⋊C4—612no—
359C22×C22⋊C4—611no—
360C22×C22⋊C4—611no—
361C22×C22⋊C4—612no—
362C22×C22⋊C4C2×D6112yes—
363C22×C42—611no—
364C22×C42—611no—
365C22×C42—611no—
366C22×C42—611no—
367C22×C42C2×D6111yescharacteristic
368C22×C42C2×D6111yescharacteristic
369C4×C4⋊C4—1224no—
370C4×C22⋊C4—24no—
371C4×C22⋊C4—618no—
372C4×C22⋊C4—1224no—
373#376—1224no—
374C2×#95—611no—
375C2×#95—611no—
376C2×#95—612no—
377C2×#95—612no—
378C2×#95—612no—
379C2×#95—612no—
380C2×#95—612no—
381C2×#95—612no—
382C2×#95—612no—
383C2×#95—612no—
384C2×#95C2×D6112yes—
385C61#1384211yescharacteristic, complemented, Sylow
386C25C22×D6111yescharacteristic
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—611no—
394C23×C4—612no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—612no—
399C23×C4C4×D6114yes—
400C23×C4C22×D6111yescharacteristic
401C23×C4C22×D6112yes—
402C23×C4C22×D6112yes—
403C23×C4C22×D6111yescharacteristic
404C2×C4⋊C4—1224no—
405C2×C4⋊C4—1224no—
406C2×C4⋊C4—1224no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—614no—
411C2×C22⋊C4—614no—
412C2×C22⋊C4—1224no—
413C2×C22⋊C4—1224no—
414C2×C22⋊C4—1224no—
415C2×C22⋊C4—1224no—
416C2×C22⋊C4—1224no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—614no—
423C2×C42—614no—
424C2×C42—614no—
425C2×C42—1222no—
426C2×C42—1222no—
427C2×C42—1222no—
428C2×C42—1222no—
429C2×C42—1222no—
430C2×C42—1222no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42—1222no—
434C2×C42C22⋊D6114yes—
435#95—24no—
436#95—614no—
437#95—614no—
438#95—1224no—
439#95—1224no—
440#95—1224no—
441#95—1224no—
442#95—1224no—
443#95—1224no—
444#95—1224no—
445#95—1224no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—21no—
455C24C2×C4×D6112yes—
456C24#1175822214yes—
457C24C23×D6111yescharacteristic
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—612no—
484C22×C4—614no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—614no—
489C22×C4—614no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1222no—
493C22×C4—1221no—
494C22×C4—1222no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1221no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4C2×C4×D6112yes—
518C22×C4C2×C4×D6112yes—
519C22×C4#1175822214yes—
520C22×C4#1175822212yes—
521C22×C4D4×D6112yes—
522C22×C4#1175822412yes—
523C22×C4#1175822412yes—
524C22×C4#1175822412yes—
525C22×C4C2×C22⋊D6114yes—
526C22×C4C2×C22⋊D6112yes—
527C4⋊C4—12216no—
528C22⋊C4—216no—
529C22⋊C4—1228no—
530C22⋊C4—12216no—
531C22⋊C4—1228no—
532C42—28no—
533C42—44no—
534C42—1228no—
535C42—1228no—
536C42—1228no—
537C42—2444no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—41no—
551C23—41no—
552C23—42no—
553C23—41no—
554C23—41no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23#1451973414yes—
561C23C22×C4×D6111yescharacteristic
562C23C2×D4×D6111yescharacteristic
563C23C22×C22⋊D6111yescharacteristic
564C23#41×D6112yes—
565C23#41×D6112yes—
566C23C2×#1175822411yescharacteristic
567C23C2×#1175822411yescharacteristic
568C23C2×#1175822411yescharacteristic
569C23C2×#1175822212yes—
570C23C2×#1175822211yescharacteristic
571C23C2×#1175822212yes—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—416no—
594C2×C4—614no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1224no—
598C2×C4—1224no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1224no—
609C2×C4—1224no—
610C2×C4—1224no—
611C2×C4—1224no—
612C2×C4—1224no—
613C2×C4—1224no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4—2442no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2442no—
627C2×C4—2442no—
628C2×C4#1451973314yes—
629C2×C4#1451973714yes—
630C2×C4C4×C22⋊D6114yes—
631C2×C4#1451974814yes—
632C2×C4#1451975814yes—
633C2×C4#1451976314yes—
634C2×C4#1451977014yes—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—44no—
642C22—44no—
643C22—42no—
644C22—44no—
645C22—44no—
646C22#117×D6111yescharacteristic
647C22C2×#1451973311yescharacteristic
648C22C2×#1451973411yescharacteristic
649C22C2×#1451973711yescharacteristic
650C22C2×C4×C22⋊D6111yescharacteristic
651C22#1684023011yescharacteristic
652C22C4×#1175822211yescharacteristic
653C22C2×#1451974811yescharacteristic
654C22C2×#1451975811yescharacteristic
655C22#1684027112yes—
656C22#1684027112yes—
657C22#1684027312yes—
658C22C2×#1451976311yescharacteristic
659C22C2×#1451977011yescharacteristic
660C22#1684029012yes—
661C22#1684029212yes—
662C22#1684029212yes—
663C22#1684029212yes—
664C22#1684029212yes—
665C22#1684029412yes—
666C22#1684029412yes—
667C22#1684029612yes—
668C22#1684030812yes—
669C4—42no—
670C4—44no—
671C4—44no—
672C4—1224no—
673C4—2442no—
674C4—2442no—
675C4—2442no—
676C4—2444no—
677C4—2444no—
678C4#1683965018yes—
679C2—44no—
680C2#2144821311yescharacteristic
681C2C2×#1683965011yescharacteristic
682C2#2144825811yescharacteristic
683C2#2144826211yescharacteristic
684C2#2144826511yescharacteristic
685C2#2144827811yescharacteristic
686C2#2144831511yescharacteristic
687C2#2144905712yes—
688C2#2144907812yes—
689C2#2144910612yes—
690C2#2144911912yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13842
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758196C2semidirect
4. C2×#16839608C2semidirect
5. #21444080C2semidirect
6. #21444074C2semidirect
9. C4×#14519684C2semidirect
10. C4×#14519684C2semidirect
22. C4×C22⋊Dic61C4semidirect
385. C61#13842semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581962
C2×C4×C22⋊Dic612
C2×#168396082
#214440802
#214440742
#214440662
#214440622
C4×#145196842
C2×C4×C22⋊C4×C612
#1384261