Finite Group Databasebeta

← #29610016

Subgroups — #29610016

Order 15616.

2074 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839665C212yesmaximal, complemented
2C2×#16839655C212yesmaximal, complemented
3#21444068C211yesmaximal, characteristic, complemented
4#21444060C212yesmaximal, complemented
5#21444060C212yesmaximal, complemented
6#21444056C211yesmaximal, characteristic, complemented
7#21444056C212yesmaximal, complemented
8#21444053C212yesmaximal, complemented
9C2×C61×#392C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×C22⋊Dic61C2212yes—
12C22×C22⋊Dic61C2211yescharacteristic
13C22×C22⋊Dic61C2212yes—
14C22×C22⋊Dic61C2212yes—
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2212yes—
20#16839665—28no—
21#16839655—28no—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C23×D4×C61C2212yes—
29C23×D4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2211yescharacteristic
32C61×#392C418yescomplemented
33C2×#95×C61C2211yescharacteristic
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C23×Dic61C2312yes—
37C23×Dic61C2312yes—
38C2×C4⋊Dic61—42no—
39C2×C4⋊Dic61—42no—
40C2×C4⋊Dic61D418yescomplemented
41C2×C22⋊Dic61—24no—
42C2×C22⋊Dic61—24no—
43C2×C22⋊Dic61—24no—
44C2×C22⋊Dic61—24no—
45C2×C22⋊Dic61—24no—
46C2×C22⋊Dic61—24no—
47C2×C22⋊Dic61—24no—
48C2×C22⋊Dic61—24no—
49C2×C22⋊Dic61—24no—
50C2×C22⋊Dic61—42no—
51C2×C22⋊Dic61—42no—
52C2×C22⋊Dic61—42no—
53C2×C22⋊Dic61—41no—
54C2×C22⋊Dic61—42no—
55C2×C22⋊Dic61—42no—
56C2×C22⋊Dic61—42no—
57C2×C22⋊Dic61—42no—
58C2×C22⋊Dic61—42no—
59C2×C22⋊Dic61—41no—
60C2×C4×Dic61—24no—
61C2×C4×Dic61—24no—
62C2×C4×Dic61—41no—
63C2×C4×Dic61—42no—
64C2×C4×Dic61—42no—
65#14519684—24no—
66#14519684—24no—
67#14519684—24no—
68#14519684—42no—
69#14519684—41no—
70#14519684—42no—
71C25×C61C2312yes—
72C25×C61C2311yescharacteristic
73C22×D4×C61—24no—
74C22×D4×C61—24no—
75C22×D4×C61—42no—
76C22×D4×C61—42no—
77C22×D4×C61—42no—
78C22×D4×C61—42no—
79C22×D4×C61—41no—
80C22×D4×C61—41no—
81C22×D4×C61—42no—
82C22×D4×C61—42no—
83C22×D4×C61C2×C418yes—
84C22×D4×C61C2×C414yes—
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2312yes—
88C2×C22⋊C4×C61—24no—
89C2×C22⋊C4×C61—24no—
90C2×C22⋊C4×C61—41no—
91C2×C22⋊C4×C61—41no—
92C2×C22⋊C4×C61C2×C418yes—
93C2×C22⋊C4×C61C2×C414yes—
94#95×C61C2×C414yes—
95C24×C61—22no—
96C24×C61—22no—
97C24×C61—22no—
98C24×C61—22no—
99C24×C61—22no—
100C24×C61—22no—
101C24×C61—22no—
102C24×C61—22no—
103C24×C61—22no—
104C24×C61—21no—
105C24×C61—21no—
106C24×C61—22no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—22no—
112C24×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61C22×C414yes—
118C24×C61C22×C412yes—
119C24×C61C2411yescharacteristic
120C2×D4×C61—216no—
121C2×D4×C61—48no—
122C2×D4×C61—48no—
123C2×D4×C61—44no—
124C2×D4×C61—48no—
125C2×D4×C61—48no—
126C2×D4×C61—48no—
127C2×D4×C61—48no—
128C2×D4×C61—48no—
129C2×D4×C61—48no—
130C2×D4×C61—44no—
131C2×D4×C61—44no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61C22×C412yes—
145C22×C4×C61C22×C412yes—
146C22×C4×C61C22×C414yes—
147C22×C4×C61C2×D414yes—
148C22×C4×C61#4114yes—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
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×Dic61C2×D414yes—
175C22×Dic61C2×D414yes—
176C22×Dic61#4114yes—
177C22⋊C4×C61—216no—
178C22⋊C4×C61—44no—
179C22⋊Dic61—48no—
180C22⋊Dic61—44no—
181C22⋊Dic61—48no—
182C22⋊Dic61—48no—
183C22⋊Dic61—48no—
184C22⋊Dic61—48no—
185C22⋊Dic61—44no—
186C4⋊Dic61—48no—
187C4×Dic61—44no—
188C4×Dic61—48no—
189C23×C61—24no—
190C23×C61—24no—
191C23×C61—24no—
192C23×C61—22no—
193C23×C61—24no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—24no—
197C23×C61—24no—
198C23×C61—24no—
199C23×C61—24no—
200C23×C61—24no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61—42no—
213C23×C61—42no—
214C23×C61—42no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—41no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—41no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—42no—
245C23×C61C23×C411yescharacteristic
246C23×C61C22×D412yes—
247C23×C61C2×#4112yes—
248C23×C61C2×#4112yes—
249C23×C61H(5,𝔽2)12yes—
250C23×C61H(5,𝔽2)12yes—
251C23×C61H(5,𝔽2)12yes—
252C23×C61H(5,𝔽2)11yescharacteristic
253C23×C61H(5,𝔽2)11yescharacteristic
254D4×C61—432no—
255D4×C61—416no—
256C2×C4×C61—24no—
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—24no—
260C2×C4×C61—24no—
261C2×C4×C61—24no—
262C2×C4×C61—24no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—24no—
266C2×C4×C61—41no—
267C2×C4×C61—42no—
268C2×C4×C61—41no—
269C2×C4×C61—42no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61C4×D418yes—
273C2×Dic61—24no—
274C2×Dic61—24no—
275C2×Dic61—24no—
276C2×Dic61—24no—
277C2×Dic61—24no—
278C2×Dic61—24no—
279C2×Dic61—24no—
280C2×Dic61—24no—
281C2×Dic61—24no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61—42no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301#14567—611nomaximal, Sylow
302C22×C61—44no—
303C22×C61—44no—
304C22×C61—44no—
305C22×C61—42no—
306C22×C61—44no—
307C22×C61—44no—
308C22×C61—44no—
309C22×C61—44no—
310C22×C61—44no—
311C22×C61—42no—
312C22×C61—44no—
313C22×C61—42no—
314C22×C61—82no—
315C22×C61—82no—
316C22×C61—82no—
317C22×C61—82no—
318C22×C61—82no—
319C22×C61—82no—
320C22×C61—82no—
321C22×C61—82no—
322C22×C61—82no—
323C22×C61—82no—
324C22×C61—82no—
325C22×C61—82no—
326C22×C61C2×C4×D412yes—
327C22×C61C4×#4111yescharacteristic
328C22×C61#51811yescharacteristic
329C22×C61#51812yes—
330C22×C61#51811yescharacteristic
331C22×C61#53412yes—
332C22×C61#53512yes—
333C22×C61#53812yes—
334C22×C61#53812yes—
335C22×C61#53812yes—
336C22×C61#54012yes—
337C22×C61D4211yescharacteristic
338C22×C61#54612yes—
339C22×C61#55012yes—
340C22×C61#55012yes—
341C22×C61#55312yes—
342C22×C61#55512yes—
343C22×C61#55911yescharacteristic
344C22×C61#56012yes—
345C22×C61#56011yescharacteristic
346C22×C61H(3,𝔽4)11yescharacteristic
347C4×C61—28no—
348C4×C61—42no—
349C4×C61—42no—
350Dic61—44no—
351Dic61—44no—
352Dic61—44no—
353Dic61—82no—
354C2×#392D6111yescharacteristic
355C2×#390—612no—
356C2×#388—612no—
357#1440—611no—
358#1438—612no—
359#1438—612no—
360#1437—611no—
361#1437—612no—
362#1436—612no—
363C2×C61—82no—
364C2×C61—84no—
365C2×C61#232112yes—
366C2×C61#233311yescharacteristic
367C2×C61#236312yes—
368C2×C61#236611yescharacteristic
369C2×C61#237511yescharacteristic
370C2×C61#267312yes—
371C2×C61#271412yes—
372C2×C61#273312yes—
373C2×C61#280312yes—
374C23×D4C2×D6112yes—
375C23×D4C2×D6111yescharacteristic
376C22×C4⋊C4—612no—
377C22×C22⋊C4—612no—
378C22×C22⋊C4—612no—
379C22×C22⋊C4—612no—
380C22×C22⋊C4—611no—
381C22×C22⋊C4—612no—
382C22×C22⋊C4—612no—
383C22×C22⋊C4—611no—
384C22×C22⋊C4C2×D6112yes—
385C22×C22⋊C4C2×D6111yescharacteristic
386C22×C42—611no—
387C22×C42—612no—
388#392Dic6118yescomplemented
389#390—1228no—
390#388—1228no—
391C2×#95—612no—
392C2×#95—612no—
393C2×#95—612no—
394C2×#95—612no—
395C2×#95—612no—
396C2×#95—611no—
397C2×#95C2×D6111yescharacteristic
398C61#1456711yescharacteristic, complemented, Sylow
399C25C22×D6112yes—
400C25C22×D6111yescharacteristic
401C22×D4—24no—
402C22×D4—24no—
403C22×D4—42no—
404C22×D4—42no—
405C22×D4—42no—
406C22×D4—42no—
407C22×D4—42no—
408C22×D4—42no—
409C22×D4—41no—
410C22×D4—41no—
411C22×D4C2×Dic6118yes—
412C22×D4C2×Dic6114yes—
413C23×C4—612no—
414C23×C4—612no—
415C23×C4—612no—
416C23×C4—612no—
417C23×C4C22×D6111yescharacteristic
418C23×C4C22×D6111yescharacteristic
419C23×C4C22×D6112yes—
420C2×C4⋊C4—618no—
421C2×C4⋊C4—2442no—
422C2×C4⋊C4—2442no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—41no—
426C2×C22⋊C4—41no—
427C2×C22⋊C4—1224no—
428C2×C22⋊C4—1224no—
429C2×C22⋊C4—1224no—
430C2×C22⋊C4—1224no—
431C2×C22⋊C4—1224no—
432C2×C22⋊C4—1224no—
433C2×C22⋊C4—1224no—
434C2×C22⋊C4—1224no—
435C2×C22⋊C4—1224no—
436C2×C22⋊C4—2442no—
437C2×C22⋊C4—2442no—
438C2×C22⋊C4—2442no—
439C2×C22⋊C4—2441no—
440C2×C22⋊C4—2442no—
441C2×C22⋊C4—2442no—
442C2×C22⋊C4—2442no—
443C2×C22⋊C4—2442no—
444C2×C22⋊C4—2442no—
445C2×C22⋊C4—2441no—
446C2×C22⋊C4C2×Dic6118yes—
447C2×C22⋊C4C2×Dic6114yes—
448C2×C42—1224no—
449C2×C42—1224no—
450C2×C42—2442no—
451C2×C42—2442no—
452C2×C42—2441no—
453#95—1224no—
454#95—1224no—
455#95—1224no—
456#95—2441no—
457#95—2442no—
458#95—2442no—
459#95C2×Dic6114yes—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24C22×Dic6114yes—
483C24C22×Dic6112yes—
484C24C23×D6111yescharacteristic
485C2×D4—216no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—44no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—44no—
496C2×D4—44no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—614no—
510C22×C4—614no—
511C22×C4—614no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—1222no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1222no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4D4×D6114yes—
538C22×C4#1175822414yes—
539C22×C4C22×Dic6112yes—
540C22×C4C22×Dic6112yes—
541C22×C4C22×Dic6114yes—
542C4⋊C4—2448no—
543C22⋊C4—216no—
544C22⋊C4—44no—
545C22⋊C4—2448no—
546C22⋊C4—2444no—
547C22⋊C4—2448no—
548C22⋊C4—2448no—
549C22⋊C4—2448no—
550C22⋊C4—2448no—
551C22⋊C4—2444no—
552C42—2448no—
553C42—2444no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—22no—
558C23—24no—
559C23—22no—
560C23—24no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—41no—
579C23—41no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—41no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23C23×Dic6111yescharacteristic
611C23C2×D4×D6112yes—
612C23#41×D6112yes—
613C23C2×#1175822412yes—
614C23#1451982212yes—
615C23#1451982212yes—
616C23#1451982211yescharacteristic
617C23#1451982211yescharacteristic
618C23#1451982212yes—
619D4—432no—
620D4—416no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—1224no—
638C2×C4—1224no—
639C2×C4—1224no—
640C2×C4—1224no—
641C2×C4—1224no—
642C2×C4—1224no—
643C2×C4—1224no—
644C2×C4—1224no—
645C2×C4—1224no—
646C2×C4—2442no—
647C2×C4—2442no—
648C2×C4—2442no—
649C2×C4—2442no—
650C2×C4—2442no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2442no—
654C2×C4—2442no—
655C2×C4—2442no—
656C2×C4—2442no—
657C2×C4—2442no—
658C2×C4—2442no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4D4×Dic6118yes—
666C22—44no—
667C22—42no—
668C22—44no—
669C22—44no—
670C22—44no—
671C22—42no—
672C22—44no—
673C22—44no—
674C22—44no—
675C22—44no—
676C22—44no—
677C22—42no—
678C22—82no—
679C22—82no—
680C22—82no—
681C22—82no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—82no—
687C22—82no—
688C22—82no—
689C22—82no—
690C22C2×D4×Dic6112yes—
691C22#41×Dic6111yescharacteristic
692C22#1684023712yes—
693C22#1684023711yescharacteristic
694C22#1684023711yescharacteristic
695C22#1684032212yes—
696C22#1684032712yes—
697C22#1684034412yes—
698C22#1684034712yes—
699C22#1684034712yes—
700C22#1684036212yes—
701C22#1684039711yescharacteristic
702C22#1684040912yes—
703C22#1684043012yes—
704C22#1684043212yes—
705C22#1684045912yes—
706C22#1684047612yes—
707C22#1684049811yescharacteristic
708C22#1684050112yes—
709C22#1684050111yescharacteristic
710C22#1684050511yescharacteristic
711C4—28no—
712C4—42no—
713C4—42no—
714C4—4882no—
715C4—2444no—
716C4—2444no—
717C4—2444no—
718C2—84no—
719C2—82no—
720C2#2144848012yes—
721C2#2144858611yescharacteristic
722C2#2144886112yes—
723C2#2144888411yescharacteristic
724C2#2144896011yescharacteristic
725C2#2145209012yes—
726C2#2145262212yes—
727C2#2145284712yes—
728C2#2145375812yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
Fitting, prime radicalC2×C61×#392C2
socle, cosocleC24×C61C24
hypercenterC2×#392D61
hypocenterC61#14567
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#16839665C2semidirect
2. C2×#16839655C2semidirect
3. #21444068C2semidirect
4. #21444060C2semidirect
5. #21444060C2semidirect
6. #21444056C2semidirect
7. #21444056C2semidirect
8. #21444053C2semidirect
32. C61×#392C4semidirect
40. C2×C4⋊Dic61D4semidirect
388. #392Dic61semidirect
398. C61#14567semidirect

Maximal subgroups

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

subgroupindex
C2×#168396652
C2×#168396552
#214440682
#214440602
#214440562
#214440532
C2×C61×#3922
#1456761