Finite Group Databasebeta

← #29601378

Subgroups — #29601378

Order 15616.

2194 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839664C211yesmaximal, characteristic
2C2×#16839640C212yesmaximal
3C2×#16839609C212yesmaximal, complemented
4#21444055C212yesmaximal, complemented
5#21444055C212yesmaximal, complemented
6#21444053C212yesmaximal, complemented
7#21444040C212yesmaximal, complemented
8C4×#14519684C211yesmaximal, characteristic, complemented
9C61×#1434C211yesmaximal, characteristic, complemented
10C23×D244C2211yescharacteristic
11C23×C4×D61C2212yes—
12C22×C4⋊Dic61C2211yescharacteristic
13C22×#11758198C2212yes—
14C22×#11758198C2212yes—
15C22×#11758198C2212yes—
16C22×#11758198C2212yes—
17C22×#11758198C2212yes—
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2212yes—
20C22×C4×Dic61C2211yescharacteristic
21#16839664C418yescomplemented
22#16839640C4116yescomplemented
23#16839609—28no—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C22×C42×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C24×D61C2312yes—
35C22×D244—41no—
36C22×D244—41no—
37C22×D244—42no—
38C22×D244C2×C418yes—
39C22×D244C2×C414yes—
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C22×C4×D61—24no—
44C22×C4×D61—24no—
45C22×C4×D61—42no—
46C22×C4×D61—42no—
47C22×C4×D61—42no—
48C22×C4×D61—42no—
49C22×C4×D61C2×C418yescomplemented
50C2×C4⋊Dic61—42no—
51C2×C4⋊Dic61C2×C414yescomplemented
52C2×#11758198—24no—
53C2×#11758198—24no—
54C2×#11758198—24no—
55C2×#11758198—24no—
56C2×#11758198—42no—
57C2×#11758198—42no—
58C2×#11758198—42no—
59C2×#11758198—42no—
60C2×#11758198—42no—
61C2×#11758198—42no—
62C2×#11758198C2×C418yes—
63C2×#11758198C2×C418yes—
64C2×#11758198C2×C418yescomplemented
65C2×#11758198C2×C418yescomplemented
66C2×#11758198C2×C418yescomplemented
67C2×C4×Dic61—22no—
68C2×C4×Dic61—24no—
69C2×C4×Dic61—41no—
70C2×C4×Dic61—41no—
71C2×C4×Dic61—42no—
72C2×C4×Dic61—42no—
73C2×C4×Dic61—41no—
74C2×C4×Dic61—41no—
75C2×C4×Dic61D414yescomplemented
76#14519684—24no—
77#14519684—24no—
78#14519684—42no—
79#14519684—42no—
80#14519684C2×C418yescomplemented
81C23×C4×C61C2312yes—
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2312yes—
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C2×C42×C61—41no—
87C2×C42×C61—41no—
88C2×C42×C61C2×C414yescomplemented
89#95×C61—24no—
90#95×C61—41no—
91#95×C61—41no—
92#95×C61C2×C418yescomplemented
93C24×C61C2411yescharacteristic
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—22no—
103C23×D61—22no—
104C23×D61—22no—
105C23×D61—22no—
106C23×D61C22×C414yes—
107C23×D61C22×C414yes—
108C23×D61C22×C414yes—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
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—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61C22×C414yes—
133C22×C4×C61C22×C414yes—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C22×C414yes—
136C22×C4×C61C22×C412yes—
137C22×C4×C61C22×C412yes—
138C22×C4×C61C2×D412yes—
139C22×C4×C61#4112yes—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61C22×C414yes—
157C22×Dic61C22×C414yes—
158C22×Dic61C22×C414yes—
159C22×Dic61C2×D414yes—
160C22×Dic61#4114yes—
161C2×D244—44no—
162C2×D244—44no—
163C2×D244—48no—
164C2×D244—48no—
165C2×D244C42116yescomplemented
166C2×C4×D61—216no—
167C2×C4×D61—48no—
168C2×C4×D61—48no—
169C2×C4×D61—48no—
170C2×C4×D61—48no—
171C2×C4×D61—48no—
172C2×C4×D61—48no—
173C42×C61—44no—
174#11758198—216no—
175#11758198—216no—
176#11758198—48no—
177#11758198—48no—
178#11758198—48no—
179C4⋊Dic61—44no—
180C4×Dic61—44no—
181C4×Dic61—48no—
182C4×Dic61—44no—
183C23×C61C23×C412yes—
184C23×C61C23×C411yescharacteristic
185C23×C61C22×D411yescharacteristic
186C23×C61C2×#4112yes—
187C23×C61C2×#4111yescharacteristic
188C23×C61H(5,𝔽2)11yescharacteristic
189C23×C61H(5,𝔽2)12yes—
190C23×C61H(5,𝔽2)11yescharacteristic
191C23×C61H(5,𝔽2)11yescharacteristic
192C23×C61H(5,𝔽2)12yes—
193C23×C612−1+411yescharacteristic
194C22×D61—24no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61—24no—
198C22×D61—24no—
199C22×D61—24no—
200C22×D61—24no—
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—24no—
207C22×D61—24no—
208C22×D61—24no—
209C22×D61—24no—
210C22×D61—24no—
211C22×D61—24no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61C2×C4218yes—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—22no—
246C2×C4×C61—24no—
247C2×C4×C61—24no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61C2×C4214yes—
259C2×C4×C61C4×D414yes—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—24no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—24no—
271C2×Dic61—24no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61C4×D418yes—
281D244—416no—
282C4×D61—432no—
283#13791—611nomaximal, Sylow
284C22×C61C22×C4211yescharacteristic
285C22×C61C2×C4×D412yes—
286C22×C61C2×C4×D411yescharacteristic
287C22×C61C4×#4111yescharacteristic
288C22×C61C4×#4112yes—
289C22×C61#51812yes—
290C22×C61#51812yes—
291C22×C61#51811yescharacteristic
292C22×C61#51812yes—
293C22×C61#51811yescharacteristic
294C22×C61#51811yescharacteristic
295C22×C61#52012yes—
296C22×C61#52011yescharacteristic
297C22×C61#53411yescharacteristic
298C22×C61#53512yes—
299C22×C61#53711yescharacteristic
300C22×C61#53812yes—
301C22×C61#53812yes—
302C22×C61#53811yescharacteristic
303C22×C61#53911yescharacteristic
304C22×C61#54012yes—
305C22×C61#54012yes—
306C22×C61#54212yes—
307C2×D61—28no—
308C2×D61—28no—
309C2×D61—28no—
310C2×D61—44no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C2×D61—44no—
315C2×D61—44no—
316C2×D61—44no—
317C2×D61—44no—
318C2×D61—44no—
319C2×D61—44no—
320C2×D61—44no—
321C2×D61—44no—
322C4×C61—24no—
323C4×C61—24no—
324C4×C61—44no—
325C4×C61—44no—
326C4×C61—42no—
327Dic61—28no—
328Dic61—44no—
329Dic61—44no—
330C2×#390—611no—
331C2×#386—612no—
332C2×C4×C22⋊C4—612no—
333#1437—612no—
334#1437—612no—
335#1436—612no—
336#1434D6111yescharacteristic, complemented
337C22⋊#95—612no—
338C4×#95—611no—
339C2×C61C42×D411yescharacteristic
340C2×C61#227311yescharacteristic
341C2×C61#227511yescharacteristic
342C2×C61#232112yes—
343C2×C61#232412yes—
344C2×C61#232511yescharacteristic
345C2×C61#232811yescharacteristic
346C2×C61#233311yescharacteristic
347C2×C61#233312yes—
348C2×C61#233512yes—
349C2×C61#233711yescharacteristic
350D61—48no—
351C23×D4—611no—
352C24×C4—612no—
353C22×C4⋊C4—611no—
354C22×C22⋊C4—612no—
355C22×C22⋊C4—612no—
356C22×C22⋊C4—612no—
357C22×C22⋊C4—612no—
358C22×C22⋊C4—612no—
359C22×C42—611no—
360C22×C42—611no—
361C22×C42—612no—
362C22×C42C2×D6111yescharacteristic
363#390—618no—
364#386—6116no—
365C4×C22⋊C4—1228no—
366C2×#95—612no—
367C2×#95—612no—
368C2×#95—612no—
369C2×#95—612no—
370C2×#95—612no—
371C2×#95C2×D6112yes—
372C2×#95C2×D6111yescharacteristic
373C2×#95C2×D6111yescharacteristic
374C2×#95C2×D6112yes—
375C61#1379111yescharacteristic, complemented, Sylow
376C25—612no—
377C22×D4—618no—
378C22×D4—614no—
379C22×D4—2441no—
380C22×D4—2441no—
381C22×D4—2442no—
382C23×C4—612no—
383C23×C4—612no—
384C23×C4—612no—
385C23×C4—618no—
386C23×C4—1224no—
387C23×C4—1224no—
388C23×C4—2442no—
389C23×C4—2442no—
390C23×C4—2442no—
391C23×C4—2442no—
392C23×C4C22×D6111yescharacteristic
393C23×C4C22×D6112yes—
394C23×C4C22×D6112yes—
395C23×C4C22×D6111yescharacteristic
396C23×C4C22×D6111yescharacteristic
397C2×C4⋊C4—614no—
398C2×C4⋊C4—2442no—
399C2×C22⋊C4—618no—
400C2×C22⋊C4—618no—
401C2×C22⋊C4—618no—
402C2×C22⋊C4—618no—
403C2×C22⋊C4—618no—
404C2×C22⋊C4—1224no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—2442no—
409C2×C22⋊C4—2442no—
410C2×C22⋊C4—2442no—
411C2×C22⋊C4—2442no—
412C2×C22⋊C4—2442no—
413C2×C22⋊C4—2442no—
414C2×C42—41no—
415C2×C42—41no—
416C2×C42—614no—
417C2×C42—1224no—
418C2×C42—1222no—
419C2×C42—2441no—
420C2×C42—2441no—
421C2×C42—2441no—
422C2×C42—2441no—
423C2×C42—2442no—
424C2×C42—2442no—
425C2×C42C4×D6114yescomplemented
426#95—24no—
427#95—41no—
428#95—41no—
429#95—618no—
430#95—1224no—
431#95—1224no—
432#95—2442no—
433#95—2442no—
434#95C4×D6118yescomplemented
435C24—614no—
436C24—614no—
437C24—614no—
438C24—1222no—
439C24—1222no—
440C24—1222no—
441C24—1222no—
442C24—1222no—
443C24—1222no—
444C24—1222no—
445C24—1222no—
446C24—1222no—
447C24—1222no—
448C24—1222no—
449C24—1222no—
450C24C23×D6111yescharacteristic
451C2×D4—6116no—
452C2×D4—2448no—
453C2×D4—2448no—
454C2×D4—2444no—
455C2×D4—2444no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—614no—
480C22×C4—614no—
481C22×C4—614no—
482C22×C4—614no—
483C22×C4—614no—
484C22×C4—12216no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—2448no—
502C22×C4—2448no—
503C22×C4—2448no—
504C22×C4—2448no—
505C22×C4—2448no—
506C22×C4—2448no—
507C22×C4C2×C4×D6114yes—
508C22×C4C2×C4×D6114yes—
509C22×C4C2×C4×D6112yes—
510C22×C4C2×C4×D6114yes—
511C22×C4C2×C4×D6112yes—
512C22×C4C2×C4×D6112yes—
513C22×C4D4×D6112yes—
514C22×C4#1175822612yes—
515C4⋊C4—2444no—
516C22⋊C4—12216no—
517C22⋊C4—12216no—
518C22⋊C4—2448no—
519C22⋊C4—2448no—
520C22⋊C4—2448no—
521C42—44no—
522C42—2444no—
523C42—2444no—
524C42—2448no—
525C23—618no—
526C23—1224no—
527C23—1224no—
528C23—1224no—
529C23—1224no—
530C23—1224no—
531C23—1224no—
532C23—1224no—
533C23—1224no—
534C23—1224no—
535C23—1224no—
536C23—1224no—
537C23—1224no—
538C23—1224no—
539C23—1224no—
540C23—1224no—
541C23—1224no—
542C23—1224no—
543C23—1224no—
544C23—2442no—
545C23—2442no—
546C23—2442no—
547C23—2442no—
548C23—2442no—
549C23—2442no—
550C23—2442no—
551C23—2442no—
552C23—2442no—
553C23—2442no—
554C23—2442no—
555C23—2442no—
556C23—2442no—
557C23—2442no—
558C23—2442no—
559C23—2442no—
560C23C22×C4×D6112yes—
561C23C22×C4×D6111yescharacteristic
562C23C2×D4×D6111yescharacteristic
563C23#41×D6112yes—
564C23C2×#1175822611yescharacteristic
565C23#1451982211yescharacteristic
566C23#1451982211yescharacteristic
567C23#1451982312yes—
568C23#1451982311yescharacteristic
569C23#1451982312yes—
570C23#1451982411yescharacteristic
571D4—24416no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—618no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—1224no—
608C2×C4—1224no—
609C2×C4—1224no—
610C2×C4—1224no—
611C2×C4—1224no—
612C2×C4—1224no—
613C2×C4—1224no—
614C2×C4—24432no—
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×C4C42×D6114yes—
624C2×C4#1451973914yes—
625C22—1228no—
626C22—1228no—
627C22—1228no—
628C22—2444no—
629C22—2444no—
630C22—2444no—
631C22—2444no—
632C22—2444no—
633C22—2444no—
634C22—2444no—
635C22—2444no—
636C22—2444no—
637C22—2444no—
638C22—2444no—
639C22—2444no—
640C22C2×C42×D6111yescharacteristic
641C22C4×D4×D6112yes—
642C22C2×#1451973911yescharacteristic
643C22#1684023011yescharacteristic
644C22C4×#1175822612yes—
645C22#1684023412yes—
646C22#1684023412yes—
647C22#1684023511yescharacteristic
648C22#1684023612yes—
649C22#1684023611yescharacteristic
650C22#1684023611yescharacteristic
651C22#1684024212yes—
652C22#1684024211yescharacteristic
653C22#1684032011yescharacteristic
654C22#1684033012yes—
655C22#1684033911yescharacteristic
656C22#1684034812yes—
657C22#1684035112yes—
658C22#1684035211yescharacteristic
659C22#1684036111yescharacteristic
660C22#1684036412yes—
661C22#1684036812yes—
662C22#1684037812yes—
663C4—24no—
664C4—24no—
665C4—44no—
666C4—44no—
667C4—42no—
668C4—1228no—
669C4—2444no—
670C4—2444no—
671C2—2448no—
672C2C4×#1451973911yescharacteristic
673C2#2144817111yescharacteristic
674C2#2144818111yescharacteristic
675C2#2144847212yes—
676C2#2144850712yes—
677C2#2144851911yescharacteristic
678C2#2144854211yescharacteristic
679C2#2144858111yescharacteristic
680C2#2144858312yes—
681C2#2144860812yes—
682C2#2144862911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#13791
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16839609C2semidirect
4. #21444055C2semidirect
5. #21444055C2semidirect
6. #21444053C2semidirect
7. #21444040C2semidirect
8. C4×#14519684C2semidirect
9. C61×#1434C2semidirect
21. #16839664C4semidirect
22. #16839640C4semidirect
49. C22×C4×D61C2×C4semidirect
51. C2×C4⋊Dic61C2×C4semidirect
64. C2×#11758198C2×C4semidirect
65. C2×#11758198C2×C4semidirect
66. C2×#11758198C2×C4semidirect
75. C2×C4×Dic61D4semidirect
80. #14519684C2×C4semidirect
88. C2×C42×C61C2×C4semidirect
92. #95×C61C2×C4semidirect
165. C2×D244C42semidirect
336. #1434D61semidirect
375. C61#13791semidirect
425. C2×C42C4×D61semidirect
434. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396642
C2×#168396402
C2×#168396092
#214440552
#214440532
#214440402
C4×#145196842
C61×#14342
#1379161