Finite Group Databasebeta

← #29610747

Subgroups — #29610747

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839688C211yesmaximal, characteristic
2C2×#16839653C211yesmaximal, characteristic
3#21444087C211yesmaximal, characteristic, complemented
4#21444082C212yesmaximal, complemented
5#21444082C211yesmaximal, characteristic, complemented
6#21444079C212yesmaximal, complemented
7#21444063C212yesmaximal
8#21444061C211yesmaximal, characteristic
9#21444061C212yesmaximal
10#21444046C211yesmaximal, characteristic, complemented
11C2×C61×#389C211yesmaximal, characteristic, complemented
12C22×#11758196C2211yescharacteristic
13C22×#11758196C2212yes—
14C22×#11758198C2211yescharacteristic
15C22×#11758198C2211yescharacteristic
16C22×#11758198C2211yescharacteristic
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19#16839688C418yescomplemented
20#16839653—24no—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2212yes—
35C22×C42×C61C2211yescharacteristic
36C61×#389—24no—
37C2×#95×C61C2212yes—
38C24×D61C2311yescharacteristic
39C23×Dic61C2311yescharacteristic
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C2×#11758196—22no—
45C2×#11758196—42no—
46C2×#11758196—42no—
47C2×#11758196—42no—
48C2×#11758196—42no—
49C2×#11758198—22no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×#11758198—22no—
53C2×#11758198—42no—
54C2×#11758198—42no—
55C2×#11758198—42no—
56C2×#11758198—42no—
57C2×#11758198—42no—
58C2×#11758198—42no—
59C2×#11758198—42no—
60C2×#11758198C2×C414yes—
61C2×#11758198C2×C418yes—
62#14519684—22no—
63#14519684—22no—
64#14519684—22no—
65#14519684—42no—
66#14519684—42no—
67#14519684—42no—
68#14519684—42no—
69#14519684—42no—
70#14519684—42no—
71#14519684C2×C418yes—
72#14519684C2×C414yes—
73C23×C4×C61C2312yes—
74C23×C4×C61C2312yes—
75C23×C4×C61C2311yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C2×C4⋊C4×C61—22no—
79C2×C4⋊C4×C61—22no—
80C2×C4⋊C4×C61—24no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—42no—
83C2×C4⋊C4×C61—42no—
84C2×C4⋊C4×C61—42no—
85C2×C4⋊C4×C61C2×C414yes—
86C2×C42×C61—42no—
87C2×C42×C61D414yes—
88#95×C61—24no—
89C24×C61C2411yescharacteristic
90C23×D61—21no—
91C23×D61—21no—
92C23×D61—21no—
93C23×D61—21no—
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—21no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—21no—
100C23×D61C22×C412yes—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—21no—
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×C61C22×C414yes—
125C22×C4×C61C22×C412yes—
126C22×C4×C61C2×D412yes—
127C22×C4×C61C2×D412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61#4112yes—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—22no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—21no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61C22×C412yes—
158C22×Dic61C22×C414yes—
159C4⋊C4×C61—28no—
160C4⋊C4×C61—44no—
161C4⋊C4×C61—48no—
162C42×C61—44no—
163#11758198—28no—
164#11758198—48no—
165#11758198—44no—
166#11758198—44no—
167#11758198—48no—
168#11758196—44no—
169#11758196—48no—
170C23×C61C23×C411yescharacteristic
171C23×C61C22×D411yescharacteristic
172C23×C61C2×#4111yescharacteristic
173C23×C61H(5,𝔽2)11yescharacteristic
174C23×C61H(5,𝔽2)11yescharacteristic
175C23×C61H(5,𝔽2)12yes—
176C23×C61H(5,𝔽2)11yescharacteristic
177C23×C61H(5,𝔽2)12yes—
178C23×C612−1+412yes—
179C23×C612−1+412yes—
180C23×C612−1+411yescharacteristic
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—24no—
184C22×D61—22no—
185C22×D61—24no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—41no—
189C22×D61—41no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—42no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C2×C4×C61—24no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—24no—
208C2×C4×C61—24no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61C4×D414yes—
233C2×Dic61—22no—
234C2×Dic61—24no—
235C2×Dic61—24no—
236C2×Dic61—24no—
237C2×Dic61—24no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262#14630—611nomaximal, Sylow
263C22×C61C2×C4×D411yescharacteristic
264C22×C61#51811yescharacteristic
265C22×C61#52011yescharacteristic
266C22×C61#52012yes—
267C22×C61#52012yes—
268C22×C61#53411yescharacteristic
269C22×C61#53511yescharacteristic
270C22×C61#53511yescharacteristic
271C22×C61#53611yescharacteristic
272C22×C61#53611yescharacteristic
273C22×C61#53711yescharacteristic
274C22×C61#53912yes—
275C22×C61#54011yescharacteristic
276C22×C61#54211yescharacteristic
277C22×C61#54212yes—
278C22×C61#56012yes—
279C22×C61#56012yes—
280C22×C61#56212yes—
281C22×C61#56212yes—
282C22×C61#56312yes—
283C22×C61#56312yes—
284C22×C61#56312yes—
285C22×C61#56312yes—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—44no—
290C2×D61—44no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—82no—
294C2×D61—82no—
295C2×D61—81no—
296C2×D61—81no—
297C4×C61—24no—
298C4×C61—44no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61—82no—
302Dic61—42no—
303Dic61—44no—
304Dic61—81no—
305Dic61—82no—
306Dic61—81no—
307C2×#397—611no—
308C2×#389D6111yescharacteristic, complemented
309C2×#388—611no—
310#1445—611no—
311#1444—612no—
312#1444—611no—
313#1443—612no—
314#1439—612no—
315#1439—611no—
316#1439—612no—
317#1434—611no—
318C2×C61#232211yescharacteristic
319C2×C61#232411yescharacteristic
320C2×C61#232611yescharacteristic
321C2×C61#237612yes—
322C2×C61#238312yes—
323C2×C61#281411yescharacteristic
324C2×C61#281511yescharacteristic
325C2×C61#282011yescharacteristic
326C2×C61#282111yescharacteristic
327C2×C61#283712yes—
328C2×C61#283812yes—
329D61—82no—
330C22×C4⋊C4—611no—
331C22×C4⋊C4—612no—
332C22×C4⋊C4C2×D6111yescharacteristic
333C22×C4⋊C4C2×D6111yescharacteristic
334C22×C4⋊C4C2×D6112yes—
335C22×C22⋊C4—611no—
336C22×C22⋊C4—612no—
337C22×C22⋊C4—611no—
338C22×C22⋊C4—611no—
339C22×C22⋊C4—612no—
340C22×C42C2×D6111yescharacteristic
341#397—618no—
342#389—24no—
343#388—1224no—
344C2×#95—611no—
345C2×#95—612no—
346C2×#95—611no—
347C2×#95—611no—
348C2×#95—611no—
349C2×#95—612no—
350C2×#95—612no—
351C2×#95—612no—
352C2×#95—612no—
353C2×#95—612no—
354C2×#95—612no—
355C2×#95C2×D6112yes—
356C61#1463011yescharacteristic, complemented, Sylow
357C25—611no—
358C23×C4—611no—
359C23×C4—612no—
360C23×C4—611no—
361C23×C4—611no—
362C23×C4—612no—
363C23×C4C22×D6112yes—
364C23×C4C22×D6112yes—
365C23×C4C22×D6111yescharacteristic
366C23×C4C22×D6111yescharacteristic
367C23×C4C22×D6111yescharacteristic
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—1222no—
376C2×C4⋊C4—2442no—
377C2×C4⋊C4—2442no—
378C2×C4⋊C4—2442no—
379C2×C4⋊C4—2442no—
380C2×C4⋊C4C4×D6114yes—
381C2×C22⋊C4—614no—
382C2×C22⋊C4—618no—
383C2×C22⋊C4—1222no—
384C2×C22⋊C4—1222no—
385C2×C22⋊C4—1222no—
386C2×C22⋊C4—1222no—
387C2×C22⋊C4—2442no—
388C2×C22⋊C4—2442no—
389C2×C22⋊C4—2442no—
390C2×C22⋊C4—2442no—
391C2×C22⋊C4—2442no—
392C2×C22⋊C4—2442no—
393C2×C22⋊C4—2442no—
394C2×C42—42no—
395C2×C42C22⋊D6114yes—
396#95—24no—
397#95—618no—
398#95—614no—
399#95—1222no—
400#95—1222no—
401#95—1222no—
402#95—2442no—
403#95—2442no—
404#95—2442no—
405#95—2442no—
406#95—2442no—
407#95—2442no—
408C24—612no—
409C24—1221no—
410C24—1221no—
411C24—1221no—
412C24—1221no—
413C24—1222no—
414C24—1221no—
415C24—1222no—
416C24—1221no—
417C24—1222no—
418C24—1222no—
419C24C23×D6111yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—612no—
444C22×C4—614no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1222no—
458C22×C4—1221no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—1221no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1221no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4C2×C4×D6114yes—
473C22×C4C2×C4×D6112yes—
474C22×C4#1175822212yes—
475C22×C4C2×C22⋊D6112yes—
476C22×C4C2×C22⋊D6112yes—
477C22×C4C2×C22⋊D6112yes—
478C4⋊C4—28no—
479C4⋊C4—44no—
480C4⋊C4—48no—
481C4⋊C4—2444no—
482C4⋊C4—2448no—
483C22⋊C4—1228no—
484C22⋊C4—2448no—
485C22⋊C4—2444no—
486C22⋊C4—2444no—
487C22⋊C4—2448no—
488C42—44no—
489C23—1222no—
490C23—1222no—
491C23—1222no—
492C23—1224no—
493C23—1224no—
494C23—2442no—
495C23—2442no—
496C23—2442no—
497C23—2442no—
498C23—2442no—
499C23—2442no—
500C23—2442no—
501C23—2442no—
502C23—2441no—
503C23—2441no—
504C23—2441no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23—2442no—
509C23—2441no—
510C23—2441no—
511C23—2442no—
512C23C22×C4×D6111yescharacteristic
513C23C22×C22⋊D6111yescharacteristic
514C23C2×#1175822211yescharacteristic
515C23#1451982211yescharacteristic
516C23#1451982211yescharacteristic
517C23#1451982212yes—
518C23#1451982311yescharacteristic
519C23#1451982312yes—
520C23#1451982411yescharacteristic
521C23#1451982512yes—
522C23#1451982512yes—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—1222no—
552C2×C4—1224no—
553C2×C4—1224no—
554C2×C4—1224no—
555C2×C4—1224no—
556C2×C4—2442no—
557C2×C4—2442no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2442no—
580C2×C4C4×C22⋊D6114yes—
581C22—4881no—
582C22—4881no—
583C22—4881no—
584C22—4881no—
585C22—4882no—
586C22—4882no—
587C22—2444no—
588C22—2442no—
589C22—2444no—
590C22—2442no—
591C22—2442no—
592C22C2×C4×C22⋊D6111yescharacteristic
593C22#1684023411yescharacteristic
594C22#1684024111yescharacteristic
595C22#1684024312yes—
596C22#1684024412yes—
597C22#1684032111yescharacteristic
598C22#1684032611yescharacteristic
599C22#1684032911yescharacteristic
600C22#1684033611yescharacteristic
601C22#1684033611yescharacteristic
602C22#1684034011yescharacteristic
603C22#1684035912yes—
604C22#1684036311yescharacteristic
605C22#1684037711yescharacteristic
606C22#1684038412yes—
607C22#1684050012yes—
608C22#1684050012yes—
609C22#1684050812yes—
610C22#1684051012yes—
611C22#1684051112yes—
612C22#1684051112yes—
613C22#1684051312yes—
614C22#1684051612yes—
615C4—24no—
616C4—42no—
617C4—42no—
618C4—44no—
619C4—82no—
620C4—4881no—
621C4—4881no—
622C4—4882no—
623C4—2444no—
624C4—2442no—
625C2—4882no—
626C2#2144848811yescharacteristic
627C2#2144850611yescharacteristic
628C2#2144852611yescharacteristic
629C2#2144896412yes—
630C2#2144901012yes—
631C2#2145383011yescharacteristic
632C2#2145384111yescharacteristic
633C2#2145386911yescharacteristic
634C2#2145387811yescharacteristic
635C2#2145402912yes—
636C2#2145404412yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#389C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#389D61
hypocenterC61#14630
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #21444087C2semidirect
4. #21444082C2semidirect
5. #21444082C2semidirect
6. #21444079C2semidirect
10. #21444046C2semidirect
11. C2×C61×#389C2semidirect
19. #16839688C4semidirect
308. C2×#389D61semidirect
356. C61#14630semidirect

Maximal subgroups

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

subgroupindex
C2×#168396882
C2×#168396532
#214440872
#214440822
#214440792
#214440632
#214440612
#214440462
C2×C61×#3892
#1463061