Finite Group Databasebeta

← #29610688

Subgroups — #29610688

Order 15616.

1586 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839679C211yesmaximal, characteristic
2C2×#16839663C211yesmaximal, characteristic
3C2×#16839648C211yesmaximal, characteristic, complemented
4#21444082C211yesmaximal, characteristic, complemented
5#21444067C212yesmaximal, complemented
6#21444065C212yesmaximal, complemented
7#21444063C212yesmaximal, complemented
8#21444063C212yesmaximal, complemented
9#21444059C211yesmaximal, characteristic
10#21444044C211yesmaximal, characteristic, complemented
11C61×#1441C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×#11758198C2212yes—
16C22×#11758198C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×C4×Dic61C2211yescharacteristic
22#16839679C418yescomplemented
23#16839663—24no—
24#16839648—24no—
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C24×D61C2312yes—
39C22×D244—22no—
40C22×D244—22no—
41C22×D244—42no—
42C22×D244—42no—
43C22×D244C2×C414yes—
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2312yes—
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—42no—
51C2×#11758196—42no—
52C2×#11758196—42no—
53C2×#11758196—42no—
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×#11758198—42no—
63C2×#11758198—42no—
64C2×#11758198—42no—
65C2×#11758198—42no—
66C2×#11758198—42no—
67C2×#11758198—42no—
68C2×#11758198—42no—
69C2×#11758198—42no—
70C2×#11758198C2×C418yes—
71C2×#11758198C2×C418yes—
72C2×C4×Dic61—42no—
73C2×C4×Dic61D414yes—
74#14519684—22no—
75#14519684—22no—
76#14519684—22no—
77#14519684—22no—
78#14519684—42no—
79#14519684—42no—
80#14519684—42no—
81#14519684C2×C414yes—
82C23×C4×C61C2312yes—
83C23×C4×C61C2312yes—
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—42no—
91C2×C4⋊C4×C61C2×C414yes—
92#95×C61—22no—
93#95×C61—42no—
94#95×C61—42no—
95C24×C61C2411yescharacteristic
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×D61—22no—
107C23×D61—22no—
108C23×D61—22no—
109C23×D61—22no—
110C23×D61C22×C414yes—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61C22×C412yes—
138C22×C4×C61C22×C412yes—
139C22×C4×C61C22×C412yes—
140C22×C4×C61C2×D412yes—
141C22×C4×C61#4112yes—
142C22×Dic61—21no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61C22×C414yes—
167C22×Dic61C2×D412yes—
168C22×Dic61C2×D412yes—
169C2×D244—28no—
170C2×D244—48no—
171C2×D244—44no—
172C2×D244—44no—
173C2×D244—48no—
174C4⋊C4×C61—28no—
175C4⋊C4×C61—44no—
176#11758198—48no—
177#11758198—48no—
178#11758198—48no—
179#11758198—48no—
180#11758198—48no—
181#11758198—48no—
182C4⋊Dic61—44no—
183#11758196—48no—
184C4×Dic61—44no—
185C23×C61C23×C411yescharacteristic
186C23×C61C22×D411yescharacteristic
187C23×C61C2×#4111yescharacteristic
188C23×C61H(5,𝔽2)12yes—
189C23×C61H(5,𝔽2)12yes—
190C23×C61H(5,𝔽2)11yescharacteristic
191C23×C61H(5,𝔽2)11yescharacteristic
192C23×C61H(5,𝔽2)11yescharacteristic
193C23×C61H(5,𝔽2)12yes—
194C23×C612−1+412yes—
195C23×C612−1+411yescharacteristic
196C22×D61—24no—
197C22×D61—24no—
198C22×D61—24no—
199C22×D61—24no—
200C22×D61—24no—
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—42no—
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×D61—42no—
229C22×D61—42no—
230C22×D61—42no—
231C2×C4×C61—24no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—42no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—42no—
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×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61C4×D414yes—
262C2×Dic61—24no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288C2×Dic61—42no—
289D244—416no—
290#14624—611nomaximal, Sylow
291C22×C61C2×C4×D411yescharacteristic
292C22×C61#51812yes—
293C22×C61#51811yescharacteristic
294C22×C61#52011yescharacteristic
295C22×C61#52012yes—
296C22×C61#53411yescharacteristic
297C22×C61#53511yescharacteristic
298C22×C61#53511yescharacteristic
299C22×C61#53511yescharacteristic
300C22×C61#53611yescharacteristic
301C22×C61#53711yescharacteristic
302C22×C61#53812yes—
303C22×C61#54011yescharacteristic
304C22×C61#54212yes—
305C22×C61#54211yescharacteristic
306C22×C61#56012yes—
307C22×C61#56012yes—
308C22×C61#56012yes—
309C22×C61#56212yes—
310C22×C61#56212yes—
311C22×C61#56212yes—
312C22×C61#56212yes—
313C22×C61#56312yes—
314C2×D61—44no—
315C2×D61—44no—
316C2×D61—44no—
317C2×D61—44no—
318C2×D61—44no—
319C2×D61—44no—
320C2×D61—44no—
321C2×D61—82no—
322C2×D61—82no—
323C2×D61—82no—
324C2×D61—82no—
325C2×D61—82no—
326C2×D61—82no—
327C2×D61—82no—
328C2×D61—82no—
329C4×C61—24no—
330C4×C61—42no—
331C4×C61—42no—
332C4×C61—82no—
333C4×C61—82no—
334Dic61—42no—
335Dic61—44no—
336Dic61—42no—
337Dic61—81no—
338Dic61—81no—
339C2×#394—611no—
340C2×#390—611no—
341C2×#387—611no—
342#1444—611no—
343#1441D6111yescharacteristic, complemented
344#1440—612no—
345#1439—612no—
346#1439—612no—
347#1439—612no—
348#1438—611no—
349#1434—611no—
350C2×C61#232111yescharacteristic
351C2×C61#232411yescharacteristic
352C2×C61#232611yescharacteristic
353C2×C61#237612yes—
354C2×C61#237712yes—
355C2×C61#281311yescharacteristic
356C2×C61#281611yescharacteristic
357C2×C61#281811yescharacteristic
358C2×C61#282011yescharacteristic
359C2×C61#282912yes—
360C2×C61#283012yes—
361D61—84no—
362C23×D4—611no—
363C22×C4⋊C4—611no—
364C22×C4⋊C4—612no—
365C22×C4⋊C4C2×D6111yescharacteristic
366C22×C4⋊C4C2×D6111yescharacteristic
367C22×C22⋊C4—612no—
368C22×C22⋊C4—612no—
369C22×C22⋊C4—612no—
370C22×C22⋊C4—612no—
371C22×C22⋊C4—612no—
372C22×C22⋊C4—612no—
373C22×C42—611no—
374#394—618no—
375#390—1224no—
376#387—1224no—
377C2×#95—611no—
378C2×#95—611no—
379C2×#95—611no—
380C2×#95—611no—
381C2×#95—611no—
382C2×#95—612no—
383C2×#95—612no—
384C2×#95—612no—
385C2×#95C2×D6111yescharacteristic
386C2×#95C2×D6112yes—
387C2×#95C2×D6112yes—
388C61#1462411yescharacteristic, complemented, Sylow
389C25—612no—
390C22×D4—614no—
391C22×D4—1222no—
392C22×D4—1222no—
393C22×D4—2442no—
394C22×D4—2442no—
395C23×C4—612no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4C22×D6112yes—
401C23×C4C22×D6112yes—
402C23×C4C22×D6111yescharacteristic
403C23×C4C22×D6111yescharacteristic
404C23×C4C22×D6111yescharacteristic
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4—2442no—
411C2×C4⋊C4—2442no—
412C2×C4⋊C4—2442no—
413C2×C4⋊C4—2442no—
414C2×C4⋊C4C4×D6114yes—
415C2×C22⋊C4—618no—
416C2×C22⋊C4—618no—
417C2×C22⋊C4—1224no—
418C2×C22⋊C4—1224no—
419C2×C22⋊C4—2442no—
420C2×C22⋊C4—2442no—
421C2×C22⋊C4—2442no—
422C2×C22⋊C4—2442no—
423C2×C22⋊C4—2442no—
424C2×C22⋊C4—2442no—
425C2×C22⋊C4—2442no—
426C2×C22⋊C4—2442no—
427C2×C22⋊C4—2442no—
428C2×C22⋊C4—2442no—
429C2×C22⋊C4—2442no—
430C2×C22⋊C4—2442no—
431C2×C22⋊C4—2442no—
432C2×C22⋊C4—2442no—
433C2×C42—614no—
434C2×C42—2442no—
435#95—22no—
436#95—42no—
437#95—42no—
438#95—614no—
439#95—1222no—
440#95—1222no—
441#95—1222no—
442#95—1222no—
443#95—2442no—
444#95—2442no—
445#95—2442no—
446C24—614no—
447C24—1222no—
448C24—1222no—
449C24—1222no—
450C24—1222no—
451C24—1222no—
452C24—1222no—
453C24—1222no—
454C24—1222no—
455C24—1222no—
456C24—1222no—
457C24—1222no—
458C24—1222no—
459C24—1222no—
460C24—1222no—
461C24C23×D6111yescharacteristic
462C2×D4—1228no—
463C2×D4—2448no—
464C2×D4—2444no—
465C2×D4—2444no—
466C2×D4—2448no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—614no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—1221no—
497C22×C4—1222no—
498C22×C4—1221no—
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—1221no—
512C22×C4—1221no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4C2×C4×D6112yes—
521C22×C4C2×C4×D6112yes—
522C22×C4C2×C4×D6112yes—
523C22×C4D4×D6112yes—
524C22×C4#1175822412yes—
525C4⋊C4—28no—
526C4⋊C4—44no—
527C4⋊C4—2444no—
528C4⋊C4—2448no—
529C22⋊C4—2448no—
530C22⋊C4—2448no—
531C22⋊C4—2448no—
532C22⋊C4—2448no—
533C22⋊C4—2448no—
534C22⋊C4—2448no—
535C42—2444no—
536C23—1224no—
537C23—1224no—
538C23—1224no—
539C23—1224no—
540C23—1224no—
541C23—1224no—
542C23—1224no—
543C23—2442no—
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—
560C23—2442no—
561C23—2442no—
562C23—2442no—
563C23—2442no—
564C23—2442no—
565C23—2442no—
566C23—2442no—
567C23—2442no—
568C23—2442no—
569C23—2442no—
570C23—2442no—
571C23C22×C4×D6111yescharacteristic
572C23C2×D4×D6111yescharacteristic
573C23C2×#1175822411yescharacteristic
574C23#1451982212yes—
575C23#1451982211yescharacteristic
576C23#1451982312yes—
577C23#1451982311yescharacteristic
578C23#1451982311yescharacteristic
579C23#1451982312yes—
580C23#1451982511yescharacteristic
581C23#1451982512yes—
582D4—24416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—1224no—
614C2×C4—1224no—
615C2×C4—1224no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—2442no—
623C2×C4—2442no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4—2442no—
638C2×C4—2442no—
639C2×C4—2442no—
640C2×C4#1451973714yes—
641C22—4882no—
642C22—4882no—
643C22—4882no—
644C22—4882no—
645C22—4882no—
646C22—4882no—
647C22—4882no—
648C22—4882no—
649C22—2444no—
650C22—2444no—
651C22—2444no—
652C22—2444no—
653C22—2444no—
654C22—2444no—
655C22—2444no—
656C22C2×#1451973711yescharacteristic
657C22#1684023412yes—
658C22#1684023611yescharacteristic
659C22#1684024311yescharacteristic
660C22#1684024412yes—
661C22#1684032311yescharacteristic
662C22#1684032711yescharacteristic
663C22#1684032811yescharacteristic
664C22#1684033011yescharacteristic
665C22#1684033711yescharacteristic
666C22#1684034211yescharacteristic
667C22#1684034912yes—
668C22#1684036511yescharacteristic
669C22#1684038511yescharacteristic
670C22#1684038512yes—
671C22#1684050012yes—
672C22#1684050212yes—
673C22#1684050312yes—
674C22#1684050812yes—
675C22#1684050812yes—
676C22#1684051012yes—
677C22#1684051012yes—
678C22#1684051112yes—
679C4—24no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—82no—
684C4—4881no—
685C4—4881no—
686C4—2442no—
687C4—2444no—
688C4—2442no—
689C2—4884no—
690C2#2144848211yescharacteristic
691C2#2144850811yescharacteristic
692C2#2144853311yescharacteristic
693C2#2144896412yes—
694C2#2144897412yes—
695C2#2145382411yescharacteristic
696C2#2145385211yescharacteristic
697C2#2145386111yescharacteristic
698C2#2145387411yescharacteristic
699C2#2145395312yes—
700C2#2145396612yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1441D61
hypocenterC61#14624
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#16839648C2semidirect
4. #21444082C2semidirect
5. #21444067C2semidirect
6. #21444065C2semidirect
7. #21444063C2semidirect
8. #21444063C2semidirect
10. #21444044C2semidirect
11. C61×#1441C2semidirect
22. #16839679C4semidirect
343. #1441D61semidirect
388. C61#14624semidirect

Maximal subgroups

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

subgroupindex
C2×#168396792
C2×#168396632
C2×#168396482
#214440822
#214440672
#214440652
#214440632
#214440592
#214440442
C61×#14412
#1462461