Finite Group Databasebeta

← #29601487

Subgroups — #29601487

Order 15616.

2154 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758198C211yesmaximal, characteristic
2C2×#16839609C212yesmaximal
3C2×#16839607C211yesmaximal, characteristic, complemented
4C2×#95×D61C211yesmaximal, characteristic
5#21444045C212yesmaximal, complemented
6#21444044C212yesmaximal, complemented
7#21444043C211yesmaximal, characteristic, complemented
8#21444040C211yesmaximal, characteristic
9#21444040C212yesmaximal
10C4×#14519684C211yesmaximal, characteristic, complemented
11C61×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D61C2212yes—
13C23×C4×D61C2211yescharacteristic
14C22×#11758198C2212yes—
15C22×#11758198C2211yescharacteristic
16C22×#11758198C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18C22×C4×Dic61C2212yes—
19C22×C4×Dic61C2212yes—
20C4×#11758198C418yescomplemented
21#16839609C4116yescomplemented
22#16839607—24no—
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33#95×D61—24no—
34C22×C42×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C24×D61C2311yescharacteristic
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2312yes—
45C22×C4×D61—24no—
46C22×C4×D61—24no—
47C22×C4×D61—24no—
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61—24no—
51C22×C4×D61—24no—
52C22×C4×D61—42no—
53C22×C4×D61—42no—
54C22×C4×D61—42no—
55C22×C4×D61C2×C418yes—
56C22×C4×D61C2×C414yes—
57C2×#11758198—24no—
58C2×#11758198—22no—
59C2×#11758198—24no—
60C2×#11758198—22no—
61C2×#11758198C2×C418yes—
62C2×#11758198C2×C414yes—
63C2×#11758198C2×C418yes—
64C2×#11758198C2×C414yes—
65C2×C4×Dic61—22no—
66C2×C4×Dic61—22no—
67C2×C4×Dic61—24no—
68C2×C4×Dic61—24no—
69C2×C4×Dic61—42no—
70C2×C4×Dic61—42no—
71C2×C4×Dic61C2×C418yescomplemented
72C2×C4×Dic61C2×C414yescomplemented
73C2×C4×Dic61C2×C418yescomplemented
74#14519684—22no—
75#14519684—24no—
76#14519684—24no—
77#14519684—24no—
78#14519684—42no—
79#14519684—42no—
80#14519684C2×C418yescomplemented
81#14519684C2×C414yescomplemented
82#14519684C2×C414yescomplemented
83#14519684D414yes—
84C23×C4×C61C2312yes—
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2312yes—
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C2×C42×C61—42no—
90C2×C42×C61C2×C414yescomplemented
91#95×C61—22no—
92#95×C61—22no—
93#95×C61—42no—
94#95×C61C2×C418yescomplemented
95C24×C61C2411yescharacteristic
96C23×D61—21no—
97C23×D61—22no—
98C23×D61—21no—
99C23×D61—22no—
100C23×D61—21no—
101C23×D61—21no—
102C23×D61C22×C414yes—
103C23×D61C22×C412yes—
104C23×D61#4114yes—
105C23×D61#4112yes—
106C23×D61#4112yes—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—21no—
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×C61C22×C414yes—
129C22×C4×C61C22×C414yes—
130C22×C4×C61C22×C412yes—
131C22×C4×C61C22×C414yes—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61#4112yes—
136C22×Dic61—21no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—21no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—21no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—21no—
159C22×Dic61C22×C412yes—
160C22×Dic61C22×C412yes—
161C22×Dic61C22×C414yes—
162C22×Dic61C22×C414yes—
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C414yes—
165C22×Dic61C2×D414yes—
166C22×Dic61#4114yes—
167C2×C4×D61—216no—
168C2×C4×D61—28no—
169C2×C4×D61—28no—
170C2×C4×D61—216no—
171C2×C4×D61—48no—
172C2×C4×D61—44no—
173C2×C4×D61—48no—
174C2×C4×D61—48no—
175C2×C4×D61—48no—
176C2×C4×D61—48no—
177C2×C4×D61—48no—
178C2×C4×D61—48no—
179C42×C61—44no—
180#11758198—216no—
181#11758198—28no—
182#11758198C42116yes—
183C4×Dic61—28no—
184C4×Dic61—216no—
185C4×Dic61—48no—
186C23×C61C23×C412yes—
187C23×C61C23×C411yescharacteristic
188C23×C61C22×D411yescharacteristic
189C23×C61C2×#4112yes—
190C23×C61C2×#4111yescharacteristic
191C23×C61C2×#4111yescharacteristic
192C23×C61C2×#4112yes—
193C23×C61C2×#4111yescharacteristic
194C23×C61H(5,𝔽2)12yes—
195C23×C61H(5,𝔽2)11yescharacteristic
196C23×C612−1+411yescharacteristic
197C22×D61—24no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—24no—
201C22×D61—24no—
202C22×D61—22no—
203C22×D61—24no—
204C22×D61—22no—
205C22×D61—24no—
206C22×D61—22no—
207C22×D61—22no—
208C22×D61—24no—
209C22×D61—24no—
210C22×D61—24no—
211C22×D61—24no—
212C22×D61—22no—
213C22×D61—24no—
214C22×D61—22no—
215C22×D61C2×C4214yes—
216C22×D61#11714yes—
217C22×D61#11718yes—
218C22×D61#11714yes—
219C22×D61#11718yes—
220C2×C4×C61—22no—
221C2×C4×C61—24no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—24no—
225C2×C4×C61—22no—
226C2×C4×C61—24no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
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×C61C2×C4214yes—
248C2×C4×C61C4×D414yes—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—42no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61C2×C4214yes—
279C2×Dic61C4×D418yes—
280C4×D61—432no—
281C4×D61—416no—
282#13809—611nomaximal, Sylow
283C22×C61C22×C4211yescharacteristic
284C22×C61C2×#11711yescharacteristic
285C22×C61C2×#11712yes—
286C22×C61C2×#11711yescharacteristic
287C22×C61C2×#11712yes—
288C22×C61C2×C4×D412yes—
289C22×C61C2×C4×D411yescharacteristic
290C22×C61C4×#4111yescharacteristic
291C22×C61C4×#4112yes—
292C22×C61#51812yes—
293C22×C61#51811yescharacteristic
294C22×C61#52012yes—
295C22×C61#52011yescharacteristic
296C22×C61#54612yes—
297C22×C61#54611yescharacteristic
298C22×C61#54811yescharacteristic
299C22×C61#55112yes—
300C22×C61#55112yes—
301C22×C61#55112yes—
302C22×C61#55212yes—
303C22×C61#55211yescharacteristic
304C22×C61#55312yes—
305C22×C61#55311yescharacteristic
306C2×D61—24no—
307C2×D61—28no—
308C2×D61—24no—
309C2×D61—28no—
310C2×D61—24no—
311C2×D61—28no—
312C2×D61—24no—
313C2×D61—28no—
314C2×D61—24no—
315C2×D61—24no—
316C2×D61#37618yescomplemented
317C4×C61—24no—
318C4×C61—24no—
319C4×C61—44no—
320C4×C61—44no—
321C4×C61—42no—
322Dic61—28no—
323Dic61—24no—
324Dic61—42no—
325Dic61—42no—
326Dic61—44no—
327C2×C4×C22⋊C4—611no—
328C2×C4×C22⋊C4—612no—
329C2×#376—611no—
330C22×#95—611no—
331#1434—611no—
332#1434—612no—
333#1434—612no—
334#1434D6111yescharacteristic, complemented
335C22⋊#95—612no—
336C22⋊#95—611no—
337C4×#95—611no—
338C2×C61C2×#37611yescharacteristic
339C2×C61C42×D411yescharacteristic
340C2×C61#227511yescharacteristic
341C2×C61#234211yescharacteristic
342C2×C61#234212yes—
343C2×C61#234311yescharacteristic
344C2×C61#234312yes—
345C2×C61#235211yescharacteristic
346C2×C61#235212yes—
347C2×C61#235311yescharacteristic
348C2×C61#235312yes—
349D61—28no—
350C24×C4—612no—
351C24×C4—611no—
352C22×C22⋊C4—611no—
353C22×C22⋊C4—611no—
354C22×C22⋊C4—612no—
355C22×C42—612no—
356C22×C42—611no—
357C22×C42—612no—
358C22×C42C2×D6111yescharacteristic
359C4×C22⋊C4—618no—
360C4×C22⋊C4—6116no—
361#376—1224no—
362C2×#95—611no—
363C2×#95—612no—
364C2×#95—611no—
365C2×#95—611no—
366C2×#95—612no—
367C2×#95—611no—
368C2×#95—612no—
369C2×#95—612no—
370C2×#95—612no—
371C2×#95—612no—
372C2×#95—1224no—
373C2×#95C2×D6111yescharacteristic
374C2×#95C2×D6111yescharacteristic
375C2×#95C2×D6112yes—
376C2×#95C2×D6112yes—
377C61#1380911yescharacteristic, complemented, Sylow
378C25—611no—
379C23×C4—611no—
380C23×C4—612no—
381C23×C4—611no—
382C23×C4—612no—
383C23×C4—611no—
384C23×C4—618no—
385C23×C4—614no—
386C23×C4—1224no—
387C23×C4—1224no—
388C23×C4—1224no—
389C23×C4—1224no—
390C23×C4—1224no—
391C23×C4—1222no—
392C23×C4—1222no—
393C23×C4—2442no—
394C23×C4—2442no—
395C23×C4—2442no—
396C23×C4C22×D6111yescharacteristic
397C23×C4C22×D6112yes—
398C23×C4C22×D6112yes—
399C23×C4C22×D6111yescharacteristic
400C23×C4C22×D6111yescharacteristic
401C2×C22⋊C4—614no—
402C2×C22⋊C4—618no—
403C2×C22⋊C4—614no—
404C2×C22⋊C4—618no—
405C2×C22⋊C4—1222no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—1222no—
409C2×C42—42no—
410C2×C42—618no—
411C2×C42—614no—
412C2×C42—618no—
413C2×C42—1224no—
414C2×C42—1224no—
415C2×C42—1222no—
416C2×C42—1222no—
417C2×C42—2442no—
418C2×C42—2442no—
419C2×C42C4×D6114yescomplemented
420#95—22no—
421#95—22no—
422#95—42no—
423#95—614no—
424#95—618no—
425#95—614no—
426#95—614no—
427#95—1224no—
428#95—1224no—
429#95—1224no—
430#95—1222no—
431#95—2442no—
432#95—2442no—
433#95C4×D6118yescomplemented
434C24—614no—
435C24—612no—
436C24—612no—
437C24—614no—
438C24—612no—
439C24—1221no—
440C24—1222no—
441C24—1221no—
442C24—1222no—
443C24—1221no—
444C24—1221no—
445C24C23×D6111yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—614no—
468C22×C4—612no—
469C22×C4—614no—
470C22×C4—614no—
471C22×C4—614no—
472C22×C4—612no—
473C22×C4—612no—
474C22×C4—614no—
475C22×C4—12216no—
476C22×C4—1228no—
477C22×C4—12216no—
478C22×C4—1221no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1222no—
488C22×C4—1221no—
489C22×C4—1222no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1221no—
499C22×C4—1222no—
500C22×C4—1221no—
501C22×C4—1228no—
502C22×C4—2444no—
503C22×C4—2448no—
504C22×C4—2448no—
505C22×C4—2448no—
506C22×C4—2448no—
507C22×C4—2448no—
508C22×C4—2448no—
509C22×C4—2448no—
510C22×C4C2×C4×D6114yes—
511C22×C4C2×C4×D6112yes—
512C22×C4C2×C4×D6114yes—
513C22×C4C2×C4×D6112yes—
514C22×C4C2×C4×D6114yes—
515C22×C4C2×C4×D6112yes—
516C22×C4D4×D6112yes—
517C22×C4#1175822612yes—
518C22⋊C4—6116no—
519C22⋊C4—12216no—
520C22⋊C4—1228no—
521C42—44no—
522C42—12216no—
523C42—1228no—
524C42—2448no—
525C23—614no—
526C23—614no—
527C23—618no—
528C23—614no—
529C23—618no—
530C23—1224no—
531C23—1222no—
532C23—1224no—
533C23—1222no—
534C23—1224no—
535C23—1222no—
536C23—1222no—
537C23—1224no—
538C23—1224no—
539C23—1222no—
540C23—1224no—
541C23—1222no—
542C23—1224no—
543C23—1222no—
544C23—1222no—
545C23—1224no—
546C23—1224no—
547C23—1224no—
548C23C22×C4×D6112yes—
549C23C22×C4×D6111yescharacteristic
550C23C2×D4×D6111yescharacteristic
551C23#41×D6112yes—
552C23#41×D6112yes—
553C23#41×D6111yescharacteristic
554C23#41×D6111yescharacteristic
555C23C2×#1175822611yescharacteristic
556C23#1451982212yes—
557C23#1451982311yescharacteristic
558C23#1451982411yescharacteristic
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—614no—
587C2×C4—618no—
588C2×C4—1224no—
589C2×C4—1224no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1224no—
598C2×C4—1222no—
599C2×C4—1224no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—24416no—
608C2×C4—24432no—
609C2×C4—2441no—
610C2×C4—2442no—
611C2×C4—2441no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4C42×D6114yes—
620C2×C4#1451973914yes—
621C22—618no—
622C22—1224no—
623C22—1228no—
624C22—1224no—
625C22—1228no—
626C22—1224no—
627C22—1228no—
628C22—1224no—
629C22—1224no—
630C22—1228no—
631C22—1224no—
632C22C2×C42×D6111yescharacteristic
633C22#117×D6111yescharacteristic
634C22#117×D6112yes—
635C22#117×D6111yescharacteristic
636C22#117×D6112yes—
637C22C4×D4×D6112yes—
638C22C2×#1451973911yescharacteristic
639C22#1684023011yescharacteristic
640C22C4×#1175822612yes—
641C22#1684023412yes—
642C22#1684023511yescharacteristic
643C22#1684024112yes—
644C22#1684024211yescharacteristic
645C22#1684040112yes—
646C22#1684040511yescharacteristic
647C22#1684042011yescharacteristic
648C22#1684043712yes—
649C22#1684043912yes—
650C22#1684044012yes—
651C22#1684044812yes—
652C22#1684045011yescharacteristic
653C22#1684045712yes—
654C22#1684046511yescharacteristic
655C4—24no—
656C4—24no—
657C4—44no—
658C4—42no—
659C4—44no—
660C4—1228no—
661C4—1224no—
662C4—2442no—
663C4—2444no—
664C4—2442no—
665C2—1228no—
666C2#376×D6111yescharacteristic
667C2C4×#1451973911yescharacteristic
668C2#2144817811yescharacteristic
669C2#2144866511yescharacteristic
670C2#2144866712yes—
671C2#2144867611yescharacteristic
672C2#2144867812yes—
673C2#2144874511yescharacteristic
674C2#2144874712yes—
675C2#2144875611yescharacteristic
676C2#2144875812yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1434D61
hypocenterC61#13809
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16839607C2semidirect
5. #21444045C2semidirect
6. #21444044C2semidirect
7. #21444043C2semidirect
10. C4×#14519684C2semidirect
11. C61×#1434C2semidirect
20. C4×#11758198C4semidirect
21. #16839609C4semidirect
71. C2×C4×Dic61C2×C4semidirect
72. C2×C4×Dic61C2×C4semidirect
73. C2×C4×Dic61C2×C4semidirect
80. #14519684C2×C4semidirect
81. #14519684C2×C4semidirect
82. #14519684C2×C4semidirect
90. C2×C42×C61C2×C4semidirect
94. #95×C61C2×C4semidirect
316. C2×D61#376semidirect
334. #1434D61semidirect
377. C61#13809semidirect
419. C2×C42C4×D61semidirect
433. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581982
C2×#168396092
C2×#168396072
C2×#95×D612
#214440452
#214440442
#214440432
#214440402
C4×#145196842
C61×#14342
#1380961