Finite Group Databasebeta

← #29603502

Subgroups — #29603502

Order 15616.

2574 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519765C211yesmaximal, characteristic
2C22×#14519739C211yesmaximal, characteristic
3C2×#16839667C211yesmaximal, characteristic, complemented
4C2×#16839667C211yesmaximal, characteristic, complemented
5C2×#16839663C211yesmaximal, characteristic
6#21444067C214yesmaximal, complemented
7#21444040C214yesmaximal, complemented
8C4×#14519684C211yesmaximal, characteristic, complemented
9C61×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×Dic122C2211yescharacteristic
11C23×D244C2211yescharacteristic
12C23×C4×D61C2212yes—
13C2×#14519765—24no—
14C2×#14519765—24no—
15C2×#14519765C418yescomplemented
16C2×#14519739—24no—
17C2×#14519739—24no—
18C2×#14519739—24no—
19C22×#11758198C2212yes—
20C22×#11758198C2214yes—
21C22×#11758198C2214yes—
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24#16839667—24no—
25#16839667—24no—
26#16839663—24no—
27C2×#14519684C2212yes—
28C2×#14519684C2214yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic
35C2×#95×C61C2214yes—
36C24×D61C2312yes—
37C22×Dic122—22no—
38C22×Dic122—22no—
39C22×Dic122—22no—
40C22×Dic122—22no—
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122C2×C414yescomplemented
44C22×D244—22no—
45C22×D244—22no—
46C22×D244—22no—
47C22×D244—22no—
48C22×D244C2×C414yes—
49C22×D244D414yes—
50C22×D244D414yes—
51C23×Dic61C2312yes—
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55C22×C4×D61—24no—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—28no—
59C22×C4×D61—44no—
60#14519765—232no—
61#14519739—232no—
62C2×#11758198—24no—
63C2×#11758198—28no—
64C2×#11758198—28no—
65C2×#11758198—24no—
66C2×#11758198—24no—
67C2×#11758198—28no—
68C2×#11758198—28no—
69C2×#11758198—44no—
70C2×#11758198C2×C4116yescomplemented
71C2×C4×Dic61—22no—
72C2×C4×Dic61—22no—
73C2×C4×Dic61—22no—
74C2×C4×Dic61—22no—
75C2×C4×Dic61—22no—
76C2×C4×Dic61D414yes—
77#14519684—28no—
78#14519684—24no—
79#14519684—24no—
80#14519684—24no—
81#14519684—24no—
82C23×C4×C61C2312yes—
83C23×C4×C61C2312yes—
84C23×C4×C61C2312yes—
85C23×C4×C61C2311yescharacteristic
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61D414yes—
92C2×C42×C61—22no—
93C2×C42×C61—22no—
94C2×C42×C61C2×C414yescomplemented
95#95×C61—44no—
96C24×C61C2411yescharacteristic
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—24no—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—24no—
103C23×D61—24no—
104C23×D61—24no—
105C23×D61C22×C414yes—
106C23×D61C2×D414yes—
107C23×D61C2×D414yes—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—24no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—24no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—24no—
122C22×C4×C61—24no—
123C22×C4×C61C22×C414yes—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C2×D414yes—
126C22×C4×C61C2×D412yes—
127C22×C4×C61C2×D412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61C2×D412yes—
130C22×C4×C61#4112yes—
131C22×C4×C61#4112yes—
132C22×Dic61—21no—
133C22×Dic61—21no—
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—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61C22×C414yes—
152C22×Dic61C2×D412yes—
153C22×Dic61C2×D412yes—
154C22×Dic61#4114yes—
155C22×Dic61#4114yes—
156C2×D244—28no—
157C2×D244—28no—
158C2×D244—28no—
159C2×D244—28no—
160C2×D244—28no—
161C2×D244—28no—
162C2×D244C22⋊C4116yes—
163C2×C4×D61—216no—
164C2×C4×D61—416no—
165C2×C4×D61—416no—
166C2×C4×D61—48no—
167C2×C4×D61—48no—
168C2×Dic122—28no—
169C2×Dic122—28no—
170C2×Dic122—28no—
171C2×Dic122—44no—
172C2×Dic122—44no—
173C2×Dic122—44no—
174C2×Dic122—44no—
175C4⋊C4×C61—28no—
176C4⋊C4×C61—44no—
177C42×C61—28no—
178#11758198—216no—
179#11758198—232no—
180#11758198—416no—
181C4×Dic61—28no—
182C4×Dic61—44no—
183C23×C61C23×C411yescharacteristic
184C23×C61C22×D411yescharacteristic
185C23×C61C22×D411yescharacteristic
186C23×C61C22×D411yescharacteristic
187C23×C61C22×D411yescharacteristic
188C23×C61C2×#4111yescharacteristic
189C23×C61C2×#4111yescharacteristic
190C23×C61C2×#4112yes—
191C23×C61C2×#4112yes—
192C23×C61H(5,𝔽2)12yes—
193C23×C612−1+412yes—
194C22×D61—24no—
195C22×D61—24no—
196C22×D61—28no—
197C22×D61—28no—
198C22×D61—24no—
199C22×D61—24no—
200C22×D61—24no—
201C22×D61—24no—
202C22×D61—28no—
203C22×D61—28no—
204C22×D61—28no—
205C22×D61—28no—
206C22×D61—42no—
207C22×D61—44no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—44no—
212C22×D61—44no—
213C22×D61—44no—
214C22×D61—44no—
215C22×D61—44no—
216C22×D61C2×C22⋊C418yes—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—24no—
221C2×C4×C61—28no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—44no—
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×C61—44no—
233C2×C4×C61—44no—
234C2×C4×C61C2×C22⋊C414yes—
235C2×C4×C61C4×D414yes—
236C2×C4×C61C4×D414yes—
237C2×C4×C61#12014yes—
238C2×C4×C61#12114yes—
239C2×C4×C61#12114yes—
240C2×C4×C61#12314yes—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—24no—
244C2×Dic61—24no—
245C2×Dic61—24no—
246C2×Dic61—24no—
247C2×Dic61—24no—
248C2×Dic61—22no—
249C2×Dic61—24no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—24no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61#12414yescomplemented
265D244—232no—
266C4×D61—432no—
267Dic122—416no—
268#14027—611nomaximal, Sylow
269C22×C61C22×C22⋊C411yescharacteristic
270C22×C61C2×C4×D411yescharacteristic
271C22×C61C2×C4×D411yescharacteristic
272C22×C61C4×#4112yes—
273C22×C61#52012yes—
274C22×C61C2×#12011yescharacteristic
275C22×C61C2×#12111yescharacteristic
276C22×C61C2×#12111yescharacteristic
277C22×C61C2×#12311yescharacteristic
278C22×C61C2×#12411yescharacteristic
279C22×C61#52912yes—
280C22×C61#53211yescharacteristic
281C22×C61#53511yescharacteristic
282C22×C61#53611yescharacteristic
283C22×C61#54212yes—
284C22×C61#54612yes—
285C22×C61#54612yes—
286C22×C61#54612yes—
287C22×C61#54712yes—
288C22×C61#54712yes—
289C22×C61#54812yes—
290C22×C61#55612yes—
291C22×C61#55912yes—
292C2×D61—216no—
293C2×D61—28no—
294C2×D61—44no—
295C2×D61—48no—
296C2×D61—48no—
297C2×D61—44no—
298C2×D61—44no—
299C2×D61—48no—
300C2×D61—44no—
301C2×D61—44no—
302C2×D61—44no—
303C4×C61—44no—
304C4×C61—44no—
305C4×C61—82no—
306C4×C61#38618yes—
307Dic61—24no—
308Dic61—44no—
309Dic61—42no—
310Dic61—44no—
311C22×#124—611no—
312C22×C4×D4—611no—
313C2×#391—611no—
314C2×#391—611no—
315C2×#390—611no—
316#1440—614no—
317C4⋊#95D6111yescharacteristic, complemented
318C22⋊#95—614no—
319C4×#95—611no—
320C2×C61C2×#38611yescharacteristic
321C2×C61C4×#12411yescharacteristic
322C2×C61#232611yescharacteristic
323C2×C61#233912yes—
324C2×C61#236712yes—
325C2×C61#242712yes—
326C2×C61#243211yescharacteristic
327C2×C61#243511yescharacteristic
328C2×C61#244712yes—
329C2×C61#254411yescharacteristic
330C2×C61#254711yescharacteristic
331D61—48no—
332C23×Q8—611no—
333C23×D4—611no—
334C24×C4—612no—
335C2×#124—618no—
336C2×#124—1224no—
337C2×#124—1224no—
338C2×C4×D4—1224no—
339C2×C4×D4—1224no—
340C2×C4×D4—1224no—
341C22×C4⋊C4C2×D6111yescharacteristic
342C22×C4⋊C4C2×D6111yescharacteristic
343C22×C22⋊C4—614no—
344C22×C22⋊C4—612no—
345C22×C22⋊C4—614no—
346C22×C42—611no—
347C22×C42—611no—
348C22×C42C2×D6111yescharacteristic
349#391—1224no—
350#391—1224no—
351#390—1224no—
352C2×#95—612no—
353C2×#95—612no—
354C2×#95—612no—
355C2×#95—614no—
356C2×#95—612no—
357C2×#95C2×D6114yes—
358C61#1402711yescharacteristic, complemented, Sylow
359C25—612no—
360C22×Q8—614no—
361C22×Q8—1222no—
362C22×Q8—1222no—
363C22×Q8—1222no—
364C22×Q8—1222no—
365C22×Q8—1222no—
366C22×Q8—1222no—
367C22×D4—614no—
368C22×D4—614no—
369C22×D4—614no—
370C22×D4—1222no—
371C22×D4—1222no—
372C22×D4—1222no—
373C22×D4—1222no—
374C23×C4—611no—
375C23×C4—612no—
376C23×C4—611no—
377C23×C4—612no—
378C23×C4—1224no—
379C23×C4—1228no—
380C23×C4—1224no—
381C23×C4—1224no—
382C23×C4—2444no—
383C23×C4C22×D6112yes—
384C23×C4C22×D6112yes—
385C23×C4C22×D6112yes—
386C23×C4C22×D6111yescharacteristic
387#124—12232no—
388C4×D4—12232no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4D24414yes—
395C2×C22⋊C4—6116no—
396C2×C22⋊C4—1224no—
397C2×C22⋊C4—1224no—
398C2×C22⋊C4—1228no—
399C2×C22⋊C4—1228no—
400C2×C22⋊C4—1224no—
401C2×C22⋊C4—1228no—
402C2×C22⋊C4—1228no—
403C2×C22⋊C4—2444no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—614no—
407C2×C42—1222no—
408C2×C42—1222no—
409C2×C42—1222no—
410C2×C42—1222no—
411C2×C42—1222no—
412C2×C42C4×D6114yescomplemented
413#95—44no—
414#95—1224no—
415#95—1224no—
416#95—1224no—
417#95—1224no—
418#95—1228no—
419C24—614no—
420C24—614no—
421C24—614no—
422C24—1222no—
423C24—1222no—
424C24—1224no—
425C24—1224no—
426C24—1222no—
427C24—1222no—
428C24—1224no—
429C24—1224no—
430C24C23×D6111yescharacteristic
431C2×Q8—1228no—
432C2×Q8—1228no—
433C2×Q8—1228no—
434C2×Q8—2444no—
435C2×Q8—2444no—
436C2×Q8—2444no—
437C2×Q8—2444no—
438C2×D4—6116no—
439C2×D4—1228no—
440C2×D4—1228no—
441C2×D4—1228no—
442C2×D4—1228no—
443C2×D4—1228no—
444C2×D4—1228no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—612no—
461C22×C4—614no—
462C22×C4—614no—
463C22×C4—612no—
464C22×C4—614no—
465C22×C4—12216no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1221no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1221no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—24416no—
486C22×C4—2448no—
487C22×C4—24416no—
488C22×C4—2448no—
489C22×C4C2×C4×D6114yes—
490C22×C4C2×C4×D6112yes—
491C22×C4C2×D24414yes—
492C22×C4C2×D24412yes—
493C22×C4#1175822212yes—
494C22×C4D4×D6112yes—
495C22×C4D4×D6112yes—
496C22×C4D4×D6112yes—
497C22×C4#1175822612yes—
498C4⋊C4—28no—
499C4⋊C4—44no—
500C22⋊C4—12232no—
501C22⋊C4—12216no—
502C22⋊C4—24416no—
503C42—28no—
504C42—1228no—
505C42—2444no—
506C23—618no—
507C23—1224no—
508C23—1224no—
509C23—1228no—
510C23—1228no—
511C23—1224no—
512C23—1224no—
513C23—1224no—
514C23—1224no—
515C23—1228no—
516C23—1228no—
517C23—1228no—
518C23—1228no—
519C23—2444no—
520C23—2444no—
521C23—2442no—
522C23—2444no—
523C23—2442no—
524C23—2442no—
525C23—2442no—
526C23—2444no—
527C23—2444no—
528C23—2444no—
529C23C22×C4×D6111yescharacteristic
530C23C2×D4×D6111yescharacteristic
531C23C2×D4×D6111yescharacteristic
532C23C2×D4×D6111yescharacteristic
533C23C22×D24411yescharacteristic
534C23#41×D6112yes—
535C23#41×D6112yes—
536C23C2×#1175822211yescharacteristic
537C23C2×#1175822611yescharacteristic
538C23#1451982212yes—
539C23#1451982512yes—
540Q8—24416no—
541D4—12232no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—28no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—614no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1224no—
563C2×C4—1224no—
564C2×C4—1224no—
565C2×C4—1224no—
566C2×C4—1224no—
567C2×C4—1222no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1224no—
572C2×C4—1224no—
573C2×C4—24432no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4C22⋊C4×D6114yes—
585C2×C4#1451973914yes—
586C2×C4C4×D24414yes—
587C2×C4#1451974714yes—
588C2×C4#1451975014yes—
589C2×C4#1451975214yes—
590C2×C4#1451976214yes—
591C22—1228no—
592C22—12216no—
593C22—2444no—
594C22—2444no—
595C22—2444no—
596C22—2448no—
597C22—2444no—
598C22—2448no—
599C22—2448no—
600C22—2444no—
601C22—2444no—
602C22C2×C22⋊C4×D6111yescharacteristic
603C22C2×#1451973911yescharacteristic
604C22C2×C4×D24411yescharacteristic
605C22#1684023012yes—
606C22#1684024312yes—
607C22C2×#1451974711yescharacteristic
608C22C2×#1451975011yescharacteristic
609C22C2×#1451975211yescharacteristic
610C22C2×#1451976211yescharacteristic
611C22#124×D6111yescharacteristic
612C22#1684029712yes—
613C22#1684031111yescharacteristic
614C22#1684032511yescharacteristic
615C22#1684033711yescharacteristic
616C22#1684038612yes—
617C22#1684040712yes—
618C22#1684040912yes—
619C22#1684040912yes—
620C22#1684041412yes—
621C22#1684041412yes—
622C22#1684042412yes—
623C22#1684048412yes—
624C22#1684049512yes—
625C4—44no—
626C4—44no—
627C4—82no—
628C4—1224no—
629C4—2444no—
630C4—2444no—
631C4—2442no—
632C4#1683964018yes—
633C2—2448no—
634C2C2×#1683964011yescharacteristic
635C2#2144835811yescharacteristic
636C2#2144852711yescharacteristic
637C2#2144864712yes—
638C2#2144889012yes—
639C2#2144939412yes—
640C2#2144944611yescharacteristic
641C2#2144946911yescharacteristic
642C2#2144960812yes—
643C2#2145079311yescharacteristic
644C2#2145081611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC4⋊#95D61
hypocenterC61#14027
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16839667C2semidirect
4. C2×#16839667C2semidirect
6. #21444067C2semidirect
7. #21444040C2semidirect
8. C4×#14519684C2semidirect
9. C61×C4⋊#95C2semidirect
15. C2×#14519765C4semidirect
43. C22×Dic122C2×C4semidirect
70. C2×#11758198C2×C4semidirect
94. C2×C42×C61C2×C4semidirect
264. C2×Dic61#124semidirect
317. C4⋊#95D61semidirect
358. C61#14027semidirect
412. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197652
C22×#145197392
C2×#168396672
C2×#168396632
#214440672
#214440402
C4×#145196842
C61×C4⋊#952
#1402761