Finite Group Databasebeta

← #29740202

Subgroups — #29740202

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839975C211yesmaximal, characteristic
2C2×C4×#11758200C211yesmaximal, characteristic, complemented
3#21449618C211yesmaximal, characteristic, complemented
4D4×#11758196C211yesmaximal, characteristic, complemented
5#21447350C211yesmaximal, characteristic, complemented
6#21447323C211yesmaximal, characteristic, complemented
7#21447231C211yesmaximal, characteristic, complemented
8#21447058C211yesmaximal, characteristic, complemented
9#21446505C211yesmaximal, characteristic, complemented
10#21446374C211yesmaximal, characteristic, complemented
11#21446169C211yesmaximal, characteristic
12#21446151C211yesmaximal, characteristic, complemented
13#21446090C211yesmaximal, characteristic, complemented
14#21446082C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×#14519764C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C22×#11758196—21no—
22#16839975—24no—
23C4×#11758200—24no—
24C2×#14519709C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34#16839698—21no—
35#16839690—21no—
36#16839667C2211yescharacteristic
37#16839665C2211yescharacteristic
38#16839661C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839656—21no—
42#16839655—21no—
43#16839635—21no—
44#16839634—21no—
45#16839631C2211yescharacteristic
46#16839620—21no—
47C4×#11758196C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×D8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C2×#11758200—22no—
65C2×#11758200—22no—
66C2×#11758200D414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519764—22no—
70#14519764—41no—
71C4×Dic122—22no—
72C4×Dic122—41no—
73D4×Dic61—22no—
74D4×Dic61—22no—
75D4×Dic61—22no—
76D4×Dic61—41no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—44no—
87C2×#11758196D411yescharacteristic
88C2×#11758196D411yescharacteristic
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98#14519709—41no—
99#14519708—22no—
100#14519706—22no—
101#14519702—22no—
102#14519702—22no—
103#14519700—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107C4×#92418—22no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684D411yescharacteristic
114#14519684D411yescharacteristic
115C22×D4×C61C2311yescharacteristic
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C2×D8×C61—22no—
119C2×D8×C61—22no—
120C2×D8×C61—22no—
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C4×D4×C61—22no—
124C4×D4×C61—41no—
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C42×C61C2311yescharacteristic
131#102×C61—22no—
132#102×C61—41no—
133C24×C61—21no—
134C24×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61C2×D412yes—
145C2×D4×C61#4112yes—
146C2×D4×C61#4112yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61—81no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C22×Dic61—24no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—42no—
161C22×Dic61—42no—
162C22×Dic61—42no—
163C22×Dic61—42no—
164C22×Dic61—81no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122C2×D412yes—
175D8×C61—44no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C22⋊C4×C61—42no—
187C22⋊C4×C61—42no—
188C22⋊C4×C61—81no—
189C42×C61—21no—
190C42×C61—21no—
191C22⋊Dic61—24no—
192C22⋊Dic61—42no—
193C22⋊Dic61—42no—
194C22⋊Dic61—42no—
195C22⋊Dic61—42no—
196C22⋊Dic61—81no—
197#11758200—28no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—81no—
204C4⋊Dic61#4112yes—
205#11758196—22no—
206#11758196—22no—
207#11758196—42no—
208#11758196—42no—
209#11758196—42no—
210#11758196—42no—
211#11758196—81no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—42no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418C2×D412yes—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61C22×D411yescharacteristic
238D4×C61—22no—
239D4×C61—22no—
240D4×C61—22no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—41no—
245D4×C61#12314yes—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—84no—
258C2×C4×C61AGL(1,ℤ/8)12yes—
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61H(5,𝔽2)11yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—22no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—22no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—48no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—84no—
290C2×Dic61#13512yes—
291Dic122—22no—
292Dic122—22no—
293Dic122—41no—
294Dic122—41no—
295C8×C61—41no—
296C8×C61—41no—
297#92418—22no—
298#92418—41no—
299#26172—611nomaximal, Sylow
300C22×C61—24no—
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—42no—
306C22×C61—42no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61#52511yescharacteristic
315C22×C61D4211yescharacteristic
316C22×C61#54811yescharacteristic
317C22×C61C2×#13511yescharacteristic
318C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C61#57711yescharacteristic
320C22×C61#57711yescharacteristic
321C4×C61—22no—
322C4×C61—41no—
323C4×C61—81no—
324C4×C61—81no—
325C4×C61C2×#12311yescharacteristic
326C4×C61#53911yescharacteristic
327C4×C61#54711yescharacteristic
328C4×C61#55311yescharacteristic
329Dic61—22no—
330Dic61—42no—
331Dic61—41no—
332Dic61—42no—
333Dic61—41no—
334Dic61—41no—
335Dic61—81no—
336Dic61—81no—
337C2×#463—611no—
338C2×C4×SD16—611no—
339#2448—611no—
340D4×C4⋊C4—611no—
341#2094—611no—
342#2088—611no—
343#2072—611no—
344#2042—611no—
345#1934—611no—
346#1916—611no—
347#1879—611no—
348#1879D6111yescharacteristic
349#1877—611no—
350#1865—611no—
351#1864—611no—
352C2×C61—44no—
353C2×C61—161no—
354C2×C61#244311yescharacteristic
355C2×C61#310511yescharacteristic
356C2×C61#312511yescharacteristic
357C2×C61#326511yescharacteristic
358C2×C61#328411yescharacteristic
359C2×C61#336011yescharacteristic
360C2×C61#337311yescharacteristic
361C22×SD16—611no—
362C22×D8C2×D6111yescharacteristic
363C2×#124—611no—
364C2×C4×Q8—611no—
365C2×C4×D4—611no—
366C2×C4×D4—611no—
367C2×C4×D4C2×D6111yescharacteristic
368C22×C4⋊C4—1221no—
369#463—1224no—
370C4×SD16—1224no—
371C2×#106—611no—
372C2×#106—611no—
373C2×C4⋊C8—611no—
374C2×#103—611no—
375C2×#103—611no—
376C2×#103—611no—
377C2×#102—611no—
378C2×#102—611no—
379C2×#102—611no—
380C2×#102C2×D6111yescharacteristic
381C2×#102C2×D6111yescharacteristic
382C2×C4×C8—611no—
383#399—1221no—
384#397—1221no—
385#391—611no—
386#390—611no—
387#390C2×D6111yescharacteristic
388#389—611no—
389#389—611no—
390#389—611no—
391#388—1221no—
392#388—1221no—
393#385—1221no—
394#385—1221no—
395#384—611no—
396#380—1221no—
397C4×C4⋊C4—611no—
398#340—611no—
399#340—611no—
400#340—611no—
401#340C2×D6111yescharacteristic
402#336—611no—
403#336—611no—
404#336—611no—
405#336C2×D6111yescharacteristic
406C61#2617211yescharacteristic, complemented, Sylow
407C22×Q8—611no—
408C22×D4C22×D6111yescharacteristic
409C22×D4C22×D6111yescharacteristic
410C23×C4—21no—
411C23×C4—1221no—
412C23×C4—1221no—
413C2×SD16—614no—
414C2×SD16—1222no—
415C2×SD16—1222no—
416C2×D8—22no—
417C2×D8—22no—
418C2×D8—22no—
419C22×C8—611no—
420C22×C8—611no—
421C22×C8C22×D6111yescharacteristic
422C22×C8C22×D6111yescharacteristic
423#124—1222no—
424#124—2441no—
425C4×Q8—1222no—
426C4×Q8—2441no—
427C4×D4—22no—
428C4×D4—41no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—2441no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—2444no—
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—1221no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—1221no—
459C2×C42C22×D6111yescharacteristic
460#106—1222no—
461#106—2441no—
462C4⋊C8—1222no—
463#103—1222no—
464#103—1222no—
465#103—1222no—
466#102—22no—
467#102—41no—
468#102—1222no—
469#102—1222no—
470#102—1222no—
471C4×C8—1222no—
472#95—611no—
473#95—611no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479C24—21no—
480C24—21no—
481C2×Q8—612no—
482C2×Q8—1221no—
483C2×Q8—1221no—
484C2×Q8—1221no—
485C2×Q8—1221no—
486C2×Q8—1221no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4#1175822212yes—
497C2×D4D4×D6112yes—
498C2×D4#1175822412yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—1224no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—4881no—
514C22×C4—2442no—
515C22×C4—2442no—
516C22×C4—2442no—
517C22×C4—2442no—
518C22×C4D4×D6111yescharacteristic
519C22×C4D4×D6111yescharacteristic
520C22×C4C23×D6111yescharacteristic
521SD16—1228no—
522D8—44no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—612no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—612no—
540C4⋊C4—1222no—
541C4⋊C4—1221no—
542C4⋊C4—1222no—
543C4⋊C4—1221no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—4881no—
548C4⋊C4—4881no—
549C4⋊C4—2442no—
550C4⋊C4—2442no—
551C4⋊C4—2442no—
552C4⋊C4—2442no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—1224no—
557C22⋊C4—4881no—
558C22⋊C4—2442no—
559C22⋊C4—2442no—
560C22⋊C4—2442no—
561C22⋊C4—2442no—
562C42—21no—
563C42—21no—
564C42—1221no—
565C42—1221no—
566C42—1221no—
567C42—1221no—
568C42—2442no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C2×D4×D6111yescharacteristic
584Q8—1222no—
585Q8—1222no—
586Q8—2441no—
587Q8—2441no—
588D4—22no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4#1451975914yes—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4—612no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1222no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1222no—
622C2×C4—4884no—
623C2×C4—2448no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4#1451980112yes—
635C2×C4C2×D4×D6111yescharacteristic
636C2×C4#41×D6111yescharacteristic
637C2×C4C2×#1175822411yescharacteristic
638C2×C4C2×#1175822211yescharacteristic
639C2×C4#1451982211yescharacteristic
640C2×C4#1451982411yescharacteristic
641C8—41no—
642C8—41no—
643C8—1222no—
644C8—2441no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22#1684027111yescharacteristic
660C22#1684039411yescharacteristic
661C22#1684041811yescharacteristic
662C22#135×D6111yescharacteristic
663C22C2×#1451980111yescharacteristic
664C22#1684057211yescharacteristic
665C22#1684057211yescharacteristic
666C4—22no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—1222no—
671C4—4881no—
672C4—4881no—
673C4—2442no—
674C4—2441no—
675C4—2441no—
676C4—2441no—
677C4—2442no—
678C4C2×#1451975911yescharacteristic
679C4#1684035411yescharacteristic
680C4#1684041011yescharacteristic
681C4#1684045511yescharacteristic
682C2—44no—
683C2—161no—
684C2#2144955611yescharacteristic
685C2#2145586411yescharacteristic
686C2#2145610011yescharacteristic
687C2#2145731811yescharacteristic
688C2#2145754711yescharacteristic
689C2#2145846311yescharacteristic
690C2#2145861511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×D8×C61C22
hypercenter#1879D61
hypocenterC61#26172
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758200C2semidirect
3. #21449618C2semidirect
4. D4×#11758196C2semidirect
5. #21447350C2semidirect
6. #21447323C2semidirect
7. #21447231C2semidirect
8. #21447058C2semidirect
9. #21446505C2semidirect
10. #21446374C2semidirect
12. #21446151C2semidirect
13. #21446090C2semidirect
14. #21446082C2semidirect
406. C61#26172semidirect

Maximal subgroups

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

subgroupindex
C2×#168399752
C2×C4×#117582002
#214496182
D4×#117581962
#214473502
#214473232
#214472312
#214470582
#214465052
#214463742
#214461692
#214461512
#214460902
#214460822
C61×#18792
#2617261