Finite Group Databasebeta

← #29739951

Subgroups — #29739951

Order 15616.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840102C211yesmaximal, characteristic, complemented
2C2×#16839804C211yesmaximal, characteristic, complemented
3#21449271C211yesmaximal, characteristic
4#21448763C211yesmaximal, characteristic
5#21447360C211yesmaximal, characteristic, complemented
6#21447299C211yesmaximal, characteristic, complemented
7#21447254C211yesmaximal, characteristic, complemented
8#21447014C211yesmaximal, characteristic, complemented
9#21446462C211yesmaximal, characteristic, complemented
10#21446410C211yesmaximal, characteristic, complemented
11#21446132C211yesmaximal, characteristic, complemented
12#21446116C211yesmaximal, characteristic
13#21446021C211yesmaximal, characteristic, complemented
14#21446011C211yesmaximal, characteristic, complemented
15C61×#1894C211yesmaximal, characteristic, complemented
16C2×#14519753C2211yescharacteristic
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21#16840102—24no—
22#16839804—24no—
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34#16839695—21no—
35#16839684—21no—
36#16839669C2211yescharacteristic
37#16839662—21no—
38#16839658C2211yescharacteristic
39#16839656—21no—
40#16839651—21no—
41#16839639—21no—
42#16839631C2211yescharacteristic
43#16839620—21no—
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839613—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C22⋊D61D411yescharacteristic
62C23×Dic61—21no—
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519753—22no—
67#14519753—41no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70#14519736—22no—
71#14519736—41no—
72#14519735—22no—
73#14519735—41no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—41no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196D411yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61D411yescharacteristic
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198D411yescharacteristic
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61C2311yescharacteristic
97#14519711—22no—
98#14519711D414yescomplemented
99#14519709—22no—
100#14519709—22no—
101#14519708—22no—
102#14519708—41no—
103#14519701—22no—
104#14519701—41no—
105C22⋊#92418—22no—
106#14519689—22no—
107#14519689—22no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114C22×Q8×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C2×M16×C61—22no—
117C2×M16×C61—22no—
118C2×M16×C61—22no—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129#103×C61—22no—
130#103×C61—22no—
131#95×C61—21no—
132C24×C61C2×D411yescharacteristic
133C23×D61C2×D411yescharacteristic
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61#4112yes—
150C22×C4×C61#4112yes—
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—41no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—42no—
160C22×Dic61—42no—
161C22×Dic61—81no—
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171M16×C61—28no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61C2×D412yes—
177C2×C8×C61#4112yes—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—42no—
185C22⋊C4×C61—42no—
186C22⋊C4×C61—81no—
187C22⋊Dic61—22no—
188C22⋊Dic61—42no—
189#11758198—22no—
190#11758198—42no—
191#11758198—42no—
192#11758198—81no—
193#11758198—81no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—42no—
201C4⋊Dic61C2×D412yes—
202C4⋊Dic61C2×D412yes—
203#11758196—22no—
204#11758196—42no—
205#11758196—42no—
206#11758196—81no—
207#11758196—81no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—42no—
211C4×Dic61—42no—
212C4×Dic61—42no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61#12312yes—
226C23×C61C22×D411yescharacteristic
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234Q8×C61—41no—
235Q8×C61—41no—
236Q8×C61—41no—
237Q8×C61—41no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61#12312yes—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61H(5,𝔽2)11yescharacteristic
262C2×C4×C612−1+411yescharacteristic
263C22⋊D61—44no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—84no—
285C2×Dic61#13712yes—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—41no—
290C8×C61—22no—
291C8×C61—22no—
292#92418—41no—
293#92418—41no—
294#26155—611nomaximal, Sylow
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61C2×#12311yescharacteristic
303C22×C61D4211yescharacteristic
304C22×C61#54711yescharacteristic
305C22×C61C2×#13711yescharacteristic
306C22×C61#57511yescharacteristic
307C22×C61#57711yescharacteristic
308C22×C61#57711yescharacteristic
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C4×C61—22no—
317C4×C61—81no—
318C4×C61—81no—
319C4×C61—81no—
320C4×C61—81no—
321C4×C61#52511yescharacteristic
322C4×C61#53911yescharacteristic
323C4×C61#54811yescharacteristic
324C4×C61#55311yescharacteristic
325Dic61—22no—
326Dic61—41no—
327Dic61—41no—
328Dic61—42no—
329Dic61—42no—
330Dic61—81no—
331Dic61—81no—
332C2×#485—611no—
333C2×#428—611no—
334#2417—611no—
335#2354—611no—
336#2096—611no—
337#2084—611no—
338#2077—611no—
339#2035—611no—
340#1928—611no—
341#1921—611no—
342#1894D6111yescharacteristic, complemented
343#1873—611no—
344#1870—611no—
345#1854—611no—
346#1853—611no—
347C2×C61—42no—
348C2×C61#244311yescharacteristic
349C2×C61#309511yescharacteristic
350C2×C61#309911yescharacteristic
351C2×C61#326711yescharacteristic
352C2×C61#327811yescharacteristic
353C2×C61#334811yescharacteristic
354C2×C61#335611yescharacteristic
355D61—81no—
356C22×M16C2×D6111yescharacteristic
357C2×C22⋊Q8—611no—
358C2×C22⋊Q8C2×D6111yescharacteristic
359C2×C4×D4—611no—
360C2×#117—611no—
361C2×#117—611no—
362C22×C4⋊C4—611no—
363#485—1224no—
364#428—1224no—
365C2×#107—611no—
366C2×#107—611no—
367C2×#106—611no—
368C2×#106—611no—
369C2×#106—611no—
370C2×#106—611no—
371C2×#103—611no—
372C2×#103—611no—
373C2×#103C2×D6111yescharacteristic
374C2×#103C2×D6111yescharacteristic
375C2×C22⋊C8—611no—
376C2×C22⋊C8—611no—
377C2×C22⋊C8—611no—
378#398—1221no—
379#396—1221no—
380#391—611no—
381#390—1221no—
382#389—611no—
383#388—1221no—
384#388—1221no—
385#386—1221no—
386#384—611no—
387#380—611no—
388#380—611no—
389#380—1221no—
390#380C2×D6111yescharacteristic
391C4×C4⋊C4—611no—
392C4×C4⋊C4—1221no—
393#340—611no—
394#340—611no—
395#340—611no—
396#340—611no—
397#340C2×D6111yescharacteristic
398#340C2×D6111yescharacteristic
399#336—611no—
400#336—611no—
401C61#2615511yescharacteristic, complemented, Sylow
402C22×Q8C22×D6111yescharacteristic
403C22×D4—611no—
404C23×C4—611no—
405C23×C4—1221no—
406C23×C4C22×D6111yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C22×C8—611no—
411C22×C8—611no—
412C22×C8C22×D6111yescharacteristic
413C22×C8C22×D6111yescharacteristic
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—1222no—
417C22⋊Q8—2441no—
418C4×D4—1222no—
419C4×D4—1222no—
420#117—1222no—
421#117—1222no—
422#117—2441no—
423#117—2441no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—1222no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—2441no—
437C2×C4⋊C4C22×D6111yescharacteristic
438C2×C4⋊C4C22×D6111yescharacteristic
439C2×C4⋊C4C22×D6111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—611no—
443C2×C22⋊C4—611no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C42—611no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42—1221no—
453#107—614no—
454#107—1222no—
455#106—1222no—
456#106—1222no—
457#106—1222no—
458#106—2441no—
459#103—22no—
460#103—22no—
461#103—1222no—
462#103—2441no—
463C22⋊C8—1222no—
464C22⋊C8—1222no—
465C22⋊C8—1222no—
466#95—21no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473C24—611no—
474C24D4×D6111yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—2441no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—4881no—
506C22×C4—2442no—
507C22×C4—2442no—
508C22×C4#1175822212yes—
509C22×C4D4×D6111yescharacteristic
510C22×C4#1175822412yes—
511C22×C4C23×D6111yescharacteristic
512M16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8D4×D6112yes—
524C2×C8#1175822412yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—612no—
533C4⋊C4—612no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1222no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—4881no—
542C4⋊C4—4881no—
543C4⋊C4—2442no—
544C4⋊C4—2442no—
545C4⋊C4—2442no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C22⋊C4—4881no—
551C22⋊C4—4881no—
552C22⋊C4—2442no—
553C22⋊C4—2442no—
554C22⋊C4—2442no—
555C42—1221no—
556C42—1221no—
557C42—2442no—
558C42—2442no—
559C42—2442no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23—1221no—
573C23#1451975912yes—
574C23C2×D4×D6111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—2444no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—612no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1222no—
606C2×C4—1221no—
607C2×C4—1222no—
608C2×C4—1221no—
609C2×C4—4884no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4#1451975912yes—
625C2×C4C2×D4×D6111yescharacteristic
626C2×C4C2×#1175822411yescharacteristic
627C2×C4C2×#1175822411yescharacteristic
628C2×C4C2×#1175822211yescharacteristic
629C2×C4#1451982311yescharacteristic
630C2×C4#1451982411yescharacteristic
631C8—22no—
632C8—22no—
633C8—2441no—
634C8—2441no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22—2441no—
648C22—2441no—
649C22C2×#1451975911yescharacteristic
650C22#1684039611yescharacteristic
651C22#1684041211yescharacteristic
652C22#137×D6111yescharacteristic
653C22#1684056111yescharacteristic
654C22#1684057111yescharacteristic
655C22#1684057211yescharacteristic
656C4—22no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—1222no—
662C4—4881no—
663C4—4881no—
664C4—2441no—
665C4—2441no—
666C4—2442no—
667C4—2442no—
668C4#1684026811yescharacteristic
669C4#1684035611yescharacteristic
670C4#1684042111yescharacteristic
671C4#1684045811yescharacteristic
672C2—42no—
673C2—4881no—
674C2#2144956011yescharacteristic
675C2#2145576511yescharacteristic
676C2#2145580711yescharacteristic
677C2#2145735111yescharacteristic
678C2#2145748211yescharacteristic
679C2#2145832911yescharacteristic
680C2#2145842911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1894C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1894D61
hypocenterC61#26155
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
1. C2×#16840102C2semidirect
2. C2×#16839804C2semidirect
5. #21447360C2semidirect
6. #21447299C2semidirect
7. #21447254C2semidirect
8. #21447014C2semidirect
9. #21446462C2semidirect
10. #21446410C2semidirect
11. #21446132C2semidirect
13. #21446021C2semidirect
14. #21446011C2semidirect
15. C61×#1894C2semidirect
98. #14519711D4semidirect
342. #1894D61semidirect
401. C61#26155semidirect

Maximal subgroups

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

subgroupindex
C2×#168401022
C2×#168398042
#214492712
#214487632
#214473602
#214472992
#214472542
#214470142
#214464622
#214464102
#214461322
#214461162
#214460212
#214460112
C61×#18942
#2615561