Finite Group Databasebeta

← #29748057

Subgroups — #29748057

Order 15616.

832 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450160C211yesmaximal, characteristic, complemented
2#21448833C211yesmaximal, characteristic
3#21447137C211yesmaximal, characteristic, complemented
4#21447002C211yesmaximal, characteristic
5#21446966C211yesmaximal, characteristic, complemented
6#21446824C211yesmaximal, characteristic
7#21446774C211yesmaximal, characteristic, complemented
8#21446495C211yesmaximal, characteristic, complemented
9#21446461C211yesmaximal, characteristic, complemented
10#21446391C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446124C211yesmaximal, characteristic, complemented
13#21445910C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×#14519737—21no—
22C22×C4⋊Dic61C2211yescharacteristic
23C2×#14519711C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30#16839703—21no—
31#16839690—21no—
32#16839668C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839654—21no—
37#16839650—21no—
38#16839639—21no—
39#16839636—21no—
40#16839626—21no—
41#16839622C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C22×C4×D61—21no—
64C2×#11758190—22no—
65C2×#11758190—41no—
66C2×#11758190—41no—
67#14519769—22no—
68#14519769—41no—
69#14519756—22no—
70#14519756—41no—
71#14519751—22no—
72#14519751—22no—
73C4×D244—22no—
74C4×D244—41no—
75#14519737—44no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—41no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97#14519711—22no—
98#14519702—22no—
99#14519702—22no—
100#14519702—41no—
101#14519699—22no—
102#14519699—22no—
103#14519699—41no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C23×C4×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C2×C22⋊C4×C61D411yescharacteristic
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C4⋊C8×C61—41no—
122C22⋊C8×C61—41no—
123C22⋊C8×C61—41no—
124C4×C8×C61—41no—
125#95×C61D411yescharacteristic
126#95×C61D411yescharacteristic
127C24×C61C2×D411yescharacteristic
128C23×D61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141C2×C22⋊D61—24no—
142C2×C22⋊D61—42no—
143C2×C22⋊D61—42no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—42no—
152C22×Dic61—42no—
153C22×Dic61—81no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244#4112yes—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61—81no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C22⋊Dic61—42no—
188C22⋊Dic61—42no—
189#11758198—24no—
190#11758198—42no—
191#11758198—42no—
192#11758198—81no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—42no—
203C4⋊Dic61#4112yes—
204C4⋊Dic61#4112yes—
205C4⋊Dic61#4112yes—
206#11758196—42no—
207#11758196—42no—
208#11758196—42no—
209#11758196—42no—
210C4×Dic61—42no—
211C4×Dic61—42no—
212#11758190—44no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61#13512yes—
220C23×C61C22×D411yescharacteristic
221C22×D61—22no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—41no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61AGL(1,ℤ/8)12yes—
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61H(5,𝔽2)11yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C22⋊D61—48no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—84no—
276D244—22no—
277D244—22no—
278D244—41no—
279D244—41no—
280C4×D61—84no—
281Dic122—41no—
282Dic122—41no—
283Dic122—41no—
284Dic122—41no—
285C8×C61—41no—
286C8×C61—41no—
287C8×C61—41no—
288C8×C61—41no—
289#26721—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61#52511yescharacteristic
298C22×C61#54611yescharacteristic
299C22×C61#54611yescharacteristic
300C22×C61C2×#13511yescharacteristic
301C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C61#57711yescharacteristic
303C22×C61#57811yescharacteristic
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—42no—
307C2×D61—81no—
308C2×D61—81no—
309C2×D61—81no—
310C2×D61—81no—
311C4×C61—22no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61#52911yescharacteristic
317C4×C61#53811yescharacteristic
318C4×C61#55511yescharacteristic
319C4×C61#55911yescharacteristic
320Dic61—42no—
321Dic61—42no—
322Dic61—42no—
323Dic61—81no—
324Dic61—81no—
325Dic61—81no—
326Dic61—81no—
327#2489—611no—
328#2361—611no—
329#2055—611no—
330#2033—611no—
331#2025—611no—
332#2000—611no—
333#1989—611no—
334#1933—611no—
335#1928—611no—
336#1923D6111yescharacteristic, complemented
337#1918—611no—
338#1877—611no—
339#1872—611no—
340#1824—611no—
341C4×#102—611no—
342C2×C61—42no—
343C2×C61#245911yescharacteristic
344C2×C61#310511yescharacteristic
345C2×C61#312011yescharacteristic
346C2×C61#330011yescharacteristic
347C2×C61#330111yescharacteristic
348C2×C61#331011yescharacteristic
349C2×C61#333011yescharacteristic
350D61—82no—
351C22×SD16—611no—
352C2×#125—611no—
353C2×C22⋊Q8—611no—
354C2×#121—611no—
355C2×C4×D4—611no—
356C2×C4×D4—1221no—
357C22×C4⋊C4—611no—
358C2×#107—611no—
359C2×C4⋊C8C2×D6111yescharacteristic
360C2×#103—611no—
361C2×#103—611no—
362C2×#103—611no—
363C2×#102—611no—
364C2×#102—611no—
365C2×#102—611no—
366C2×C22⋊C8C2×D6111yescharacteristic
367C2×C22⋊C8C2×D6111yescharacteristic
368C2×C4×C8C2×D6111yescharacteristic
369#400—1221no—
370#397—1221no—
371#391—611no—
372#391—611no—
373#390—611no—
374#389—611no—
375#388—1221no—
376#388—1221no—
377#386—1221no—
378#385—1221no—
379#382—1221no—
380#380—611no—
381C4×C4⋊C4—611no—
382C4×C4⋊C4—611no—
383C4×C22⋊C4C2×D6111yescharacteristic
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340—611no—
392#336C2×D6111yescharacteristic
393#336C2×D6111yescharacteristic
394C61#2672111yescharacteristic, complemented, Sylow
395C22×Q8—611no—
396C22×D4—611no—
397C22×D4—1221no—
398C23×C4—1221no—
399C23×C4—1221no—
400C23×C4C22×D6111yescharacteristic
401C2×SD16—1222no—
402C2×SD16—2441no—
403C2×SD16—2441no—
404C22×C8C22×D6111yescharacteristic
405C22×C8C22×D6111yescharacteristic
406C22×C8C22×D6111yescharacteristic
407C22×C8C22×D6111yescharacteristic
408#125—1222no—
409#125—2441no—
410C22⋊Q8—1222no—
411C22⋊Q8—2441no—
412#121—1222no—
413#121—1222no—
414C4×D4—1222no—
415C4×D4—2441no—
416C4×D4—2444no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—2441no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4D24411yescharacteristic
437C2×C22⋊C4D24411yescharacteristic
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42C22×D6111yescharacteristic
441C2×C42C22×D6111yescharacteristic
442#107—1222no—
443C4⋊C8—41no—
444#103—1222no—
445#103—1222no—
446#103—2441no—
447#102—1222no—
448#102—1222no—
449#102—2441no—
450C22⋊C8—41no—
451C22⋊C8—41no—
452C4×C8—41no—
453#95—1221no—
454#95—1221no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460#95—1221no—
461#95D24411yescharacteristic
462#95D24411yescharacteristic
463C24—1221no—
464C24C2×D24411yescharacteristic
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×Q8—1221no—
470C2×Q8—1221no—
471C2×D4—612no—
472C2×D4—1224no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4—1221no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—2442no—
479C2×D4—2442no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—4881no—
494C22×C4—4881no—
495C22×C4—2442no—
496C22×C4—2442no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4C2×D24411yescharacteristic
500C22×C4C2×D24411yescharacteristic
501C22×C4C2×D24411yescharacteristic
502C22×C4C2×D24411yescharacteristic
503C22×C4C2×D24411yescharacteristic
504C22×C4C23×D6111yescharacteristic
505SD16—2444no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C4⋊C4—612no—
519C4⋊C4—612no—
520C4⋊C4—612no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—2442no—
531C4⋊C4—2442no—
532C4⋊C4—2442no—
533C4⋊C4—2442no—
534C4⋊C4—2442no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—1224no—
538C22⋊C4—4881no—
539C22⋊C4—2442no—
540C22⋊C4—2442no—
541C22⋊C4—2442no—
542C22⋊C4—2442no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—2442no—
548C42—2442no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—1222no—
556C23—2441no—
557C23—2441no—
558C23—2441no—
559C23—2441no—
560C23—2441no—
561C23—2441no—
562C23#1451979912yes—
563C23C22×D24411yescharacteristic
564Q8—2441no—
565Q8—2441no—
566Q8—2441no—
567Q8—2441no—
568D4—1222no—
569D4—1222no—
570D4—2448no—
571D4—2441no—
572D4—2441no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—4884no—
595C2×C4—4884no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4#1451980512yes—
615C2×C4#41×D6111yescharacteristic
616C2×C4#41×D6111yescharacteristic
617C2×C4#41×D6111yescharacteristic
618C2×C4#41×D6111yescharacteristic
619C2×C4#1451982211yescharacteristic
620C2×C4#1451982211yescharacteristic
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—4881no—
633C22—4881no—
634C22—4881no—
635C22—4881no—
636C22—2442no—
637C22—2442no—
638C22—2442no—
639C22#1684027411yescharacteristic
640C22#1684040711yescharacteristic
641C22#1684040711yescharacteristic
642C22C2×#1451979911yescharacteristic
643C22C2×#1451980511yescharacteristic
644C22#1684057411yescharacteristic
645C22#1684057911yescharacteristic
646C4—22no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—4881no—
652C4—4881no—
653C4—4881no—
654C4—4881no—
655C4—2442no—
656C4—2442no—
657C4—2442no—
658C4#1684029511yescharacteristic
659C4#1684034411yescharacteristic
660C4#1684047411yescharacteristic
661C4#1684049611yescharacteristic
662C2—42no—
663C2—4882no—
664C2#2144975411yescharacteristic
665C2#2145586811yescharacteristic
666C2#2145603511yescharacteristic
667C2#2145770811yescharacteristic
668C2#2145772311yescharacteristic
669C2#2145784211yescharacteristic
670C2#2145812511yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1923C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#1923D61
hypocenterC61#26721
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. #21450160C2semidirect
3. #21447137C2semidirect
5. #21446966C2semidirect
7. #21446774C2semidirect
8. #21446495C2semidirect
9. #21446461C2semidirect
10. #21446391C2semidirect
11. #21446152C2semidirect
12. #21446124C2semidirect
13. #21445910C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1923C2semidirect
336. #1923D61semidirect
394. C61#26721semidirect

Maximal subgroups

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

subgroupindex
#214501602
#214488332
#214471372
#214470022
#214469662
#214468242
#214467742
#214464952
#214464612
#214463912
#214461522
#214461242
#214459102
C4×#145196992
C61×#19232
#2672161