Finite Group Databasebeta

← #29699848

Subgroups — #29699848

Order 15616.

886 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839872C211yesmaximal, characteristic
2#21448766C211yesmaximal, characteristic, complemented
3#21446694C211yesmaximal, characteristic
4#21446684C211yesmaximal, characteristic
5#21446446C211yesmaximal, characteristic, complemented
6#21446443C211yesmaximal, characteristic, complemented
7#21446439C211yesmaximal, characteristic, complemented
8#21446436C211yesmaximal, characteristic, complemented
9#21445988C211yesmaximal, characteristic, complemented
10#21445826C211yesmaximal, characteristic, complemented
11#21445819C211yesmaximal, characteristic, complemented
12#21445717C211yesmaximal, characteristic, complemented
13C4×#14519708C211yesmaximal, characteristic, complemented
14#21445694C211yesmaximal, characteristic, complemented
15C61×#2357C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519735—21no—
19#16839872C418yescomplemented
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839654—21no—
38#16839654—21no—
39#16839632C2211yescharacteristic
40#16839619—21no—
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#388—21no—
53C61×#388—21no—
54C61×#382C2211yescharacteristic
55C61×#381—21no—
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C22⋊C4×C61—21no—
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×#11758199—22no—
63C2×#11758199—22no—
64C2×#11758199C2×C414yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C4×D244—22no—
70C4×D244C2×C414yes—
71#14519735—44no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84#14519710—22no—
85#14519710—41no—
86#14519708—22no—
87#14519708—41no—
88#14519708C2×C414yes—
89C4⋊#92418—22no—
90#14519698—41no—
91#14519698—41no—
92#14519698C2×C414yes—
93#14519697—41no—
94#14519697—41no—
95#14519697C2×C414yes—
96#14519688—22no—
97#14519688C2×C414yes—
98C4×#92418—22no—
99#14519684—21no—
100#14519684—21no—
101C22×D4×C61C2311yescharacteristic
102C23×C4×C61—21no—
103C4×D4×C61—22no—
104C4×D4×C61C2×C414yes—
105C2×C4⋊C4×C61D411yescharacteristic
106C2×C4⋊C4×C61D411yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C24×C61—21no—
127C23×D61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61C22×C412yes—
134C22×C4×C61—21no—
135C22×C4×C61—24no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—81no—
139C22×C4×C61—81no—
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244C22×C412yes—
156C2×C4×D61—24no—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—41no—
166C4⋊C4×C61C22×C412yes—
167C22⋊C4×C61—24no—
168C22⋊C4×C61—42no—
169C22⋊C4×C61—42no—
170C22⋊C4×C61—81no—
171C22⋊C4×C61—81no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—81no—
177C42×C61—81no—
178C42×C61C22×C412yes—
179C42×C61#4112yes—
180#11758199—28no—
181#11758198—24no—
182#11758198—42no—
183#11758198—42no—
184#11758198—81no—
185#11758198—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—42no—
192C4⋊Dic61—81no—
193C4⋊Dic61C22×C412yes—
194C4×Dic61—42no—
195C4×Dic61—42no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C22×C412yes—
205C2×#92418C22×C412yes—
206C2×#92418#4112yes—
207C2×#92418#4112yes—
208C23×C61—22no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61C22×D411yescharacteristic
216C22×D61—22no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223D4×C61—22no—
224D4×C61—22no—
225D4×C61—41no—
226D4×C61—41no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—22no—
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—21no—
243C2×C4×C61—41no—
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—84no—
252C2×C4×C61C4×D412yes—
253C2×C4×C61C4×D412yes—
254C2×C4×C61AGL(1,ℤ/8)12yes—
255C2×C4×C61C23×C411yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C2×C4×C612−1+411yescharacteristic
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270D244—22no—
271D244—22no—
272D244—41no—
273D244—41no—
274C4×D61—48no—
275#92418—22no—
276#92418—41no—
277#92418—41no—
278#92418#11714yescomplemented
279#22817—611nomaximal, Sylow
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61C2×C4×D411yescharacteristic
288C22×C61#54711yescharacteristic
289C22×C61#55011yescharacteristic
290C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C61#57511yescharacteristic
292C22×C61#57611yescharacteristic
293C22×C61#57711yescharacteristic
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C2×D61—81no—
301C4×C61—22no—
302C4×C61—22no—
303C4×C61—22no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—41no—
307C4×C61—42no—
308C4×C61—81no—
309C4×C61—81no—
310C4×C61C2×#11711yescharacteristic
311C4×C61#52011yescharacteristic
312C4×C61#55511yescharacteristic
313C4×C61#55611yescharacteristic
314Dic61—42no—
315Dic61—81no—
316Dic61—81no—
317C2×#442—611no—
318#2357D6111yescharacteristic, complemented
319#2354—611no—
320#1972—611no—
321#1970—611no—
322#1926—611no—
323#1926—611no—
324#1925—611no—
325#1925—611no—
326#1847—611no—
327#1804—611no—
328#1802—611no—
329#1776—611no—
330C4×#106—611no—
331#1771—611no—
332C2×C61—82no—
333C2×C61#235411yescharacteristic
334C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
335C2×C61#294611yescharacteristic
336C2×C61#334511yescharacteristic
337C2×C61#334711yescharacteristic
338C2×C61#339911yescharacteristic
339C2×C61#340111yescharacteristic
340D61—82no—
341C22×D8—611no—
342C2×C4×D4—611no—
343C2×C4×D4C2×D6111yescharacteristic
344C2×#117—1221no—
345#442—618no—
346C2×#107—611no—
347C2×#107—611no—
348C2×#106—611no—
349C2×#106—611no—
350C2×#106—611no—
351C2×C4⋊C8—611no—
352C2×#102—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102—611no—
356C2×#102—611no—
357C2×#102—611no—
358C2×#97—611no—
359C2×#97—611no—
360C2×C4×C8—611no—
361#390—611no—
362#390—611no—
363#390C2×D6111yescharacteristic
364#390C2×D6111yescharacteristic
365#388—21no—
366#388—21no—
367#388—1221no—
368#388—1221no—
369#384—611no—
370#382C2×D6111yescharacteristic
371#381—21no—
372#380—1221no—
373C4×C4⋊C4—611no—
374C4×C4⋊C4—611no—
375C4×C4⋊C4C2×D6111yescharacteristic
376C4×C4⋊C4C2×D6111yescharacteristic
377C4×C4⋊C4C2×D6111yescharacteristic
378C4×C22⋊C4—21no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#336—611no—
384#336—611no—
385C61#2281711yescharacteristic, complemented, Sylow
386C22×D4—611no—
387C22×D4C22×D6111yescharacteristic
388C23×C4—21no—
389C23×C4—1221no—
390C2×D8—614no—
391C2×D8—1222no—
392C2×D8—1222no—
393C22×C8—611no—
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—611no—
397C4×D4—22no—
398C4×D4—614no—
399C4×D4—1222no—
400C4×D4C4×D6114yes—
401#117—2444no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4C22⋊D6111yescharacteristic
408C2×C4⋊C4C22⋊D6111yescharacteristic
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—1221no—
425C2×C42—1221no—
426C2×C42C22×D6111yescharacteristic
427C2×C42C22×D6111yescharacteristic
428C2×C42C22×D6111yescharacteristic
429#107—1222no—
430#107—2441no—
431#106—614no—
432#106—1222no—
433#106—2441no—
434C4⋊C8—1222no—
435#102—614no—
436#102—614no—
437#102—2441no—
438#102—2441no—
439#102—2441no—
440#102—2441no—
441#97—614no—
442#97—1222no—
443C4×C8—1222no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—1221no—
449#95—1221no—
450#95C22⋊D6111yescharacteristic
451#95C22⋊D6111yescharacteristic
452C24—21no—
453C24—1221no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—612no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4C2×C4×D6112yes—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—81no—
471C22×C4—81no—
472C22×C4—1221no—
473C22×C4—1224no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4C2×C22⋊D6111yescharacteristic
479C22×C4C2×C22⋊D6111yescharacteristic
480C22×C4C2×C22⋊D6111yescharacteristic
481C22×C4C2×C22⋊D6111yescharacteristic
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485D8—1228no—
486C2×C8—612no—
487C2×C8—612no—
488C2×C8—612no—
489C2×C8—612no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—612no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—4881no—
512C4⋊C4—2442no—
513C4⋊C4C2×C4×D6112yes—
514C22⋊C4—24no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C22⋊C4—1224no—
520C22⋊C4—4881no—
521C22⋊C4—4881no—
522C22⋊C4—2442no—
523C22⋊C4—2442no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—81no—
529C42—81no—
530C42—2442no—
531C42—2442no—
532C42C2×C4×D6112yes—
533C42#1175822212yes—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—1222no—
542C23—2441no—
543C23—2441no—
544C23—2441no—
545C23—2441no—
546C23—2441no—
547C23—2441no—
548C23C22×C22⋊D6111yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—1222no—
554D4—1222no—
555D4—2441no—
556D4—2441no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—84no—
582C2×C4—1222no—
583C2×C4—2448no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4C4×C22⋊D6112yes—
593C2×C4C4×C22⋊D6112yes—
594C2×C4#1451980212yes—
595C2×C4C22×C4×D6111yescharacteristic
596C2×C4#41×D6111yescharacteristic
597C2×C4#41×D6111yescharacteristic
598C2×C4C2×#1175822211yescharacteristic
599C2×C4#1451982311yescharacteristic
600C2×C4#1451982411yescharacteristic
601C8—614no—
602C8—1222no—
603C8—2441no—
604C8—2441no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22—4881no—
616C22—2442no—
617C22—2442no—
618C22—2442no—
619C22C2×C4×C22⋊D6111yescharacteristic
620C22#1684041111yescharacteristic
621C22#1684043111yescharacteristic
622C22C2×#1451980211yescharacteristic
623C22#1684056011yescharacteristic
624C22#1684056511yescharacteristic
625C22#1684057311yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—4881no—
636C4—4881no—
637C4—2442no—
638C4#117×D6111yescharacteristic
639C4#1684024211yescharacteristic
640C4#1684047511yescharacteristic
641C4#1684048011yescharacteristic
642C2—82no—
643C2—4882no—
644C2#2144876911yescharacteristic
645C2C4×#1451980211yescharacteristic
646C2#2145465111yescharacteristic
647C2#2145828311yescharacteristic
648C2#2145831311yescharacteristic
649C2#2145885711yescharacteristic
650C2#2145887911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2357C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenter#2357D61
hypocenterC61#22817
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #21448766C2semidirect
5. #21446446C2semidirect
6. #21446443C2semidirect
7. #21446439C2semidirect
8. #21446436C2semidirect
9. #21445988C2semidirect
10. #21445826C2semidirect
11. #21445819C2semidirect
12. #21445717C2semidirect
13. C4×#14519708C2semidirect
14. #21445694C2semidirect
15. C61×#2357C2semidirect
19. #16839872C4semidirect
278. #92418#117semidirect
318. #2357D61semidirect
385. C61#22817semidirect

Maximal subgroups

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

subgroupindex
C2×#168398722
#214487662
#214466942
#214466842
#214464462
#214464432
#214464392
#214464362
#214459882
#214458262
#214458192
#214457172
C4×#145197082
#214456942
C61×#23572
#2281761