Finite Group Databasebeta

← #29582308

Subgroups — #29582308

Order 15616.

828 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839954C211yesmaximal, characteristic, complemented
2#21450732C211yesmaximal, characteristic, complemented
3#21446626C211yesmaximal, characteristic, complemented
4C2×D4⋊#92418C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×#459C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×#14519751—21no—
10C2×#14519748—21no—
11C2×C4×D244C2211yescharacteristic
12#16839954—22no—
13#16839954—22no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519698—21no—
16C2×#14519698—22no—
17C2×C4×#92418C2211yescharacteristic
18#16839678—22no—
19#16839632C2211yescharacteristic
20#16839622—21no—
21#16839619—21no—
22D4⋊#92418—22no—
23#16839489—22no—
24C22×D8×C61—21no—
25C2×#127×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#459—22no—
28C61×#459—22no—
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#102×C61—21no—
31C22×D244D411yescharacteristic
32C22×C22⋊D61—22no—
33C22×C4×D61—21no—
34C2×#11758199—24no—
35C2×#11758199—42no—
36C2×#11758199—42no—
37C22×#92418—21no—
38C22×#92418—21no—
39#14519751—42no—
40#14519751—42no—
41#14519748—42no—
42#14519748—42no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C4×D244—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61D411yescharacteristic
50C2×C4⋊Dic61D412yes—
51C2×C22⋊Dic61—22no—
52C2×#11758198—22no—
53C2×#11758198—21no—
54C4⋊#92418—21no—
55C4⋊#92418D412yescomplemented
56#14519698—24no—
57#14519698—44no—
58C4×#92418—21no—
59C4×#92418—21no—
60#14519684—22no—
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61D411yescharacteristic
65C23×C4×C61—21no—
66C2×D8×C61—24no—
67C2×D8×C61—42no—
68C2×D8×C61—42no—
69C22×C8×C61—21no—
70#127×C61—21no—
71#127×C61—21no—
72#127×C61—21no—
73#127×C61D412yescomplemented
74C4×D4×C61—21no—
75C4×D4×C61—21no—
76C4×D4×C61—21no—
77C4×D4×C61—21no—
78C2×C4⋊C4×C61D411yescharacteristic
79C2×C22⋊C4×C61—21no—
80C2×C42×C61C2311yescharacteristic
81C4⋊C8×C61—21no—
82C4⋊C8×C61D412yescomplemented
83#102×C61—24no—
84C24×C61—21no—
85C24×C61—41no—
86C23×D61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—22no—
89C2×D4×C61—22no—
90C2×D4×C61—21no—
91C2×D4×C61—22no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—42no—
96C2×D4×C61—42no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—41no—
102C2×D4×C61—41no—
103C2×D4×C61—41no—
104C2×D4×C61—41no—
105C2×D4×C61—41no—
106C2×D4×C61—41no—
107C2×D4×C61—41no—
108C2×D4×C61D812yescomplemented
109C22×C4×C61—21no—
110C22×C4×C61—41no—
111C22×C4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61—41no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61—44no—
120C2×C22⋊D61—44no—
121C2×C22⋊D61—82no—
122C22×Dic61—21no—
123C22×Dic61—22no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244—21no—
127C2×D244—21no—
128C2×D244—21no—
129C2×D244D812yescomplemented
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136D8×C61—48no—
137C2×C8×C61—22no—
138C2×C8×C61—41no—
139C2×C8×C61—41no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C22⋊C4×C61—41no—
143C22⋊C4×C61—41no—
144C42×C61C2×D411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61#4111yescharacteristic
148C22⋊Dic61—44no—
149#11758199—48no—
150#11758198—44no—
151#11758198—41no—
152#11758198—41no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—41no—
156C4⋊Dic61—41no—
157C4⋊Dic61—41no—
158C4⋊Dic61—41no—
159C4⋊Dic61—42no—
160C2×#92418—22no—
161C2×#92418—22no—
162C2×#92418—41no—
163C2×#92418—41no—
164C2×#92418—41no—
165C2×#92418—41no—
166C23×C61—22no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61—41no—
171C23×C61—41no—
172C23×C61—41no—
173C23×C61—42no—
174C23×C61—81no—
175C23×C61—81no—
176C23×C61—81no—
177C23×C61—81no—
178C23×C61—81no—
179C23×C61—81no—
180C23×C61#12011yescharacteristic
181C22×D61—22no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188D4×C61—22no—
189D4×C61—22no—
190D4×C61—44no—
191D4×C61—42no—
192D4×C61—42no—
193D4×C61—41no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—41no—
197D4×C61—82no—
198D4×C61—81no—
199D4×C61—81no—
200D4×C61—81no—
201D4×C61—81no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—81no—
208C2×C4×C61—81no—
209C2×C4×C61—81no—
210C2×C4×C61—81no—
211C2×C4×C61#12011yescharacteristic
212C2×C4×C61#12011yescharacteristic
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61#12111yescharacteristic
215C2×C4×C61#12111yescharacteristic
216C2×C4×C61#12711yescharacteristic
217C2×C4×C61C2×D811yescharacteristic
218C2×C4×C61C2×D811yescharacteristic
219C2×C4×C61#13511yescharacteristic
220C2×C4×C61#13511yescharacteristic
221C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
222C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
223C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
224C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
225C22⋊D61—88no—
226C2×Dic61—41no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—42no—
232D244—22no—
233D244—22no—
234D244—41no—
235D244—41no—
236C4×D61—81no—
237C4×D61—81no—
238C4×D61—81no—
239C4×D61—81no—
240C8×C61—42no—
241#92418—42no—
242#92418—42no—
243#10228—611nomaximal, Sylow
244C22×C61—42no—
245C22×C61—42no—
246C22×C61—42no—
247C22×C61—81no—
248C22×C61—81no—
249C22×C61—81no—
250C22×C61—81no—
251C22×C61—82no—
252C22×C61—82no—
253C22×C61—82no—
254C22×C61—161no—
255C22×C61—161no—
256C22×C61—161no—
257C22×C61—161no—
258C22×C61#39211yescharacteristic
259C22×C61#44711yescharacteristic
260C22×C61#44711yescharacteristic
261C22×C61#44911yescharacteristic
262C22×C61#44911yescharacteristic
263C22×C61#45311yescharacteristic
264C22×C61#45411yescharacteristic
265C2×D61—42no—
266C2×D61—42no—
267C2×D61—42no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—81no—
275C4×C61#44711yescharacteristic
276C4×C61#44711yescharacteristic
277C4×C61#44911yescharacteristic
278C4×C61#44911yescharacteristic
279C4×C61#46611yescharacteristic
280C4×C61#46611yescharacteristic
281C4×C61#46911yescharacteristic
282C4×C61#46911yescharacteristic
283Dic61—82no—
284Dic61—81no—
285C2×#459—611no—
286C2×#459D6111yescharacteristic, complemented
287#2537—611no—
288#1957—611no—
289C2×D4⋊C8—611no—
290C2×D4⋊C8—611no—
291#1296—611no—
292C2×C61—82no—
293C2×C61—162no—
294C2×C61#161911yescharacteristic
295C2×C61#162411yescharacteristic
296C2×C61#162511yescharacteristic
297C2×C61#162511yescharacteristic
298C2×C61#199911yescharacteristic
299C2×C61#199911yescharacteristic
300C2×C61#200611yescharacteristic
301D61—82no—
302C22×D8—21no—
303C22×D8—1221no—
304C2×#127C2×D6111yescharacteristic
305C2×#121—1221no—
306C2×#121—1221no—
307C2×C4×D4—611no—
308C2×C4×D4C2×D6111yescharacteristic
309#459—22no—
310#459—22no—
311#459—1222no—
312#459—1222no—
313C2×C4⋊C8—611no—
314C2×C4⋊C8C2×D6111yescharacteristic
315C2×#102—21no—
316C2×#102—1221no—
317C2×#102—1222no—
318C2×C4×C8—611no—
319#394—1222no—
320#384—611no—
321#380—1221no—
322#380—1221no—
323D4⋊C8—1222no—
324D4⋊C8—1222no—
325C61#1022811yescharacteristic, complemented, Sylow
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—611no—
330C22×D4—1222no—
331C22×D4C22⋊D6111yescharacteristic
332C23×C4—21no—
333C23×C4—1221no—
334C2×D8—24no—
335C2×D8—42no—
336C2×D8—42no—
337C2×D8—1224no—
338C2×D8—2442no—
339C2×D8—2442no—
340C22×C8—21no—
341C22×C8—1221no—
342C22×C8—1221no—
343#127—21no—
344#127—21no—
345#127—21no—
346#127C22⋊D6112yescomplemented
347#121—2442no—
348#121—2442no—
349#121—2442no—
350#121—2442no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—1221no—
356C4×D4—1221no—
357C4×D4—1221no—
358C4×D4—1221no—
359C2×C4⋊C4—611no—
360C2×C4⋊C4—612no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4C22⋊D6111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—1222no—
366C2×C22⋊C4—1222no—
367C2×C22⋊C4—1221no—
368C2×C42C22×D6111yescharacteristic
369C4⋊C8—21no—
370C4⋊C8—612no—
371C4⋊C8—1221no—
372C4⋊C8C22⋊D6112yescomplemented
373#102—24no—
374#102—1224no—
375#102—2444no—
376C4×C8—1221no—
377C4×C8—1221no—
378#95—1222no—
379C24—21no—
380C24—41no—
381C24—1221no—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—612no—
404C2×D4—1221no—
405C2×D4—1221no—
406C2×D4—1221no—
407C2×D4—1221no—
408C2×D4—1221no—
409C2×D4—4882no—
410C2×D4—2444no—
411C2×D4—2444no—
412C2×D4#1175819912yescomplemented
413C22×C4—21no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—1221no—
421C22×C4—1222no—
422C22×C4—2441no—
423C22×C4—2441no—
424C22×C4—2441no—
425C22×C4—2441no—
426C22×C4—2441no—
427C22×C4—2441no—
428C22×C4D4×D6111yescharacteristic
429C22×C4D4×D6111yescharacteristic
430C22×C4C2×C22⋊D6111yescharacteristic
431D8—48no—
432D8—2448no—
433C2×C8—22no—
434C2×C8—41no—
435C2×C8—41no—
436C2×C8—1222no—
437C2×C8—1222no—
438C2×C8—2441no—
439C2×C8—2441no—
440C2×C8—2441no—
441C2×C8—2441no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—1221no—
445C4⋊C4—1221no—
446C4⋊C4—2442no—
447C4⋊C4—2441no—
448C4⋊C4—2441no—
449C4⋊C4—2441no—
450C4⋊C4—2441no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—2444no—
454C22⋊C4—2444no—
455C22⋊C4—2441no—
456C22⋊C4—2441no—
457C42D4×D6111yescharacteristic
458C42#1175822411yescharacteristic
459C42C2×C22⋊D6111yescharacteristic
460C42C2×C22⋊D6111yescharacteristic
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—81no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—1222no—
476C23—2441no—
477C23—2441no—
478C23—2441no—
479C23—2441no—
480C23—2441no—
481C23—2441no—
482C23#1451974511yescharacteristic
483D4—22no—
484D4—22no—
485D4—44no—
486D4—41no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—41no—
491D4—42no—
492D4—82no—
493D4—81no—
494D4—81no—
495D4—81no—
496D4—81no—
497D4—1222no—
498D4—1222no—
499D4—4888no—
500D4—2441no—
501D4—2441no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—4881no—
512C2×C4—4881no—
513C2×C4—4881no—
514C2×C4—4881no—
515C2×C4—2442no—
516C2×C4—2441no—
517C2×C4—2442no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2442no—
521C2×C4#1451974511yescharacteristic
522C2×C4#1451974611yescharacteristic
523C2×C4#1451974811yescharacteristic
524C2×C4#1451974911yescharacteristic
525C2×C4#1451974911yescharacteristic
526C2×C4#1451977311yescharacteristic
527C2×C4D8×D6111yescharacteristic
528C2×C4C2×#1175819911yescharacteristic
529C2×C4#1451979611yescharacteristic
530C2×C4#1451979711yescharacteristic
531C2×C4#1451980111yescharacteristic
532C2×C4#1451980111yescharacteristic
533C2×C4#1451980211yescharacteristic
534C2×C4#1451980311yescharacteristic
535C8—42no—
536C8—2442no—
537C8—2442no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—82no—
546C22—82no—
547C22—82no—
548C22—161no—
549C22—161no—
550C22—161no—
551C22—161no—
552C22—4881no—
553C22—4881no—
554C22—4881no—
555C22—4881no—
556C22—2442no—
557C22—2442no—
558C22—2442no—
559C22#1683967011yescharacteristic
560C22#1683989411yescharacteristic
561C22#1683989511yescharacteristic
562C22#1683990411yescharacteristic
563C22#1683990511yescharacteristic
564C22#1683992811yescharacteristic
565C22#1683993311yescharacteristic
566C4—21no—
567C4—21no—
568C4—81no—
569C4—4882no—
570C4—4881no—
571C4#1683989411yescharacteristic
572C4#1683989611yescharacteristic
573C4#1683990411yescharacteristic
574C4#1683990711yescharacteristic
575C4#1683999511yescharacteristic
576C4#1683999611yescharacteristic
577C4#1684001211yescharacteristic
578C4#1684001311yescharacteristic
579C2—82no—
580C2—162no—
581C2—4882no—
582C2#2144487211yescharacteristic
583C2#2144490111yescharacteristic
584C2#2144490611yescharacteristic
585C2#2144490711yescharacteristic
586C2#2144681411yescharacteristic
587C2#2144681511yescharacteristic
588C2#2144685911yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#459C2
socleC23×C61#120
hypercenterC2×#459D61
hypocenterC61#10228
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16839954C2semidirect
2. #21450732C2semidirect
3. #21446626C2semidirect
4. C2×D4⋊#92418C2semidirect
5. C2×#16839489C2semidirect
6. #21443703C2semidirect
7. C2×C61×#459C2semidirect
55. C4⋊#92418D4semidirect
73. #127×C61D4semidirect
82. C4⋊C8×C61D4semidirect
108. C2×D4×C61D8semidirect
129. C2×D244D8semidirect
286. C2×#459D61semidirect
325. C61#10228semidirect
346. #127C22⋊D61semidirect
372. C4⋊C8C22⋊D61semidirect
412. C2×D4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
#214507322
#214466262
C2×D4⋊#924182
C2×#168394892
#214437032
C2×C61×#4592
#1022861