Finite Group Databasebeta

← #30616391

Subgroups — #30616391

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462278C211yesmaximal, characteristic, complemented
2#21462276C211yesmaximal, characteristic
3#21461969C212yesmaximal
4#21461925C212yesmaximal, complemented
5#21461911C212yesmaximal
6#21461910C212yesmaximal, complemented
7C4×#14519846C211yesmaximal, characteristic, complemented
8C4×#14519840C211yesmaximal, characteristic, complemented
9C4×#14519839C211yesmaximal, characteristic
10C4×#14519831C211yesmaximal, characteristic, complemented
11C4×SD16×D61C211yesmaximal, characteristic
12C2×#14519856—21no—
13C2×#14519846C2212yes—
14C2×#14519840C2212yes—
15C2×#14519839C2212yes—
16C2×#14519831C2212yes—
17C2×#14519831C2212yes—
18C4×D61⋊C8C2211yescharacteristic
19(C2×#6923)⋊Q8C2212yes—
20#16840714C2212yes—
21#16840713C2212yes—
22#16840713C2212yes—
23#16840712—22no—
24#16840711—22no—
25C4×C4⋊#6923—21no—
26C4×C4⋊#6923C2211yescharacteristic
27C4×C4⋊#6923C2211yescharacteristic
28C4×C22⋊#6923—21no—
29#16840698—21no—
30C42×#6923C2211yescharacteristic
31#16840636C2212yes—
32#16840635C2212yes—
33#16840635C2212yes—
34C2×SD16×D61C2211yescharacteristic
35C4×Q8×D61C2211yescharacteristic
36C4×D4×D61C2211yescharacteristic
37#16839853C411yescharacteristic, complemented
38C4×#11758190C411yescharacteristic, complemented
39SD16×Dic61C411yescharacteristic, complemented
40C4×#11758201C411yescharacteristic, complemented
41#16839849C411yescharacteristic, complemented
42C4×#11758200C411yescharacteristic, complemented
43#16839847C411yescharacteristic, complemented
44#106×D61C2211yescharacteristic
45#103×D61C2211yescharacteristic
46#102×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×SD16×C61C411yescharacteristic, complemented
49C2×D61⋊C8C2312yes—
50#14519856—44no—
51C2×C4⋊#6923—22no—
52C2×C4⋊#6923—22no—
53C2×C4⋊#6923C2312yes—
54C2×C4⋊#6923C2312yes—
55C2×C22⋊#6923—22no—
56C2×C22⋊#6923—22no—
57C2×C4×#6923—21no—
58C2×C4×#6923—21no—
59C2×C4×#6923D411yescharacteristic
60C2×C4×#6923D411yescharacteristic
61C2×C4×#6923D412yes—
62C2×C4×#6923C2312yes—
63#14519846—24no—
64#14519840—24no—
65#14519839—24no—
66#14519831—24no—
67#14519831—24no—
68C4×#92420—21no—
69C4×#92420—21no—
70(C2×#6923)⋊C4—22no—
71(C2×#6923)⋊C4—22no—
72(C2×#6923)⋊C4—22no—
73(C2×#6923)⋊C4—22no—
74(C2×#6923)⋊C4—21no—
75(C2×#6923)⋊C4—21no—
76C2×Q8×D61C2311yescharacteristic
77C2×D4×D61C2311yescharacteristic
78C22×C4×D61—21no—
79C2×#11758190C2×C411yescharacteristic
80C2×#11758200C2×C411yescharacteristic
81C2×#11758201C2×C411yescharacteristic
82SD16×D61—24no—
83C2×C8×D61C2311yescharacteristic
84C2×C8×D61C2311yescharacteristic
85Q8×Dic61C2×C411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122C2×C411yescharacteristic
88#14519742—21no—
89#14519742C2×C411yescharacteristic
90C4×D244C2×C411yescharacteristic
91D4×Dic61C2×C411yescharacteristic
92#14519739C2×C411yescharacteristic
93C4×C22⋊D61—21no—
94#14519737—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61C2311yescharacteristic
97C4⋊C4×D61C2311yescharacteristic
98C22⋊C4×D61—21no—
99C42×D61—21no—
100C42×D61C2311yescharacteristic
101#14519709C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103#14519708C2×C411yescharacteristic
104#14519702C2×C411yescharacteristic
105#14519701C2×C411yescharacteristic
106#14519700C2×C411yescharacteristic
107#14519699C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic
109#14519697C2×C411yescharacteristic
110C4×#92418C2×C411yescharacteristic
111C8×Dic61C2×C411yescharacteristic
112C8×Dic61C2×C411yescharacteristic
113C2×SD16×C61C2×C411yescharacteristic
114C4×Q8×C61C2×C411yescharacteristic
115C4×D4×C61C2×C411yescharacteristic
116#106×C61C2×C411yescharacteristic
117#103×C61C2×C411yescharacteristic
118#102×C61C2×C411yescharacteristic
119C4×C8×C61C2×C411yescharacteristic
120C23×D61—21no—
121C22×#6923—22no—
122C22×#6923—22no—
123C22×#6923C2×D412yes—
124C22×#6923C2×D412yes—
125C2×Q8×C61C22×C411yescharacteristic
126C2×D4×C61C22×C411yescharacteristic
127C22×C4×C61—21no—
128C2×C22⋊D61—21no—
129C22×Dic61—21no—
130Q8×D61—22no—
131Q8×D61—22no—
132D4×D61—22no—
133D4×D61—22no—
134C2×D244C22×C411yescharacteristic
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—42no—
141C2×C4×D61—42no—
142C2×C4×D61C2×D411yescharacteristic
143C2×C4×D61C2×D411yescharacteristic
144C2×C4×D61C2411yescharacteristic
145C2×Dic122—21no—
146C2×Dic122C22×C411yescharacteristic
147C22⋊#6923—44no—
148C22⋊#6923—44no—
149C2×#92420—22no—
150C4⋊#6923—22no—
151C4⋊#6923—22no—
152C4⋊#6923—22no—
153C4⋊#6923—22no—
154C4⋊#6923—44no—
155C4⋊#6923—44no—
156C4×#6923—22no—
157C4×#6923—22no—
158C4×#6923—22no—
159C4×#6923—22no—
160C4×#6923—42no—
161C4×#6923—42no—
162C4×#6923—42no—
163D61⋊C8—22no—
164D61⋊C8#4114yes—
165SD16×C61—22no—
166C2×C8×C61C22×C411yescharacteristic
167C2×C8×C61C22×C411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61C22×C411yescharacteristic
170C4⋊C4×C61C22×C411yescharacteristic
171C22⋊C4×C61—21no—
172C42×C61—21no—
173C42×C61C22×C411yescharacteristic
174C22⋊Dic61—21no—
175#11758201—22no—
176#11758200—22no—
177#11758198—21no—
178#11758198—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61C22×C411yescharacteristic
181C4⋊Dic61C22×C411yescharacteristic
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186C4×Dic61—21no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61C22×C411yescharacteristic
190C4×Dic61#4111yescharacteristic
191C4×Dic61#4111yescharacteristic
192C2×#92418C22×C411yescharacteristic
193C2×#92418C22×C411yescharacteristic
194#11758190—22no—
195C8×D61—22no—
196C8×D61#4114yes—
197C23×C61—21no—
198C22×D61—21no—
199C22×D61—42no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—42no—
203C22×D61C22×D411yescharacteristic
204C2×#6923—22no—
205C2×#6923—22no—
206C2×#6923—22no—
207C2×#6923—22no—
208C2×#6923—22no—
209C2×#6923—22no—
210C2×#6923—42no—
211C2×#6923—42no—
212C2×#6923—42no—
213C2×#6923—42no—
214C2×#6923—42no—
215C2×#6923—42no—
216Q8×C61—21no—
217Q8×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—42no—
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C22⋊D61—42no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—42no—
232C2×Dic61C4×D411yescharacteristic
233C2×Dic61C4×D411yescharacteristic
234C2×Dic61C2×#4111yescharacteristic
235D244—21no—
236D244—21no—
237C4×D61—22no—
238C4×D61—42no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—42no—
242C4×D61—42no—
243C4×D61—42no—
244C4×D61AGL(1,ℤ/8)12yes—
245C4×D61#13712yes—
246C4×D61C2×#4112yes—
247C4×D61C2×#4112yes—
248Dic122—21no—
249Dic122—21no—
250Dic122—42no—
251#92420—24no—
252C8×C61—21no—
253C8×C61#11712yescomplemented
254#92418—21no—
255#92418#11712yescomplemented
256#21279—611nomaximal, Sylow
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61C2×C4×D411yescharacteristic
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—41no—
264C2×D61—82no—
265C2×D61—82no—
266C2×D61#53212yes—
267C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
268C2×D61C2×#13711yescharacteristic
269C2×D61#57512yes—
270#6923—42no—
271#6923—42no—
272#6923—82no—
273#6923—82no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61#44012yes—
279C4×C61C2×#11711yescharacteristic
280C4×C61C4×#4111yescharacteristic
281Dic61—21no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285Dic61#44012yes—
286Dic61#52912yes—
287C2×C4×SD16—611no—
288#2295—611no—
289#2293—611no—
290#1973—612no—
291#1944—612no—
292#1936—612no—
293#1935—612no—
294C4×#107—611no—
295C4×#103—611no—
296C4×#102—611no—
297C4×#97—611no—
298C2×C61—81no—
299C2×C61#229311yescharacteristic
300C2×C61C2×#44011yescharacteristic
301C2×C61#294311yescharacteristic
302D61—81no—
303D61#317112yes—
304D61#317212yes—
305C22×SD16—611no—
306C2×C4×Q8—611no—
307C2×C4×D4—611no—
308C2×#117—1221no—
309C4×SD16—611no—
310C4×SD16—611no—
311C4×SD16—611no—
312C4×SD16—611no—
313C4×SD16—611no—
314C4×SD16—611no—
315C4×SD16—611no—
316C4×SD16#692311yescharacteristic, complemented
317C2×#107—612no—
318C2×#106—611no—
319C2×#103—611no—
320C2×#103—612no—
321C2×#102—611no—
322C2×#102—612no—
323C2×#97—612no—
324C2×#97—612no—
325C2×C4×C8—611no—
326C2×C4×C8—611no—
327#391—612no—
328#390—612no—
329#389—612no—
330#389—612no—
331#388—1222no—
332#387—1222no—
333C4×C4⋊C4—611no—
334C4×C4⋊C4—611no—
335C4×C4⋊C4—1221no—
336C4×C22⋊C4—1221no—
337#376—1221no—
338C43—611no—
339#340—612no—
340#340—612no—
341#340—612no—
342C61#2127911yescharacteristic, complemented, Sylow
343C22×Q8—611no—
344C22×D4—611no—
345C23×C4—1221no—
346C2×SD16—611no—
347C2×SD16—611no—
348C2×SD16—611no—
349C2×SD16—1224no—
350C2×SD16C2×#692311yescharacteristic
351C22×C8—611no—
352C22×C8—612no—
353C22×C8—611no—
354C4×Q8—611no—
355C4×Q8—611no—
356C4×Q8—611no—
357C4×Q8—1221no—
358C4×Q8—1221no—
359C4×Q8C2×#692311yescharacteristic
360C4×D4—611no—
361C4×D4—611no—
362C4×D4—611no—
363C4×D4—1221no—
364C4×D4—1221no—
365C4×D4C2×#692311yescharacteristic
366#117—2444no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—612no—
370C2×C4⋊C4—612no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1222no—
373C2×C4⋊C4—1222no—
374C2×C22⋊C4—1221no—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—1222no—
377C2×C42—611no—
378C2×C42—611no—
379C2×C42—611no—
380C2×C42—612no—
381C2×C42—612no—
382C2×C42—1221no—
383C2×C42—1221no—
384C2×C42—1221no—
385#107—1224no—
386#106—611no—
387#106—611no—
388#106—611no—
389#106C2×#692311yescharacteristic
390#103—611no—
391#103—611no—
392#103—611no—
393#103—1224no—
394#103C2×#692311yescharacteristic
395#102—611no—
396#102—611no—
397#102—611no—
398#102—1224no—
399#102C2×#692311yescharacteristic
400#97—1224no—
401#97—1224no—
402C4×C8—611no—
403C4×C8—611no—
404C4×C8—611no—
405C4×C8—1221no—
406C4×C8—1221no—
407C4×C8C2×#692311yescharacteristic
408#95—1222no—
409#95—1222no—
410#95—1222no—
411#95—1221no—
412#95—1221no—
413#95—1222no—
414C24—1221no—
415C2×Q8—611no—
416C2×Q8—1221no—
417C2×Q8—1222no—
418C2×Q8—1222no—
419C2×Q8C22×#692311yescharacteristic
420C2×D4—611no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1221no—
424C2×D4C22×#692311yescharacteristic
425C22×C4—21no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—612no—
430C22×C4—612no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—2442no—
440C22×C4—2442no—
441SD16—22no—
442SD16—1222no—
443SD16—1222no—
444SD16—1222no—
445C2×C8—611no—
446C2×C8—614no—
447C2×C8—614no—
448C2×C8—611no—
449C2×C8—1222no—
450C2×C8—1222no—
451C2×C8—1222no—
452C2×C8C22×#692311yescharacteristic
453C2×C8C22×#692311yescharacteristic
454C4⋊C4—21no—
455C4⋊C4—611no—
456C4⋊C4—611no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—1222no—
464C4⋊C4—1222no—
465C4⋊C4—1221no—
466C4⋊C4—2444no—
467C4⋊C4—2444no—
468C4⋊C4C22×#692311yescharacteristic
469C4⋊C4C22×#692311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—2444no—
475C22⋊C4—2444no—
476C42—21no—
477C42—611no—
478C42—611no—
479C42—611no—
480C42—1221no—
481C42—1221no—
482C42—1222no—
483C42—1222no—
484C42—1222no—
485C42—1222no—
486C42—1221no—
487C42—2442no—
488C42—2442no—
489C42—2442no—
490C42C22×#692311yescharacteristic
491C23—21no—
492C23—611no—
493C23—1221no—
494C23—2441no—
495C23—2442no—
496C23—2441no—
497C23—2442no—
498Q8—21no—
499Q8—21no—
500Q8—1221no—
501Q8—1221no—
502Q8—2442no—
503D4—21no—
504D4—21no—
505D4—1221no—
506D4—1221no—
507D4—2442no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—611no—
513C2×C4—611no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—611no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—2442no—
530C2×C4—2441no—
531C2×C4—2442no—
532C2×C4—2441no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4D4×#692311yescharacteristic
543C2×C4D4×#692311yescharacteristic
544C2×C4C23×#692311yescharacteristic
545C8—21no—
546C8—612no—
547C8—1224no—
548C8—1221no—
549C8#1451985612yescomplemented
550C22—41no—
551C22—41no—
552C22—41no—
553C22—612no—
554C22—611no—
555C22—611no—
556C22—612no—
557C22—4882no—
558C22—4882no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22C2×D4×#692311yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—612no—
568C4—612no—
569C4—1221no—
570C4—4882no—
571C4—4882no—
572C4—2442no—
573C4—2442no—
574C4—2441no—
575C4—2441no—
576C4—2441no—
577C4#1684080112yes—
578C4C2×#1451985611yescharacteristic
579C4#41×#692311yescharacteristic
580C2—81no—
581C2—612no—
582C2—612no—
583C2—4881no—
584C2#2146227611yescharacteristic
585C2C2×#1684080111yescharacteristic
586C2#2146257311yescharacteristic
subgroupG/H
centerC2×C4D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×SD16×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenterC4×SD16#6923
hypocenterC61#21279
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #21462278C2semidirect
4. #21461925C2semidirect
6. #21461910C2semidirect
7. C4×#14519846C2semidirect
8. C4×#14519840C2semidirect
10. C4×#14519831C2semidirect
37. #16839853C4semidirect
38. C4×#11758190C4semidirect
39. SD16×Dic61C4semidirect
40. C4×#11758201C4semidirect
41. #16839849C4semidirect
42. C4×#11758200C4semidirect
43. #16839847C4semidirect
48. C4×SD16×C61C4semidirect
253. C8×C61#117semidirect
255. #92418#117semidirect
316. C4×SD16#6923semidirect
342. C61#21279semidirect
549. C8#14519856semidirect

Maximal subgroups

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

subgroupindex
#214622782
#214622762
#214619692
#214619252
#214619112
#214619102
C4×#145198462
C4×#145198402
C4×#145198392
C4×#145198312
C4×SD16×D612
#2127961