Finite Group Databasebeta

← #30616065

Subgroups — #30616065

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462276C211yesmaximal, characteristic
2C4×Q8×#6923C211yesmaximal, characteristic, complemented
3#21461896C212yesmaximal
4#21461882C212yesmaximal, complemented
5#21461815C212yesmaximal
6#21461783C212yesmaximal, complemented
7C4×#14519846C211yesmaximal, characteristic, complemented
8C4×#14519840C211yesmaximal, characteristic, complemented
9C4×#14519839C211yesmaximal, characteristic
10#21461532C211yesmaximal, characteristic, complemented
11C4×SD16×D61C211yesmaximal, characteristic
12C2×Q8×#6923C2212yes—
13C2×#14519856—21no—
14C2×#14519846C2212yes—
15C2×#14519840C2212yes—
16C2×#14519839C2212yes—
17C4×D61⋊C8C2211yescharacteristic
18#16840714C2212yes—
19#16840713C2212yes—
20#16840712—22no—
21C4⋊C4×#6923—22no—
22C4⋊C4×#6923C2212yes—
23C4×C4⋊#6923—21no—
24C4×C4⋊#6923C2211yescharacteristic
25C4×C4⋊#6923C2211yescharacteristic
26C4×C22⋊#6923—21no—
27C42×#6923—21no—
28C42×#6923C2211yescharacteristic
29#16840636C2212yes—
30#16840635C2212yes—
31#16840635C2212yes—
32(C2×#6923)⋊C8C2212yes—
33(C2×#6923)⋊C8C2212yes—
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—
50Q8×#6923—24no—
51Q8×#6923—24no—
52#14519856—44no—
53C2×C4⋊#6923—22no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923C2312yes—
56C2×C4⋊#6923C2312yes—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923—22no—
61C2×C4×#6923—21no—
62C2×C4×#6923—21no—
63C2×C4×#6923D412yes—
64C2×C4×#6923D411yescharacteristic
65C2×C4×#6923D411yescharacteristic
66C2×C4×#6923C2312yes—
67#14519846—24no—
68#14519840—24no—
69#14519839—24no—
70C4×#92420—21no—
71C4×#92420—21no—
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#4114yes—
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—28no—
151C4⋊#6923—22no—
152C4⋊#6923—22no—
153C4⋊#6923—22no—
154C4⋊#6923—44no—
155C4⋊#6923#4114yes—
156C4×#6923—28no—
157C4×#6923—24no—
158C4×#6923—22no—
159C4×#6923—22no—
160C4×#6923—22no—
161C4×#6923—22no—
162C4×#6923—44no—
163C4×#6923—42no—
164C4×#6923—42no—
165D61⋊C8—22no—
166D61⋊C8—22no—
167SD16×C61—22no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C42×C61—21no—
175C42×C61C22×C411yescharacteristic
176C22⋊Dic61—21no—
177#11758201—22no—
178#11758200—22no—
179#11758198—21no—
180#11758198—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61C22×C411yescharacteristic
183C4⋊Dic61C22×C411yescharacteristic
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61C22×C411yescharacteristic
192C4×Dic61#4111yescharacteristic
193C4×Dic61#4111yescharacteristic
194C2×#92418C22×C411yescharacteristic
195C2×#92418C22×C411yescharacteristic
196#11758190—22no—
197C8×D61—22no—
198C8×D61—22no—
199C23×C61—21no—
200C22×D61—21no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61C22×D411yescharacteristic
206C2×#6923—22no—
207C2×#6923—22no—
208C2×#6923—22no—
209C2×#6923—24no—
210C2×#6923—22no—
211C2×#6923—22no—
212C2×#6923—42no—
213C2×#6923—42no—
214C2×#6923—42no—
215C2×#6923—42no—
216C2×#6923—42no—
217C2×#6923#13514yes—
218Q8×C61—21no—
219Q8×C61#11712yescomplemented
220D4×C61—21no—
221D4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—42no—
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C22⋊D61—42no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—42no—
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C2×#4111yescharacteristic
237D244—21no—
238D244—21no—
239C4×D61—24no—
240C4×D61—22no—
241C4×D61—42no—
242C4×D61—41no—
243C4×D61—41no—
244C4×D61—42no—
245C4×D61—42no—
246C4×D61AGL(1,ℤ/8)12yes—
247C4×D61#13712yes—
248C4×D61C2×#4112yes—
249C4×D61C2×#4112yes—
250Dic122—21no—
251Dic122—24no—
252Dic122#11712yescomplemented
253#92420—42no—
254C8×C61—21no—
255C8×C61—21no—
256#92418—21no—
257#92418—21no—
258#21120—611nomaximal, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61C2×C4×D411yescharacteristic
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—82no—
267C2×D61—82no—
268C2×D61#52512yes—
269C2×D61C2×#13512yes—
270C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
271C2×D61C2×#13711yescharacteristic
272#6923—24no—
273#6923—42no—
274#6923—44no—
275#6923—82no—
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61#44012yes—
281C4×C61C2×#11711yescharacteristic
282C4×C61C4×#4111yescharacteristic
283Dic61—21no—
284Dic61—22no—
285Dic61—41no—
286Dic61—41no—
287Dic61#44012yes—
288Dic61#52912yes—
289C2×C4×SD16—611no—
290#2293—611no—
291C42×Q8—611no—
292#1925—612no—
293#1920—612no—
294#1880—612no—
295#1863—612no—
296C4×#107—611no—
297C4×#103—611no—
298C4×#102—611no—
299#1744—611no—
300C2×C61—81no—
301C2×C61#229011yescharacteristic
302C2×C61C4×#13511yescharacteristic
303C2×C61C2×#44011yescharacteristic
304D61—81no—
305D61#310612yes—
306D61#310812yes—
307C22×SD16—611no—
308C2×C4×Q8—611no—
309C2×C4×Q8—612no—
310C2×C4×D4—611no—
311C2×#117—1221no—
312C4×SD16—611no—
313C4×SD16—611no—
314C4×SD16—611no—
315C4×SD16—611no—
316C4×SD16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319C4×SD16#692311yescharacteristic, complemented
320C2×#107—612no—
321C2×#106—611no—
322C2×#103—611no—
323C2×#103—612no—
324C2×#102—611no—
325C2×#102—612no—
326C2×C4×C8—611no—
327C2×C4×C8—611no—
328#390—612no—
329#389—612no—
330#388—1222no—
331C4×C4⋊C4—612no—
332C4×C4⋊C4—611no—
333C4×C4⋊C4—611no—
334C4×C4⋊C4—1221no—
335C4×C4⋊C4—1222no—
336C4×C22⋊C4—1221no—
337C43—611no—
338C43—1221no—
339#340—612no—
340#340—612no—
341#340—612no—
342#336—612no—
343#336—612no—
344C61#2112011yescharacteristic, complemented, Sylow
345C22×Q8—611no—
346C22×D4—611no—
347C23×C4—1221no—
348C2×SD16—611no—
349C2×SD16—611no—
350C2×SD16—611no—
351C2×SD16—1224no—
352C2×SD16C2×#692311yescharacteristic
353C22×C8—611no—
354C22×C8—611no—
355C22×C8—612no—
356C4×Q8—611no—
357C4×Q8—611no—
358C4×Q8—611no—
359C4×Q8—1221no—
360C4×Q8—1221no—
361C4×Q8—1224no—
362C4×Q8—1224no—
363C4×Q8C2×#692311yescharacteristic
364C4×D4—611no—
365C4×D4—611no—
366C4×D4—611no—
367C4×D4—1221no—
368C4×D4—1221no—
369C4×D4C2×#692311yescharacteristic
370#117—2444no—
371C2×C4⋊C4—612no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—612no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1222no—
377C2×C4⋊C4—1222no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1222no—
380C2×C22⋊C4—1222no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—612no—
384C2×C42—611no—
385C2×C42—612no—
386C2×C42—1221no—
387C2×C42—1222no—
388C2×C42—1221no—
389C2×C42—1221no—
390C2×C42—1222no—
391#107—1224no—
392#106—611no—
393#106—611no—
394#106—611no—
395#106C2×#692311yescharacteristic
396#103—611no—
397#103—611no—
398#103—611no—
399#103—1224no—
400#103C2×#692311yescharacteristic
401#102—611no—
402#102—611no—
403#102—611no—
404#102—1224no—
405#102C2×#692311yescharacteristic
406C4×C8—611no—
407C4×C8—611no—
408C4×C8—611no—
409C4×C8—1221no—
410C4×C8—1221no—
411C4×C8C2×#692311yescharacteristic
412#95—1222no—
413#95—1221no—
414#95—1222no—
415#95—1221no—
416C24—1221no—
417C2×Q8—614no—
418C2×Q8—611no—
419C2×Q8—1221no—
420C2×Q8—1222no—
421C2×Q8C22×#692311yescharacteristic
422C2×D4—611no—
423C2×D4—1222no—
424C2×D4—1222no—
425C2×D4—1221no—
426C2×D4C22×#692311yescharacteristic
427C22×C4—21no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—612no—
431C22×C4—611no—
432C22×C4—612no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1222no—
439C22×C4—1221no—
440C22×C4—1222no—
441C22×C4—2442no—
442C22×C4—2442no—
443SD16—22no—
444SD16—1222no—
445SD16—1222no—
446SD16—1222no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—1222no—
450C2×C8—1222no—
451C2×C8—1222no—
452C2×C8—1222no—
453C2×C8—1222no—
454C2×C8C22×#692311yescharacteristic
455C2×C8C22×#692311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—614no—
458C4⋊C4—611no—
459C4⋊C4—611no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1222no—
465C4⋊C4—1222no—
466C4⋊C4—1222no—
467C4⋊C4—1228no—
468C4⋊C4—1221no—
469C4⋊C4—2444no—
470C4⋊C4C22×#692311yescharacteristic
471C4⋊C4C22×#692311yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—2444no—
477C22⋊C4—2444no—
478C42—21no—
479C42—611no—
480C42—611no—
481C42—611no—
482C42—1221no—
483C42—1221no—
484C42—1222no—
485C42—1222no—
486C42—1222no—
487C42—1222no—
488C42—1224no—
489C42—1228no—
490C42—1221no—
491C42—2442no—
492C42—2442no—
493C42—2444no—
494C42C22×#692311yescharacteristic
495C23—21no—
496C23—611no—
497C23—1221no—
498C23—2441no—
499C23—2442no—
500C23—2441no—
501C23—2442no—
502Q8—21no—
503Q8—612no—
504Q8—1224no—
505Q8—1221no—
506Q8#1451985612yescomplemented
507D4—21no—
508D4—21no—
509D4—1221no—
510D4—1221no—
511D4—2442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—42no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—614no—
523C2×C4—611no—
524C2×C4—1224no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1221no—
529C2×C4—1222no—
530C2×C4—1224no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4—2442no—
546C2×C4D4×#692311yescharacteristic
547C2×C4D4×#692311yescharacteristic
548C2×C4C23×#692311yescharacteristic
549C8—21no—
550C8—21no—
551C8—1221no—
552C8—1221no—
553C8—2442no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—612no—
558C22—612no—
559C22—611no—
560C22—611no—
561C22—4882no—
562C22—4882no—
563C22—2441no—
564C22—2441no—
565C22—2441no—
566C22C2×D4×#692311yescharacteristic
567C4—22no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—612no—
572C4—612no—
573C4—1224no—
574C4—1222no—
575C4—1221no—
576C4—4882no—
577C4—2442no—
578C4—2444no—
579C4—2441no—
580C4—2441no—
581C4#1684080112yes—
582C4C2×#1451985611yescharacteristic
583C4#41×#692311yescharacteristic
584C2—81no—
585C2—612no—
586C2—612no—
587C2—4881no—
588C2#2146227311yescharacteristic
589C2#135×#692311yescharacteristic
590C2C2×#1684080111yescharacteristic
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#21120
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
2. C4×Q8×#6923C2semidirect
4. #21461882C2semidirect
6. #21461783C2semidirect
7. C4×#14519846C2semidirect
8. C4×#14519840C2semidirect
10. #21461532C2semidirect
37. #16839853C4semidirect
38. C4×#11758190C4semidirect
39. SD16×Dic61C4semidirect
40. C4×#11758201C4semidirect
41. #16839849C4semidirect
42. C4×#11758200C4semidirect
43. #16839847C4semidirect
48. C4×SD16×C61C4semidirect
219. Q8×C61#117semidirect
252. Dic122#117semidirect
319. C4×SD16#6923semidirect
344. C61#21120semidirect
506. Q8#14519856semidirect

Maximal subgroups

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

subgroupindex
#214622762
C4×Q8×#69232
#214618962
#214618822
#214618152
#214617832
C4×#145198462
C4×#145198402
C4×#145198392
#214615322
C4×SD16×D612
#2112061