Finite Group Databasebeta

← #30599957

Subgroups — #30599957

Order 15616.

664 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊#6923C211yesmaximal, characteristic
2#21462000C211yesmaximal, characteristic, complemented
3#21461985C211yesmaximal, characteristic, complemented
4D61⋊(D4⋊C8)C211yesmaximal, characteristic
5#21460698C211yesmaximal, characteristic, complemented
6#21460653C211yesmaximal, characteristic, complemented
7#474×D61C211yesmaximal, characteristic
8C2×D4×#6923—21no—
9C22×C4⋊#6923—21no—
10D61⋊(C4⋊C8)C2211yescharacteristic
11C2×#14519840—21no—
12C2×#14519840—21no—
13C4×D61⋊C8C2211yescharacteristic
14#16840713—21no—
15#16840709—22no—
16#16840708C2211yescharacteristic
17#16840704—21no—
18C4×C4⋊#6923C2211yescharacteristic
19#16840635—22no—
20#16840610—21no—
21D4⋊#92420—21no—
22C4⋊Q8×D61C2211yescharacteristic
23C4×D4×D61C2211yescharacteristic
24#16840043C411yescharacteristic, complemented
25#16840042C411yescharacteristic, complemented
26#16840041—21no—
27#16840040—21no—
28#16840039C411yescharacteristic, complemented
29#107×D61—21no—
30C4⋊C8×D61C2211yescharacteristic
31#102×D61—21no—
32C61×#474C411yescharacteristic, complemented
33C23×#6923—22no—
34C2×D61⋊C8—21no—
35C2×D61⋊C8—21no—
36D4×#6923—42no—
37D4×#6923—42no—
38C2×C4⋊#6923—22no—
39C2×C4⋊#6923—21no—
40C2×C4⋊#6923—21no—
41C2×C4⋊#6923—42no—
42C2×C4⋊#6923—42no—
43C2×C4⋊#6923D411yescharacteristic
44C2×C4⋊#6923D411yescharacteristic
45C2×C4⋊#6923D412yes—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—21no—
48#14519844—21no—
49C4⋊#92420—21no—
50#14519840—42no—
51#14519840—42no—
52C4×#92420—21no—
53C4×#92420—21no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—21no—
56C2×Q8×D61—21no—
57C2×D4×D61D411yescharacteristic
58C22×C4×D61—21no—
59C2×C8×D61—21no—
60#14519777C2×C411yescharacteristic, complemented
61#14519776—21no—
62#14519776—21no—
63#14519775—21no—
64C4×D244C2×C411yescharacteristic
65D4×Dic61D411yescharacteristic
66#14519739D411yescharacteristic
67C4×C22⋊D61—21no—
68#14519737—21no—
69C4⋊C4×D61—21no—
70C4⋊C4×D61—21no—
71C4⋊C4×D61D411yescharacteristic
72C22⋊C4×D61—21no—
73C42×D61C2311yescharacteristic
74#14519711—21no—
75#14519710—21no—
76#14519710—21no—
77C4⋊#92418C2×C411yescharacteristic, complemented
78#14519706—21no—
79#14519699—21no—
80#14519698—21no—
81#14519697—21no—
82C4⋊Q8×C61C2×C411yescharacteristic, complemented
83C4×D4×C61C2×C411yescharacteristic
84#107×C61—21no—
85C4⋊C8×C61C2×C411yescharacteristic, complemented
86#102×C61—21no—
87C23×D61—21no—
88C22×#6923—21no—
89C22×#6923—21no—
90C22×#6923—22no—
91C22×#6923—44no—
92C22×#6923—44no—
93C22×#6923—82no—
94C2×Q8×C61—21no—
95C2×D4×C61C22⋊C411yescharacteristic
96C22×C4×C61—21no—
97C2×C22⋊D61—21no—
98C22×Dic61—21no—
99Q8×D61—41no—
100Q8×D61—41no—
101Q8×D61—41no—
102Q8×D61—41no—
103D4×D61—21no—
104D4×D61—21no—
105D4×D61SD1612yes—
106D4×D61Q1612yes—
107C2×D244C22⋊C411yescharacteristic
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61C2×D411yescharacteristic
117C2×C4×D61C2×D411yescharacteristic
118C2×C4×D61C2×D411yescharacteristic
119C2×Dic122—21no—
120C2×Dic122—41no—
121C22⋊#6923—44no—
122C2×#92420—41no—
123C2×#92420—41no—
124C4⋊#6923—21no—
125C4⋊#6923—21no—
126C4⋊#6923—21no—
127C4⋊#6923—42no—
128C4⋊#6923—44no—
129C4⋊#6923—41no—
130C4⋊#6923—41no—
131C4⋊#6923—41no—
132C4⋊#6923—41no—
133C4⋊#6923D812yes—
134C4×#6923—41no—
135C4×#6923—41no—
136D61⋊C8—22no—
137D61⋊C8—41no—
138D61⋊C8—41no—
139D61⋊C8—41no—
140C2×C8×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61C22⋊C411yescharacteristic
144C22⋊C4×C61—21no—
145C42×C61C22×C411yescharacteristic
146C22⋊Dic61—21no—
147#11758198—21no—
148#11758198—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61C22⋊C411yescharacteristic
152#11758196—21no—
153#11758196—41no—
154#11758196—41no—
155C4×Dic61C2×D411yescharacteristic
156C4×Dic61#4111yescharacteristic
157C4×Dic61#4111yescharacteristic
158C2×#92418—21no—
159C8×D61—41no—
160C8×D61—41no—
161C23×C61—21no—
162C22×D61—21no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61#12011yescharacteristic
170C2×#6923—22no—
171C2×#6923—41no—
172C2×#6923—41no—
173C2×#6923—42no—
174C2×#6923—41no—
175C2×#6923—41no—
176C2×#6923—42no—
177C2×#6923—42no—
178C2×#6923—41no—
179C2×#6923—88no—
180Q8×C61—41no—
181Q8×C61—41no—
182D4×C61—21no—
183D4×C61#10312yescomplemented
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C4×D411yescharacteristic
190C2×C4×C61C4×D411yescharacteristic
191C22⋊D61—22no—
192C22⋊D61—22no—
193C2×Dic61—21no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61#12111yescharacteristic
198C2×Dic61#12111yescharacteristic
199C2×Dic61#12311yescharacteristic
200D244—21no—
201D244#10312yescomplemented
202C4×D61—21no—
203C4×D61—21no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61—81no—
211C4×D61—81no—
212C4×D61C2×D811yescharacteristic
213C4×D61C2×SD1611yescharacteristic
214C4×D61C2×Q1611yescharacteristic
215C4×D61#13511yescharacteristic
216C4×D61AGL(1,ℤ/8)11yescharacteristic
217C4×D61AGL(1,ℤ/8)11yescharacteristic
218C4×D61AGL(1,ℤ/8)11yescharacteristic
219C4×D61#13711yescharacteristic
220Dic122—41no—
221Dic122—41no—
222Dic122—81no—
223Dic122—81no—
224#92420—42no—
225#92420—81no—
226C8×C61—41no—
227#92418—41no—
228#8981—611nomaximal, Sylow
229C22×C61—22no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61#38611yescharacteristic
233C2×D61—22no—
234C2×D61—41no—
235C2×D61—41no—
236C2×D61—42no—
237C2×D61—42no—
238C2×D61—42no—
239C2×D61—42no—
240C2×D61#44711yescharacteristic
241C2×D61#44911yescharacteristic
242C2×D61#45011yescharacteristic
243C2×D61#45111yescharacteristic
244C2×D61#45511yescharacteristic
245C2×D61#45611yescharacteristic
246#6923—42no—
247#6923—82no—
248#6923—81no—
249C4×C61—21no—
250C4×C61—41no—
251C4×C61—81no—
252C4×C61C2×#10311yescharacteristic
253C4×C61#41711yescharacteristic
254C4×C61C4×D811yescharacteristic
255C4×C61#44211yescharacteristic
256Dic61—21no—
257Dic61—41no—
258Dic61—81no—
259Dic61#45911yescharacteristic
260Dic61#46311yescharacteristic
261Dic61#48311yescharacteristic
262Dic61#48411yescharacteristic
263C2×#474—611no—
264D4×C4⋊C4—611no—
265#1990—611no—
266#1981—611no—
267C2×D4⋊C8—611no—
268#1296—611no—
269#1279—611no—
270C2×C61—42no—
271C2×C61#187211yescharacteristic
272C2×C61#187911yescharacteristic
273C2×C61#188211yescharacteristic
274D61—42no—
275D61#163911yescharacteristic
276D61#164411yescharacteristic
277D61#164911yescharacteristic
278D61#165411yescharacteristic
279C2×C4⋊Q8—611no—
280C2×C4×D4—611no—
281C2×C4×D4—1221no—
282C22×C4⋊C4—1221no—
283#474—611no—
284#474—611no—
285#474—611no—
286#474—1221no—
287#474—1221no—
288#474#692311yescharacteristic, complemented
289C2×#107—1221no—
290C2×C4⋊C8—611no—
291C2×C4⋊C8—611no—
292C2×#103—1221no—
293C2×#103—1221no—
294C2×#102—1221no—
295C2×C4×C8—611no—
296#389—1221no—
297#385—1222no—
298#384—611no—
299#380—1221no—
300C4×C4⋊C4—611no—
301#340—1222no—
302D4⋊C8—1221no—
303D4⋊C8—1221no—
304C61#898111yescharacteristic, complemented, Sylow
305C22×Q8—1221no—
306C22×D4—611no—
307C23×C4—1221no—
308C23×C4—1222no—
309C22×C8—1221no—
310C22×C8—1221no—
311C22×C8—1221no—
312C4⋊Q8—611no—
313C4⋊Q8—1221no—
314C4⋊Q8—1221no—
315C4⋊Q8—1221no—
316C4⋊Q8C2×#692311yescharacteristic, complemented
317C4×D4—611no—
318C4×D4—611no—
319C4×D4—611no—
320C4×D4—1221no—
321C4×D4—1221no—
322C4×D4—2442no—
323C4×D4—2442no—
324C4×D4C2×#692311yescharacteristic
325C2×C4⋊C4—611no—
326C2×C4⋊C4—611no—
327C2×C4⋊C4—611no—
328C2×C4⋊C4—612no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4—1221no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4—1222no—
334C2×C4⋊C4—2442no—
335C2×C4⋊C4—2442no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1222no—
338C2×C42—611no—
339C2×C42—1221no—
340#107—21no—
341#107—1221no—
342#107—1221no—
343#107—1221no—
344C4⋊C8—611no—
345C4⋊C8—1221no—
346C4⋊C8—1221no—
347C4⋊C8—1221no—
348C4⋊C8C2×#692311yescharacteristic, complemented
349#103—2442no—
350#103—2442no—
351#102—21no—
352#102—1221no—
353#102—1221no—
354#102—1221no—
355C4×C8—1221no—
356C4×C8—1221no—
357#95—1221no—
358#95—1222no—
359C24—1221no—
360C2×Q8—21no—
361C2×Q8—1221no—
362C2×Q8—2441no—
363C2×Q8—2441no—
364C2×Q8—2441no—
365C2×Q8—2441no—
366C2×Q8—2441no—
367C2×D4—612no—
368C2×D4—612no—
369C2×D4—611no—
370C2×D4—1221no—
371C2×D4—1221no—
372C2×D4—1221no—
373C2×D4C22⋊#692311yescharacteristic
374C22×C4—21no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1221no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1222no—
385C22×C4—4882no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2444no—
392C22×C4—2444no—
393C2×C8—21no—
394C2×C8—1222no—
395C2×C8—1221no—
396C2×C8—2441no—
397C2×C8—2441no—
398C2×C8—2441no—
399C2×C8—2441no—
400C2×C8—2441no—
401C2×C8—2441no—
402C2×C8—2441no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—612no—
406C4⋊C4—611no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—1221no—
410C4⋊C4—1221no—
411C4⋊C4—1221no—
412C4⋊C4—1221no—
413C4⋊C4—2441no—
414C4⋊C4—2441no—
415C4⋊C4—2441no—
416C4⋊C4—2441no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C4⋊C4—2442no—
420C4⋊C4—2444no—
421C4⋊C4C22⋊#692311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—1221no—
424C22⋊C4—1221no—
425C22⋊C4—1221no—
426C22⋊C4—2444no—
427C42—611no—
428C42—611no—
429C42—611no—
430C42—2441no—
431C42—2441no—
432C42C22×#692311yescharacteristic
433C23—21no—
434C23—611no—
435C23—1222no—
436C23—1222no—
437C23—1221no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442Q8—41no—
443Q8—41no—
444Q8—4881no—
445Q8—4881no—
446Q8—2441no—
447Q8—2441no—
448D4—21no—
449D4—612no—
450D4—1222no—
451D4—1222no—
452D4—1221no—
453D4#1451984012yescomplemented
454C2×C4—21no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—611no—
461C2×C4—611no—
462C2×C4—611no—
463C2×C4—611no—
464C2×C4—611no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1222no—
472C2×C4—1221no—
473C2×C4—4881no—
474C2×C4—4881no—
475C2×C4—4888no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4C2×C22⋊#692311yescharacteristic
494C2×C4D4×#692311yescharacteristic
495C2×C4D4×#692311yescharacteristic
496C8—41no—
497C8—4881no—
498C8—2442no—
499C8—2441no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—611no—
504C22—611no—
505C22—611no—
506C22—611no—
507C22—611no—
508C22—611no—
509C22—1222no—
510C22—2442no—
511C22—2442no—
512C22—2442no—
513C22—2442no—
514C22—2441no—
515C22—2441no—
516C22#1684071011yescharacteristic
517C4—21no—
518C4—41no—
519C4—81no—
520C4—611no—
521C4—611no—
522C4—611no—
523C4—611no—
524C4—1221no—
525C4—4882no—
526C4—4881no—
527C4—4881no—
528C4—2442no—
529C4—2441no—
530C4C2×#1451984011yescharacteristic
531C4#1684075311yescharacteristic
532C4D8×#692311yescharacteristic
533C4#1684080311yescharacteristic
534C2—42no—
535C2—611no—
536C2—611no—
537C2—611no—
538C2—611no—
539C2—2442no—
540C2#2146180411yescharacteristic
541C2#2146181411yescharacteristic
542C2#2146181811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#474C4
socleC22×C61#386
prime radicalC2×D4×D61D4
cosocleC42×D61C23
hypercenter#474#6923
hypocenterC61#8981
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #21462000C2semidirect
3. #21461985C2semidirect
5. #21460698C2semidirect
6. #21460653C2semidirect
24. #16840043C4semidirect
25. #16840042C4semidirect
28. #16840039C4semidirect
32. C61×#474C4semidirect
60. #14519777C2×C4semidirect
77. C4⋊#92418C2×C4semidirect
82. C4⋊Q8×C61C2×C4semidirect
85. C4⋊C8×C61C2×C4semidirect
183. D4×C61#103semidirect
201. D244#103semidirect
288. #474#6923semidirect
304. C61#8981semidirect
316. C4⋊Q8C2×#6923semidirect
348. C4⋊C8C2×#6923semidirect
453. D4#14519840semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊#69232
#214620002
#214619852
D61⋊(D4⋊C8)2
#214606982
#214606532
#474×D612
#898161