Finite Group Databasebeta

← #30599696

Subgroups — #30599696

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462337C211yesmaximal, characteristic
2#21461931C211yesmaximal, characteristic, complemented
3#21461740C211yesmaximal, characteristic, complemented
4#21461687C211yesmaximal, characteristic
5#21460698C211yesmaximal, characteristic, complemented
6#21460654C211yesmaximal, characteristic, complemented
7D4⋊C8×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9C2×#14519845—21no—
10D61⋊(C4⋊C8)C2211yescharacteristic
11C2×#14519839—21no—
12#16840714—21no—
13#16840712—22no—
14#16840708C2211yescharacteristic
15#16840708C2211yescharacteristic
16#16840704—21no—
17C4⋊C4×#6923—21no—
18C4×C4⋊#6923C2211yescharacteristic
19#16840636—21no—
20#16840636—22no—
21#16840635—21no—
22C4×D4×D61C2211yescharacteristic
23C4⋊C8×D61C2211yescharacteristic
24C4×C8×D61C2211yescharacteristic
25#16839491C411yescharacteristic, complemented
26D4⋊#92418C411yescharacteristic, complemented
27#16839489C411yescharacteristic, complemented
28C61×D4⋊C8C411yescharacteristic, complemented
29C2×D61⋊C8—21no—
30#14519856—42no—
31#14519856—42no—
32C2×C4⋊#6923—21no—
33C2×C4⋊#6923—21no—
34C2×C4⋊#6923—21no—
35C2×C4⋊#6923—21no—
36C2×C4⋊#6923—21no—
37C2×C4⋊#6923D411yescharacteristic
38C2×C4⋊#6923D411yescharacteristic
39C2×C4⋊#6923D412yes—
40C2×C22⋊#6923—22no—
41C2×C22⋊#6923—22no—
42C2×C4×#6923—22no—
43C2×C4×#6923—21no—
44#14519845—42no—
45#14519844—21no—
46C4⋊#92420—21no—
47#14519839—42no—
48(C2×#6923)⋊C4—22no—
49(C2×#6923)⋊C4—21no—
50C2×D4×D61D411yescharacteristic
51C22×C4×D61—21no—
52C2×C8×D61—21no—
53C2×C8×D61—21no—
54C4×D244C2×C411yescharacteristic
55D4×Dic61Q811yescharacteristic
56#14519739Q811yescharacteristic
57C4×C22⋊D61—21no—
58#14519737—21no—
59C4⋊C4×D61D411yescharacteristic
60C22⋊C4×D61—21no—
61C42×D61C2311yescharacteristic
62C4⋊#92418C2×C411yescharacteristic
63#14519706—21no—
64C4×#92418C2×C411yescharacteristic
65C8×Dic61—21no—
66C4×D4×C61C2×C411yescharacteristic
67C4⋊C8×C61C2×C411yescharacteristic
68C4×C8×C61C2×C411yescharacteristic
69C23×D61—21no—
70C22×#6923—21no—
71C22×#6923—21no—
72C22×#6923—22no—
73C22×#6923—41no—
74C2×D4×C61C4⋊C411yescharacteristic
75C22×C4×C61—21no—
76C2×C22⋊D61—21no—
77C22×Dic61—21no—
78D4×D61—21no—
79D4×D61—21no—
80D4×D61—21no—
81D4×D61—21no—
82C2×D244C4⋊C411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61C2×D411yescharacteristic
91C2×C4×D61C2×D411yescharacteristic
92C2×C4×D61C2×D411yescharacteristic
93C22⋊#6923—44no—
94C22⋊#6923—82no—
95C2×#92420—41no—
96C4⋊#6923—21no—
97C4⋊#6923—21no—
98C4⋊#6923—21no—
99C4⋊#6923—42no—
100C4⋊#6923—42no—
101C4⋊#6923—41no—
102C4⋊#6923—41no—
103C4⋊#6923—41no—
104C4⋊#6923—41no—
105C4⋊#6923—41no—
106C4⋊#6923—41no—
107C4⋊#6923—41no—
108C4⋊#6923—41no—
109C4⋊#6923SD1612yes—
110C4×#6923—44no—
111C4×#6923—41no—
112C4×#6923—41no—
113D61⋊C8—41no—
114D61⋊C8—41no—
115C2×C8×C61—21no—
116C2×C8×C61—21no—
117C4⋊C4×C61C4⋊C411yescharacteristic
118C22⋊C4×C61—21no—
119C42×C61C22×C411yescharacteristic
120C22⋊Dic61—21no—
121#11758198—21no—
122#11758198—21no—
123C4⋊Dic61C4⋊C411yescharacteristic
124#11758196—21no—
125C4×Dic61C2×Q811yescharacteristic
126C4×Dic61#4111yescharacteristic
127C4×Dic61#4111yescharacteristic
128C2×#92418—21no—
129C2×#92418—21no—
130C8×D61—41no—
131C8×D61—41no—
132C8×D61—41no—
133C8×D61—41no—
134C23×C61—21no—
135C22×D61—21no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61#12011yescharacteristic
143C2×#6923—22no—
144C2×#6923—41no—
145C2×#6923—41no—
146C2×#6923—41no—
147C2×#6923—42no—
148C2×#6923—42no—
149C2×#6923—41no—
150C2×#6923—42no—
151C2×#6923—41no—
152C2×#6923—81no—
153C2×#6923—81no—
154C2×#6923—81no—
155D4×C61—21no—
156D4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61C2×C4⋊C411yescharacteristic
161C2×C4×C61C4×D411yescharacteristic
162C2×C4×C61C4×D411yescharacteristic
163C22⋊D61—41no—
164C22⋊D61—41no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61C22⋊Q811yescharacteristic
169C2×Dic61C22⋊Q811yescharacteristic
170C2×Dic61#12311yescharacteristic
171D244—21no—
172D244—21no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—41no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—41no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61C2×SD1611yescharacteristic
182C4×D61#13511yescharacteristic
183C4×D61#13511yescharacteristic
184C4×D61#13511yescharacteristic
185C4×D61AGL(1,ℤ/8)11yescharacteristic
186C4×D61AGL(1,ℤ/8)11yescharacteristic
187C4×D61AGL(1,ℤ/8)11yescharacteristic
188C4×D61#13711yescharacteristic
189#92420—81no—
190C8×C61—41no—
191C8×C61—41no—
192#92418—41no—
193#92418—41no—
194#8893—611nomaximal, Sylow
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61#38511yescharacteristic
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61#44911yescharacteristic
207C2×D61#44911yescharacteristic
208C2×D61#45011yescharacteristic
209C2×D61#45211yescharacteristic
210C2×D61#45411yescharacteristic
211C2×D61#45511yescharacteristic
212#6923—42no—
213#6923—82no—
214#6923—81no—
215#6923—161no—
216C4×C61—21no—
217C4×C61—41no—
218C4×C61#42711yescharacteristic
219C4×C61#42811yescharacteristic
220C4×C61C4×SD1611yescharacteristic
221C4×C61#44211yescharacteristic
222Dic61—21no—
223Dic61—41no—
224Dic61#47611yescharacteristic
225Dic61#47811yescharacteristic
226Dic61#48211yescharacteristic
227Dic61#48511yescharacteristic
228#2354—611no—
229#1948—611no—
230#1834—611no—
231#1802—611no—
232C2×D4⋊C8—611no—
233#1296—611no—
234#1279—611no—
235C2×C61—81no—
236C2×C61#185411yescharacteristic
237C2×C61#186011yescharacteristic
238C2×C61#186411yescharacteristic
239D61—81no—
240D61#162811yescharacteristic
241D61#163511yescharacteristic
242D61#164211yescharacteristic
243D61#164611yescharacteristic
244C2×C4×D4—611no—
245C2×#117—1221no—
246C2×#106—1221no—
247C2×C4⋊C8—611no—
248C2×C4⋊C8—611no—
249C2×#102—1221no—
250C2×C4×C8—611no—
251#390—1221no—
252#388—1222no—
253#384—611no—
254#384—611no—
255#380—1221no—
256C4×C4⋊C4—611no—
257C4×C4⋊C4—1221no—
258#340—1221no—
259#340—1222no—
260#340—1221no—
261D4⋊C8—611no—
262D4⋊C8—611no—
263D4⋊C8—611no—
264D4⋊C8#692311yescharacteristic, complemented
265C61#889311yescharacteristic, complemented, Sylow
266C22×D4—611no—
267C23×C4—1221no—
268C22×C8—1221no—
269C22×C8—1221no—
270C22×C8—1221no—
271C4×D4—611no—
272C4×D4—611no—
273C4×D4—611no—
274C4×D4—1221no—
275C4×D4—1221no—
276C4×D4C2×#692311yescharacteristic
277#117—2442no—
278#117—2442no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—611no—
282C2×C4⋊C4—612no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1221no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4—1221no—
287C2×C4⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1222no—
290C2×C22⋊C4—1222no—
291C2×C42—611no—
292C2×C42—1221no—
293C2×C42—1222no—
294#106—2442no—
295C4⋊C8—611no—
296C4⋊C8—1221no—
297C4⋊C8—1221no—
298C4⋊C8—1221no—
299C4⋊C8C2×#692311yescharacteristic
300#102—2442no—
301C4×C8—611no—
302C4×C8—1221no—
303C4×C8C2×#692311yescharacteristic
304#95—1221no—
305#95—1222no—
306C24—1221no—
307C2×D4—611no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—1221no—
312C2×D4—1221no—
313C2×D4C4⋊#692311yescharacteristic
314C22×C4—21no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1222no—
325C22×C4—2441no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4—2441no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C4⋊C4—612no—
342C4⋊C4—611no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—2441no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C4⋊C4—2442no—
356C4⋊C4—2442no—
357C4⋊C4C4⋊#692311yescharacteristic
358C22⋊C4—21no—
359C22⋊C4—1221no—
360C22⋊C4—1221no—
361C22⋊C4—1221no—
362C22⋊C4—4882no—
363C22⋊C4—2444no—
364C42—611no—
365C42—611no—
366C42—611no—
367C42—2441no—
368C42—2441no—
369C42—2444no—
370C42C22×#692311yescharacteristic
371C23—21no—
372C23—611no—
373C23—1221no—
374C23—2441no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380D4—21no—
381D4—21no—
382D4—1221no—
383D4—1221no—
384D4—2441no—
385D4—2441no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—611no—
390C2×C4—611no—
391C2×C4—611no—
392C2×C4—611no—
393C2×C4—611no—
394C2×C4—611no—
395C2×C4—611no—
396C2×C4—611no—
397C2×C4—611no—
398C2×C4—611no—
399C2×C4—611no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1222no—
403C2×C4—1221no—
404C2×C4—4881no—
405C2×C4—4881no—
406C2×C4—4881no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2442no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2442no—
417C2×C4—2441no—
418C2×C4—2442no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4C2×C4⋊#692311yescharacteristic
424C2×C4D4×#692311yescharacteristic
425C2×C4D4×#692311yescharacteristic
426C8—41no—
427C8—41no—
428C8—4881no—
429C8—2441no—
430C8—2441no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—611no—
435C22—611no—
436C22—611no—
437C22—611no—
438C22—611no—
439C22—611no—
440C22—4881no—
441C22—4881no—
442C22—4881no—
443C22—4881no—
444C22—2441no—
445C22—2441no—
446C22—2441no—
447C22#1684070911yescharacteristic
448C4—21no—
449C4—41no—
450C4—611no—
451C4—611no—
452C4—611no—
453C4—611no—
454C4—1221no—
455C4—9761no—
456C4—4882no—
457C4—4881no—
458C4—2442no—
459C4—2441no—
460C4#1684077211yescharacteristic
461C4#1684077311yescharacteristic
462C4SD16×#692311yescharacteristic
463C4#1684080311yescharacteristic
464C2—81no—
465C2—611no—
466C2—611no—
467C2—611no—
468C2—611no—
469C2—4881no—
470C2#2146177011yescharacteristic
471C2#2146177911yescharacteristic
472C2#2146178411yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×D4⋊C8C4
socleC22×C61#385
prime radicalC2×D4×D61D4
cosocleC42×D61C23
hypercenterD4⋊C8#6923
hypocenterC61#8893
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21461931C2semidirect
3. #21461740C2semidirect
5. #21460698C2semidirect
6. #21460654C2semidirect
25. #16839491C4semidirect
26. D4⋊#92418C4semidirect
27. #16839489C4semidirect
28. C61×D4⋊C8C4semidirect
264. D4⋊C8#6923semidirect
265. C61#8893semidirect

Maximal subgroups

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

subgroupindex
#214623372
#214619312
#214617402
#214616872
#214606982
#214606542
D4⋊C8×D612
#889361