Finite Group Databasebeta

← #30599693

Subgroups — #30599693

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊#6923C211yesmaximal, characteristic
2#21461930C211yesmaximal, characteristic, complemented
3#21461740C211yesmaximal, characteristic, complemented
4#21461687C211yesmaximal, characteristic
5#21460698C211yesmaximal, characteristic, complemented
6#21460654C211yesmaximal, characteristic, complemented
7D4⋊C8×D61C211yesmaximal, characteristic
8C2×D4×#6923—21no—
9C22×C4⋊#6923—21no—
10C2×#14519846—21no—
11D61⋊(C4⋊C8)C2211yescharacteristic
12C2×#14519839—21no—
13#16840713—21no—
14#16840709—22no—
15#16840708C2211yescharacteristic
16#16840708C2211yescharacteristic
17#16840704—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
29C23×#6923—22no—
30C2×D61⋊C8—21no—
31D4×#6923—42no—
32D4×#6923—42no—
33C2×C4⋊#6923—22no—
34C2×C4⋊#6923—21no—
35C2×C4⋊#6923—21no—
36C2×C4⋊#6923—21no—
37C2×C4⋊#6923—21no—
38C2×C4⋊#6923—21no—
39C2×C4⋊#6923—42no—
40C2×C4⋊#6923—42no—
41C2×C4⋊#6923D411yescharacteristic
42C2×C4⋊#6923D411yescharacteristic
43C2×C4⋊#6923D412yes—
44C2×C22⋊#6923—22no—
45C2×C4×#6923—21no—
46#14519846—42no—
47#14519844—21no—
48C4⋊#92420—21no—
49#14519839—42no—
50(C2×#6923)⋊C4—22no—
51(C2×#6923)⋊C4—21no—
52C2×D4×D61D411yescharacteristic
53C22×C4×D61—21no—
54C2×C8×D61—21no—
55C2×C8×D61—21no—
56C4×D244C2×C411yescharacteristic
57D4×Dic61Q811yescharacteristic
58#14519739Q811yescharacteristic
59C4×C22⋊D61—21no—
60#14519737—21no—
61C4⋊C4×D61D411yescharacteristic
62C22⋊C4×D61—21no—
63C42×D61C2311yescharacteristic
64C4⋊#92418C2×C411yescharacteristic, complemented
65#14519706—21no—
66C4×#92418C2×C411yescharacteristic, complemented
67C8×Dic61—21no—
68C4×D4×C61C2×C411yescharacteristic
69C4⋊C8×C61C2×C411yescharacteristic, complemented
70C4×C8×C61C2×C411yescharacteristic, complemented
71C23×D61—21no—
72C22×#6923—21no—
73C22×#6923—21no—
74C22×#6923—22no—
75C22×#6923—44no—
76C22×#6923—44no—
77C22×#6923—41no—
78C22×#6923—82no—
79C2×D4×C61C4⋊C411yescharacteristic
80C22×C4×C61—21no—
81C2×C22⋊D61—21no—
82C22×Dic61—21no—
83D4×D61—21no—
84D4×D61—21no—
85D4×D61D812yes—
86D4×D61Q1612yes—
87C2×D244C4⋊C411yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61C2×D411yescharacteristic
96C2×C4×D61C2×D411yescharacteristic
97C2×C4×D61C2×D411yescharacteristic
98C22⋊#6923—44no—
99C2×#92420—41no—
100C4⋊#6923—21no—
101C4⋊#6923—21no—
102C4⋊#6923—21no—
103C4⋊#6923—42no—
104C4⋊#6923—42no—
105C4⋊#6923—44no—
106C4⋊#6923—41no—
107C4⋊#6923—41no—
108C4⋊#6923—41no—
109C4⋊#6923—41no—
110C4⋊#6923—41no—
111C4⋊#6923—41no—
112C4⋊#6923—41no—
113C4⋊#6923—41no—
114C4⋊#6923SD1612yes—
115C4×#6923—41no—
116C4×#6923—41no—
117D61⋊C8—41no—
118D61⋊C8—41no—
119C2×C8×C61—21no—
120C2×C8×C61—21no—
121C4⋊C4×C61C4⋊C411yescharacteristic
122C22⋊C4×C61—21no—
123C42×C61C22×C411yescharacteristic
124C22⋊Dic61—21no—
125#11758198—21no—
126#11758198—21no—
127C4⋊Dic61C4⋊C411yescharacteristic
128#11758196—21no—
129C4×Dic61C2×Q811yescharacteristic
130C4×Dic61#4111yescharacteristic
131C4×Dic61#4111yescharacteristic
132C2×#92418—21no—
133C2×#92418—21no—
134C8×D61—41no—
135C8×D61—41no—
136C8×D61—41no—
137C8×D61—41no—
138C23×C61—21no—
139C22×D61—21no—
140C22×D61—22no—
141C22×D61—22no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61#12011yescharacteristic
147C2×#6923—22no—
148C2×#6923—41no—
149C2×#6923—41no—
150C2×#6923—41no—
151C2×#6923—42no—
152C2×#6923—41no—
153C2×#6923—42no—
154C2×#6923—41no—
155C2×#6923—42no—
156C2×#6923—88no—
157C2×#6923—81no—
158C2×#6923—81no—
159C2×#6923—81no—
160D4×C61—21no—
161D4×C61#10712yescomplemented
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61C2×C4⋊C411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C22⋊D61—22no—
169C22⋊D61—22no—
170C2×Dic61—21no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61C22⋊Q811yescharacteristic
174C2×Dic61C22⋊Q811yescharacteristic
175C2×Dic61#12311yescharacteristic
176D244—21no—
177D244#10712yescomplemented
178C4×D61—21no—
179C4×D61—21no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186C4×D61C2×D811yescharacteristic
187C4×D61C2×SD1611yescharacteristic
188C4×D61C2×Q1611yescharacteristic
189C4×D61#13511yescharacteristic
190C4×D61AGL(1,ℤ/8)11yescharacteristic
191C4×D61AGL(1,ℤ/8)11yescharacteristic
192C4×D61AGL(1,ℤ/8)11yescharacteristic
193C4×D61#13711yescharacteristic
194#92420—81no—
195C8×C61—41no—
196C8×C61—41no—
197#92418—41no—
198#92418—41no—
199#8890—611nomaximal, Sylow
200C22×C61—22no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61#38511yescharacteristic
204C2×D61—22no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—42no—
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61#44711yescharacteristic
212C2×D61#44911yescharacteristic
213C2×D61#45011yescharacteristic
214C2×D61#45111yescharacteristic
215C2×D61#45411yescharacteristic
216C2×D61#45511yescharacteristic
217#6923—42no—
218#6923—81no—
219#6923—82no—
220#6923—161no—
221C4×C61—21no—
222C4×C61—41no—
223C4×C61C2×#10711yescharacteristic
224C4×C61#42811yescharacteristic
225C4×C61C4×SD1611yescharacteristic
226C4×C61#44211yescharacteristic
227Dic61—21no—
228Dic61—41no—
229Dic61#47611yescharacteristic
230Dic61#47811yescharacteristic
231Dic61#48011yescharacteristic
232Dic61#48411yescharacteristic
233D4×C4⋊C4—611no—
234#1947—611no—
235#1834—611no—
236#1802—611no—
237C2×D4⋊C8—611no—
238#1296—611no—
239#1279—611no—
240C2×C61—42no—
241C2×C61#185211yescharacteristic
242C2×C61#186011yescharacteristic
243C2×C61#186411yescharacteristic
244D61—42no—
245D61#162511yescharacteristic
246D61#163711yescharacteristic
247D61#163911yescharacteristic
248D61#164411yescharacteristic
249C2×C4×D4—611no—
250C2×C4×D4—1221no—
251C22×C4⋊C4—1221no—
252C2×#107—1221no—
253C2×C4⋊C8—611no—
254C2×C4⋊C8—611no—
255C2×#102—1221no—
256C2×C4×C8—611no—
257#389—1221no—
258#385—1222no—
259#384—611no—
260#384—611no—
261#380—1221no—
262C4×C4⋊C4—611no—
263#340—1221no—
264#340—1222no—
265#340—1221no—
266D4⋊C8—611no—
267D4⋊C8—611no—
268D4⋊C8—611no—
269D4⋊C8#692311yescharacteristic, complemented
270C61#889011yescharacteristic, complemented, Sylow
271C22×D4—611no—
272C23×C4—1221no—
273C23×C4—1222no—
274C22×C8—1221no—
275C22×C8—1221no—
276C22×C8—1221no—
277C4×D4—611no—
278C4×D4—611no—
279C4×D4—611no—
280C4×D4—1221no—
281C4×D4—1221no—
282C4×D4—2442no—
283C4×D4—2442no—
284C4×D4C2×#692311yescharacteristic
285C2×C4⋊C4—611no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—612no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4—1221no—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1222no—
295C2×C4⋊C4—2442no—
296C2×C4⋊C4—2442no—
297C2×C22⋊C4—1221no—
298C2×C22⋊C4—1222no—
299C2×C42—611no—
300C2×C42—1221no—
301#107—2442no—
302C4⋊C8—611no—
303C4⋊C8—1221no—
304C4⋊C8—1221no—
305C4⋊C8—1221no—
306C4⋊C8C2×#692311yescharacteristic, complemented
307#102—2442no—
308C4×C8—611no—
309C4×C8—1221no—
310C4×C8C2×#692311yescharacteristic, complemented
311#95—1221no—
312#95—1222no—
313C24—1221no—
314C2×D4—612no—
315C2×D4—612no—
316C2×D4—611no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4C4⋊#692311yescharacteristic
321C22×C4—21no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1222no—
332C22×C4—4882no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2444no—
338C22×C4—2441no—
339C22×C4—2444no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—1221no—
343C2×C8—1221no—
344C2×C8—2441no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C2×C8—2441no—
350C2×C8—2441no—
351C4⋊C4—612no—
352C4⋊C4—611no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C4⋊C4—1221no—
357C4⋊C4—2441no—
358C4⋊C4—2441no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C4⋊C4—2441no—
365C4⋊C4—2442no—
366C4⋊C4—2442no—
367C4⋊C4—2444no—
368C4⋊C4C4⋊#692311yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—1221no—
371C22⋊C4—1221no—
372C22⋊C4—1221no—
373C22⋊C4—2444no—
374C42—611no—
375C42—611no—
376C42—611no—
377C42—2441no—
378C42—2441no—
379C42C22×#692311yescharacteristic
380C23—21no—
381C23—611no—
382C23—1222no—
383C23—1222no—
384C23—1221no—
385C23—2441no—
386C23—2441no—
387C23—2441no—
388C23—2441no—
389D4—21no—
390D4—612no—
391D4—1222no—
392D4—1222no—
393D4—1221no—
394D4#1451984612yescomplemented
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—611no—
399C2×C4—611no—
400C2×C4—611no—
401C2×C4—611no—
402C2×C4—611no—
403C2×C4—611no—
404C2×C4—611no—
405C2×C4—611no—
406C2×C4—611no—
407C2×C4—611no—
408C2×C4—611no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1222no—
412C2×C4—1221no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—4888no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2442no—
425C2×C4—2441no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4C2×C4⋊#692311yescharacteristic
434C2×C4D4×#692311yescharacteristic
435C2×C4D4×#692311yescharacteristic
436C8—41no—
437C8—41no—
438C8—4881no—
439C8—2441no—
440C8—2441no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22—611no—
445C22—611no—
446C22—611no—
447C22—611no—
448C22—611no—
449C22—611no—
450C22—1222no—
451C22—2442no—
452C22—2442no—
453C22—2442no—
454C22—2442no—
455C22—2441no—
456C22—2441no—
457C22#1684070911yescharacteristic
458C4—21no—
459C4—41no—
460C4—611no—
461C4—611no—
462C4—611no—
463C4—611no—
464C4—1221no—
465C4—9761no—
466C4—4882no—
467C4—4881no—
468C4—2442no—
469C4—2441no—
470C4C2×#1451984611yescharacteristic
471C4#1684077311yescharacteristic
472C4SD16×#692311yescharacteristic
473C4#1684080311yescharacteristic
474C2—42no—
475C2—611no—
476C2—611no—
477C2—611no—
478C2—611no—
479C2—2442no—
480C2#2146176811yescharacteristic
481C2#2146177911yescharacteristic
482C2#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#8890
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. #21461930C2semidirect
3. #21461740C2semidirect
5. #21460698C2semidirect
6. #21460654C2semidirect
25. #16839491C4semidirect
26. D4⋊#92418C4semidirect
27. #16839489C4semidirect
28. C61×D4⋊C8C4semidirect
64. C4⋊#92418C2×C4semidirect
66. C4×#92418C2×C4semidirect
69. C4⋊C8×C61C2×C4semidirect
70. C4×C8×C61C2×C4semidirect
161. D4×C61#107semidirect
177. D244#107semidirect
269. D4⋊C8#6923semidirect
270. C61#8890semidirect
306. C4⋊C8C2×#6923semidirect
310. C4×C8C2×#6923semidirect
394. D4#14519846semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊#69232
#214619302
#214617402
#214616872
#214606982
#214606542
D4⋊C8×D612
#889061