Finite Group Databasebeta

← #30599689

Subgroups — #30599689

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊#6923C211yesmaximal, characteristic
2#21461931C211yesmaximal, characteristic, complemented
3#21461754C211yesmaximal, 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×#14519845—21no—
11C2×#14519845—22no—
12D61⋊(C4⋊C8)C2211yescharacteristic
13C2×#14519839—21no—
14#16840713—21no—
15#16840709—22no—
16#16840708C2211yescharacteristic
17#16840708C2211yescharacteristic
18#16840704—21no—
19C4×C4⋊#6923C2211yescharacteristic
20#16840636—21no—
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#14519845—44no—
47#14519845—42no—
48#14519844—21no—
49C4⋊#92420—21no—
50#14519839—42no—
51(C2×#6923)⋊C4—22no—
52(C2×#6923)⋊C4—21no—
53C2×D4×D61D411yescharacteristic
54C22×C4×D61—21no—
55C2×C8×D61—21no—
56C2×C8×D61—21no—
57C4×D244C2×C411yescharacteristic
58D4×Dic61Q811yescharacteristic
59#14519739Q811yescharacteristic
60C4×C22⋊D61—21no—
61#14519737—21no—
62C4⋊C4×D61D411yescharacteristic
63C22⋊C4×D61—21no—
64C42×D61C2311yescharacteristic
65C4⋊#92418C2×C411yescharacteristic, complemented
66#14519706—21no—
67C4×#92418C2×C411yescharacteristic, complemented
68C8×Dic61—21no—
69C4×D4×C61C2×C411yescharacteristic
70C4⋊C8×C61C2×C411yescharacteristic, complemented
71C4×C8×C61C2×C411yescharacteristic, complemented
72C23×D61—21no—
73C22×#6923—21no—
74C22×#6923—21no—
75C22×#6923—22no—
76C22×#6923—44no—
77C22×#6923—44no—
78C22×#6923—41no—
79C22×#6923—82no—
80C2×D4×C61C4⋊C411yescharacteristic
81C22×C4×C61—21no—
82C2×C22⋊D61—21no—
83C22×Dic61—21no—
84D4×D61—21no—
85D4×D61—21no—
86D4×D61SD1612yes—
87D4×D61SD1612yes—
88C2×D244C4⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61C2×D411yescharacteristic
97C2×C4×D61C2×D411yescharacteristic
98C2×C4×D61C2×D411yescharacteristic
99C22⋊#6923—44no—
100C2×#92420—41no—
101C4⋊#6923—21no—
102C4⋊#6923—21no—
103C4⋊#6923—21no—
104C4⋊#6923—42no—
105C4⋊#6923—42no—
106C4⋊#6923—44no—
107C4⋊#6923—41no—
108C4⋊#6923—41no—
109C4⋊#6923—41no—
110C4⋊#6923—41no—
111C4⋊#6923—41no—
112C4⋊#6923—41no—
113C4⋊#6923—41no—
114C4⋊#6923—41no—
115C4⋊#6923SD1612yes—
116C4×#6923—41no—
117C4×#6923—41no—
118D61⋊C8—41no—
119D61⋊C8—41no—
120C2×C8×C61—21no—
121C2×C8×C61—21no—
122C4⋊C4×C61C4⋊C411yescharacteristic
123C22⋊C4×C61—21no—
124C42×C61C22×C411yescharacteristic
125C22⋊Dic61—21no—
126#11758198—21no—
127#11758198—21no—
128C4⋊Dic61C4⋊C411yescharacteristic
129#11758196—21no—
130C4×Dic61C2×Q811yescharacteristic
131C4×Dic61#4111yescharacteristic
132C4×Dic61#4111yescharacteristic
133C2×#92418—21no—
134C2×#92418—21no—
135C8×D61—22no—
136C8×D61—22no—
137C8×D61—41no—
138C8×D61—41no—
139C23×C61—21no—
140C22×D61—21no—
141C22×D61—22no—
142C22×D61—22no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61#12011yescharacteristic
148C2×#6923—22no—
149C2×#6923—41no—
150C2×#6923—41no—
151C2×#6923—41no—
152C2×#6923—41no—
153C2×#6923—42no—
154C2×#6923—42no—
155C2×#6923—42no—
156C2×#6923—41no—
157C2×#6923—88no—
158C2×#6923—81no—
159C2×#6923—81no—
160C2×#6923—81no—
161D4×C61—21no—
162D4×C61#10612yescomplemented
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61C2×C4⋊C411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C2×C4×C61C4×D411yescharacteristic
169C22⋊D61—22no—
170C22⋊D61—22no—
171C2×Dic61—21no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61C22⋊Q811yescharacteristic
175C2×Dic61C22⋊Q811yescharacteristic
176C2×Dic61#12311yescharacteristic
177D244—21no—
178D244#10612yescomplemented
179C4×D61—21no—
180C4×D61—21no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186C4×D61—41no—
187C4×D61C2×SD1611yescharacteristic
188C4×D61C2×SD1611yescharacteristic
189C4×D61C2×SD1611yescharacteristic
190C4×D61#13511yescharacteristic
191C4×D61AGL(1,ℤ/8)11yescharacteristic
192C4×D61AGL(1,ℤ/8)11yescharacteristic
193C4×D61AGL(1,ℤ/8)11yescharacteristic
194C4×D61#13711yescharacteristic
195#92420—81no—
196C8×C61—22no—
197C8×C61—41no—
198#92418—22no—
199#92418—41no—
200#8886—611nomaximal, Sylow
201C22×C61—22no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61#38511yescharacteristic
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61#44811yescharacteristic
213C2×D61#44911yescharacteristic
214C2×D61#45011yescharacteristic
215C2×D61#45011yescharacteristic
216C2×D61#45311yescharacteristic
217C2×D61#45611yescharacteristic
218#6923—42no—
219#6923—82no—
220#6923—81no—
221#6923—161no—
222C4×C61—21no—
223C4×C61—41no—
224C4×C61C2×#10611yescharacteristic
225C4×C61#42811yescharacteristic
226C4×C61C4×SD1611yescharacteristic
227C4×C61#44211yescharacteristic
228Dic61—21no—
229Dic61—41no—
230Dic61#47611yescharacteristic
231Dic61#47811yescharacteristic
232Dic61#48111yescharacteristic
233Dic61#48311yescharacteristic
234D4×C4⋊C4—611no—
235#1948—611no—
236#1844—611no—
237#1802—611no—
238C2×D4⋊C8—611no—
239#1296—611no—
240#1279—611no—
241C2×C61—42no—
242C2×C61#185311yescharacteristic
243C2×C61#185911yescharacteristic
244C2×C61#186411yescharacteristic
245D61—42no—
246D61#162211yescharacteristic
247D61#162911yescharacteristic
248D61#165111yescharacteristic
249D61#165411yescharacteristic
250C2×C4×D4—611no—
251C2×C4×D4—1221no—
252C22×C4⋊C4—1221no—
253C2×#106—1222no—
254C2×#106—1221no—
255C2×C4⋊C8—611no—
256C2×C4⋊C8—611no—
257C2×#102—1221no—
258C2×C4×C8—611no—
259#389—1221no—
260#385—1222no—
261#384—611no—
262#384—611no—
263#380—1221no—
264C4×C4⋊C4—611no—
265#340—1221no—
266#340—1221no—
267D4⋊C8—611no—
268D4⋊C8—611no—
269D4⋊C8—611no—
270D4⋊C8#692311yescharacteristic, complemented
271C61#888611yescharacteristic, complemented, Sylow
272C22×D4—611no—
273C23×C4—1221no—
274C23×C4—1222no—
275C22×C8—1221no—
276C22×C8—1221no—
277C22×C8—1221no—
278C4×D4—611no—
279C4×D4—611no—
280C4×D4—611no—
281C4×D4—1221no—
282C4×D4—1221no—
283C4×D4—2442no—
284C4×D4—2442no—
285C4×D4C2×#692311yescharacteristic
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—612no—
290C2×C4⋊C4—1221no—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1222no—
296C2×C4⋊C4—2442no—
297C2×C4⋊C4—2442no—
298C2×C22⋊C4—1221no—
299C2×C22⋊C4—1222no—
300C2×C42—611no—
301C2×C42—1221no—
302#106—2442no—
303#106—2444no—
304C4⋊C8—611no—
305C4⋊C8—1221no—
306C4⋊C8—1221no—
307C4⋊C8—1221no—
308C4⋊C8C2×#692311yescharacteristic, complemented
309#102—2442no—
310C4×C8—611no—
311C4×C8—1221no—
312C4×C8C2×#692311yescharacteristic, complemented
313#95—1221no—
314#95—1222no—
315C24—1221no—
316C2×D4—612no—
317C2×D4—612no—
318C2×D4—611no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4C4⋊#692311yescharacteristic
323C22×C4—21no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1222no—
334C22×C4—4882no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2444no—
340C22×C4—2441no—
341C22×C4—2444no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—1222no—
345C2×C8—1222no—
346C2×C8—1221no—
347C2×C8—1221no—
348C2×C8—2441no—
349C2×C8—2441no—
350C2×C8—2441no—
351C2×C8—2441no—
352C2×C8—2441no—
353C4⋊C4—612no—
354C4⋊C4—611no—
355C4⋊C4—1221no—
356C4⋊C4—1221no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C4⋊C4—2441no—
365C4⋊C4—2441no—
366C4⋊C4—2441no—
367C4⋊C4—2442no—
368C4⋊C4—2442no—
369C4⋊C4—2444no—
370C4⋊C4C4⋊#692311yescharacteristic
371C22⋊C4—21no—
372C22⋊C4—1221no—
373C22⋊C4—1221no—
374C22⋊C4—1221no—
375C22⋊C4—2444no—
376C42—611no—
377C42—611no—
378C42—611no—
379C42—2441no—
380C42—2441no—
381C42C22×#692311yescharacteristic
382C23—21no—
383C23—611no—
384C23—1222no—
385C23—1222no—
386C23—1221no—
387C23—2441no—
388C23—2441no—
389C23—2441no—
390C23—2441no—
391D4—21no—
392D4—612no—
393D4—1222no—
394D4—1222no—
395D4—1221no—
396D4#1451984512yescomplemented
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
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—611no—
410C2×C4—611no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1222no—
414C2×C4—1221no—
415C2×C4—4881no—
416C2×C4—4881no—
417C2×C4—4881no—
418C2×C4—4888no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2442no—
427C2×C4—2441no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4C2×C4⋊#692311yescharacteristic
436C2×C4D4×#692311yescharacteristic
437C2×C4D4×#692311yescharacteristic
438C8—22no—
439C8—41no—
440C8—1222no—
441C8—4881no—
442C8—2441no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—611no—
447C22—611no—
448C22—611no—
449C22—611no—
450C22—611no—
451C22—611no—
452C22—1222no—
453C22—2442no—
454C22—2442no—
455C22—2442no—
456C22—2442no—
457C22—2441no—
458C22—2441no—
459C22#1684070911yescharacteristic
460C4—21no—
461C4—41no—
462C4—611no—
463C4—611no—
464C4—611no—
465C4—611no—
466C4—1221no—
467C4—9761no—
468C4—4882no—
469C4—4881no—
470C4—2442no—
471C4—2441no—
472C4C2×#1451984511yescharacteristic
473C4#1684077311yescharacteristic
474C4SD16×#692311yescharacteristic
475C4#1684080311yescharacteristic
476C2—42no—
477C2—611no—
478C2—611no—
479C2—611no—
480C2—611no—
481C2—2442no—
482C2#2146176911yescharacteristic
483C2#2146177811yescharacteristic
484C2#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#8886
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. #21461754C2semidirect
5. #21460698C2semidirect
6. #21460654C2semidirect
25. #16839491C4semidirect
26. D4⋊#92418C4semidirect
27. #16839489C4semidirect
28. C61×D4⋊C8C4semidirect
65. C4⋊#92418C2×C4semidirect
67. C4×#92418C2×C4semidirect
70. C4⋊C8×C61C2×C4semidirect
71. C4×C8×C61C2×C4semidirect
162. D4×C61#106semidirect
178. D244#106semidirect
270. D4⋊C8#6923semidirect
271. C61#8886semidirect
308. C4⋊C8C2×#6923semidirect
312. C4×C8C2×#6923semidirect
396. D4#14519845semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊#69232
#214619312
#214617542
#214616872
#214606982
#214606542
D4⋊C8×D612
#888661