Finite Group Databasebeta

← #30599692

Subgroups — #30599692

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462337C211yesmaximal, characteristic
2#21461930C211yesmaximal, characteristic, complemented
3#21461754C211yesmaximal, characteristic, complemented
4#21461687C211yesmaximal, characteristic
5#21460698C211yesmaximal, characteristic, complemented
6#21460654C211yesmaximal, characteristic, complemented
7D4⋊C8×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9C2×#14519846—21no—
10C2×#14519845—22no—
11D61⋊(C4⋊C8)C2211yescharacteristic
12C2×#14519839—21no—
13#16840714—21no—
14#16840712—22no—
15#16840708C2211yescharacteristic
16#16840708C2211yescharacteristic
17#16840704—21no—
18C4⋊C4×#6923—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
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#14519846—42no—
45#14519845—44no—
46#14519844—21no—
47C4⋊#92420—21no—
48#14519839—42no—
49(C2×#6923)⋊C4—22no—
50(C2×#6923)⋊C4—21no—
51C2×D4×D61D411yescharacteristic
52C22×C4×D61—21no—
53C2×C8×D61—21no—
54C2×C8×D61—21no—
55C4×D244C2×C411yescharacteristic
56D4×Dic61Q811yescharacteristic
57#14519739Q811yescharacteristic
58C4×C22⋊D61—21no—
59#14519737—21no—
60C4⋊C4×D61D411yescharacteristic
61C22⋊C4×D61—21no—
62C42×D61C2311yescharacteristic
63C4⋊#92418C2×C411yescharacteristic
64#14519706—21no—
65C4×#92418C2×C411yescharacteristic
66C8×Dic61—21no—
67C4×D4×C61C2×C411yescharacteristic
68C4⋊C8×C61C2×C411yescharacteristic
69C4×C8×C61C2×C411yescharacteristic
70C23×D61—21no—
71C22×#6923—21no—
72C22×#6923—21no—
73C22×#6923—22no—
74C22×#6923—41no—
75C2×D4×C61C4⋊C411yescharacteristic
76C22×C4×C61—21no—
77C2×C22⋊D61—21no—
78C22×Dic61—21no—
79D4×D61—21no—
80D4×D61—21no—
81D4×D61—21no—
82D4×D61—21no—
83C2×D244C4⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61C2×D411yescharacteristic
92C2×C4×D61C2×D411yescharacteristic
93C2×C4×D61C2×D411yescharacteristic
94C22⋊#6923—44no—
95C22⋊#6923—82no—
96C2×#92420—41no—
97C4⋊#6923—21no—
98C4⋊#6923—21no—
99C4⋊#6923—21no—
100C4⋊#6923—42no—
101C4⋊#6923—42no—
102C4⋊#6923—41no—
103C4⋊#6923—41no—
104C4⋊#6923—41no—
105C4⋊#6923—41no—
106C4⋊#6923—41no—
107C4⋊#6923—41no—
108C4⋊#6923—41no—
109C4⋊#6923—41no—
110C4⋊#6923SD1612yes—
111C4×#6923—44no—
112C4×#6923—41no—
113C4×#6923—41no—
114D61⋊C8—41no—
115D61⋊C8—41no—
116C2×C8×C61—21no—
117C2×C8×C61—21no—
118C4⋊C4×C61C4⋊C411yescharacteristic
119C22⋊C4×C61—21no—
120C42×C61C22×C411yescharacteristic
121C22⋊Dic61—21no—
122#11758198—21no—
123#11758198—21no—
124C4⋊Dic61C4⋊C411yescharacteristic
125#11758196—21no—
126C4×Dic61C2×Q811yescharacteristic
127C4×Dic61#4111yescharacteristic
128C4×Dic61#4111yescharacteristic
129C2×#92418—21no—
130C2×#92418—21no—
131C8×D61—22no—
132C8×D61—22no—
133C8×D61—41no—
134C8×D61—41no—
135C23×C61—21no—
136C22×D61—21no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61#12011yescharacteristic
144C2×#6923—22no—
145C2×#6923—41no—
146C2×#6923—41no—
147C2×#6923—41no—
148C2×#6923—41no—
149C2×#6923—42no—
150C2×#6923—42no—
151C2×#6923—42no—
152C2×#6923—41no—
153C2×#6923—81no—
154C2×#6923—81no—
155C2×#6923—81no—
156D4×C61—21no—
157D4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61C2×C4⋊C411yescharacteristic
162C2×C4×C61C4×D411yescharacteristic
163C2×C4×C61C4×D411yescharacteristic
164C22⋊D61—41no—
165C22⋊D61—41no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61C22⋊Q811yescharacteristic
170C2×Dic61C22⋊Q811yescharacteristic
171C2×Dic61#12311yescharacteristic
172D244—21no—
173D244—21no—
174C4×D61—21no—
175C4×D61—21no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—41no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61C2×SD1611yescharacteristic
183C4×D61#13511yescharacteristic
184C4×D61#13511yescharacteristic
185C4×D61#13511yescharacteristic
186C4×D61AGL(1,ℤ/8)11yescharacteristic
187C4×D61AGL(1,ℤ/8)11yescharacteristic
188C4×D61AGL(1,ℤ/8)11yescharacteristic
189C4×D61#13711yescharacteristic
190#92420—81no—
191C8×C61—22no—
192C8×C61—41no—
193#92418—22no—
194#92418—41no—
195#8889—611nomaximal, Sylow
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61#38511yescharacteristic
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61#44911yescharacteristic
208C2×D61#44911yescharacteristic
209C2×D61#45011yescharacteristic
210C2×D61#45211yescharacteristic
211C2×D61#45311yescharacteristic
212C2×D61#45611yescharacteristic
213#6923—42no—
214#6923—81no—
215#6923—82no—
216#6923—161no—
217C4×C61—21no—
218C4×C61—41no—
219C4×C61#42711yescharacteristic
220C4×C61#42811yescharacteristic
221C4×C61C4×SD1611yescharacteristic
222C4×C61#44211yescharacteristic
223Dic61—21no—
224Dic61—41no—
225Dic61#47611yescharacteristic
226Dic61#47811yescharacteristic
227Dic61#48211yescharacteristic
228Dic61#48511yescharacteristic
229#2354—611no—
230#1947—611no—
231#1844—611no—
232#1802—611no—
233C2×D4⋊C8—611no—
234#1296—611no—
235#1279—611no—
236C2×C61—81no—
237C2×C61#185411yescharacteristic
238C2×C61#185911yescharacteristic
239C2×C61#186411yescharacteristic
240D61—81no—
241D61#162411yescharacteristic
242D61#163111yescharacteristic
243D61#165211yescharacteristic
244D61#165411yescharacteristic
245C2×C4×D4—611no—
246C2×#117—1221no—
247C2×#107—1221no—
248C2×#106—1222no—
249C2×C4⋊C8—611no—
250C2×C4⋊C8—611no—
251C2×#102—1221no—
252C2×C4×C8—611no—
253#390—1221no—
254#388—1222no—
255#384—611no—
256#384—611no—
257#380—1221no—
258C4×C4⋊C4—611no—
259C4×C4⋊C4—1221no—
260#340—1221no—
261#340—1221no—
262D4⋊C8—611no—
263D4⋊C8—611no—
264D4⋊C8—611no—
265D4⋊C8#692311yescharacteristic, complemented
266C61#888911yescharacteristic, complemented, Sylow
267C22×D4—611no—
268C23×C4—1221no—
269C22×C8—1221no—
270C22×C8—1221no—
271C22×C8—1221no—
272C4×D4—611no—
273C4×D4—611no—
274C4×D4—611no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4C2×#692311yescharacteristic
278#117—2442no—
279#117—2442no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—611no—
282C2×C4⋊C4—611no—
283C2×C4⋊C4—612no—
284C2×C4⋊C4—1221no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4—1221no—
287C2×C4⋊C4—1221no—
288C2×C4⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1222no—
291C2×C22⋊C4—1222no—
292C2×C42—611no—
293C2×C42—1221no—
294C2×C42—1222no—
295#107—2442no—
296#106—2444no—
297C4⋊C8—611no—
298C4⋊C8—1221no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8C2×#692311yescharacteristic
302#102—2442no—
303C4×C8—611no—
304C4×C8—1221no—
305C4×C8C2×#692311yescharacteristic
306#95—1221no—
307#95—1222no—
308C24—1221no—
309C2×D4—611no—
310C2×D4—1221no—
311C2×D4—1221no—
312C2×D4—1221no—
313C2×D4—1221no—
314C2×D4—1221no—
315C2×D4C4⋊#692311yescharacteristic
316C22×C4—21no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1222no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—1222no—
335C2×C8—1222no—
336C2×C8—1221no—
337C2×C8—1221no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C2×C8—2441no—
343C4⋊C4—612no—
344C4⋊C4—611no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C4⋊C4—2441no—
356C4⋊C4—2441no—
357C4⋊C4—2442no—
358C4⋊C4—2442no—
359C4⋊C4C4⋊#692311yescharacteristic
360C22⋊C4—21no—
361C22⋊C4—1221no—
362C22⋊C4—1221no—
363C22⋊C4—1221no—
364C22⋊C4—4882no—
365C22⋊C4—2444no—
366C42—611no—
367C42—611no—
368C42—611no—
369C42—2441no—
370C42—2441no—
371C42—2444no—
372C42C22×#692311yescharacteristic
373C23—21no—
374C23—611no—
375C23—1221no—
376C23—2441no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381C23—2441no—
382D4—21no—
383D4—21no—
384D4—1221no—
385D4—1221no—
386D4—2441no—
387D4—2441no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—41no—
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—611no—
401C2×C4—611no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1222no—
405C2×C4—1221no—
406C2×C4—4881no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2442no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2442no—
419C2×C4—2441no—
420C2×C4—2442no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4C2×C4⋊#692311yescharacteristic
426C2×C4D4×#692311yescharacteristic
427C2×C4D4×#692311yescharacteristic
428C8—22no—
429C8—41no—
430C8—1222no—
431C8—4881no—
432C8—2441no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—611no—
437C22—611no—
438C22—611no—
439C22—611no—
440C22—611no—
441C22—611no—
442C22—4881no—
443C22—4881no—
444C22—4881no—
445C22—4881no—
446C22—2441no—
447C22—2441no—
448C22—2441no—
449C22#1684070911yescharacteristic
450C4—21no—
451C4—41no—
452C4—611no—
453C4—611no—
454C4—611no—
455C4—611no—
456C4—1221no—
457C4—9761no—
458C4—4881no—
459C4—4882no—
460C4—2442no—
461C4—2441no—
462C4#1684077211yescharacteristic
463C4#1684077311yescharacteristic
464C4SD16×#692311yescharacteristic
465C4#1684080311yescharacteristic
466C2—81no—
467C2—611no—
468C2—611no—
469C2—611no—
470C2—611no—
471C2—4881no—
472C2#2146177011yescharacteristic
473C2#2146177811yescharacteristic
474C2#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#8889
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. #21461754C2semidirect
5. #21460698C2semidirect
6. #21460654C2semidirect
25. #16839491C4semidirect
26. D4⋊#92418C4semidirect
27. #16839489C4semidirect
28. C61×D4⋊C8C4semidirect
265. D4⋊C8#6923semidirect
266. C61#8889semidirect

Maximal subgroups

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

subgroupindex
#214623372
#214619302
#214617542
#214616872
#214606982
#214606542
D4⋊C8×D612
#888961