Finite Group Databasebeta

← #29579162

Subgroups — #29579162

Order 15616.

468 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456378C211yesmaximal, characteristic
2#21446763C211yesmaximal, characteristic, complemented
3#21446738C211yesmaximal, characteristic
4C4×#14519709C211yesmaximal, characteristic, complemented
5#21444319C211yesmaximal, characteristic, complemented
6#21444315C211yesmaximal, characteristic
7C8×M16×C61C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840160C411yescharacteristic, complemented
11#16840135C411yescharacteristic, complemented
12#16840113C411yescharacteristic, complemented
13#16840109C411yescharacteristic, complemented
14#16839991—21no—
15#16839991—21no—
16C4×#11758190—21no—
17C4×#11758190—21no—
18C2×#14519709—21no—
19C2×#14519703—22no—
20C4×C4⋊Dic61C2211yescharacteristic
21C4×C4⋊Dic61C2211yescharacteristic
22#16839525—21no—
23#16839523—22no—
24#16839500—22no—
25#16839497—22no—
26C61×#431C2211yescharacteristic
27C4×M16×C61C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C61×#322—21no—
30C82×C61—21no—
31C2×#11758222—21no—
32C2×#11758190—21no—
33C2×#11758190—21no—
34#14519777C2×C411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519777C2×C411yescharacteristic
37#14519774C2×C411yescharacteristic
38#14519769—21no—
39#14519765—21no—
40#14519756—21no—
41#14519756—21no—
42#14519751—21no—
43#14519751—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×D244—21no—
47C4×D244—21no—
48#14519736—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61—21no—
53#14519709—24no—
54#14519709—21no—
55#14519709—21no—
56#14519703—44no—
57#14519702—21no—
58#14519702—21no—
59#14519699—21no—
60#14519699—21no—
61#14519684—21no—
62#14519684—21no—
63C2×M16×C61D412yes—
64C22×C8×C61D411yescharacteristic
65C22×C8×C61D411yescharacteristic
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C22⋊C8×C61D412yes—
69#97×C61—21no—
70C4×C8×C61—21no—
71C4×C8×C61—21no—
72C4×C8×C61C2×C411yescharacteristic
73C4×C8×C61C2×C411yescharacteristic
74C4×C8×C61D411yescharacteristic
75C4×C8×C61D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C2×C22⋊D61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82#11758222—42no—
83#11758222—42no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×C4×D61—41no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91M16×C61—22no—
92M16×C61SD1614yescomplemented
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61C22⋊C411yescharacteristic
98C2×C8×C61C22⋊C411yescharacteristic
99C2×C8×C61C22⋊C411yescharacteristic
100C2×C8×C61C22⋊C411yescharacteristic
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—41no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118#11758196—41no—
119#11758196—41no—
120C4×Dic61—41no—
121C4×Dic61—42no—
122C4×Dic61—42no—
123#11758190—42no—
124#11758190—42no—
125C23×C61#12711yescharacteristic
126C22×D61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12411yescharacteristic
136C2×C4×C61C2×SD1612yes—
137C2×C4×C61#13512yes—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149D244—41no—
150D244—41no—
151D244—42no—
152D244—81no—
153C4×D61—82no—
154Dic122—41no—
155Dic122—41no—
156Dic122—42no—
157Dic122—81no—
158C8×C61—21no—
159C8×C61—21no—
160C8×C61—21no—
161C8×C61—24no—
162C8×C61—42no—
163C8×C61#10412yescomplemented
164#9717—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#39011yescharacteristic
168C22×C61#49211yescharacteristic
169C22×C61#49511yescharacteristic
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61C2×#10411yescharacteristic
177C4×C61#42111yescharacteristic
178C4×C61C4×SD1612yes—
179C4×C61#46512yes—
180Dic61—82no—
181Dic61—82no—
182Dic61—81no—
183Dic61—81no—
184Dic61—81no—
185#3167—611no—
186#1986—611no—
187#1980—611no—
188C4×#106—611no—
189#1503—611no—
190#1502—611no—
191C8×M16D6111yescharacteristic, complemented
192C2×C61—21no—
193C2×C61—21no—
194C2×C61#196811yescharacteristic
195C2×C61#197611yescharacteristic
196C2×C61#198011yescharacteristic
197D61—161no—
198#533—611no—
199#532—611no—
200#498—611no—
201#492—611no—
202#487—611no—
203#486—611no—
204#465—1221no—
205#465—1221no—
206C4×SD16—1221no—
207C4×SD16—1221no—
208#431C2×D6111yescharacteristic
209C2×#106—1221no—
210C2×#104—1222no—
211C4×M16C2×D6111yescharacteristic
212C2×C4×C8C2×D6111yescharacteristic
213C4×C4⋊C4—611no—
214C4×C4⋊C4—611no—
215#340—1221no—
216#339—1222no—
217#328—1222no—
218#327—1222no—
219#322—21no—
220C82—21no—
221C61#971711yescharacteristic, complemented, Sylow
222C2×#41—1221no—
223C2×SD16—1221no—
224C2×SD16—1221no—
225C2×M16D24412yes—
226C22×C8D24411yescharacteristic
227C22×C8D24411yescharacteristic
228C4⋊Q8—611no—
229C4⋊Q8—611no—
230C4⋊Q8—611no—
231#127—611no—
232#125—1221no—
233#124—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236#121—1221no—
237#121—1221no—
238C4×Q8—1221no—
239C4×Q8—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242#117—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C42—1221no—
246C2×C42—1221no—
247C2×C42C22×D6111yescharacteristic
248#106—1224no—
249#106—1221no—
250#106—1221no—
251C4⋊C8—21no—
252#104—2444no—
253#103—1221no—
254#103—1221no—
255#102—1221no—
256#102—1221no—
257C22⋊C8D24412yes—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8C4×D6111yescharacteristic
262C4×C8C4×D6111yescharacteristic
263C4×C8C22⋊D6111yescharacteristic
264C4×C8C22⋊D6111yescharacteristic
265#95—1221no—
266#95—1221no—
267#41—2442no—
268#41—2442no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×Q8—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4C2×D24411yescharacteristic
280C22×C4C2×D24411yescharacteristic
281C22×C4C2×D24411yescharacteristic
282SD16—2442no—
283SD16—2442no—
284M16—22no—
285M16#1175819014yescomplemented
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8#1175819811yescharacteristic
291C2×C8#1175819811yescharacteristic
292C2×C8#1175819811yescharacteristic
293C2×C8#1175819811yescharacteristic
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—2442no—
310C42—2442no—
311C42—2441no—
312C42C2×C4×D6111yescharacteristic
313C42#1175822211yescharacteristic
314C42#1175822211yescharacteristic
315C42C2×C22⋊D6111yescharacteristic
316C23—2441no—
317C23#1451977411yescharacteristic
318Q8—4881no—
319Q8—2441no—
320Q8—2441no—
321Q8—2442no—
322D4—4881no—
323D4—4881no—
324D4—4881no—
325D4—2441no—
326D4—2441no—
327D4—2442no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4882no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4C2×#1175819811yescharacteristic
342C2×C4C4×D24411yescharacteristic
343C2×C4C4×D24411yescharacteristic
344C2×C4#1451975111yescharacteristic
345C2×C4#1451975111yescharacteristic
346C2×C4#1451976511yescharacteristic
347C2×C4C2×#1175819012yes—
348C2×C4#1451979912yes—
349C8—24no—
350C8—21no—
351C8—21no—
352C8—21no—
353C8—42no—
354C8#1451970312yescomplemented
355C22—21no—
356C22—21no—
357C22—4881no—
358C22—4881no—
359C22—4881no—
360C22#1683966411yescharacteristic
361C22#1684013511yescharacteristic
362C22#1684014611yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—4882no—
367C4—4882no—
368C4—4881no—
369C4—4881no—
370C4—4881no—
371C4C2×#1451970311yescharacteristic
372C4#1683977811yescharacteristic
373C4C4×#1175819012yes—
374C4#1683999112yes—
375C2—21no—
376C2—21no—
377C2—9761no—
378C2#2144667311yescharacteristic
379C2#2144671711yescharacteristic
380C2#2144673811yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC8×M16×C61C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenterC8×M16D61
hypocenterC61#9717
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #21446763C2semidirect
4. C4×#14519709C2semidirect
5. #21444319C2semidirect
7. C8×M16×C61C2semidirect
10. #16840160C4semidirect
11. #16840135C4semidirect
12. #16840113C4semidirect
13. #16840109C4semidirect
92. M16×C61SD16semidirect
163. C8×C61#104semidirect
191. C8×M16D61semidirect
221. C61#9717semidirect
285. M16#11758190semidirect
354. C8#14519703semidirect

Maximal subgroups

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

subgroupindex
#214563782
#214467632
#214467382
C4×#145197092
#214443192
#214443152
C8×M16×C612
#971761