Finite Group Databasebeta

← #29579161

Subgroups — #29579161

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#21456374C211yesmaximal, characteristic
2#21446763C211yesmaximal, characteristic, complemented
3C4×#14519708C211yesmaximal, characteristic, complemented
4#21444317C211yesmaximal, characteristic, complemented
5#21444314C211yesmaximal, characteristic
6M16×#92418C211yesmaximal, characteristic, complemented
7C61×#1980C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840158C411yescharacteristic, complemented
10#16840134C411yescharacteristic, complemented
11#16840114C411yescharacteristic, complemented
12#16840108C411yescharacteristic, complemented
13#16839989—21no—
14#16839989—21no—
15C4×#11758200—21no—
16C4×#11758200—21no—
17#16839815C2211yescharacteristic
18C2×#14519708—21no—
19C2×C4×#92418C2211yescharacteristic
20C4×C4⋊Dic61C2211yescharacteristic
21#16839524—21no—
22#16839523—22no—
23#16839498—22no—
24#16839496—22no—
25#16839483—21no—
26C8×#92418—21no—
27C61×#532C2211yescharacteristic
28C2×#104×C61—22no—
29C4×M16×C61C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C2×#11758200—21no—
32C2×#11758200—21no—
33C22×#92418D411yescharacteristic
34C22×#92418D411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519777C2×C411yescharacteristic
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43C2×C4⋊Dic61—21no—
44C2×C4×Dic61—21no—
45#14519708—24no—
46#14519708—21no—
47#14519708—21no—
48C4⋊#92418—21no—
49#14519700—21no—
50#14519700—21no—
51#14519698—21no—
52#14519698—21no—
53C22⋊#92418D412yes—
54C4×#92418—21no—
55C4×#92418C2×C411yescharacteristic
56C4×#92418C2×C411yescharacteristic
57C4×#92418D411yescharacteristic
58C4×#92418D411yescharacteristic
59#14519684—21no—
60C2×#41×C61—21no—
61C2×M16×C61D412yes—
62C4⋊Q8×C61C2×C411yescharacteristic
63#127×C61C2×C411yescharacteristic
64#124×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72#104×C61—44no—
73#97×C61—21no—
74C4×C8×C61—21no—
75#95×C61—21no—
76#41×C61—42no—
77#41×C61—42no—
78C2×Q8×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×Dic61—41no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91M16×C61—22no—
92M16×C61SD1614yescomplemented
93C2×C8×C61—22no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C42×C61—42no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—41no—
106#11758200—42no—
107#11758200—42no—
108C4⋊Dic61—22no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—41no—
114#11758196—41no—
115#11758196—41no—
116C4×Dic61—41no—
117C4×Dic61—42no—
118C2×#92418—22no—
119C2×#92418—22no—
120C2×#92418—41no—
121C2×#92418C22⋊C411yescharacteristic
122C2×#92418C22⋊C411yescharacteristic
123C2×#92418C22⋊C411yescharacteristic
124C2×#92418C22⋊C411yescharacteristic
125C23×C61—41no—
126C23×C61#12711yescharacteristic
127Q8×C61—42no—
128D4×C61—41no—
129D4×C61—41no—
130D4×C61—42no—
131D4×C61—81no—
132D4×C61—81no—
133D4×C61—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—82no—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12411yescharacteristic
148C2×C4×C61C2×SD1612yes—
149C2×C4×C61#13512yes—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155Dic122—41no—
156Dic122—41no—
157Dic122—81no—
158C8×C61—24no—
159#92418—21no—
160#92418—21no—
161#92418—21no—
162#92418—42no—
163#92418#10412yescomplemented
164#9717—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61#39011yescharacteristic
171C22×C61#49211yescharacteristic
172C22×C61#49511yescharacteristic
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—82no—
177C4×C61—81no—
178C4×C61C2×#10411yescharacteristic
179C4×C61#42111yescharacteristic
180C4×C61C4×SD1612yes—
181C4×C61#46512yes—
182Dic61—82no—
183Dic61—81no—
184Dic61—81no—
185#3167—611no—
186#1986—611no—
187#1980D6111yescharacteristic
188C4×#106—611no—
189#1503—611no—
190#1502—611no—
191C8×M16—611no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61—161no—
195C2×C61#196811yescharacteristic
196C2×C61#197611yescharacteristic
197C2×C61#198011yescharacteristic
198#533—611no—
199#532C2×D6111yescharacteristic
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#431—611no—
209C2×#106—1221no—
210C2×#104—22no—
211C4×M16C2×D6111yescharacteristic
212C2×C4×C8—611no—
213C4×C4⋊C4—611no—
214C4×C4⋊C4C2×D6111yescharacteristic
215#340—1221no—
216#339—1222no—
217#328—1222no—
218#327—1222no—
219#322—1221no—
220C82—1221no—
221C61#971711yescharacteristic, complemented, Sylow
222C2×#41—21no—
223C2×SD16—1221no—
224C2×SD16—1221no—
225C2×M16C22⋊D6112yes—
226C22×C8—611no—
227C22×C8—611no—
228C4⋊Q8—611no—
229C4⋊Q8—611no—
230C4⋊Q8C4×D6111yescharacteristic
231#127C4×D6111yescharacteristic
232#125—1221no—
233#124—21no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236#121—21no—
237#121—21no—
238C4×Q8—1221no—
239C4×Q8—1221no—
240C4×D4—21no—
241C4×D4—21no—
242#117—1221no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—1221no—
245C2×C42—21no—
246C2×C42—1221no—
247C2×C42C22×D6111yescharacteristic
248#106—1221no—
249#106—1221no—
250#106—1224no—
251C4⋊C8—1221no—
252#104—44no—
253#103—1221no—
254#103—1221no—
255#102—1221no—
256#102—1221no—
257C22⋊C8—612no—
258#97—21no—
259C4×C8—21no—
260C4×C8—611no—
261C4×C8—611no—
262C4×C8—611no—
263C4×C8—611no—
264C4×C8—1221no—
265#95—21no—
266#95—1221no—
267#41—42no—
268#41—42no—
269C2×Q8—21no—
270C2×Q8—1221no—
271C2×Q8—1221no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—2441no—
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282SD16—2442no—
283SD16—2442no—
284M16—22no—
285M16#1175820014yescomplemented
286C2×C8—22no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—611no—
291C2×C8—1222no—
292C2×C8—1222no—
293C2×C8—2441no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—1222no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—2441no—
309C42—42no—
310C42—2442no—
311C42—2441no—
312C42C2×C4×D6111yescharacteristic
313C42#1175822211yescharacteristic
314C42D4×D6111yescharacteristic
315C42#1175822411yescharacteristic
316C23—41no—
317C23#1451977311yescharacteristic
318Q8—42no—
319Q8—4881no—
320Q8—2441no—
321Q8—2441no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—2442no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4C22⋊C4×D6111yescharacteristic
342C2×C4#1451973711yescharacteristic
343C2×C4C4×C22⋊D6111yescharacteristic
344C2×C4#1451974911yescharacteristic
345C2×C4#1451975011yescharacteristic
346C2×C4#1451976311yescharacteristic
347C2×C4C2×#1175820012yes—
348C2×C4#1451979712yes—
349C8—24no—
350C8—612no—
351C8—1221no—
352C8—1221no—
353C8—1221no—
354C8—2442no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1683966211yescharacteristic
361C22#1684013411yescharacteristic
362C22#1684014411yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—4882no—
369C4—4881no—
370C4—4881no—
371C4#104×D6111yescharacteristic
372C4#1683977711yescharacteristic
373C4C4×#1175820012yes—
374C4#1683998912yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2#2144667211yescharacteristic
379C2#2144671611yescharacteristic
380C2#2144673611yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1980C2
socleC22×C61#390
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1980D61
hypocenterC61#9717
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #21446763C2semidirect
3. C4×#14519708C2semidirect
4. #21444317C2semidirect
6. M16×#92418C2semidirect
9. #16840158C4semidirect
10. #16840134C4semidirect
11. #16840114C4semidirect
12. #16840108C4semidirect
92. M16×C61SD16semidirect
163. #92418#104semidirect
221. C61#9717semidirect
285. M16#11758200semidirect

Maximal subgroups

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

subgroupindex
#214563742
#214467632
C4×#145197082
#214443172
#214443142
M16×#924182
C61×#19802
#971761