Finite Group Databasebeta

← #29578392

Subgroups — #29578392

Order 15616.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446622C211yesmaximal, characteristic
2#21446582C211yesmaximal, characteristic
3#21445688C211yesmaximal, characteristic
4C2×#16839508C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic
7C61×#1988C211yesmaximal, characteristic
8C2×#14519708—21no—
9C2×C4⋊#92418C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519701—21no—
12C2×#14519701—21no—
13C2×#14519688—21no—
14C2×C4×#92418C2211yescharacteristic
15#16839632C2211yescharacteristic
16#16839524—21no—
17#16839517—21no—
18#16839508C414yescomplemented
19C2×C4⋊Q8×C61C2211yescharacteristic
20C2×C4⋊C8×C61C2211yescharacteristic
21C4×C4⋊C4×C61C2211yescharacteristic
22C61×#340—21no—
23C61×#340—21no—
24C22×#92418—21no—
25C22×#92418—21no—
26C22×#92418D411yescharacteristic
27C22×#92418D411yescharacteristic
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31#14519708—42no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C4⋊#92418C2×C412yes—
35C4⋊#92418C2×C412yes—
36#14519701—42no—
37#14519701—42no—
38#14519688—42no—
39C4×#92418—21no—
40C4×#92418—21no—
41C22×Q8×C61—21no—
42C22×C8×C61—21no—
43C4⋊Q8×C61—21no—
44C4⋊Q8×C61—21no—
45C4⋊Q8×C61—21no—
46C4⋊Q8×C61C2×C412yes—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C42×C61—21no—
52C2×C42×C61C2311yescharacteristic
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55#95×C61—21no—
56C2×Q8×C61—22no—
57C2×Q8×C61—41no—
58C2×Q8×C61—41no—
59C2×Q8×C61—41no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—41no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61#4111yescharacteristic
68C22×Dic61—41no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—22no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C42×C61—41no—
81C42×C61—41no—
82C42×C61C22×C411yescharacteristic
83C42×C61#4111yescharacteristic
84C42×C61#4111yescharacteristic
85C42×C61#4111yescharacteristic
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—81no—
91C2×#92418—21no—
92C2×#92418—21no—
93C2×#92418—22no—
94C2×#92418—22no—
95C2×#92418—21no—
96C2×#92418—21no—
97C2×#92418—21no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418SD1612yes—
103C23×C61#12111yescharacteristic
104Q8×C61—42no—
105Q8×C61—42no—
106Q8×C61—81no—
107Q8×C61—81no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—42no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—81no—
118C2×C4×C61—81no—
119C2×C4×C61#11711yescharacteristic
120C2×C4×C61C4×D411yescharacteristic
121C2×C4×C61C4×D411yescharacteristic
122C2×C4×C61#12311yescharacteristic
123C2×C4×C61#12411yescharacteristic
124C2×C4×C61#12611yescharacteristic
125C2×C4×C61C2×SD1611yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×C4×C61#13711yescharacteristic
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C8×C61—81no—
137#92418—22no—
138#92418—42no—
139#92418—42no—
140#92418—41no—
141#9570—611nomaximal, Sylow
142C22×C61#38811yescharacteristic
143C22×C61#46011yescharacteristic
144C22×C61#46311yescharacteristic
145C22×C61#46811yescharacteristic
146C22×C61#47011yescharacteristic
147C22×C61#47111yescharacteristic
148C22×C61#47311yescharacteristic
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—82no—
152C4×C61—81no—
153C4×C61—81no—
154C4×C61C4×SD1611yescharacteristic
155C4×C61#44011yescharacteristic
156C4×C61#44111yescharacteristic
157C4×C61#44211yescharacteristic
158C4×C61#48111yescharacteristic
159C4×C61#48211yescharacteristic
160C4×C61#48911yescharacteristic
161C4×C61#49111yescharacteristic
162Dic61—161no—
163#1988D6111yescharacteristic
164#1956—611no—
165#1948—611no—
166#1770—611no—
167C2×#332—611no—
168#1296—611no—
169#1277—611no—
170C2×C61#168611yescharacteristic
171C2×C61#169011yescharacteristic
172C2×C61#169911yescharacteristic
173C2×C61#170311yescharacteristic
174C2×C61#192611yescharacteristic
175C2×C61#193011yescharacteristic
176C2×C61#193511yescharacteristic
177C2×C4⋊Q8C2×D6111yescharacteristic
178C2×#106—1221no—
179C2×C4⋊C8—611no—
180C2×C4⋊C8—611no—
181C2×C4⋊C8C2×D6111yescharacteristic
182C2×#103—1221no—
183C2×#103—1221no—
184C2×#97—1221no—
185C2×C4×C8—611no—
186#384—611no—
187C4×C4⋊C4C2×D6111yescharacteristic
188#340—21no—
189#340—21no—
190#340—1221no—
191#336—1221no—
192#332—614no—
193C61#957011yescharacteristic, complemented, Sylow
194C22×Q8—21no—
195C22×C8—21no—
196C22×C8—611no—
197C22×C8—611no—
198C22×C8—1221no—
199C22×C8—1221no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8C4×D6112yes—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C22⋊D6111yescharacteristic
210C2×C4⋊C4C22⋊D6111yescharacteristic
211C2×C42—21no—
212C2×C42C22×D6111yescharacteristic
213#106—2442no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—612no—
217C4⋊C8—612no—
218C4⋊C8—1221no—
219C4⋊C8—1221no—
220#103—2442no—
221#103—2442no—
222#97—2442no—
223C4×C8—1221no—
224C4×C8—1221no—
225#95—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—2441no—
236C22×C4D4×D6111yescharacteristic
237C22×C4#1175822411yescharacteristic
238C22×C4C2×C22⋊D6111yescharacteristic
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—612no—
243C2×C8—1221no—
244C2×C8—1221no—
245C2×C8—1222no—
246C2×C8—1222no—
247C2×C8—1221no—
248C2×C8—1221no—
249C2×C8—1221no—
250C2×C8—2441no—
251C2×C8—2441no—
252C2×C8—2441no—
253C2×C8—2441no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—4881no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C42—41no—
268C42—41no—
269C42C2×C4×D6111yescharacteristic
270C42#1175822211yescharacteristic
271C42#1175822411yescharacteristic
272C42#1175822411yescharacteristic
273C23#1451974911yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—4881no—
290C2×C4—4881no—
291C2×C4—4881no—
292C2×C4#1451973311yescharacteristic
293C2×C4#1451973711yescharacteristic
294C2×C4C4×C22⋊D6111yescharacteristic
295C2×C4#1451975911yescharacteristic
296C2×C4#1451976411yescharacteristic
297C2×C4#1451977011yescharacteristic
298C2×C4SD16×D6111yescharacteristic
299C2×C4#1451979611yescharacteristic
300C2×C4#1451980111yescharacteristic
301C2×C4#1451980211yescharacteristic
302C2×C4#1451980411yescharacteristic
303C2×C4#1451980711yescharacteristic
304C2×C4#1451980811yescharacteristic
305C2×C4#1451980811yescharacteristic
306C8—81no—
307C8—1222no—
308C8—2441no—
309C8—2442no—
310C8—2442no—
311C22#1683965611yescharacteristic
312C22#1683996011yescharacteristic
313C22#1683997511yescharacteristic
314C22#1684001011yescharacteristic
315C22#1684001811yescharacteristic
316C22#1684002711yescharacteristic
317C22#1684003511yescharacteristic
318C4—21no—
319C4—21no—
320C4—81no—
321C4—82no—
322C4—81no—
323C4—9761no—
324C4#1683985311yescharacteristic
325C4#1683986011yescharacteristic
326C4#1683986711yescharacteristic
327C4#1683987111yescharacteristic
328C4#1684007911yescharacteristic
329C4#1684008411yescharacteristic
330C4#1684012111yescharacteristic
331C4#1684013011yescharacteristic
332C2#2144529311yescharacteristic
333C2#2144531111yescharacteristic
334C2#2144536411yescharacteristic
335C2#2144539211yescharacteristic
336C2#2144644911yescharacteristic
337C2#2144647711yescharacteristic
338C2#2144651211yescharacteristic
subgroupG/H
centerC23#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1988C2
socle, prime radicalC23×C61#121
cosocleC2×C42×C61C23
hypercenter#1988D61
hypocenterC61#9570
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
18. #16839508C4semidirect
193. C61#9570semidirect

Maximal subgroups

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

subgroupindex
#214466222
#214465822
#214456882
C2×#168395082
#214437032
#214436532
C61×#19882
#957061