Finite Group Databasebeta

← #29580943

Subgroups — #29580943

Order 15616.

564 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455906C212yesmaximal, complemented
2#21446616C211yesmaximal, characteristic, complemented
3#21444430C212yesmaximal, complemented
4#21443689C211yesmaximal, characteristic, complemented
5C61×#3245C211yesmaximal, characteristic, complemented
6C2×C4×D244C2211yescharacteristic
7#16840078—22no—
8#16840049—22no—
9#16839954—22no—
10#16839895—22no—
11#16839872—24no—
12#16839819C2212yes—
13C2×#14519689—22no—
14C2×#14519688C2211yescharacteristic
15#16839502—24no—
16C61×#532C2212yes—
17C61×#474—22no—
18C61×#466—22no—
19C61×#459—22no—
20C2×C4⋊C8×C61C2211yescharacteristic
21C22×D244D411yescharacteristic
22C22×C4×D61—21no—
23C2×#11758199—24no—
24C22×#92418—21no—
25C4×D244—22no—
26C4×D244—22no—
27C2×C4⋊Dic61D411yescharacteristic
28C2×#11758198—21no—
29#14519708—24no—
30C4⋊#92418—22no—
31#14519698—24no—
32#14519697—24no—
33C22⋊#92418—22no—
34#14519689—44no—
35#14519688—22no—
36#14519688D414yes—
37C2×#41×C61—22no—
38C2×D8×C61—22no—
39C22×C8×C61D412yes—
40C4⋊Q8×C61D412yes—
41#127×C61D412yes—
42#124×C61—22no—
43#121×C61—22no—
44#121×C61—22no—
45C4×D4×C61—22no—
46C4×D4×C61—22no—
47C2×C42×C61C2311yescharacteristic
48#107×C61—22no—
49C4⋊C8×C61—22no—
50#102×C61—24no—
51C23×D61—21no—
52#41×C61—84no—
53C2×Q8×C61—22no—
54C2×D4×C61—22no—
55C2×D4×C61—22no—
56C2×D4×C61—22no—
57C2×D4×C61—42no—
58C22×C4×C61—42no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C22×Dic61—21no—
63C2×D244—22no—
64C2×D244—42no—
65C2×C4×D61—42no—
66C2×C4×D61—42no—
67C2×C4×D61—41no—
68C2×C4×D61—41no—
69D8×C61—82no—
70C2×C8×C61—22no—
71C2×C8×C61—42no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—22no—
74C22⋊C4×C61—42no—
75C22⋊C4×C61—42no—
76C42×C61C2×D412yes—
77C42×C61C2×D412yes—
78#11758199—48no—
79#11758198—42no—
80C4⋊Dic61—22no—
81C2×#92418—22no—
82C2×#92418—24no—
83C2×#92418—41no—
84C2×#92418—41no—
85C23×C61—42no—
86C23×C61#12111yescharacteristic
87C22×D61—22no—
88C22×D61—42no—
89C22×D61—41no—
90C22×D61—41no—
91C22×D61—42no—
92Q8×C61—82no—
93D4×C61—44no—
94D4×C61—42no—
95D4×C61—42no—
96D4×C61—82no—
97D4×C61—84no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—84no—
104C2×C4×C61#12012yes—
105C2×C4×C61#12011yescharacteristic
106C2×C4×C61#12112yes—
107C2×C4×C61#12711yescharacteristic
108C2×Dic61—42no—
109C2×Dic61—41no—
110D244—24no—
111D244—42no—
112C4×D61—82no—
113C4×D61—81no—
114C4×D61—81no—
115C8×C61—42no—
116#92418—42no—
117#92418—44no—
118#10026—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—82no—
122C22×C61—82no—
123C22×C61—82no—
124C22×C61#39211yescharacteristic
125C22×C61#47212yes—
126C2×D61—44no—
127C2×D61—42no—
128C2×D61—82no—
129C2×D61—81no—
130C2×D61—81no—
131C4×C61—21no—
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—82no—
135C4×C61#45311yescharacteristic
136C4×C61#45411yescharacteristic
137Dic61—81no—
138#3245D6111yescharacteristic, complemented
139#3109—612no—
140#1955—611no—
141#1530—612no—
142#1290—611no—
143C2×C61—22no—
144C2×C61—162no—
145C2×C61#200611yescharacteristic
146C2×C61#201011yescharacteristic
147C2×C61#201811yescharacteristic
148D61—82no—
149#532C2×D6112yes—
150C2×C4×D4—611no—
151#481—1222no—
152#476—1222no—
153#474—22no—
154#466—22no—
155#459—22no—
156#459—1222no—
157#447—1222no—
158#442—1224no—
159#432—612no—
160C2×C4⋊C8C2×D6111yescharacteristic
161C2×C22⋊C8—1222no—
162C2×#97—611no—
163#329—1224no—
164C61#1002611yescharacteristic, complemented, Sylow
165C2×#41—22no—
166C22×D4—611no—
167C23×C4—1221no—
168C2×D8—22no—
169C2×D8—1224no—
170C22×C8—1221no—
171C22×C8C22⋊D6112yes—
172C4⋊Q8C22⋊D6112yes—
173#127C22⋊D6112yes—
174#124—22no—
175#121—22no—
176#121—22no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—1222no—
180C4×D4—1222no—
181C2×C4⋊C4—611no—
182C2×C22⋊C4—1221no—
183C2×C42C22×D6111yescharacteristic
184#107—22no—
185#106—1224no—
186C4⋊C8—22no—
187C4⋊C8—1222no—
188#102—24no—
189#102—1224no—
190#102—1224no—
191C22⋊C8—1222no—
192C22⋊C8—2444no—
193#97—614no—
194#97—1222no—
195C24—1221no—
196#41—84no—
197C2×Q8—22no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—1222no—
203C2×D4—2442no—
204C22×C4—42no—
205C22×C4—1221no—
206C22×C4—2442no—
207C22×C4—2442no—
208C22×C4—2441no—
209C22×C4—2441no—
210C22×C4D4×D6111yescharacteristic
211C22×C4#1175822411yescharacteristic
212C22×C4C2×C22⋊D6111yescharacteristic
213D8—82no—
214D8—2448no—
215C2×C8—22no—
216C2×C8—42no—
217C2×C8—1222no—
218C2×C8—1224no—
219C2×C8—2441no—
220C2×C8—2441no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—1222no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—2442no—
227C42D4×D6112yes—
228C42C2×C22⋊D6112yes—
229C23—42no—
230C23—1222no—
231C23—2442no—
232C23—2441no—
233C23—2442no—
234C23—2441no—
235C23#1451974811yescharacteristic
236Q8—82no—
237D4—44no—
238D4—42no—
239D4—42no—
240D4—82no—
241D4—84no—
242D4—1224no—
243D4—2442no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—84no—
250C2×C4—4882no—
251C2×C4—4881no—
252C2×C4—4881no—
253C2×C4—2442no—
254C2×C4—2441no—
255C2×C4#1451974512yes—
256C2×C4#1451974611yescharacteristic
257C2×C4#1451974912yes—
258C2×C4#1451977311yescharacteristic
259C8—42no—
260C8—2442no—
261C8—2444no—
262C22—21no—
263C22—21no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—4882no—
268C22—4881no—
269C22—4881no—
270C22—2444no—
271C22—2442no—
272C22#1683967011yescharacteristic
273C22#1684002912yes—
274C4—22no—
275C4—21no—
276C4—22no—
277C4—82no—
278C4—4881no—
279C4#1683993011yescharacteristic
280C4#1683993511yescharacteristic
281C2—22no—
282C2—162no—
283C2—4882no—
284C2#2144686111yescharacteristic
285C2#2144688311yescharacteristic
286C2#2144692611yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3245C2
socleC22×C61#392
hypercenter#3245D61
hypocenterC61#10026
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #21455906C2semidirect
2. #21446616C2semidirect
3. #21444430C2semidirect
4. #21443689C2semidirect
5. C61×#3245C2semidirect
138. #3245D61semidirect
164. C61#10026semidirect

Maximal subgroups

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

subgroupindex
#214559062
#214466162
#214444302
#214436892
C61×#32452
#1002661