Finite Group Databasebeta

← #29580945

Subgroups — #29580945

Order 15616.

564 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 83 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#21457129C211yesmaximal, characteristic, complemented
2#21455910C212yesmaximal, complemented
3#21444429C212yesmaximal, complemented
4#21443689C211yesmaximal, characteristic, complemented
5C61×#1955C211yesmaximal, characteristic, complemented
6#16840312C2212yes—
7#16840080—22no—
8#16840052—22no—
9#16840043—22no—
10#16839998—22no—
11#16839958—22no—
12#16839957—22no—
13#16839896—22no—
14#16839872—24no—
15#16839819C2212yes—
16#16839501—24no—
17C2×C4×D4×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×C22⋊C8×C61—22no—
20C2×#97×C61C2211yescharacteristic
21C2×#11758222—22no—
22C2×D488—22no—
23C2×#11758199—24no—
24#14519777D412yes—
25#14519774D412yes—
26#14519765—22no—
27#14519751—22no—
28#14519751—22no—
29C4×D244—22no—
30C4×D244—22no—
31#14519711—22no—
32#14519708—24no—
33C4⋊#92418—22no—
34#14519699—24no—
35#14519698—24no—
36#14519697—24no—
37C22⋊#92418—22no—
38#14519688D414yes—
39C22×D4×C61D411yescharacteristic
40C23×C4×C61—21no—
41C22×C8×C61—21no—
42C22×C8×C61D412yes—
43C4×D4×C61—22no—
44C4×D4×C61—22no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C22⋊C4×C61—21no—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61—22no—
49C22⋊C8×C61—44no—
50#97×C61—22no—
51C24×C61—21no—
52C2×D4×C61—22no—
53C2×D4×C61—42no—
54C22×C4×C61—21no—
55C22×C4×C61—42no—
56C22×C4×C61—42no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C2×C22⋊D61—42no—
63#11758222—84no—
64C2×D244—22no—
65C2×D244—22no—
66C2×D244—22no—
67C2×C4×D61—42no—
68C2×Dic122—22no—
69C2×C8×C61—22no—
70C2×C8×C61—22no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61—42no—
74C4⋊C4×C61—22no—
75C22⋊C4×C61—42no—
76C42×C61C2×D412yes—
77C42×C61C2×D412yes—
78#11758199—48no—
79#11758198—42no—
80#11758198—42no—
81C4⋊Dic61—22no—
82C4⋊Dic61—22no—
83C2×#92418—24no—
84D488—82no—
85C23×C61—22no—
86C23×C61—42no—
87C23×C61—41no—
88C23×C61—41no—
89C23×C61—42no—
90C23×C61#12111yescharacteristic
91C22×D61—42no—
92D4×C61—24no—
93D4×C61—42no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61—41no—
100C2×C4×C61—82no—
101C2×C4×C61—81no—
102C2×C4×C61—81no—
103C2×C4×C61#12012yes—
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61#12112yes—
106C2×C4×C61#12711yescharacteristic
107C22⋊D61—84no—
108C2×Dic61—42no—
109D244—44no—
110D244—42no—
111D244—42no—
112D244—82no—
113C4×D61—84no—
114Dic122—82no—
115C8×C61—42no—
116C8×C61—42no—
117#92418—44no—
118#10026—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—44no—
122C22×C61—42no—
123C22×C61—82no—
124C22×C61—81no—
125C22×C61—81no—
126C22×C61#39211yescharacteristic
127C22×C61#47212yes—
128C2×D61—82no—
129C2×D61—82no—
130C2×D61—82no—
131C4×C61—21no—
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—81no—
135C4×C61#45311yescharacteristic
136C4×C61#45411yescharacteristic
137Dic61—82no—
138#3245—611no—
139#3109—612no—
140#1955D6111yescharacteristic, complemented
141#1530—612no—
142#1290—611no—
143C2×C61—22no—
144C2×C61—82no—
145C2×C61#200611yescharacteristic
146C2×C61#201011yescharacteristic
147C2×C61#201811yescharacteristic
148D61—162no—
149#532—612no—
150C2×C4×D4C2×D6111yescharacteristic
151#481—1222no—
152#476—1222no—
153#474—1222no—
154#466—1222no—
155#459—1222no—
156#459—1222no—
157#447—1222no—
158#442—1224no—
159#432—612no—
160C2×C4⋊C8C2×D6111yescharacteristic
161C2×C22⋊C8—22no—
162C2×#97C2×D6111yescharacteristic
163#329—1224no—
164C61#1002611yescharacteristic, complemented, Sylow
165C2×#41—1222no—
166C22×D4D24411yescharacteristic
167C23×C4—21no—
168C2×D8—1222no—
169C2×D8—1224no—
170C22×C8—21no—
171C22×C8C22⋊D6112yes—
172C4⋊Q8—612no—
173#127—612no—
174#124—1222no—
175#121—1222no—
176#121—1222no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—1222no—
180C4×D4—1222no—
181C2×C4⋊C4D24411yescharacteristic
182C2×C22⋊C4—21no—
183C2×C42C22×D6111yescharacteristic
184#107—1222no—
185#106—1224no—
186C4⋊C8—22no—
187C4⋊C8—1222no—
188#102—1224no—
189#102—1224no—
190#102—1224no—
191C22⋊C8—44no—
192C22⋊C8—1222no—
193#97—22no—
194#97—614no—
195C24—21no—
196#41—4884no—
197C2×Q8—1222no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—1222no—
201C2×D4—1222no—
202C2×D4—1222no—
203C2×D4—2442no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—2442no—
210C22×C4C2×D24411yescharacteristic
211C22×C4#1175822211yescharacteristic
212C22×C4C2×C22⋊D6111yescharacteristic
213D8—4882no—
214D8—2448no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—42no—
220C2×C8—1224no—
221C4⋊C4—22no—
222C4⋊C4—1222no—
223C4⋊C4—1222no—
224C22⋊C4—42no—
225C22⋊C4—2442no—
226C22⋊C4—2442no—
227C42D4×D6112yes—
228C42D4×D6112yes—
229C23—22no—
230C23—42no—
231C23—41no—
232C23—42no—
233C23—41no—
234C23—2442no—
235C23#1451975111yescharacteristic
236Q8—4882no—
237D4—24no—
238D4—42no—
239D4—4882no—
240D4—4884no—
241D4—2444no—
242D4—2442no—
243D4—2442no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—4884no—
254C2×C4—2442no—
255C2×C4#1451974511yescharacteristic
256C2×C4#1451974712yes—
257C2×C4#1451975012yes—
258C2×C4#1451977311yescharacteristic
259C8—42no—
260C8—42no—
261C8—2444no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22—4882no—
270C22—4882no—
271C22—4882no—
272C22#1683967111yescharacteristic
273C22#1684003212yes—
274C4—22no—
275C4—21no—
276C4—22no—
277C4—81no—
278C4—4882no—
279C4#1683992911yescharacteristic
280C4#1683993411yescharacteristic
281C2—22no—
282C2—82no—
283C2—9762no—
284C2#2144686011yescharacteristic
285C2#2144688611yescharacteristic
286C2#2144692811yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1955C2
socleC22×C61#392
hypercenter#1955D61
hypocenterC61#10026
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #21457129C2semidirect
2. #21455910C2semidirect
3. #21444429C2semidirect
4. #21443689C2semidirect
5. C61×#1955C2semidirect
140. #1955D61semidirect
164. C61#10026semidirect

Maximal subgroups

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

subgroupindex
#214571292
#214559102
#214444292
#214436892
C61×#19552
#1002661