Finite Group Databasebeta

← #29581304

Subgroups — #29581304

Order 15616.

552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#16840128C212yesmaximal
2#21446642C211yesmaximal, characteristic
3C2×#16839504C212yesmaximal, complemented
4#21443700C211yesmaximal, characteristic, complemented
5C61×#2822C211yesmaximal, characteristic, complemented
6C2×#14519774C2211yescharacteristic
7#16840128—24no—
8#16840128—24no—
9C2×#14519697—22no—
10C2×#14519697—22no—
11C2×#14519697—22no—
12C2×#14519688C2211yescharacteristic
13C2×#14519688C2212yes—
14#16839504—24no—
15C2×#125×C61C2212yes—
16C61×#400—22no—
17C61×#398—22no—
18C61×#398—22no—
19C61×#382C2211yescharacteristic
20C22×D244—22no—
21C22×D244—21no—
22C22×#92418—21no—
23C22×#92418—22no—
24#14519774—22no—
25#14519774—21no—
26#14519774D412yes—
27#14519697—28no—
28#14519697—28no—
29#14519697—44no—
30#14519688—22no—
31#14519688—22no—
32#14519688D414yes—
33#125×C61—22no—
34#125×C61—22no—
35#125×C61—22no—
36#125×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61D412yes—
41C2×C4⋊C4×C61D412yes—
42C2×C4⋊C4×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44#95×C61—24no—
45#95×C61—22no—
46#95×C61—22no—
47C23×D61—41no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61C2×D412yes—
52C22×C4×C61C2×D411yescharacteristic
53C2×D244—24no—
54C2×D244—22no—
55C2×D244—48no—
56C2×D244—42no—
57C2×D244—42no—
58C2×D244—42no—
59C2×D244—41no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—22no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—82no—
70C42×C61C2×D411yescharacteristic
71C42×C61C2×D412yes—
72C42×C61#4111yescharacteristic
73C2×#92418—22no—
74C2×#92418—24no—
75C2×#92418—44no—
76C2×#92418—41no—
77C2×#92418—41no—
78C23×C61#12011yescharacteristic
79C22×D61—42no—
80C22×D61—81no—
81C22×D61—84no—
82C22×D61—81no—
83C2×C4×C61—21no—
84C2×C4×C61—24no—
85C2×C4×C61—21no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—44no—
91C2×C4×C61—44no—
92C2×C4×C61—42no—
93C2×C4×C61#12012yes—
94C2×C4×C61#12111yescharacteristic
95C2×C4×C61#12112yes—
96C2×C4×C61#12711yescharacteristic
97D244—48no—
98D244—44no—
99D244—84no—
100D244—82no—
101#92418—44no—
102#92418—42no—
103#10080—611nomaximal, Sylow
104C22×C61#39211yescharacteristic
105C22×C61#45311yescharacteristic
106C22×C61#45414yes—
107C22×C61#45411yescharacteristic
108C2×D61—84no—
109C2×D61—82no—
110C2×D61—162no—
111C2×D61—162no—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—82no—
117C4×C61—82no—
118C4×C61—82no—
119C2×#490—612no—
120#2822D6111yescharacteristic, complemented
121#1961—611no—
122C2×#330—612no—
123#1295—611no—
124C2×C61#165712yes—
125C2×C61#165812yes—
126C2×C61#200312yes—
127C2×C61#200611yescharacteristic
128D61—162no—
129C2×#127—611no—
130C2×#125C2×D6112yes—
131#490—1224no—
132#490—1224no—
133C2×#102—1222no—
134C2×#102—1222no—
135C2×#102—1222no—
136C2×#97—612no—
137C2×#97—611no—
138#400—22no—
139#398—22no—
140#398—22no—
141#382C2×D6111yescharacteristic
142#330—1224no—
143C61#1008011yescharacteristic, complemented, Sylow
144C22×D4—1222no—
145C22×D4—1221no—
146C22×C8—1221no—
147C22×C8—1222no—
148#127—612no—
149#127—1222no—
150#127—1221no—
151#125—22no—
152#125—22no—
153#125—22no—
154#125—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4C22⋊D6112yes—
159C2×C4⋊C4C22⋊D6112yes—
160C2×C4⋊C4C22⋊D6112yes—
161C2×C42C22×D6111yescharacteristic
162#102—1228no—
163#102—1228no—
164#102—2444no—
165#97—614no—
166#97—1222no—
167#97—1222no—
168#95—24no—
169#95—22no—
170#95—22no—
171C24—2441no—
172C2×D4—1224no—
173C2×D4—1222no—
174C2×D4—2442no—
175C2×D4—2448no—
176C2×D4—2442no—
177C2×D4—2442no—
178C2×D4—2441no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C2×C22⋊D6112yes—
183C22×C4C2×C22⋊D6111yescharacteristic
184C2×C8—1222no—
185C2×C8—1224no—
186C2×C8—2444no—
187C2×C8—2441no—
188C2×C8—2441no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—82no—
199C42D4×D6111yescharacteristic
200C42D4×D6112yes—
201C42#1175822411yescharacteristic
202C23—4881no—
203C23—4881no—
204C23—4884no—
205C23—2442no—
206C23#1451974611yescharacteristic
207D4—4884no—
208D4—4882no—
209D4—2448no—
210D4—2444no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—44no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4#1451974512yes—
222C2×C4#1451974811yescharacteristic
223C2×C4#1451974912yes—
224C2×C4#1451977311yescharacteristic
225C8—2444no—
226C8—2442no—
227C22—9762no—
228C22—9762no—
229C22—4884no—
230C22—4882no—
231C22#1683967011yescharacteristic
232C22#1683993011yescharacteristic
233C22#1683993511yescharacteristic
234C22#1683993514yes—
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—82no—
241C4—82no—
242C2—9762no—
243C2#2144511712yes—
244C2#2144512112yes—
245C2#2144683912yes—
246C2#2144686111yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2822C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenter#2822D61
hypocenterC61#10080
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
3. C2×#16839504C2semidirect
4. #21443700C2semidirect
5. C61×#2822C2semidirect
120. #2822D61semidirect
143. C61#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#168401282
#214466422
C2×#168395042
#214437002
C61×#28222
#1008061