Finite Group Databasebeta

← #30604024

Subgroups — #30604024

Order 15616.

368 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462056C212yesmaximal, complemented
2#21460768C212yesmaximal, complemented
3#21460751C212yesmaximal, complemented
4#21454522C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C2×#14519783C2211yescharacteristic
9#16840273C411yescharacteristic
10#16839838—22no—
11#16839831—22no—
12#16839788C2211yescharacteristic
13#16839728C411yescharacteristic
14#16839726C2211yescharacteristic
15#16839717C411yescharacteristic
16C22×M16×C61C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×#11758222C2×C411yescharacteristic
21#14519783—42no—
22C2×#11758194C2×C411yescharacteristic
23C2×#11758194C2311yescharacteristic
24C2×#11758189D412yes—
25C2×C8×D61D412yes—
26#14519760C812yes—
27#14519756—21no—
28#14519751—21no—
29#14519746C812yes—
30C4×C22⋊D61—22no—
31#14519736C2×C411yescharacteristic
32#14519706—22no—
33C22⋊#92418—22no—
34#14519689—22no—
35#14519687—21no—
36C8×Dic61—21no—
37C23×C4×C61C2×C411yescharacteristic
38C2×M16×C61—21no—
39C2×M16×C61—21no—
40C2×M16×C61—42no—
41C22×C8×C61C2×C411yescharacteristic
42C22×C8×C61C2×C411yescharacteristic
43C24×C61C2×C811yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61C2×C811yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C2×C22⋊D61—22no—
51C2×C22⋊D61C2×C812yes—
52#11758222—41no—
53#11758222—41no—
54C2×D244M1611yescharacteristic
55C2×C4×D61C22⋊C412yes—
56C2×Dic122M1611yescharacteristic
57M16×C61—42no—
58M16×C61—42no—
59C2×C8×C61—22no—
60C2×C8×C61—21no—
61C2×C8×C61—41no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22⋊C411yescharacteristic
64C22⋊Dic61—22no—
65C22⋊Dic61C2×C812yes—
66#11758198—22no—
67C4⋊Dic61—21no—
68#11758196—22no—
69C4×Dic61—21no—
70#11758194—41no—
71#11758194—41no—
72C2×#92418—21no—
73C2×#92418C2×D412yes—
74#11758189—42no—
75C8×D61—22no—
76C8×D61—22no—
77#11758187—44no—
78C23×C61—21no—
79C23×C61—41no—
80C23×C61—81no—
81C23×C61C22×C811yescharacteristic
82C22×D61C22⋊C812yes—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—42no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61C2×M1611yescharacteristic
92C22⋊D61—42no—
93C22⋊D61—82no—
94C2×Dic61—22no—
95C2×Dic61C22⋊C812yes—
96D244—41no—
97C4×D61—22no—
98C4×D61—22no—
99Dic122—41no—
100C8×C61—21no—
101C8×C61—41no—
102C8×C61#9912yes—
103#92418—22no—
104#92418—41no—
105#11484—611nomaximal, Sylow
106C22×C61—21no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—82no—
112C22×C61C2×C22⋊C811yescharacteristic
113C2×D61—22no—
114C2×D61—42no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61C2×#9911yescharacteristic
118C4×C61#41311yescharacteristic
119Dic61—22no—
120Dic61—42no—
121#2930—611no—
122#2115—612no—
123#1328—612no—
124#1320—612no—
125C2×C61—21no—
126C2×C61—41no—
127C2×C61—81no—
128C2×C61#145911yescharacteristic
129D61—42no—
130C2×#131—611no—
131C22×M16#692311yescharacteristic
132#525—611no—
133C2×M32—1222no—
134#436—1222no—
135#435—1222no—
136#424—611no—
137#408—611no—
138#407—611no—
139#405—611no—
140#349—614no—
141#349—1222no—
142C61#1148411yescharacteristic, complemented, Sylow
143C2×#41—611no—
144C23×C4C2×#692311yescharacteristic
145#131—2442no—
146C2×M16—21no—
147C2×M16—21no—
148C2×M16—42no—
149C2×M16—611no—
150C2×M16—612no—
151C2×M16—611no—
152C22×C8—612no—
153C22×C8C2×#692311yescharacteristic
154C22×C8C2×#692311yescharacteristic
155#123—612no—
156C22⋊Q8—1221no—
157#121—1221no—
158#120—612no—
159C4×D4—1222no—
160#117—611no—
161M32—1224no—
162M32—2442no—
163C2×C16—2442no—
164C4⋊C8—1222no—
165C22⋊C8—1222no—
166C22⋊C8—1222no—
167#97—1221no—
168C4×C8—1221no—
169C24D61⋊C811yescharacteristic
170#41—2441no—
171#41—2441no—
172C2×Q8—611no—
173C2×D4—612no—
174C2×D4—611no—
175C2×D4—1222no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—612no—
181C22×C4D61⋊C811yescharacteristic
182C22×C4C22×#692311yescharacteristic
183M16—42no—
184M16—42no—
185M16—2442no—
186M16—2441no—
187M16—2441no—
188C2×C8—22no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—612no—
192C2×C8—1222no—
193C2×C8—1222no—
194C2×C8—1221no—
195C2×C8C22⋊#692311yescharacteristic
196C2×C8C22⋊#692311yescharacteristic
197C4⋊C4—1222no—
198C4⋊C4—1221no—
199C22⋊C4—612no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C42—1221no—
203C16—2444no—
204C23—21no—
205C23—41no—
206C23—81no—
207C23—612no—
208C23C2×D61⋊C811yescharacteristic
209Q8—2441no—
210D4—4882no—
211D4—2441no—
212D4—2442no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—612no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4C2×C22⋊#692311yescharacteristic
225C2×C4D61⋊M1611yescharacteristic
226C8—21no—
227C8—41no—
228C8—1222no—
229C8—2441no—
230C8#1451983512yes—
231C22—21no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—82no—
237C22—1222no—
238C22—2442no—
239C22D61⋊(C22⋊C8)11yescharacteristic
240C4—21no—
241C4—41no—
242C4—1222no—
243C4—2442no—
244C4C2×#1451983511yescharacteristic
245C4#1684074811yescharacteristic
246C2—21no—
247C2—41no—
248C2—81no—
249C2—2442no—
250C2#2146105411yescharacteristic
subgroupG/H
centerC4C2×#14519835
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC2×C61#1459
prime radical#16840273C4
cosocleC2×#11758194C23
hypercenterC22×M16#6923
hypocenterC61#11484
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #21462056C2semidirect
2. #21460768C2semidirect
3. #21460751C2semidirect
142. C61#11484semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214607682
#214607512
#214545222
#1148461