Finite Group Databasebeta

← #30604027

Subgroups — #30604027

Order 15616.

368 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462055C212yesmaximal, complemented
2#21460768C212yesmaximal, complemented
3#21460752C212yesmaximal, complemented
4#21454525C211yesmaximal, characteristic
5C2×#14519851—22no—
6#16840658—22no—
7#16840658C2214yes—
8C2×#14519784C2211yescharacteristic
9C22×#11758189C411yescharacteristic
10#16840269C411yescharacteristic
11#16839837—22no—
12#16839830—22no—
13#16839788C2211yescharacteristic
14#16839725C2211yescharacteristic
15#16839720C411yescharacteristic
16C61×#408C411yescharacteristic
17#14519851—24no—
18#14519851—42no—
19C2×#11758187—42no—
20C22×C4×D61C2×C411yescharacteristic
21#14519784—42no—
22C2×#11758194D412yes—
23C2×#11758194C2311yescharacteristic
24C2×#11758189—21no—
25C2×#11758189—21no—
26C2×#11758189—42no—
27C22×#92418C2×C411yescharacteristic
28C22×#92418D412yes—
29#14519758C812yes—
30#14519753—21no—
31#14519748—21no—
32#14519745C812yes—
33C4×C22⋊D61—22no—
34#14519736C2×C411yescharacteristic
35#14519706—22no—
36#14519689—22no—
37#14519687—21no—
38C8×Dic61—21no—
39C2×#41×C61C2×C411yescharacteristic
40C2×M16×C61C2×C411yescharacteristic
41C22×C8×C61C2×C411yescharacteristic
42C22⋊C8×C61—22no—
43C23×D61C2×C811yescharacteristic
44#41×C61—41no—
45#41×C61—41no—
46C2×Q8×C61M1611yescharacteristic
47C2×D4×C61C2×C812yes—
48C2×D4×C61M1611yescharacteristic
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C22×C411yescharacteristic
51C2×C22⋊D61—22no—
52C22×Dic61C2×C811yescharacteristic
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—41no—
56C2×C4×D61—41no—
57M16×C61—41no—
58C2×C8×C61—21no—
59C2×C8×C61—21no—
60C2×C8×C61—41no—
61C22⋊Dic61—22no—
62C22⋊Dic61C2×C812yes—
63#11758198—22no—
64C4⋊Dic61—21no—
65#11758196—22no—
66C4×Dic61—21no—
67#11758194—42no—
68#11758194—41no—
69C2×#92418—22no—
70C2×#92418—22no—
71C2×#92418—22no—
72C2×#92418C22⋊C411yescharacteristic
73C2×#92418C22⋊C411yescharacteristic
74C2×#92418C2×D412yes—
75#11758189—42no—
76#11758189—42no—
77#11758187—44no—
78C23×C61C22⋊C812yes—
79C23×C61C22×C811yescharacteristic
80C22×D61—21no—
81C22×D61—41no—
82C22×D61—81no—
83Q8×C61—41no—
84D4×C61—42no—
85D4×C61—41no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61C22⋊C812yes—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61C2×M1611yescharacteristic
93C22⋊D61—82no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96C2×Dic61—41no—
97C4×D61—42no—
98C4×D61—41no—
99C4×D61—41no—
100C8×C61—41no—
101C8×C61—41no—
102#92418—22no—
103#92418—21no—
104#92418#9912yes—
105#11484—611nomaximal, Sylow
106C22×C61—21no—
107C22×C61—22no—
108C22×C61—42no—
109C22×C61—41no—
110C22×C61C2×C22⋊C811yescharacteristic
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—82no—
115C4×C61—21no—
116C4×C61—22no—
117C4×C61C2×#9911yescharacteristic
118C4×C61#41311yescharacteristic
119Dic61—42no—
120Dic61—41no—
121#2930—611no—
122#2115—612no—
123#1328—612no—
124#1320—612no—
125C2×C61—21no—
126C2×C61—41no—
127C2×C61—42no—
128C2×C61#145911yescharacteristic
129D61—81no—
130C2×#131—611no—
131C22×M16—611no—
132#525—611no—
133C2×M32—1222no—
134#436—1222no—
135#435—1222no—
136#424—611no—
137#408#692311yescharacteristic
138#407—611no—
139#405—611no—
140#349—614no—
141#349—1222no—
142C61#1148411yescharacteristic, complemented, Sylow
143C2×#41C2×#692311yescharacteristic
144C23×C4—611no—
145#131—2442no—
146C2×M16—612no—
147C2×M16—611no—
148C2×M16—1221no—
149C2×M16—1221no—
150C2×M16—2442no—
151C2×M16C2×#692311yescharacteristic
152C22×C8—612no—
153C22×C8—611no—
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—22no—
166C22⋊C8—1222no—
167#97—1221no—
168C4×C8—1221no—
169C24—611no—
170#41—41no—
171#41—41no—
172C2×Q8#1175821311yescharacteristic
173C2×D4—1222no—
174C2×D4D61⋊C812yes—
175C2×D4#1175821311yescharacteristic
176C22×C4—611no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—2441no—
180C22×C4—2441no—
181C22×C4C22⋊#692312yes—
182C22×C4C22×#692311yescharacteristic
183M16—41no—
184M16—2442no—
185M16—2442no—
186M16—2441no—
187M16—2442no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—611no—
192C2×C8—611no—
193C2×C8—612no—
194C2×C8—1222no—
195C2×C8—1222no—
196C2×C8—1222no—
197C4⋊C4—1222no—
198C4⋊C4—1221no—
199C22⋊C4—612no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C42—1221no—
203C16—2444no—
204C23—1221no—
205C23—4881no—
206C23—2441no—
207C23#1451983412yes—
208C23C2×D61⋊C811yescharacteristic
209Q8—41no—
210D4—42no—
211D4—41no—
212D4—4882no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—2442no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4#1451983412yes—
224C2×C4C2×C22⋊#692311yescharacteristic
225C2×C4C2×#1175821311yescharacteristic
226C8—41no—
227C8—41no—
228C8—612no—
229C8—1222no—
230C8—1221no—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—41no—
235C22—4882no—
236C22—2441no—
237C22—2441no—
238C22—2441no—
239C22C2×#1451983411yescharacteristic
240C4—21no—
241C4—22no—
242C4—2442no—
243C4—2441no—
244C4D61⋊#9911yescharacteristic
245C4#1684074911yescharacteristic
246C2—21no—
247C2—41no—
248C2—42no—
249C2—4881no—
250C2#2146105711yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61#1459
prime radical#16840269C4
cosocleC2×#11758194C23
hypercenter#408#6923
hypocenterC61#11484
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #21462055C2semidirect
2. #21460768C2semidirect
3. #21460752C2semidirect
142. C61#11484semidirect

Maximal subgroups

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

subgroupindex
#214620552
#214607682
#214607522
#214545252
#1148461