Finite Group Databasebeta

← #30594932

Subgroups — #30594932

Order 15616.

296 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460752C211yesmaximal, characteristic, complemented
2#21460699C211yesmaximal, characteristic, complemented
3#21446883C211yesmaximal, characteristic
4C4×C22⋊#6923—21no—
5#16840658—21no—
6#16840269—21no—
7#16839779—21no—
8#16839725C2211yescharacteristic
9#16839519C411yescharacteristic, complemented
10C61×#575C411yescharacteristic, complemented
11C2×C22⋊#6923—41no—
12C2×C4×#6923—41no—
13#14519851—41no—
14(C2×#6923)⋊C4—22no—
15C22×C4×D61D411yescharacteristic
16C2×#11758194D411yescharacteristic
17#14519758—41no—
18#14519753—41no—
19#14519748—41no—
20#14519745—41no—
21C4×C22⋊D61—42no—
22#14519736—21no—
23#14519704—42no—
24#14519689—41no—
25C2×#41×C61—21no—
26#137×C61—41no—
27AGL(1,ℤ/8)×C61—41no—
28#135×C61—41no—
29C2×M16×C61C2×C411yescharacteristic
30C23×D61D811yescharacteristic
31C22×#6923—42no—
32#41×C61—41no—
33#41×C61—41no—
34#41×C61—41no—
35#41×C61—41no—
36C2×Q8×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—41no—
39C22×C4×C61—41no—
40C22×C4×C61C22⋊C411yescharacteristic
41C2×C22⋊D61—42no—
42C22×Dic61SD1611yescharacteristic
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—41no—
46C2×C4×D61—41no—
47C22⋊#6923—44no—
48C4×#6923—81no—
49C4×#6923—81no—
50Q16×C61—41no—
51SD16×C61—42no—
52D8×C61—41no—
53M16×C61—41no—
54C2×C8×C61—21no—
55C22⋊Dic61—42no—
56C22⋊Dic61—41no—
57#11758198—42no—
58C4⋊Dic61—41no—
59#11758196—42no—
60C4×Dic61—22no—
61#11758194—41no—
62C2×#92418—21no—
63#11758187—81no—
64C23×C61—41no—
65C23×C61#10211yescharacteristic
66C22×D61—21no—
67C22×D61—42no—
68C22×D61—41no—
69C2×#6923—44no—
70C2×#6923—82no—
71C2×#6923—82no—
72Q8×C61—41no—
73Q8×C61—41no—
74D4×C61—41no—
75D4×C61—41no—
76D4×C61—81no—
77D4×C61—81no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—41no—
81C2×C4×C61—81no—
82C2×C4×C61—81no—
83C2×C4×C61#9911yescharacteristic
84C2×C4×C61#10411yescharacteristic
85C22⋊D61—84no—
86C2×Dic61—21no—
87C2×Dic61—41no—
88C2×Dic61—42no—
89C4×D61—41no—
90C4×D61—41no—
91C4×D61—81no—
92C8×C61—41no—
93#92418—41no—
94#7396—611nomaximal, Sylow
95C22×C61—21no—
96C22×C61—41no—
97C22×C61—82no—
98C22×C61—81no—
99C22×C61#32711yescharacteristic
100C2×D61—22no—
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—42no—
104C2×D61—81no—
105#6923—84no—
106C4×C61—21no—
107C4×C61—81no—
108C4×C61AΣL(1,𝔽16)11yescharacteristic
109C4×C61#35311yescharacteristic
110Dic61—41no—
111Dic61—82no—
112#2010—611no—
113#1320—611no—
114#1297—611no—
115C2×C61—21no—
116C2×C61—41no—
117C2×C61—161no—
118C2×C61#134311yescharacteristic
119D61—42no—
120#575#692311yescharacteristic, complemented
121#525—1221no—
122#421—1221no—
123#407—611no—
124C4×C22⋊C4—1221no—
125#349—1221no—
126H(3,ℤ/4)—611no—
127C61#739611yescharacteristic, complemented, Sylow
128C2×#41—21no—
129C23×C4—611no—
130#137—41no—
131AGL(1,ℤ/8)—41no—
132#135—41no—
133C2×M16—611no—
134C2×M16C2×#692311yescharacteristic
135#123—2441no—
136C22⋊Q8—2441no—
137#121—2441no—
138#120—2441no—
139C4×D4—2442no—
140#117—1221no—
141C2×C22⋊C4—2441no—
142C2×C42—2441no—
143M32—2441no—
144#104—2442no—
145C22⋊C8—2441no—
146#95—1222no—
147C24—611no—
148#41—41no—
149#41—41no—
150#41—41no—
151#41—41no—
152C2×Q8—21no—
153C2×D4—21no—
154C2×D4—41no—
155C2×D4—2442no—
156C22×C4—41no—
157C22×C4—611no—
158C22×C4—1221no—
159C22×C4—1221no—
160C22×C4—2441no—
161C22×C4—2441no—
162C22×C4—2442no—
163C22×C4C22⋊#692311yescharacteristic
164Q16—41no—
165SD16—42no—
166D8—41no—
167M16—41no—
168M16—2441no—
169C2×C8—21no—
170C2×C8—1221no—
171C4⋊C4—2441no—
172C4⋊C4—2442no—
173C22⋊C4—2442no—
174C22⋊C4—2442no—
175C22⋊C4—2444no—
176C22⋊C4—2441no—
177C42—1222no—
178C42—4881no—
179C42—4881no—
180C16—4881no—
181C23—41no—
182C23—1221no—
183C23—2441no—
184C23—2442no—
185C23#1451983911yescharacteristic
186Q8—41no—
187Q8—41no—
188D4—41no—
189D4—41no—
190D4—81no—
191D4—81no—
192D4—4884no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—1221no—
199C2×C4—4881no—
200C2×C4—4882no—
201C2×C4—4882no—
202C2×C4—2442no—
203C2×C4—2444no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4#1451983511yescharacteristic
208C2×C4#1451984111yescharacteristic
209C8—41no—
210C8—2441no—
211C22—21no—
212C22—41no—
213C22—82no—
214C22—81no—
215C22—1222no—
216C22—4881no—
217C22—2441no—
218C22—2442no—
219C22—2441no—
220C22#1684061311yescharacteristic
221C4—21no—
222C4—81no—
223C4—4882no—
224C4—4884no—
225C4—2441no—
226C4#1684066211yescharacteristic
227C4#1684066611yescharacteristic
228C2—21no—
229C2—41no—
230C2—161no—
231C2—2442no—
232C2#2146079711yescharacteristic
subgroupG/H
centerC4#16840666
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×#575C4
socleC2×C61#1343
prime radical#21446883C2
cosocle#16839725C22
hypercenter#575#6923
hypocenterC61#7396
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #21460752C2semidirect
2. #21460699C2semidirect
9. #16839519C4semidirect
10. C61×#575C4semidirect
120. #575#6923semidirect
127. C61#7396semidirect

Maximal subgroups

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

subgroupindex
#214607522
#214606992
#214468832
#739661