Finite Group Databasebeta

← #30594413

Subgroups — #30594413

Order 15616.

248 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 70 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#21462055C211yesmaximal, characteristic
2#21462049C211yesmaximal, characteristic
3#21445622C211yesmaximal, characteristic
4C2×#14519851—21no—
5C2×#14519851C411yescharacteristic, complemented
6C22×#11758187C411yescharacteristic, complemented
7#16840658—21no—
8#16840658C412yescomplemented
9C22⋊#11758187—21no—
10C22⋊#11758187—21no—
11C2×#14519784C2211yescharacteristic
12#16839736C411yescharacteristic
13#16839720—21no—
14#16839534—21no—
15C61×#413C411yescharacteristic
16#14519851—22no—
17#14519851—41no—
18#14519851—41no—
19C2×#11758187—21no—
20C2×#11758187—21no—
21C2×#11758187—41no—
22C2×#11758187—41no—
23#14519784—41no—
24#14519784—41no—
25C2×#11758194C2×C411yescharacteristic
26C2×#11758194D411yescharacteristic
27C2×#11758194Q811yescharacteristic
28C22×#92418C2×C411yescharacteristic
29C22×#92418D411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519736—21no—
32#14519692—21no—
33#14519692C812yes—
34#14519687—41no—
35C8×Dic61—41no—
36C2×#41×C61C2×C411yescharacteristic
37C2×M16×C61—21no—
38#101×C61C812yes—
39#100×C61—21no—
40#41×C61—41no—
41#41×C61—41no—
42C2×Q8×C61C2×C811yescharacteristic
43C2×D4×C61C2×C811yescharacteristic
44C2×D4×C61M1611yescharacteristic
45C2×D4×C61M1611yescharacteristic
46C22×C4×C61C4211yescharacteristic
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C4⋊C411yescharacteristic
49M16×C61—22no—
50M16×C61—41no—
51C2×C8×C61—41no—
52C22⋊Dic61—22no—
53C4⋊Dic61—41no—
54C4×Dic61—41no—
55#11758194—41no—
56#11758194—41no—
57#11758194—41no—
58C2×#92418—21no—
59C2×#92418—21no—
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418—21no—
63C2×#92418—21no—
64C2×#92418C22⋊C411yescharacteristic
65C2×#92418C22⋊C411yescharacteristic
66C2×#92418C4⋊C411yescharacteristic
67C2×#92418C4⋊C411yescharacteristic
68#11758187—42no—
69#11758187—41no—
70#11758187—41no—
71C23×C61#9711yescharacteristic
72C23×C61C22⋊C811yescharacteristic
73C23×C61C4⋊C811yescharacteristic
74Q8×C61—41no—
75D4×C61—41no—
76D4×C61—41no—
77D4×C61—41no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61#9511yescharacteristic
85C2×C4×C61C4×C811yescharacteristic
86C2×C4×C61C22⋊C811yescharacteristic
87C2×C4×C61C4⋊C811yescharacteristic
88C2×Dic61—42no—
89C8×C61—42no—
90#92418—21no—
91#92418—21no—
92#92418—21no—
93#92418#9911yescharacteristic
94#92418#9911yescharacteristic
95#7208—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61#33611yescharacteristic
103C4×C61—21no—
104C4×C61—21no—
105C4×C61—21no—
106C4×C61#34211yescharacteristic
107C4×C61#34411yescharacteristic
108Dic61—82no—
109#2115—611no—
110#2113—611no—
111#1757—611no—
112C2×C61—21no—
113C2×C61—41no—
114C2×C61—41no—
115C2×C61—41no—
116C2×C61#128211yescharacteristic
117C2×#131—611no—
118C2×M32—611no—
119C2×M32—1221no—
120C22×C16—611no—
121#413#692311yescharacteristic
122#410—611no—
123#405—1221no—
124#349—612no—
125#349—1221no—
126C22⋊C16—1221no—
127C22⋊C16—1221no—
128#344—1221no—
129C61#720811yescharacteristic, complemented, Sylow
130C2×#41C2×#692311yescharacteristic
131#131—2441no—
132#131—2441no—
133C2×M16—21no—
134C2×M16—611no—
135C2×M16—611no—
136C2×M16—611no—
137C22×C8—611no—
138C22×C8—611no—
139C22×C8—611no—
140#117—1221no—
141M32—1222no—
142M32—2441no—
143M32—2441no—
144C2×C16—1221no—
145C2×C16—1221no—
146C2×C16—2441no—
147C2×C16—2441no—
148#101#9242012yes—
149#100—21no—
150#99—612no—
151#99—1221no—
152#97—2441no—
153C4×C8—2441no—
154#41—41no—
155#41—41no—
156C2×Q8C2×#9242011yescharacteristic
157C2×D4D61⋊C811yescharacteristic
158C2×D4#1175821311yescharacteristic
159C2×D4#1175821711yescharacteristic
160C22×C4C4×#692311yescharacteristic
161C22×C4C4⋊#692311yescharacteristic
162C22×C4C22⋊#692311yescharacteristic
163M16—22no—
164M16—41no—
165M16—2441no—
166M16—2441no—
167M16—2441no—
168C2×C8—41no—
169C2×C8—611no—
170C2×C8—611no—
171C2×C8—611no—
172C2×C8—611no—
173C2×C8—1221no—
174C2×C8—1221no—
175C2×C8—1221no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8—1221no—
179C4⋊C4—2441no—
180C22⋊C4—1222no—
181C42—2441no—
182C16—2441no—
183C16—2441no—
184C16—2442no—
185C23#1451983211yescharacteristic
186C23#1451983411yescharacteristic
187C23#1451984411yescharacteristic
188Q8—41no—
189D4—41no—
190D4—41no—
191D4—41no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—2442no—
199C2×C4(C2×#6923)⋊C411yescharacteristic
200C2×C4C4×#9242011yescharacteristic
201C2×C4C22⋊#9242011yescharacteristic
202C2×C4C4⋊#9242011yescharacteristic
203C8—42no—
204C8—611no—
205C8—611no—
206C8—1221no—
207C8—1221no—
208C8—1221no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22#1684062811yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—4882no—
220C4#1684063911yescharacteristic
221C4#1684064311yescharacteristic
222C2—21no—
223C2—41no—
224C2—41no—
225C2—41no—
226C2#2146066211yescharacteristic
subgroupG/H
centerC4#16840639
commutatorC2×C4×C61C4×C8
FrattiniC2×#41C2×#6923
FittingC61×#413C4
socleC2×C61#1282
prime radicalC2×#41×C61C2×C4
cosocleC2×#14519784C22
hypercenter#413#6923
hypocenterC61#7208
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
5. C2×#14519851C4semidirect
6. C22×#11758187C4semidirect
8. #16840658C4semidirect
129. C61#7208semidirect

Maximal subgroups

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

subgroupindex
#214620552
#214620492
#214456222
#720861