Finite Group Databasebeta

← #30594503

Subgroups — #30594503

Order 15616.

286 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462047C211yesmaximal, characteristic
2#21461696C211yesmaximal, characteristic
3#21445856C211yesmaximal, characteristic
4C2×#14519852C412yescomplemented
5C2×#14519846—21no—
6#16840704—21no—
7#16840657—21no—
8C22⋊#11758187—21no—
9#16840636C412yes—
10C22×C8×D61C2211yescharacteristic
11C2×#14519712—21no—
12#16839725—21no—
13#16839527C411yescharacteristic, complemented
14C61×#341C411yescharacteristic, complemented
15C2×C4⋊#6923—22no—
16C2×C22⋊#6923—41no—
17#14519852—42no—
18C2×#11758187—22no—
19#14519846—42no—
20(C2×#6923)⋊C4—41no—
21C22×C4×D61D411yescharacteristic
22C2×#11758194—21no—
23C22×#92418D411yescharacteristic
24C2×C8×D61—42no—
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61C2×C411yescharacteristic
27C2×C8×D61D411yescharacteristic
28C2×C8×D61Q811yescharacteristic
29#14519712—42no—
30#14519689—41no—
31#14519689—41no—
32C2×M16×C61—21no—
33C22×C8×C61C2×C411yescharacteristic
34C23×D61SD1611yescharacteristic
35C22×#6923—42no—
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61Q1611yescharacteristic
38C2×C4×D61—41no—
39C2×C4×D61—41no—
40C2×C4×D61C22⋊C411yescharacteristic
41C2×C4×D61C4⋊C411yescharacteristic
42C2×C4×D61D811yescharacteristic
43C2×C4×D61SD1611yescharacteristic
44C22⋊#6923—82no—
45C4⋊#6923—42no—
46C4⋊#6923—42no—
47M16×C61—41no—
48M16×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61C4211yescharacteristic
52C2×C8×C61C4⋊C411yescharacteristic
53#11758194—41no—
54#11758194—41no—
55C2×#92418—22no—
56C2×#92418—41no—
57C2×#92418C22⋊C411yescharacteristic
58C2×#92418C4⋊C411yescharacteristic
59C8×D61—22no—
60C8×D61—22no—
61C8×D61—41no—
62C8×D61—41no—
63#11758187—42no—
64C23×C61#10311yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61#10211yescharacteristic
70C22×D61#10611yescharacteristic
71C2×#6923—82no—
72C2×#6923—82no—
73C2×#6923—82no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61#9511yescharacteristic
77C2×C4×C61#10211yescharacteristic
78C2×Dic61—41no—
79C2×Dic61#10311yescharacteristic
80C2×Dic61#10711yescharacteristic
81C4×D61—21no—
82C4×D61—21no—
83C4×D61—21no—
84C4×D61—21no—
85C4×D61—41no—
86C4×D61—41no—
87C8×C61—21no—
88C8×C61—21no—
89C8×C61—81no—
90#92418—21no—
91#92418—81no—
92#92418#9912yes—
93#7235—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61#34011yescharacteristic
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61#36111yescharacteristic
106C2×D61#36211yescharacteristic
107#6923—162no—
108C4×C61—21no—
109C4×C61H(3,ℤ/4)11yescharacteristic
110C4×C61#34211yescharacteristic
111Dic61—21no—
112Dic61—21no—
113#2112—611no—
114#1810—611no—
115#1808—611no—
116C2×C61—41no—
117C2×C61#128911yescharacteristic
118C2×C61#138711yescharacteristic
119C2×C61#138911yescharacteristic
120D61—21no—
121D61—21no—
122D61—41no—
123C23×C8—611no—
124C2×M32—612no—
125C2×#108—1221no—
126C2×#107—1221no—
127#407—1221no—
128#380—1221no—
129C22⋊C16—1221no—
130C22⋊C16—1221no—
131#341—611no—
132#341#692311yescharacteristic, complemented
133#340—612no—
134C61#723511yescharacteristic, complemented, Sylow
135C23×C4—611no—
136C2×M16—21no—
137C2×M16—1221no—
138C22×C8—611no—
139C22×C8—611no—
140C22×C8—611no—
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—2442no—
144C22×C8C2×#692311yescharacteristic
145C2×C4⋊C4—1222no—
146C2×C22⋊C4—2441no—
147M32—2442no—
148C2×C16—1222no—
149#108—2442no—
150#107—2442no—
151C22⋊C8—2441no—
152C22⋊C8—2441no—
153#95—2441no—
154C24—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—2441no—
161C22×C4—2441no—
162C22×C4—2442no—
163C22×C4C22⋊#692311yescharacteristic
164M16—41no—
165M16—41no—
166M16—2441no—
167M16—2441no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—611no—
171C2×C8—611no—
172C2×C8—1222no—
173C2×C8—1222no—
174C2×C8—1222no—
175C2×C8—2441no—
176C2×C8—2441no—
177C2×C8—2441no—
178C2×C8C4×#692311yescharacteristic
179C2×C8C4⋊#692311yescharacteristic
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C22⋊C4—4882no—
183C16—2442no—
184C23—611no—
185C23—611no—
186C23—1221no—
187C23—1221no—
188C23—2441no—
189C23—2441no—
190C23#1451984011yescharacteristic
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—4882no—
200C2×C4—4882no—
201C2×C4—4882no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4(C2×#6923)⋊C411yescharacteristic
206C2×C4#1451983911yescharacteristic
207C8—21no—
208C8—21no—
209C8—81no—
210C8—612no—
211C8—1221no—
212C8—4881no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—611no—
217C22—611no—
218C22—1221no—
219C22—1221no—
220C22—1221no—
221C22—1221no—
222C22—1221no—
223C22—2442no—
224C22—2442no—
225C22#1684063511yescharacteristic
226C4—21no—
227C4—1221no—
228C4—1221no—
229C4—9762no—
230C4#1684062911yescharacteristic
231C4#1684063911yescharacteristic
232C2—41no—
233C2—1221no—
234C2—1221no—
235C2—2441no—
236C2#2146068111yescharacteristic
237C2#2146089511yescharacteristic
238C2#2146089911yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenter#341#6923
hypocenterC61#7235
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
4. C2×#14519852C4semidirect
13. #16839527C4semidirect
14. C61×#341C4semidirect
132. #341#6923semidirect
134. C61#7235semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214616962
#214458562
#723561