Finite Group Databasebeta

← #30595147

Subgroups — #30595147

Order 15616.

286 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 46 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#21462090C211yesmaximal, characteristic
2#21461273C211yesmaximal, characteristic
3#21446200C211yesmaximal, characteristic
4#16840741—21no—
5C4×#11758217—21no—
6#16840668—21no—
7#16840666C412yescomplemented
8#16840618—21no—
9#16840617C412yescomplemented
10#16840529C411yescharacteristic, complemented
11#16840308C2211yescharacteristic
12#16839780—21no—
13#16839521—21no—
14C61×#410C411yescharacteristic, complemented
15C2×#11758217—41no—
16#14519856—41no—
17#14519836—22no—
18#14519835—41no—
19#14519832—22no—
20C4×#92420—41no—
21C2×#11758222D411yescharacteristic
22#14519784—42no—
23C2×#11758194—21no—
24C2×#11758194—41no—
25#14519775Q811yescharacteristic
26#14519773C2×C411yescharacteristic
27#14519766D411yescharacteristic
28#14519764C2×C411yescharacteristic
29#14519749—41no—
30C4×C22⋊D61—41no—
31C2×C4×Dic61D411yescharacteristic
32#14519705—42no—
33C2×#41×C61C2×C411yescharacteristic
34#117×C61—21no—
35#99×C61—41no—
36#41×C61—41no—
37#41×C61—41no—
38C2×Q8×C61C4⋊C411yescharacteristic
39C2×D4×C61—21no—
40C2×D4×C61C4211yescharacteristic
41C22×C4×C61—21no—
42C22×C4×C61C22⋊C411yescharacteristic
43C2×C22⋊D61—21no—
44C2×C22⋊D61—41no—
45C22×Dic61—21no—
46#11758222—41no—
47#11758222—41no—
48C2×D244C22⋊C411yescharacteristic
49C2×C4×D61—21no—
50C2×Dic122C4⋊C411yescharacteristic
51C22⋊#6923—42no—
52#11758217—44no—
53C2×#92420—42no—
54C4⋊#6923—81no—
55C4×#6923—81no—
56C4⋊C4×C61—41no—
57C22⋊C4×C61—41no—
58C42×C61—41no—
59C22⋊Dic61—41no—
60#11758198—41no—
61#11758196—41no—
62C4×Dic61—21no—
63C4×Dic61C22⋊C411yescharacteristic
64C4×Dic61C4⋊C411yescharacteristic
65#11758194—22no—
66#11758194—42no—
67#11758194—41no—
68C2×#92418—41no—
69C2×#92418—42no—
70C23×C61—21no—
71C23×C61#9911yescharacteristic
72C22×D61—21no—
73C2×#6923—82no—
74Q8×C61—41no—
75D4×C61—41no—
76D4×C61—42no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—81no—
83C2×C4×C61#9511yescharacteristic
84C2×C4×C61#9911yescharacteristic
85C22⋊D61—82no—
86C22⋊D61—81no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—42no—
91D244—41no—
92C4×D61—41no—
93C4×D61—41no—
94Dic122—41no—
95#92420—44no—
96#92418—42no—
97#7486—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—81no—
102C22×C61#34211yescharacteristic
103C2×D61—41no—
104C2×D61—81no—
105#6923—162no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—161no—
109C4×C61AΣL(1,𝔽16)11yescharacteristic
110C4×C61#35211yescharacteristic
111Dic61—22no—
112Dic61—41no—
113Dic61—41no—
114#2126—611no—
115#1884—611no—
116#1525—611no—
117C2×C61—21no—
118C2×C61—41no—
119C2×C61—81no—
120C2×C61#139011yescharacteristic
121D61—81no—
122#568—611no—
123#532—611no—
124#421—1221no—
125#410—1221no—
126#410#692311yescharacteristic, complemented
127C4×M16—1221no—
128#354—1221no—
129#353—612no—
130#339—1221no—
131#329—612no—
132#329—1221no—
133C61#748611yescharacteristic, complemented, Sylow
134C2×#41—611no—
135C2×#41C2×#692311yescharacteristic
136#131—2442no—
137C2×M16—1221no—
138C2×M16—2441no—
139C2×M16—2441no—
140C4⋊Q8—611no—
141#127—611no—
142#124—611no—
143#124—611no—
144#121—2441no—
145C4×D4—2441no—
146#117—21no—
147#117—2441no—
148C2×C42—611no—
149#104—2442no—
150#99—41no—
151#99—1222no—
152#99—2441no—
153#97—1222no—
154C4×C8—2441no—
155#41—41no—
156#41—41no—
157#41—2441no—
158#41—2441no—
159C2×Q8—611no—
160C2×Q8C4⋊#692311yescharacteristic
161C2×D4—21no—
162C2×D4—611no—
163C2×D4—1221no—
164C2×D4—2441no—
165C2×D4C4×#692311yescharacteristic
166C22×C4—21no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4C22⋊#692311yescharacteristic
170M16—1222no—
171M16—2442no—
172M16—2444no—
173M16—2441no—
174C2×C8—2441no—
175C2×C8—2442no—
176C2×C8—2442no—
177C4⋊C4—41no—
178C4⋊C4—4881no—
179C4⋊C4—2441no—
180C22⋊C4—41no—
181C22⋊C4—2441no—
182C22⋊C4—2441no—
183C22⋊C4—2442no—
184C42—41no—
185C42—611no—
186C42—611no—
187C42—1221no—
188C42—4881no—
189C23—21no—
190C23—1221no—
191C23#1451983511yescharacteristic
192Q8—41no—
193Q8—2441no—
194D4—41no—
195D4—42no—
196D4—4882no—
197D4—4881no—
198D4—2441no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—81no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—4882no—
209C2×C4—2442no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4(C2×#6923)⋊C411yescharacteristic
213C2×C4#1451983611yescharacteristic
214C8—2444no—
215C8—2442no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—4881no—
221C22—2441no—
222C22#1684064011yescharacteristic
223C4—21no—
224C4—41no—
225C4—161no—
226C4—1222no—
227C4—9762no—
228C4—2441no—
229C4—2441no—
230C4#1684066311yescharacteristic
231C4#1684066511yescharacteristic
232C2—21no—
233C2—41no—
234C2—81no—
235C2—4881no—
236C2#2146090411yescharacteristic
subgroupG/H
centerC4#16840663
commutatorC2×D4×C61C42
FrattiniC2×#41C2×#6923
FittingC61×#410C4
socleC2×C61#1390
prime radical, cosocle#16840308C22
hypercenter#410#6923
hypocenterC61#7486
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
7. #16840666C4semidirect
9. #16840617C4semidirect
10. #16840529C4semidirect
14. C61×#410C4semidirect
126. #410#6923semidirect
133. C61#7486semidirect

Maximal subgroups

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

subgroupindex
#214620902
#214612732
#214462002
#748661