Finite Group Databasebeta

← #30595162

Subgroups — #30595162

Order 15616.

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

normal subgroups only

This group has 274 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#21461322C211yesmaximal, characteristic
3#21446202C211yesmaximal, characteristic
4#16840779—21no—
5#16840741—21no—
6#16840668C412yescomplemented
7#16840666—21no—
8#16840622C412yescomplemented
9#16840620—21no—
10#16840308C2211yescharacteristic
11#16839778—21no—
12#16839736C411yescharacteristic, complemented
13#16839523—21no—
14C61×#568C411yescharacteristic, complemented
15#14519856—41no—
16#14519844—22no—
17#14519836—22no—
18#14519835—41no—
19C22⋊#92420—41no—
20C4×#92420—41no—
21C2×#11758222D411yescharacteristic
22#14519775C2×C411yescharacteristic
23#14519773D411yescharacteristic
24#14519766C2×C411yescharacteristic
25#14519764Q811yescharacteristic
26#14519749—41no—
27C4×C22⋊D61—41no—
28#14519736—21no—
29C2×C4×Dic61D411yescharacteristic
30#14519703—42no—
31#14519692—41no—
32C2×#41×C61C2×C411yescharacteristic
33#131×C61—42no—
34C2×M16×C61—21no—
35C2×M16×C61—41no—
36#41×C61—41no—
37#41×C61—41no—
38C2×Q8×C61C4211yescharacteristic
39C2×D4×C61—21no—
40C2×D4×C61C4⋊C411yescharacteristic
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—
52C2×#92420—42no—
53C4⋊#6923—81no—
54C4×#6923—81no—
55M16×C61—22no—
56M16×C61—41no—
57M16×C61—42no—
58C2×C8×C61—41no—
59C2×C8×C61—42no—
60C22⋊Dic61—41no—
61C22⋊Dic61—41no—
62#11758198—41no—
63C4⋊Dic61—41no—
64#11758196—41no—
65C4×Dic61—21no—
66C4×Dic61—41no—
67C4×Dic61C22⋊C411yescharacteristic
68C4×Dic61C4⋊C411yescharacteristic
69C23×C61—21no—
70C23×C61#9911yescharacteristic
71C22×D61—21no—
72C2×#6923—82no—
73Q8×C61—41no—
74D4×C61—41no—
75D4×C61—42no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61#9511yescharacteristic
82C2×C4×C61#9911yescharacteristic
83C22⋊D61—82no—
84C22⋊D61—81no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—42no—
89C2×Dic61—81no—
90D244—41no—
91C4×D61—41no—
92C4×D61—41no—
93Dic122—41no—
94#92420—82no—
95C8×C61—42no—
96#7490—611nomaximal, Sylow
97C22×C61—21no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—81no—
101C22×C61#34211yescharacteristic
102C2×D61—41no—
103C2×D61—81no—
104#6923—162no—
105C4×C61—21no—
106C4×C61—41no—
107C4×C61AΣL(1,𝔽16)11yescharacteristic
108C4×C61#35211yescharacteristic
109Dic61—22no—
110Dic61—41no—
111Dic61—41no—
112Dic61—161no—
113#2126—611no—
114#1884—611no—
115#1543—611no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—81no—
119C2×C61#139011yescharacteristic
120D61—81no—
121#568#692311yescharacteristic, complemented
122#532—611no—
123#431—1221no—
124#421—1221no—
125#410—611no—
126#410—1221no—
127#354—612no—
128#353—1221no—
129#339—1221no—
130#333—612no—
131#331—1221no—
132C61#749011yescharacteristic, complemented, Sylow
133C2×#41—611no—
134C2×#41C2×#692311yescharacteristic
135#131—42no—
136C2×M16—21no—
137C2×M16—41no—
138C4⋊Q8—611no—
139#127—611no—
140#124—611no—
141#124—611no—
142#121—2441no—
143C4×D4—2441no—
144#117—1221no—
145#117—2441no—
146C2×C42—611no—
147C4⋊C8—1222no—
148#104—2442no—
149#99—1222no—
150#99—2441no—
151#99—2441no—
152C22⋊C8—2441no—
153C4×C8—2441no—
154#41—41no—
155#41—41no—
156#41—2441no—
157#41—2441no—
158C2×Q8—611no—
159C2×Q8C4×#692311yescharacteristic
160C2×D4—21no—
161C2×D4—611no—
162C2×D4—1221no—
163C2×D4—2441no—
164C2×D4C4⋊#692311yescharacteristic
165C22×C4—21no—
166C22×C4—1221no—
167C22×C4—1221no—
168C22×C4C22⋊#692311yescharacteristic
169M16—22no—
170M16—41no—
171M16—42no—
172C2×C8—41no—
173C2×C8—42no—
174C2×C8—2442no—
175C4⋊C4—4881no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C22⋊C4—2441no—
179C22⋊C4—2441no—
180C22⋊C4—2442no—
181C22⋊C4—2441no—
182C42—611no—
183C42—611no—
184C42—1221no—
185C42—4881no—
186C42—2441no—
187C23—21no—
188C23—1221no—
189C23#1451983611yescharacteristic
190Q8—41no—
191Q8—2441no—
192D4—41no—
193D4—42no—
194D4—4882no—
195D4—4881no—
196D4—2441no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—4881no—
206C2×C4—4882no—
207C2×C4—2442no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4(C2×#6923)⋊C411yescharacteristic
211C2×C4#1451983511yescharacteristic
212C8—42no—
213C8—4882no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22—4881no—
219C22—2441no—
220C22#1684064011yescharacteristic
221C4—21no—
222C4—41no—
223C4—1222no—
224C4—9761no—
225C4—9762no—
226C4—2441no—
227C4—2441no—
228C4#1684066211yescharacteristic
229C4#1684066411yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—4881no—
234C2#2146090311yescharacteristic
subgroupG/H
centerC4#16840662
commutatorC2×Q8×C61C42
FrattiniC2×#41C2×#6923
FittingC61×#568C4
socleC2×C61#1390
prime radical, cosocle#16840308C22
hypercenter#568#6923
hypocenterC61#7490
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 ◁ #568

Complements

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

NH ≅ G/Ntype
6. #16840668C4semidirect
8. #16840622C4semidirect
12. #16839736C4semidirect
14. C61×#568C4semidirect
121. #568#6923semidirect
132. C61#7490semidirect

Maximal subgroups

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

subgroupindex
#214620902
#214613222
#214462022
#749061