Finite Group Databasebeta

← #29583113

Subgroups — #29583113

Order 15616.

400 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 101 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#21446796C211yesmaximal, characteristic
2#21444382C212yesmaximal
3#21443677C212yesmaximal
4#21443652C211yesmaximal, characteristic
5C61×#2859C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16839815C2212yes—
8#16839786C2211yescharacteristic
9#16839522—21no—
10#16839522—21no—
11#16839498—24no—
12C2×#125×C61—21no—
13C61×#389—24no—
14C61×#384—21no—
15C61×#382C2212yes—
16C43×C61C2211yescharacteristic
17C2×#11758194—21no—
18#14519777Q812yes—
19#14519769—21no—
20#14519756—22no—
21C4×Dic122—22no—
22#14519736—21no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C22⋊#92418—22no—
26C4×#92418—22no—
27#125×C61—42no—
28#125×C61—42no—
29C2×C4⋊C4×C61—24no—
30C2×C4⋊C4×C61—24no—
31C2×C4⋊C4×C61—22no—
32C2×C42×C61—22no—
33C2×C42×C61D411yescharacteristic
34C2×C42×C61D411yescharacteristic
35C2×C42×C61C2311yescharacteristic
36#95×C61—22no—
37#95×C61D414yes—
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61—24no—
41C22×C4×C61C2×D412yes—
42C22×C4×C61C2×D411yescharacteristic
43C2×Dic122—22no—
44C4⋊C4×C61—48no—
45C4⋊C4×C61—48no—
46C4⋊C4×C61—42no—
47C4⋊C4×C61—42no—
48C42×C61—21no—
49C42×C61—21no—
50C42×C61—44no—
51C42×C61SD1612yes—
52C42×C61Q1612yes—
53C42×C61C2×Q811yescharacteristic
54C42×C61#4111yescharacteristic
55C42×C61#4112yes—
56C22⋊Dic61—41no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59#11758196—42no—
60C4×Dic61—41no—
61#11758194—41no—
62#11758194—41no—
63C2×#92418—42no—
64C2×#92418—41no—
65C23×C61#12011yescharacteristic
66C2×C4×C61—24no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—48no—
72C2×C4×C61—44no—
73C2×C4×C61C22⋊Q812yes—
74C2×C4×C61C22⋊Q811yescharacteristic
75C2×C4×C61#12412yes—
76C2×C4×C61#12411yescharacteristic
77C2×C4×C61C2×SD1611yescharacteristic
78C2×C4×C61C2×Q1611yescharacteristic
79C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C61#13711yescharacteristic
81C2×Dic61—42no—
82Dic122—82no—
83#92418—82no—
84#92418—81no—
85#10365—611nomaximal, Sylow
86C22×C61—22no—
87C22×C61#39311yescharacteristic
88C22×C61#45011yescharacteristic
89C22×C61#45111yescharacteristic
90C4×C61—24no—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—42no—
94C4×C61—84no—
95C4×C61#47511yescharacteristic
96C4×C61#47711yescharacteristic
97C4×C61#48711yescharacteristic
98C4×C61#48911yescharacteristic
99Dic61—82no—
100#2859D6111yescharacteristic
101#1994—611no—
102#1518—612no—
103#1286—612no—
104#1276—611no—
105C2×C61—21no—
106C2×C61—21no—
107C2×C61#202411yescharacteristic
108C2×C61#203112yes—
109#533—611no—
110C2×#125—21no—
111#431—612no—
112#423—611no—
113#389—24no—
114#384—21no—
115#382C2×D6112yes—
116C43C2×D6111yescharacteristic
117#339—1221no—
118#339—1221no—
119#328—1224no—
120C61#1036511yescharacteristic, complemented, Sylow
121C2×M16—1221no—
122C4⋊Q8—612no—
123#125—42no—
124#125—42no—
125#125—1221no—
126C22⋊Q8—1222no—
127C4×Q8—1222no—
128#117—1221no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C42—22no—
133C2×C42C22⋊D6111yescharacteristic
134C2×C42C22⋊D6111yescharacteristic
135C2×C42C22×D6111yescharacteristic
136C4⋊C8—1222no—
137C4⋊C8—1222no—
138C22⋊C8—1222no—
139C4×C8—1222no—
140#95—22no—
141#95C22⋊D6114yes—
142C2×Q8—1222no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—24no—
146C22×C4C2×C22⋊D6112yes—
147C22×C4C2×C22⋊D6111yescharacteristic
148M16—2441no—
149M16—2441no—
150C2×C8—2442no—
151C2×C8—2441no—
152C4⋊C4—48no—
153C4⋊C4—48no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—2442no—
159C22⋊C4—2441no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—2441no—
164C42#1175820012yes—
165C42#1175820212yes—
166C42Q8×D6111yescharacteristic
167C42#1175822611yescharacteristic
168C42#1175822612yes—
169C23#1451974611yescharacteristic
170Q8—4882no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—2442no—
179C2×C4#1451975312yes—
180C2×C4#1451975311yescharacteristic
181C2×C4#1451976612yes—
182C2×C4#1451976611yescharacteristic
183C2×C4C2×#1175820011yescharacteristic
184C2×C4C2×#1175820211yescharacteristic
185C2×C4#1451980311yescharacteristic
186C2×C4#1451980811yescharacteristic
187C8—4882no—
188C8—4881no—
189C22—22no—
190C22#1683967311yescharacteristic
191C22#1683991311yescharacteristic
192C22#1683991811yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—84no—
198C4—4882no—
199C4#1684004411yescharacteristic
200C4#1684005411yescharacteristic
201C4#1684011411yescharacteristic
202C4#1684012411yescharacteristic
203C2—21no—
204C2—21no—
205C2#2144695711yescharacteristic
206C2#2144698812yes—
subgroupG/H
centerC22#16839673
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2859C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#2859D61
hypocenterC61#10365
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2859

Complements

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

NH ≅ G/Ntype
120. C61#10365semidirect

Maximal subgroups

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

subgroupindex
#214467962
#214443822
#214436772
#214436522
C61×#28592
#1036561