Finite Group Databasebeta

← #29583117

Subgroups — #29583117

Order 15616.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454182C211yesmaximal, characteristic
2#21446796C211yesmaximal, characteristic
3#21444384C212yesmaximal
4#21443678C212yesmaximal
5C61×#1276C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7C2×#14519769—21no—
8#16839786C2211yescharacteristic
9#16839660—24no—
10#16839632—21no—
11#16839628C2212yes—
12#16839522—21no—
13#16839522—21no—
14#16839500—24no—
15C61×#431C2212yes—
16C43×C61C2211yescharacteristic
17C2×#11758194—21no—
18#14519777Q812yes—
19#14519769—21no—
20#14519769—42no—
21#14519769—42no—
22#14519756—22no—
23C4×Dic122—22no—
24#14519736—21no—
25C2×C4⋊Dic61—24no—
26C2×C4⋊Dic61—22no—
27C2×#11758196—24no—
28C4⋊#92418—22no—
29#14519684—22no—
30#14519684D414yes—
31C2×C42×C61—22no—
32C2×C42×C61D411yescharacteristic
33C2×C42×C61D411yescharacteristic
34C2×C42×C61C2311yescharacteristic
35C4⋊C8×C61—22no—
36C22⋊C8×C61—22no—
37C4×C8×C61—22no—
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61C2×D412yes—
41C22×C4×C61C2×D411yescharacteristic
42C22×Dic61—24no—
43C2×Dic122—22no—
44C2×C8×C61—42no—
45C42×C61—21no—
46C42×C61—21no—
47C42×C61—44no—
48C42×C61SD1612yes—
49C42×C61Q1612yes—
50C42×C61C2×Q811yescharacteristic
51C42×C61#4112yes—
52C42×C61#4111yescharacteristic
53C22⋊Dic61—41no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61—48no—
57C4⋊Dic61—42no—
58C4⋊Dic61—42no—
59#11758196—48no—
60#11758196—42no—
61C4×Dic61—41no—
62#11758194—41no—
63#11758194—41no—
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×C61C22⋊Q812yes—
72C2×C4×C61C22⋊Q811yescharacteristic
73C2×C4×C61#12412yes—
74C2×C4×C61#12411yescharacteristic
75C2×C4×C61C2×SD1611yescharacteristic
76C2×C4×C61C2×Q1611yescharacteristic
77C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C61#13711yescharacteristic
79C2×Dic61—48no—
80C2×Dic61—42no—
81C2×Dic61—44no—
82Dic122—82no—
83C8×C61—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#47511yescharacteristic
95C4×C61#47711yescharacteristic
96C4×C61#48711yescharacteristic
97C4×C61#48911yescharacteristic
98Dic61—84no—
99Dic61—82no—
100#2859—611no—
101#1994—611no—
102#1518—612no—
103#1286—612no—
104#1276D6111yescharacteristic
105C2×C61—21no—
106C2×C61—21no—
107C2×C61#202411yescharacteristic
108C2×C61#203112yes—
109#533—611no—
110C2×#125—1221no—
111#431C2×D6112yes—
112#423—611no—
113#389—1224no—
114#384—1221no—
115#382—612no—
116C43C2×D6111yescharacteristic
117#339—1221no—
118#339—1221no—
119#328—1224no—
120C61#1036511yescharacteristic, complemented, Sylow
121C2×M16—1221no—
122C4⋊Q8—612no—
123#125—1221no—
124#125—2442no—
125#125—2442no—
126C22⋊Q8—1222no—
127C4×Q8—1222no—
128#117—1221no—
129C2×C4⋊C4—1224no—
130C2×C4⋊C4—1224no—
131C2×C4⋊C4—1222no—
132C2×C42—22no—
133C2×C42D24411yescharacteristic
134C2×C42D24411yescharacteristic
135C2×C42C22×D6111yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—1222no—
138C22⋊C8—22no—
139C4×C8—22no—
140#95—614no—
141#95—1222no—
142C2×Q8—1222no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1224no—
146C22×C4C2×D24411yescharacteristic
147C22×C4D4×D6112yes—
148M16—2441no—
149M16—2441no—
150C2×C8—42no—
151C2×C8—2441no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—2448no—
155C4⋊C4—2448no—
156C4⋊C4—2442no—
157C4⋊C4—2442no—
158C4⋊C4—2442no—
159C22⋊C4—2441no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—2441no—
164C42#1175819012yes—
165C42Dic24412yes—
166C42#1175822212yes—
167C42#1175822411yescharacteristic
168C42Q8×D6111yescharacteristic
169C23#1451974711yescharacteristic
170Q8—4882no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—2448no—
177C2×C4—2444no—
178C2×C4—2442no—
179C2×C4#1451975512yes—
180C2×C4#1451975711yescharacteristic
181C2×C4#1451976312yes—
182C2×C4#1451976511yescharacteristic
183C2×C4C2×#1175819011yescharacteristic
184C2×C4C2×Dic24411yescharacteristic
185C2×C4#1451980511yescharacteristic
186C2×C4#1451981011yescharacteristic
187C8—82no—
188C8—4881no—
189C22—22no—
190C22#1683967511yescharacteristic
191C22#1683991511yescharacteristic
192C22#1683992011yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—4884no—
198C4—4882no—
199C4#1684004811yescharacteristic
200C4#1684005811yescharacteristic
201C4#1684011311yescharacteristic
202C4#1684012211yescharacteristic
203C2—21no—
204C2—21no—
205C2#2144696111yescharacteristic
206C2#2144699212yes—
subgroupG/H
centerC22#16839675
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1276C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1276D61
hypocenterC61#10365
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

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
#214541822
#214467962
#214443842
#214436782
C61×#12762
#1036561