Finite Group Databasebeta

← #29593396

Subgroups — #29593396

Order 15616.

274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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#21457213C211yesmaximal, characteristic
2#21448039C212yesmaximal
3#21447394C211yesmaximal, characteristic
4#21443808C212yesmaximal
5C61×#1327C211yesmaximal, characteristic
6#16840319—21no—
7#16840048—22no—
8#16840020—21no—
9#16840020C2212yes—
10#16839973—22no—
11#16839811C2211yescharacteristic
12#16839585—22no—
13#16839579—22no—
14#16839534—21no—
15#16839522—21no—
16#16839519C2211yescharacteristic
17C61×#423C2211yescharacteristic
18C61×#349C2212yes—
19C2×Dic244—21no—
20C2×Dic244D412yes—
21C2×#11758194—21no—
22#14519777—21no—
23#14519777—21no—
24#14519769—41no—
25#14519756—22no—
26#14519756—41no—
27C4×Dic122—22no—
28C4×Dic122—41no—
29#14519736—21no—
30#14519736—41no—
31#14519713—22no—
32#14519709—21no—
33#14519709D412yes—
34#14519702—22no—
35#14519702—22no—
36C2×M16×C61D411yescharacteristic
37C2×M16×C61C2311yescharacteristic
38C2×C42×C61D411yescharacteristic
39M32×C61—22no—
40C4⋊C8×C61—22no—
41C22×C4×C61—21no—
42C22×C4×C61C2×D411yescharacteristic
43C2×Dic122—22no—
44C2×Dic122—41no—
45M16×C61—41no—
46M16×C61—41no—
47C2×C8×C61—21no—
48C2×C8×C61C2×D412yes—
49C42×C61—21no—
50C42×C61SD1611yescharacteristic
51C42×C61SD1611yescharacteristic
52C22⋊Dic61—42no—
53C22⋊Dic61—41no—
54C4⋊Dic61—22no—
55C4⋊Dic61—41no—
56C4⋊Dic61—41no—
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59#11758196—42no—
60#11758196—42no—
61C4×Dic61—42no—
62C4×Dic61—41no—
63#11758194—41no—
64#11758194—41no—
65C2×#92418—41no—
66Dic244—42no—
67Dic244—81no—
68C16×C61—42no—
69C23×C61AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—42no—
75C2×C4×C61#12011yescharacteristic
76C2×C4×C61C2×SD1611yescharacteristic
77C2×Dic61—42no—
78C2×Dic61—42no—
79C2×Dic61—81no—
80Dic122—42no—
81Dic122—42no—
82Dic122—82no—
83C8×C61—22no—
84C8×C61—41no—
85#92418—81no—
86#12308—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—41no—
89C22×C61#45011yescharacteristic
90C4×C61—22no—
91C4×C61—21no—
92C4×C61—41no—
93C4×C61#45411yescharacteristic
94C4×C61#45811yescharacteristic
95Dic61—82no—
96Dic61—82no—
97Dic61—161no—
98#3255—611no—
99#2239—612no—
100#2102—611no—
101#1340—612no—
102#1327D6111yescharacteristic
103C2×C61—21no—
104C2×C61—41no—
105C2×C61#161611yescharacteristic
106#533—1221no—
107#475—1222no—
108#470—612no—
109#470—1221no—
110#462—1222no—
111#430—611no—
112#423C2×D6111yescharacteristic
113#365—1222no—
114#362—1222no—
115#349C2×D6112yes—
116#344—1221no—
117#339—1221no—
118H(3,ℤ/4)—611no—
119C61#1230811yescharacteristic, complemented, Sylow
120C2×Q16—612no—
121C2×Q16—1221no—
122C2×M16—1221no—
123C2×M16D24411yescharacteristic
124C2×M16C22×D6111yescharacteristic
125C4⋊Q8—1221no—
126C4⋊Q8—1221no—
127#125—2441no—
128C22⋊Q8—1222no—
129C22⋊Q8—2441no—
130C4×Q8—1222no—
131C4×Q8—2441no—
132#117—1221no—
133#117—2441no—
134C2×C42D24411yescharacteristic
135M32—22no—
136#108—1222no—
137#106—612no—
138#106—1221no—
139C4⋊C8—22no—
140#103—1222no—
141#103—1222no—
142C2×Q8—1222no—
143C2×Q8—2441no—
144C22×C4—21no—
145C22×C4C2×D24411yescharacteristic
146Q16—4881no—
147Q16—2442no—
148M16—41no—
149M16—41no—
150M16—2441no—
151M16—2441no—
152C2×C8—21no—
153C2×C8—2441no—
154C2×C8D4×D6112yes—
155C4⋊C4—1222no—
156C4⋊C4—2441no—
157C4⋊C4—2442no—
158C4⋊C4—2441no—
159C4⋊C4—2441no—
160C4⋊C4—2441no—
161C4⋊C4—2442no—
162C22⋊C4—2441no—
163C22⋊C4—2442no—
164C42—21no—
165C42—2441no—
166C42—2442no—
167C42#1175819011yescharacteristic
168C42#1175819011yescharacteristic
169C16—42no—
170C23#1451980511yescharacteristic
171Q8—4882no—
172Q8—2442no—
173Q8—2442no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—4881no—
180C2×C4—2442no—
181C2×C4—2442no—
182C2×C4#1451974711yescharacteristic
183C2×C4C2×#1175819011yescharacteristic
184C8—22no—
185C8—41no—
186C8—4881no—
187C22—21no—
188C22—41no—
189C22#1683991511yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—9761no—
194C4—4882no—
195C4—4882no—
196C4#1683993711yescharacteristic
197C4#1683995311yescharacteristic
198C2—21no—
199C2—41no—
200C2#2144485811yescharacteristic
subgroupG/H
centerC2#21444858
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#1327C2
socleC2×C61#1616
prime radicalC23×C61AGL(1,ℤ/8)
hypercenter#1327D61
hypocenterC61#12308
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
119. C61#12308semidirect

Maximal subgroups

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

subgroupindex
#214572132
#214480392
#214473942
#214438082
C61×#13272
#1230861