Finite Group Databasebeta

← #29589522

Subgroups — #29589522

Order 15616.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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#21454756C211yesmaximal, characteristic
2#21447632C212yesmaximal
3#21443771C212yesmaximal
4#21443770C211yesmaximal, characteristic
5C61×#1327C211yesmaximal, characteristic
6#16840319C411yescharacteristic
7#16839891—22no—
8#16839891—22no—
9#16839790C411yescharacteristic
10#16839790C2211yescharacteristic
11#16839720C411yescharacteristic
12#16839720C2211yescharacteristic
13C2×#14519688C411yescharacteristic
14#16839582—22no—
15#16839544C2212yes—
16#16839539—22no—
17C61×#423C2211yescharacteristic
18C61×#349C2212yes—
19C22×#92418C2×C411yescharacteristic
20C22×#92418C2×C411yescharacteristic
21#14519777—21no—
22#14519769—21no—
23#14519756—22no—
24C4×Dic122—22no—
25#14519736C2×C411yescharacteristic
26#14519736C2×C411yescharacteristic
27#14519717—22no—
28#14519706—22no—
29#14519706—22no—
30#14519688—21no—
31#14519688—21no—
32#14519687—21no—
33#14519687D412yes—
34C8×Dic61—21no—
35C8×Dic61D412yes—
36C2×M16×C61C2×C411yescharacteristic
37C2×M16×C61C2311yescharacteristic
38C2×C42×C61C2×C411yescharacteristic
39M32×C61—22no—
40C4⋊C8×C61—22no—
41C22×C4×C61—21no—
42C22×C4×C61C22×C411yescharacteristic
43C2×Dic122—22no—
44M16×C61—41no—
45M16×C61—41no—
46C2×C8×C61—21no—
47C2×C8×C61C2×D412yes—
48C42×C61—21no—
49C42×C61M1611yescharacteristic
50C42×C61M1611yescharacteristic
51C22⋊Dic61—21no—
52C22⋊Dic61M1612yes—
53C4⋊Dic61—22no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56#11758196—24no—
57C4×Dic61—21no—
58C4×Dic61C22⋊C412yes—
59C2×#92418—22no—
60C2×#92418—21no—
61C2×#92418—41no—
62C2×#92418C22⋊C411yescharacteristic
63C2×#92418C22⋊C411yescharacteristic
64C16×C61—42no—
65#11758185—42no—
66C23×C61C2×M1611yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—81no—
72C2×C4×C61C2×C22⋊C411yescharacteristic
73C2×C4×C61C2×M1611yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—22no—
76Dic122—82no—
77C8×C61—22no—
78C8×C61—41no—
79#92418—21no—
80#92418—41no—
81#92418#10112yes—
82#11540—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—41no—
85C22×C61#40711yescharacteristic
86C4×C61—21no—
87C4×C61—41no—
88C4×C61—41no—
89C4×C61#41011yescharacteristic
90C4×C61C2×#10111yescharacteristic
91Dic61—42no—
92Dic61—42no—
93#2961—611no—
94#2166—612no—
95#1328—612no—
96#1327—611no—
97#1327D6111yescharacteristic
98C2×C61—21no—
99C2×C61—41no—
100C2×C61#146711yescharacteristic
101#533—611no—
102#446—1222no—
103#446—1222no—
104#424—611no—
105#424—611no—
106#423C2×D6111yescharacteristic
107#405—611no—
108#405—611no—
109C2×#97—611no—
110#364—1222no—
111#349—612no—
112#349C2×D6112yes—
113#347—1222no—
114C61#1154011yescharacteristic, complemented, Sylow
115C2×M16C4×D6111yescharacteristic
116C2×M16C22×D6111yescharacteristic
117C22×C8—611no—
118C22×C8—611no—
119C4⋊Q8—1221no—
120#125—1221no—
121C22⋊Q8—1222no—
122C4×Q8—1222no—
123#117—611no—
124#117—611no—
125C2×C42C4×D6111yescharacteristic
126M32—22no—
127M32—1222no—
128C4⋊C8—22no—
129C4⋊C8—1222no—
130C4⋊C8—1222no—
131#97—612no—
132#97—1221no—
133#97—1221no—
134#97—1221no—
135C4×C8—612no—
136C4×C8—1221no—
137C2×Q8—1222no—
138C22×C4—21no—
139C22×C4C2×C4×D6111yescharacteristic
140M16—41no—
141M16—41no—
142C2×C8—21no—
143C2×C8—611no—
144C2×C8—611no—
145C2×C8—1222no—
146C2×C8—1221no—
147C2×C8—2441no—
148C2×C8D4×D6112yes—
149C4⋊C4—1224no—
150C4⋊C4—1222no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C22⋊C4—612no—
154C22⋊C4—1221no—
155C42—21no—
156C42—612no—
157C42—1221no—
158C42#1175818911yescharacteristic
159C42#1175818911yescharacteristic
160C16—42no—
161C16—2442no—
162C23M16×D6111yescharacteristic
163Q8—4882no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4C22⋊C4×D6111yescharacteristic
172C2×C4C2×#1175818911yescharacteristic
173C8—22no—
174C8—41no—
175C8—612no—
176C8—1221no—
177C8—2441no—
178C22—21no—
179C22—41no—
180C22#1683972411yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—2442no—
185C4—2442no—
186C4#1683973411yescharacteristic
187C4#101×D6111yescharacteristic
188C2—21no—
189C2—41no—
190C2#2144416111yescharacteristic
subgroupG/H
centerC4#16839734
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1327C2
socleC2×C61#1467
prime radicalC23×C61C2×M16
cosocleC2×M16×C61C23
hypercenter#1327D61
hypocenterC61#11540
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
114. C61#11540semidirect

Maximal subgroups

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

subgroupindex
#214547562
#214476322
#214437712
#214437702
C61×#13272
#1154061