Finite Group Databasebeta

← #29589520

Subgroups — #29589520

Order 15616.

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

normal subgroups only

This group has 270 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#21454752C211yesmaximal, characteristic
2#21447632C212yesmaximal
3#21443772C211yesmaximal, characteristic
4#21443769C212yesmaximal
5C61×#1328C211yesmaximal, characteristic
6#16840315C411yescharacteristic
7#16839891—22no—
8#16839886—22no—
9#16839788C411yescharacteristic
10#16839785C2211yescharacteristic
11#16839720C2211yescharacteristic
12#16839718C411yescharacteristic
13C2×C8×Dic61C411yescharacteristic
14#16839582—22no—
15#16839544C2212yes—
16#16839539—22no—
17C61×#424C2211yescharacteristic
18C61×#349C2212yes—
19C2×#11758194C2×C411yescharacteristic
20C22×#92418C2×C411yescharacteristic
21#14519776—21no—
22#14519768—21no—
23#14519754—22no—
24C4×Dic122—22no—
25#14519736C2×C411yescharacteristic
26C2×C4×Dic61C2×C411yescharacteristic
27#14519717—22no—
28#14519706—22no—
29#14519706—22no—
30#14519688—21no—
31#14519687D412yes—
32C4×#92418—21no—
33C8×Dic61—21no—
34C8×Dic61—21no—
35C8×Dic61D412yes—
36C2×M16×C61C2311yescharacteristic
37C22×C8×C61C2×C411yescharacteristic
38#117×C61C2×C411yescharacteristic
39M32×C61—22no—
40C4⋊C8×C61—22no—
41C22×C4×C61C22×C411yescharacteristic
42C22×Dic61—21no—
43C2×Dic122—22no—
44M16×C61—41no—
45C2×C8×C61—21no—
46C2×C8×C61—41no—
47C2×C8×C61C2×D412yes—
48C4⋊C4×C61—21no—
49C22⋊C4×C61M1612yes—
50C42×C61—21no—
51C22⋊Dic61—21no—
52C4⋊Dic61—22no—
53C4⋊Dic61—21no—
54#11758196—22no—
55#11758196—22no—
56C4×Dic61—21no—
57C4×Dic61C22⋊C412yes—
58C4×Dic61M1611yescharacteristic
59C4×Dic61M1611yescharacteristic
60#11758194—41no—
61C2×#92418—22no—
62C2×#92418—21no—
63C2×#92418C22⋊C411yescharacteristic
64C2×#92418C22⋊C411yescharacteristic
65C16×C61—42no—
66#11758185—42no—
67C23×C61C2×M1611yescharacteristic
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61C2×C22⋊C411yescharacteristic
72C2×C4×C61C2×M1611yescharacteristic
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—22no—
76C2×Dic61—42no—
77Dic122—44no—
78C8×C61—22no—
79C8×C61—41no—
80#92418—21no—
81#92418—41no—
82#92418#10112yes—
83#11539—611nomaximal, Sylow
84C22×C61—21no—
85C22×C61—41no—
86C22×C61#40711yescharacteristic
87C4×C61—21no—
88C4×C61—42no—
89C4×C61#41011yescharacteristic
90C4×C61C2×#10111yescharacteristic
91Dic61—22no—
92Dic61—42no—
93Dic61—41no—
94#2960—611no—
95#2166—612no—
96#1328—611no—
97#1328D6111yescharacteristic
98#1327—612no—
99C2×C61—21no—
100C2×C61—41no—
101C2×C61#146711yescharacteristic
102#533—611no—
103#446—1222no—
104C8×Q8—1222no—
105#424—611no—
106#424C2×D6111yescharacteristic
107#423—611no—
108#405—611no—
109#405—611no—
110C2×C4×C8—611no—
111#364—1222no—
112#349—612no—
113#349C2×D6112yes—
114#347—1222no—
115C61#1153911yescharacteristic, complemented, Sylow
116C2×M16—611no—
117C2×M16C22×D6111yescharacteristic
118C22×C8—611no—
119C22×C8C4×D6111yescharacteristic
120C4⋊Q8—1221no—
121#125—1221no—
122C22⋊Q8—1222no—
123C4×Q8—1222no—
124#117—611no—
125#117C4×D6111yescharacteristic
126C2×C42—611no—
127M32—22no—
128M32—1222no—
129C4⋊C8—22no—
130C4⋊C8—1222no—
131C4⋊C8—1222no—
132#97—612no—
133#97—1221no—
134C4×C8—612no—
135C4×C8—1221no—
136C4×C8—1221no—
137C4×C8—1221no—
138C2×Q8—1222no—
139C22×C4—1221no—
140C22×C4C2×C4×D6111yescharacteristic
141M16—41no—
142M16—2441no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—611no—
146C2×C8—611no—
147C2×C8—1222no—
148C2×C8—1221no—
149C2×C8D4×D6112yes—
150C4⋊C4—21no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1221no—
155C22⋊C4—1221no—
156C22⋊C4#1175818912yes—
157C42—21no—
158C42—612no—
159C42—611no—
160C42—611no—
161C42—1221no—
162C16—42no—
163C16—2442no—
164C23C2×#1175818911yescharacteristic
165Q8—2444no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—1222no—
172C2×C4—2442no—
173C2×C4C22⋊C4×D6111yescharacteristic
174C2×C4M16×D6111yescharacteristic
175C8—22no—
176C8—41no—
177C8—612no—
178C8—1221no—
179C8—2441no—
180C22—21no—
181C22—41no—
182C22#1683972411yescharacteristic
183C4—21no—
184C4—42no—
185C4—1222no—
186C4—2441no—
187C4—2442no—
188C4#1683973411yescharacteristic
189C4#101×D6111yescharacteristic
190C2—21no—
191C2—41no—
192C2#2144416111yescharacteristic
subgroupG/H
centerC4#16839734
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1328C2
socleC2×C61#1467
prime radicalC23×C61C2×M16
cosocleC2×M16×C61C23
hypercenter#1328D61
hypocenterC61#11539
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
115. C61#11539semidirect

Maximal subgroups

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

subgroupindex
#214547522
#214476322
#214437722
#214437692
C61×#13282
#1153961