Finite Group Databasebeta

← #29574967

Subgroups — #29574967

Order 15616.

376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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#21456341C211yesmaximal, characteristic
2#21444484C211yesmaximal, characteristic
3#21444291C212yesmaximal
4#21443717C212yesmaximal
5C61×#2987C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840172C414yes—
8#16840168—22no—
9#16839815C2212yes—
10#16839798—22no—
11C2×#14519688C2211yescharacteristic
12#16839508—22no—
13#16839492—24no—
14C61×#533C2211yescharacteristic
15C61×#446—24no—
16C61×#433—22no—
17C61×#432C2212yes—
18C22×#92418—21no—
19#14519777C2×C412yes—
20#14519769—21no—
21#14519756—22no—
22C4×Dic122—22no—
23#14519736—21no—
24#14519710—24no—
25#14519708—24no—
26C4⋊#92418—22no—
27C22⋊#92418—22no—
28#14519688—21no—
29#14519688C2×C412yes—
30C4×#92418—22no—
31C4⋊Q8×C61D412yes—
32#125×C61C2×C412yes—
33C22⋊Q8×C61—22no—
34C4×Q8×C61—22no—
35#117×C61D412yes—
36C2×C42×C61C2311yescharacteristic
37C4⋊C8×C61—24no—
38C4⋊C8×C61D414yes—
39C22⋊C8×C61—22no—
40#97×C61—22no—
41#97×C61—22no—
42C4×C8×C61—22no—
43C2×Q8×C61—22no—
44C22×C4×C61C2×D411yescharacteristic
45C22×C4×C61#4112yes—
46C2×Dic122—22no—
47C2×C8×C61—24no—
48C4⋊C4×C61—24no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61C22⋊C414yes—
51C22⋊C4×C61—22no—
52C42×C61—22no—
53C42×C61C22×C411yescharacteristic
54C42×C61C2×D411yescharacteristic
55C42×C61C2×D412yes—
56C22⋊Dic61—41no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59#11758196—42no—
60C4×Dic61—41no—
61C2×#92418—24no—
62C2×#92418—22no—
63C2×#92418—42no—
64C23×C61#12311yescharacteristic
65Q8×C61—82no—
66C2×C4×C61—22no—
67C2×C4×C61—24no—
68C2×C4×C61—42no—
69C2×C4×C61C2×C22⋊C411yescharacteristic
70C2×C4×C61C4×D412yes—
71C2×C4×C61#12011yescharacteristic
72C2×C4×C61#12112yes—
73C2×Dic61—42no—
74Dic122—44no—
75C8×C61—44no—
76#92418—24no—
77#92418—82no—
78#9006—611nomaximal, Sylow
79C22×C61—22no—
80C22×C61—21no—
81C22×C61#38611yescharacteristic
82C4×C61—22no—
83C4×C61—22no—
84C4×C61—21no—
85C4×C61—44no—
86C4×C61#45612yes—
87Dic61—82no—
88#3162—611no—
89#2987D6111yescharacteristic
90#1544—611no—
91#1497—612no—
92#1302—612no—
93C2×C61—41no—
94C2×C61#188112yes—
95C2×C61#188611yescharacteristic
96#533—611no—
97#533C2×D6111yescharacteristic
98#501—614no—
99#501—1222no—
100#446—24no—
101#433—22no—
102#432C2×D6112yes—
103#431—612no—
104#427—1222no—
105C2×#97—611no—
106#332—1222no—
107Q8⋊C8—1224no—
108C61#900611yescharacteristic, complemented, Sylow
109C22×C8—1221no—
110C4⋊Q8—612no—
111C4⋊Q8D24412yes—
112#125—1221no—
113#125C4×D6112yes—
114C22⋊Q8—22no—
115C22⋊Q8—1222no—
116C4×Q8—22no—
117C4×Q8—1222no—
118#117—1221no—
119#117C22⋊D6112yes—
120C2×C42C22×D6111yescharacteristic
121#107—1224no—
122#106—1224no—
123C4⋊C8—24no—
124C4⋊C8—1222no—
125C4⋊C8C22⋊D6114yes—
126C22⋊C8—22no—
127C22⋊C8—1222no—
128#97—22no—
129#97—22no—
130#97—612no—
131#97—1221no—
132C4×C8—22no—
133C4×C8—1222no—
134C2×Q8—22no—
135C2×Q8—1222no—
136C22×C4#1175822212yes—
137C22×C4C2×C22⋊D6111yescharacteristic
138C2×C8—24no—
139C2×C8—1224no—
140C2×C8—1222no—
141C2×C8—2442no—
142C4⋊C4—24no—
143C4⋊C4—22no—
144C4⋊C4—1222no—
145C4⋊C4—1222no—
146C4⋊C4—2442no—
147C4⋊C4#1175819814yes—
148C22⋊C4—22no—
149C22⋊C4—2441no—
150C42—22no—
151C42—2441no—
152C42C2×C4×D6111yescharacteristic
153C42C2×D24411yescharacteristic
154C42C2×C22⋊D6112yes—
155C23#1451976011yescharacteristic
156Q8—82no—
157Q8—2444no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—42no—
161C2×C4—2442no—
162C2×C4C2×#1175819811yescharacteristic
163C2×C4C4×C22⋊D6112yes—
164C2×C4#1451974611yescharacteristic
165C2×C4#1451975112yes—
166C8—44no—
167C8—1224no—
168C8—4882no—
169C22—22no—
170C22—21no—
171C22#1683964111yescharacteristic
172C4—22no—
173C4—22no—
174C4—21no—
175C4—44no—
176C4—4882no—
177C4#1683994512yes—
178C2—41no—
179C2#2144618112yes—
180C2#2144621211yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2987C2
socleC22×C61#386
prime radicalC23×C61#123
cosocleC2×C42×C61C23
hypercenter#2987D61
hypocenterC61#9006
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2987

Complements

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

NH ≅ G/Ntype
108. C61#9006semidirect

Maximal subgroups

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

subgroupindex
#214563412
#214444842
#214442912
#214437172
C61×#29872
#900661