Finite Group Databasebeta

← #30608407

Subgroups — #30608407

Order 15616.

312 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C2×#16840673C212yesmaximal
2#21460963C214yesmaximal, complemented
3#21456200C211yesmaximal, characteristic
4C2×#14519838—22no—
5#16840673—22no—
6#16840673C2214yes—
7#16840319C411yescharacteristic
8C2×#14519777C2211yescharacteristic
9#16840131C412yes—
10#16840131C2212yes—
11#16840113—22no—
12#16839772—22no—
13C4×M16×C61C411yescharacteristic
14C2×#11758217—42no—
15#14519838—24no—
16#14519838—42no—
17C22×Dic122D412yes—
18#14519777—21no—
19#14519777—41no—
20#14519777C2×C411yescharacteristic
21#14519777D412yes—
22#14519777C2311yescharacteristic
23#14519769C2×C412yes—
24#14519756—41no—
25C4×Dic122—41no—
26#14519736—21no—
27C2×C4⋊Dic61—41no—
28#14519702—24no—
29#14519702—24no—
30C2×M16×C61—21no—
31C2×C42×C61C2×C411yescharacteristic
32#97×C61C2×C412yes—
33C4×C8×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C22⋊C411yescharacteristic
36C22×Dic61—22no—
37C2×Dic122—22no—
38C2×Dic122—42no—
39C2×Dic122—42no—
40C2×Dic122—41no—
41C2×Dic122C22⋊C412yes—
42C2×Dic122C2×D412yes—
43#11758217—44no—
44#11758217—82no—
45C2×#92420—82no—
46M16×C61—42no—
47C2×C8×C61—22no—
48C42×C61—21no—
49C42×C61C22⋊C411yescharacteristic
50C42×C61C22×C411yescharacteristic
51C22⋊Dic61—41no—
52C4⋊Dic61—22no—
53C4⋊Dic61—41no—
54C4⋊Dic61—42no—
55C4⋊Dic61—41no—
56C4⋊Dic61—41no—
57#11758196—42no—
58C4×Dic61—41no—
59C23×C61#9911yescharacteristic
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—42no—
64C2×C4×C61#9911yescharacteristic
65C2×C4×C61C2×C22⋊C411yescharacteristic
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—42no—
69C2×Dic61—42no—
70C2×Dic61—42no—
71Dic122—42no—
72Dic122—42no—
73Dic122—82no—
74Dic122—82no—
75#92420—84no—
76C8×C61—42no—
77#13599—611nomaximal, Sylow
78C22×C61—41no—
79C22×C61#35412yes—
80C22×C61C2×#9911yescharacteristic
81C4×C61—22no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—41no—
85Dic61—42no—
86Dic61—42no—
87Dic61—82no—
88#3139—611no—
89C2×#356—612no—
90#1413—614no—
91C2×C61—21no—
92C2×C61—22no—
93C2×C61C2×#35411yescharacteristic
94#533—611no—
95C2×C4⋊Q8—611no—
96#491—612no—
97#491—612no—
98#487—1222no—
99#419—1222no—
100C2×#101—1222no—
101C4×M16#692311yescharacteristic
102#356—614no—
103#356—1222no—
104C61#1359911yescharacteristic, complemented, Sylow
105C22×Q8—612no—
106C2×M16—21no—
107C2×M16—2442no—
108C4⋊Q8—612no—
109C4⋊Q8—611no—
110C4⋊Q8—611no—
111C4⋊Q8—1221no—
112C4⋊Q8—2441no—
113#125—612no—
114C22⋊Q8—2441no—
115C4×Q8—2441no—
116#117—1221no—
117C2×C4⋊C4—2441no—
118C2×C42C2×#692311yescharacteristic
119#103—1224no—
120#103—1224no—
121#101—1224no—
122#101—2442no—
123#97C2×#692312yes—
124C4×C8—21no—
125C2×Q8—612no—
126C2×Q8—612no—
127C2×Q8—1222no—
128C2×Q8—2441no—
129C2×Q8—2442no—
130C2×Q8—2442no—
131C22×C4—21no—
132C22×C4—1222no—
133C22×C4C22⋊#692311yescharacteristic
134M16—42no—
135M16—4882no—
136M16—2444no—
137C2×C8—22no—
138C2×C8—4882no—
139C4⋊C4—1222no—
140C4⋊C4—2442no—
141C4⋊C4—2441no—
142C4⋊C4—2441no—
143C4⋊C4—2442no—
144C4⋊C4—2441no—
145C22⋊C4—2441no—
146C42—21no—
147C42—2441no—
148C42C22⋊#692311yescharacteristic
149C42C22×#692311yescharacteristic
150C23#1451983611yescharacteristic
151Q8—4882no—
152Q8—4882no—
153Q8—2442no—
154Q8—2442no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—1222no—
160C2×C4—1222no—
161C2×C4—2442no—
162C2×C4—2442no—
163C2×C4—2442no—
164C2×C4#1451983611yescharacteristic
165C2×C4C2×C22⋊#692311yescharacteristic
166C8—42no—
167C8—4884no—
168C22—41no—
169C22#1684066912yes—
170C22C2×#1451983611yescharacteristic
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—4882no—
176C4—2442no—
177C4—2442no—
178C2—21no—
179C2—22no—
180C2C2×#1684066911yescharacteristic
subgroupG/H
centerC2C2×#16840669
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC4×M16×C61C4
socleC2×C61C2×#354
prime radicalC23×C61#99
cosocle#14519777C23
hypercenterC4×M16#6923
hypocenterC61#13599
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #21460963C2semidirect
104. C61#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#168406732
#214609632
#214562002
#1359961