Finite Group Databasebeta

← #30605528

Subgroups — #30605528

Order 15616.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462194C211yesmaximal, characteristic
2#21462041C211yesmaximal, characteristic
3#21460826C212yesmaximal, complemented
4#21460825C212yesmaximal, complemented
5#21456479C211yesmaximal, characteristic
6D61⋊M32—21no—
7#16840684—21no—
8#16840659—21no—
9#16840655—21no—
10#16840654C2211yescharacteristic
11#16840654C2211yescharacteristic
12#16840654C2212yes—
13#16840375C412yes—
14#16840142C411yescharacteristic
15#16840132C2212yes—
16#16840021—21no—
17#16840004—21no—
18#16839868—21no—
19#16839856—21no—
20#16839716C2211yescharacteristic
21C61×#499C411yescharacteristic
22#14519852—22no—
23#14519851—21no—
24#14519851—21no—
25#14519851—22no—
26D61⋊C16—22no—
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×#11758189D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519777C2×C412yes—
32#14519772—42no—
33#14519768—42no—
34#14519757—22no—
35#14519742—22no—
36#14519734C2×C411yescharacteristic
37#14519700—22no—
38#14519700—22no—
39#14519688C2311yescharacteristic
40#14519687D411yescharacteristic
41C8×Dic61D411yescharacteristic
42#125×C61C2×C412yes—
43#107×C61—21no—
44#106×C61—21no—
45C4×C8×C61C2×C411yescharacteristic
46C2×C4×D61C22⋊C411yescharacteristic
47C2×Dic122—22no—
48C2×C8×C61C22⋊C411yescharacteristic
49C2×C8×C61C22⋊C411yescharacteristic
50C4⋊C4×C61—22no—
51C4⋊C4×C61—42no—
52C42×C61C22×C411yescharacteristic
53#11758198—21no—
54#11758198—42no—
55C4⋊Dic61—42no—
56C4⋊Dic61—42no—
57#11758196—21no—
58#11758196—42no—
59C4×Dic61—42no—
60C4×Dic61C22⋊C411yescharacteristic
61C2×#92418C2×D411yescharacteristic
62C2×#92418C2×D411yescharacteristic
63Dic244—42no—
64Dic244—41no—
65Dic244—41no—
66#11758189—41no—
67C8×D61—21no—
68C8×D61—21no—
69#11758187—22no—
70#11758187—22no—
71#11758187—42no—
72C22×D61#10011yescharacteristic
73C2×C4×C61—21no—
74C2×C4×C61—42no—
75C2×C4×C61C2×C22⋊C411yescharacteristic
76C2×Dic61—21no—
77C2×Dic61—42no—
78C2×Dic61#10011yescharacteristic
79C4×D61—21no—
80C4×D61—21no—
81Dic122—42no—
82Dic122—42no—
83C8×C61—21no—
84C8×C61#10411yescharacteristic
85C8×C61#10411yescharacteristic
86#92418—21no—
87#92418—21no—
88#11914—611nomaximal, Sylow
89C22×C61C2×#10011yescharacteristic
90C2×D61—21no—
91C2×D61—41no—
92C4×C61—41no—
93C4×C61—82no—
94C4×C61C2×#10411yescharacteristic
95C4×C61#42111yescharacteristic
96Dic61—21no—
97Dic61—41no—
98Dic61—82no—
99#3177—611no—
100#2166—611no—
101#2110—611no—
102#1356—612no—
103#1356—612no—
104C2×C61—21no—
105C2×C61#153011yescharacteristic
106D61—41no—
107#541—612no—
108C2×M32—1221no—
109#499#692311yescharacteristic
110#494—611no—
111#491—612no—
112#470—1221no—
113#467—1221no—
114#441—1221no—
115C4×Q16—1221no—
116#405—611no—
117#364—1221no—
118#349—1221no—
119#347—611no—
120#347—611no—
121#347—612no—
122#347—1221no—
123C61#1191411yescharacteristic, complemented, Sylow
124C2×Q16—1221no—
125C2×Q16—1221no—
126C2×M16—611no—
127C22×C8—611no—
128C4⋊Q8—612no—
129#126—2442no—
130#125—2442no—
131#125C2×#692312yes—
132C22⋊Q8—1222no—
133C4×Q8—1222no—
134#117—611no—
135M32—1221no—
136M32—1221no—
137M32—1222no—
138M32—1222no—
139C2×C16—1222no—
140#107—21no—
141#106—21no—
142#103—1222no—
143#103—1222no—
144#97—611no—
145#97—611no—
146C4×C8—611no—
147C4×C8C2×#692311yescharacteristic
148C2×Q8—1222no—
149C22×C4—611no—
150Q16—2442no—
151Q16—2441no—
152Q16—2441no—
153M16—2441no—
154C2×C8—611no—
155C2×C8—611no—
156C2×C8—1221no—
157C2×C8—1221no—
158C2×C8C22⋊#692311yescharacteristic
159C2×C8C22⋊#692311yescharacteristic
160C4⋊C4—22no—
161C4⋊C4—42no—
162C4⋊C4—1221no—
163C4⋊C4—2442no—
164C4⋊C4—2442no—
165C4⋊C4—2442no—
166C22⋊C4—1221no—
167C22⋊C4—2442no—
168C42—611no—
169C42—2442no—
170C42C22×#692311yescharacteristic
171C16—1222no—
172C16—1222no—
173C16—2442no—
174C23—611no—
175Q8—2442no—
176Q8—2442no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—611no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—2442no—
184C2×C4C2×C22⋊#692311yescharacteristic
185C8—21no—
186C8—1221no—
187C8—1221no—
188C8#1451984211yescharacteristic
189C8#1451984211yescharacteristic
190C22—1221no—
191C22—2441no—
192C22D61⋊#10011yescharacteristic
193C4—41no—
194C4—82no—
195C4—1221no—
196C4—4882no—
197C4—2441no—
198C4C2×#1451984211yescharacteristic
199C4#1684076111yescharacteristic
200C2—21no—
201C2—2441no—
202C2#2146129011yescharacteristic
subgroupG/H
centerC2#21461290
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#499C4
socleC2×C61#1530
prime radicalC22×D61#100
cosocle#14519688C23
hypercenter#499#6923
hypocenterC61#11914
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
3. #21460826C2semidirect
4. #21460825C2semidirect
123. C61#11914semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214620412
#214608262
#214608252
#214564792
#1191461