Finite Group Databasebeta

← #30607915

Subgroups — #30607915

Order 15616.

286 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 88 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×#16840690C211yesmaximal, characteristic
2C2×C16×#6923C211yesmaximal, characteristic
3#21461927C212yesmaximal
4#21460880C212yesmaximal
5#21447600C211yesmaximal, characteristic
6C2×D61⋊C16C2211yescharacteristic
7C2×#14519848C2212yes—
8#16840769—22no—
9C2×C8×#6923C2211yescharacteristic
10#16840690—22no—
11C16×#6923—22no—
12#16840632—22no—
13C2×C16×D61C2211yescharacteristic
14#16839799C2212yes—
15#16839589C412yescomplemented
16#16839588C411yescharacteristic, complemented
17C61×#366C411yescharacteristic, complemented
18C2×#11758213—22no—
19C2×D61⋊C8D411yescharacteristic
20C2×C4×#6923D411yescharacteristic
21D61⋊C16—21no—
22D61⋊C16Q812yes—
23C2×#11758187—21no—
24#14519848—22no—
25#14519848—22no—
26#14519844—42no—
27C4⋊#92420—42no—
28C8×#6923—21no—
29C8×#6923—21no—
30C2×C8×D61C2311yescharacteristic
31#14519735—22no—
32C2×#11758185C2×C411yescharacteristic
33C16×D61D412yes—
34C16×D61Q812yes—
35#14519711C2×C412yes—
36#14519708—22no—
37C2×C16×C61C2×C411yescharacteristic
38#107×C61C2×C412yes—
39C22×#6923—21no—
40C2×C4×D61C2×D411yescharacteristic
41C2×#92420—42no—
42C2×#92420D811yescharacteristic
43C2×#92420D811yescharacteristic
44C4×#6923—21no—
45C4×#6923Q1612yes—
46#11758213—42no—
47#11758213—42no—
48D61⋊C8—21no—
49D61⋊C8—21no—
50C2×C8×C61C22×C411yescharacteristic
51C4⋊C4×C61—22no—
52#11758198—42no—
53C4⋊Dic61—22no—
54C4×Dic61—42no—
55C2×#92418#4111yescharacteristic
56C8×D61C2×D411yescharacteristic
57C8×D61C2×Q811yescharacteristic
58C8×D61C2×Q811yescharacteristic
59C8×D61#4111yescharacteristic
60#11758187—22no—
61C16×C61C4⋊C412yes—
62#11758185C4⋊C412yes—
63C22×D61#13511yescharacteristic
64C2×#6923—22no—
65C2×#6923—22no—
66C2×#6923—22no—
67C2×C4×C61—42no—
68C2×C4×C61C4×D411yescharacteristic
69C2×Dic61—42no—
70C2×Dic61C2×D811yescharacteristic
71C4×D61#12111yescharacteristic
72C4×D61C4⋊Q811yescharacteristic
73C4×D61C2×Q1611yescharacteristic
74C4×D61#13511yescharacteristic
75#92420—21no—
76#92420—21no—
77#92420—82no—
78C8×C61C2×C4⋊C411yescharacteristic
79C8×C61C4×Q811yescharacteristic
80#92418C22⋊Q811yescharacteristic
81#92418#12511yescharacteristic
82#13169—611nomaximal, Sylow
83C22×C61C4×D811yescharacteristic
84C2×D61—21no—
85C2×D61—21no—
86C2×D61#46711yescharacteristic
87C2×D61#49911yescharacteristic
88#6923—24no—
89C4×C61—82no—
90C4×C61#38911yescharacteristic
91C4×C61C4×Q1611yescharacteristic
92Dic61—82no—
93Dic61#46611yescharacteristic
94Dic61#50011yescharacteristic
95C2×#368—611no—
96#2158—611no—
97C2×C4×C16—611no—
98#1945—612no—
99#1382—612no—
100C2×C61#194211yescharacteristic
101C2×C61#217811yescharacteristic
102C2×C61#217811yescharacteristic
103D61—21no—
104D61—21no—
105C22×C16—611no—
106C22×C16—611no—
107C2×#108—612no—
108#427—612no—
109#424—1222no—
110C2×C4×C8—611no—
111#368—1222no—
112#367—612no—
113#366—611no—
114#366#692311yescharacteristic, complemented
115C4×C16—1222no—
116#339—1222no—
117C61#1316911yescharacteristic, complemented, Sylow
118C2×M16—1222no—
119C22×C8—611no—
120C22×C8—611no—
121#117—1222no—
122C2×C42—611no—
123C2×C16—611no—
124C2×C16—612no—
125C2×C16—612no—
126C2×C16—612no—
127C2×C16—1221no—
128C2×C16—1221no—
129C2×C16C2×#692311yescharacteristic
130#108—1222no—
131#108—1222no—
132#107—612no—
133#107C2×#692312yes—
134#106—1222no—
135C4⋊C8—2442no—
136C4⋊C8—2442no—
137C4×C8—1221no—
138C4×C8—1221no—
139C22×C4—611no—
140C22×C4—1221no—
141M16—2442no—
142M16—2442no—
143C2×C8—611no—
144C2×C8—611no—
145C2×C8—611no—
146C2×C8—611no—
147C2×C8—611no—
148C2×C8—611no—
149C2×C8—611no—
150C2×C8—1221no—
151C2×C8—1221no—
152C2×C8—2442no—
153C2×C8C22×#692311yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—1222no—
156C22⋊C4—2442no—
157C42—612no—
158C42—1221no—
159C42—2442no—
160C16—612no—
161C16—1222no—
162C16C4⋊#692312yes—
163C23—611no—
164C2×C4—42no—
165C2×C4—611no—
166C2×C4—611no—
167C2×C4—611no—
168C2×C4—611no—
169C2×C4—611no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—2442no—
174C2×C4D4×#692311yescharacteristic
175C8—611no—
176C8—611no—
177C8—1221no—
178C8—1221no—
179C8—4882no—
180C8C2×C4⋊#692311yescharacteristic
181C8Q8×#692311yescharacteristic
182C22—611no—
183C22—611no—
184C22—1221no—
185C22—1221no—
186C22D8×#692311yescharacteristic
187C4—82no—
188C4—611no—
189C4—611no—
190C4—1224no—
191C4—4882no—
192C4#1684071311yescharacteristic
193C4Q16×#692311yescharacteristic
194C2—1221no—
195C2—1221no—
196C2#2146192311yescharacteristic
197C2#2146221811yescharacteristic
198C2#2146222011yescharacteristic
subgroupG/H
centerC22D8×#6923
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#366C4
socleC22×C61C4×D8
prime radicalC22×D61#135
cosocleC2×C8×D61C23
hypercenter#366#6923
hypocenterC61#13169
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
15. #16839589C4semidirect
16. #16839588C4semidirect
17. C61×#366C4semidirect
114. #366#6923semidirect
117. C61#13169semidirect

Maximal subgroups

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

subgroupindex
C2×#168406902
C2×C16×#69232
#214619272
#214608802
#214476002
#1316961