Finite Group Databasebeta

← #30639976

Subgroups — #30639976

Order 16256.

298 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16861209C211yesmaximal, characteristic
2C2×#16861132C212yesmaximal
3C2×#16861132C212yesmaximal
4#22549631C211yesmaximal, characteristic
5#389×C127C211yesmaximal, characteristic
6C22×Dic254C2212yes—
7C22×C127⋊C8C2212yes—
8#16861209—24no—
9C2×C4⋊Dic127—21no—
10C2×C4⋊Dic127—21no—
11#16861132—24no—
12#16861132—24no—
13C2×C4⋊C4×C127—21no—
14C2×C4⋊C4×C127C2211yescharacteristic
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C42×C127C2211yescharacteristic
17#95×C127—21no—
18C2×Dic254—22no—
19C2×Dic254—22no—
20C2×Dic254—22no—
21C2×Dic254—22no—
22C2×Dic254—22no—
23C2×Dic254D414yes—
24C22×Dic127—22no—
25C2×C127⋊C8—22no—
26C2×C127⋊C8—22no—
27C2×C127⋊C8—22no—
28C4⋊Dic127—24no—
29C4⋊Dic127—24no—
30C22×C4×C127—21no—
31C22×C4×C127—21no—
32C22×C4×C127D411yescharacteristic
33C22×C4×C127D411yescharacteristic
34C22×C4×C127C2311yescharacteristic
35C4⋊C4×C127—21no—
36C4⋊C4×C127—22no—
37C4⋊C4×C127—42no—
38C4⋊C4×C127D412yes—
39C42×C127—22no—
40Dic254—24no—
41Dic254—24no—
42Dic254—42no—
43Dic254—42no—
44C2×Dic127—24no—
45C2×Dic127—42no—
46C2×Dic127—42no—
47C127⋊C8—42no—
48C23×C127C2×D411yescharacteristic
49C2×C4×C127—21no—
50C2×C4×C127—21no—
51C2×C4×C127—21no—
52C2×C4×C127—21no—
53C2×C4×C127—22no—
54C2×C4×C127—41no—
55C2×C4×C127—41no—
56C2×C4×C127—41no—
57C2×C4×C127—41no—
58C2×C4×C127—41no—
59C2×C4×C127SD1612yes—
60C2×C4×C127Q1612yes—
61C2×C4×C127C2×D412yes—
62C2×C4×C127C2×D411yescharacteristic
63C2×C4×C127#4111yescharacteristic
64C2×C4×C127#4112yes—
65C22×C127#12011yescharacteristic
66C22×C127#12111yescharacteristic
67C22×C127#12411yescharacteristic
68C22×C127C2×SD1611yescharacteristic
69C22×C127C2×Q1611yescharacteristic
70C22×C127#13711yescharacteristic
71C22×C127#13711yescharacteristic
72C4×C127—22no—
73C4×C127—22no—
74C4×C127—42no—
75C4×C127—81no—
76C4×C127#12112yes—
77C4×C127#12312yes—
78Dic127—44no—
79C2×C127#39411yescharacteristic
80C2×C127#44811yescharacteristic
81C2×C127#45111yescharacteristic
82C2×C127#46111yescharacteristic
83C2×C127#46211yescharacteristic
84C2×C127#48711yescharacteristic
85C2×C127#49111yescharacteristic
86#2043—1271nomaximal, Sylow
87C127#204311yescharacteristic, complemented, Sylow
88C2×C4⋊Q8—1271no—
89C2×#103—1272no—
90C2×#103—1272no—
91#389D12711yescharacteristic
92#336—1271no—
93C22×Q8—1272no—
94C22×C8—1272no—
95C4⋊Q8—2544no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—2541no—
98C2×C4⋊C4—2541no—
99C2×C4⋊C4C2×D12711yescharacteristic
100C2×C4⋊C4C2×D12711yescharacteristic
101C2×C42C2×D12711yescharacteristic
102#103—2544no—
103#103—2544no—
104#95—21no—
105C2×Q8—1274no—
106C2×Q8—2542no—
107C2×Q8—2542no—
108C2×Q8—2542no—
109C2×Q8—2542no—
110C2×Q8—2542no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—2542no—
114C22×C4C22⋊D12711yescharacteristic
115C22×C4C22⋊D12711yescharacteristic
116C22×C4C22×D12711yescharacteristic
117C2×C8—2542no—
118C2×C8—2542no—
119C2×C8—2542no—
120C4⋊C4—21no—
121C4⋊C4—22no—
122C4⋊C4—42no—
123C4⋊C4—2544no—
124C4⋊C4—2544no—
125C4⋊C4D50812yes—
126C42—22no—
127C23C2×C22⋊D12711yescharacteristic
128Q8—5082no—
129Q8—5082no—
130Q8—2544no—
131Q8—2544no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—5082no—
143C2×C4—5082no—
144C2×C4—2544no—
145C2×C4#1452323612yes—
146C2×C4#1452323812yes—
147C2×C4D4×D12712yes—
148C2×C4C2×D50811yescharacteristic
149C2×C4#1452324811yescharacteristic
150C2×C4#1452324912yes—
151C8—5082no—
152C22#1686117711yescharacteristic
153C22#1686118311yescharacteristic
154C22#1686119811yescharacteristic
155C22C2×#1452323611yescharacteristic
156C22C2×#1452323811yescharacteristic
157C22#1686123911yescharacteristic
158C22#1686123911yescharacteristic
159C4—22no—
160C4—22no—
161C4—42no—
162C4—81no—
163C4—5084no—
164C4#1686118412yes—
165C4#1686119412yes—
166C2#2254979311yescharacteristic
167C2#2255001411yescharacteristic
168C2#2255003111yescharacteristic
169C2#2255008111yescharacteristic
170C2#2255008611yescharacteristic
171C2#2255022811yescharacteristic
172C2#2255024611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D127
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
Fitting#389×C127C2
socle, prime radicalC23×C127C2×D4
hypercenter#389D127
hypocenterC127#2043
LCSG ▷ C22×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
87. C127#2043semidirect

Maximal subgroups

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

subgroupindex
C2×#168612092
C2×#168611322
#225496312
#389×C1272
#2043127