Finite Group Databasebeta

← C127×#2057 #30635009

Subgroups — C127×#2057 #30635009

Order 16256.

282 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 116 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×C4⋊Q8×C127C211yesmaximal, characteristic
2C2×#107×C127C212yesmaximal
3#389×C127C211yesmaximal, characteristic
4#340×C127C212yesmaximal
5#336×C127C211yesmaximal, characteristic
6C22×Q8×C127—21no—
7C22×C8×C127C2212yes—
8C4⋊Q8×C127—24no—
9C2×C4⋊C4×C127—21no—
10C2×C4⋊C4×C127—21no—
11C2×C4⋊C4×C127C2211yescharacteristic
12C2×C4⋊C4×C127C2212yes—
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C42×C127C2211yescharacteristic
15#107×C127—24no—
16#95×C127—21no—
17C2×Q8×C127—24no—
18C2×Q8×C127—42no—
19C2×Q8×C127—42no—
20C22×C4×C127—21no—
21C22×C4×C127—22no—
22C22×C4×C127—21no—
23C22×C4×C127D411yescharacteristic
24C22×C4×C127D411yescharacteristic
25C22×C4×C127C2311yescharacteristic
26C2×C8×C127—22no—
27C2×C8×C127—22no—
28C2×C8×C127Q814yescomplemented
29C4⋊C4×C127—24no—
30C4⋊C4×C127—22no—
31C4⋊C4×C127—21no—
32C4⋊C4×C127—22no—
33C4⋊C4×C127—42no—
34C4⋊C4×C127D414yes—
35C4⋊C4×C127Q812yescomplemented
36C42×C127—22no—
37C23×C127C2×D411yescharacteristic
38Q8×C127—48no—
39C2×C4×C127—21no—
40C2×C4×C127—21no—
41C2×C4×C127—21no—
42C2×C4×C127—21no—
43C2×C4×C127—24no—
44C2×C4×C127—22no—
45C2×C4×C127—41no—
46C2×C4×C127—42no—
47C2×C4×C127—42no—
48C2×C4×C127—41no—
49C2×C4×C127—41no—
50C2×C4×C127—41no—
51C2×C4×C127—41no—
52C2×C4×C127D812yes—
53C2×C4×C127Q1612yes—
54C2×C4×C127C2×D412yes—
55C2×C4×C127C2×Q812yes—
56C2×C4×C127C2×Q811yescharacteristic
57C2×C4×C127#4111yescharacteristic
58C8×C127—24no—
59C22×C127#12011yescharacteristic
60C22×C127C22⋊Q811yescharacteristic
61C22×C127C4⋊Q811yescharacteristic
62C22×C127C2×D811yescharacteristic
63C22×C127C2×Q1611yescharacteristic
64C22×C127AGL(1,ℤ/8)11yescharacteristic
65C22×C127#13711yescharacteristic
66C4×C127—22no—
67C4×C127—22no—
68C4×C127—44no—
69C4×C127—42no—
70C4×C127—81no—
71C4×C127C22⋊Q812yes—
72C4×C127C4⋊Q812yes—
73C2×C127#39511yescharacteristic
74C2×C127#44711yescharacteristic
75C2×C127#45111yescharacteristic
76C2×C127#47411yescharacteristic
77C2×C127#47711yescharacteristic
78C2×C127#50011yescharacteristic
79C2×C127#50111yescharacteristic
80#2057C12711yesmaximal, characteristic, direct product factor, Sylow
81C127#205711yescharacteristic, direct product factor, Sylow
82C2×C4⋊Q8C2×C12711yescharacteristic
83C2×#107C2×C12712yes—
84#389C2×C12711yescharacteristic
85#340C2×C12712yes—
86#336C2×C12711yescharacteristic
87C22×Q8—21no—
88C22×C8C22×C12712yes—
89C4⋊Q8—24no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4C22×C12711yescharacteristic
93C2×C4⋊C4C22×C12712yes—
94C2×C4⋊C4C22×C12711yescharacteristic
95C2×C42C22×C12711yescharacteristic
96#107—24no—
97#95—21no—
98C2×Q8—24no—
99C2×Q8—42no—
100C2×Q8—42no—
101C22×C4—21no—
102C22×C4—22no—
103C22×C4—21no—
104C22×C4D4×C12711yescharacteristic
105C22×C4D4×C12711yescharacteristic
106C22×C4C23×C12711yescharacteristic
107C2×C8—22no—
108C2×C8—22no—
109C2×C8Q8×C12714yescomplemented
110C4⋊C4—24no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—42no—
115C4⋊C4D4×C12714yes—
116C4⋊C4Q8×C12712yescomplemented
117C42—22no—
118C23C2×D4×C12711yescharacteristic
119Q8—48no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—24no—
125C2×C4—22no—
126C2×C4—41no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4D8×C12712yes—
134C2×C4Q16×C12712yes—
135C2×C4C2×D4×C12712yes—
136C2×C4C2×Q8×C12712yes—
137C2×C4C2×Q8×C12711yescharacteristic
138C2×C4#41×C12711yescharacteristic
139C8—24no—
140C22#120×C12711yescharacteristic
141C22C22⋊Q8×C12711yescharacteristic
142C22C4⋊Q8×C12711yescharacteristic
143C22C2×D8×C12711yescharacteristic
144C22C2×Q16×C12711yescharacteristic
145C22AGL(1,ℤ/8)×C12711yescharacteristic
146C22#137×C12711yescharacteristic
147C4—22no—
148C4—22no—
149C4—44no—
150C4—42no—
151C4—81no—
152C4C22⋊Q8×C12712yes—
153C4C4⋊Q8×C12712yes—
154C2#395×C12711yescharacteristic
155C2#447×C12711yescharacteristic
156C2#451×C12711yescharacteristic
157C2#474×C12711yescharacteristic
158C2#477×C12711yescharacteristic
159C2#500×C12711yescharacteristic
160C2#501×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127C2×D4
commutator, Frattini, cosocleC22×C4C23×C127
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
28. C2×C8×C127Q8semidirect
35. C4⋊C4×C127Q8semidirect
80. #2057C127direct (N × H)
81. C127#2057direct (N × H)
109. C2×C8Q8×C127semidirect
116. C4⋊C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×C1272
C2×#107×C1272
#389×C1272
#340×C1272
#336×C1272
#2057127