Finite Group Databasebeta

← C127×#1682 #30634634

Subgroups — C127×#1682 #30634634

Order 16256.

166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 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#486×C127C211yesmaximal, characteristic
2#462×C127C211yesmaximal, characteristic, complemented
3#460×C127C211yesmaximal, characteristic
4C8×Q8×C127C211yesmaximal, characteristic, complemented
5#335×C127C211yesmaximal, characteristic, complemented
6#332×C127C211yesmaximal, characteristic, complemented
7#331×C127C211yesmaximal, characteristic
8C2×Q16×C127—21no—
9C2×SD16×C127—21no—
10C4⋊Q8×C127C2211yescharacteristic
11#127×C127C2211yescharacteristic
12C4×Q8×C127C2211yescharacteristic
13C4⋊C8×C127—21no—
14C4⋊C8×C127C2211yescharacteristic
15C4⋊C8×C127C2211yescharacteristic
16C4⋊C8×C127C2211yescharacteristic
17#103×C127—21no—
18#102×C127—21no—
19#102×C127—21no—
20#102×C127—21no—
21C4×C8×C127—21no—
22C4×C8×C127C2211yescharacteristic
23C2×Q8×C127—21no—
24C2×Q8×C127D411yescharacteristic
25C2×D4×C127—21no—
26C2×D4×C127—21no—
27C2×D4×C127—21no—
28Q16×C127—42no—
29SD16×C127—42no—
30C2×C8×C127—21no—
31C2×C8×C127—21no—
32C2×C8×C127—21no—
33C2×C8×C127D411yescharacteristic
34C2×C8×C127D411yescharacteristic
35C4⋊C4×C127—21no—
36C4⋊C4×C127—21no—
37C4⋊C4×C127—21no—
38C4⋊C4×C127D411yescharacteristic
39C42×C127—21no—
40C42×C127C2311yescharacteristic
41C23×C127—41no—
42Q8×C127—21no—
43Q8×C127—41no—
44Q8×C127—41no—
45Q8×C127D812yes—
46D4×C127—41no—
47D4×C127—41no—
48D4×C127—41no—
49D4×C127—41no—
50D4×C127—81no—
51C2×C4×C127—21no—
52C2×C4×C127—21no—
53C2×C4×C127—41no—
54C2×C4×C127C2×D411yescharacteristic
55C2×C4×C127C2×D411yescharacteristic
56C2×C4×C127#4111yescharacteristic
57C8×C127—21no—
58C8×C127—21no—
59C8×C127—41no—
60C8×C127—41no—
61C8×C127—41no—
62C22×C127—81no—
63C22×C127—81no—
64C22×C127—81no—
65C22×C127#12111yescharacteristic
66C4×C127—22no—
67C4×C127—21no—
68C4×C127—41no—
69C4×C127—81no—
70C4×C127C2×D811yescharacteristic
71C4×C127#13511yescharacteristic
72C4×C127#13511yescharacteristic
73C4×C127#13711yescharacteristic
74C2×C127—161no—
75C2×C127#46411yescharacteristic
76C2×C127#46611yescharacteristic
77C2×C127#47111yescharacteristic
78#1682C12711yesmaximal, characteristic, direct product factor, Sylow
79C127#168211yescharacteristic, direct product factor, Sylow
80#486C2×C12711yescharacteristic
81#462C2×C12711yescharacteristic, complemented
82#460C2×C12711yescharacteristic
83C8×Q8C2×C12711yescharacteristic, complemented
84#335C2×C12711yescharacteristic, complemented
85#332C2×C12711yescharacteristic, complemented
86#331C2×C12711yescharacteristic
87C2×Q16—21no—
88C2×SD16—21no—
89C4⋊Q8C22×C12711yescharacteristic
90#127C22×C12711yescharacteristic
91C4×Q8C22×C12711yescharacteristic
92C4⋊C8—21no—
93C4⋊C8C22×C12711yescharacteristic
94C4⋊C8C22×C12711yescharacteristic
95C4⋊C8C22×C12711yescharacteristic
96#103—21no—
97#102—21no—
98#102—21no—
99#102—21no—
100C4×C8—21no—
101C4×C8C22×C12711yescharacteristic
102C2×Q8—21no—
103C2×Q8D4×C12711yescharacteristic
104C2×D4—21no—
105C2×D4—21no—
106C2×D4—21no—
107Q16—42no—
108SD16—42no—
109C2×C8—21no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8D4×C12711yescharacteristic
113C2×C8D4×C12711yescharacteristic
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4D4×C12711yescharacteristic
118C42—21no—
119C42C23×C12711yescharacteristic
120C23—41no—
121Q8—21no—
122Q8—41no—
123Q8—41no—
124Q8D8×C12712yes—
125D4—41no—
126D4—41no—
127D4—41no—
128D4—41no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4C2×D4×C12711yescharacteristic
134C2×C4C2×D4×C12711yescharacteristic
135C2×C4#41×C12711yescharacteristic
136C8—21no—
137C8—21no—
138C8—41no—
139C8—41no—
140C8—41no—
141C22—81no—
142C22—81no—
143C22—81no—
144C22#121×C12711yescharacteristic
145C4—22no—
146C4—21no—
147C4—41no—
148C4—81no—
149C4C2×D8×C12711yescharacteristic
150C4#135×C12711yescharacteristic
151C4#135×C12711yescharacteristic
152C4#137×C12711yescharacteristic
153C2—161no—
154C2#464×C12711yescharacteristic
155C2#466×C12711yescharacteristic
156C2#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#121
commutator, Frattini, cosocleC42C23×C127
prime radical#127×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #462×C127C2semidirect
4. C8×Q8×C127C2semidirect
5. #335×C127C2semidirect
6. #332×C127C2semidirect
78. #1682C127direct (N × H)
79. C127#1682direct (N × H)
81. #462C2×C127semidirect
83. C8×Q8C2×C127semidirect
84. #335C2×C127semidirect
85. #332C2×C127semidirect

Maximal subgroups

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

subgroupindex
#486×C1272
#462×C1272
#460×C1272
C8×Q8×C1272
#335×C1272
#332×C1272
#331×C1272
#1682127