Finite Group Databasebeta

← C127×#12459 #44576132

Subgroups — C127×#12459 #44576132

Order 32512.

198 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C127×#2254C211yesmaximal, characteristic
2Q8×C16×C127C211yesmaximal, characteristic
3C127×#1676C211yesmaximal, characteristic
4C127×#1674C211yesmaximal, characteristic
5C127×#1372C211yesmaximal, characteristic
6C127×#1365C211yesmaximal, characteristic
7C127×#1364C211yesmaximal, characteristic
8#500×C127C2211yescharacteristic
9#500×C127C2211yescharacteristic
10#477×C127—21no—
11#462×C127—21no—
12C8×Q8×C127C2211yescharacteristic
13#367×C127—21no—
14#367×C127—21no—
15C4⋊C16×C127—21no—
16C4⋊C16×C127C2211yescharacteristic
17C4×C16×C127—21no—
18C4×C16×C127C2211yescharacteristic
19#335×C127C2211yescharacteristic
20#335×C127C2211yescharacteristic
21#333×C127—21no—
22#332×C127—21no—
23C2×Q16×C127—41no—
24C4⋊Q8×C127—21no—
25C4⋊Q8×C127—21no—
26C4×Q8×C127D411yescharacteristic
27C2×C16×C127—21no—
28C2×C16×C127D411yescharacteristic
29C2×C16×C127D411yescharacteristic
30#107×C127—21no—
31#107×C127—21no—
32#107×C127—21no—
33#107×C127—21no—
34#107×C127—41no—
35C4⋊C8×C127—21no—
36C4⋊C8×C127—21no—
37C4⋊C8×C127—21no—
38C4⋊C8×C127D411yescharacteristic
39#103×C127—41no—
40#103×C127—41no—
41C4×C8×C127—21no—
42C4×C8×C127C2311yescharacteristic
43C2×Q8×C127—41no—
44C2×Q8×C127—41no—
45C2×Q8×C127D811yescharacteristic
46Q16×C127—82no—
47C2×C8×C127—21no—
48C2×C8×C127—41no—
49C2×C8×C127—41no—
50C2×C8×C127C2×D411yescharacteristic
51C2×C8×C127#4111yescharacteristic
52C4⋊C4×C127—21no—
53C4⋊C4×C127—41no—
54C4⋊C4×C127—41no—
55C4⋊C4×C127—41no—
56C4⋊C4×C127—41no—
57C4⋊C4×C127D811yescharacteristic
58C42×C127—21no—
59C42×C127C2×D411yescharacteristic
60C16×C127—21no—
61C16×C127—41no—
62C16×C127Q1612yescomplemented
63Q8×C127—21no—
64Q8×C127—81no—
65Q8×C127—81no—
66Q8×C127—161no—
67Q8×C127SD3212yes—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—81no—
71C2×C4×C127—81no—
72C2×C4×C127#12111yescharacteristic
73C2×C4×C127C2×D811yescharacteristic
74C2×C4×C127#13511yescharacteristic
75C8×C127—21no—
76C8×C127—41no—
77C8×C127—81no—
78C8×C127—81no—
79C8×C127C2×Q1611yescharacteristic
80C8×C127#13711yescharacteristic
81C22×C127#46611yescharacteristic
82C4×C127—22no—
83C4×C127—21no—
84C4×C127—41no—
85C4×C127—161no—
86C4×C127—161no—
87C4×C127#46211yescharacteristic
88C4×C127#47311yescharacteristic
89C4×C127C2×SD3211yescharacteristic
90C4×C127#50811yescharacteristic
91#12459C12711yesmaximal, characteristic, direct product factor, Sylow
92C2×C127#167411yescharacteristic
93C2×C127#221711yescharacteristic
94C2×C127#222311yescharacteristic
95#2254C2×C12711yescharacteristic
96Q8×C16C2×C12711yescharacteristic
97#1676C2×C12711yescharacteristic
98#1674C2×C12711yescharacteristic
99#1372C2×C12711yescharacteristic
100#1365C2×C12711yescharacteristic
101#1364C2×C12711yescharacteristic
102C127#1245911yescharacteristic, direct product factor, Sylow
103#500C22×C12711yescharacteristic
104#500C22×C12711yescharacteristic
105#477—21no—
106#462—21no—
107C8×Q8C22×C12711yescharacteristic
108#367—21no—
109#367—21no—
110C4⋊C16—21no—
111C4⋊C16C22×C12711yescharacteristic
112C4×C16—21no—
113C4×C16C22×C12711yescharacteristic
114#335C22×C12711yescharacteristic
115#335C22×C12711yescharacteristic
116#333—21no—
117#332—21no—
118C2×Q16—41no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4×Q8D4×C12711yescharacteristic
122C2×C16—21no—
123C2×C16D4×C12711yescharacteristic
124C2×C16D4×C12711yescharacteristic
125#107—21no—
126#107—21no—
127#107—21no—
128#107—21no—
129#107—41no—
130C4⋊C8—21no—
131C4⋊C8—21no—
132C4⋊C8—21no—
133C4⋊C8D4×C12711yescharacteristic
134#103—41no—
135#103—41no—
136C4×C8—21no—
137C4×C8C23×C12711yescharacteristic
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8D8×C12711yescharacteristic
141Q16—82no—
142C2×C8—21no—
143C2×C8—41no—
144C2×C8—41no—
145C2×C8C2×D4×C12711yescharacteristic
146C2×C8#41×C12711yescharacteristic
147C4⋊C4—21no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4D8×C12711yescharacteristic
153C42—21no—
154C42C2×D4×C12711yescharacteristic
155C16—21no—
156C16—41no—
157C16Q16×C12712yescomplemented
158Q8—21no—
159Q8—81no—
160Q8—81no—
161Q8—161no—
162Q8SD32×C12712yes—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4#121×C12711yescharacteristic
168C2×C4C2×D8×C12711yescharacteristic
169C2×C4#135×C12711yescharacteristic
170C8—21no—
171C8—41no—
172C8—81no—
173C8—81no—
174C8C2×Q16×C12711yescharacteristic
175C8#137×C12711yescharacteristic
176C22#466×C12711yescharacteristic
177C4—22no—
178C4—21no—
179C4—41no—
180C4—161no—
181C4—161no—
182C4#462×C12711yescharacteristic
183C4#473×C12711yescharacteristic
184C4C2×SD32×C12711yescharacteristic
185C4#508×C12711yescharacteristic
186C2C127×#167411yescharacteristic
187C2C127×#221711yescharacteristic
188C2C127×#222311yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#466
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
62. C16×C127Q16semidirect
91. #12459C127direct (N × H)
102. C127#12459direct (N × H)
157. C16Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22542
Q8×C16×C1272
C127×#16762
C127×#16742
C127×#13722
C127×#13652
C127×#13642
#12459127