Finite Group Databasebeta

← C127×#12482 #44576155

Subgroups — C127×#12482 #44576155

Order 32512.

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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×#2241C211yesmaximal, characteristic
2C127×#2183C211yesmaximal, characteristic
3C127×#1674C211yesmaximal, characteristic
4C127×#1670C211yesmaximal, characteristic
5C127×#1371C211yesmaximal, characteristic
6C127×#1364C211yesmaximal, characteristic
7C127×#1362C211yesmaximal, characteristic
8#500×C127C2211yescharacteristic
9#494×C127C2211yescharacteristic
10#475×C127—21no—
11#462×C127—21no—
12C8×Q8×C127C2211yescharacteristic
13C4⋊C16×C127—21no—
14C4⋊C16×C127C2211yescharacteristic
15#358×C127—21no—
16#358×C127—21no—
17#346×C127—21no—
18C4×C16×C127C2211yescharacteristic
19#335×C127C2211yescharacteristic
20#335×C127C2211yescharacteristic
21#332×C127—21no—
22#332×C127—21no—
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C2×Q16×C127—41no—
26C4⋊Q8×C127—21no—
27C4⋊Q8×C127—21no—
28C4×Q8×C127D411yescharacteristic
29C2×C16×C127—21no—
30C2×C16×C127D411yescharacteristic
31C2×C16×C127D411yescharacteristic
32#107×C127—21no—
33#107×C127—21no—
34#106×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—41no—
47Q16×C127—41no—
48Q16×C127—81no—
49Q16×C127—82no—
50C2×C8×C127—21no—
51C2×C8×C127—41no—
52C2×C8×C127—41no—
53C2×C8×C127C2×D411yescharacteristic
54C2×C8×C127#4111yescharacteristic
55C4⋊C4×C127—21no—
56C4⋊C4×C127—41no—
57C4⋊C4×C127—41no—
58C4⋊C4×C127—41no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127D811yescharacteristic
61C42×C127—21no—
62C42×C127C2×D411yescharacteristic
63C16×C127—21no—
64C16×C127—21no—
65C16×C127—41no—
66Q8×C127—21no—
67Q8×C127—21no—
68Q8×C127—81no—
69Q8×C127—81no—
70Q8×C127—81no—
71Q8×C127—81no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—81no—
75C2×C4×C127—81no—
76C2×C4×C127#12111yescharacteristic
77C2×C4×C127C2×D811yescharacteristic
78C2×C4×C127#13511yescharacteristic
79C8×C127—21no—
80C8×C127—41no—
81C8×C127—81no—
82C8×C127—81no—
83C8×C127#13511yescharacteristic
84C8×C127#13711yescharacteristic
85C22×C127#46611yescharacteristic
86C4×C127—21no—
87C4×C127—41no—
88C4×C127—41no—
89C4×C127—161no—
90C4×C127—161no—
91C4×C127#46411yescharacteristic
92C4×C127#47111yescharacteristic
93C4×C127#50911yescharacteristic
94C4×C127#51011yescharacteristic
95#12482C12711yesmaximal, characteristic, direct product factor, Sylow
96C2×C127#168211yescharacteristic
97C2×C127#222011yescharacteristic
98C2×C127#222211yescharacteristic
99#2241C2×C12711yescharacteristic
100#2183C2×C12711yescharacteristic
101#1674C2×C12711yescharacteristic
102#1670C2×C12711yescharacteristic
103#1371C2×C12711yescharacteristic
104#1364C2×C12711yescharacteristic
105#1362C2×C12711yescharacteristic
106C127#1248211yescharacteristic, direct product factor, Sylow
107#500C22×C12711yescharacteristic
108#494C22×C12711yescharacteristic
109#475—21no—
110#462—21no—
111C8×Q8C22×C12711yescharacteristic
112C4⋊C16—21no—
113C4⋊C16C22×C12711yescharacteristic
114#358—21no—
115#358—21no—
116#346—21no—
117C4×C16C22×C12711yescharacteristic
118#335C22×C12711yescharacteristic
119#335C22×C12711yescharacteristic
120#332—21no—
121#332—21no—
122C2×Q16—21no—
123C2×Q16—21no—
124C2×Q16—41no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4×Q8D4×C12711yescharacteristic
128C2×C16—21no—
129C2×C16D4×C12711yescharacteristic
130C2×C16D4×C12711yescharacteristic
131#107—21no—
132#107—21no—
133#106—41no—
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8D4×C12711yescharacteristic
138#103—41no—
139#103—41no—
140C4×C8—21no—
141C4×C8C23×C12711yescharacteristic
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8D8×C12711yescharacteristic
145Q16—41no—
146Q16—41no—
147Q16—81no—
148Q16—82no—
149C2×C8—21no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8C2×D4×C12711yescharacteristic
153C2×C8#41×C12711yescharacteristic
154C4⋊C4—21no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4D8×C12711yescharacteristic
160C42—21no—
161C42C2×D4×C12711yescharacteristic
162C16—21no—
163C16—21no—
164C16—41no—
165Q8—21no—
166Q8—21no—
167Q8—81no—
168Q8—81no—
169Q8—81no—
170Q8—81no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4#121×C12711yescharacteristic
176C2×C4C2×D8×C12711yescharacteristic
177C2×C4#135×C12711yescharacteristic
178C8—21no—
179C8—41no—
180C8—81no—
181C8—81no—
182C8#135×C12711yescharacteristic
183C8#137×C12711yescharacteristic
184C22#466×C12711yescharacteristic
185C4—21no—
186C4—41no—
187C4—41no—
188C4—161no—
189C4—161no—
190C4#464×C12711yescharacteristic
191C4#471×C12711yescharacteristic
192C4#509×C12711yescharacteristic
193C4#510×C12711yescharacteristic
194C2C127×#168211yescharacteristic
195C2C127×#222011yescharacteristic
196C2C127×#222211yescharacteristic
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
95. #12482C127direct (N × H)
106. C127#12482direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22412
C127×#21832
C127×#16742
C127×#16702
C127×#13712
C127×#13642
C127×#13622
#12482127