Finite Group Databasebeta

← C127×#12481 #44576154

Subgroups — C127×#12481 #44576154

Order 32512.

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

normal subgroups only

This group has 194 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×#1676C211yesmaximal, characteristic
4C127×#1670C211yesmaximal, characteristic
5C127×#1372C211yesmaximal, characteristic
6C127×#1365C211yesmaximal, characteristic
7C127×#1362C211yesmaximal, characteristic
8#500×C127C2211yescharacteristic
9#494×C127C2211yescharacteristic
10#477×C127—21no—
11#475×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#333×C127—21no—
22#332×C127—21no—
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C4⋊Q8×C127—21no—
26C4⋊Q8×C127—21no—
27C4×Q8×C127D411yescharacteristic
28C2×C16×C127—21no—
29C2×C16×C127D411yescharacteristic
30C2×C16×C127D411yescharacteristic
31#107×C127—21no—
32#107×C127—21no—
33#107×C127—41no—
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—
49C2×C8×C127—21no—
50C2×C8×C127—41no—
51C2×C8×C127—41no—
52C2×C8×C127C2×D411yescharacteristic
53C2×C8×C127#4111yescharacteristic
54C4⋊C4×C127—21no—
55C4⋊C4×C127—41no—
56C4⋊C4×C127—41no—
57C4⋊C4×C127—41no—
58C4⋊C4×C127—41no—
59C4⋊C4×C127D811yescharacteristic
60C42×C127—21no—
61C42×C127C2×D411yescharacteristic
62C16×C127—21no—
63C16×C127—21no—
64C16×C127—41no—
65Q8×C127—21no—
66Q8×C127—21no—
67Q8×C127—81no—
68Q8×C127—81no—
69Q8×C127—161no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—81no—
73C2×C4×C127—81no—
74C2×C4×C127#12111yescharacteristic
75C2×C4×C127C2×D811yescharacteristic
76C2×C4×C127#13511yescharacteristic
77C8×C127—21no—
78C8×C127—41no—
79C8×C127—81no—
80C8×C127—81no—
81C8×C127#13511yescharacteristic
82C8×C127#13711yescharacteristic
83C22×C127#46611yescharacteristic
84C4×C127—21no—
85C4×C127—41no—
86C4×C127—41no—
87C4×C127—161no—
88C4×C127—161no—
89C4×C127#46411yescharacteristic
90C4×C127#47111yescharacteristic
91C4×C127#51011yescharacteristic
92C4×C127#51011yescharacteristic
93#12481C12711yesmaximal, characteristic, direct product factor, Sylow
94C2×C127#168211yescharacteristic
95C2×C127#221911yescharacteristic
96C2×C127#222311yescharacteristic
97#2241C2×C12711yescharacteristic
98#2183C2×C12711yescharacteristic
99#1676C2×C12711yescharacteristic
100#1670C2×C12711yescharacteristic
101#1372C2×C12711yescharacteristic
102#1365C2×C12711yescharacteristic
103#1362C2×C12711yescharacteristic
104C127#1248111yescharacteristic, direct product factor, Sylow
105#500C22×C12711yescharacteristic
106#494C22×C12711yescharacteristic
107#477—21no—
108#475—21no—
109C8×Q8C22×C12711yescharacteristic
110C4⋊C16—21no—
111C4⋊C16C22×C12711yescharacteristic
112#358—21no—
113#358—21no—
114#346—21no—
115C4×C16C22×C12711yescharacteristic
116#335C22×C12711yescharacteristic
117#335C22×C12711yescharacteristic
118#333—21no—
119#332—21no—
120C2×Q16—21no—
121C2×Q16—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4×Q8D4×C12711yescharacteristic
125C2×C16—21no—
126C2×C16D4×C12711yescharacteristic
127C2×C16D4×C12711yescharacteristic
128#107—21no—
129#107—21no—
130#107—41no—
131#106—41no—
132C4⋊C8—21no—
133C4⋊C8—21no—
134C4⋊C8—21no—
135C4⋊C8D4×C12711yescharacteristic
136#103—41no—
137#103—41no—
138C4×C8—21no—
139C4×C8C23×C12711yescharacteristic
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8D8×C12711yescharacteristic
143Q16—41no—
144Q16—41no—
145Q16—81no—
146C2×C8—21no—
147C2×C8—41no—
148C2×C8—41no—
149C2×C8C2×D4×C12711yescharacteristic
150C2×C8#41×C12711yescharacteristic
151C4⋊C4—21no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4D8×C12711yescharacteristic
157C42—21no—
158C42C2×D4×C12711yescharacteristic
159C16—21no—
160C16—21no—
161C16—41no—
162Q8—21no—
163Q8—21no—
164Q8—81no—
165Q8—81no—
166Q8—161no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4#121×C12711yescharacteristic
172C2×C4C2×D8×C12711yescharacteristic
173C2×C4#135×C12711yescharacteristic
174C8—21no—
175C8—41no—
176C8—81no—
177C8—81no—
178C8#135×C12711yescharacteristic
179C8#137×C12711yescharacteristic
180C22#466×C12711yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—161no—
185C4—161no—
186C4#464×C12711yescharacteristic
187C4#471×C12711yescharacteristic
188C4#510×C12711yescharacteristic
189C4#510×C12711yescharacteristic
190C2C127×#168211yescharacteristic
191C2C127×#221911yescharacteristic
192C2C127×#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
93. #12481C127direct (N × H)
104. C127#12481direct (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×#16762
C127×#16702
C127×#13722
C127×#13652
C127×#13622
#12481127