Finite Group Databasebeta

← C127×#10623 #44574296

Subgroups — C127×#10623 #44574296

Order 32512.

350 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 134 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×#1984C211yesmaximal, characteristic
2C127×#1834C211yesmaximal, characteristic
3C127×#1803C212yesmaximal
4C127×#1296C212yesmaximal
5C127×#1277C211yesmaximal, characteristic
6C2×C4×Q8×C127C2211yescharacteristic
7C2×C4⋊C8×C127C2212yes—
8C2×C4⋊C8×C127C2211yescharacteristic
9C2×#103×C127—22no—
10C2×C4×C8×C127C2211yescharacteristic
11#384×C127C2212yes—
12#340×C127—22no—
13#340×C127—22no—
14#336×C127—22no—
15C22×Q8×C127D411yescharacteristic
16C22×C8×C127—21no—
17C22×C8×C127—22no—
18C22×C8×C127D412yes—
19C4×Q8×C127—22no—
20C4×Q8×C127—22no—
21C2×C4⋊C4×C127—21no—
22C2×C4⋊C4×C127—22no—
23C2×C4⋊C4×C127—22no—
24C2×C4⋊C4×C127—22no—
25C2×C4⋊C4×C127D411yescharacteristic
26C2×C42×C127—21no—
27C2×C42×C127C2311yescharacteristic
28C4⋊C8×C127—22no—
29C4⋊C8×C127—22no—
30C4⋊C8×C127—22no—
31#103×C127—44no—
32C4×C8×C127—22no—
33C2×Q8×C127—21no—
34C2×Q8×C127—22no—
35C2×Q8×C127—22no—
36C2×Q8×C127D812yes—
37C22×C4×C127—21no—
38C22×C4×C127—21no—
39C22×C4×C127—42no—
40C22×C4×C127C2×D411yescharacteristic
41C22×C4×C127C2×D411yescharacteristic
42C22×C4×C127#4111yescharacteristic
43C2×C8×C127—22no—
44C2×C8×C127—22no—
45C2×C8×C127—22no—
46C2×C8×C127—42no—
47C2×C8×C127—41no—
48C2×C8×C127—42no—
49C2×C8×C127—42no—
50C2×C8×C127—42no—
51C4⋊C4×C127—22no—
52C4⋊C4×C127—42no—
53C4⋊C4×C127—42no—
54C4⋊C4×C127—42no—
55C4⋊C4×C127—42no—
56C4⋊C4×C127—42no—
57C4⋊C4×C127—82no—
58C42×C127—41no—
59C42×C127—41no—
60C42×C127#4112yes—
61C42×C127#4112yes—
62C23×C127#12111yescharacteristic
63Q8×C127—24no—
64Q8×C127—42no—
65C2×C4×C127—22no—
66C2×C4×C127—22no—
67C2×C4×C127—41no—
68C2×C4×C127—41no—
69C2×C4×C127—41no—
70C2×C4×C127—42no—
71C2×C4×C127—82no—
72C2×C4×C127—82no—
73C2×C4×C127—82no—
74C2×C4×C127#12312yes—
75C2×C4×C127#12311yescharacteristic
76C2×C4×C127#12411yescharacteristic
77C2×C4×C127#12612yes—
78C2×C4×C127C2×D811yescharacteristic
79C2×C4×C127#13511yescharacteristic
80C2×C4×C127#13512yes—
81C2×C4×C127#13712yes—
82C2×C4×C127#13712yes—
83C8×C127—42no—
84C8×C127—82no—
85C8×C127—81no—
86C22×C127#39711yescharacteristic
87C22×C127#46412yes—
88C22×C127#46611yescharacteristic
89C22×C127#47011yescharacteristic
90C22×C127#47112yes—
91C4×C127—22no—
92C4×C127—42no—
93C4×C127—81no—
94C4×C127—162no—
95C4×C127#48012yes—
96C4×C127#48512yes—
97C4×C127#48512yes—
98C4×C127#48811yescharacteristic
99C4×C127#49111yescharacteristic
100#10623C12711yesmaximal, characteristic, direct product factor, Sylow
101C2×C127#168212yes—
102C2×C127#170412yes—
103C2×C127#207411yescharacteristic
104C2×C127#207511yescharacteristic
105C2×C127#207911yescharacteristic
106#1984C2×C12711yescharacteristic
107#1834C2×C12711yescharacteristic
108#1803C2×C12712yes—
109#1296C2×C12712yes—
110#1277C2×C12711yescharacteristic
111C127#1062311yescharacteristic, direct product factor, Sylow
112C2×C4×Q8C22×C12711yescharacteristic
113C2×C4⋊C8C22×C12712yes—
114C2×C4⋊C8C22×C12711yescharacteristic
115C2×#103—22no—
116C2×C4×C8C22×C12711yescharacteristic
117#384C22×C12712yes—
118#340—22no—
119#340—22no—
120#336—22no—
121C22×Q8D4×C12711yescharacteristic
122C22×C8—21no—
123C22×C8—22no—
124C22×C8D4×C12712yes—
125C4×Q8—22no—
126C4×Q8—22no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4D4×C12711yescharacteristic
132C2×C42—21no—
133C2×C42C23×C12711yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137#103—44no—
138C4×C8—22no—
139C2×Q8—21no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8D8×C12712yes—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—42no—
146C22×C4C2×D4×C12711yescharacteristic
147C22×C4C2×D4×C12711yescharacteristic
148C22×C4#41×C12711yescharacteristic
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—42no—
155C2×C8—42no—
156C2×C8—42no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—82no—
164C42—41no—
165C42—41no—
166C42#41×C12712yes—
167C42#41×C12712yes—
168C23#121×C12711yescharacteristic
169Q8—24no—
170Q8—42no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—82no—
180C2×C4#123×C12712yes—
181C2×C4#123×C12711yescharacteristic
182C2×C4#124×C12711yescharacteristic
183C2×C4#126×C12712yes—
184C2×C4C2×D8×C12711yescharacteristic
185C2×C4#135×C12711yescharacteristic
186C2×C4#135×C12712yes—
187C2×C4#137×C12712yes—
188C2×C4#137×C12712yes—
189C8—42no—
190C8—82no—
191C8—81no—
192C22#397×C12711yescharacteristic
193C22#464×C12712yes—
194C22#466×C12711yescharacteristic
195C22#470×C12711yescharacteristic
196C22#471×C12712yes—
197C4—22no—
198C4—42no—
199C4—81no—
200C4—162no—
201C4#480×C12712yes—
202C4#485×C12712yes—
203C4#485×C12712yes—
204C4#488×C12711yescharacteristic
205C4#491×C12711yescharacteristic
206C2C127×#168212yes—
207C2C127×#170412yes—
208C2C127×#207411yescharacteristic
209C2C127×#207511yescharacteristic
210C2C127×#207911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#121
commutator, Frattini, cosocleC2×C42C23×C127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
100. #10623C127direct (N × H)
111. C127#10623direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19842
C127×#18342
C127×#18032
C127×#12962
C127×#12772
#10623127