Finite Group Databasebeta

← C127×#10576 #44574249

Subgroups — C127×#10576 #44574249

Order 32512.

406 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 146 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×#2571C211yesmaximal, characteristic
2C127×#1948C212yesmaximal
3C127×#1845C211yesmaximal, characteristic
4C127×#1296C211yesmaximal, characteristic
5C127×#1279C212yesmaximal
6C2×#107×C127—22no—
7C2×#106×C127—22no—
8C2×C4⋊C8×C127C2212yes—
9C2×C4×C8×C127C2211yescharacteristic
10#400×C127—22no—
11#389×C127—22no—
12#384×C127C2211yescharacteristic
13#384×C127C2211yescharacteristic
14#382×C127—22no—
15C4×C4⋊C4×C127C2212yes—
16#340×C127—22no—
17C22×C8×C127—21no—
18C22×C8×C127—22no—
19C2×C4⋊C4×C127—22no—
20C2×C4⋊C4×C127—22no—
21C2×C4⋊C4×C127—21no—
22C2×C4⋊C4×C127—22no—
23C2×C4⋊C4×C127D412yes—
24C2×C4⋊C4×C127D412yes—
25C2×C4⋊C4×C127D412yes—
26C2×C42×C127—22no—
27C2×C42×C127C2311yescharacteristic
28#107×C127—44no—
29#106×C127—44no—
30C4⋊C8×C127—22no—
31C4⋊C8×C127Q814yes—
32C4×C8×C127—21no—
33C4×C8×C127Q812yes—
34#95×C127—22no—
35#95×C127—24no—
36#95×C127—22no—
37C22×C4×C127—22no—
38C22×C4×C127—22no—
39C22×C4×C127—22no—
40C22×C4×C127—41no—
41C22×C4×C127C2×D411yescharacteristic
42C22×C4×C127C2×D412yes—
43C2×C8×C127—22no—
44C2×C8×C127—22no—
45C2×C8×C127—22no—
46C2×C8×C127—24no—
47C2×C8×C127—42no—
48C2×C8×C127—42no—
49C4⋊C4×C127—22no—
50C4⋊C4×C127—22no—
51C4⋊C4×C127—22no—
52C4⋊C4×C127—22no—
53C4⋊C4×C127—42no—
54C4⋊C4×C127—42no—
55C4⋊C4×C127—42no—
56C4⋊C4×C127—42no—
57C4⋊C4×C127—42no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—82no—
60C42×C127—42no—
61C42×C127—42no—
62C42×C127C2×Q811yescharacteristic
63C42×C127C2×Q812yes—
64C42×C127#4111yescharacteristic
65C23×C127#12011yescharacteristic
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—42no—
69C2×C4×C127—44no—
70C2×C4×C127—42no—
71C2×C4×C127—42no—
72C2×C4×C127—42no—
73C2×C4×C127—42no—
74C2×C4×C127—42no—
75C2×C4×C127—42no—
76C2×C4×C127—82no—
77C2×C4×C127—81no—
78C2×C4×C127C22⋊Q811yescharacteristic
79C2×C4×C127C22⋊Q812yes—
80C2×C4×C127C4⋊Q811yescharacteristic
81C2×C4×C127C4⋊Q812yes—
82C2×C4×C127#13512yes—
83C2×C4×C127#13512yes—
84C2×C4×C127AGL(1,ℤ/8)12yes—
85C2×C4×C127#13712yes—
86C8×C127—24no—
87C8×C127—44no—
88C22×C127#39511yescharacteristic
89C22×C127#44912yes—
90C22×C127#45212yes—
91C22×C127#45311yescharacteristic
92C22×C127#45611yescharacteristic
93C4×C127—21no—
94C4×C127—21no—
95C4×C127—82no—
96C4×C127—82no—
97C4×C127—82no—
98C4×C127—161no—
99C4×C127#47812yes—
100C4×C127#47912yes—
101C4×C127#49912yes—
102C4×C127#50112yes—
103#10576C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127#162011yescharacteristic
105C2×C127#163411yescharacteristic
106C2×C127#165012yes—
107C2×C127#205912yes—
108C2×C127#206011yescharacteristic
109#2571C2×C12711yescharacteristic
110#1948C2×C12712yes—
111#1845C2×C12711yescharacteristic
112#1296C2×C12711yescharacteristic
113#1279C2×C12712yes—
114C127#1057611yescharacteristic, direct product factor, Sylow
115C2×#107—22no—
116C2×#106—22no—
117C2×C4⋊C8C22×C12712yes—
118C2×C4×C8C22×C12711yescharacteristic
119#400—22no—
120#389—22no—
121#384C22×C12711yescharacteristic
122#384C22×C12711yescharacteristic
123#382—22no—
124C4×C4⋊C4C22×C12712yes—
125#340—22no—
126C22×C8—21no—
127C22×C8—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4D4×C12712yes—
133C2×C4⋊C4D4×C12712yes—
134C2×C4⋊C4D4×C12712yes—
135C2×C42—22no—
136C2×C42C23×C12711yescharacteristic
137#107—44no—
138#106—44no—
139C4⋊C8—22no—
140C4⋊C8Q8×C12714yes—
141C4×C8—21no—
142C4×C8Q8×C12712yes—
143#95—22no—
144#95—24no—
145#95—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4C2×D4×C12711yescharacteristic
151C22×C4C2×D4×C12712yes—
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—24no—
156C2×C8—42no—
157C2×C8—42no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C42—42no—
170C42—42no—
171C42C2×Q8×C12711yescharacteristic
172C42C2×Q8×C12712yes—
173C42#41×C12711yescharacteristic
174C23#120×C12711yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4C22⋊Q8×C12711yescharacteristic
188C2×C4C22⋊Q8×C12712yes—
189C2×C4C4⋊Q8×C12711yescharacteristic
190C2×C4C4⋊Q8×C12712yes—
191C2×C4#135×C12712yes—
192C2×C4#135×C12712yes—
193C2×C4AGL(1,ℤ/8)×C12712yes—
194C2×C4#137×C12712yes—
195C8—24no—
196C8—44no—
197C22#395×C12711yescharacteristic
198C22#449×C12712yes—
199C22#452×C12712yes—
200C22#453×C12711yescharacteristic
201C22#456×C12711yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—161no—
208C4#478×C12712yes—
209C4#479×C12712yes—
210C4#499×C12712yes—
211C4#501×C12712yes—
212C2C127×#162011yescharacteristic
213C2C127×#163411yescharacteristic
214C2C127×#165012yes—
215C2C127×#205912yes—
216C2C127×#206011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#120
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
103. #10576C127direct (N × H)
114. C127#10576direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25712
C127×#19482
C127×#18452
C127×#12962
C127×#12792
#10576127