Finite Group Databasebeta

← C127×#10535 #44574208

Subgroups — C127×#10535 #44574208

Order 32512.

342 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3255C211yesmaximal, characteristic
2C127×#1837C211yesmaximal, characteristic
3C127×#1561C212yesmaximal
4C127×#1493C212yesmaximal
5C127×#1309C211yesmaximal, characteristic
6#533×C127C2212yes—
7#475×C127—22no—
8#470×C127—22no—
9#462×C127—22no—
10#423×C127C2211yescharacteristic
11#423×C127C2212yes—
12#423×C127C2211yescharacteristic
13C2×C4×C8×C127C2211yescharacteristic
14#341×C127—22no—
15#332×C127—22no—
16#332×C127—22no—
17Q8⋊C8×C127—24no—
18C2×Q16×C127—22no—
19C2×M16×C127—21no—
20C2×M16×C127—22no—
21C2×M16×C127D412yes—
22C22×C8×C127—21no—
23C4⋊Q8×C127D412yes—
24C4⋊Q8×C127D412yes—
25#125×C127—22no—
26C22⋊Q8×C127—22no—
27C22⋊Q8×C127—22no—
28C4×Q8×C127—22no—
29C4×Q8×C127—22no—
30#117×C127—22no—
31C2×C42×C127C2311yescharacteristic
32#106×C127—22no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35C4⋊C8×C127—22no—
36C4⋊C8×C127—22no—
37#103×C127—24no—
38C4×C8×C127—21no—
39C4×C8×C127D412yes—
40C2×Q8×C127—22no—
41C2×Q8×C127—22no—
42C22×C4×C127C2×D411yescharacteristic
43C22×C4×C127#4112yes—
44Q16×C127—82no—
45M16×C127—42no—
46M16×C127—42no—
47M16×C127—82no—
48C2×C8×C127—22no—
49C2×C8×C127—22no—
50C2×C8×C127—41no—
51C2×C8×C127—41no—
52C2×C8×C127—41no—
53C2×C8×C127—42no—
54C4⋊C4×C127—22no—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—42no—
60C22⋊C4×C127—42no—
61C42×C127—42no—
62C42×C127C2×D412yes—
63C42×C127C2×D411yescharacteristic
64C42×C127#4111yescharacteristic
65C23×C127#12411yescharacteristic
66Q8×C127—42no—
67Q8×C127—42no—
68Q8×C127—42no—
69Q8×C127—42no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—22no—
73C2×C4×C127—22no—
74C2×C4×C127—42no—
75C2×C4×C127—42no—
76C2×C4×C127#12011yescharacteristic
77C2×C4×C127#12111yescharacteristic
78C2×C4×C127#12112yes—
79C2×C4×C127#12312yes—
80C8×C127—42no—
81C8×C127—42no—
82C8×C127—81no—
83C8×C127—82no—
84C22×C127—22no—
85C22×C127—21no—
86C22×C127#39411yescharacteristic
87C4×C127—22no—
88C4×C127—21no—
89C4×C127—82no—
90C4×C127—82no—
91C4×C127#45411yescharacteristic
92C4×C127#45511yescharacteristic
93C4×C127#47112yes—
94C4×C127#47312yes—
95#10535C12711yesmaximal, characteristic, direct product factor, Sylow
96C2×C127—41no—
97C2×C127#204011yescharacteristic
98C2×C127#205212yes—
99#3255C2×C12711yescharacteristic
100#1837C2×C12711yescharacteristic
101#1561C2×C12712yes—
102#1493C2×C12712yes—
103#1309C2×C12711yescharacteristic
104C127#1053511yescharacteristic, direct product factor, Sylow
105#533C22×C12712yes—
106#475—22no—
107#470—22no—
108#462—22no—
109#423C22×C12711yescharacteristic
110#423C22×C12712yes—
111#423C22×C12711yescharacteristic
112C2×C4×C8C22×C12711yescharacteristic
113#341—22no—
114#332—22no—
115#332—22no—
116Q8⋊C8—24no—
117C2×Q16—22no—
118C2×M16—21no—
119C2×M16—22no—
120C2×M16D4×C12712yes—
121C22×C8—21no—
122C4⋊Q8D4×C12712yes—
123C4⋊Q8D4×C12712yes—
124#125—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129#117—22no—
130C2×C42C23×C12711yescharacteristic
131#106—22no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136#103—24no—
137C4×C8—21no—
138C4×C8D4×C12712yes—
139C2×Q8—22no—
140C2×Q8—22no—
141C22×C4C2×D4×C12711yescharacteristic
142C22×C4#41×C12712yes—
143Q16—82no—
144M16—42no—
145M16—42no—
146M16—82no—
147C2×C8—22no—
148C2×C8—22no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8—42no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—42no—
161C42C2×D4×C12712yes—
162C42C2×D4×C12711yescharacteristic
163C42#41×C12711yescharacteristic
164C23#124×C12711yescharacteristic
165Q8—42no—
166Q8—42no—
167Q8—42no—
168Q8—42no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4#120×C12711yescharacteristic
176C2×C4#121×C12711yescharacteristic
177C2×C4#121×C12712yes—
178C2×C4#123×C12712yes—
179C8—42no—
180C8—42no—
181C8—81no—
182C8—82no—
183C22—21no—
184C22—22no—
185C22#394×C12711yescharacteristic
186C4—21no—
187C4—22no—
188C4—82no—
189C4—82no—
190C4#454×C12711yescharacteristic
191C4#455×C12711yescharacteristic
192C4#471×C12712yes—
193C4#473×C12712yes—
194C2—41no—
195C2C127×#204011yescharacteristic
196C2C127×#205212yes—
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
95. #10535C127direct (N × H)
104. C127#10535direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32552
C127×#18372
C127×#15612
C127×#14932
C127×#13092
#10535127