Finite Group Databasebeta

← C127×#10516 #44574189

Subgroups — C127×#10516 #44574189

Order 32512.

364 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3249C211yesmaximal, characteristic
2C127×#1843C211yesmaximal, characteristic
3C127×#1552C212yesmaximal
4C127×#1506C212yesmaximal
5C127×#1290C211yesmaximal, characteristic
6#533×C127C2212yes—
7#477×C127—22no—
8#467×C127—22no—
9#462×C127—22no—
10#432×C127C2212yes—
11C2×C4⋊C8×C127—22no—
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14#376×C127C2211yescharacteristic
15#332×C127—22no—
16#332×C127—22no—
17#328×C127—24no—
18C2×Q16×C127—22no—
19C22×C8×C127—21no—
20C22×C8×C127D412yes—
21C4⋊Q8×C127D412yes—
22C4⋊Q8×C127D412yes—
23#125×C127—22no—
24C22⋊Q8×C127—22no—
25C22⋊Q8×C127—22no—
26C4×Q8×C127—22no—
27C4×Q8×C127—22no—
28#117×C127—22no—
29C2×C42×C127—21no—
30C2×C42×C127C2311yescharacteristic
31#107×C127—22no—
32C4⋊C8×C127—22no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35C4⋊C8×C127—44no—
36#103×C127—24no—
37C22⋊C8×C127—22no—
38#97×C127—22no—
39#95×C127—21no—
40#95×C127D412yes—
41C2×Q8×C127—22no—
42C2×Q8×C127—22no—
43C22×C4×C127—22no—
44C22×C4×C127C2×D411yescharacteristic
45C22×C4×C127C2×D411yescharacteristic
46C22×C4×C127#4111yescharacteristic
47Q16×C127—82no—
48C2×C8×C127—22no—
49C2×C8×C127—42no—
50C2×C8×C127—42no—
51C2×C8×C127—41no—
52C2×C8×C127—42no—
53C4⋊C4×C127—22no—
54C4⋊C4×C127—22no—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—42no—
58C4⋊C4×C127—42no—
59C22⋊C4×C127—42no—
60C42×C127—22no—
61C42×C127—22no—
62C42×C127—42no—
63C42×C127C2×D412yes—
64C42×C127#4112yes—
65C23×C127#12111yescharacteristic
66Q8×C127—42no—
67Q8×C127—42no—
68Q8×C127—82no—
69C2×C4×C127—22no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—24no—
73C2×C4×C127—41no—
74C2×C4×C127—42no—
75C2×C4×C127—42no—
76C2×C4×C127—42no—
77C2×C4×C127—42no—
78C2×C4×C127#12011yescharacteristic
79C2×C4×C127#12112yes—
80C2×C4×C127#12312yes—
81C2×C4×C127#12411yescharacteristic
82C8×C127—42no—
83C8×C127—82no—
84C8×C127—81no—
85C22×C127—21no—
86C22×C127—21no—
87C22×C127#39411yescharacteristic
88C22×C127#47312yes—
89C4×C127—22no—
90C4×C127—21no—
91C4×C127—22no—
92C4×C127—44no—
93C4×C127—82no—
94C4×C127—82no—
95C4×C127#45311yescharacteristic
96C4×C127#45611yescharacteristic
97#10516C12711yesmaximal, characteristic, direct product factor, Sylow
98C2×C127—22no—
99C2×C127#203911yescharacteristic
100C2×C127#204711yescharacteristic
101C2×C127#205311yescharacteristic
102#3249C2×C12711yescharacteristic
103#1843C2×C12711yescharacteristic
104#1552C2×C12712yes—
105#1506C2×C12712yes—
106#1290C2×C12711yescharacteristic
107C127#1051611yescharacteristic, direct product factor, Sylow
108#533C22×C12712yes—
109#477—22no—
110#467—22no—
111#462—22no—
112#432C22×C12712yes—
113C2×C4⋊C8—22no—
114C2×C4⋊C8C22×C12711yescharacteristic
115C2×C4⋊C8C22×C12711yescharacteristic
116#376C22×C12711yescharacteristic
117#332—22no—
118#332—22no—
119#328—24no—
120C2×Q16—22no—
121C22×C8—21no—
122C22×C8D4×C12712yes—
123C4⋊Q8D4×C12712yes—
124C4⋊Q8D4×C12712yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42—21no—
132C2×C42C23×C12711yescharacteristic
133#107—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—44no—
138#103—24no—
139C22⋊C8—22no—
140#97—22no—
141#95—21no—
142#95D4×C12712yes—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—22no—
146C22×C4C2×D4×C12711yescharacteristic
147C22×C4C2×D4×C12711yescharacteristic
148C22×C4#41×C12711yescharacteristic
149Q16—82no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—42no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—22no—
163C42—22no—
164C42—42no—
165C42C2×D4×C12712yes—
166C42#41×C12712yes—
167C23#121×C12711yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4#120×C12711yescharacteristic
181C2×C4#121×C12712yes—
182C2×C4#123×C12712yes—
183C2×C4#124×C12711yescharacteristic
184C8—42no—
185C8—82no—
186C8—81no—
187C22—21no—
188C22—21no—
189C22#394×C12711yescharacteristic
190C22#473×C12712yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—82no—
196C4—82no—
197C4#453×C12711yescharacteristic
198C4#456×C12711yescharacteristic
199C2—22no—
200C2C127×#203911yescharacteristic
201C2C127×#204711yescharacteristic
202C2C127×#205311yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#121
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
97. #10516C127direct (N × H)
107. C127#10516direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32492
C127×#18432
C127×#15522
C127×#15062
C127×#12902
#10516127