Finite Group Databasebeta

← C127×#13536 #44577209

Subgroups — C127×#13536 #44577209

Order 32512.

318 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×#365×C127C212yesmaximal
2C2×#362×C127C212yesmaximal
3C127×#1971C211yesmaximal, characteristic
4C127×#1849C211yesmaximal, characteristic
5C127×#1377C211yesmaximal, characteristic
6C22×Q16×C127C2211yescharacteristic
7C2×M32×C127C2212yes—
8C2×#108×C127—21no—
9C2×#108×C127C2212yes—
10C2×#106×C127C2211yescharacteristic
11#423×C127—21no—
12C2×#103×C127—21no—
13C2×#97×C127C2211yescharacteristic
14#391×C127—21no—
15#365×C127—24no—
16#362×C127—24no—
17C22×Q8×C127—21no—
18C2×Q16×C127—22no—
19C2×Q16×C127—22no—
20C2×Q16×C127—21no—
21C2×Q16×C127Q812yes—
22C2×M16×C127—22no—
23C22×C8×C127D411yescharacteristic
24C22×C8×C127C2311yescharacteristic
25C2×C4⋊C4×C127—21no—
26C2×C42×C127D411yescharacteristic
27M32×C127—22no—
28M32×C127D414yes—
29C2×C16×C127—22no—
30#108×C127—22no—
31#108×C127—22no—
32#108×C127—42no—
33#106×C127—22no—
34C4⋊C8×C127—42no—
35#103×C127—42no—
36#97×C127—22no—
37#95×C127—42no—
38C2×Q8×C127—22no—
39C2×Q8×C127—41no—
40C2×Q8×C127—41no—
41C2×Q8×C127—41no—
42C2×Q8×C127—41no—
43C2×Q8×C127—41no—
44C22×C4×C127—41no—
45C22×C4×C127—41no—
46C22×C4×C127SD1612yes—
47C22×C4×C127C2×D411yescharacteristic
48Q16×C127—24no—
49Q16×C127—42no—
50M16×C127—42no—
51M16×C127—42no—
52C2×C8×C127—21no—
53C2×C8×C127—21no—
54C2×C8×C127—42no—
55C2×C8×C127SD1612yes—
56C2×C8×C127C2×D412yes—
57C2×C8×C127C2×Q811yescharacteristic
58C2×C8×C127#4112yes—
59C2×C8×C127#4111yescharacteristic
60C4⋊C4×C127—41no—
61C4⋊C4×C127—41no—
62C42×C127—21no—
63C42×C127—21no—
64C16×C127—24no—
65C23×C127C2×SD1611yescharacteristic
66Q8×C127—42no—
67Q8×C127—42no—
68Q8×C127—81no—
69Q8×C127—81no—
70C2×C4×C127—22no—
71C2×C4×C127—42no—
72C2×C4×C127—42no—
73C2×C4×C127—81no—
74C2×C4×C127—81no—
75C2×C4×C127—82no—
76C2×C4×C127—81no—
77C2×C4×C127C22⋊Q811yescharacteristic
78C2×C4×C127#12311yescharacteristic
79C2×C4×C127#12711yescharacteristic
80C2×C4×C127C2×SD1611yescharacteristic
81C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
83C8×C127—22no—
84C8×C127—82no—
85C8×C127C22⋊Q812yes—
86C8×C127#12312yes—
87C22×C127—22no—
88C22×C127#47611yescharacteristic
89C22×C127#48111yescharacteristic
90C22×C127#49211yescharacteristic
91C4×C127—42no—
92C4×C127—82no—
93C4×C127—161no—
94C4×C127#39911yescharacteristic
95C4×C127#47611yescharacteristic
96C4×C127#48111yescharacteristic
97C4×C127#49611yescharacteristic
98#13536C12711yesmaximal, characteristic, direct product factor, Sylow
99C2×C127—21no—
100C2×C127—21no—
101C2×C127#209411yescharacteristic
102C2×C127#223912yes—
103C2×#365C2×C12712yes—
104C2×#362C2×C12712yes—
105#1971C2×C12711yescharacteristic
106#1849C2×C12711yescharacteristic
107#1377C2×C12711yescharacteristic
108C127#1353611yescharacteristic, direct product factor, Sylow
109C22×Q16C22×C12711yescharacteristic
110C2×M32C22×C12712yes—
111C2×#108—21no—
112C2×#108C22×C12712yes—
113C2×#106C22×C12711yescharacteristic
114#423—21no—
115C2×#103—21no—
116C2×#97C22×C12711yescharacteristic
117#391—21no—
118#365—24no—
119#362—24no—
120C22×Q8—21no—
121C2×Q16—22no—
122C2×Q16—22no—
123C2×Q16—21no—
124C2×Q16Q8×C12712yes—
125C2×M16—22no—
126C22×C8D4×C12711yescharacteristic
127C22×C8C23×C12711yescharacteristic
128C2×C4⋊C4—21no—
129C2×C42D4×C12711yescharacteristic
130M32—22no—
131M32D4×C12714yes—
132C2×C16—22no—
133#108—22no—
134#108—22no—
135#108—42no—
136#106—22no—
137C4⋊C8—42no—
138#103—42no—
139#97—22no—
140#95—42no—
141C2×Q8—22no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4SD16×C12712yes—
150C22×C4C2×D4×C12711yescharacteristic
151Q16—24no—
152Q16—42no—
153M16—42no—
154M16—42no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—42no—
158C2×C8SD16×C12712yes—
159C2×C8C2×D4×C12712yes—
160C2×C8C2×Q8×C12711yescharacteristic
161C2×C8#41×C12712yes—
162C2×C8#41×C12711yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—41no—
165C42—21no—
166C42—21no—
167C16—24no—
168C23C2×SD16×C12711yescharacteristic
169Q8—42no—
170Q8—42no—
171Q8—81no—
172Q8—81no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—82no—
179C2×C4—81no—
180C2×C4C22⋊Q8×C12711yescharacteristic
181C2×C4#123×C12711yescharacteristic
182C2×C4#127×C12711yescharacteristic
183C2×C4C2×SD16×C12711yescharacteristic
184C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
185C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
186C8—22no—
187C8—82no—
188C8C22⋊Q8×C12712yes—
189C8#123×C12712yes—
190C22—22no—
191C22#476×C12711yescharacteristic
192C22#481×C12711yescharacteristic
193C22#492×C12711yescharacteristic
194C4—42no—
195C4—82no—
196C4—161no—
197C4#399×C12711yescharacteristic
198C4#476×C12711yescharacteristic
199C4#481×C12711yescharacteristic
200C4#496×C12711yescharacteristic
201C2—21no—
202C2—21no—
203C2C127×#209411yescharacteristic
204C2C127×#223912yes—
subgroupG/H
center, socleC22×C127#481
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127C2×SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
98. #13536C127direct (N × H)
108. C127#13536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#365×C1272
C2×#362×C1272
C127×#19712
C127×#18492
C127×#13772
#13536127