Finite Group Databasebeta

← C127×#13535 #44577208

Subgroups — C127×#13535 #44577208

Order 32512.

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

normal subgroups only

This group has 354 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, complemented
2C2×#361×C127C212yesmaximal
3C127×#1972C211yesmaximal, characteristic
4C127×#1849C211yesmaximal, characteristic, complemented
5C127×#1377C211yesmaximal, characteristic, complemented
6C22×D8×C127C2211yescharacteristic
7C2×M32×C127C2212yes—
8C2×#108×C127—21no—
9C2×#108×C127C2212yes—
10C2×#106×C127C2211yescharacteristic
11#423×C127—21no—
12C2×#102×C127—21no—
13C2×#97×C127C2211yescharacteristic
14#390×C127—21no—
15#365×C127—24no—
16#361×C127—24no—
17C22×D4×C127—21no—
18C2×D8×C127—22no—
19C2×D8×C127—22no—
20C2×D8×C127—21no—
21C2×D8×C127Q812yes—
22C2×M16×C127—22no—
23C22×C8×C127D411yescharacteristic
24C22×C8×C127C2311yescharacteristic
25C2×C4⋊C4×C127—21no—
26C2×C22⋊C4×C127—42no—
27C2×C42×C127D411yescharacteristic
28M32×C127—22no—
29M32×C127D414yes—
30C2×C16×C127—22no—
31#108×C127—22no—
32#108×C127—22no—
33#108×C127—42no—
34#106×C127—22no—
35C4⋊C8×C127—42no—
36#102×C127—42no—
37#97×C127—22no—
38C24×C127—41no—
39C2×D4×C127—22no—
40C2×D4×C127—41no—
41C2×D4×C127—41no—
42C2×D4×C127—41no—
43C2×D4×C127—41no—
44C2×D4×C127—41no—
45C22×C4×C127—41no—
46C22×C4×C127SD1612yes—
47C22×C4×C127C2×D411yescharacteristic
48D8×C127—24no—
49D8×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—
62C22⋊C4×C127—84no—
63C42×C127—21no—
64C42×C127—21no—
65C16×C127—24no—
66C23×C127—42no—
67C23×C127—82no—
68C23×C127—82no—
69C23×C127—81no—
70C23×C127—81no—
71C23×C127C2×SD1611yescharacteristic
72D4×C127—42no—
73D4×C127—42no—
74D4×C127—81no—
75D4×C127—81no—
76C2×C4×C127—22no—
77C2×C4×C127—42no—
78C2×C4×C127—82no—
79C2×C4×C127—81no—
80C2×C4×C127C22⋊Q811yescharacteristic
81C2×C4×C127#12311yescharacteristic
82C2×C4×C127#12711yescharacteristic
83C2×C4×C127C2×SD1611yescharacteristic
84C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
85C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
86C8×C127—22no—
87C8×C127—82no—
88C8×C127C22⋊Q812yes—
89C8×C127#12312yes—
90C22×C127—22no—
91C22×C127—84no—
92C22×C127—82no—
93C22×C127—161no—
94C22×C127—161no—
95C22×C127—162no—
96C22×C127#47611yescharacteristic
97C22×C127#48111yescharacteristic
98C22×C127#49211yescharacteristic
99C4×C127—42no—
100C4×C127—161no—
101C4×C127#39911yescharacteristic
102C4×C127#47611yescharacteristic
103C4×C127#48111yescharacteristic
104C4×C127#49611yescharacteristic
105#13535C12711yesmaximal, characteristic, direct product factor, Sylow
106C2×C127—21no—
107C2×C127—21no—
108C2×C127—162no—
109C2×C127#209411yescharacteristic
110C2×C127#223812yes—
111C2×#365C2×C12712yescomplemented
112C2×#361C2×C12712yes—
113#1972C2×C12711yescharacteristic
114#1849C2×C12711yescharacteristic, complemented
115#1377C2×C12711yescharacteristic, complemented
116C127#1353511yescharacteristic, direct product factor, Sylow
117C22×D8C22×C12711yescharacteristic
118C2×M32C22×C12712yes—
119C2×#108—21no—
120C2×#108C22×C12712yes—
121C2×#106C22×C12711yescharacteristic
122#423—21no—
123C2×#102—21no—
124C2×#97C22×C12711yescharacteristic
125#390—21no—
126#365—24no—
127#361—24no—
128C22×D4—21no—
129C2×D8—22no—
130C2×D8—22no—
131C2×D8—21no—
132C2×D8Q8×C12712yes—
133C2×M16—22no—
134C22×C8D4×C12711yescharacteristic
135C22×C8C23×C12711yescharacteristic
136C2×C4⋊C4—21no—
137C2×C22⋊C4—42no—
138C2×C42D4×C12711yescharacteristic
139M32—22no—
140M32D4×C12714yes—
141C2×C16—22no—
142#108—22no—
143#108—22no—
144#108—42no—
145#106—22no—
146C4⋊C8—42no—
147#102—42no—
148#97—22no—
149C24—41no—
150C2×D4—22no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—41no—
156C22×C4—41no—
157C22×C4SD16×C12712yes—
158C22×C4C2×D4×C12711yescharacteristic
159D8—24no—
160D8—42no—
161M16—42no—
162M16—42no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—42no—
166C2×C8SD16×C12712yes—
167C2×C8C2×D4×C12712yes—
168C2×C8C2×Q8×C12711yescharacteristic
169C2×C8#41×C12712yes—
170C2×C8#41×C12711yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C22⋊C4—84no—
174C42—21no—
175C42—21no—
176C16—24no—
177C23—42no—
178C23—82no—
179C23—82no—
180C23—81no—
181C23—81no—
182C23C2×SD16×C12711yescharacteristic
183D4—42no—
184D4—42no—
185D4—81no—
186D4—81no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C22⋊Q8×C12711yescharacteristic
192C2×C4#123×C12711yescharacteristic
193C2×C4#127×C12711yescharacteristic
194C2×C4C2×SD16×C12711yescharacteristic
195C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
196C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
197C8—22no—
198C8—82no—
199C8C22⋊Q8×C12712yes—
200C8#123×C12712yes—
201C22—22no—
202C22—84no—
203C22—82no—
204C22—161no—
205C22—161no—
206C22—162no—
207C22#476×C12711yescharacteristic
208C22#481×C12711yescharacteristic
209C22#492×C12711yescharacteristic
210C4—42no—
211C4—161no—
212C4#399×C12711yescharacteristic
213C4#476×C12711yescharacteristic
214C4#481×C12711yescharacteristic
215C4#496×C12711yescharacteristic
216C2—21no—
217C2—21no—
218C2—162no—
219C2C127×#209411yescharacteristic
220C2C127×#223812yes—
subgroupG/H
center, socleC22×C127#481
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
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
1. C2×#365×C127C2semidirect
4. C127×#1849C2semidirect
5. C127×#1377C2semidirect
105. #13535C127direct (N × H)
111. C2×#365C2×C127semidirect
114. #1849C2×C127semidirect
115. #1377C2×C127semidirect
116. C127#13535direct (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×#361×C1272
C127×#19722
C127×#18492
C127×#13772
#13535127