Finite Group Databasebeta

← C127×#13487 #44577160

Subgroups — C127×#13487 #44577160

Order 32512.

338 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 106 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×#361×C127C212yesmaximal
2C127×#1972C211yesmaximal, characteristic
3C127×#1849C211yesmaximal, characteristic, complemented
4C127×#1383C212yesmaximal, 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#361×C127—24no—
16C22×D4×C127—21no—
17C2×D8×C127—22no—
18C2×D8×C127—22no—
19C2×D8×C127—21no—
20C2×D8×C127D412yes—
21C2×M16×C127—22no—
22C22×C8×C127D411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24C2×C4⋊C4×C127—21no—
25C2×C22⋊C4×C127—42no—
26C2×C42×C127D411yescharacteristic
27M32×C127—22no—
28M32×C127—22no—
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#102×C127—42no—
36#97×C127—22no—
37C24×C127—41no—
38C2×D4×C127—22no—
39C2×D4×C127—41no—
40C2×D4×C127—41no—
41C2×D4×C127—41no—
42C2×D4×C127—41no—
43C2×D4×C127—41no—
44C22×C4×C127—41no—
45C22×C4×C127SD1612yes—
46C22×C4×C127C2×D411yescharacteristic
47D8×C127—24no—
48D8×C127—42no—
49M16×C127—42no—
50M16×C127—42no—
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C2×C8×C127—42no—
54C2×C8×C127D812yes—
55C2×C8×C127C2×D411yescharacteristic
56C2×C8×C127#4112yes—
57C2×C8×C127#4112yes—
58C2×C8×C127#4111yescharacteristic
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C22⋊C4×C127—84no—
62C42×C127—21no—
63C42×C127—21no—
64C16×C127—42no—
65C23×C127—42no—
66C23×C127—82no—
67C23×C127—82no—
68C23×C127—81no—
69C23×C127—81no—
70C23×C127C2×SD1611yescharacteristic
71D4×C127—42no—
72D4×C127—42no—
73D4×C127—81no—
74D4×C127—81no—
75C2×C4×C127—22no—
76C2×C4×C127—42no—
77C2×C4×C127—82no—
78C2×C4×C127—81no—
79C2×C4×C127#12111yescharacteristic
80C2×C4×C127#12311yescharacteristic
81C2×C4×C127#12411yescharacteristic
82C2×C4×C127C2×D811yescharacteristic
83C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
84C2×C4×C127#13711yescharacteristic
85C8×C127—22no—
86C8×C127—82no—
87C8×C127#12312yes—
88C8×C127#12612yes—
89C22×C127—22no—
90C22×C127—84no—
91C22×C127—82no—
92C22×C127—161no—
93C22×C127—161no—
94C22×C127—162no—
95C22×C127#46111yescharacteristic
96C22×C127#48111yescharacteristic
97C22×C127#48611yescharacteristic
98C4×C127—42no—
99C4×C127—161no—
100C4×C127#39711yescharacteristic
101C4×C127#45911yescharacteristic
102C4×C127#48011yescharacteristic
103C4×C127#48911yescharacteristic
104#13487C12711yesmaximal, characteristic, direct product factor, Sylow
105C2×C127—21no—
106C2×C127—21no—
107C2×C127—162no—
108C2×C127#207111yescharacteristic
109C2×C127#223812yes—
110C2×#361C2×C12712yes—
111#1972C2×C12711yescharacteristic
112#1849C2×C12711yescharacteristic, complemented
113#1383C2×C12712yescomplemented
114#1377C2×C12711yescharacteristic, complemented
115C127#1348711yescharacteristic, direct product factor, Sylow
116C22×D8C22×C12711yescharacteristic
117C2×M32C22×C12712yes—
118C2×#108—21no—
119C2×#108C22×C12712yes—
120C2×#106C22×C12711yescharacteristic
121#423—21no—
122C2×#102—21no—
123C2×#97C22×C12711yescharacteristic
124#390—21no—
125#361—24no—
126C22×D4—21no—
127C2×D8—22no—
128C2×D8—22no—
129C2×D8—21no—
130C2×D8D4×C12712yes—
131C2×M16—22no—
132C22×C8D4×C12711yescharacteristic
133C22×C8C23×C12711yescharacteristic
134C2×C4⋊C4—21no—
135C2×C22⋊C4—42no—
136C2×C42D4×C12711yescharacteristic
137M32—22no—
138M32—22no—
139C2×C16—22no—
140#108—22no—
141#108—22no—
142#108—42no—
143#106—22no—
144C4⋊C8—42no—
145#102—42no—
146#97—22no—
147C24—41no—
148C2×D4—22no—
149C2×D4—41no—
150C2×D4—41no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4—41no—
154C22×C4—41no—
155C22×C4SD16×C12712yes—
156C22×C4C2×D4×C12711yescharacteristic
157D8—24no—
158D8—42no—
159M16—42no—
160M16—42no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—42no—
164C2×C8D8×C12712yes—
165C2×C8C2×D4×C12711yescharacteristic
166C2×C8#41×C12712yes—
167C2×C8#41×C12712yes—
168C2×C8#41×C12711yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—41no—
171C22⋊C4—84no—
172C42—21no—
173C42—21no—
174C16—42no—
175C23—42no—
176C23—82no—
177C23—82no—
178C23—81no—
179C23—81no—
180C23C2×SD16×C12711yescharacteristic
181D4—42no—
182D4—42no—
183D4—81no—
184D4—81no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—82no—
188C2×C4—81no—
189C2×C4#121×C12711yescharacteristic
190C2×C4#123×C12711yescharacteristic
191C2×C4#124×C12711yescharacteristic
192C2×C4C2×D8×C12711yescharacteristic
193C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
194C2×C4#137×C12711yescharacteristic
195C8—22no—
196C8—82no—
197C8#123×C12712yes—
198C8#126×C12712yes—
199C22—22no—
200C22—84no—
201C22—82no—
202C22—161no—
203C22—161no—
204C22—162no—
205C22#461×C12711yescharacteristic
206C22#481×C12711yescharacteristic
207C22#486×C12711yescharacteristic
208C4—42no—
209C4—161no—
210C4#397×C12711yescharacteristic
211C4#459×C12711yescharacteristic
212C4#480×C12711yescharacteristic
213C4#489×C12711yescharacteristic
214C2—21no—
215C2—21no—
216C2—162no—
217C2C127×#207111yescharacteristic
218C2C127×#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
3. C127×#1849C2semidirect
4. C127×#1383C2semidirect
5. C127×#1377C2semidirect
104. #13487C127direct (N × H)
112. #1849C2×C127semidirect
113. #1383C2×C127semidirect
114. #1377C2×C127semidirect
115. C127#13487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#361×C1272
C127×#19722
C127×#18492
C127×#13832
C127×#13772
#13487127