Finite Group Databasebeta

← C127×#12438 #44576111

Subgroups — C127×#12438 #44576111

Order 32512.

224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2248C211yesmaximal, characteristic, complemented
2C127×#2214C211yesmaximal, characteristic, complemented
3C127×#2213C211yesmaximal, characteristic
4C127×#2170C211yesmaximal, characteristic, complemented
5C127×#1373C211yesmaximal, characteristic, complemented
6C127×#1358C211yesmaximal, characteristic, complemented
7C127×#1357C211yesmaximal, characteristic, complemented
8#510×C127—21no—
9#509×C127—21no—
10C2×SD32×C127—21no—
11C2×SD32×C127—21no—
12#504×C127—21no—
13#494×C127C2211yescharacteristic
14#493×C127C2211yescharacteristic
15#443×C127C2211yescharacteristic
16#364×C127C2211yescharacteristic
17#364×C127C2211yescharacteristic
18#364×C127C2211yescharacteristic
19#362×C127—21no—
20#361×C127—21no—
21#350×C127—21no—
22C4×C16×C127C2211yescharacteristic
23#135×C127D411yescharacteristic
24C2×Q16×C127—21no—
25C2×Q16×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28#131×C127—21no—
29C4⋊Q8×C127—21no—
30#127×C127—21no—
31Q32×C127—41no—
32SD32×C127—42no—
33SD32×C127—41no—
34SD32×C127—41no—
35SD32×C127—41no—
36SD32×C127—41no—
37D16×C127—41no—
38M32×C127—21no—
39M32×C127—21no—
40M32×C127—21no—
41M32×C127—41no—
42C2×C16×C127—41no—
43C2×C16×C127D411yescharacteristic
44C2×C16×C127D411yescharacteristic
45#108×C127D411yescharacteristic
46#104×C127—21no—
47C4×C8×C127C2311yescharacteristic
48#41×C127—21no—
49C2×Q8×C127—41no—
50C2×D4×C127—41no—
51C2×D4×C127—81no—
52Q16×C127—41no—
53Q16×C127—41no—
54Q16×C127—41no—
55Q16×C127—41no—
56Q16×C127D811yescharacteristic
57SD16×C127—21no—
58D8×C127—41no—
59D8×C127—41no—
60D8×C127—41no—
61D8×C127—41no—
62D8×C127D811yescharacteristic
63M16×C127—21no—
64M16×C127—41no—
65C2×C8×C127—41no—
66C2×C8×C127C2×D411yescharacteristic
67C2×C8×C127C2×D411yescharacteristic
68C4⋊C4×C127—81no—
69C42×C127#4111yescharacteristic
70C16×C127—21no—
71C16×C127—41no—
72C16×C127—41no—
73C16×C127—41no—
74C16×C127D811yescharacteristic
75C16×C127D811yescharacteristic
76C23×C127—81no—
77Q8×C127—21no—
78Q8×C127—81no—
79Q8×C127—81no—
80D4×C127—21no—
81D4×C127—41no—
82D4×C127—81no—
83D4×C127—81no—
84D4×C127—162no—
85C2×C4×C127—21no—
86C2×C4×C127—41no—
87C2×C4×C127—81no—
88C2×C4×C127#12111yescharacteristic
89C8×C127—41no—
90C8×C127C2×D811yescharacteristic
91C8×C127C2×D811yescharacteristic
92C8×C127#13511yescharacteristic
93C8×C127AGL(1,ℤ/8)11yescharacteristic
94C22×C127—41no—
95C22×C127—162no—
96C22×C127—161no—
97C22×C127#47211yescharacteristic
98C4×C127—22no—
99C4×C127—41no—
100C4×C127—161no—
101C4×C127#45911yescharacteristic
102C4×C127#46611yescharacteristic
103#12438C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127—21no—
105C2×C127—81no—
106C2×C127—321no—
107C2×C127#166711yescharacteristic
108#2248C2×C12711yescharacteristic, complemented
109#2214C2×C12711yescharacteristic, complemented
110#2213C2×C12711yescharacteristic
111#2170C2×C12711yescharacteristic, complemented
112#1373C2×C12711yescharacteristic, complemented
113#1358C2×C12711yescharacteristic, complemented
114#1357C2×C12711yescharacteristic, complemented
115C127#1243811yescharacteristic, direct product factor, Sylow
116#510—21no—
117#509—21no—
118C2×SD32—21no—
119C2×SD32—21no—
120#504—21no—
121#494C22×C12711yescharacteristic
122#493C22×C12711yescharacteristic
123#443C22×C12711yescharacteristic
124#364C22×C12711yescharacteristic
125#364C22×C12711yescharacteristic
126#364C22×C12711yescharacteristic
127#362—21no—
128#361—21no—
129#350—21no—
130C4×C16C22×C12711yescharacteristic
131#135D4×C12711yescharacteristic
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—21no—
135C2×D8—21no—
136#131—21no—
137C4⋊Q8—21no—
138#127—21no—
139Q32—41no—
140SD32—42no—
141SD32—41no—
142SD32—41no—
143SD32—41no—
144SD32—41no—
145D16—41no—
146M32—21no—
147M32—21no—
148M32—21no—
149M32—41no—
150C2×C16—41no—
151C2×C16D4×C12711yescharacteristic
152C2×C16D4×C12711yescharacteristic
153#108D4×C12711yescharacteristic
154#104—21no—
155C4×C8C23×C12711yescharacteristic
156#41—21no—
157C2×Q8—41no—
158C2×D4—41no—
159C2×D4—81no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16D8×C12711yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8D8×C12711yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8C2×D4×C12711yescharacteristic
175C2×C8C2×D4×C12711yescharacteristic
176C4⋊C4—81no—
177C42#41×C12711yescharacteristic
178C16—21no—
179C16—41no—
180C16—41no—
181C16—41no—
182C16D8×C12711yescharacteristic
183C16D8×C12711yescharacteristic
184C23—81no—
185Q8—21no—
186Q8—81no—
187Q8—81no—
188D4—21no—
189D4—41no—
190D4—81no—
191D4—81no—
192D4—162no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—81no—
196C2×C4#121×C12711yescharacteristic
197C8—41no—
198C8C2×D8×C12711yescharacteristic
199C8C2×D8×C12711yescharacteristic
200C8#135×C12711yescharacteristic
201C8AGL(1,ℤ/8)×C12711yescharacteristic
202C22—41no—
203C22—162no—
204C22—161no—
205C22#472×C12711yescharacteristic
206C4—22no—
207C4—41no—
208C4—161no—
209C4#459×C12711yescharacteristic
210C4#466×C12711yescharacteristic
211C2—21no—
212C2—81no—
213C2—321no—
214C2C127×#166711yescharacteristic
subgroupG/H
center, socleC2×C127#1667
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#2213C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2248C2semidirect
2. C127×#2214C2semidirect
4. C127×#2170C2semidirect
5. C127×#1373C2semidirect
6. C127×#1358C2semidirect
7. C127×#1357C2semidirect
103. #12438C127direct (N × H)
108. #2248C2×C127semidirect
109. #2214C2×C127semidirect
111. #2170C2×C127semidirect
112. #1373C2×C127semidirect
113. #1358C2×C127semidirect
114. #1357C2×C127semidirect
115. C127#12438direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22482
C127×#22142
C127×#22132
C127×#21702
C127×#13732
C127×#13582
C127×#13572
#12438127