Finite Group Databasebeta

← C127×#13668 #44577341

Subgroups — C127×#13668 #44577341

Order 32512.

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

normal subgroups only

This group has 284 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×#3414C211yesmaximal, characteristic
2C127×#2264C212yesmaximal, complemented
3C127×#2219C211yesmaximal, characteristic, complemented
4C127×#1418C212yesmaximal, complemented
5C127×#1400C211yesmaximal, characteristic, complemented
6C2×#135×C127—21no—
7#510×C127—22no—
8#509×C127—22no—
9#508×C127—21no—
10#508×C127C2212yes—
11C2×Q32×C127C2211yescharacteristic, complemented
12C2×M32×C127C2211yescharacteristic
13#467×C127—21no—
14Q64×C127—22no—
15SD64×C127—22no—
16M64×C127C2212yescomplemented
17#367×C127C2211yescharacteristic, complemented
18#358×C127—21no—
19C2×#41×C127—41no—
20#135×C127—22no—
21#135×C127—22no—
22#135×C127—41no—
23#135×C127—41no—
24C2×Q16×C127—21no—
25C2×Q16×C127—21no—
26C2×SD16×C127—41no—
27C2×D8×C127—21no—
28C22×C8×C127D411yescharacteristic
29C22⋊Q8×C127—41no—
30Q32×C127—21no—
31Q32×C127—22no—
32Q32×C127D412yes—
33SD32×C127—22no—
34SD32×C127—22no—
35D16×C127—21no—
36D16×C127D412yes—
37M32×C127—22no—
38C2×C16×C127D411yescharacteristic
39C2×C16×C127C2311yescharacteristic
40#107×C127—21no—
41#103×C127—41no—
42C32×C127—22no—
43#41×C127—42no—
44#41×C127—42no—
45#41×C127—81no—
46#41×C127—81no—
47C2×Q8×C127—41no—
48C2×Q8×C127—41no—
49C2×D4×C127—41no—
50C2×D4×C127—81no—
51C22×C4×C127—81no—
52C22×C4×C127D811yescharacteristic
53Q16×C127—22no—
54Q16×C127—41no—
55Q16×C127—41no—
56Q16×C127—41no—
57SD16×C127—42no—
58SD16×C127—42no—
59D8×C127—22no—
60D8×C127—41no—
61C2×C8×C127—21no—
62C2×C8×C127—21no—
63C2×C8×C127D811yescharacteristic
64C2×C8×C127C2×D411yescharacteristic
65C4⋊C4×C127—41no—
66C4⋊C4×C127—81no—
67C22⋊C4×C127—81no—
68C16×C127—21no—
69C16×C127C2×D412yes—
70C23×C127—81no—
71C23×C127D1611yescharacteristic
72Q8×C127—42no—
73Q8×C127—81no—
74Q8×C127—81no—
75Q8×C127—81no—
76D4×C127—42no—
77D4×C127—81no—
78D4×C127—82no—
79D4×C127—82no—
80C2×C4×C127—21no—
81C2×C4×C127—21no—
82C2×C4×C127—82no—
83C2×C4×C127—81no—
84C2×C4×C127—82no—
85C2×C4×C127—81no—
86C2×C4×C127—81no—
87C2×C4×C127D1611yescharacteristic
88C2×C4×C127C2×D811yescharacteristic
89C8×C127—21no—
90C8×C127#12011yescharacteristic
91C8×C127AGL(1,ℤ/8)11yescharacteristic
92C22×C127—21no—
93C22×C127—41no—
94C22×C127—82no—
95C22×C127—162no—
96C22×C127C2×D1611yescharacteristic
97C4×C127—21no—
98C4×C127—82no—
99C4×C127—161no—
100C4×C127—161no—
101C4×C127#44711yescharacteristic
102C4×C127#50911yescharacteristic
103#13668C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127—21no—
105C2×C127—41no—
106C2×C127—162no—
107C2×C127#218411yescharacteristic
108#3414C2×C12711yescharacteristic
109#2264C2×C12712yescomplemented
110#2219C2×C12711yescharacteristic, complemented
111#1418C2×C12712yescomplemented
112#1400C2×C12711yescharacteristic, complemented
113C127#1366811yescharacteristic, direct product factor, Sylow
114C2×#135—21no—
115#510—22no—
116#509—22no—
117#508—21no—
118#508C22×C12712yes—
119C2×Q32C22×C12711yescharacteristic, complemented
120C2×M32C22×C12711yescharacteristic
121#467—21no—
122Q64—22no—
123SD64—22no—
124M64C22×C12712yescomplemented
125#367C22×C12711yescharacteristic, complemented
126#358—21no—
127C2×#41—41no—
128#135—22no—
129#135—22no—
130#135—41no—
131#135—41no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×SD16—41no—
135C2×D8—21no—
136C22×C8D4×C12711yescharacteristic
137C22⋊Q8—41no—
138Q32—21no—
139Q32—22no—
140Q32D4×C12712yes—
141SD32—22no—
142SD32—22no—
143D16—21no—
144D16D4×C12712yes—
145M32—22no—
146C2×C16D4×C12711yescharacteristic
147C2×C16C23×C12711yescharacteristic
148#107—21no—
149#103—41no—
150C32—22no—
151#41—42no—
152#41—42no—
153#41—81no—
154#41—81no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×D4—41no—
158C2×D4—81no—
159C22×C4—81no—
160C22×C4D8×C12711yescharacteristic
161Q16—22no—
162Q16—41no—
163Q16—41no—
164Q16—41no—
165SD16—42no—
166SD16—42no—
167D8—22no—
168D8—41no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8D8×C12711yescharacteristic
172C2×C8C2×D4×C12711yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—81no—
175C22⋊C4—81no—
176C16—21no—
177C16C2×D4×C12712yes—
178C23—81no—
179C23D16×C12711yescharacteristic
180Q8—42no—
181Q8—81no—
182Q8—81no—
183Q8—81no—
184D4—42no—
185D4—81no—
186D4—82no—
187D4—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—82no—
191C2×C4—81no—
192C2×C4—82no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4D16×C12711yescharacteristic
196C2×C4C2×D8×C12711yescharacteristic
197C8—21no—
198C8#120×C12711yescharacteristic
199C8AGL(1,ℤ/8)×C12711yescharacteristic
200C22—21no—
201C22—41no—
202C22—82no—
203C22—162no—
204C22C2×D16×C12711yescharacteristic
205C4—21no—
206C4—82no—
207C4—161no—
208C4—161no—
209C4#447×C12711yescharacteristic
210C4#509×C12711yescharacteristic
211C2—21no—
212C2—41no—
213C2—162no—
214C2C127×#218411yescharacteristic
subgroupG/H
center, socleC2×C127#2184
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC127×#3414C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C22×C8×C127 ◁ C2×M32×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2264C2semidirect
3. C127×#2219C2semidirect
4. C127×#1418C2semidirect
5. C127×#1400C2semidirect
11. C2×Q32×C127C22semidirect
16. M64×C127C22semidirect
17. #367×C127C22semidirect
103. #13668C127direct (N × H)
109. #2264C2×C127semidirect
110. #2219C2×C127semidirect
111. #1418C2×C127semidirect
112. #1400C2×C127semidirect
113. C127#13668direct (N × H)
119. C2×Q32C22×C127semidirect
124. M64C22×C127semidirect
125. #367C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34142
C127×#22642
C127×#22192
C127×#14182
C127×#14002
#13668127