Finite Group Databasebeta

← C127×#13591 #44577264

Subgroups — C127×#13591 #44577264

Order 32512.

450 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3151C211yesmaximal, characteristic
2C127×#2132C212yesmaximal, complemented
3C127×#1410C214yesmaximal, complemented
4C2×AGL(1,ℤ/8)×C127—22no—
5#532×C127C2211yescharacteristic
6C2×#127×C127C411yescharacteristic
7#496×C127—22no—
8#493×C127C412yes—
9#492×C127C2212yes—
10#413×C127—22no—
11C4×M16×C127C411yescharacteristic
12#356×C127C2214yescomplemented
13#355×C127—22no—
14C2×#41×C127D412yes—
15C22×D4×C127—21no—
16C22×D4×C127—41no—
17AGL(1,ℤ/8)×C127—44no—
18AGL(1,ℤ/8)×C127—44no—
19C2×SD16×C127—24no—
20C2×D8×C127—24no—
21C2×M16×C127—21no—
22C2×M16×C127—42no—
23C4⋊Q8×C127C2311yescharacteristic
24#127×C127—21no—
25#127×C127—41no—
26#127×C127C2×C412yes—
27#127×C127C2×C411yescharacteristic
28#124×C127D412yes—
29#121×C127—41no—
30C4×D4×C127—41no—
31C2×C42×C127C2×C411yescharacteristic
32#101×C127—24no—
33#100×C127—42no—
34#97×C127—21no—
35C4×C8×C127C2×C412yes—
36C24×C127—41no—
37#41×C127—42no—
38#41×C127—42no—
39C2×Q8×C127C2×D412yes—
40C2×D4×C127—22no—
41C2×D4×C127—22no—
42C2×D4×C127—42no—
43C2×D4×C127—42no—
44C2×D4×C127—41no—
45C2×D4×C127—42no—
46C2×D4×C127—42no—
47C2×D4×C127—41no—
48C2×D4×C127—84no—
49C2×D4×C127C22⋊C412yes—
50C22×C4×C127—21no—
51C22×C4×C127—22no—
52C22×C4×C127C22⋊C411yescharacteristic
53SD16×C127—48no—
54D8×C127—48no—
55M16×C127—24no—
56M16×C127—44no—
57M16×C127—82no—
58C2×C8×C127—22no—
59C2×C8×C127—82no—
60C4⋊C4×C127—41no—
61C22⋊C4×C127—42no—
62C42×C127—21no—
63C42×C127C22⋊C411yescharacteristic
64C42×C127C22×C411yescharacteristic
65C23×C127—22no—
66C23×C127—42no—
67C23×C127—81no—
68C23×C127—81no—
69C23×C127—84no—
70C23×C127#9911yescharacteristic
71Q8×C127—42no—
72D4×C127—42no—
73D4×C127—44no—
74D4×C127—82no—
75D4×C127—84no—
76D4×C127—82no—
77D4×C127—84no—
78D4×C127—82no—
79C2×C4×C127—21no—
80C2×C4×C127—22no—
81C2×C4×C127—21no—
82C2×C4×C127—22no—
83C2×C4×C127—42no—
84C2×C4×C127—42no—
85C2×C4×C127—42no—
86C2×C4×C127#9911yescharacteristic
87C2×C4×C127C2×C22⋊C411yescharacteristic
88C8×C127—24no—
89C8×C127—84no—
90C22×C127—21no—
91C22×C127—41no—
92C22×C127—42no—
93C22×C127—82no—
94C22×C127—84no—
95C22×C127—82no—
96C22×C127—162no—
97C22×C127—162no—
98C22×C127C2×#9911yescharacteristic
99C4×C127—22no—
100C4×C127—21no—
101C4×C127—41no—
102C4×C127—42no—
103C4×C127#35312yes—
104#13591C12711yesmaximal, characteristic, direct product factor, Sylow
105C2×C127—21no—
106C2×C127—41no—
107C2×C127—82no—
108C2×C127—162no—
109C2×C127C2×#35311yescharacteristic
110#3151C2×C12711yescharacteristic
111#2132C2×C12712yescomplemented
112#1410C2×C12714yescomplemented
113C127#1359111yescharacteristic, direct product factor, Sylow
114C2×AGL(1,ℤ/8)—22no—
115#532C22×C12711yescharacteristic
116C2×#127C4×C12711yescharacteristic
117#496—22no—
118#493C4×C12712yes—
119#492C22×C12712yes—
120#413—22no—
121C4×M16C4×C12711yescharacteristic
122#356C22×C12714yescomplemented
123#355—22no—
124C2×#41D4×C12712yes—
125C22×D4—21no—
126C22×D4—41no—
127AGL(1,ℤ/8)—44no—
128AGL(1,ℤ/8)—44no—
129C2×SD16—24no—
130C2×D8—24no—
131C2×M16—21no—
132C2×M16—42no—
133C4⋊Q8C23×C12711yescharacteristic
134#127—21no—
135#127—41no—
136#127C2×C4×C12712yes—
137#127C2×C4×C12711yescharacteristic
138#124D4×C12712yes—
139#121—41no—
140C4×D4—41no—
141C2×C42C2×C4×C12711yescharacteristic
142#101—24no—
143#100—42no—
144#97—21no—
145C4×C8C2×C4×C12712yes—
146C24—41no—
147#41—42no—
148#41—42no—
149C2×Q8C2×D4×C12712yes—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—42no—
153C2×D4—42no—
154C2×D4—41no—
155C2×D4—42no—
156C2×D4—42no—
157C2×D4—41no—
158C2×D4—84no—
159C2×D4C22⋊C4×C12712yes—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4C22⋊C4×C12711yescharacteristic
163SD16—48no—
164D8—48no—
165M16—24no—
166M16—44no—
167M16—82no—
168C2×C8—22no—
169C2×C8—82no—
170C4⋊C4—41no—
171C22⋊C4—42no—
172C42—21no—
173C42C22⋊C4×C12711yescharacteristic
174C42C22×C4×C12711yescharacteristic
175C23—22no—
176C23—42no—
177C23—81no—
178C23—81no—
179C23—84no—
180C23#99×C12711yescharacteristic
181Q8—42no—
182D4—42no—
183D4—44no—
184D4—84no—
185D4—82no—
186D4—82no—
187D4—84no—
188D4—82no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4#99×C12711yescharacteristic
197C2×C4C2×C22⋊C4×C12711yescharacteristic
198C8—24no—
199C8—84no—
200C22—21no—
201C22—41no—
202C22—42no—
203C22—82no—
204C22—84no—
205C22—82no—
206C22—162no—
207C22—162no—
208C22C2×#99×C12711yescharacteristic
209C4—22no—
210C4—21no—
211C4—41no—
212C4—42no—
213C4#353×C12712yes—
214C2—21no—
215C2—41no—
216C2—82no—
217C2—162no—
218C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC2×C127C2×#353
commutatorC42C22×C4×C127
Frattini, cosocleC4⋊Q8C23×C127
prime radicalC127×#3151C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ #532×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2132C2semidirect
3. C127×#1410C2semidirect
12. #356×C127C22semidirect
104. #13591C127direct (N × H)
111. #2132C2×C127semidirect
112. #1410C2×C127semidirect
113. C127#13591direct (N × H)
122. #356C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31512
C127×#21322
C127×#14102
#13591127