Finite Group Databasebeta

← C127×#10513 #44574186

Subgroups — C127×#10513 #44574186

Order 32512.

388 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3245C211yesmaximal, characteristic
2C127×#1832C211yesmaximal, characteristic, complemented
3C127×#1551C212yesmaximal, complemented
4C127×#1505C212yesmaximal, complemented
5C127×#1290C211yesmaximal, characteristic, complemented
6#532×C127C2212yes—
7#474×C127—22no—
8#466×C127—22no—
9#459×C127—22no—
10#432×C127C2212yes—
11C2×C4⋊C8×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13#376×C127C2211yescharacteristic
14#336×C127—22no—
15#333×C127—22no—
16#331×C127—22no—
17#327×C127—24no—
18C2×#41×C127—22no—
19C2×D8×C127—22no—
20C22×C8×C127—21no—
21C22×C8×C127D412yes—
22C4⋊Q8×C127D412yes—
23#127×C127D412yes—
24#124×C127—22no—
25#121×C127—22no—
26#121×C127—22no—
27C4×D4×C127—22no—
28C4×D4×C127—22no—
29C2×C42×C127—21no—
30C2×C42×C127C2311yescharacteristic
31#107×C127—22no—
32C4⋊C8×C127—22no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35#102×C127—24no—
36C22⋊C8×C127—22no—
37#97×C127—22no—
38#95×C127—21no—
39#95×C127D412yes—
40#41×C127—84no—
41C2×Q8×C127—22no—
42C2×D4×C127—22no—
43C2×D4×C127—22no—
44C2×D4×C127—22no—
45C2×D4×C127—42no—
46C22×C4×C127—22no—
47C22×C4×C127—42no—
48C22×C4×C127C2×D411yescharacteristic
49C22×C4×C127C2×D411yescharacteristic
50C22×C4×C127#4111yescharacteristic
51D8×C127—82no—
52C2×C8×C127—22no—
53C2×C8×C127—42no—
54C2×C8×C127—42no—
55C2×C8×C127—41no—
56C2×C8×C127—42no—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—22no—
59C22⋊C4×C127—42no—
60C22⋊C4×C127—42no—
61C42×C127—41no—
62C42×C127—41no—
63C42×C127C2×D412yes—
64C42×C127#4112yes—
65C23×C127—42no—
66C23×C127#12111yescharacteristic
67Q8×C127—82no—
68D4×C127—42no—
69D4×C127—42no—
70D4×C127—82no—
71D4×C127—82no—
72D4×C127—84no—
73C2×C4×C127—22no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—41no—
77C2×C4×C127—42no—
78C2×C4×C127—42no—
79C2×C4×C127—42no—
80C2×C4×C127—42no—
81C2×C4×C127—84no—
82C2×C4×C127#12011yescharacteristic
83C2×C4×C127#12112yes—
84C2×C4×C127#12312yes—
85C2×C4×C127#12411yescharacteristic
86C8×C127—42no—
87C8×C127—82no—
88C8×C127—81no—
89C22×C127—21no—
90C22×C127—21no—
91C22×C127—82no—
92C22×C127—82no—
93C22×C127—82no—
94C22×C127#39411yescharacteristic
95C22×C127#47212yes—
96C4×C127—22no—
97C4×C127—21no—
98C4×C127—22no—
99C4×C127—82no—
100C4×C127—82no—
101C4×C127#45411yescharacteristic
102C4×C127#45511yescharacteristic
103#10513C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127—22no—
105C2×C127—162no—
106C2×C127#204011yescharacteristic
107C2×C127#204511yescharacteristic
108C2×C127#205311yescharacteristic
109#3245C2×C12711yescharacteristic
110#1832C2×C12711yescharacteristic, complemented
111#1551C2×C12712yescomplemented
112#1505C2×C12712yescomplemented
113#1290C2×C12711yescharacteristic, complemented
114C127#1051311yescharacteristic, direct product factor, Sylow
115#532C22×C12712yes—
116#474—22no—
117#466—22no—
118#459—22no—
119#432C22×C12712yes—
120C2×C4⋊C8C22×C12711yescharacteristic
121C2×C4⋊C8C22×C12711yescharacteristic
122#376C22×C12711yescharacteristic
123#336—22no—
124#333—22no—
125#331—22no—
126#327—24no—
127C2×#41—22no—
128C2×D8—22no—
129C22×C8—21no—
130C22×C8D4×C12712yes—
131C4⋊Q8D4×C12712yes—
132#127D4×C12712yes—
133#124—22no—
134#121—22no—
135#121—22no—
136C4×D4—22no—
137C4×D4—22no—
138C2×C42—21no—
139C2×C42C23×C12711yescharacteristic
140#107—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144#102—24no—
145C22⋊C8—22no—
146#97—22no—
147#95—21no—
148#95D4×C12712yes—
149#41—84no—
150C2×Q8—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—42no—
155C22×C4—22no—
156C22×C4—42no—
157C22×C4C2×D4×C12711yescharacteristic
158C22×C4C2×D4×C12711yescharacteristic
159C22×C4#41×C12711yescharacteristic
160D8—82no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C2×C8—42no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42—41no—
171C42—41no—
172C42C2×D4×C12712yes—
173C42#41×C12712yes—
174C23—42no—
175C23#121×C12711yescharacteristic
176Q8—82no—
177D4—42no—
178D4—42no—
179D4—82no—
180D4—82no—
181D4—84no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—84no—
191C2×C4#120×C12711yescharacteristic
192C2×C4#121×C12712yes—
193C2×C4#123×C12712yes—
194C2×C4#124×C12711yescharacteristic
195C8—42no—
196C8—82no—
197C8—81no—
198C22—21no—
199C22—21no—
200C22—82no—
201C22—82no—
202C22—82no—
203C22#394×C12711yescharacteristic
204C22#472×C12712yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—82no—
210C4#454×C12711yescharacteristic
211C4#455×C12711yescharacteristic
212C2—22no—
213C2—162no—
214C2C127×#204011yescharacteristic
215C2C127×#204511yescharacteristic
216C2C127×#205311yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3245C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1832C2semidirect
3. C127×#1551C2semidirect
4. C127×#1505C2semidirect
5. C127×#1290C2semidirect
103. #10513C127direct (N × H)
110. #1832C2×C127semidirect
111. #1551C2×C127semidirect
112. #1505C2×C127semidirect
113. #1290C2×C127semidirect
114. C127#10513direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32452
C127×#18322
C127×#15512
C127×#15052
C127×#12902
#10513127