Finite Group Databasebeta

← C127×#10512 #44574185

Subgroups — C127×#10512 #44574185

Order 32512.

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

normal subgroups only

This group has 408 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×#1843C211yesmaximal, 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×C127—22no—
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14#376×C127C2211yescharacteristic
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—
35C4⋊C8×C127—44no—
36#102×C127—24no—
37C22⋊C8×C127—22no—
38#97×C127—22no—
39#95×C127—21no—
40#95×C127D412yes—
41#41×C127—84no—
42C2×Q8×C127—22no—
43C2×D4×C127—22no—
44C2×D4×C127—22no—
45C2×D4×C127—22no—
46C2×D4×C127—42no—
47C22×C4×C127—22no—
48C22×C4×C127—42no—
49C22×C4×C127C2×D411yescharacteristic
50C22×C4×C127C2×D411yescharacteristic
51C22×C4×C127#4111yescharacteristic
52D8×C127—82no—
53C2×C8×C127—22no—
54C2×C8×C127—42no—
55C2×C8×C127—42no—
56C2×C8×C127—41no—
57C2×C8×C127—42no—
58C4⋊C4×C127—22no—
59C4⋊C4×C127—22no—
60C22⋊C4×C127—42no—
61C22⋊C4×C127—42no—
62C42×C127—22no—
63C42×C127—22no—
64C42×C127C2×D412yes—
65C42×C127#4112yes—
66C23×C127—42no—
67C23×C127#12111yescharacteristic
68Q8×C127—82no—
69D4×C127—42no—
70D4×C127—42no—
71D4×C127—82no—
72D4×C127—82no—
73D4×C127—84no—
74C2×C4×C127—22no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—24no—
78C2×C4×C127—41no—
79C2×C4×C127—42no—
80C2×C4×C127—42no—
81C2×C4×C127—42no—
82C2×C4×C127—84no—
83C2×C4×C127#12011yescharacteristic
84C2×C4×C127#12112yes—
85C2×C4×C127#12312yes—
86C2×C4×C127#12411yescharacteristic
87C8×C127—42no—
88C8×C127—82no—
89C8×C127—81no—
90C22×C127—21no—
91C22×C127—21no—
92C22×C127—82no—
93C22×C127—82no—
94C22×C127—82no—
95C22×C127#39411yescharacteristic
96C22×C127#47212yes—
97C4×C127—22no—
98C4×C127—21no—
99C4×C127—22no—
100C4×C127—44no—
101C4×C127—82no—
102C4×C127#45311yescharacteristic
103C4×C127#45611yescharacteristic
104#10512C12711yesmaximal, characteristic, direct product factor, Sylow
105C2×C127—22no—
106C2×C127—162no—
107C2×C127#203911yescharacteristic
108C2×C127#204511yescharacteristic
109C2×C127#205311yescharacteristic
110#3245C2×C12711yescharacteristic
111#1843C2×C12711yescharacteristic, complemented
112#1551C2×C12712yescomplemented
113#1505C2×C12712yescomplemented
114#1290C2×C12711yescharacteristic, complemented
115C127#1051211yescharacteristic, direct product factor, Sylow
116#532C22×C12712yes—
117#474—22no—
118#466—22no—
119#459—22no—
120#432C22×C12712yes—
121C2×C4⋊C8—22no—
122C2×C4⋊C8C22×C12711yescharacteristic
123C2×C4⋊C8C22×C12711yescharacteristic
124#376C22×C12711yescharacteristic
125#333—22no—
126#331—22no—
127#327—24no—
128C2×#41—22no—
129C2×D8—22no—
130C22×C8—21no—
131C22×C8D4×C12712yes—
132C4⋊Q8D4×C12712yes—
133#127D4×C12712yes—
134#124—22no—
135#121—22no—
136#121—22no—
137C4×D4—22no—
138C4×D4—22no—
139C2×C42—21no—
140C2×C42C23×C12711yescharacteristic
141#107—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—44no—
146#102—24no—
147C22⋊C8—22no—
148#97—22no—
149#95—21no—
150#95D4×C12712yes—
151#41—84no—
152C2×Q8—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—42no—
157C22×C4—22no—
158C22×C4—42no—
159C22×C4C2×D4×C12711yescharacteristic
160C22×C4C2×D4×C12711yescharacteristic
161C22×C4#41×C12711yescharacteristic
162D8—82no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—41no—
167C2×C8—42no—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C42—22no—
173C42—22no—
174C42C2×D4×C12712yes—
175C42#41×C12712yes—
176C23—42no—
177C23#121×C12711yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—82no—
182D4—82no—
183D4—84no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—84no—
193C2×C4#120×C12711yescharacteristic
194C2×C4#121×C12712yes—
195C2×C4#123×C12712yes—
196C2×C4#124×C12711yescharacteristic
197C8—42no—
198C8—82no—
199C8—81no—
200C22—21no—
201C22—21no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#394×C12711yescharacteristic
206C22#472×C12712yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—44no—
211C4—82no—
212C4#453×C12711yescharacteristic
213C4#456×C12711yescharacteristic
214C2—22no—
215C2—162no—
216C2C127×#203911yescharacteristic
217C2C127×#204511yescharacteristic
218C2C127×#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×#1843C2semidirect
3. C127×#1551C2semidirect
4. C127×#1505C2semidirect
5. C127×#1290C2semidirect
104. #10512C127direct (N × H)
111. #1843C2×C127semidirect
112. #1551C2×C127semidirect
113. #1505C2×C127semidirect
114. #1290C2×C127semidirect
115. C127#10512direct (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×#18432
C127×#15512
C127×#15052
C127×#12902
#10512127