Finite Group Databasebeta

← C127×#12873 #44576546

Subgroups — C127×#12873 #44576546

Order 32512.

380 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2912C211yesmaximal, characteristic
2C127×#2115C211yesmaximal, characteristic
3C127×#1812C211yesmaximal, characteristic
4C127×#1386C212yesmaximal, complemented
5C127×#1384C212yesmaximal, complemented
6C2×#131×C127C2211yescharacteristic
7#520×C127—21no—
8C2×M32×C127C2212yes—
9#428×C127—21no—
10#428×C127—22no—
11#427×C127C412yescomplemented
12#427×C127C2212yes—
13#427×C127C2211yescharacteristic
14C2×#106×C127C412yescomplemented
15C2×#106×C127C2211yescharacteristic
16#410×C127—21no—
17#349×C127—22no—
18H(3,ℤ/4)×C127—21no—
19C2×#41×C127D411yescharacteristic
20#131×C127—22no—
21#131×C127—22no—
22C2×M16×C127D411yescharacteristic
23C2×M16×C127D412yes—
24C22×C8×C127C2×C412yes—
25C22×C8×C127C2311yescharacteristic
26C4×Q8×C127—41no—
27C4×D4×C127—42no—
28C4×D4×C127—41no—
29#117×C127—22no—
30#117×C127—21no—
31#117×C127—22no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—21no—
34M32×C127—22no—
35M32×C127—22no—
36C2×C16×C127—22no—
37#107×C127—22no—
38#107×C127—21no—
39#107×C127—22no—
40#106×C127—22no—
41#106×C127—21no—
42#106×C127—22no—
43#106×C127C2×C411yescharacteristic
44#106×C127C2×C412yes—
45#106×C127C2×C411yescharacteristic
46#99×C127—42no—
47#41×C127—22no—
48#41×C127—22no—
49C2×Q8×C127SD1611yescharacteristic
50C2×D4×C127D812yes—
51C2×D4×C127SD1611yescharacteristic
52C22×C4×C127—42no—
53C22×C4×C127—41no—
54C22×C4×C127C22⋊C412yes—
55C22×C4×C127C2×D411yescharacteristic
56M16×C127—22no—
57M16×C127—24no—
58C2×C8×C127—22no—
59C2×C8×C127—22no—
60C2×C8×C127C22⋊C412yes—
61C2×C8×C127C22×C411yescharacteristic
62C2×C8×C127C2×D411yescharacteristic
63C2×C8×C127#4112yes—
64C2×C8×C127#4112yes—
65C4⋊C4×C127—21no—
66C4⋊C4×C127—22no—
67C4⋊C4×C127—21no—
68C4⋊C4×C127—42no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—42no—
71C22⋊C4×C127—42no—
72C22⋊C4×C127—41no—
73C22⋊C4×C127—42no—
74C42×C127—42no—
75C42×C127—41no—
76C42×C127—42no—
77C16×C127—42no—
78C23×C127#10212yes—
79C23×C127C2×D811yescharacteristic
80Q8×C127—22no—
81D4×C127—24no—
82D4×C127—22no—
83C2×C4×C127—22no—
84C2×C4×C127—22no—
85C2×C4×C127—41no—
86C2×C4×C127—42no—
87C2×C4×C127—41no—
88C2×C4×C127—82no—
89C2×C4×C127—161no—
90C2×C4×C127—162no—
91C2×C4×C127#10212yes—
92C2×C4×C127C2×C22⋊C411yescharacteristic
93C2×C4×C127#12312yes—
94C2×C4×C127C2×SD1611yescharacteristic
95C2×C4×C127#13712yes—
96C8×C127—22no—
97C8×C127#11711yescharacteristic
98C8×C127#11711yescharacteristic
99C8×C127#12312yes—
100C22×C127—22no—
101C22×C127—41no—
102C22×C127—42no—
103C22×C127C2×#10211yescharacteristic
104C22×C127#48012yes—
105C4×C127—22no—
106C4×C127—81no—
107C4×C127—82no—
108C4×C127—81no—
109C4×C127—162no—
110C4×C127#38111yescharacteristic
111C4×C127#41911yescharacteristic
112C4×C127#48312yes—
113#12873C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—21no—
115C2×C127—22no—
116C2×C127—42no—
117C2×C127#182311yescharacteristic
118#2912C2×C12711yescharacteristic
119#2115C2×C12711yescharacteristic
120#1812C2×C12711yescharacteristic
121#1386C2×C12712yescomplemented
122#1384C2×C12712yescomplemented
123C127#1287311yescharacteristic, direct product factor, Sylow
124C2×#131C22×C12711yescharacteristic
125#520—21no—
126C2×M32C22×C12712yes—
127#428—21no—
128#428—22no—
129#427C4×C12712yescomplemented
130#427C22×C12712yes—
131#427C22×C12711yescharacteristic
132C2×#106C4×C12712yescomplemented
133C2×#106C22×C12711yescharacteristic
134#410—21no—
135#349—22no—
136H(3,ℤ/4)—21no—
137C2×#41D4×C12711yescharacteristic
138#131—22no—
139#131—22no—
140C2×M16D4×C12711yescharacteristic
141C2×M16D4×C12712yes—
142C22×C8C2×C4×C12712yes—
143C22×C8C23×C12711yescharacteristic
144C4×Q8—41no—
145C4×D4—42no—
146C4×D4—41no—
147#117—22no—
148#117—21no—
149#117—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152M32—22no—
153M32—22no—
154C2×C16—22no—
155#107—22no—
156#107—21no—
157#107—22no—
158#106—22no—
159#106—21no—
160#106—22no—
161#106C2×C4×C12711yescharacteristic
162#106C2×C4×C12712yes—
163#106C2×C4×C12711yescharacteristic
164#99—42no—
165#41—22no—
166#41—22no—
167C2×Q8SD16×C12711yescharacteristic
168C2×D4D8×C12712yes—
169C2×D4SD16×C12711yescharacteristic
170C22×C4—42no—
171C22×C4—41no—
172C22×C4C22⋊C4×C12712yes—
173C22×C4C2×D4×C12711yescharacteristic
174M16—22no—
175M16—24no—
176C2×C8—22no—
177C2×C8—22no—
178C2×C8C22⋊C4×C12712yes—
179C2×C8C22×C4×C12711yescharacteristic
180C2×C8C2×D4×C12711yescharacteristic
181C2×C8#41×C12712yes—
182C2×C8#41×C12712yes—
183C4⋊C4—21no—
184C4⋊C4—22no—
185C4⋊C4—21no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C22⋊C4—42no—
190C22⋊C4—41no—
191C22⋊C4—42no—
192C42—42no—
193C42—41no—
194C42—42no—
195C16—42no—
196C23#102×C12712yes—
197C23C2×D8×C12711yescharacteristic
198Q8—22no—
199D4—24no—
200D4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—82no—
207C2×C4—161no—
208C2×C4—162no—
209C2×C4#102×C12712yes—
210C2×C4C2×C22⋊C4×C12711yescharacteristic
211C2×C4#123×C12712yes—
212C2×C4C2×SD16×C12711yescharacteristic
213C2×C4#137×C12712yes—
214C8—22no—
215C8#117×C12711yescharacteristic
216C8#117×C12711yescharacteristic
217C8#123×C12712yes—
218C22—22no—
219C22—41no—
220C22—42no—
221C22C2×#102×C12711yescharacteristic
222C22#480×C12712yes—
223C4—22no—
224C4—82no—
225C4—81no—
226C4—81no—
227C4—162no—
228C4#381×C12711yescharacteristic
229C4#419×C12711yescharacteristic
230C4#483×C12712yes—
231C2—21no—
232C2—22no—
233C2—42no—
234C2C127×#182311yescharacteristic
subgroupG/H
center, socleC2×C127#1823
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1386C2semidirect
5. C127×#1384C2semidirect
11. #427×C127C4semidirect
14. C2×#106×C127C4semidirect
113. #12873C127direct (N × H)
121. #1386C2×C127semidirect
122. #1384C2×C127semidirect
123. C127#12873direct (N × H)
129. #427C4×C127semidirect
132. C2×#106C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29122
C127×#21152
C127×#18122
C127×#13862
C127×#13842
#12873127