Finite Group Databasebeta

← C127×#12874 #44576547

Subgroups — C127×#12874 #44576547

Order 32512.

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

normal subgroups only

This group has 376 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×#1813C211yesmaximal, characteristic
4C127×#1389C212yesmaximal, complemented
5C127×#1383C212yesmaximal, complemented
6C2×#131×C127C2211yescharacteristic
7#520×C127—21no—
8C2×M32×C127C2212yes—
9C2×#108×C127C2212yes—
10#428×C127—21no—
11#428×C127—22no—
12#427×C127C412yes—
13#427×C127C2211yescharacteristic
14C2×#106×C127C412yes—
15C2×#106×C127C2211yescharacteristic
16#413×C127—21no—
17#349×C127—22no—
18#338×C127—21no—
19C2×#41×C127D411yescharacteristic
20#131×C127—22no—
21#131×C127—22no—
22C2×M16×C127—22no—
23C2×M16×C127D411yescharacteristic
24C2×M16×C127D412yes—
25C22×C8×C127C2×C412yes—
26C22×C8×C127C2311yescharacteristic
27C4×Q8×C127—41no—
28C4×D4×C127—41no—
29C4×D4×C127—42no—
30#117×C127—22no—
31#117×C127—21no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—21no—
34M32×C127—22no—
35M32×C127—22no—
36C2×C16×C127—22no—
37#108×C127—22no—
38#108×C127—22no—
39#107×C127—22no—
40#107×C127—21no—
41#106×C127—22no—
42#106×C127—21no—
43#106×C127C2×C411yescharacteristic
44#106×C127C2×C412yes—
45#106×C127C2×C411yescharacteristic
46#101×C127—41no—
47#100×C127—41no—
48#41×C127—22no—
49#41×C127—22no—
50C2×Q8×C127D811yescharacteristic
51C2×D4×C127D811yescharacteristic
52C2×D4×C127SD1612yes—
53C22×C4×C127—42no—
54C22×C4×C127—41no—
55C22×C4×C127C22⋊C412yes—
56C22×C4×C127C2×D411yescharacteristic
57M16×C127—22no—
58M16×C127—24no—
59M16×C127—42no—
60M16×C127—42no—
61C2×C8×C127—22no—
62C2×C8×C127—22no—
63C2×C8×C127—42no—
64C2×C8×C127C22⋊C412yes—
65C2×C8×C127C22×C411yescharacteristic
66C2×C8×C127C2×D411yescharacteristic
67C2×C8×C127#4112yes—
68C2×C8×C127#4112yes—
69C4⋊C4×C127—21no—
70C4⋊C4×C127—22no—
71C4⋊C4×C127—21no—
72C4⋊C4×C127—42no—
73C4⋊C4×C127—41no—
74C22⋊C4×C127—42no—
75C22⋊C4×C127—41no—
76C42×C127—42no—
77C42×C127—41no—
78C16×C127—42no—
79C23×C127#10212yes—
80C23×C127C2×SD1611yescharacteristic
81Q8×C127—22no—
82D4×C127—24no—
83D4×C127—22no—
84C2×C4×C127—22no—
85C2×C4×C127—22no—
86C2×C4×C127—41no—
87C2×C4×C127—42no—
88C2×C4×C127—41no—
89C2×C4×C127—161no—
90C2×C4×C127—162no—
91C2×C4×C127#10212yes—
92C2×C4×C127C2×C22⋊C411yescharacteristic
93C2×C4×C127#12312yes—
94C2×C4×C127C2×D811yescharacteristic
95C2×C4×C127#13712yes—
96C8×C127—22no—
97C8×C127—82no—
98C8×C127#11711yescharacteristic
99C8×C127#11711yescharacteristic
100C8×C127#12312yes—
101C22×C127—22no—
102C22×C127—41no—
103C22×C127—42no—
104C22×C127C2×#10211yescharacteristic
105C22×C127#48312yes—
106C4×C127—22no—
107C4×C127—81no—
108C4×C127—82no—
109C4×C127—81no—
110C4×C127#38111yescharacteristic
111C4×C127#41911yescharacteristic
112C4×C127#48012yes—
113#12874C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—21no—
115C2×C127—22no—
116C2×C127—42no—
117C2×C127#182311yescharacteristic
118#2912C2×C12711yescharacteristic
119#2115C2×C12711yescharacteristic
120#1813C2×C12711yescharacteristic
121#1389C2×C12712yescomplemented
122#1383C2×C12712yescomplemented
123C127#1287411yescharacteristic, direct product factor, Sylow
124C2×#131C22×C12711yescharacteristic
125#520—21no—
126C2×M32C22×C12712yes—
127C2×#108C22×C12712yes—
128#428—21no—
129#428—22no—
130#427C4×C12712yes—
131#427C22×C12711yescharacteristic
132C2×#106C4×C12712yes—
133C2×#106C22×C12711yescharacteristic
134#413—21no—
135#349—22no—
136#338—21no—
137C2×#41D4×C12711yescharacteristic
138#131—22no—
139#131—22no—
140C2×M16—22no—
141C2×M16D4×C12711yescharacteristic
142C2×M16D4×C12712yes—
143C22×C8C2×C4×C12712yes—
144C22×C8C23×C12711yescharacteristic
145C4×Q8—41no—
146C4×D4—41no—
147C4×D4—42no—
148#117—22no—
149#117—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152M32—22no—
153M32—22no—
154C2×C16—22no—
155#108—22no—
156#108—22no—
157#107—22no—
158#107—21no—
159#106—22no—
160#106—21no—
161#106C2×C4×C12711yescharacteristic
162#106C2×C4×C12712yes—
163#106C2×C4×C12711yescharacteristic
164#101—41no—
165#100—41no—
166#41—22no—
167#41—22no—
168C2×Q8D8×C12711yescharacteristic
169C2×D4D8×C12711yescharacteristic
170C2×D4SD16×C12712yes—
171C22×C4—42no—
172C22×C4—41no—
173C22×C4C22⋊C4×C12712yes—
174C22×C4C2×D4×C12711yescharacteristic
175M16—22no—
176M16—24no—
177M16—42no—
178M16—42no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—42no—
182C2×C8C22⋊C4×C12712yes—
183C2×C8C22×C4×C12711yescharacteristic
184C2×C8C2×D4×C12711yescharacteristic
185C2×C8#41×C12712yes—
186C2×C8#41×C12712yes—
187C4⋊C4—21no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C22⋊C4—42no—
193C22⋊C4—41no—
194C42—42no—
195C42—41no—
196C16—42no—
197C23#102×C12712yes—
198C23C2×SD16×C12711yescharacteristic
199Q8—22no—
200D4—24no—
201D4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—161no—
208C2×C4—162no—
209C2×C4#102×C12712yes—
210C2×C4C2×C22⋊C4×C12711yescharacteristic
211C2×C4#123×C12712yes—
212C2×C4C2×D8×C12711yescharacteristic
213C2×C4#137×C12712yes—
214C8—22no—
215C8—82no—
216C8#117×C12711yescharacteristic
217C8#117×C12711yescharacteristic
218C8#123×C12712yes—
219C22—22no—
220C22—41no—
221C22—42no—
222C22C2×#102×C12711yescharacteristic
223C22#483×C12712yes—
224C4—22no—
225C4—82no—
226C4—81no—
227C4—81no—
228C4#381×C12711yescharacteristic
229C4#419×C12711yescharacteristic
230C4#480×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×#1389C2semidirect
5. C127×#1383C2semidirect
113. #12874C127direct (N × H)
121. #1389C2×C127semidirect
122. #1383C2×C127semidirect
123. C127#12874direct (N × H)

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×#18132
C127×#13892
C127×#13832
#12874127