Finite Group Databasebeta

← C127×#1861 #30634813

Subgroups — C127×#1861 #30634813

Order 16256.

262 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#568×C127C211yesmaximal, characteristic
2#430×C127C211yesmaximal, characteristic, complemented
3#423×C127C211yesmaximal, characteristic, complemented
4#421×C127C211yesmaximal, characteristic
5C2×#104×C127C211yesmaximal, characteristic
6#344×C127C211yesmaximal, characteristic, complemented
7#339×C127C211yesmaximal, characteristic, complemented
8C2×#41×C127C2211yescharacteristic
9#131×C127—22no—
10#131×C127—22no—
11C2×M16×C127—22no—
12C2×M16×C127C2211yescharacteristic
13C2×M16×C127C2211yescharacteristic
14C2×M16×C127C2211yescharacteristic
15C2×M16×C127C2211yescharacteristic
16#117×C127C2211yescharacteristic
17C2×C42×C127C2211yescharacteristic
18#108×C127—22no—
19C4⋊C8×C127—22no—
20#104×C127—22no—
21#104×C127C412yescomplemented
22#104×C127C412yescomplemented
23#41×C127—21no—
24#41×C127—21no—
25#41×C127C2×C412yes—
26#41×C127D412yes—
27C2×Q8×C127Q811yescharacteristic
28C2×D4×C127—21no—
29C2×D4×C127Q811yescharacteristic
30C22×C4×C127—21no—
31C22×C4×C127—21no—
32C22×C4×C127C2311yescharacteristic
33M16×C127—24no—
34M16×C127—21no—
35M16×C127—21no—
36M16×C127—21no—
37M16×C127—21no—
38M16×C127—21no—
39M16×C127—21no—
40M16×C127C2×C412yes—
41M16×C127D412yes—
42C2×C8×C127—24no—
43C2×C8×C127—21no—
44C2×C8×C127—21no—
45C2×C8×C127—21no—
46C2×C8×C127D412yes—
47C4⋊C4×C127—21no—
48C22⋊C4×C127—21no—
49C42×C127—21no—
50C42×C127—21no—
51C42×C127C2×C411yescharacteristic
52C42×C127C2×C411yescharacteristic
53C23×C127—21no—
54C23×C127#4111yescharacteristic
55Q8×C127—21no—
56Q8×C127C4⋊C412yes—
57D4×C127—22no—
58D4×C127—22no—
59D4×C127—21no—
60D4×C127C4⋊C412yes—
61C2×C4×C127—21no—
62C2×C4×C127—21no—
63C2×C4×C127—22no—
64C2×C4×C127—22no—
65C2×C4×C127—21no—
66C2×C4×C127—42no—
67C2×C4×C127—41no—
68C2×C4×C127C22×C411yescharacteristic
69C2×C4×C127C2×D411yescharacteristic
70C2×C4×C127C2×D411yescharacteristic
71C2×C4×C127C2×D411yescharacteristic
72C2×C4×C127C2×Q811yescharacteristic
73C2×C4×C127#4111yescharacteristic
74C8×C127—22no—
75C8×C127—22no—
76C8×C127—22no—
77C8×C127—41no—
78C22×C127—22no—
79C22×C127—41no—
80C22×C127—81no—
81C22×C127C4×D411yescharacteristic
82C22×C127C22⋊Q811yescharacteristic
83C22×C127#12311yescharacteristic
84C4×C127—22no—
85C4×C127—22no—
86C4×C127—41no—
87C4×C127—81no—
88C4×C127C2×C4⋊C411yescharacteristic
89C4×C127C4×D411yescharacteristic
90C4×C127#12011yescharacteristic
91C4×C127C22⋊Q811yescharacteristic
92C2×C127—21no—
93C2×C127—21no—
94C2×C127—21no—
95C2×C127—42no—
96C2×C127#38511yescharacteristic
97#1861C12711yesmaximal, characteristic, direct product factor, Sylow
98C127#186111yescharacteristic, direct product factor, Sylow
99#568C2×C12711yescharacteristic
100#430C2×C12711yescharacteristic, complemented
101#423C2×C12711yescharacteristic, complemented
102#421C2×C12711yescharacteristic
103C2×#104C2×C12711yescharacteristic
104#344C2×C12711yescharacteristic, complemented
105#339C2×C12711yescharacteristic, complemented
106C2×#41C22×C12711yescharacteristic
107#131—22no—
108#131—22no—
109C2×M16—22no—
110C2×M16C22×C12711yescharacteristic
111C2×M16C22×C12711yescharacteristic
112C2×M16C22×C12711yescharacteristic
113C2×M16C22×C12711yescharacteristic
114#117C22×C12711yescharacteristic
115C2×C42C22×C12711yescharacteristic
116#108—22no—
117C4⋊C8—22no—
118#104—22no—
119#104C4×C12712yescomplemented
120#104C4×C12712yescomplemented
121#41—21no—
122#41—21no—
123#41C2×C4×C12712yes—
124#41D4×C12712yes—
125C2×Q8Q8×C12711yescharacteristic
126C2×D4—21no—
127C2×D4Q8×C12711yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4C23×C12711yescharacteristic
131M16—24no—
132M16—21no—
133M16—21no—
134M16—21no—
135M16—21no—
136M16—21no—
137M16—21no—
138M16C2×C4×C12712yes—
139M16D4×C12712yes—
140C2×C8—24no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8D4×C12712yes—
145C4⋊C4—21no—
146C22⋊C4—21no—
147C42—21no—
148C42—21no—
149C42C2×C4×C12711yescharacteristic
150C42C2×C4×C12711yescharacteristic
151C23—21no—
152C23#41×C12711yescharacteristic
153Q8—21no—
154Q8C4⋊C4×C12712yes—
155D4—22no—
156D4—22no—
157D4—21no—
158D4C4⋊C4×C12712yes—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4C22×C4×C12711yescharacteristic
167C2×C4C2×D4×C12711yescharacteristic
168C2×C4C2×D4×C12711yescharacteristic
169C2×C4C2×D4×C12711yescharacteristic
170C2×C4C2×Q8×C12711yescharacteristic
171C2×C4#41×C12711yescharacteristic
172C8—22no—
173C8—22no—
174C8—22no—
175C8—41no—
176C22—22no—
177C22—41no—
178C22—81no—
179C22C4×D4×C12711yescharacteristic
180C22C22⋊Q8×C12711yescharacteristic
181C22#123×C12711yescharacteristic
182C4—22no—
183C4—22no—
184C4—41no—
185C4—81no—
186C4C2×C4⋊C4×C12711yescharacteristic
187C4C4×D4×C12711yescharacteristic
188C4#120×C12711yescharacteristic
189C4C22⋊Q8×C12711yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—42no—
194C2#385×C12711yescharacteristic
subgroupG/H
centerC4×C127#120
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
socleC2×C127#385
prime radicalC2×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #430×C127C2semidirect
3. #423×C127C2semidirect
6. #344×C127C2semidirect
7. #339×C127C2semidirect
21. #104×C127C4semidirect
22. #104×C127C4semidirect
97. #1861C127direct (N × H)
98. C127#1861direct (N × H)
100. #430C2×C127semidirect
101. #423C2×C127semidirect
104. #344C2×C127semidirect
105. #339C2×C127semidirect
119. #104C4×C127semidirect
120. #104C4×C127semidirect

Maximal subgroups

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

subgroupindex
#568×C1272
#430×C1272
#423×C1272
#421×C1272
C2×#104×C1272
#344×C1272
#339×C1272
#1861127