Finite Group Databasebeta

← C127×#1905 #30634857

Subgroups — C127×#1905 #30634857

Order 16256.

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

normal subgroups only

This group has 310 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
1C2×#137×C127C211yesmaximal, characteristic
2#519×C127C211yesmaximal, characteristic, complemented
3#421×C127C211yesmaximal, characteristic
4#419×C127C211yesmaximal, characteristic, complemented
5#410×C127C211yesmaximal, characteristic
6#344×C127C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C127C211yesmaximal, characteristic, complemented
8C2×#41×C127C2211yescharacteristic
9C22×Q8×C127C2211yescharacteristic
10#137×C127—22no—
11#137×C127—22no—
12C2×Q16×C127C412yescomplemented
13C2×SD16×C127C412yescomplemented
14C2×M16×C127C2211yescharacteristic
15C2×M16×C127C2211yescharacteristic
16C4×Q8×C127—22no—
17C4×Q8×C127—22no—
18#117×C127—22no—
19#117×C127C2211yescharacteristic
20#117×C127C2211yescharacteristic
21#117×C127C2211yescharacteristic
22#104×C127—22no—
23#103×C127—22no—
24#99×C127—22no—
25#41×C127—21no—
26#41×C127—21no—
27#41×C127—21no—
28#41×C127—21no—
29C2×Q8×C127—21no—
30C2×Q8×C127—21no—
31C2×Q8×C127—21no—
32C2×Q8×C127C2×C411yescharacteristic
33C2×Q8×C127C2×C412yes—
34C2×Q8×C127D412yes—
35C2×Q8×C127D412yes—
36C2×D4×C127—21no—
37C2×D4×C127C2×C411yescharacteristic
38C22×C4×C127—21no—
39C22×C4×C127—21no—
40C22×C4×C127C2311yescharacteristic
41Q16×C127—24no—
42SD16×C127—24no—
43M16×C127—21no—
44M16×C127—21no—
45M16×C127—21no—
46M16×C127—21no—
47C2×C8×C127—21no—
48C2×C8×C127C2×C412yes—
49C4⋊C4×C127—24no—
50C4⋊C4×C127—21no—
51C4⋊C4×C127—21no—
52C4⋊C4×C127—21no—
53C22⋊C4×C127—21no—
54C22⋊C4×C127—21no—
55C22⋊C4×C127D412yes—
56C42×C127—24no—
57C42×C127—21no—
58C42×C127—21no—
59C42×C127D412yes—
60C23×C127—21no—
61C23×C127C2×D411yescharacteristic
62Q8×C127—22no—
63Q8×C127—22no—
64Q8×C127—22no—
65Q8×C127—21no—
66Q8×C127—21no—
67Q8×C127C22⋊C414yes—
68D4×C127—21no—
69D4×C127—21no—
70D4×C127—41no—
71D4×C127—41no—
72C2×C4×C127—22no—
73C2×C4×C127—22no—
74C2×C4×C127—22no—
75C2×C4×C127—21no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—41no—
79C2×C4×C127—41no—
80C2×C4×C127—41no—
81C2×C4×C127C22×C411yescharacteristic
82C2×C4×C127C2×D411yescharacteristic
83C2×C4×C127C2×D411yescharacteristic
84C2×C4×C127C2×D411yescharacteristic
85C2×C4×C127#4111yescharacteristic
86C2×C4×C127#4111yescharacteristic
87C8×C127—22no—
88C8×C127—41no—
89C22×C127—41no—
90C22×C127—41no—
91C22×C127—81no—
92C22×C127C4×D411yescharacteristic
93C22×C127#12011yescharacteristic
94C22×C127#12111yescharacteristic
95C4×C127—24no—
96C4×C127—42no—
97C4×C127—42no—
98C4×C127—41no—
99C4×C127—81no—
100C4×C127C2×C22⋊C411yescharacteristic
101C4×C127C4×D411yescharacteristic
102C4×C127#12111yescharacteristic
103C4×C127#12311yescharacteristic
104C2×C127—21no—
105C2×C127—21no—
106C2×C127—21no—
107C2×C127—81no—
108C2×C127#38611yescharacteristic
109#1905C12711yesmaximal, characteristic, direct product factor, Sylow
110C127#190511yescharacteristic, direct product factor, Sylow
111C2×#137C2×C12711yescharacteristic
112#519C2×C12711yescharacteristic, complemented
113#421C2×C12711yescharacteristic
114#419C2×C12711yescharacteristic, complemented
115#410C2×C12711yescharacteristic
116#344C2×C12711yescharacteristic, complemented
117H(3,ℤ/4)C2×C12711yescharacteristic, complemented
118C2×#41C22×C12711yescharacteristic
119C22×Q8C22×C12711yescharacteristic
120#137—22no—
121#137—22no—
122C2×Q16C4×C12712yescomplemented
123C2×SD16C4×C12712yescomplemented
124C2×M16C22×C12711yescharacteristic
125C2×M16C22×C12711yescharacteristic
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129#117C22×C12711yescharacteristic
130#117C22×C12711yescharacteristic
131#117C22×C12711yescharacteristic
132#104—22no—
133#103—22no—
134#99—22no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C2×C4×C12711yescharacteristic
143C2×Q8C2×C4×C12712yes—
144C2×Q8D4×C12712yes—
145C2×Q8D4×C12712yes—
146C2×D4—21no—
147C2×D4C2×C4×C12711yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4C23×C12711yescharacteristic
151Q16—24no—
152SD16—24no—
153M16—21no—
154M16—21no—
155M16—21no—
156M16—21no—
157C2×C8—21no—
158C2×C8C2×C4×C12712yes—
159C4⋊C4—24no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4D4×C12712yes—
166C42—24no—
167C42—21no—
168C42—21no—
169C42D4×C12712yes—
170C23—21no—
171C23C2×D4×C12711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—21no—
176Q8—21no—
177Q8C22⋊C4×C12714yes—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4C22×C4×C12711yescharacteristic
192C2×C4C2×D4×C12711yescharacteristic
193C2×C4C2×D4×C12711yescharacteristic
194C2×C4C2×D4×C12711yescharacteristic
195C2×C4#41×C12711yescharacteristic
196C2×C4#41×C12711yescharacteristic
197C8—22no—
198C8—41no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22C4×D4×C12711yescharacteristic
203C22#120×C12711yescharacteristic
204C22#121×C12711yescharacteristic
205C4—24no—
206C4—42no—
207C4—42no—
208C4—41no—
209C4—81no—
210C4C2×C22⋊C4×C12711yescharacteristic
211C4C4×D4×C12711yescharacteristic
212C4#121×C12711yescharacteristic
213C4#123×C12711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#386×C12711yescharacteristic
subgroupG/H
center, socleC2×C127#386
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC2×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #519×C127C2semidirect
4. #419×C127C2semidirect
6. #344×C127C2semidirect
7. H(3,ℤ/4)×C127C2semidirect
12. C2×Q16×C127C4semidirect
13. C2×SD16×C127C4semidirect
109. #1905C127direct (N × H)
110. C127#1905direct (N × H)
112. #519C2×C127semidirect
114. #419C2×C127semidirect
116. #344C2×C127semidirect
117. H(3,ℤ/4)C2×C127semidirect
122. C2×Q16C4×C127semidirect
123. C2×SD16C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#137×C1272
#519×C1272
#421×C1272
#419×C1272
#410×C1272
#344×C1272
H(3,ℤ/4)×C1272
#1905127