Finite Group Databasebeta

← C127×#12260 #44575933

Subgroups — C127×#12260 #44575933

Order 32512.

342 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2844C211yesmaximal, characteristic
2C127×#2061C211yesmaximal, characteristic
3C127×#1605C212yesmaximal
4C127×#1354C212yesmaximal
5C127×#1324C211yesmaximal, characteristic
6#544×C127C2211yescharacteristic
7#451×C127—22no—
8#428×C127—21no—
9#400×C127—21no—
10#400×C127—22no—
11#395×C127—22no—
12#395×C127C2212yes—
13#382×C127—21no—
14#382×C127C2211yescharacteristic
15#343×C127C2211yescharacteristic
16#339×C127—21no—
17#328×C127—22no—
18#324×C127C2212yes—
19C22×Q8×C127D412yes—
20C2×Q16×C127—42no—
21C2×M16×C127—21no—
22C4⋊Q8×C127—41no—
23#125×C127—41no—
24C22⋊Q8×C127—22no—
25#117×C127—21no—
26C2×C4⋊C4×C127—21no—
27C2×C4⋊C4×C127—21no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127—22no—
30C2×C4⋊C4×C127D411yescharacteristic
31C2×C4⋊C4×C127C2311yescharacteristic
32C2×C42×C127D411yescharacteristic
33#107×C127—41no—
34#106×C127—41no—
35#103×C127—42no—
36C22⋊C8×C127—22no—
37#95×C127—22no—
38#95×C127—22no—
39#95×C127—21no—
40#95×C127—22no—
41#95×C127—22no—
42#95×C127D412yes—
43C2×Q8×C127—22no—
44C2×Q8×C127—42no—
45C2×Q8×C127—82no—
46C22×C4×C127—21no—
47C22×C4×C127—21no—
48C22×C4×C127—22no—
49C22×C4×C127—22no—
50C22×C4×C127C2×D411yescharacteristic
51C22×C4×C127C2×D412yes—
52Q16×C127—84no—
53M16×C127—22no—
54M16×C127—41no—
55C2×C8×C127—41no—
56C2×C8×C127—42no—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—21no—
59C4⋊C4×C127—21no—
60C4⋊C4×C127—41no—
61C4⋊C4×C127—41no—
62C4⋊C4×C127—42no—
63C4⋊C4×C127—81no—
64C4⋊C4×C127—81no—
65C4⋊C4×C127—82no—
66C4⋊C4×C127—81no—
67C22⋊C4×C127—41no—
68C42×C127—21no—
69C42×C127—41no—
70C42×C127Q1612yescomplemented
71C23×C127#12011yescharacteristic
72Q8×C127—44no—
73Q8×C127—82no—
74Q8×C127—82no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—22no—
78C2×C4×C127—22no—
79C2×C4×C127—41no—
80C2×C4×C127—41no—
81C2×C4×C127—42no—
82C2×C4×C127—42no—
83C2×C4×C127—42no—
84C2×C4×C127—42no—
85C2×C4×C127—42no—
86C2×C4×C127—42no—
87C2×C4×C127—42no—
88C2×C4×C127—41no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—42no—
92C2×C4×C127C2×Q1611yescharacteristic
93C2×C4×C127#13711yescharacteristic
94C8×C127—42no—
95C8×C127—82no—
96C22×C127—21no—
97C22×C127—21no—
98C22×C127#45111yescharacteristic
99C22×C127#45611yescharacteristic
100C22×C127B(4,𝔽2)11yescharacteristic
101C4×C127—21no—
102C4×C127—21no—
103C4×C127—42no—
104C4×C127—42no—
105C4×C127—82no—
106C4×C127—82no—
107C4×C127—81no—
108C4×C127—81no—
109C4×C127—81no—
110#12260C12711yesmaximal, characteristic, direct product factor, Sylow
111C2×C127—21no—
112C2×C127—21no—
113C2×C127#160511yescharacteristic
114C2×C127#219911yescharacteristic
115C2×C127#220311yescharacteristic
116#2844C2×C12711yescharacteristic
117#2061C2×C12711yescharacteristic
118#1605C2×C12712yes—
119#1354C2×C12712yes—
120#1324C2×C12711yescharacteristic
121C127#1226011yescharacteristic, direct product factor, Sylow
122#544C22×C12711yescharacteristic
123#451—22no—
124#428—21no—
125#400—21no—
126#400—22no—
127#395—22no—
128#395C22×C12712yes—
129#382—21no—
130#382C22×C12711yescharacteristic
131#343C22×C12711yescharacteristic
132#339—21no—
133#328—22no—
134#324C22×C12712yes—
135C22×Q8D4×C12712yes—
136C2×Q16—42no—
137C2×M16—21no—
138C4⋊Q8—41no—
139#125—41no—
140C22⋊Q8—22no—
141#117—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4D4×C12711yescharacteristic
147C2×C4⋊C4C23×C12711yescharacteristic
148C2×C42D4×C12711yescharacteristic
149#107—41no—
150#106—41no—
151#103—42no—
152C22⋊C8—22no—
153#95—22no—
154#95—22no—
155#95—21no—
156#95—22no—
157#95—22no—
158#95D4×C12712yes—
159C2×Q8—22no—
160C2×Q8—42no—
161C2×Q8—82no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4C2×D4×C12711yescharacteristic
167C22×C4C2×D4×C12712yes—
168Q16—84no—
169M16—22no—
170M16—41no—
171C2×C8—41no—
172C2×C8—42no—
173C4⋊C4—22no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—81no—
180C4⋊C4—81no—
181C4⋊C4—82no—
182C4⋊C4—81no—
183C22⋊C4—41no—
184C42—21no—
185C42—41no—
186C42Q16×C12712yescomplemented
187C23#120×C12711yescharacteristic
188Q8—44no—
189Q8—82no—
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4C2×Q16×C12711yescharacteristic
209C2×C4#137×C12711yescharacteristic
210C8—42no—
211C8—82no—
212C22—21no—
213C22—21no—
214C22#451×C12711yescharacteristic
215C22#456×C12711yescharacteristic
216C22B(4,𝔽2)×C12711yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—82no—
223C4—81no—
224C4—81no—
225C4—81no—
226C2—21no—
227C2—21no—
228C2C127×#160511yescharacteristic
229C2C127×#219911yescharacteristic
230C2C127×#220311yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC23×C127#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
70. C42×C127Q16semidirect
110. #12260C127direct (N × H)
121. C127#12260direct (N × H)
186. C42Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#28442
C127×#20612
C127×#16052
C127×#13542
C127×#13242
#12260127