Finite Group Databasebeta

← C127×#12631 #44576304

Subgroups — C127×#12631 #44576304

Order 32512.

464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 162 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×#2327C211yesmaximal, characteristic
2C2×#356×C127C212yesmaximal
3C4×#101×C127C212yesmaximal
4C127×#1394C212yesmaximal
5C2×C4⋊Q8×C127C2211yescharacteristic
6C2×C4×Q8×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8C2×#101×C127C2214yes—
9C4×M16×C127—22no—
10#391×C127C411yescharacteristic
11#391×C127C2211yescharacteristic
12#387×C127—22no—
13#387×C127—22no—
14#382×C127C411yescharacteristic
15#376×C127C411yescharacteristic
16#356×C127C418yescomplemented
17#343×C127—22no—
18C22×Q8×C127C2×C411yescharacteristic
19C22×Q8×C127C2311yescharacteristic
20C2×M16×C127—24no—
21C4⋊Q8×C127—22no—
22C4⋊Q8×C127C2×C414yes—
23C4×Q8×C127—42no—
24C4×Q8×C127—42no—
25C2×C4⋊C4×C127—22no—
26C2×C4⋊C4×C127—21no—
27C2×C4⋊C4×C127C2×C411yescharacteristic
28C2×C4⋊C4×C127C2×C411yescharacteristic
29C2×C4⋊C4×C127D412yes—
30C2×C42×C127—21no—
31C2×C42×C127C2×C411yescharacteristic
32C2×C42×C127C2×C411yescharacteristic
33C2×C42×C127C2×C411yescharacteristic
34C2×C42×C127D412yes—
35#101×C127—24no—
36#101×C127C2×C418yes—
37#97×C127—42no—
38C4×C8×C127—42no—
39#95×C127—21no—
40#95×C127—22no—
41#95×C127—22no—
42#95×C127—21no—
43#95×C127—22no—
44C2×Q8×C127—21no—
45C2×Q8×C127—41no—
46C2×Q8×C127—41no—
47C2×Q8×C127—41no—
48C2×Q8×C127—41no—
49C2×Q8×C127C4212yes—
50C2×Q8×C127C22×C412yes—
51C2×Q8×C127#4112yes—
52C22×C4×C127—21no—
53C22×C4×C127—21no—
54C22×C4×C127—21no—
55C22×C4×C127—21no—
56C22×C4×C127C22⋊C412yes—
57C22×C4×C127C22⋊C411yescharacteristic
58C22×C4×C127C22⋊C411yescharacteristic
59C22×C4×C127C22×C411yescharacteristic
60C22×C4×C127C2×D412yes—
61M16×C127—28no—
62M16×C127—44no—
63C2×C8×C127—44no—
64C4⋊C4×C127—28no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—42no—
67C4⋊C4×C127—41no—
68C4⋊C4×C127—42no—
69C42×C127—22no—
70C42×C127—22no—
71C42×C127—22no—
72C42×C127—21no—
73C42×C127—41no—
74C42×C127—42no—
75C42×C127C4212yes—
76C23×C127C2×C22⋊C411yescharacteristic
77Q8×C127—42no—
78Q8×C127—42no—
79Q8×C127—42no—
80Q8×C127—42no—
81C2×C4×C127—21no—
82C2×C4×C127—22no—
83C2×C4×C127—21no—
84C2×C4×C127—22no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—21no—
88C2×C4×C127—22no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—41no—
94C2×C4×C127—42no—
95C2×C4×C127—41no—
96C2×C4×C127—41no—
97C2×C4×C127—41no—
98C2×C4×C127—42no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127#9912yes—
102C2×C4×C127C2×C4211yescharacteristic
103C2×C4×C127#11711yescharacteristic
104C2×C4×C127C4×D414yes—
105C8×C127—48no—
106C22×C127—21no—
107C22×C127—21no—
108C22×C127C4×C22⋊C411yescharacteristic
109C22×C127C2×#9911yescharacteristic
110C22×C127#41011yescharacteristic
111C4×C127—22no—
112C4×C127—24no—
113C4×C127—21no—
114C4×C127—21no—
115C4×C127—42no—
116C4×C127—41no—
117C4×C127—42no—
118C4×C127—42no—
119C4×C127—81no—
120C4×C127—81no—
121#12631C12711yesmaximal, characteristic, direct product factor, Sylow
122C2×C127—21no—
123C2×C127—21no—
124C2×C127C4×#9911yescharacteristic
125C2×C127#213311yescharacteristic
126C2×C127#213511yescharacteristic
127#2327C2×C12711yescharacteristic
128C2×#356C2×C12712yes—
129C4×#101C2×C12712yes—
130#1394C2×C12712yes—
131C127#1263111yescharacteristic, direct product factor, Sylow
132C2×C4⋊Q8C22×C12711yescharacteristic
133C2×C4×Q8C4×C12711yescharacteristic
134C2×C4×Q8C22×C12711yescharacteristic
135C2×#101C22×C12714yes—
136C4×M16—22no—
137#391C4×C12711yescharacteristic
138#391C22×C12711yescharacteristic
139#387—22no—
140#387—22no—
141#382C4×C12711yescharacteristic
142#376C4×C12711yescharacteristic
143#356C4×C12718yescomplemented
144#343—22no—
145C22×Q8C2×C4×C12711yescharacteristic
146C22×Q8C23×C12711yescharacteristic
147C2×M16—24no—
148C4⋊Q8—22no—
149C4⋊Q8C2×C4×C12714yes—
150C4×Q8—42no—
151C4×Q8—42no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4C2×C4×C12711yescharacteristic
155C2×C4⋊C4C2×C4×C12711yescharacteristic
156C2×C4⋊C4D4×C12712yes—
157C2×C42—21no—
158C2×C42C2×C4×C12711yescharacteristic
159C2×C42C2×C4×C12711yescharacteristic
160C2×C42C2×C4×C12711yescharacteristic
161C2×C42D4×C12712yes—
162#101—24no—
163#101C2×C4×C12718yes—
164#97—42no—
165C4×C8—42no—
166#95—21no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95—22no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C42×C12712yes—
177C2×Q8C22×C4×C12712yes—
178C2×Q8#41×C12712yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4C22⋊C4×C12712yes—
184C22×C4C22⋊C4×C12711yescharacteristic
185C22×C4C22⋊C4×C12711yescharacteristic
186C22×C4C22×C4×C12711yescharacteristic
187C22×C4C2×D4×C12712yes—
188M16—28no—
189M16—44no—
190C2×C8—44no—
191C4⋊C4—28no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C42—22no—
197C42—22no—
198C42—22no—
199C42—21no—
200C42—41no—
201C42—42no—
202C42C42×C12712yes—
203C23C2×C22⋊C4×C12711yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—42no—
207Q8—42no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4#99×C12712yes—
229C2×C4C2×C42×C12711yescharacteristic
230C2×C4#117×C12711yescharacteristic
231C2×C4C4×D4×C12714yes—
232C8—48no—
233C22—21no—
234C22—21no—
235C22C4×C22⋊C4×C12711yescharacteristic
236C22C2×#99×C12711yescharacteristic
237C22#410×C12711yescharacteristic
238C4—22no—
239C4—24no—
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—42no—
245C4—42no—
246C4—81no—
247C4—81no—
248C2—21no—
249C2—21no—
250C2C4×#99×C12711yescharacteristic
251C2C127×#213311yescharacteristic
252C2C127×#213511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC22×Q8C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
16. #356×C127C4semidirect
121. #12631C127direct (N × H)
131. C127#12631direct (N × H)
143. #356C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23272
C2×#356×C1272
C4×#101×C1272
C127×#13942
#12631127