Finite Group Databasebeta

← C127×#9710 #44573383

Subgroups — C127×#9710 #44573383

Order 32512.

590 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2858C211yesmaximal, characteristic
2C127×#1831C211yesmaximal, characteristic, complemented
3C127×#1767C211yesmaximal, characteristic, complemented
4C2×#332×C127C212yesmaximal, complemented
5C2×#331×C127C212yesmaximal
6C2×C4⋊Q8×C127C2211yescharacteristic
7C2×#127×C127C2211yescharacteristic
8C2×#124×C127—22no—
9C2×C4⋊C8×C127C2212yes—
10C2×C4⋊C8×C127C2212yes—
11C2×#97×C127—21no—
12#390×C127—21no—
13#390×C127—21no—
14#390×C127C414yes—
15C43×C127C2211yescharacteristic
16#336×C127—22no—
17#336×C127—21no—
18#332×C127—24no—
19#331×C127—24no—
20C22×Q8×C127—21no—
21C22×D4×C127—21no—
22C22×D4×C127—21no—
23C22×D4×C127C2×C412yes—
24C22×C8×C127—22no—
25C22×C8×C127—22no—
26C4⋊Q8×C127—22no—
27C4⋊Q8×C127—22no—
28#127×C127—22no—
29#127×C127—22no—
30#124×C127—48no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127C2×C412yes—
33C2×C22⋊C4×C127—24no—
34C2×C22⋊C4×C127—24no—
35C2×C42×C127C2×C412yes—
36C2×C42×C127D412yes—
37C2×C42×C127D411yescharacteristic
38C2×C42×C127D411yescharacteristic
39C2×C42×C127C2311yescharacteristic
40C4⋊C8×C127—22no—
41C4⋊C8×C127—22no—
42C4⋊C8×C127—22no—
43C4⋊C8×C127D414yes—
44#97×C127—42no—
45C24×C127—22no—
46C2×Q8×C127—41no—
47C2×Q8×C127—41no—
48C2×Q8×C127—44no—
49C2×D4×C127—24no—
50C2×D4×C127—44no—
51C2×D4×C127—42no—
52C2×D4×C127—41no—
53C2×D4×C127—41no—
54C2×D4×C127—42no—
55C2×D4×C127—44no—
56C2×D4×C127—41no—
57C2×D4×C127—41no—
58C22×C4×C127—22no—
59C22×C4×C127C22⋊C412yes—
60C22×C4×C127C22⋊C412yes—
61C22×C4×C127C22×C411yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63C22×C4×C127C2×D411yescharacteristic
64C2×C8×C127—24no—
65C2×C8×C127—42no—
66C2×C8×C127—42no—
67C2×C8×C127—42no—
68C2×C8×C127—44no—
69C4⋊C4×C127—24no—
70C4⋊C4×C127—42no—
71C22⋊C4×C127—48no—
72C22⋊C4×C127—48no—
73C42×C127—22no—
74C42×C127—21no—
75C42×C127—24no—
76C42×C127—21no—
77C42×C127—42no—
78C42×C127C2×D412yes—
79C42×C127#4112yes—
80C23×C127—42no—
81C23×C127—44no—
82C23×C127—42no—
83C23×C127—42no—
84C23×C127—44no—
85C23×C127C2×C22⋊C411yescharacteristic
86Q8×C127—82no—
87Q8×C127—82no—
88D4×C127—84no—
89D4×C127—82no—
90D4×C127—82no—
91D4×C127—82no—
92D4×C127—82no—
93C2×C4×C127—22no—
94C2×C4×C127—22no—
95C2×C4×C127—22no—
96C2×C4×C127—22no—
97C2×C4×C127—22no—
98C2×C4×C127—22no—
99C2×C4×C127—22no—
100C2×C4×C127—42no—
101C2×C4×C127—44no—
102C2×C4×C127C4×D412yes—
103C2×C4×C127#12112yes—
104C2×C4×C127#12411yescharacteristic
105C2×C4×C127#12711yescharacteristic
106C2×C4×C127#13512yes—
107C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C127AGL(1,ℤ/8)14yes—
109C2×C4×C127#13711yescharacteristic
110C8×C127—44no—
111C8×C127—82no—
112C22×C127—84no—
113C22×C127—84no—
114C22×C127—82no—
115C22×C127—82no—
116C22×C127—82no—
117C22×C127#39011yescharacteristic
118C22×C127#41312yes—
119C22×C127#41611yescharacteristic
120C22×C127#41711yescharacteristic
121C22×C127#41812yes—
122C4×C127—22no—
123C4×C127—42no—
124C4×C127—42no—
125C4×C127—82no—
126C4×C127#46312yes—
127C4×C127#46412yes—
128C4×C127#49012yes—
129C4×C127#49612yes—
130#9710C12711yesmaximal, characteristic, direct product factor, Sylow
131C2×C127—162no—
132C2×C127#155312yes—
133C2×C127#155712yes—
134C2×C127#196111yescharacteristic
135C2×C127#196711yescharacteristic
136C2×C127#198311yescharacteristic
137#2858C2×C12711yescharacteristic
138#1831C2×C12711yescharacteristic, complemented
139#1767C2×C12711yescharacteristic, complemented
140C2×#332C2×C12712yescomplemented
141C2×#331C2×C12712yes—
142C127#971011yescharacteristic, direct product factor, Sylow
143C2×C4⋊Q8C22×C12711yescharacteristic
144C2×#127C22×C12711yescharacteristic
145C2×#124—22no—
146C2×C4⋊C8C22×C12712yes—
147C2×C4⋊C8C22×C12712yes—
148C2×#97—21no—
149#390—21no—
150#390—21no—
151#390C4×C12714yes—
152C43C22×C12711yescharacteristic
153#336—22no—
154#336—21no—
155#332—24no—
156#331—24no—
157C22×Q8—21no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4C2×C4×C12712yes—
161C22×C8—22no—
162C22×C8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165#127—22no—
166#127—22no—
167#124—48no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C2×C4×C12712yes—
170C2×C22⋊C4—24no—
171C2×C22⋊C4—24no—
172C2×C42C2×C4×C12712yes—
173C2×C42D4×C12712yes—
174C2×C42D4×C12711yescharacteristic
175C2×C42D4×C12711yescharacteristic
176C2×C42C23×C12711yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8D4×C12714yes—
181#97—42no—
182C24—22no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—44no—
186C2×D4—24no—
187C2×D4—44no—
188C2×D4—42no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—42no—
192C2×D4—44no—
193C2×D4—41no—
194C2×D4—41no—
195C22×C4—22no—
196C22×C4C22⋊C4×C12712yes—
197C22×C4C22⋊C4×C12712yes—
198C22×C4C22×C4×C12711yescharacteristic
199C22×C4C2×D4×C12711yescharacteristic
200C22×C4C2×D4×C12711yescharacteristic
201C2×C8—24no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—44no—
206C4⋊C4—24no—
207C4⋊C4—42no—
208C22⋊C4—48no—
209C22⋊C4—48no—
210C42—22no—
211C42—21no—
212C42—24no—
213C42—21no—
214C42—42no—
215C42C2×D4×C12712yes—
216C42#41×C12712yes—
217C23—42no—
218C23—44no—
219C23—42no—
220C23—42no—
221C23—44no—
222C23C2×C22⋊C4×C12711yescharacteristic
223Q8—82no—
224Q8—82no—
225D4—84no—
226D4—82no—
227D4—82no—
228D4—82no—
229D4—82no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4C4×D4×C12712yes—
240C2×C4#121×C12712yes—
241C2×C4#124×C12711yescharacteristic
242C2×C4#127×C12711yescharacteristic
243C2×C4#135×C12712yes—
244C2×C4AGL(1,ℤ/8)×C12714yes—
245C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
246C2×C4#137×C12711yescharacteristic
247C8—44no—
248C8—82no—
249C22—84no—
250C22—84no—
251C22—82no—
252C22—82no—
253C22—82no—
254C22#390×C12711yescharacteristic
255C22#413×C12712yes—
256C22#416×C12711yescharacteristic
257C22#417×C12711yescharacteristic
258C22#418×C12712yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—82no—
263C4#463×C12712yes—
264C4#464×C12712yes—
265C4#490×C12712yes—
266C4#496×C12712yes—
267C2—162no—
268C2C127×#155312yes—
269C2C127×#155712yes—
270C2C127×#196111yescharacteristic
271C2C127×#196711yescharacteristic
272C2C127×#198311yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1831C2semidirect
3. C127×#1767C2semidirect
4. C2×#332×C127C2semidirect
130. #9710C127direct (N × H)
138. #1831C2×C127semidirect
139. #1767C2×C127semidirect
140. C2×#332C2×C127semidirect
142. C127#9710direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28582
C127×#18312
C127×#17672
C2×#332×C1272
C2×#331×C1272
#9710127