Finite Group Databasebeta

← C127×#13200 #44576873

Subgroups — C127×#13200 #44576873

Order 32512.

438 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2929C211yesmaximal, characteristic
2C127×#2153C211yesmaximal, characteristic, complemented
3C127×#2117C212yesmaximal, complemented
4C127×#2112C212yesmaximal, complemented
5C127×#2110C211yesmaximal, characteristic, complemented
6C2×#131×C127C2211yescharacteristic
7C23×C8×C127C2211yescharacteristic
8#525×C127C411yescharacteristic
9C2×M32×C127C2212yes—
10C2×M32×C127C2212yes—
11#435×C127—22no—
12C8×D4×C127—22no—
13#424×C127C411yescharacteristic
14#408×C127C411yescharacteristic
15#407×C127C411yescharacteristic
16#405×C127C2211yescharacteristic
17#364×C127—22no—
18#350×C127—24no—
19C22⋊C16×C127—24no—
20#347×C127—22no—
21C2×#41×C127C2×C411yescharacteristic
22C23×C4×C127C2×C411yescharacteristic
23#131×C127—22no—
24#131×C127—22no—
25C2×M16×C127—21no—
26C2×M16×C127C2×C411yescharacteristic
27C2×M16×C127C2×C411yescharacteristic
28C22×C8×C127—22no—
29C22×C8×C127—21no—
30C22×C8×C127—21no—
31C22×C8×C127—21no—
32C22×C8×C127—22no—
33C22×C8×C127C2×C411yescharacteristic
34C22×C8×C127C2311yescharacteristic
35#123×C127—21no—
36C22⋊Q8×C127—21no—
37#121×C127—21no—
38#120×C127—21no—
39C4×D4×C127—22no—
40#117×C127C2×C411yescharacteristic
41M32×C127—22no—
42M32×C127—22no—
43M32×C127—22no—
44M32×C127—22no—
45C2×C16×C127—22no—
46C2×C16×C127D414yescomplemented
47C4⋊C8×C127—22no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50#97×C127D412yes—
51C4×C8×C127D412yes—
52C24×C127M1611yescharacteristic
53#41×C127—22no—
54#41×C127—22no—
55C2×Q8×C127M1611yescharacteristic
56C2×D4×C127—22no—
57C2×D4×C127—21no—
58C2×D4×C127M1611yescharacteristic
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—22no—
62C22×C4×C127—21no—
63C22×C4×C127—22no—
64C22×C4×C127M1611yescharacteristic
65C22×C4×C127C22×C411yescharacteristic
66M16×C127—22no—
67M16×C127—22no—
68M16×C127—42no—
69C2×C8×C127—21no—
70C2×C8×C127—21no—
71C2×C8×C127—22no—
72C2×C8×C127—42no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—41no—
77C2×C8×C127C22⋊C412yes—
78C2×C8×C127C2×D411yescharacteristic
79C2×C8×C127C2×D412yes—
80C2×C8×C127C2×D411yescharacteristic
81C2×C8×C127#4112yes—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—21no—
84C22⋊C4×C127—22no—
85C22⋊C4×C127—22no—
86C22⋊C4×C127—21no—
87C42×C127C22⋊C412yes—
88C16×C127—24no—
89C16×C127—42no—
90C23×C127—21no—
91C23×C127—22no—
92C23×C127—21no—
93C23×C127—42no—
94C23×C127C2×M1611yescharacteristic
95Q8×C127—22no—
96D4×C127—22no—
97D4×C127—44no—
98D4×C127—42no—
99C2×C4×C127—22no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—22no—
103C2×C4×C127—41no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—41no—
107C2×C4×C127—42no—
108C2×C4×C127C2×C22⋊C411yescharacteristic
109C2×C4×C127C4×D412yes—
110C2×C4×C127C2×M1611yescharacteristic
111C2×C4×C127#13112yes—
112C8×C127—22no—
113C8×C127—41no—
114C8×C127—41no—
115C8×C127#12112yes—
116C8×C127#12411yescharacteristic
117C8×C127#12711yescharacteristic
118C22×C127—22no—
119C22×C127—24no—
120C22×C127—41no—
121C22×C127—41no—
122C22×C127—42no—
123C22×C127—42no—
124C22×C127—41no—
125C22×C127—41no—
126C22×C127#40711yescharacteristic
127C22×C127#43512yes—
128C4×C127—42no—
129C4×C127—41no—
130C4×C127—41no—
131C4×C127#39011yescharacteristic
132C4×C127#40811yescharacteristic
133C4×C127#43512yes—
134#13200C12711yesmaximal, characteristic, direct product factor, Sylow
135C2×C127—21no—
136C2×C127—22no—
137C2×C127—42no—
138C2×C127—81no—
139C2×C127#195511yescharacteristic
140#2929C2×C12711yescharacteristic
141#2153C2×C12711yescharacteristic, complemented
142#2117C2×C12712yescomplemented
143#2112C2×C12712yescomplemented
144#2110C2×C12711yescharacteristic, complemented
145C127#1320011yescharacteristic, direct product factor, Sylow
146C2×#131C22×C12711yescharacteristic
147C23×C8C22×C12711yescharacteristic
148#525C4×C12711yescharacteristic
149C2×M32C22×C12712yes—
150C2×M32C22×C12712yes—
151#435—22no—
152C8×D4—22no—
153#424C4×C12711yescharacteristic
154#408C4×C12711yescharacteristic
155#407C4×C12711yescharacteristic
156#405C22×C12711yescharacteristic
157#364—22no—
158#350—24no—
159C22⋊C16—24no—
160#347—22no—
161C2×#41C2×C4×C12711yescharacteristic
162C23×C4C2×C4×C12711yescharacteristic
163#131—22no—
164#131—22no—
165C2×M16—21no—
166C2×M16C2×C4×C12711yescharacteristic
167C2×M16C2×C4×C12711yescharacteristic
168C22×C8—22no—
169C22×C8—21no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—22no—
173C22×C8C2×C4×C12711yescharacteristic
174C22×C8C23×C12711yescharacteristic
175#123—21no—
176C22⋊Q8—21no—
177#121—21no—
178#120—21no—
179C4×D4—22no—
180#117C2×C4×C12711yescharacteristic
181M32—22no—
182M32—22no—
183M32—22no—
184M32—22no—
185C2×C16—22no—
186C2×C16D4×C12714yescomplemented
187C4⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190#97D4×C12712yes—
191C4×C8D4×C12712yes—
192C24M16×C12711yescharacteristic
193#41—22no—
194#41—22no—
195C2×Q8M16×C12711yescharacteristic
196C2×D4—22no—
197C2×D4—21no—
198C2×D4M16×C12711yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4M16×C12711yescharacteristic
205C22×C4C22×C4×C12711yescharacteristic
206M16—22no—
207M16—22no—
208M16—42no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—22no—
212C2×C8—42no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C22⋊C4×C12712yes—
218C2×C8C2×D4×C12711yescharacteristic
219C2×C8C2×D4×C12712yes—
220C2×C8C2×D4×C12711yescharacteristic
221C2×C8#41×C12712yes—
222C4⋊C4—22no—
223C4⋊C4—21no—
224C22⋊C4—22no—
225C22⋊C4—22no—
226C22⋊C4—21no—
227C42C22⋊C4×C12712yes—
228C16—24no—
229C16—42no—
230C23—21no—
231C23—22no—
232C23—21no—
233C23—42no—
234C23C2×M16×C12711yescharacteristic
235Q8—22no—
236D4—22no—
237D4—44no—
238D4—42no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4C2×C22⋊C4×C12711yescharacteristic
249C2×C4C4×D4×C12712yes—
250C2×C4C2×M16×C12711yescharacteristic
251C2×C4#131×C12712yes—
252C8—22no—
253C8—41no—
254C8—41no—
255C8#121×C12712yes—
256C8#124×C12711yescharacteristic
257C8#127×C12711yescharacteristic
258C22—22no—
259C22—24no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—42no—
264C22—41no—
265C22—41no—
266C22#407×C12711yescharacteristic
267C22#435×C12712yes—
268C4—42no—
269C4—41no—
270C4—41no—
271C4#390×C12711yescharacteristic
272C4#408×C12711yescharacteristic
273C4#435×C12712yes—
274C2—21no—
275C2—22no—
276C2—42no—
277C2—81no—
278C2C127×#195511yescharacteristic
subgroupG/H
centerC8×C127#127
commutatorC22×C4C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC2×C127#1955
prime radical#525×C127C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C127 ◁ C22×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2153C2semidirect
3. C127×#2117C2semidirect
4. C127×#2112C2semidirect
5. C127×#2110C2semidirect
46. C2×C16×C127D4semidirect
134. #13200C127direct (N × H)
141. #2153C2×C127semidirect
142. #2117C2×C127semidirect
143. #2112C2×C127semidirect
144. #2110C2×C127semidirect
145. C127#13200direct (N × H)
186. C2×C16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29292
C127×#21532
C127×#21172
C127×#21122
C127×#21102
#13200127