Finite Group Databasebeta

← C127×#8396 #44572069

Subgroups — C127×#8396 #44572069

Order 32512.

738 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C127C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic
3C127×#1549C212yesmaximal
4C127×#1487C212yesmaximal
5C127×#1461C211yesmaximal, characteristic
6Q82×C127—24no—
7Q82×C127—24no—
8C2×C4⋊Q8×C127—22no—
9C2×C4⋊Q8×C127—21no—
10C2×C4⋊Q8×C127C412yes—
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×C4×Q8×C127—21no—
13C2×C4×Q8×C127C412yes—
14C2×C4×Q8×C127C2211yescharacteristic
15C2×C4×Q8×C127C2211yescharacteristic
16#431×C127C2212yes—
17#423×C127C2212yes—
18C2×#101×C127—21no—
19#343×C127—21no—
20#332×C127—24no—
21Q8⋊C8×C127—24no—
22#324×C127—22no—
23C22×Q8×C127—22no—
24C22×Q8×C127—21no—
25C22×Q8×C127C2×C411yescharacteristic
26C22×Q8×C127D411yescharacteristic
27C2×M16×C127—22no—
28C4⋊Q8×C127—216no—
29C4⋊Q8×C127—28no—
30C4⋊Q8×C127—24no—
31C4⋊Q8×C127—24no—
32C4⋊Q8×C127—22no—
33C4⋊Q8×C127D414yes—
34C4×Q8×C127—28no—
35C4×Q8×C127—24no—
36C4×Q8×C127—24no—
37C4×Q8×C127—22no—
38C4×Q8×C127—22no—
39C4×Q8×C127—22no—
40C4×Q8×C127D414yes—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127C2×C412yes—
46C2×C4⋊C4×C127C2×C411yescharacteristic
47C2×C4⋊C4×C127D412yes—
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C42×C127—22no—
50C2×C42×C127—21no—
51C2×C42×C127C2×C412yes—
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127—22no—
54C4⋊C8×C127—22no—
55C4⋊C8×C127—22no—
56#101×C127—42no—
57C22⋊C8×C127—22no—
58C4×C8×C127—22no—
59C2×Q8×C127—24no—
60C2×Q8×C127—28no—
61C2×Q8×C127—21no—
62C2×Q8×C127—22no—
63C2×Q8×C127—24no—
64C2×Q8×C127—22no—
65C2×Q8×C127—82no—
66C2×Q8×C127—84no—
67C2×Q8×C127C22⋊C412yes—
68C2×Q8×C127SD1612yes—
69C2×Q8×C127Q1612yes—
70C22×C4×C127—21no—
71C22×C4×C127—22no—
72C22×C4×C127—21no—
73C22×C4×C127C22⋊C412yes—
74C22×C4×C127C22⋊C412yes—
75C22×C4×C127C22×C411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78M16×C127—42no—
79M16×C127—42no—
80C2×C8×C127—42no—
81C2×C8×C127—42no—
82C4⋊C4×C127—28no—
83C4⋊C4×C127—28no—
84C4⋊C4×C127—21no—
85C4⋊C4×C127—22no—
86C4⋊C4×C127—24no—
87C4⋊C4×C127—24no—
88C4⋊C4×C127—24no—
89C4⋊C4×C127—22no—
90C4⋊C4×C127C22⋊C414yes—
91C4⋊C4×C127C22⋊C412yes—
92C42×C127—28no—
93C42×C127—22no—
94C42×C127—22no—
95C42×C127—24no—
96C42×C127C2×D412yes—
97C42×C127C2×D412yes—
98C23×C127C2×C22⋊C411yescharacteristic
99Q8×C127—24no—
100Q8×C127—22no—
101Q8×C127—24no—
102Q8×C127—24no—
103Q8×C127—84no—
104Q8×C127—88no—
105Q8×C127#10114yescomplemented
106C2×C4×C127—24no—
107C2×C4×C127—22no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—24no—
113C2×C4×C127—22no—
114C2×C4×C127—41no—
115C2×C4×C127—44no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127#10314yes—
119C2×C4×C127C2×C22⋊C411yescharacteristic
120C2×C4×C127C2×C22⋊C411yescharacteristic
121C2×C4×C127#12012yes—
122C2×C4×C127#12012yes—
123C2×C4×C127C2×SD1611yescharacteristic
124C2×C4×C127C2×Q1611yescharacteristic
125C2×C4×C127#13712yes—
126C8×C127—82no—
127C8×C127—82no—
128C22×C127—21no—
129C22×C127—21no—
130C22×C127#37911yescharacteristic
131C22×C127C2×#10311yescharacteristic
132C22×C127#41911yescharacteristic
133C4×C127—22no—
134C4×C127—24no—
135C4×C127—21no—
136C4×C127—24no—
137C4×C127—44no—
138C4×C127—42no—
139C4×C127—42no—
140C4×C127C2×#10112yes—
141C4×C127#44812yes—
142C4×C127#45112yes—
143#8396C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127—21no—
145C2×C127—21no—
146C2×C127#178411yescharacteristic
147C2×C127#178711yescharacteristic
148C2×C127#179511yescharacteristic
149C2×Q82C2×C12711yescharacteristic
150#1801C2×C12711yescharacteristic
151#1549C2×C12712yes—
152#1487C2×C12712yes—
153#1461C2×C12711yescharacteristic
154C127#839611yescharacteristic, direct product factor, Sylow
155Q82—24no—
156Q82—24no—
157C2×C4⋊Q8—22no—
158C2×C4⋊Q8—21no—
159C2×C4⋊Q8C4×C12712yes—
160C2×C4⋊Q8C22×C12711yescharacteristic
161C2×C4×Q8—21no—
162C2×C4×Q8C4×C12712yes—
163C2×C4×Q8C22×C12711yescharacteristic
164C2×C4×Q8C22×C12711yescharacteristic
165#431C22×C12712yes—
166#423C22×C12712yes—
167C2×#101—21no—
168#343—21no—
169#332—24no—
170Q8⋊C8—24no—
171#324—22no—
172C22×Q8—22no—
173C22×Q8—21no—
174C22×Q8C2×C4×C12711yescharacteristic
175C22×Q8D4×C12711yescharacteristic
176C2×M16—22no—
177C4⋊Q8—216no—
178C4⋊Q8—28no—
179C4⋊Q8—24no—
180C4⋊Q8—24no—
181C4⋊Q8—22no—
182C4⋊Q8D4×C12714yes—
183C4×Q8—28no—
184C4×Q8—24no—
185C4×Q8—24no—
186C4×Q8—22no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8D4×C12714yes—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×C4×C12712yes—
195C2×C4⋊C4C2×C4×C12711yescharacteristic
196C2×C4⋊C4D4×C12712yes—
197C2×C4⋊C4D4×C12711yescharacteristic
198C2×C42—22no—
199C2×C42—21no—
200C2×C42C2×C4×C12712yes—
201C2×C42C23×C12711yescharacteristic
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205#101—42no—
206C22⋊C8—22no—
207C4×C8—22no—
208C2×Q8—24no—
209C2×Q8—28no—
210C2×Q8—21no—
211C2×Q8—22no—
212C2×Q8—24no—
213C2×Q8—22no—
214C2×Q8—82no—
215C2×Q8—84no—
216C2×Q8C22⋊C4×C12712yes—
217C2×Q8SD16×C12712yes—
218C2×Q8Q16×C12712yes—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4C22⋊C4×C12712yes—
223C22×C4C22⋊C4×C12712yes—
224C22×C4C22×C4×C12711yescharacteristic
225C22×C4C2×D4×C12711yescharacteristic
226C22×C4C2×D4×C12711yescharacteristic
227M16—42no—
228M16—42no—
229C2×C8—42no—
230C2×C8—42no—
231C4⋊C4—28no—
232C4⋊C4—28no—
233C4⋊C4—21no—
234C4⋊C4—22no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4C22⋊C4×C12714yes—
240C4⋊C4C22⋊C4×C12712yes—
241C42—28no—
242C42—22no—
243C42—22no—
244C42—24no—
245C42C2×D4×C12712yes—
246C42C2×D4×C12712yes—
247C23C2×C22⋊C4×C12711yescharacteristic
248Q8—24no—
249Q8—22no—
250Q8—24no—
251Q8—24no—
252Q8—84no—
253Q8—88no—
254Q8#101×C12714yescomplemented
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4#103×C12714yes—
268C2×C4C2×C22⋊C4×C12711yescharacteristic
269C2×C4C2×C22⋊C4×C12711yescharacteristic
270C2×C4#120×C12712yes—
271C2×C4#120×C12712yes—
272C2×C4C2×SD16×C12711yescharacteristic
273C2×C4C2×Q16×C12711yescharacteristic
274C2×C4#137×C12712yes—
275C8—82no—
276C8—82no—
277C22—21no—
278C22—21no—
279C22#379×C12711yescharacteristic
280C22C2×#103×C12711yescharacteristic
281C22#419×C12711yescharacteristic
282C4—24no—
283C4—21no—
284C4—24no—
285C4—22no—
286C4—44no—
287C4—42no—
288C4—42no—
289C4C2×#101×C12712yes—
290C4#448×C12712yes—
291C4#451×C12712yes—
292C2—21no—
293C2—21no—
294C2C127×#178411yescharacteristic
295C2C127×#178711yescharacteristic
296C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
105. Q8×C127#101semidirect
143. #8396C127direct (N × H)
154. C127#8396direct (N × H)
254. Q8#101×C127semidirect

Maximal subgroups

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

subgroupindex
C2×Q82×C1272
C127×#18012
C127×#15492
C127×#14872
C127×#14612
#8396127