Finite Group Databasebeta

← C127×#8392 #44572065

Subgroups — C127×#8392 #44572065

Order 32512.

706 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C127C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic
3C127×#1548C212yesmaximal
4C127×#1487C212yesmaximal
5C127×#1461C211yesmaximal, characteristic
6#557×C127—24no—
7#557×C127—24no—
8C2×C4⋊Q8×C127C412yes—
9C2×C4⋊Q8×C127C2211yescharacteristic
10C2×#125×C127—22no—
11C2×#125×C127—21no—
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#333×C127—24no—
21Q8⋊C8×C127—24no—
22#324×C127—22no—
23C22×Q8×C127C2×C412yes—
24C22×Q8×C127C2×C411yescharacteristic
25C22×Q8×C127D411yescharacteristic
26C2×M16×C127—22no—
27C4⋊Q8×C127—24no—
28C4⋊Q8×C127—24no—
29C4⋊Q8×C127—22no—
30C4⋊Q8×C127D414yes—
31#125×C127—216no—
32#125×C127—28no—
33C4×Q8×C127—28no—
34C4×Q8×C127—24no—
35C4×Q8×C127—24no—
36C4×Q8×C127—22no—
37C4×Q8×C127—22no—
38C4×Q8×C127—22no—
39C4×Q8×C127D414yes—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127—21no—
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—21no—
60C2×Q8×C127—22no—
61C2×Q8×C127—22no—
62C2×Q8×C127—22no—
63C2×Q8×C127—42no—
64C2×Q8×C127—44no—
65C2×Q8×C127C22⋊C412yes—
66C2×Q8×C127C22⋊C414yes—
67C2×Q8×C127SD1612yes—
68C2×Q8×C127Q1612yes—
69C22×C4×C127—21no—
70C22×C4×C127—22no—
71C22×C4×C127—21no—
72C22×C4×C127C22⋊C412yes—
73C22×C4×C127C22⋊C412yes—
74C22×C4×C127C22×C411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77M16×C127—42no—
78M16×C127—42no—
79C2×C8×C127—42no—
80C2×C8×C127—42no—
81C4⋊C4×C127—28no—
82C4⋊C4×C127—28no—
83C4⋊C4×C127—28no—
84C4⋊C4×C127—21no—
85C4⋊C4×C127—24no—
86C4⋊C4×C127—24no—
87C4⋊C4×C127—24no—
88C4⋊C4×C127—24no—
89C4⋊C4×C127—22no—
90C4⋊C4×C127C22⋊C412yes—
91C42×C127—28no—
92C42×C127—22no—
93C42×C127—22no—
94C42×C127—24no—
95C42×C127C2×D412yes—
96C42×C127C2×D412yes—
97C23×C127C2×C22⋊C411yescharacteristic
98Q8×C127—24no—
99Q8×C127—24no—
100Q8×C127—24no—
101Q8×C127—44no—
102Q8×C127—42no—
103Q8×C127—44no—
104C2×C4×C127—22no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—22no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—24no—
111C2×C4×C127—41no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127—44no—
115C2×C4×C127—42no—
116C2×C4×C127#10314yes—
117C2×C4×C127C2×C22⋊C411yescharacteristic
118C2×C4×C127C2×C22⋊C411yescharacteristic
119C2×C4×C127#12012yes—
120C2×C4×C127#12012yes—
121C2×C4×C127C2×SD1611yescharacteristic
122C2×C4×C127C2×Q1611yescharacteristic
123C2×C4×C127#13712yes—
124C8×C127—82no—
125C8×C127—82no—
126C22×C127—21no—
127C22×C127—21no—
128C22×C127#37911yescharacteristic
129C22×C127C2×#10311yescharacteristic
130C22×C127#41911yescharacteristic
131C4×C127—22no—
132C4×C127—21no—
133C4×C127—24no—
134C4×C127—42no—
135C4×C127—42no—
136C4×C127—42no—
137C4×C127—44no—
138C4×C127#41312yes—
139C4×C127#44812yes—
140C4×C127#45112yes—
141#8392C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127—21no—
143C2×C127—21no—
144C2×C127#178511yescharacteristic
145C2×C127#178711yescharacteristic
146C2×C127#179611yescharacteristic
147C2×#557C2×C12711yescharacteristic
148#1801C2×C12711yescharacteristic
149#1548C2×C12712yes—
150#1487C2×C12712yes—
151#1461C2×C12711yescharacteristic
152C127#839211yescharacteristic, direct product factor, Sylow
153#557—24no—
154#557—24no—
155C2×C4⋊Q8C4×C12712yes—
156C2×C4⋊Q8C22×C12711yescharacteristic
157C2×#125—22no—
158C2×#125—21no—
159C2×C4×Q8—21no—
160C2×C4×Q8C4×C12712yes—
161C2×C4×Q8C22×C12711yescharacteristic
162C2×C4×Q8C22×C12711yescharacteristic
163#431C22×C12712yes—
164#423C22×C12712yes—
165C2×#101—21no—
166#343—21no—
167#333—24no—
168Q8⋊C8—24no—
169#324—22no—
170C22×Q8C2×C4×C12712yes—
171C22×Q8C2×C4×C12711yescharacteristic
172C22×Q8D4×C12711yescharacteristic
173C2×M16—22no—
174C4⋊Q8—24no—
175C4⋊Q8—24no—
176C4⋊Q8—22no—
177C4⋊Q8D4×C12714yes—
178#125—216no—
179#125—28no—
180C4×Q8—28no—
181C4×Q8—24no—
182C4×Q8—24no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—22no—
186C4×Q8D4×C12714yes—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×C4×C12711yescharacteristic
194C2×C4⋊C4D4×C12712yes—
195C2×C4⋊C4D4×C12711yescharacteristic
196C2×C42—22no—
197C2×C42—21no—
198C2×C42C2×C4×C12712yes—
199C2×C42C23×C12711yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203#101—42no—
204C22⋊C8—22no—
205C4×C8—22no—
206C2×Q8—21no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—42no—
211C2×Q8—44no—
212C2×Q8C22⋊C4×C12712yes—
213C2×Q8C22⋊C4×C12714yes—
214C2×Q8SD16×C12712yes—
215C2×Q8Q16×C12712yes—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4C22⋊C4×C12712yes—
220C22×C4C22⋊C4×C12712yes—
221C22×C4C22×C4×C12711yescharacteristic
222C22×C4C2×D4×C12711yescharacteristic
223C22×C4C2×D4×C12711yescharacteristic
224M16—42no—
225M16—42no—
226C2×C8—42no—
227C2×C8—42no—
228C4⋊C4—28no—
229C4⋊C4—28no—
230C4⋊C4—28no—
231C4⋊C4—21no—
232C4⋊C4—24no—
233C4⋊C4—24no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—22no—
237C4⋊C4C22⋊C4×C12712yes—
238C42—28no—
239C42—22no—
240C42—22no—
241C42—24no—
242C42C2×D4×C12712yes—
243C42C2×D4×C12712yes—
244C23C2×C22⋊C4×C12711yescharacteristic
245Q8—24no—
246Q8—24no—
247Q8—24no—
248Q8—44no—
249Q8—42no—
250Q8—44no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—24no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4#103×C12714yes—
264C2×C4C2×C22⋊C4×C12711yescharacteristic
265C2×C4C2×C22⋊C4×C12711yescharacteristic
266C2×C4#120×C12712yes—
267C2×C4#120×C12712yes—
268C2×C4C2×SD16×C12711yescharacteristic
269C2×C4C2×Q16×C12711yescharacteristic
270C2×C4#137×C12712yes—
271C8—82no—
272C8—82no—
273C22—21no—
274C22—21no—
275C22#379×C12711yescharacteristic
276C22C2×#103×C12711yescharacteristic
277C22#419×C12711yescharacteristic
278C4—21no—
279C4—24no—
280C4—22no—
281C4—42no—
282C4—44no—
283C4—42no—
284C4—42no—
285C4#413×C12712yes—
286C4#448×C12712yes—
287C4#451×C12712yes—
288C2—21no—
289C2—21no—
290C2C127×#178511yescharacteristic
291C2C127×#178711yescharacteristic
292C2C127×#179611yescharacteristic
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
141. #8392C127direct (N × H)
152. C127#8392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#557×C1272
C127×#18012
C127×#15482
C127×#14872
C127×#14612
#8392127