Finite Group Databasebeta

← C127×#8390 #44572063

Subgroups — C127×#8390 #44572063

Order 32512.

706 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C127C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic
3C127×#1546C212yesmaximal
4C127×#1487C212yesmaximal
5C127×#1461C211yesmaximal, characteristic
6#557×C127—24no—
7#557×C127—24no—
8C2×C4⋊Q8×C127—21no—
9C2×C4⋊Q8×C127C2211yescharacteristic
10C2×#125×C127—22no—
11C2×#125×C127C412yes—
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—21no—
24C22×Q8×C127C2×C411yescharacteristic
25C22×Q8×C127D411yescharacteristic
26C2×M16×C127—22no—
27C4⋊Q8×C127—28no—
28C4⋊Q8×C127—22no—
29C4⋊Q8×C127D414yes—
30#125×C127—216no—
31#125×C127—24no—
32#125×C127—24no—
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×C127C2×C412yes—
46C2×C4⋊C4×C127C2×C411yescharacteristic
47C2×C4⋊C4×C127D411yescharacteristic
48C2×C4⋊C4×C127D412yes—
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—21no—
61C2×Q8×C127—22no—
62C2×Q8×C127—24no—
63C2×Q8×C127—22no—
64C2×Q8×C127—21no—
65C2×Q8×C127—21no—
66C2×Q8×C127—42no—
67C2×Q8×C127—41no—
68C2×Q8×C127—41no—
69C2×Q8×C127C22⋊C412yes—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—22no—
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—28no—
85C4⋊C4×C127—21no—
86C4⋊C4×C127—22no—
87C4⋊C4×C127—24no—
88C4⋊C4×C127—24no—
89C4⋊C4×C127—22no—
90C4⋊C4×C127—24no—
91C4⋊C4×C127C22⋊C414yes—
92C4⋊C4×C127C22⋊C412yes—
93C42×C127—28no—
94C42×C127—22no—
95C42×C127—22no—
96C42×C127—24no—
97C42×C127C2×D412yes—
98C42×C127C2×D412yes—
99C23×C127C2×C22⋊C411yescharacteristic
100Q8×C127—24no—
101Q8×C127—22no—
102Q8×C127—42no—
103Q8×C127—44no—
104Q8×C127—42no—
105Q8×C127—44no—
106Q8×C127#10114yescomplemented
107C2×C4×C127—24no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—24no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—41no—
117C2×C4×C127—42no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—42no—
121C2×C4×C127C2×C22⋊C411yescharacteristic
122C2×C4×C127C2×C22⋊C411yescharacteristic
123C2×C4×C127#12012yes—
124C2×C4×C127#12012yes—
125C2×C4×C127#13512yes—
126C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C127#13711yescharacteristic
128C8×C127—82no—
129C8×C127—82no—
130C22×C127—21no—
131C22×C127—21no—
132C22×C127#37911yescharacteristic
133C22×C127#41611yescharacteristic
134C22×C127#41711yescharacteristic
135C4×C127—22no—
136C4×C127—24no—
137C4×C127—21no—
138C4×C127—42no—
139C4×C127—42no—
140C4×C127—42no—
141C4×C127—44no—
142C4×C127C2×#10112yes—
143C4×C127#44912yes—
144C4×C127#45212yes—
145#8390C12711yesmaximal, characteristic, direct product factor, Sylow
146C2×C127—21no—
147C2×C127—21no—
148C2×C127#178411yescharacteristic
149C2×C127#178811yescharacteristic
150C2×C127#179611yescharacteristic
151C2×#557C2×C12711yescharacteristic
152#1801C2×C12711yescharacteristic
153#1546C2×C12712yes—
154#1487C2×C12712yes—
155#1461C2×C12711yescharacteristic
156C127#839011yescharacteristic, direct product factor, Sylow
157#557—24no—
158#557—24no—
159C2×C4⋊Q8—21no—
160C2×C4⋊Q8C22×C12711yescharacteristic
161C2×#125—22no—
162C2×#125C4×C12712yes—
163C2×C4×Q8—21no—
164C2×C4×Q8C4×C12712yes—
165C2×C4×Q8C22×C12711yescharacteristic
166C2×C4×Q8C22×C12711yescharacteristic
167#431C22×C12712yes—
168#423C22×C12712yes—
169C2×#101—21no—
170#343—21no—
171#332—24no—
172Q8⋊C8—24no—
173#324—22no—
174C22×Q8—21no—
175C22×Q8C2×C4×C12711yescharacteristic
176C22×Q8D4×C12711yescharacteristic
177C2×M16—22no—
178C4⋊Q8—28no—
179C4⋊Q8—22no—
180C4⋊Q8D4×C12714yes—
181#125—216no—
182#125—24no—
183#125—24no—
184C4×Q8—28no—
185C4×Q8—24no—
186C4×Q8—24no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8D4×C12714yes—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C2×C4×C12712yes—
197C2×C4⋊C4C2×C4×C12711yescharacteristic
198C2×C4⋊C4D4×C12711yescharacteristic
199C2×C4⋊C4D4×C12712yes—
200C2×C42—22no—
201C2×C42—21no—
202C2×C42C2×C4×C12712yes—
203C2×C42C23×C12711yescharacteristic
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—22no—
207#101—42no—
208C22⋊C8—22no—
209C4×C8—22no—
210C2×Q8—24no—
211C2×Q8—21no—
212C2×Q8—22no—
213C2×Q8—24no—
214C2×Q8—22no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—42no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8C22⋊C4×C12712yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4C22⋊C4×C12712yes—
225C22×C4C22⋊C4×C12712yes—
226C22×C4C22×C4×C12711yescharacteristic
227C22×C4C2×D4×C12711yescharacteristic
228C22×C4C2×D4×C12711yescharacteristic
229M16—42no—
230M16—42no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—28no—
234C4⋊C4—28no—
235C4⋊C4—28no—
236C4⋊C4—21no—
237C4⋊C4—22no—
238C4⋊C4—24no—
239C4⋊C4—24no—
240C4⋊C4—22no—
241C4⋊C4—24no—
242C4⋊C4C22⋊C4×C12714yes—
243C4⋊C4C22⋊C4×C12712yes—
244C42—28no—
245C42—22no—
246C42—22no—
247C42—24no—
248C42C2×D4×C12712yes—
249C42C2×D4×C12712yes—
250C23C2×C22⋊C4×C12711yescharacteristic
251Q8—24no—
252Q8—22no—
253Q8—42no—
254Q8—44no—
255Q8—42no—
256Q8—44no—
257Q8#101×C12714yescomplemented
258C2×C4—24no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4C2×C22⋊C4×C12711yescharacteristic
273C2×C4C2×C22⋊C4×C12711yescharacteristic
274C2×C4#120×C12712yes—
275C2×C4#120×C12712yes—
276C2×C4#135×C12712yes—
277C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
278C2×C4#137×C12711yescharacteristic
279C8—82no—
280C8—82no—
281C22—21no—
282C22—21no—
283C22#379×C12711yescharacteristic
284C22#416×C12711yescharacteristic
285C22#417×C12711yescharacteristic
286C4—24no—
287C4—21no—
288C4—22no—
289C4—42no—
290C4—44no—
291C4—42no—
292C4—42no—
293C4C2×#101×C12712yes—
294C4#449×C12712yes—
295C4#452×C12712yes—
296C2—21no—
297C2—21no—
298C2C127×#178411yescharacteristic
299C2C127×#178811yescharacteristic
300C2C127×#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
106. Q8×C127#101semidirect
145. #8390C127direct (N × H)
156. C127#8390direct (N × H)
257. Q8#101×C127semidirect

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×#15462
C127×#14872
C127×#14612
#8390127