Finite Group Databasebeta

← C127×#8395 #44572068

Subgroups — C127×#8395 #44572068

Order 32512.

782 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C127C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic
3C127×#1549C212yesmaximal, complemented
4C127×#1487C212yesmaximal, complemented
5C127×#1460C211yesmaximal, characteristic
6#554×C127—24no—
7#554×C127—24no—
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×#125×C127—21no—
10C2×C22⋊Q8×C127—22no—
11C2×C22⋊Q8×C127C412yes—
12C2×C4×Q8×C127C2211yescharacteristic
13C2×C4×D4×C127—21no—
14C2×C4×D4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C412yes—
16#431×C127C2212yes—
17#423×C127C2212yes—
18C2×#100×C127—21no—
19#343×C127—21no—
20#332×C127—24no—
21Q8⋊C8×C127—24no—
22#323×C127—22no—
23C22×Q8×C127—21no—
24C22×Q8×C127C2×C411yescharacteristic
25C22×D4×C127D411yescharacteristic
26C23×C4×C127—22no—
27C23×C4×C127C2×C412yes—
28C2×M16×C127—22no—
29C4⋊Q8×C127—22no—
30C4⋊Q8×C127D414yes—
31#125×C127—28no—
32C22⋊Q8×C127—216no—
33C22⋊Q8×C127—24no—
34C22⋊Q8×C127—24no—
35C4×Q8×C127—22no—
36C4×Q8×C127D414yes—
37C4×D4×C127—28no—
38C4×D4×C127—22no—
39C4×D4×C127—22no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127C2×C411yescharacteristic
47C2×C4⋊C4×C127C2×C412yes—
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127—22no—
50C2×C22⋊C4×C127D412yes—
51C2×C42×C127—21no—
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127—22no—
54C4⋊C8×C127—22no—
55C4⋊C8×C127—22no—
56#100×C127—42no—
57C22⋊C8×C127—22no—
58C4×C8×C127—22no—
59C24×C127C22⋊C412yes—
60C2×Q8×C127—21no—
61C2×Q8×C127—24no—
62C2×Q8×C127—42no—
63C2×Q8×C127—82no—
64C2×Q8×C127C22⋊C412yes—
65C2×D4×C127—22no—
66C2×D4×C127—22no—
67C2×D4×C127SD1612yes—
68C2×D4×C127Q1612yes—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—22no—
72C22×C4×C127—28no—
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—44no—
76C22×C4×C127—84no—
77C22×C4×C127C22⋊C412yes—
78C22×C4×C127C22×C411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81M16×C127—42no—
82M16×C127—42no—
83C2×C8×C127—42no—
84C2×C8×C127—42no—
85C4⋊C4×C127—28no—
86C4⋊C4×C127—28no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—24no—
90C4⋊C4×C127—24no—
91C4⋊C4×C127—22no—
92C4⋊C4×C127C22⋊C412yes—
93C4⋊C4×C127C22⋊C414yes—
94C22⋊C4×C127—28no—
95C22⋊C4×C127—24no—
96C42×C127—24no—
97C42×C127C2×D412yes—
98C42×C127C2×D412yes—
99C23×C127—22no—
100C23×C127—22no—
101C23×C127—42no—
102C23×C127—42no—
103C23×C127#10314yes—
104C23×C127C2×C22⋊C411yescharacteristic
105Q8×C127—24no—
106Q8×C127—42no—
107Q8×C127—84no—
108D4×C127—24no—
109D4×C127—24no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—22no—
114C2×C4×C127—24no—
115C2×C4×C127—41no—
116C2×C4×C127—44no—
117C2×C4×C127—42no—
118C2×C4×C127—44no—
119C2×C4×C127—42no—
120C2×C4×C127—44no—
121C2×C4×C127—42no—
122C2×C4×C127—88no—
123C2×C4×C127C2×C22⋊C411yescharacteristic
124C2×C4×C127C2×C22⋊C411yescharacteristic
125C2×C4×C127#12012yes—
126C2×C4×C127#12012yes—
127C2×C4×C127C2×SD1611yescharacteristic
128C2×C4×C127C2×Q1611yescharacteristic
129C2×C4×C127#13712yes—
130C8×C127—82no—
131C8×C127—82no—
132C22×C127—21no—
133C22×C127—21no—
134C22×C127—24no—
135C22×C127—44no—
136C22×C127—44no—
137C22×C127—42no—
138C22×C127—42no—
139C22×C127#37911yescharacteristic
140C22×C127C2×#10311yescharacteristic
141C22×C127#41911yescharacteristic
142C4×C127—22no—
143C4×C127—21no—
144C4×C127—42no—
145C4×C127—44no—
146C4×C127—42no—
147C4×C127—42no—
148C4×C127#41312yes—
149C4×C127#44812yes—
150C4×C127#45112yes—
151#8395C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—21no—
153C2×C127—21no—
154C2×C127—44no—
155C2×C127#178511yescharacteristic
156C2×C127#178711yescharacteristic
157C2×C127#179511yescharacteristic
158C2×#554C2×C12711yescharacteristic
159#1800C2×C12711yescharacteristic
160#1549C2×C12712yescomplemented
161#1487C2×C12712yescomplemented
162#1460C2×C12711yescharacteristic
163C127#839511yescharacteristic, direct product factor, Sylow
164#554—24no—
165#554—24no—
166C2×C4⋊Q8C22×C12711yescharacteristic
167C2×#125—21no—
168C2×C22⋊Q8—22no—
169C2×C22⋊Q8C4×C12712yes—
170C2×C4×Q8C22×C12711yescharacteristic
171C2×C4×D4—21no—
172C2×C4×D4C22×C12711yescharacteristic
173C22×C4⋊C4C4×C12712yes—
174#431C22×C12712yes—
175#423C22×C12712yes—
176C2×#100—21no—
177#343—21no—
178#332—24no—
179Q8⋊C8—24no—
180#323—22no—
181C22×Q8—21no—
182C22×Q8C2×C4×C12711yescharacteristic
183C22×D4D4×C12711yescharacteristic
184C23×C4—22no—
185C23×C4C2×C4×C12712yes—
186C2×M16—22no—
187C4⋊Q8—22no—
188C4⋊Q8D4×C12714yes—
189#125—28no—
190C22⋊Q8—216no—
191C22⋊Q8—24no—
192C22⋊Q8—24no—
193C4×Q8—22no—
194C4×Q8D4×C12714yes—
195C4×D4—28no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4C2×C4×C12711yescharacteristic
205C2×C4⋊C4C2×C4×C12712yes—
206C2×C4⋊C4D4×C12711yescharacteristic
207C2×C22⋊C4—22no—
208C2×C22⋊C4D4×C12712yes—
209C2×C42—21no—
210C2×C42C23×C12711yescharacteristic
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—22no—
214#100—42no—
215C22⋊C8—22no—
216C4×C8—22no—
217C24C22⋊C4×C12712yes—
218C2×Q8—21no—
219C2×Q8—24no—
220C2×Q8—42no—
221C2×Q8—82no—
222C2×Q8C22⋊C4×C12712yes—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4SD16×C12712yes—
226C2×D4Q16×C12712yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—28no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—44no—
234C22×C4—84no—
235C22×C4C22⋊C4×C12712yes—
236C22×C4C22×C4×C12711yescharacteristic
237C22×C4C2×D4×C12711yescharacteristic
238C22×C4C2×D4×C12711yescharacteristic
239M16—42no—
240M16—42no—
241C2×C8—42no—
242C2×C8—42no—
243C4⋊C4—28no—
244C4⋊C4—28no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—24no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4C22⋊C4×C12712yes—
251C4⋊C4C22⋊C4×C12714yes—
252C22⋊C4—28no—
253C22⋊C4—24no—
254C42—24no—
255C42C2×D4×C12712yes—
256C42C2×D4×C12712yes—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—42no—
261C23#103×C12714yes—
262C23C2×C22⋊C4×C12711yescharacteristic
263Q8—24no—
264Q8—42no—
265Q8—84no—
266D4—24no—
267D4—24no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—88no—
281C2×C4C2×C22⋊C4×C12711yescharacteristic
282C2×C4C2×C22⋊C4×C12711yescharacteristic
283C2×C4#120×C12712yes—
284C2×C4#120×C12712yes—
285C2×C4C2×SD16×C12711yescharacteristic
286C2×C4C2×Q16×C12711yescharacteristic
287C2×C4#137×C12712yes—
288C8—82no—
289C8—82no—
290C22—21no—
291C22—21no—
292C22—24no—
293C22—44no—
294C22—44no—
295C22—42no—
296C22—42no—
297C22#379×C12711yescharacteristic
298C22C2×#103×C12711yescharacteristic
299C22#419×C12711yescharacteristic
300C4—21no—
301C4—22no—
302C4—42no—
303C4—42no—
304C4—42no—
305C4—44no—
306C4#413×C12712yes—
307C4#448×C12712yes—
308C4#451×C12712yes—
309C2—21no—
310C2—21no—
311C2—44no—
312C2C127×#178511yescharacteristic
313C2C127×#178711yescharacteristic
314C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
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
3. C127×#1549C2semidirect
4. C127×#1487C2semidirect
151. #8395C127direct (N × H)
160. #1549C2×C127semidirect
161. #1487C2×C127semidirect
163. C127#8395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#554×C1272
C127×#18002
C127×#15492
C127×#14872
C127×#14602
#8395127