Finite Group Databasebeta

← C127×#10615 #44574288

Subgroups — C127×#10615 #44574288

Order 32512.

418 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1954C211yesmaximal, characteristic
2C127×#1845C211yesmaximal, characteristic, complemented
3C127×#1802C212yesmaximal
4C127×#1296C212yesmaximal, complemented
5C127×#1277C211yesmaximal, characteristic, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C2×#107×C127—21no—
8C2×#107×C127—21no—
9C2×C4⋊C8×C127C2212yes—
10C2×C4⋊C8×C127C2211yescharacteristic
11C2×#102×C127—22no—
12C2×C22⋊C8×C127—21no—
13C2×C22⋊C8×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15#384×C127C2212yes—
16#340×C127—22no—
17C22×D4×C127D411yescharacteristic
18C23×C4×C127—21no—
19C22×C8×C127—22no—
20C22×C8×C127—21no—
21C22×C8×C127D411yescharacteristic
22C22×C8×C127D411yescharacteristic
23C4×D4×C127—22no—
24C4×D4×C127—22no—
25C2×C4⋊C4×C127—22no—
26C2×C4⋊C4×C127—22no—
27C2×C4⋊C4×C127—22no—
28C2×C4⋊C4×C127D411yescharacteristic
29C2×C22⋊C4×C127—21no—
30C2×C42×C127C2311yescharacteristic
31#107×C127—42no—
32#107×C127—42no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35C4⋊C8×C127—22no—
36#102×C127—44no—
37C22⋊C8×C127—42no—
38C22⋊C8×C127—42no—
39C4×C8×C127—22no—
40C24×C127—21no—
41C2×D4×C127—22no—
42C2×D4×C127—21no—
43C2×D4×C127—22no—
44C2×D4×C127D812yes—
45C22×C4×C127—21no—
46C22×C4×C127—41no—
47C22×C4×C127—41no—
48C22×C4×C127—41no—
49C22×C4×C127—41no—
50C22×C4×C127—41no—
51C22×C4×C127—41no—
52C22×C4×C127—42no—
53C22×C4×C127C2×D411yescharacteristic
54C22×C4×C127C2×D411yescharacteristic
55C22×C4×C127#4111yescharacteristic
56C2×C8×C127—21no—
57C2×C8×C127—21no—
58C2×C8×C127—21no—
59C2×C8×C127—21no—
60C2×C8×C127—42no—
61C2×C8×C127—41no—
62C2×C8×C127—41no—
63C2×C8×C127—42no—
64C2×C8×C127—41no—
65C2×C8×C127—42no—
66C2×C8×C127D812yes—
67C2×C8×C127SD1612yes—
68C4⋊C4×C127—22no—
69C4⋊C4×C127—42no—
70C4⋊C4×C127—42no—
71C4⋊C4×C127—42no—
72C4⋊C4×C127—42no—
73C4⋊C4×C127—82no—
74C22⋊C4×C127—42no—
75C42×C127#4112yes—
76C42×C127#4112yes—
77C23×C127—22no—
78C23×C127—41no—
79C23×C127—41no—
80C23×C127—41no—
81C23×C127—41no—
82C23×C127—41no—
83C23×C127—41no—
84C23×C127#12111yescharacteristic
85D4×C127—24no—
86D4×C127—42no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—81no—
93C2×C4×C127—81no—
94C2×C4×C127—81no—
95C2×C4×C127—81no—
96C2×C4×C127—82no—
97C2×C4×C127—82no—
98C2×C4×C127—82no—
99C2×C4×C127#12311yescharacteristic
100C2×C4×C127#12312yes—
101C2×C4×C127#12411yescharacteristic
102C2×C4×C127#12612yes—
103C2×C4×C127C2×D811yescharacteristic
104C2×C4×C127C2×D811yescharacteristic
105C2×C4×C127C2×SD1611yescharacteristic
106C2×C4×C127#13511yescharacteristic
107C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C127#13712yes—
109C2×C4×C127#13711yescharacteristic
110C8×C127—22no—
111C8×C127—22no—
112C8×C127—82no—
113C8×C127—81no—
114C22×C127—42no—
115C22×C127—42no—
116C22×C127—42no—
117C22×C127—81no—
118C22×C127—81no—
119C22×C127—81no—
120C22×C127—81no—
121C22×C127#39711yescharacteristic
122C22×C127#45911yescharacteristic
123C22×C127#46111yescharacteristic
124C22×C127#46611yescharacteristic
125C22×C127#47011yescharacteristic
126C22×C127#47211yescharacteristic
127C22×C127#47311yescharacteristic
128C4×C127—22no—
129C4×C127—81no—
130C4×C127—162no—
131C4×C127#48011yescharacteristic
132C4×C127#48012yes—
133C4×C127#48111yescharacteristic
134C4×C127#48512yes—
135C4×C127#48611yescharacteristic
136C4×C127#48911yescharacteristic
137#10615C12711yesmaximal, characteristic, direct product factor, Sylow
138C2×C127—82no—
139C2×C127#166711yescharacteristic
140C2×C127#167311yescharacteristic
141C2×C127#168911yescharacteristic
142C2×C127#169511yescharacteristic
143C2×C127#207111yescharacteristic
144C2×C127#207511yescharacteristic
145C2×C127#207811yescharacteristic
146#1954C2×C12711yescharacteristic
147#1845C2×C12711yescharacteristic, complemented
148#1802C2×C12712yes—
149#1296C2×C12712yescomplemented
150#1277C2×C12711yescharacteristic, complemented
151C127#1061511yescharacteristic, direct product factor, Sylow
152C2×C4×D4C22×C12711yescharacteristic
153C2×#107—21no—
154C2×#107—21no—
155C2×C4⋊C8C22×C12712yes—
156C2×C4⋊C8C22×C12711yescharacteristic
157C2×#102—22no—
158C2×C22⋊C8—21no—
159C2×C22⋊C8—21no—
160C2×C4×C8C22×C12711yescharacteristic
161#384C22×C12712yes—
162#340—22no—
163C22×D4D4×C12711yescharacteristic
164C23×C4—21no—
165C22×C8—22no—
166C22×C8—21no—
167C22×C8D4×C12711yescharacteristic
168C22×C8D4×C12711yescharacteristic
169C4×D4—22no—
170C4×D4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4D4×C12711yescharacteristic
175C2×C22⋊C4—21no—
176C2×C42C23×C12711yescharacteristic
177#107—42no—
178#107—42no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182#102—44no—
183C22⋊C8—42no—
184C22⋊C8—42no—
185C4×C8—22no—
186C24—21no—
187C2×D4—22no—
188C2×D4—21no—
189C2×D4—22no—
190C2×D4D8×C12712yes—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—42no—
199C22×C4C2×D4×C12711yescharacteristic
200C22×C4C2×D4×C12711yescharacteristic
201C22×C4#41×C12711yescharacteristic
202C2×C8—21no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8D8×C12712yes—
213C2×C8SD16×C12712yes—
214C4⋊C4—22no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—82no—
220C22⋊C4—42no—
221C42#41×C12712yes—
222C42#41×C12712yes—
223C23—22no—
224C23—41no—
225C23—41no—
226C23—41no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23#121×C12711yescharacteristic
231D4—24no—
232D4—42no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4#123×C12711yescharacteristic
246C2×C4#123×C12712yes—
247C2×C4#124×C12711yescharacteristic
248C2×C4#126×C12712yes—
249C2×C4C2×D8×C12711yescharacteristic
250C2×C4C2×D8×C12711yescharacteristic
251C2×C4C2×SD16×C12711yescharacteristic
252C2×C4#135×C12711yescharacteristic
253C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
254C2×C4#137×C12712yes—
255C2×C4#137×C12711yescharacteristic
256C8—22no—
257C8—22no—
258C8—82no—
259C8—81no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—81no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22#397×C12711yescharacteristic
268C22#459×C12711yescharacteristic
269C22#461×C12711yescharacteristic
270C22#466×C12711yescharacteristic
271C22#470×C12711yescharacteristic
272C22#472×C12711yescharacteristic
273C22#473×C12711yescharacteristic
274C4—22no—
275C4—81no—
276C4—162no—
277C4#480×C12711yescharacteristic
278C4#480×C12712yes—
279C4#481×C12711yescharacteristic
280C4#485×C12712yes—
281C4#486×C12711yescharacteristic
282C4#489×C12711yescharacteristic
283C2—82no—
284C2C127×#166711yescharacteristic
285C2C127×#167311yescharacteristic
286C2C127×#168911yescharacteristic
287C2C127×#169511yescharacteristic
288C2C127×#207111yescharacteristic
289C2C127×#207511yescharacteristic
290C2C127×#207811yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1845C2semidirect
4. C127×#1296C2semidirect
5. C127×#1277C2semidirect
137. #10615C127direct (N × H)
147. #1845C2×C127semidirect
149. #1296C2×C127semidirect
150. #1277C2×C127semidirect
151. C127#10615direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19542
C127×#18452
C127×#18022
C127×#12962
C127×#12772
#10615127