Finite Group Databasebeta

← C127×#12290 #44575963

Subgroups — C127×#12290 #44575963

Order 32512.

316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3250C211yesmaximal, characteristic
2C127×#2235C211yesmaximal, characteristic, complemented
3C127×#2232C211yesmaximal, characteristic
4C127×#2086C211yesmaximal, characteristic, complemented
5C127×#1348C211yesmaximal, characteristic, complemented
6C127×#1347C211yesmaximal, characteristic
7C127×#1322C211yesmaximal, characteristic, complemented
8#529×C127—21no—
9#479×C127—21no—
10#478×C127—21no—
11#467×C127C2211yescharacteristic
12#466×C127C2211yescharacteristic
13#465×C127—21no—
14#464×C127—21no—
15#463×C127—21no—
16C2×#107×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18#389×C127—21no—
19#367×C127—21no—
20#366×C127—21no—
21#358×C127—21no—
22#357×C127—21no—
23C22⋊C16×C127C2211yescharacteristic
24C22⋊C16×C127C2211yescharacteristic
25#340×C127—21no—
26#340×C127C2211yescharacteristic
27C2×Q16×C127D411yescharacteristic
28C2×SD16×C127—21no—
29C2×D8×C127D411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C22×C8×C127C2311yescharacteristic
32#126×C127—41no—
33#125×C127—21no—
34#124×C127—21no—
35#123×C127—41no—
36C22⋊Q8×C127—21no—
37#121×C127—21no—
38C4×Q8×C127—21no—
39C4×D4×C127—21no—
40C4×D4×C127—41no—
41#117×C127—41no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—41no—
45C2×C42×C127D411yescharacteristic
46C2×C16×C127—21no—
47C2×C16×C127—21no—
48#107×C127—21no—
49#107×C127—21no—
50#107×C127D411yescharacteristic
51#107×C127D411yescharacteristic
52#106×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55#103×C127—21no—
56#103×C127—21no—
57#102×C127—21no—
58#102×C127—21no—
59#95×C127—41no—
60C2×Q8×C127—21no—
61C2×D4×C127—21no—
62C2×D4×C127—41no—
63C22×C4×C127—41no—
64C22×C4×C127—41no—
65C22×C4×C127—41no—
66C22×C4×C127D811yescharacteristic
67C22×C4×C127D811yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69Q16×C127—41no—
70SD16×C127—81no—
71D8×C127—41no—
72C2×C8×C127—21no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127C2×D411yescharacteristic
76C2×C8×C127C2×D411yescharacteristic
77C4⋊C4×C127—22no—
78C4⋊C4×C127—21no—
79C4⋊C4×C127—21no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—82no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C42×C127—21no—
94C42×C127—21no—
95C42×C127—41no—
96C16×C127—41no—
97C16×C127—41no—
98C23×C127—41no—
99C23×C127C2×D811yescharacteristic
100Q8×C127—41no—
101Q8×C127—41no—
102D4×C127—41no—
103D4×C127—41no—
104D4×C127—81no—
105D4×C127—81no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—41no—
113C2×C4×C127—42no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—82no—
118C2×C4×C127—81no—
119C2×C4×C127—81no—
120C2×C4×C127—81no—
121C2×C4×C127—81no—
122C2×C4×C127—81no—
123C2×C4×C127#12011yescharacteristic
124C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
125C8×C127—21no—
126C8×C127—21no—
127C8×C127—41no—
128C22×C127—21no—
129C22×C127—21no—
130C22×C127—81no—
131C22×C127—81no—
132C22×C127—81no—
133C22×C127#44711yescharacteristic
134C22×C127#50811yescharacteristic
135C22×C127#50911yescharacteristic
136C4×C127—21no—
137C4×C127—41no—
138C4×C127—41no—
139C4×C127—82no—
140C4×C127—81no—
141C4×C127—81no—
142C4×C127—81no—
143C4×C127—161no—
144C4×C127#45611yescharacteristic
145C4×C127#45811yescharacteristic
146#12290C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—21no—
148C2×C127—21no—
149C2×C127—161no—
150C2×C127#161011yescharacteristic
151C2×C127#218611yescharacteristic
152C2×C127#219111yescharacteristic
153#3250C2×C12711yescharacteristic
154#2235C2×C12711yescharacteristic, complemented
155#2232C2×C12711yescharacteristic
156#2086C2×C12711yescharacteristic, complemented
157#1348C2×C12711yescharacteristic, complemented
158#1347C2×C12711yescharacteristic
159#1322C2×C12711yescharacteristic, complemented
160C127#1229011yescharacteristic, direct product factor, Sylow
161#529—21no—
162#479—21no—
163#478—21no—
164#467C22×C12711yescharacteristic
165#466C22×C12711yescharacteristic
166#465—21no—
167#464—21no—
168#463—21no—
169C2×#107C22×C12711yescharacteristic
170C2×C4⋊C8C22×C12711yescharacteristic
171#389—21no—
172#367—21no—
173#366—21no—
174#358—21no—
175#357—21no—
176C22⋊C16C22×C12711yescharacteristic
177C22⋊C16C22×C12711yescharacteristic
178#340—21no—
179#340C22×C12711yescharacteristic
180C2×Q16D4×C12711yescharacteristic
181C2×SD16—21no—
182C2×D8D4×C12711yescharacteristic
183C22×C8D4×C12711yescharacteristic
184C22×C8C23×C12711yescharacteristic
185#126—41no—
186#125—21no—
187#124—21no—
188#123—41no—
189C22⋊Q8—21no—
190#121—21no—
191C4×Q8—21no—
192C4×D4—21no—
193C4×D4—41no—
194#117—41no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C42D4×C12711yescharacteristic
199C2×C16—21no—
200C2×C16—21no—
201#107—21no—
202#107—21no—
203#107D4×C12711yescharacteristic
204#107D4×C12711yescharacteristic
205#106—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208#103—21no—
209#103—21no—
210#102—21no—
211#102—21no—
212#95—41no—
213C2×Q8—21no—
214C2×D4—21no—
215C2×D4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4D8×C12711yescharacteristic
220C22×C4D8×C12711yescharacteristic
221C22×C4C2×D4×C12711yescharacteristic
222Q16—41no—
223SD16—81no—
224D8—41no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8C2×D4×C12711yescharacteristic
229C2×C8C2×D4×C12711yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—82no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C42—21no—
247C42—21no—
248C42—41no—
249C16—41no—
250C16—41no—
251C23—41no—
252C23C2×D8×C12711yescharacteristic
253Q8—41no—
254Q8—41no—
255D4—41no—
256D4—41no—
257D4—81no—
258D4—81no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4#120×C12711yescharacteristic
277C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
278C8—21no—
279C8—21no—
280C8—41no—
281C22—21no—
282C22—21no—
283C22—81no—
284C22—81no—
285C22—81no—
286C22#447×C12711yescharacteristic
287C22#508×C12711yescharacteristic
288C22#509×C12711yescharacteristic
289C4—21no—
290C4—41no—
291C4—41no—
292C4—82no—
293C4—81no—
294C4—81no—
295C4—81no—
296C4—161no—
297C4#456×C12711yescharacteristic
298C4#458×C12711yescharacteristic
299C2—21no—
300C2—21no—
301C2—161no—
302C2C127×#161011yescharacteristic
303C2C127×#218611yescharacteristic
304C2C127×#219111yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radical#466×C127C22
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4⋊C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2235C2semidirect
4. C127×#2086C2semidirect
5. C127×#1348C2semidirect
7. C127×#1322C2semidirect
146. #12290C127direct (N × H)
154. #2235C2×C127semidirect
156. #2086C2×C127semidirect
157. #1348C2×C127semidirect
159. #1322C2×C127semidirect
160. C127#12290direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32502
C127×#22352
C127×#22322
C127×#20862
C127×#13482
C127×#13472
C127×#13222
#12290127