Finite Group Databasebeta

← C127×#11870 #44575543

Subgroups — C127×#11870 #44575543

Order 32512.

392 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 110 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×#3058C211yesmaximal, characteristic
2C127×#2115C211yesmaximal, characteristic, complemented
3C127×#1813C211yesmaximal, characteristic, complemented
4C127×#1341C214yesmaximal, complemented
5C22×D8×C127C411yescharacteristic
6C2×#131×C127C2211yescharacteristic
7#535×C127—21no—
8C2×M32×C127—21no—
9#469×C127C412yes—
10#469×C127C2212yes—
11#466×C127—21no—
12#466×C127—21no—
13C2×#108×C127—21no—
14#427×C127C411yescharacteristic
15#418×C127—21no—
16#413×C127—21no—
17#349×C127—21no—
18#349×C127C2212yescomplemented
19#338×C127C2212yescomplemented
20C2×#41×C127D411yescharacteristic
21C22×D4×C127—21no—
22C2×D8×C127—21no—
23C2×D8×C127—41no—
24C2×D8×C127—41no—
25C2×D8×C127C2×C412yes—
26#131×C127—41no—
27#131×C127—41no—
28C2×M16×C127—22no—
29C2×M16×C127C2×C411yescharacteristic
30C2×M16×C127D411yescharacteristic
31C2×M16×C127C2311yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35#127×C127—41no—
36#124×C127—41no—
37#121×C127—22no—
38#121×C127—22no—
39#120×C127—41no—
40#120×C127—41no—
41#117×C127—21no—
42M32×C127—22no—
43M32×C127—41no—
44C2×C16×C127—41no—
45#108×C127—41no—
46#108×C127—41no—
47#107×C127—21no—
48#106×C127C2×C412yes—
49#102×C127—22no—
50#102×C127—22no—
51#101×C127—41no—
52#100×C127—41no—
53C24×C127—41no—
54#41×C127—41no—
55#41×C127—41no—
56C2×Q8×C127D811yescharacteristic
57C2×D4×C127—22no—
58C2×D4×C127—42no—
59C2×D4×C127—42no—
60C2×D4×C127—42no—
61C2×D4×C127—42no—
62C2×D4×C127—41no—
63C2×D4×C127D811yescharacteristic
64C2×D4×C127SD1611yescharacteristic
65C2×D4×C127SD1611yescharacteristic
66C22×C4×C127C22⋊C411yescharacteristic
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69D8×C127—42no—
70D8×C127—41no—
71D8×C127—41no—
72M16×C127—41no—
73M16×C127—41no—
74M16×C127—41no—
75M16×C127—42no—
76M16×C127—42no—
77C2×C8×C127—21no—
78C2×C8×C127—21no—
79C2×C8×C127—21no—
80C2×C8×C127—21no—
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—42no—
84C2×C8×C127C22⋊C411yescharacteristic
85C2×C8×C127C22⋊C411yescharacteristic
86C2×C8×C127C22×C411yescharacteristic
87C2×C8×C127C2×D411yescharacteristic
88C4⋊C4×C127—22no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C42×C127—41no—
93C16×C127—42no—
94C23×C127—42no—
95C23×C127—82no—
96C23×C127—162no—
97C23×C127#10211yescharacteristic
98C23×C127#10211yescharacteristic
99C23×C127C2×SD1611yescharacteristic
100Q8×C127—41no—
101D4×C127—41no—
102D4×C127—41no—
103D4×C127—41no—
104D4×C127—42no—
105D4×C127—42no—
106D4×C127—82no—
107D4×C127—162no—
108D4×C127—162no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—42no—
116C2×C4×C127#10211yescharacteristic
117C2×C4×C127#10211yescharacteristic
118C2×C4×C127C2×C22⋊C411yescharacteristic
119C2×C4×C127C2×D811yescharacteristic
120C8×C127—21no—
121C8×C127—21no—
122C8×C127—21no—
123C8×C127—82no—
124C8×C127#9911yescharacteristic
125C8×C127#9911yescharacteristic
126C22×C127—21no—
127C22×C127—21no—
128C22×C127—21no—
129C22×C127—41no—
130C22×C127—41no—
131C22×C127—41no—
132C22×C127—82no—
133C22×C127—82no—
134C22×C127—82no—
135C22×C127—164no—
136C22×C127C2×#10211yescharacteristic
137C4×C127—21no—
138C4×C127—21no—
139C4×C127—21no—
140C4×C127—82no—
141C4×C127C2×#9911yescharacteristic
142C4×C127#42111yescharacteristic
143#11870C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127—21no—
145C2×C127—41no—
146C2×C127—41no—
147C2×C127—41no—
148C2×C127—162no—
149C2×C127#151911yescharacteristic
150#3058C2×C12711yescharacteristic
151#2115C2×C12711yescharacteristic, complemented
152#1813C2×C12711yescharacteristic, complemented
153#1341C2×C12714yescomplemented
154C127#1187011yescharacteristic, direct product factor, Sylow
155C22×D8C4×C12711yescharacteristic
156C2×#131C22×C12711yescharacteristic
157#535—21no—
158C2×M32—21no—
159#469C4×C12712yes—
160#469C22×C12712yes—
161#466—21no—
162#466—21no—
163C2×#108—21no—
164#427C4×C12711yescharacteristic
165#418—21no—
166#413—21no—
167#349—21no—
168#349C22×C12712yescomplemented
169#338C22×C12712yescomplemented
170C2×#41D4×C12711yescharacteristic
171C22×D4—21no—
172C2×D8—21no—
173C2×D8—41no—
174C2×D8—41no—
175C2×D8C2×C4×C12712yes—
176#131—41no—
177#131—41no—
178C2×M16—22no—
179C2×M16C2×C4×C12711yescharacteristic
180C2×M16D4×C12711yescharacteristic
181C2×M16C23×C12711yescharacteristic
182C22×C8C2×C4×C12711yescharacteristic
183C22×C8D4×C12711yescharacteristic
184C22×C8D4×C12711yescharacteristic
185#127—41no—
186#124—41no—
187#121—22no—
188#121—22no—
189#120—41no—
190#120—41no—
191#117—21no—
192M32—22no—
193M32—41no—
194C2×C16—41no—
195#108—41no—
196#108—41no—
197#107—21no—
198#106C2×C4×C12712yes—
199#102—22no—
200#102—22no—
201#101—41no—
202#100—41no—
203C24—41no—
204#41—41no—
205#41—41no—
206C2×Q8D8×C12711yescharacteristic
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—41no—
213C2×D4D8×C12711yescharacteristic
214C2×D4SD16×C12711yescharacteristic
215C2×D4SD16×C12711yescharacteristic
216C22×C4C22⋊C4×C12711yescharacteristic
217C22×C4C22⋊C4×C12711yescharacteristic
218C22×C4C2×D4×C12711yescharacteristic
219D8—42no—
220D8—41no—
221D8—41no—
222M16—41no—
223M16—41no—
224M16—41no—
225M16—42no—
226M16—42no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—42no—
234C2×C8C22⋊C4×C12711yescharacteristic
235C2×C8C22⋊C4×C12711yescharacteristic
236C2×C8C22×C4×C12711yescharacteristic
237C2×C8C2×D4×C12711yescharacteristic
238C4⋊C4—22no—
239C22⋊C4—41no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C42—41no—
243C16—42no—
244C23—42no—
245C23—82no—
246C23—162no—
247C23#102×C12711yescharacteristic
248C23#102×C12711yescharacteristic
249C23C2×SD16×C12711yescharacteristic
250Q8—41no—
251D4—41no—
252D4—41no—
253D4—41no—
254D4—42no—
255D4—42no—
256D4—82no—
257D4—162no—
258D4—162no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4#102×C12711yescharacteristic
267C2×C4#102×C12711yescharacteristic
268C2×C4C2×C22⋊C4×C12711yescharacteristic
269C2×C4C2×D8×C12711yescharacteristic
270C8—21no—
271C8—21no—
272C8—21no—
273C8—82no—
274C8#99×C12711yescharacteristic
275C8#99×C12711yescharacteristic
276C22—21no—
277C22—21no—
278C22—21no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—82no—
283C22—82no—
284C22—82no—
285C22—164no—
286C22C2×#102×C12711yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—82no—
291C4C2×#99×C12711yescharacteristic
292C4#421×C12711yescharacteristic
293C2—21no—
294C2—41no—
295C2—41no—
296C2—41no—
297C2—162no—
298C2C127×#151911yescharacteristic
subgroupG/H
center, socleC2×C127#1519
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
prime radicalC127×#3058C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2115C2semidirect
3. C127×#1813C2semidirect
4. C127×#1341C2semidirect
18. #349×C127C22semidirect
19. #338×C127C22semidirect
143. #11870C127direct (N × H)
151. #2115C2×C127semidirect
152. #1813C2×C127semidirect
153. #1341C2×C127semidirect
154. C127#11870direct (N × H)
168. #349C22×C127semidirect
169. #338C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30582
C127×#21152
C127×#18132
C127×#13412
#11870127