Finite Group Databasebeta

← C127×#7830 #44571503

Subgroups — C127×#7830 #44571503

Order 32512.

494 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2733C211yesmaximal, characteristic
2C127×#2095C211yesmaximal, characteristic, complemented
3C127×#2094C212yesmaximal, complemented
4C127×#1272C211yesmaximal, characteristic, complemented
5C127×#1270C212yesmaximal, complemented
6C2×#124×C127—21no—
7C2×#107×C127—21no—
8C2×#106×C127—22no—
9C2×#103×C127—21no—
10C2×#102×C127—22no—
11#394×C127—21no—
12#392×C127—22no—
13#391×C127C2211yescharacteristic
14#390×C127C2212yes—
15#388×C127—22no—
16#384×C127C2211yescharacteristic
17#336×C127C2212yes—
18#336×C127C2211yescharacteristic
19C22×Q8×C127D411yescharacteristic
20C22×D4×C127—21no—
21C22×D4×C127—21no—
22C22×D4×C127D412yes—
23C22×C8×C127—22no—
24C22×C8×C127—21no—
25#124×C127—42no—
26#124×C127—42no—
27C2×C4⋊C4×C127—22no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127D412yes—
30C2×C4⋊C4×C127D411yescharacteristic
31C2×C22⋊C4×C127—22no—
32C2×C22⋊C4×C127—22no—
33C2×C22⋊C4×C127—22no—
34C2×C22⋊C4×C127—22no—
35C2×C42×C127—21no—
36C2×C42×C127C2311yescharacteristic
37#107×C127—42no—
38#106×C127—44no—
39#103×C127—42no—
40#102×C127—44no—
41#95×C127—21no—
42#95×C127—22no—
43C24×C127—22no—
44C2×Q8×C127—21no—
45C2×Q8×C127—41no—
46C2×Q8×C127—41no—
47C2×Q8×C127SD1612yes—
48C2×D4×C127—22no—
49C2×D4×C127—22no—
50C2×D4×C127—42no—
51C2×D4×C127—42no—
52C2×D4×C127—42no—
53C2×D4×C127—81no—
54C2×D4×C127—81no—
55C2×D4×C127—82no—
56C2×D4×C127—81no—
57C22×C4×C127—21no—
58C22×C4×C127—21no—
59C22×C4×C127—22no—
60C22×C4×C127—41no—
61C22×C4×C127C2×D411yescharacteristic
62C22×C4×C127C2×D412yes—
63C2×C8×C127—24no—
64C2×C8×C127—22no—
65C2×C8×C127—42no—
66C2×C8×C127—41no—
67C2×C8×C127—42no—
68C2×C8×C127—41no—
69C4⋊C4×C127—42no—
70C4⋊C4×C127—41no—
71C4⋊C4×C127—42no—
72C4⋊C4×C127—41no—
73C4⋊C4×C127—42no—
74C4⋊C4×C127—41no—
75C22⋊C4×C127—44no—
76C22⋊C4×C127—42no—
77C22⋊C4×C127—42no—
78C22⋊C4×C127—42no—
79C22⋊C4×C127—42no—
80C22⋊C4×C127—82no—
81C42×C127—41no—
82C42×C127—42no—
83C23×C127—42no—
84C23×C127—42no—
85C23×C127—42no—
86C23×C127—42no—
87C23×C127—42no—
88C23×C127—42no—
89C23×C127—42no—
90C23×C127#12011yescharacteristic
91Q8×C127—42no—
92Q8×C127—81no—
93D4×C127—44no—
94D4×C127—82no—
95D4×C127—84no—
96D4×C127—84no—
97C2×C4×C127—22no—
98C2×C4×C127—21no—
99C2×C4×C127—22no—
100C2×C4×C127—21no—
101C2×C4×C127—22no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127—42no—
107C2×C4×C127—42no—
108C2×C4×C127—41no—
109C2×C4×C127—81no—
110C2×C4×C127—82no—
111C2×C4×C127C2×SD1611yescharacteristic
112C2×C4×C127#13512yes—
113C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C127#13712yes—
115C8×C127—42no—
116C8×C127—44no—
117C22×C127—82no—
118C22×C127—82no—
119C22×C127—82no—
120C22×C127—82no—
121C22×C127—82no—
122C22×C127—82no—
123C22×C127—82no—
124C22×C127#45011yescharacteristic
125C22×C127#45212yes—
126C22×C127#45311yescharacteristic
127C22×C127#45312yes—
128C22×C127#45811yescharacteristic
129C4×C127—21no—
130C4×C127—21no—
131C4×C127—22no—
132C4×C127—22no—
133C4×C127—42no—
134C4×C127—82no—
135C4×C127—81no—
136C4×C127—161no—
137#7830C12711yesmaximal, characteristic, direct product factor, Sylow
138C2×C127—162no—
139C2×C127#161311yescharacteristic
140C2×C127#161812yes—
141C2×C127#163112yes—
142C2×C127#163411yescharacteristic
143C2×C127#165511yescharacteristic
144#2733C2×C12711yescharacteristic
145#2095C2×C12711yescharacteristic, complemented
146#2094C2×C12712yescomplemented
147#1272C2×C12711yescharacteristic, complemented
148#1270C2×C12712yescomplemented
149C127#783011yescharacteristic, direct product factor, Sylow
150C2×#124—21no—
151C2×#107—21no—
152C2×#106—22no—
153C2×#103—21no—
154C2×#102—22no—
155#394—21no—
156#392—22no—
157#391C22×C12711yescharacteristic
158#390C22×C12712yes—
159#388—22no—
160#384C22×C12711yescharacteristic
161#336C22×C12712yes—
162#336C22×C12711yescharacteristic
163C22×Q8D4×C12711yescharacteristic
164C22×D4—21no—
165C22×D4—21no—
166C22×D4D4×C12712yes—
167C22×C8—22no—
168C22×C8—21no—
169#124—42no—
170#124—42no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4D4×C12712yes—
174C2×C4⋊C4D4×C12711yescharacteristic
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C42—21no—
180C2×C42C23×C12711yescharacteristic
181#107—42no—
182#106—44no—
183#103—42no—
184#102—44no—
185#95—21no—
186#95—22no—
187C24—22no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8SD16×C12712yes—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—81no—
198C2×D4—81no—
199C2×D4—82no—
200C2×D4—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—41no—
205C22×C4C2×D4×C12711yescharacteristic
206C22×C4C2×D4×C12712yes—
207C2×C8—24no—
208C2×C8—22no—
209C2×C8—42no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8—41no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C42—41no—
226C42—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23#120×C12711yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—44no—
238D4—82no—
239D4—84no—
240D4—84no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4C2×SD16×C12711yescharacteristic
256C2×C4#135×C12712yes—
257C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
258C2×C4#137×C12712yes—
259C8—42no—
260C8—44no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22#450×C12711yescharacteristic
269C22#452×C12712yes—
270C22#453×C12711yescharacteristic
271C22#453×C12712yes—
272C22#458×C12711yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—82no—
279C4—81no—
280C4—161no—
281C2—162no—
282C2C127×#161311yescharacteristic
283C2C127×#161812yes—
284C2C127×#163112yes—
285C2C127×#163411yescharacteristic
286C2C127×#165511yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC127×#2733C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2095C2semidirect
3. C127×#2094C2semidirect
4. C127×#1272C2semidirect
5. C127×#1270C2semidirect
137. #7830C127direct (N × H)
145. #2095C2×C127semidirect
146. #2094C2×C127semidirect
147. #1272C2×C127semidirect
148. #1270C2×C127semidirect
149. C127#7830direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#27332
C127×#20952
C127×#20942
C127×#12722
C127×#12702
#7830127