Finite Group Databasebeta

← C127×#11782 #44575455

Subgroups — C127×#11782 #44575455

Order 32512.

414 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2546C211yesmaximal, characteristic
2C4×#101×C127C211yesmaximal, characteristic
3C127×#1467C211yesmaximal, characteristic
4C127×#1346C214yesmaximal
5C2×C4⋊Q8×C127—21no—
6C2×C4⋊Q8×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#432×C127—21no—
9C2×#101×C127—21no—
10C4×M16×C127—21no—
11#398×C127C412yes—
12#398×C127C2212yes—
13#391×C127—21no—
14#389×C127—21no—
15#389×C127—21no—
16C4×C4⋊C4×C127C411yescharacteristic
17#343×C127C2212yes—
18#324×C127—21no—
19#324×C127C2212yes—
20C22×Q8×C127—21no—
21C22×Q8×C127D411yescharacteristic
22C2×M16×C127—22no—
23C4⋊Q8×C127—41no—
24C4⋊Q8×C127—41no—
25C4⋊Q8×C127—44no—
26C4×Q8×C127—41no—
27C4×Q8×C127—41no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127—22no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—22no—
32C2×C4⋊C4×C127C2×C412yes—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C4⋊C4×C127C2311yescharacteristic
36C2×C42×C127—21no—
37C2×C42×C127C2×C411yescharacteristic
38C2×C42×C127D411yescharacteristic
39C2×C42×C127D411yescharacteristic
40C4⋊C8×C127—41no—
41#101×C127—24no—
42C22⋊C8×C127—22no—
43#97×C127—41no—
44#97×C127—41no—
45C4×C8×C127—41no—
46#95×C127—22no—
47#95×C127—22no—
48#95×C127C2×C412yes—
49C2×Q8×C127—22no—
50C2×Q8×C127—22no—
51C2×Q8×C127—41no—
52C2×Q8×C127—42no—
53C2×Q8×C127—42no—
54C2×Q8×C127—42no—
55C22×C4×C127—22no—
56C22×C4×C127—22no—
57C22×C4×C127C22⋊C411yescharacteristic
58C22×C4×C127C22⋊C411yescharacteristic
59C22×C4×C127C22⋊C411yescharacteristic
60C22×C4×C127C22⋊C411yescharacteristic
61C22×C4×C127C22×C411yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63C22×C4×C127C2×D411yescharacteristic
64M16×C127—24no—
65M16×C127—42no—
66C2×C8×C127—42no—
67C2×C8×C127—42no—
68C4⋊C4×C127—24no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—41no—
71C4⋊C4×C127—41no—
72C4⋊C4×C127—42no—
73C4⋊C4×C127—44no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—44no—
77C42×C127—21no—
78C42×C127—21no—
79C42×C127—21no—
80C42×C127—21no—
81C42×C127—21no—
82C42×C127—21no—
83C42×C127—42no—
84C23×C127C2×C22⋊C411yescharacteristic
85Q8×C127—44no—
86Q8×C127—84no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—22no—
92C2×C4×C127—24no—
93C2×C4×C127—21no—
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—42no—
100C2×C4×C127—42no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127—42no—
107C2×C4×C127#9911yescharacteristic
108C2×C4×C127#9911yescharacteristic
109C2×C4×C127#10412yes—
110C2×C4×C127AGL(1,ℤ/8)12yes—
111C8×C127—44no—
112C8×C127—82no—
113C22×C127—21no—
114C22×C127—21no—
115C22×C127C2×#9911yescharacteristic
116C22×C127#41811yescharacteristic
117C22×C127C2×#10411yescharacteristic
118C4×C127—21no—
119C4×C127—22no—
120C4×C127—22no—
121C4×C127—44no—
122C4×C127—41no—
123C4×C127—41no—
124C4×C127—41no—
125C4×C127—41no—
126C4×C127—82no—
127C4×C127#35612yes—
128#11782C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—21no—
130C2×C127—21no—
131C2×C127#150711yescharacteristic
132C2×C127#212311yescharacteristic
133C2×C127C2×#35611yescharacteristic
134#2546C2×C12711yescharacteristic
135C4×#101C2×C12711yescharacteristic
136#1467C2×C12711yescharacteristic
137#1346C2×C12714yes—
138C127#1178211yescharacteristic, direct product factor, Sylow
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8C4×C12711yescharacteristic
141C2×C4×Q8C22×C12711yescharacteristic
142#432—21no—
143C2×#101—21no—
144C4×M16—21no—
145#398C4×C12712yes—
146#398C22×C12712yes—
147#391—21no—
148#389—21no—
149#389—21no—
150C4×C4⋊C4C4×C12711yescharacteristic
151#343C22×C12712yes—
152#324—21no—
153#324C22×C12712yes—
154C22×Q8—21no—
155C22×Q8D4×C12711yescharacteristic
156C2×M16—22no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—44no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×C4×C12712yes—
167C2×C4⋊C4C2×C4×C12711yescharacteristic
168C2×C4⋊C4D4×C12711yescharacteristic
169C2×C4⋊C4C23×C12711yescharacteristic
170C2×C42—21no—
171C2×C42C2×C4×C12711yescharacteristic
172C2×C42D4×C12711yescharacteristic
173C2×C42D4×C12711yescharacteristic
174C4⋊C8—41no—
175#101—24no—
176C22⋊C8—22no—
177#97—41no—
178#97—41no—
179C4×C8—41no—
180#95—22no—
181#95—22no—
182#95C2×C4×C12712yes—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊C4×C12711yescharacteristic
192C22×C4C22⋊C4×C12711yescharacteristic
193C22×C4C22⋊C4×C12711yescharacteristic
194C22×C4C22⋊C4×C12711yescharacteristic
195C22×C4C22×C4×C12711yescharacteristic
196C22×C4C2×D4×C12711yescharacteristic
197C22×C4C2×D4×C12711yescharacteristic
198M16—24no—
199M16—42no—
200C2×C8—42no—
201C2×C8—42no—
202C4⋊C4—24no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C23C2×C22⋊C4×C12711yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4#99×C12711yescharacteristic
242C2×C4#99×C12711yescharacteristic
243C2×C4#104×C12712yes—
244C2×C4AGL(1,ℤ/8)×C12712yes—
245C8—44no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22C2×#99×C12711yescharacteristic
250C22#418×C12711yescharacteristic
251C22C2×#104×C12711yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4#356×C12712yes—
262C2—21no—
263C2—21no—
264C2C127×#150711yescharacteristic
265C2C127×#212311yescharacteristic
266C2C2×#356×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
128. #11782C127direct (N × H)
138. C127#11782direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25462
C4×#101×C1272
C127×#14672
C127×#13462
#11782127