Finite Group Databasebeta

← C127×#17430 #44581103

Subgroups — C127×#17430 #44581103

Order 32512.

884 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C127C211yesmaximal, characteristic
2C127×#2984C212yesmaximal
3C127×#1470C216yesmaximal
4C127×#1467C213yesmaximal
5C127×#1461C213yesmaximal
6#557×C127—22no—
7#557×C127—26no—
8C2×C4⋊Q8×C127C413yes—
9C2×#125×C127C413yes—
10C2×#125×C127C2213yes—
11C2×C4×Q8×C127C411yescharacteristic
12C2×C4×Q8×C127C411yescharacteristic
13C2×C4×Q8×C127C2213yes—
14C2×C4×Q8×C127C2211yescharacteristic
15#446×C127—26no—
16C8×Q8×C127—22no—
17#432×C127C2216yes—
18#431×C127C2216yes—
19#324×C127C2211yescharacteristic
20#324×C127C2213yes—
21#324×C127C2216yes—
22#324×C127C2216yes—
23C22×Q8×C127C2×C413yes—
24C22×Q8×C127C2×C411yescharacteristic
25C4⋊Q8×C127—26no—
26C4⋊Q8×C127—26no—
27#125×C127—26no—
28#125×C127—26no—
29#125×C127—26no—
30#125×C127—26no—
31C4×Q8×C127—23no—
32C4×Q8×C127—21no—
33C4×Q8×C127—23no—
34C4×Q8×C127—21no—
35C4×Q8×C127—26no—
36C4×Q8×C127—26no—
37C4×Q8×C127D412yes—
38C4×Q8×C127D416yes—
39C2×C4⋊C4×C127C2×C413yes—
40C2×C4⋊C4×C127C2×C413yes—
41C2×C4⋊C4×C127C2×C413yes—
42C2×C4⋊C4×C127C2×C416yes—
43C2×C4⋊C4×C127C2×C413yes—
44C2×C4⋊C4×C127C2311yescharacteristic
45C2×C4⋊C4×C127C2313yes—
46C2×C42×C127C2×C413yes—
47C2×C42×C127C2×C413yes—
48C2×C42×C127C2313yes—
49C4⋊C8×C127—26no—
50C4⋊C8×C127—26no—
51C22⋊C8×C127C2312yes—
52C22⋊C8×C127C2316yes—
53#97×C127—26no—
54C4×C8×C127—26no—
55C2×Q8×C127—24no—
56C2×Q8×C127—26no—
57C2×Q8×C127—26no—
58C2×Q8×C127—43no—
59C2×Q8×C127C22⋊C413yes—
60C2×Q8×C127C22⋊C411yescharacteristic
61C22×C4×C127C22×C413yes—
62C22×C4×C127C22×C413yes—
63C22×C4×C127C22×C413yes—
64C22×C4×C127C22×C411yescharacteristic
65C22×C4×C127C22×C411yescharacteristic
66C22×C4×C127C22×C413yes—
67C22×C4×C127C2411yescharacteristic
68C2×C8×C127—22no—
69C2×C8×C127—26no—
70C4⋊C4×C127—26no—
71C4⋊C4×C127—23no—
72C4⋊C4×C127—23no—
73C4⋊C4×C127—23no—
74C4⋊C4×C127—23no—
75C4⋊C4×C127—212no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—26no—
78C4⋊C4×C127C22⋊C416yes—
79C4⋊C4×C127C22⋊C416yes—
80C42×C127—23no—
81C42×C127—23no—
82C42×C127—23no—
83C42×C127—23no—
84C42×C127C2×D416yes—
85C42×C127C2×D416yes—
86C23×C127C23×C411yescharacteristic
87Q8×C127—26no—
88Q8×C127—412no—
89Q8×C127#10114yes—
90C2×C4×C127—21no—
91C2×C4×C127—23no—
92C2×C4×C127—23no—
93C2×C4×C127—21no—
94C2×C4×C127—26no—
95C2×C4×C127—21no—
96C2×C4×C127—23no—
97C2×C4×C127—23no—
98C2×C4×C127—23no—
99C2×C4×C127—23no—
100C2×C4×C127—41no—
101C2×C4×C127—41no—
102C2×C4×C127—43no—
103C2×C4×C127C2×C22⋊C413yes—
104C2×C4×C127C2×C22⋊C416yes—
105C2×C4×C127C2×C22⋊C413yes—
106C2×C4×C127#13112yes—
107C2×C4×C127C22×D412yes—
108C8×C127—42no—
109C8×C127—46no—
110C22×C127—21no—
111C22×C127—21no—
112C22×C127C22×C22⋊C411yescharacteristic
113C22×C127C2×#13111yescharacteristic
114C22×C127#56811yescharacteristic
115C4×C127—26no—
116C4×C127—22no—
117C4×C127—22no—
118C4×C127—23no—
119C4×C127—43no—
120C4×C127—41no—
121C4×C127—43no—
122C4×C127C2×#10116yes—
123#17430C12711yesmaximal, characteristic, direct product factor, Sylow
124C2×C127—21no—
125C2×C127—21no—
126C2×C127#288011yescharacteristic
127C2×C127#288411yescharacteristic
128C2×C127C22×#10111yescharacteristic
129C2×#557C2×C12711yescharacteristic
130#2984C2×C12712yes—
131#1470C2×C12716yes—
132#1467C2×C12713yes—
133#1461C2×C12713yes—
134C127#1743011yescharacteristic, direct product factor, Sylow
135#557—22no—
136#557—26no—
137C2×C4⋊Q8C4×C12713yes—
138C2×#125C4×C12713yes—
139C2×#125C22×C12713yes—
140C2×C4×Q8C4×C12711yescharacteristic
141C2×C4×Q8C4×C12711yescharacteristic
142C2×C4×Q8C22×C12713yes—
143C2×C4×Q8C22×C12711yescharacteristic
144#446—26no—
145C8×Q8—22no—
146#432C22×C12716yes—
147#431C22×C12716yes—
148#324C22×C12711yescharacteristic
149#324C22×C12713yes—
150#324C22×C12716yes—
151#324C22×C12716yes—
152C22×Q8C2×C4×C12713yes—
153C22×Q8C2×C4×C12711yescharacteristic
154C4⋊Q8—26no—
155C4⋊Q8—26no—
156#125—26no—
157#125—26no—
158#125—26no—
159#125—26no—
160C4×Q8—23no—
161C4×Q8—21no—
162C4×Q8—23no—
163C4×Q8—21no—
164C4×Q8—26no—
165C4×Q8—26no—
166C4×Q8D4×C12712yes—
167C4×Q8D4×C12716yes—
168C2×C4⋊C4C2×C4×C12713yes—
169C2×C4⋊C4C2×C4×C12713yes—
170C2×C4⋊C4C2×C4×C12713yes—
171C2×C4⋊C4C2×C4×C12716yes—
172C2×C4⋊C4C2×C4×C12713yes—
173C2×C4⋊C4C23×C12711yescharacteristic
174C2×C4⋊C4C23×C12713yes—
175C2×C42C2×C4×C12713yes—
176C2×C42C2×C4×C12713yes—
177C2×C42C23×C12713yes—
178C4⋊C8—26no—
179C4⋊C8—26no—
180C22⋊C8C23×C12712yes—
181C22⋊C8C23×C12716yes—
182#97—26no—
183C4×C8—26no—
184C2×Q8—24no—
185C2×Q8—26no—
186C2×Q8—26no—
187C2×Q8—43no—
188C2×Q8C22⋊C4×C12713yes—
189C2×Q8C22⋊C4×C12711yescharacteristic
190C22×C4C22×C4×C12713yes—
191C22×C4C22×C4×C12713yes—
192C22×C4C22×C4×C12713yes—
193C22×C4C22×C4×C12711yescharacteristic
194C22×C4C22×C4×C12711yescharacteristic
195C22×C4C22×C4×C12713yes—
196C22×C4C24×C12711yescharacteristic
197C2×C8—22no—
198C2×C8—26no—
199C4⋊C4—26no—
200C4⋊C4—23no—
201C4⋊C4—23no—
202C4⋊C4—23no—
203C4⋊C4—23no—
204C4⋊C4—212no—
205C4⋊C4—22no—
206C4⋊C4—26no—
207C4⋊C4C22⋊C4×C12716yes—
208C4⋊C4C22⋊C4×C12716yes—
209C42—23no—
210C42—23no—
211C42—23no—
212C42—23no—
213C42C2×D4×C12716yes—
214C42C2×D4×C12716yes—
215C23C23×C4×C12711yescharacteristic
216Q8—26no—
217Q8—412no—
218Q8#101×C12714yes—
219C2×C4—21no—
220C2×C4—23no—
221C2×C4—21no—
222C2×C4—23no—
223C2×C4—26no—
224C2×C4—21no—
225C2×C4—23no—
226C2×C4—23no—
227C2×C4—23no—
228C2×C4—23no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—43no—
232C2×C4C2×C22⋊C4×C12713yes—
233C2×C4C2×C22⋊C4×C12716yes—
234C2×C4C2×C22⋊C4×C12713yes—
235C2×C4#131×C12712yes—
236C2×C4C22×D4×C12712yes—
237C8—42no—
238C8—46no—
239C22—21no—
240C22—21no—
241C22C22×C22⋊C4×C12711yescharacteristic
242C22C2×#131×C12711yescharacteristic
243C22#568×C12711yescharacteristic
244C4—26no—
245C4—22no—
246C4—22no—
247C4—23no—
248C4—43no—
249C4—41no—
250C4—43no—
251C4C2×#101×C12716yes—
252C2—21no—
253C2—21no—
254C2C127×#288011yescharacteristic
255C2C127×#288411yescharacteristic
256C2C22×#101×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×C127C23×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
123. #17430C127direct (N × H)
134. C127#17430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#557×C1272
C127×#29842
C127×#14702
C127×#14672
C127×#14612
#17430127