Finite Group Databasebeta

← C127×#17619 #44581292

Subgroups — C127×#17619 #44581292

Order 32512.

938 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3502C211yesmaximal, characteristic
2C127×#2982C211yesmaximal, characteristic
3C127×#2351C211yesmaximal, characteristic
4C127×#1518C216yesmaximal
5C127×#1503C216yesmaximal
6Q82×C127C414yescomplemented
7#557×C127—24no—
8#557×C127C414yescomplemented
9#544×C127—23no—
10#533×C127C2216yes—
11#519×C127—21no—
12C2×C4×Q8×C127—21no—
13C2×C4×Q8×C127C2211yescharacteristic
14C8×Q8×C127—24no—
15#431×C127C2216yes—
16#389×C127—23no—
17#382×C127C2213yes—
18C4×C4⋊C4×C127C2213yes—
19#328×C127C2214yes—
20#328×C127C22112yes—
21C22×Q8×C127D411yescharacteristic
22C4⋊Q8×C127—212no—
23C4⋊Q8×C127C2×C416yes—
24C4⋊Q8×C127C2×C416yes—
25#125×C127—212no—
26#125×C127—26no—
27C22⋊Q8×C127—26no—
28C22⋊Q8×C127C2314yes—
29C4×Q8×C127—24no—
30C4×Q8×C127—24no—
31C4×Q8×C127—26no—
32C4×Q8×C127—44no—
33C4×Q8×C127C2×C4112yes—
34C4×Q8×C127C2×C414yes—
35C4×Q8×C127D414yes—
36#117×C127—26no—
37C2×C4⋊C4×C127—23no—
38C2×C4⋊C4×C127—23no—
39C2×C4⋊C4×C127D413yes—
40C2×C42×C127—23no—
41C2×C42×C127C2313yes—
42C4⋊C8×C127—26no—
43C22⋊C8×C127C2314yes—
44C4×C8×C127—26no—
45#95×C127—23no—
46#95×C127C2311yescharacteristic
47#95×C127C2313yes—
48C2×Q8×C127—26no—
49C2×Q8×C127C22⋊C414yes—
50C2×Q8×C127SD1614yes—
51C2×Q8×C127Q1614yes—
52C2×Q8×C127C22×C414yes—
53C22×C4×C127—21no—
54C22×C4×C127—23no—
55C22×C4×C127C2×D413yes—
56C22×C4×C127C2×D413yes—
57C22×C4×C127C2411yescharacteristic
58C2×C8×C127—24no—
59C4⋊C4×C127—26no—
60C4⋊C4×C127—26no—
61C4⋊C4×C127—26no—
62C4⋊C4×C127—212no—
63C4⋊C4×C127—24no—
64C4⋊C4×C127—46no—
65C4⋊C4×C127—46no—
66C4⋊C4×C127C22⋊C4112yes—
67C4⋊C4×C127C22×C414yes—
68C22⋊C4×C127—24no—
69C42×C127—212no—
70C42×C127—46no—
71C42×C127C22×C416yes—
72C42×C127C2×D416yes—
73C23×C127C22×D411yescharacteristic
74Q8×C127—44no—
75Q8×C127—86no—
76Q8×C127#103116yes—
77C2×C4×C127—22no—
78C2×C4×C127—24no—
79C2×C4×C127—24no—
80C2×C4×C127—43no—
81C2×C4×C127—41no—
82C2×C4×C127—41no—
83C2×C4×C127—41no—
84C2×C4×C127—43no—
85C2×C4×C127—43no—
86C2×C4×C127—43no—
87C2×C4×C127C2×C22⋊C416yes—
88C2×C4×C127C2×C22⋊C416yes—
89C2×C4×C127C2×SD1616yes—
90C2×C4×C127C2×Q1616yes—
91C2×C4×C127C23×C411yescharacteristic
92C2×C4×C127C22×D411yescharacteristic
93C8×C127—44no—
94C22×C127—21no—
95C22×C127—21no—
96C22×C127C22×C22⋊C411yescharacteristic
97C22×C127C22×SD1611yescharacteristic
98C22×C127C22×Q1611yescharacteristic
99C4×C127—21no—
100C4×C127—21no—
101C4×C127—26no—
102C4×C127—42no—
103C4×C127—44no—
104C4×C127—44no—
105C4×C127—83no—
106C4×C127C2×#103112yes—
107#17619C12711yesmaximal, characteristic, direct product factor, Sylow
108C2×C127—21no—
109C2×C127—21no—
110C2×C127#288411yescharacteristic
111C2×C127C22×#10311yescharacteristic
112C2×C127#290111yescharacteristic
113#3502C2×C12711yescharacteristic
114#2982C2×C12711yescharacteristic
115#2351C2×C12711yescharacteristic
116#1518C2×C12716yes—
117#1503C2×C12716yes—
118C127#1761911yescharacteristic, direct product factor, Sylow
119Q82C4×C12714yescomplemented
120#557—24no—
121#557C4×C12714yescomplemented
122#544—23no—
123#533C22×C12716yes—
124#519—21no—
125C2×C4×Q8—21no—
126C2×C4×Q8C22×C12711yescharacteristic
127C8×Q8—24no—
128#431C22×C12716yes—
129#389—23no—
130#382C22×C12713yes—
131C4×C4⋊C4C22×C12713yes—
132#328C22×C12714yes—
133#328C22×C127112yes—
134C22×Q8D4×C12711yescharacteristic
135C4⋊Q8—212no—
136C4⋊Q8C2×C4×C12716yes—
137C4⋊Q8C2×C4×C12716yes—
138#125—212no—
139#125—26no—
140C22⋊Q8—26no—
141C22⋊Q8C23×C12714yes—
142C4×Q8—24no—
143C4×Q8—24no—
144C4×Q8—26no—
145C4×Q8—44no—
146C4×Q8C2×C4×C127112yes—
147C4×Q8C2×C4×C12714yes—
148C4×Q8D4×C12714yes—
149#117—26no—
150C2×C4⋊C4—23no—
151C2×C4⋊C4—23no—
152C2×C4⋊C4D4×C12713yes—
153C2×C42—23no—
154C2×C42C23×C12713yes—
155C4⋊C8—26no—
156C22⋊C8C23×C12714yes—
157C4×C8—26no—
158#95—23no—
159#95C23×C12711yescharacteristic
160#95C23×C12713yes—
161C2×Q8—26no—
162C2×Q8C22⋊C4×C12714yes—
163C2×Q8SD16×C12714yes—
164C2×Q8Q16×C12714yes—
165C2×Q8C22×C4×C12714yes—
166C22×C4—21no—
167C22×C4—23no—
168C22×C4C2×D4×C12713yes—
169C22×C4C2×D4×C12713yes—
170C22×C4C24×C12711yescharacteristic
171C2×C8—24no—
172C4⋊C4—26no—
173C4⋊C4—26no—
174C4⋊C4—26no—
175C4⋊C4—212no—
176C4⋊C4—24no—
177C4⋊C4—46no—
178C4⋊C4—46no—
179C4⋊C4C22⋊C4×C127112yes—
180C4⋊C4C22×C4×C12714yes—
181C22⋊C4—24no—
182C42—212no—
183C42—46no—
184C42C22×C4×C12716yes—
185C42C2×D4×C12716yes—
186C23C22×D4×C12711yescharacteristic
187Q8—44no—
188Q8—86no—
189Q8#103×C127116yes—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—43no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—43no—
198C2×C4—43no—
199C2×C4—43no—
200C2×C4C2×C22⋊C4×C12716yes—
201C2×C4C2×C22⋊C4×C12716yes—
202C2×C4C2×SD16×C12716yes—
203C2×C4C2×Q16×C12716yes—
204C2×C4C23×C4×C12711yescharacteristic
205C2×C4C22×D4×C12711yescharacteristic
206C8—44no—
207C22—21no—
208C22—21no—
209C22C22×C22⋊C4×C12711yescharacteristic
210C22C22×SD16×C12711yescharacteristic
211C22C22×Q16×C12711yescharacteristic
212C4—21no—
213C4—21no—
214C4—26no—
215C4—42no—
216C4—44no—
217C4—44no—
218C4—83no—
219C4C2×#103×C127112yes—
220C2—21no—
221C2—21no—
222C2C127×#288411yescharacteristic
223C2C22×#103×C12711yescharacteristic
224C2C127×#290111yescharacteristic
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×C127C22×D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. Q82×C127C4semidirect
8. #557×C127C4semidirect
107. #17619C127direct (N × H)
118. C127#17619direct (N × H)
119. Q82C4×C127semidirect
121. #557C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35022
C127×#29822
C127×#23512
C127×#15182
C127×#15032
#17619127