Finite Group Databasebeta

← C127×#11668 #44575341

Subgroups — C127×#11668 #44575341

Order 32512.

354 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C2×C4×Q16×C127C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic
3C127×#1568C211yesmaximal, characteristic
4C127×#1334C214yesmaximal, complemented
5C22×Q16×C127C411yescharacteristic
6C2×C4×Q8×C127—21no—
7C4×Q16×C127—21no—
8C4×Q16×C127—21no—
9C4×Q16×C127C412yes—
10C4×Q16×C127C2212yes—
11#432×C127—21no—
12C2×#107×C127C411yescharacteristic
13C2×#103×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15C4⋊C16×C127—21no—
16C22⋊C16×C127—21no—
17#346×C127C2212yes—
18#335×C127—21no—
19#334×C127C2212yes—
20C22×Q8×C127—21no—
21C2×Q16×C127—24no—
22C2×Q16×C127—21no—
23C2×Q16×C127C2×C412yes—
24C22×C8×C127C2×C411yescharacteristic
25C22×C8×C127D411yescharacteristic
26C4×Q8×C127—22no—
27C4×Q8×C127—22no—
28C4×Q8×C127—41no—
29C4×Q8×C127—41no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—41no—
32C2×C42×C127—41no—
33C2×C42×C127D411yescharacteristic
34C2×C16×C127—22no—
35#107×C127—21no—
36#107×C127C2×C412yes—
37C4⋊C8×C127—22no—
38#103×C127—22no—
39#103×C127—22no—
40C22⋊C8×C127—41no—
41#97×C127—41no—
42C4×C8×C127C2×C411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127C2311yescharacteristic
46C2×Q8×C127—24no—
47C2×Q8×C127—22no—
48C2×Q8×C127—42no—
49C2×Q8×C127—41no—
50C22×C4×C127—41no—
51C22×C4×C127—41no—
52C22×C4×C127C22⋊C411yescharacteristic
53C22×C4×C127D811yescharacteristic
54C22×C4×C127SD1611yescharacteristic
55Q16×C127—24no—
56Q16×C127—22no—
57Q16×C127M1614yes—
58C2×C8×C127—22no—
59C2×C8×C127—41no—
60C2×C8×C127—42no—
61C2×C8×C127C22⋊C411yescharacteristic
62C2×C8×C127C22⋊C411yescharacteristic
63C2×C8×C127C22×C411yescharacteristic
64C2×C8×C127C2×D411yescharacteristic
65C4⋊C4×C127—22no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—42no—
68C4⋊C4×C127—42no—
69C42×C127—42no—
70C42×C127—42no—
71C42×C127C22⋊C411yescharacteristic
72C42×C127D811yescharacteristic
73C42×C127SD1611yescharacteristic
74C42×C127C2×D411yescharacteristic
75C16×C127—42no—
76C23×C127#10211yescharacteristic
77Q8×C127—24no—
78Q8×C127—44no—
79Q8×C127—42no—
80C2×C4×C127—22no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—41no—
84C2×C4×C127—44no—
85C2×C4×C127—42no—
86C2×C4×C127—42no—
87C2×C4×C127—82no—
88C2×C4×C127#10211yescharacteristic
89C2×C4×C127#10211yescharacteristic
90C2×C4×C127#10211yescharacteristic
91C2×C4×C127C2×C22⋊C411yescharacteristic
92C2×C4×C127C2×D811yescharacteristic
93C2×C4×C127C2×SD1611yescharacteristic
94C8×C127—21no—
95C8×C127—21no—
96C8×C127—21no—
97C8×C127—82no—
98C8×C127C2×M1612yes—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127#36212yes—
102C22×C127C2×#10211yescharacteristic
103C4×C127—21no—
104C4×C127—21no—
105C4×C127—21no—
106C4×C127—21no—
107C4×C127—21no—
108C4×C127—44no—
109C4×C127—82no—
110C4×C127#40711yescharacteristic
111C4×C127#42111yescharacteristic
112#11668C12711yesmaximal, characteristic, direct product factor, Sylow
113C2×C127—22no—
114C2×C127#148611yescharacteristic
115C2×C127#214511yescharacteristic
116C2×C127C2×#36211yescharacteristic
117C2×C4×Q16C2×C12711yescharacteristic
118#2163C2×C12711yescharacteristic
119#1568C2×C12711yescharacteristic
120#1334C2×C12714yescomplemented
121C127#1166811yescharacteristic, direct product factor, Sylow
122C22×Q16C4×C12711yescharacteristic
123C2×C4×Q8—21no—
124C4×Q16—21no—
125C4×Q16—21no—
126C4×Q16C4×C12712yes—
127C4×Q16C22×C12712yes—
128#432—21no—
129C2×#107C4×C12711yescharacteristic
130C2×#103—21no—
131C2×C4×C8C22×C12711yescharacteristic
132C4⋊C16—21no—
133C22⋊C16—21no—
134#346C22×C12712yes—
135#335—21no—
136#334C22×C12712yes—
137C22×Q8—21no—
138C2×Q16—24no—
139C2×Q16—21no—
140C2×Q16C2×C4×C12712yes—
141C22×C8C2×C4×C12711yescharacteristic
142C22×C8D4×C12711yescharacteristic
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—41no—
146C4×Q8—41no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C42—41no—
150C2×C42D4×C12711yescharacteristic
151C2×C16—22no—
152#107—21no—
153#107C2×C4×C12712yes—
154C4⋊C8—22no—
155#103—22no—
156#103—22no—
157C22⋊C8—41no—
158#97—41no—
159C4×C8C2×C4×C12711yescharacteristic
160C4×C8D4×C12711yescharacteristic
161C4×C8D4×C12711yescharacteristic
162C4×C8C23×C12711yescharacteristic
163C2×Q8—24no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4C22⋊C4×C12711yescharacteristic
170C22×C4D8×C12711yescharacteristic
171C22×C4SD16×C12711yescharacteristic
172Q16—24no—
173Q16—22no—
174Q16M16×C12714yes—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8C22⋊C4×C12711yescharacteristic
179C2×C8C22⋊C4×C12711yescharacteristic
180C2×C8C22×C4×C12711yescharacteristic
181C2×C8C2×D4×C12711yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C42—42no—
187C42—42no—
188C42C22⋊C4×C12711yescharacteristic
189C42D8×C12711yescharacteristic
190C42SD16×C12711yescharacteristic
191C42C2×D4×C12711yescharacteristic
192C16—42no—
193C23#102×C12711yescharacteristic
194Q8—24no—
195Q8—44no—
196Q8—42no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—82no—
205C2×C4#102×C12711yescharacteristic
206C2×C4#102×C12711yescharacteristic
207C2×C4#102×C12711yescharacteristic
208C2×C4C2×C22⋊C4×C12711yescharacteristic
209C2×C4C2×D8×C12711yescharacteristic
210C2×C4C2×SD16×C12711yescharacteristic
211C8—21no—
212C8—21no—
213C8—21no—
214C8—82no—
215C8C2×M16×C12712yes—
216C22—21no—
217C22—21no—
218C22#362×C12712yes—
219C22C2×#102×C12711yescharacteristic
220C4—21no—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—44no—
226C4—82no—
227C4#407×C12711yescharacteristic
228C4#421×C12711yescharacteristic
229C2—22no—
230C2C127×#148611yescharacteristic
231C2C127×#214511yescharacteristic
232C2C2×#362×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC23×C127#102
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1334C2semidirect
112. #11668C127direct (N × H)
120. #1334C2×C127semidirect
121. C127#11668direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q16×C1272
C127×#21632
C127×#15682
C127×#13342
#11668127