Finite Group Databasebeta

← C127×#11748 #44575421

Subgroups — C127×#11748 #44575421

Order 32512.

324 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3170C211yesmaximal, characteristic
2C127×#2162C211yesmaximal, characteristic
3C4×#108×C127C211yesmaximal, characteristic
4C127×#1350C214yesmaximal
5#533×C127—21no—
6#500×C127C411yescharacteristic
7#494×C127C411yescharacteristic
8#487×C127—21no—
9#467×C127—21no—
10#467×C127C2212yes—
11C4×Q16×C127—21no—
12C4×Q16×C127C412yes—
13C2×#108×C127—21no—
14C4×M16×C127—21no—
15C2×C4×C8×C127C2211yescharacteristic
16C4⋊C16×C127—21no—
17C22⋊C16×C127C2212yes—
18C4×C16×C127—21no—
19#341×C127C2212yes—
20C2×Q16×C127—21no—
21C2×Q16×C127C2×C412yes—
22C2×M16×C127—22no—
23C22×C8×C127D411yescharacteristic
24C22×C8×C127C2311yescharacteristic
25C4⋊Q8×C127—21no—
26C4⋊Q8×C127—21no—
27#125×C127—41no—
28C22⋊Q8×C127—22no—
29C22⋊Q8×C127—41no—
30C4×Q8×C127—22no—
31C4×Q8×C127—41no—
32#117×C127—41no—
33C2×C42×C127D411yescharacteristic
34C2×C16×C127—22no—
35#108×C127—24no—
36#107×C127—21no—
37#107×C127C2×C412yes—
38#103×C127—22no—
39#103×C127—22no—
40#97×C127—41no—
41C4×C8×C127—41no—
42C4×C8×C127C2×C411yescharacteristic
43C4×C8×C127C2×C411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127D411yescharacteristic
46C2×Q8×C127—22no—
47C2×Q8×C127—41no—
48C22×C4×C127SD1611yescharacteristic
49C22×C4×C127SD1611yescharacteristic
50C22×C4×C127C2×D411yescharacteristic
51Q16×C127—42no—
52Q16×C127—42no—
53M16×C127—24no—
54M16×C127—42no—
55C2×C8×C127—22no—
56C2×C8×C127—41no—
57C2×C8×C127—42no—
58C2×C8×C127C22⋊C411yescharacteristic
59C2×C8×C127C22⋊C411yescharacteristic
60C2×C8×C127C22×C411yescharacteristic
61C2×C8×C127C2×D411yescharacteristic
62C4⋊C4×C127—22no—
63C4⋊C4×C127—41no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—42no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—42no—
68C22⋊C4×C127—42no—
69C42×C127—42no—
70C42×C127C22⋊C411yescharacteristic
71C42×C127C22⋊C411yescharacteristic
72C42×C127D811yescharacteristic
73C42×C127D811yescharacteristic
74C16×C127—42no—
75C23×C127C2×SD1611yescharacteristic
76Q8×C127—42no—
77Q8×C127—42no—
78Q8×C127—82no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—42no—
84C2×C4×C127—42no—
85C2×C4×C127#10211yescharacteristic
86C2×C4×C127#10211yescharacteristic
87C2×C4×C127#10211yescharacteristic
88C2×C4×C127#10211yescharacteristic
89C2×C4×C127C2×C22⋊C411yescharacteristic
90C2×C4×C127C2×D811yescharacteristic
91C8×C127—21no—
92C8×C127—21no—
93C8×C127—21no—
94C8×C127—44no—
95C8×C127#10412yes—
96C22×C127—21no—
97C22×C127—21no—
98C22×C127—21no—
99C22×C127C2×#10211yescharacteristic
100C4×C127—21no—
101C4×C127—21no—
102C4×C127—21no—
103C4×C127—82no—
104C4×C127—82no—
105C4×C127#35912yes—
106C4×C127#36212yes—
107C4×C127#41011yescharacteristic
108C4×C127C2×#10411yescharacteristic
109#11748C12711yesmaximal, characteristic, direct product factor, Sylow
110C2×C127—41no—
111C2×C127#150211yescharacteristic
112C2×C127C2×#35911yescharacteristic
113C2×C127C2×#36211yescharacteristic
114#3170C2×C12711yescharacteristic
115#2162C2×C12711yescharacteristic
116C4×#108C2×C12711yescharacteristic
117#1350C2×C12714yes—
118C127#1174811yescharacteristic, direct product factor, Sylow
119#533—21no—
120#500C4×C12711yescharacteristic
121#494C4×C12711yescharacteristic
122#487—21no—
123#467—21no—
124#467C22×C12712yes—
125C4×Q16—21no—
126C4×Q16C4×C12712yes—
127C2×#108—21no—
128C4×M16—21no—
129C2×C4×C8C22×C12711yescharacteristic
130C4⋊C16—21no—
131C22⋊C16C22×C12712yes—
132C4×C16—21no—
133#341C22×C12712yes—
134C2×Q16—21no—
135C2×Q16C2×C4×C12712yes—
136C2×M16—22no—
137C22×C8D4×C12711yescharacteristic
138C22×C8C23×C12711yescharacteristic
139C4⋊Q8—21no—
140C4⋊Q8—21no—
141#125—41no—
142C22⋊Q8—22no—
143C22⋊Q8—41no—
144C4×Q8—22no—
145C4×Q8—41no—
146#117—41no—
147C2×C42D4×C12711yescharacteristic
148C2×C16—22no—
149#108—24no—
150#107—21no—
151#107C2×C4×C12712yes—
152#103—22no—
153#103—22no—
154#97—41no—
155C4×C8—41no—
156C4×C8C2×C4×C12711yescharacteristic
157C4×C8C2×C4×C12711yescharacteristic
158C4×C8D4×C12711yescharacteristic
159C4×C8D4×C12711yescharacteristic
160C2×Q8—22no—
161C2×Q8—41no—
162C22×C4SD16×C12711yescharacteristic
163C22×C4SD16×C12711yescharacteristic
164C22×C4C2×D4×C12711yescharacteristic
165Q16—42no—
166Q16—42no—
167M16—24no—
168M16—42no—
169C2×C8—22no—
170C2×C8—41no—
171C2×C8—42no—
172C2×C8C22⋊C4×C12711yescharacteristic
173C2×C8C22⋊C4×C12711yescharacteristic
174C2×C8C22×C4×C12711yescharacteristic
175C2×C8C2×D4×C12711yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C22⋊C4—42no—
183C42—42no—
184C42C22⋊C4×C12711yescharacteristic
185C42C22⋊C4×C12711yescharacteristic
186C42D8×C12711yescharacteristic
187C42D8×C12711yescharacteristic
188C16—42no—
189C23C2×SD16×C12711yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—82no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4#102×C12711yescharacteristic
200C2×C4#102×C12711yescharacteristic
201C2×C4#102×C12711yescharacteristic
202C2×C4#102×C12711yescharacteristic
203C2×C4C2×C22⋊C4×C12711yescharacteristic
204C2×C4C2×D8×C12711yescharacteristic
205C8—21no—
206C8—21no—
207C8—21no—
208C8—44no—
209C8#104×C12712yes—
210C22—21no—
211C22—21no—
212C22—21no—
213C22C2×#102×C12711yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—82no—
218C4—82no—
219C4#359×C12712yes—
220C4#362×C12712yes—
221C4#410×C12711yescharacteristic
222C4C2×#104×C12711yescharacteristic
223C2—41no—
224C2C127×#150211yescharacteristic
225C2C2×#359×C12711yescharacteristic
226C2C2×#362×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×#102
prime radicalC23×C127C2×SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
109. #11748C127direct (N × H)
118. C127#11748direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31702
C127×#21622
C4×#108×C1272
C127×#13502
#11748127