Finite Group Databasebeta

← C127×#11650 #44575323

Subgroups — C127×#11650 #44575323

Order 32512.

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

normal subgroups only

This group has 304 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
3C127×#1564C211yesmaximal, characteristic
4C127×#1332C214yesmaximal, complemented
5#533×C127—21no—
6#500×C127C411yescharacteristic
7#494×C127C411yescharacteristic
8#487×C127—21no—
9#467×C127—21no—
10#467×C127C412yes—
11C4×Q16×C127—21no—
12C4×Q16×C127C2212yes—
13#431×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15C4⋊C16×C127—21no—
16C22⋊C16×C127—21no—
17C4×C16×C127C2212yes—
18#335×C127C2212yes—
19#334×C127—21no—
20C2×Q16×C127—21no—
21C2×Q16×C127C2×C412yes—
22C22×C8×C127C2×C411yescharacteristic
23C22×C8×C127D411yescharacteristic
24C4⋊Q8×C127—21no—
25C4⋊Q8×C127—21no—
26#125×C127—41no—
27C22⋊Q8×C127—22no—
28C22⋊Q8×C127—41no—
29C4×Q8×C127—22no—
30C4×Q8×C127—41no—
31#117×C127—41no—
32C2×C42×C127D411yescharacteristic
33C2×C16×C127—22no—
34#107×C127—21no—
35#107×C127C2×C412yes—
36C4⋊C8×C127—22no—
37#103×C127—22no—
38#103×C127—22no—
39C22⋊C8×C127—41no—
40C4×C8×C127—41no—
41C4×C8×C127C2×C411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127C2311yescharacteristic
45C2×Q8×C127—22no—
46C2×Q8×C127—41no—
47C22×C4×C127C22⋊C411yescharacteristic
48C22×C4×C127D811yescharacteristic
49C22×C4×C127SD1611yescharacteristic
50Q16×C127—24no—
51Q16×C127—42no—
52C2×C8×C127—22no—
53C2×C8×C127—41no—
54C2×C8×C127—42no—
55C2×C8×C127C22⋊C411yescharacteristic
56C2×C8×C127C22⋊C411yescharacteristic
57C2×C8×C127C22×C411yescharacteristic
58C2×C8×C127C2×D411yescharacteristic
59C4⋊C4×C127—22no—
60C4⋊C4×C127—41no—
61C4⋊C4×C127—41no—
62C4⋊C4×C127—42no—
63C4⋊C4×C127—41no—
64C4⋊C4×C127—42no—
65C22⋊C4×C127—42no—
66C42×C127—42no—
67C42×C127C22⋊C411yescharacteristic
68C42×C127D811yescharacteristic
69C42×C127SD1611yescharacteristic
70C42×C127C2×D411yescharacteristic
71C16×C127—42no—
72C23×C127#10211yescharacteristic
73Q8×C127—42no—
74Q8×C127—42no—
75Q8×C127—82no—
76C2×C4×C127—22no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—22no—
80C2×C4×C127—42no—
81C2×C4×C127—42no—
82C2×C4×C127#10211yescharacteristic
83C2×C4×C127#10211yescharacteristic
84C2×C4×C127#10211yescharacteristic
85C2×C4×C127C2×C22⋊C411yescharacteristic
86C2×C4×C127C2×D811yescharacteristic
87C2×C4×C127C2×SD1611yescharacteristic
88C8×C127—21no—
89C8×C127—21no—
90C8×C127—21no—
91C8×C127—82no—
92C8×C127#13112yes—
93C22×C127—21no—
94C22×C127—21no—
95C22×C127—21no—
96C22×C127C2×#10211yescharacteristic
97C4×C127—21no—
98C4×C127—21no—
99C4×C127—21no—
100C4×C127—82no—
101C4×C127—82no—
102C4×C127#35912yes—
103C4×C127#40811yescharacteristic
104C4×C127#42111yescharacteristic
105C4×C127#51012yes—
106#11650C12711yesmaximal, characteristic, direct product factor, Sylow
107C2×C127—41no—
108C2×C127#148011yescharacteristic
109C2×C127#214111yescharacteristic
110C2×C127C2×#35911yescharacteristic
111#3170C2×C12711yescharacteristic
112#2162C2×C12711yescharacteristic
113#1564C2×C12711yescharacteristic
114#1332C2×C12714yescomplemented
115C127#1165011yescharacteristic, direct product factor, Sylow
116#533—21no—
117#500C4×C12711yescharacteristic
118#494C4×C12711yescharacteristic
119#487—21no—
120#467—21no—
121#467C4×C12712yes—
122C4×Q16—21no—
123C4×Q16C22×C12712yes—
124#431—21no—
125C2×C4×C8C22×C12711yescharacteristic
126C4⋊C16—21no—
127C22⋊C16—21no—
128C4×C16C22×C12712yes—
129#335C22×C12712yes—
130#334—21no—
131C2×Q16—21no—
132C2×Q16C2×C4×C12712yes—
133C22×C8C2×C4×C12711yescharacteristic
134C22×C8D4×C12711yescharacteristic
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137#125—41no—
138C22⋊Q8—22no—
139C22⋊Q8—41no—
140C4×Q8—22no—
141C4×Q8—41no—
142#117—41no—
143C2×C42D4×C12711yescharacteristic
144C2×C16—22no—
145#107—21no—
146#107C2×C4×C12712yes—
147C4⋊C8—22no—
148#103—22no—
149#103—22no—
150C22⋊C8—41no—
151C4×C8—41no—
152C4×C8C2×C4×C12711yescharacteristic
153C4×C8D4×C12711yescharacteristic
154C4×C8D4×C12711yescharacteristic
155C4×C8C23×C12711yescharacteristic
156C2×Q8—22no—
157C2×Q8—41no—
158C22×C4C22⋊C4×C12711yescharacteristic
159C22×C4D8×C12711yescharacteristic
160C22×C4SD16×C12711yescharacteristic
161Q16—24no—
162Q16—42no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—42no—
166C2×C8C22⋊C4×C12711yescharacteristic
167C2×C8C22⋊C4×C12711yescharacteristic
168C2×C8C22×C4×C12711yescharacteristic
169C2×C8C2×D4×C12711yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C22⋊C4—42no—
177C42—42no—
178C42C22⋊C4×C12711yescharacteristic
179C42D8×C12711yescharacteristic
180C42SD16×C12711yescharacteristic
181C42C2×D4×C12711yescharacteristic
182C16—42no—
183C23#102×C12711yescharacteristic
184Q8—42no—
185Q8—42no—
186Q8—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4#102×C12711yescharacteristic
194C2×C4#102×C12711yescharacteristic
195C2×C4#102×C12711yescharacteristic
196C2×C4C2×C22⋊C4×C12711yescharacteristic
197C2×C4C2×D8×C12711yescharacteristic
198C2×C4C2×SD16×C12711yescharacteristic
199C8—21no—
200C8—21no—
201C8—21no—
202C8—82no—
203C8#131×C12712yes—
204C22—21no—
205C22—21no—
206C22—21no—
207C22C2×#102×C12711yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—82no—
212C4—82no—
213C4#359×C12712yes—
214C4#408×C12711yescharacteristic
215C4#421×C12711yescharacteristic
216C4#510×C12712yes—
217C2—41no—
218C2C127×#148011yescharacteristic
219C2C127×#214111yescharacteristic
220C2C2×#359×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
socleC22×C127C2×#102
prime radicalC23×C127#102
LCSG ▷ C2×C8 ▷ 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
4. C127×#1332C2semidirect
106. #11650C127direct (N × H)
114. #1332C2×C127semidirect
115. C127#11650direct (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
C127×#15642
C127×#13322
#11650127