Finite Group Databasebeta

← C127×#11859 #44575532

Subgroups — C127×#11859 #44575532

Order 32512.

314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2163C211yesmaximal, characteristic
3C127×#1835C211yesmaximal, characteristic
4C127×#1348C214yesmaximal
5#533×C127—21no—
6#500×C127C411yescharacteristic, complemented
7#494×C127C411yescharacteristic, complemented
8#487×C127—21no—
9#467×C127—21no—
10#467×C127C2212yes—
11C4×Q16×C127—21no—
12C4×Q16×C127C412yescomplemented
13C2×C4×C8×C127C2211yescharacteristic
14#382×C127—21no—
15C4⋊C16×C127—21no—
16C22⋊C16×C127C2212yes—
17#346×C127—21no—
18#340×C127—21no—
19#340×C127C2212yes—
20C2×Q16×C127—21no—
21C2×Q16×C127C2×C412yes—
22C22×C8×C127D411yescharacteristic
23C22×C8×C127C2311yescharacteristic
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×C4⋊C4×C127—22no—
33C2×C42×C127D411yescharacteristic
34C2×C16×C127—22no—
35#107×C127—21no—
36#107×C127C2×C412yes—
37#103×C127—22no—
38#103×C127—22no—
39C4×C8×C127C2×C411yescharacteristic
40C4×C8×C127C2×C411yescharacteristic
41C4×C8×C127D411yescharacteristic
42C4×C8×C127D411yescharacteristic
43#95×C127—41no—
44#95×C127—41no—
45C2×Q8×C127—22no—
46C2×Q8×C127—41no—
47C22×C4×C127—42no—
48C22×C4×C127D811yescharacteristic
49C22×C4×C127D811yescharacteristic
50C22×C4×C127C2×D411yescharacteristic
51Q16×C127—42no—
52Q16×C127—42no—
53C2×C8×C127—41no—
54C2×C8×C127—41no—
55C2×C8×C127C22⋊C411yescharacteristic
56C2×C8×C127C22⋊C411yescharacteristic
57C2×C8×C127C22×C411yescharacteristic
58C2×C8×C127C2×D411yescharacteristic
59C4⋊C4×C127—22no—
60C4⋊C4×C127—42no—
61C4⋊C4×C127—42no—
62C4⋊C4×C127—41no—
63C4⋊C4×C127—41no—
64C4⋊C4×C127—42no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—42no—
67C22⋊C4×C127—42no—
68C42×C127—42no—
69C42×C127C22⋊C411yescharacteristic
70C42×C127C22⋊C411yescharacteristic
71C42×C127SD1611yescharacteristic
72C42×C127SD1611yescharacteristic
73C16×C127—42no—
74C23×C127C2×D811yescharacteristic
75Q8×C127—42no—
76Q8×C127—42no—
77Q8×C127—82no—
78C2×C4×C127—22no—
79C2×C4×C127—21no—
80C2×C4×C127—21no—
81C2×C4×C127—41no—
82C2×C4×C127—42no—
83C2×C4×C127—42no—
84C2×C4×C127—82no—
85C2×C4×C127—82no—
86C2×C4×C127—82no—
87C2×C4×C127#10211yescharacteristic
88C2×C4×C127#10211yescharacteristic
89C2×C4×C127#10211yescharacteristic
90C2×C4×C127#10211yescharacteristic
91C2×C4×C127C2×C22⋊C411yescharacteristic
92C2×C4×C127C2×SD1611yescharacteristic
93C8×C127—21no—
94C8×C127—21no—
95C8×C127—21no—
96C8×C127—21no—
97C22×C127—21no—
98C22×C127—21no—
99C22×C127C2×#10211yescharacteristic
100C22×C127#51012yes—
101C4×C127—21no—
102C4×C127—21no—
103C4×C127—21no—
104C4×C127—21no—
105C4×C127—21no—
106C4×C127—82no—
107C4×C127—82no—
108C4×C127—162no—
109C4×C127#41011yescharacteristic
110C4×C127#42111yescharacteristic
111#11859C12711yesmaximal, characteristic, direct product factor, Sylow
112C2×C127—22no—
113C2×C127#151711yescharacteristic
114C2×C127#214111yescharacteristic
115C2×C127#214511yescharacteristic
116#3170C2×C12711yescharacteristic
117#2163C2×C12711yescharacteristic
118#1835C2×C12711yescharacteristic
119#1348C2×C12714yes—
120C127#1185911yescharacteristic, direct product factor, Sylow
121#533—21no—
122#500C4×C12711yescharacteristic, complemented
123#494C4×C12711yescharacteristic, complemented
124#487—21no—
125#467—21no—
126#467C22×C12712yes—
127C4×Q16—21no—
128C4×Q16C4×C12712yescomplemented
129C2×C4×C8C22×C12711yescharacteristic
130#382—21no—
131C4⋊C16—21no—
132C22⋊C16C22×C12712yes—
133#346—21no—
134#340—21no—
135#340C22×C12712yes—
136C2×Q16—21no—
137C2×Q16C2×C4×C12712yes—
138C22×C8D4×C12711yescharacteristic
139C22×C8C23×C12711yescharacteristic
140C4⋊Q8—21no—
141C4⋊Q8—21no—
142#125—41no—
143C22⋊Q8—22no—
144C22⋊Q8—41no—
145C4×Q8—22no—
146C4×Q8—41no—
147#117—41no—
148C2×C4⋊C4—22no—
149C2×C42D4×C12711yescharacteristic
150C2×C16—22no—
151#107—21no—
152#107C2×C4×C12712yes—
153#103—22no—
154#103—22no—
155C4×C8C2×C4×C12711yescharacteristic
156C4×C8C2×C4×C12711yescharacteristic
157C4×C8D4×C12711yescharacteristic
158C4×C8D4×C12711yescharacteristic
159#95—41no—
160#95—41no—
161C2×Q8—22no—
162C2×Q8—41no—
163C22×C4—42no—
164C22×C4D8×C12711yescharacteristic
165C22×C4D8×C12711yescharacteristic
166C22×C4C2×D4×C12711yescharacteristic
167Q16—42no—
168Q16—42no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8C22⋊C4×C12711yescharacteristic
172C2×C8C22⋊C4×C12711yescharacteristic
173C2×C8C22×C4×C12711yescharacteristic
174C2×C8C2×D4×C12711yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C22⋊C4—42no—
184C42—42no—
185C42C22⋊C4×C12711yescharacteristic
186C42C22⋊C4×C12711yescharacteristic
187C42SD16×C12711yescharacteristic
188C42SD16×C12711yescharacteristic
189C16—42no—
190C23C2×D8×C12711yescharacteristic
191Q8—42no—
192Q8—42no—
193Q8—82no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—82no—
201C2×C4—82no—
202C2×C4—82no—
203C2×C4#102×C12711yescharacteristic
204C2×C4#102×C12711yescharacteristic
205C2×C4#102×C12711yescharacteristic
206C2×C4#102×C12711yescharacteristic
207C2×C4C2×C22⋊C4×C12711yescharacteristic
208C2×C4C2×SD16×C12711yescharacteristic
209C8—21no—
210C8—21no—
211C8—21no—
212C8—21no—
213C22—21no—
214C22—21no—
215C22C2×#102×C12711yescharacteristic
216C22#510×C12712yes—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—82no—
224C4—162no—
225C4#410×C12711yescharacteristic
226C4#421×C12711yescharacteristic
227C2—22no—
228C2C127×#151711yescharacteristic
229C2C127×#214111yescharacteristic
230C2C127×#214511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127C2×D8
LCSG ▷ C2×C8 ▷ C2×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
6. #500×C127C4semidirect
7. #494×C127C4semidirect
12. C4×Q16×C127C4semidirect
111. #11859C127direct (N × H)
120. C127#11859direct (N × H)
122. #500C4×C127semidirect
123. #494C4×C127semidirect
128. C4×Q16C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31702
C127×#21632
C127×#18352
C127×#13482
#11859127