Finite Group Databasebeta

← C127×#10523 #44574196

Subgroups — C127×#10523 #44574196

Order 32512.

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

normal subgroups only

This group has 382 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×#3249C211yesmaximal, characteristic
2C127×#1994C212yesmaximal
3C127×#1831C211yesmaximal, characteristic
4C127×#1550C212yesmaximal
5C127×#1292C211yesmaximal, characteristic
6#533×C127C2212yes—
7#477×C127—22no—
8#467×C127—22no—
9#462×C127—22no—
10#423×C127C2212yes—
11C2×C4⋊C8×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C43×C127C2211yescharacteristic
14#339×C127—22no—
15#339×C127—22no—
16#336×C127—22no—
17#333×C127—22no—
18#332×C127—22no—
19C2×Q16×C127—22no—
20C2×M16×C127—22no—
21C22×C8×C127—21no—
22C22×C8×C127D412yes—
23C4⋊Q8×C127D412yes—
24C4⋊Q8×C127D412yes—
25#125×C127—22no—
26C22⋊Q8×C127—22no—
27C22⋊Q8×C127—22no—
28C4×Q8×C127—22no—
29C4×Q8×C127—22no—
30#117×C127—22no—
31C2×C42×C127—21no—
32C2×C42×C127—21no—
33C2×C42×C127D411yescharacteristic
34C2×C42×C127D411yescharacteristic
35C2×C42×C127C2311yescharacteristic
36#107×C127—22no—
37C4⋊C8×C127—22no—
38C4⋊C8×C127—22no—
39C4⋊C8×C127—22no—
40C4⋊C8×C127—22no—
41#103×C127—24no—
42C2×Q8×C127—22no—
43C2×Q8×C127—22no—
44C22×C4×C127—21no—
45C22×C4×C127—21no—
46C22×C4×C127C2×D411yescharacteristic
47C22×C4×C127C2×D411yescharacteristic
48C22×C4×C127#4111yescharacteristic
49Q16×C127—82no—
50M16×C127—42no—
51M16×C127—42no—
52C2×C8×C127—22no—
53C2×C8×C127—42no—
54C2×C8×C127—42no—
55C2×C8×C127—41no—
56C2×C8×C127—42no—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—22no—
59C4⋊C4×C127—22no—
60C4⋊C4×C127—22no—
61C4⋊C4×C127—42no—
62C4⋊C4×C127—42no—
63C22⋊C4×C127—42no—
64C42×C127—21no—
65C42×C127—22no—
66C42×C127—41no—
67C42×C127—41no—
68C42×C127—42no—
69C42×C127—42no—
70C42×C127Q1612yescomplemented
71C42×C127C2×D412yes—
72C42×C127#4112yes—
73C23×C127#12111yescharacteristic
74Q8×C127—42no—
75Q8×C127—42no—
76Q8×C127—82no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—41no—
82C2×C4×C127—41no—
83C2×C4×C127—41no—
84C2×C4×C127—41no—
85C2×C4×C127—41no—
86C2×C4×C127—42no—
87C2×C4×C127—42no—
88C2×C4×C127#12011yescharacteristic
89C2×C4×C127#12112yes—
90C2×C4×C127#12312yes—
91C2×C4×C127#12411yescharacteristic
92C2×C4×C127C2×Q1611yescharacteristic
93C2×C4×C127#13511yescharacteristic
94C2×C4×C127#13712yes—
95C8×C127—42no—
96C8×C127—81no—
97C8×C127—82no—
98C22×C127—21no—
99C22×C127—21no—
100C22×C127#39411yescharacteristic
101C22×C127#46711yescharacteristic
102C22×C127#47011yescharacteristic
103C4×C127—22no—
104C4×C127—21no—
105C4×C127—42no—
106C4×C127—42no—
107C4×C127—82no—
108C4×C127—82no—
109C4×C127#45411yescharacteristic
110C4×C127#45511yescharacteristic
111C4×C127#46212yes—
112C4×C127#46412yes—
113#10523C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—21no—
115C2×C127—21no—
116C2×C127#204011yescharacteristic
117C2×C127#205011yescharacteristic
118C2×C127#205611yescharacteristic
119#3249C2×C12711yescharacteristic
120#1994C2×C12712yes—
121#1831C2×C12711yescharacteristic
122#1550C2×C12712yes—
123#1292C2×C12711yescharacteristic
124C127#1052311yescharacteristic, direct product factor, Sylow
125#533C22×C12712yes—
126#477—22no—
127#467—22no—
128#462—22no—
129#423C22×C12712yes—
130C2×C4⋊C8C22×C12711yescharacteristic
131C2×C4⋊C8C22×C12711yescharacteristic
132C43C22×C12711yescharacteristic
133#339—22no—
134#339—22no—
135#336—22no—
136#333—22no—
137#332—22no—
138C2×Q16—22no—
139C2×M16—22no—
140C22×C8—21no—
141C22×C8D4×C12712yes—
142C4⋊Q8D4×C12712yes—
143C4⋊Q8D4×C12712yes—
144#125—22no—
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149#117—22no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42D4×C12711yescharacteristic
153C2×C42D4×C12711yescharacteristic
154C2×C42C23×C12711yescharacteristic
155#107—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160#103—24no—
161C2×Q8—22no—
162C2×Q8—22no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C2×D4×C12711yescharacteristic
166C22×C4C2×D4×C12711yescharacteristic
167C22×C4#41×C12711yescharacteristic
168Q16—82no—
169M16—42no—
170M16—42no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—42no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—42no—
183C42—21no—
184C42—22no—
185C42—41no—
186C42—41no—
187C42—42no—
188C42—42no—
189C42Q16×C12712yescomplemented
190C42C2×D4×C12712yes—
191C42#41×C12712yes—
192C23#121×C12711yescharacteristic
193Q8—42no—
194Q8—42no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4#120×C12711yescharacteristic
208C2×C4#121×C12712yes—
209C2×C4#123×C12712yes—
210C2×C4#124×C12711yescharacteristic
211C2×C4C2×Q16×C12711yescharacteristic
212C2×C4#135×C12711yescharacteristic
213C2×C4#137×C12712yes—
214C8—42no—
215C8—81no—
216C8—82no—
217C22—21no—
218C22—21no—
219C22#394×C12711yescharacteristic
220C22#467×C12711yescharacteristic
221C22#470×C12711yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—82no—
227C4—82no—
228C4#454×C12711yescharacteristic
229C4#455×C12711yescharacteristic
230C4#462×C12712yes—
231C4#464×C12712yes—
232C2—21no—
233C2—21no—
234C2C127×#204011yescharacteristic
235C2C127×#205011yescharacteristic
236C2C127×#205611yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
70. C42×C127Q16semidirect
113. #10523C127direct (N × H)
124. C127#10523direct (N × H)
189. C42Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32492
C127×#19942
C127×#18312
C127×#15502
C127×#12922
#10523127