Finite Group Databasebeta

← C127×#10036 #44573709

Subgroups — C127×#10036 #44573709

Order 32512.

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

normal subgroups only

This group has 528 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×#3162C211yesmaximal, characteristic, complemented
2C127×#3101C212yesmaximal
3C127×#1955C211yesmaximal, characteristic
4C127×#1481C212yesmaximal, complemented
5C127×#1275C211yesmaximal, characteristic, complemented
6#533×C127C2212yes—
7C2×C4×D4×C127C2211yescharacteristic
8#501×C127—22no—
9#501×C127—22no—
10#483×C127—22no—
11#476×C127—22no—
12#461×C127—22no—
13#450×C127—22no—
14C4×SD16×C127—24no—
15#431×C127C2212yes—
16#427×C127—22no—
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×C22⋊C8×C127—22no—
19C2×#97×C127C2211yescharacteristic
20Q8⋊C8×C127—24no—
21C22×D4×C127D411yescharacteristic
22C23×C4×C127—21no—
23C2×SD16×C127—24no—
24C22×C8×C127—21no—
25C22×C8×C127D412yes—
26C4⋊Q8×C127D412yes—
27C4⋊Q8×C127D412yes—
28#125×C127—22no—
29C22⋊Q8×C127—22no—
30C22⋊Q8×C127—22no—
31C4×Q8×C127—22no—
32C4×Q8×C127—22no—
33C4×D4×C127—22no—
34C4×D4×C127—22no—
35#117×C127—22no—
36C2×C4⋊C4×C127D411yescharacteristic
37C2×C22⋊C4×C127—21no—
38C2×C42×C127C2311yescharacteristic
39#107×C127—22no—
40#107×C127—22no—
41#106×C127—24no—
42#106×C127—24no—
43C4⋊C8×C127—22no—
44C4⋊C8×C127—22no—
45#103×C127—24no—
46#102×C127—24no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—44no—
49#97×C127—22no—
50C4×C8×C127D414yes—
51C24×C127—21no—
52C2×Q8×C127—22no—
53C2×Q8×C127—22no—
54C2×D4×C127—22no—
55C2×D4×C127—42no—
56C22×C4×C127—21no—
57C22×C4×C127—41no—
58C22×C4×C127—41no—
59C22×C4×C127—42no—
60C22×C4×C127—42no—
61C22×C4×C127C2×D411yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63C22×C4×C127#4111yescharacteristic
64SD16×C127—48no—
65C2×C8×C127—22no—
66C2×C8×C127—22no—
67C2×C8×C127—24no—
68C2×C8×C127—41no—
69C2×C8×C127—42no—
70C2×C8×C127SD1614yescomplemented
71C4⋊C4×C127—22no—
72C4⋊C4×C127—22no—
73C4⋊C4×C127—22no—
74C4⋊C4×C127—22no—
75C4⋊C4×C127—22no—
76C4⋊C4×C127—42no—
77C4⋊C4×C127—42no—
78C22⋊C4×C127—42no—
79C22⋊C4×C127—42no—
80C42×C127—42no—
81C42×C127C2×D412yes—
82C42×C127C2×D412yes—
83C23×C127—22no—
84C23×C127—41no—
85C23×C127—42no—
86C23×C127—41no—
87C23×C127—42no—
88C23×C127#12111yescharacteristic
89Q8×C127—44no—
90Q8×C127—44no—
91D4×C127—24no—
92D4×C127—42no—
93C2×C4×C127—41no—
94C2×C4×C127—41no—
95C2×C4×C127—42no—
96C2×C4×C127—42no—
97C2×C4×C127—41no—
98C2×C4×C127—42no—
99C2×C4×C127—82no—
100C2×C4×C127—81no—
101C2×C4×C127—81no—
102C2×C4×C127#12012yes—
103C2×C4×C127#12011yescharacteristic
104C2×C4×C127#12112yes—
105C2×C4×C127#12711yescharacteristic
106C2×C4×C127C2×SD1612yes—
107C2×C4×C127#13712yes—
108C8×C127—24no—
109C8×C127—44no—
110C8×C127—81no—
111C22×C127—21no—
112C22×C127—21no—
113C22×C127—44no—
114C22×C127—42no—
115C22×C127—82no—
116C22×C127—81no—
117C22×C127—81no—
118C22×C127#39211yescharacteristic
119C22×C127#46112yes—
120C4×C127—22no—
121C4×C127—22no—
122C4×C127—82no—
123C4×C127—81no—
124C4×C127—82no—
125C4×C127#44812yes—
126C4×C127#49211yescharacteristic
127C4×C127#49711yescharacteristic
128#10036C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—22no—
130C2×C127—82no—
131C2×C127#201011yescharacteristic
132C2×C127#201311yescharacteristic
133C2×C127#201711yescharacteristic
134#3162C2×C12711yescharacteristic, complemented
135#3101C2×C12712yes—
136#1955C2×C12711yescharacteristic
137#1481C2×C12712yescomplemented
138#1275C2×C12711yescharacteristic, complemented
139C127#1003611yescharacteristic, direct product factor, Sylow
140#533C22×C12712yes—
141C2×C4×D4C22×C12711yescharacteristic
142#501—22no—
143#501—22no—
144#483—22no—
145#476—22no—
146#461—22no—
147#450—22no—
148C4×SD16—24no—
149#431C22×C12712yes—
150#427—22no—
151C2×C4⋊C8C22×C12711yescharacteristic
152C2×C22⋊C8—22no—
153C2×#97C22×C12711yescharacteristic
154Q8⋊C8—24no—
155C22×D4D4×C12711yescharacteristic
156C23×C4—21no—
157C2×SD16—24no—
158C22×C8—21no—
159C22×C8D4×C12712yes—
160C4⋊Q8D4×C12712yes—
161C4⋊Q8D4×C12712yes—
162#125—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×D4—22no—
168C4×D4—22no—
169#117—22no—
170C2×C4⋊C4D4×C12711yescharacteristic
171C2×C22⋊C4—21no—
172C2×C42C23×C12711yescharacteristic
173#107—22no—
174#107—22no—
175#106—24no—
176#106—24no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179#103—24no—
180#102—24no—
181C22⋊C8—22no—
182C22⋊C8—44no—
183#97—22no—
184C4×C8D4×C12714yes—
185C24—21no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×D4—22no—
189C2×D4—42no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4C2×D4×C12711yescharacteristic
196C22×C4C2×D4×C12711yescharacteristic
197C22×C4#41×C12711yescharacteristic
198SD16—48no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—24no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8SD16×C12714yescomplemented
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C42—42no—
215C42C2×D4×C12712yes—
216C42C2×D4×C12712yes—
217C23—22no—
218C23—41no—
219C23—42no—
220C23—41no—
221C23—42no—
222C23#121×C12711yescharacteristic
223Q8—44no—
224Q8—44no—
225D4—24no—
226D4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—81no—
234C2×C4—82no—
235C2×C4—81no—
236C2×C4#120×C12712yes—
237C2×C4#120×C12711yescharacteristic
238C2×C4#121×C12712yes—
239C2×C4#127×C12711yescharacteristic
240C2×C4C2×SD16×C12712yes—
241C2×C4#137×C12712yes—
242C8—24no—
243C8—44no—
244C8—81no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#392×C12711yescharacteristic
253C22#461×C12712yes—
254C4—22no—
255C4—22no—
256C4—82no—
257C4—81no—
258C4—82no—
259C4#448×C12712yes—
260C4#492×C12711yescharacteristic
261C4#497×C12711yescharacteristic
262C2—22no—
263C2—82no—
264C2C127×#201011yescharacteristic
265C2C127×#201311yescharacteristic
266C2C127×#201711yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#392
prime radicalC22×D4×C127D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3162C2semidirect
4. C127×#1481C2semidirect
5. C127×#1275C2semidirect
70. C2×C8×C127SD16semidirect
128. #10036C127direct (N × H)
134. #3162C2×C127semidirect
137. #1481C2×C127semidirect
138. #1275C2×C127semidirect
139. C127#10036direct (N × H)
204. C2×C8SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31622
C127×#31012
C127×#19552
C127×#14812
C127×#12752
#10036127