Finite Group Databasebeta

← C127×#10334 #44574007

Subgroups — C127×#10334 #44574007

Order 32512.

754 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3195C211yesmaximal, characteristic
2C127×#2434C212yesmaximal
3C127×#1784C211yesmaximal, characteristic
4C127×#1508C212yesmaximal
5C127×#1297C211yesmaximal, characteristic
6C23×Q8×C127C2211yescharacteristic
7C2×C4⋊Q8×C127—22no—
8C2×C22⋊Q8×C127C2212yes—
9#483×C127—22no—
10#470×C127—22no—
11#451×C127—22no—
12C2×#101×C127—22no—
13#407×C127C2211yescharacteristic
14#407×C127C2211yescharacteristic
15#395×C127—24no—
16#391×C127—22no—
17#385×C127—24no—
18C4×C22⋊C4×C127C2212yes—
19#328×C127—24no—
20C22×Q8×C127—22no—
21C22×Q8×C127—21no—
22C22×Q8×C127—22no—
23C22×Q8×C127—21no—
24C22×Q8×C127—44no—
25C22×Q8×C127D412yes—
26C23×C4×C127D412yes—
27C23×C4×C127C2311yescharacteristic
28C2×Q16×C127—22no—
29C2×M16×C127—21no—
30C2×M16×C127D412yes—
31C4⋊Q8×C127—48no—
32C22⋊Q8×C127—22no—
33C22⋊Q8×C127—22no—
34C22⋊Q8×C127—22no—
35C22⋊Q8×C127—22no—
36C2×C4⋊C4×C127—28no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127D412yes—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—22no—
41C2×C42×C127—22no—
42#106×C127—22no—
43#103×C127—24no—
44#101×C127—44no—
45C22⋊C8×C127—22no—
46C22⋊C8×C127—22no—
47#95×C127—28no—
48#95×C127D414yes—
49C24×C127C2×D411yescharacteristic
50C2×Q8×C127—24no—
51C2×Q8×C127—28no—
52C2×Q8×C127—22no—
53C2×Q8×C127—22no—
54C2×Q8×C127—44no—
55C2×Q8×C127—42no—
56C2×Q8×C127—48no—
57C2×Q8×C127—44no—
58C2×Q8×C127—44no—
59C2×Q8×C127—41no—
60C2×Q8×C127—42no—
61C2×Q8×C127—41no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—44no—
68C22×C4×C127—42no—
69C22×C4×C127C2×D412yes—
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D412yes—
72C22×C4×C127#4111yescharacteristic
73Q16×C127—82no—
74M16×C127—42no—
75M16×C127—42no—
76C2×C8×C127—22no—
77C2×C8×C127—41no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—22no—
80C4⋊C4×C127—416no—
81C4⋊C4×C127—42no—
82C4⋊C4×C127—42no—
83C22⋊C4×C127—28no—
84C22⋊C4×C127—42no—
85C22⋊C4×C127—42no—
86C42×C127—44no—
87C23×C127—24no—
88C23×C127—41no—
89C23×C127#12012yes—
90C23×C127#12111yescharacteristic
91Q8×C127—44no—
92Q8×C127—48no—
93Q8×C127—44no—
94Q8×C127—44no—
95Q8×C127—82no—
96C2×C4×C127—24no—
97C2×C4×C127—22no—
98C2×C4×C127—28no—
99C2×C4×C127—28no—
100C2×C4×C127—24no—
101C2×C4×C127—42no—
102C2×C4×C127—41no—
103C2×C4×C127—44no—
104C2×C4×C127—44no—
105C2×C4×C127—42no—
106C2×C4×C127—42no—
107C2×C4×C127—44no—
108C2×C4×C127—44no—
109C2×C4×C127—42no—
110C2×C4×C127—42no—
111C2×C4×C127—44no—
112C2×C4×C127#12011yescharacteristic
113C2×C4×C127#12112yes—
114C2×C4×C127#12711yescharacteristic
115C8×C127—42no—
116C8×C127—81no—
117C22×C127—22no—
118C22×C127—22no—
119C22×C127—22no—
120C22×C127—21no—
121C22×C127—44no—
122C22×C127#39211yescharacteristic
123C22×C127#45614yes—
124C4×C127—21no—
125C4×C127—22no—
126C4×C127—48no—
127C4×C127—44no—
128C4×C127—82no—
129C4×C127—82no—
130C4×C127B(4,𝔽2)12yes—
131#10334C12711yesmaximal, characteristic, direct product factor, Sylow
132C2×C127—24no—
133C2×C127—41no—
134C2×C127#200512yes—
135C2×C127#202111yescharacteristic
136#3195C2×C12711yescharacteristic
137#2434C2×C12712yes—
138#1784C2×C12711yescharacteristic
139#1508C2×C12712yes—
140#1297C2×C12711yescharacteristic
141C127#1033411yescharacteristic, direct product factor, Sylow
142C23×Q8C22×C12711yescharacteristic
143C2×C4⋊Q8—22no—
144C2×C22⋊Q8C22×C12712yes—
145#483—22no—
146#470—22no—
147#451—22no—
148C2×#101—22no—
149#407C22×C12711yescharacteristic
150#407C22×C12711yescharacteristic
151#395—24no—
152#391—22no—
153#385—24no—
154C4×C22⋊C4C22×C12712yes—
155#328—24no—
156C22×Q8—22no—
157C22×Q8—21no—
158C22×Q8—22no—
159C22×Q8—21no—
160C22×Q8—44no—
161C22×Q8D4×C12712yes—
162C23×C4D4×C12712yes—
163C23×C4C23×C12711yescharacteristic
164C2×Q16—22no—
165C2×M16—21no—
166C2×M16D4×C12712yes—
167C4⋊Q8—48no—
168C22⋊Q8—22no—
169C22⋊Q8—22no—
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C2×C4⋊C4—28no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4D4×C12712yes—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C42—22no—
178#106—22no—
179#103—24no—
180#101—44no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183#95—28no—
184#95D4×C12714yes—
185C24C2×D4×C12711yescharacteristic
186C2×Q8—24no—
187C2×Q8—28no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—44no—
191C2×Q8—42no—
192C2×Q8—48no—
193C2×Q8—44no—
194C2×Q8—44no—
195C2×Q8—41no—
196C2×Q8—42no—
197C2×Q8—41no—
198C22×C4—24no—
199C22×C4—24no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—44no—
204C22×C4—42no—
205C22×C4C2×D4×C12712yes—
206C22×C4C2×D4×C12711yescharacteristic
207C22×C4C2×D4×C12712yes—
208C22×C4#41×C12711yescharacteristic
209Q16—82no—
210M16—42no—
211M16—42no—
212C2×C8—22no—
213C2×C8—41no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—416no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C22⋊C4—28no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C42—44no—
223C23—24no—
224C23—41no—
225C23#120×C12712yes—
226C23#121×C12711yescharacteristic
227Q8—44no—
228Q8—48no—
229Q8—44no—
230Q8—44no—
231Q8—82no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—28no—
235C2×C4—28no—
236C2×C4—24no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4#120×C12711yescharacteristic
249C2×C4#121×C12712yes—
250C2×C4#127×C12711yescharacteristic
251C8—42no—
252C8—81no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—44no—
258C22#392×C12711yescharacteristic
259C22#456×C12714yes—
260C4—21no—
261C4—22no—
262C4—48no—
263C4—44no—
264C4—82no—
265C4—82no—
266C4B(4,𝔽2)×C12712yes—
267C2—24no—
268C2—41no—
269C2C127×#200512yes—
270C2C127×#202111yescharacteristic
subgroupG/H
center, socleC22×C127#392
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
131. #10334C127direct (N × H)
141. C127#10334direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31952
C127×#24342
C127×#17842
C127×#15082
C127×#12972
#10334127