Finite Group Databasebeta

← C127×#11769 #44575442

Subgroups — C127×#11769 #44575442

Order 32512.

304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3173C211yesmaximal, characteristic
2C127×#2166C211yesmaximal, characteristic, complemented
3C127×#1747C211yesmaximal, characteristic, complemented
4C127×#1342C211yesmaximal, characteristic, complemented
5C127×#1341C211yesmaximal, characteristic
6C127×#1340C211yesmaximal, characteristic, complemented
7C127×#1339C211yesmaximal, characteristic
8#542×C127—21no—
9#498×C127C411yescharacteristic, complemented
10#495×C127C411yescharacteristic, complemented
11#489×C127—21no—
12#470×C127C2211yescharacteristic
13#469×C127C2211yescharacteristic
14#465×C127—21no—
15#442×C127C411yescharacteristic, complemented
16#441×C127C411yescharacteristic, complemented
17C4×SD16×C127—21no—
18#405×C127—21no—
19#405×C127C2211yescharacteristic
20#364×C127—21no—
21#349×C127C2211yescharacteristic
22#349×C127C2211yescharacteristic
23#347×C127—21no—
24#338×C127C2211yescharacteristic
25H(3,ℤ/4)×C127—21no—
26H(3,ℤ/4)×C127C2211yescharacteristic
27C2×Q16×C127C2×C411yescharacteristic
28C2×SD16×C127—21no—
29C2×D8×C127C2×C411yescharacteristic
30C2×M16×C127—21no—
31C2×M16×C127C2311yescharacteristic
32C22×C8×C127D411yescharacteristic
33C4⋊Q8×C127—21no—
34#126×C127—41no—
35#124×C127—21no—
36#124×C127—41no—
37#123×C127—41no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—41no—
40#121×C127—21no—
41C4×Q8×C127—21no—
42C4×D4×C127—21no—
43#117×C127—21no—
44#117×C127D411yescharacteristic
45M32×C127—21no—
46M32×C127—21no—
47#106×C127—21no—
48#106×C127C2×C411yescharacteristic
49#106×C127C2×C411yescharacteristic
50#103×C127—21no—
51#103×C127—21no—
52#102×C127—21no—
53#102×C127—21no—
54#97×C127—22no—
55#97×C127C2×C411yescharacteristic
56#97×C127D411yescharacteristic
57C4×C8×C127—22no—
58C4×C8×C127C2×C411yescharacteristic
59C4×C8×C127D411yescharacteristic
60C2×Q8×C127—21no—
61C2×Q8×C127—41no—
62C2×D4×C127—21no—
63C2×D4×C127—41no—
64C22×C4×C127—41no—
65C22×C4×C127C2×D411yescharacteristic
66Q16×C127—41no—
67SD16×C127—41no—
68SD16×C127—41no—
69D8×C127—41no—
70M16×C127—41no—
71M16×C127—41no—
72M16×C127—41no—
73C2×C8×C127—21no—
74C2×C8×C127—21no—
75C2×C8×C127—22no—
76C2×C8×C127C22⋊C411yescharacteristic
77C2×C8×C127C22⋊C411yescharacteristic
78C2×C8×C127C22×C411yescharacteristic
79C2×C8×C127C2×D411yescharacteristic
80C4⋊C4×C127—21no—
81C4⋊C4×C127—21no—
82C4⋊C4×C127—21no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C22⋊C4×C127—21no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C42×C127—22no—
95C42×C127—41no—
96C42×C127C22⋊C411yescharacteristic
97C42×C127C22⋊C411yescharacteristic
98C16×C127—41no—
99C16×C127—41no—
100C23×C127—41no—
101C23×C127AGL(1,ℤ/8)11yescharacteristic
102Q8×C127—41no—
103Q8×C127—41no—
104Q8×C127—161no—
105D4×C127—41no—
106D4×C127—41no—
107D4×C127—161no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—42no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—161no—
117C2×C4×C127C2×C22⋊C411yescharacteristic
118C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
119C8×C127—21no—
120C8×C127—21no—
121C8×C127—21no—
122C8×C127—42no—
123C8×C127#10411yescharacteristic
124C8×C127#10411yescharacteristic
125C22×C127—21no—
126C22×C127—41no—
127C22×C127—81no—
128C22×C127—81no—
129C22×C127—81no—
130C22×C127#41811yescharacteristic
131C4×C127—21no—
132C4×C127—41no—
133C4×C127—41no—
134C4×C127—81no—
135C4×C127—81no—
136C4×C127—82no—
137C4×C127—81no—
138C4×C127#41011yescharacteristic
139C4×C127C2×#10411yescharacteristic
140#11769C12711yesmaximal, characteristic, direct product factor, Sylow
141C2×C127—21no—
142C2×C127—41no—
143C2×C127—161no—
144C2×C127#150511yescharacteristic
145#3173C2×C12711yescharacteristic
146#2166C2×C12711yescharacteristic, complemented
147#1747C2×C12711yescharacteristic, complemented
148#1342C2×C12711yescharacteristic, complemented
149#1341C2×C12711yescharacteristic
150#1340C2×C12711yescharacteristic, complemented
151#1339C2×C12711yescharacteristic
152C127#1176911yescharacteristic, direct product factor, Sylow
153#542—21no—
154#498C4×C12711yescharacteristic, complemented
155#495C4×C12711yescharacteristic, complemented
156#489—21no—
157#470C22×C12711yescharacteristic
158#469C22×C12711yescharacteristic
159#465—21no—
160#442C4×C12711yescharacteristic, complemented
161#441C4×C12711yescharacteristic, complemented
162C4×SD16—21no—
163#405—21no—
164#405C22×C12711yescharacteristic
165#364—21no—
166#349C22×C12711yescharacteristic
167#349C22×C12711yescharacteristic
168#347—21no—
169#338C22×C12711yescharacteristic
170H(3,ℤ/4)—21no—
171H(3,ℤ/4)C22×C12711yescharacteristic
172C2×Q16C2×C4×C12711yescharacteristic
173C2×SD16—21no—
174C2×D8C2×C4×C12711yescharacteristic
175C2×M16—21no—
176C2×M16C23×C12711yescharacteristic
177C22×C8D4×C12711yescharacteristic
178C4⋊Q8—21no—
179#126—41no—
180#124—21no—
181#124—41no—
182#123—41no—
183C22⋊Q8—21no—
184C22⋊Q8—41no—
185#121—21no—
186C4×Q8—21no—
187C4×D4—21no—
188#117—21no—
189#117D4×C12711yescharacteristic
190M32—21no—
191M32—21no—
192#106—21no—
193#106C2×C4×C12711yescharacteristic
194#106C2×C4×C12711yescharacteristic
195#103—21no—
196#103—21no—
197#102—21no—
198#102—21no—
199#97—22no—
200#97C2×C4×C12711yescharacteristic
201#97D4×C12711yescharacteristic
202C4×C8—22no—
203C4×C8C2×C4×C12711yescharacteristic
204C4×C8D4×C12711yescharacteristic
205C2×Q8—21no—
206C2×Q8—41no—
207C2×D4—21no—
208C2×D4—41no—
209C22×C4—41no—
210C22×C4C2×D4×C12711yescharacteristic
211Q16—41no—
212SD16—41no—
213SD16—41no—
214D8—41no—
215M16—41no—
216M16—41no—
217M16—41no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—22no—
221C2×C8C22⋊C4×C12711yescharacteristic
222C2×C8C22⋊C4×C12711yescharacteristic
223C2×C8C22×C4×C12711yescharacteristic
224C2×C8C2×D4×C12711yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C22⋊C4—21no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C42—22no—
240C42—41no—
241C42C22⋊C4×C12711yescharacteristic
242C42C22⋊C4×C12711yescharacteristic
243C16—41no—
244C16—41no—
245C23—41no—
246C23AGL(1,ℤ/8)×C12711yescharacteristic
247Q8—41no—
248Q8—41no—
249Q8—161no—
250D4—41no—
251D4—41no—
252D4—161no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—161no—
262C2×C4C2×C22⋊C4×C12711yescharacteristic
263C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
264C8—21no—
265C8—21no—
266C8—21no—
267C8—42no—
268C8#104×C12711yescharacteristic
269C8#104×C12711yescharacteristic
270C22—21no—
271C22—41no—
272C22—81no—
273C22—81no—
274C22—81no—
275C22#418×C12711yescharacteristic
276C4—21no—
277C4—41no—
278C4—41no—
279C4—81no—
280C4—81no—
281C4—82no—
282C4—81no—
283C4#410×C12711yescharacteristic
284C4C2×#104×C12711yescharacteristic
285C2—21no—
286C2—41no—
287C2—161no—
288C2C127×#150511yescharacteristic
subgroupG/H
center, socleC2×C127#1505
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
prime radical#469×C127C22
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2166C2semidirect
3. C127×#1747C2semidirect
4. C127×#1342C2semidirect
6. C127×#1340C2semidirect
9. #498×C127C4semidirect
10. #495×C127C4semidirect
15. #442×C127C4semidirect
16. #441×C127C4semidirect
140. #11769C127direct (N × H)
146. #2166C2×C127semidirect
147. #1747C2×C127semidirect
148. #1342C2×C127semidirect
150. #1340C2×C127semidirect
152. C127#11769direct (N × H)
154. #498C4×C127semidirect
155. #495C4×C127semidirect
160. #442C4×C127semidirect
161. #441C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31732
C127×#21662
C127×#17472
C127×#13422
C127×#13412
C127×#13402
C127×#13392
#11769127