Finite Group Databasebeta

← C127×#13608 #44577281

Subgroups — C127×#13608 #44577281

Order 32512.

308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3223C211yesmaximal, characteristic
2C127×#2133C211yesmaximal, characteristic
3C127×#2129C211yesmaximal, characteristic
4C127×#1414C212yesmaximal, complemented
5C127×#1407C212yesmaximal, complemented
6#541×C127C411yescharacteristic, complemented
7#536×C127C2211yescharacteristic
8#497×C127C2211yescharacteristic
9#494×C127C411yescharacteristic, complemented
10#491×C127C411yescharacteristic, complemented
11#488×C127C2211yescharacteristic
12#464×C127—21no—
13#462×C127—21no—
14#452×C127—21no—
15#451×C127—21no—
16#433×C127C411yescharacteristic, complemented
17C2×#101×C127—21no—
18#410×C127—21no—
19#356×C127—21no—
20#355×C127C2212yes—
21#354×C127—21no—
22#354×C127C2212yes—
23C2×#41×C127D411yescharacteristic
24C22×Q8×C127D411yescharacteristic
25C2×Q16×C127—21no—
26C2×Q16×C127—21no—
27C2×Q16×C127—21no—
28C2×SD16×C127—21no—
29C2×M16×C127—41no—
30C4⋊Q8×C127C2×C411yescharacteristic
31C4⋊Q8×C127C2×C411yescharacteristic
32C4⋊Q8×C127D411yescharacteristic
33#126×C127—41no—
34#125×C127—41no—
35#125×C127C2×C411yescharacteristic
36#124×C127D411yescharacteristic
37#124×C127C2311yescharacteristic
38#123×C127—41no—
39C22⋊Q8×C127—21no—
40C22⋊Q8×C127—41no—
41C4×Q8×C127—21no—
42#117×C127—41no—
43#117×C127C2×C411yescharacteristic
44C4⋊C8×C127—21no—
45#103×C127—21no—
46#103×C127—21no—
47#103×C127—21no—
48#102×C127—21no—
49#101×C127—22no—
50#101×C127—41no—
51#99×C127—22no—
52#99×C127—41no—
53C22⋊C8×C127—21no—
54#97×C127C2×C411yescharacteristic
55C4×C8×C127C2×C411yescharacteristic
56#41×C127—81no—
57C2×Q8×C127—21no—
58C2×Q8×C127—21no—
59C2×Q8×C127—81no—
60C2×Q8×C127C22⋊C411yescharacteristic
61C2×Q8×C127C22⋊C411yescharacteristic
62C2×Q8×C127C2×D411yescharacteristic
63C2×D4×C127—21no—
64C2×D4×C127C2×D411yescharacteristic
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127C22⋊C411yescharacteristic
68Q16×C127—81no—
69Q16×C127—81no—
70Q16×C127—81no—
71SD16×C127—81no—
72M16×C127—42no—
73M16×C127—81no—
74C2×C8×C127—21no—
75C2×C8×C127—21no—
76C2×C8×C127—81no—
77C4⋊C4×C127—21no—
78C4⋊C4×C127—21no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—81no—
86C22⋊C4×C127—21no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—42no—
91C42×C127—41no—
92C42×C127—81no—
93C42×C127C22⋊C411yescharacteristic
94C42×C127C22×C411yescharacteristic
95C23×C127—21no—
96C23×C127#9911yescharacteristic
97Q8×C127—41no—
98Q8×C127—41no—
99Q8×C127—41no—
100Q8×C127—41no—
101Q8×C127—41no—
102Q8×C127—81no—
103D4×C127—41no—
104D4×C127—81no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—82no—
118C2×C4×C127#9911yescharacteristic
119C2×C4×C127C2×C22⋊C411yescharacteristic
120C8×C127—41no—
121C8×C127—41no—
122C8×C127—82no—
123C22×C127—21no—
124C22×C127—41no—
125C22×C127—41no—
126C22×C127—81no—
127C22×C127C2×#9911yescharacteristic
128C4×C127—21no—
129C4×C127—21no—
130C4×C127—41no—
131C4×C127—41no—
132C4×C127—41no—
133C4×C127—41no—
134C4×C127—41no—
135C4×C127—81no—
136C4×C127—81no—
137C4×C127—162no—
138#13608C12711yesmaximal, characteristic, direct product factor, Sylow
139C2×C127—21no—
140C2×C127—41no—
141C2×C127—81no—
142C2×C127#212711yescharacteristic
143#3223C2×C12711yescharacteristic
144#2133C2×C12711yescharacteristic
145#2129C2×C12711yescharacteristic
146#1414C2×C12712yescomplemented
147#1407C2×C12712yescomplemented
148C127#1360811yescharacteristic, direct product factor, Sylow
149#541C4×C12711yescharacteristic, complemented
150#536C22×C12711yescharacteristic
151#497C22×C12711yescharacteristic
152#494C4×C12711yescharacteristic, complemented
153#491C4×C12711yescharacteristic, complemented
154#488C22×C12711yescharacteristic
155#464—21no—
156#462—21no—
157#452—21no—
158#451—21no—
159#433C4×C12711yescharacteristic, complemented
160C2×#101—21no—
161#410—21no—
162#356—21no—
163#355C22×C12712yes—
164#354—21no—
165#354C22×C12712yes—
166C2×#41D4×C12711yescharacteristic
167C22×Q8D4×C12711yescharacteristic
168C2×Q16—21no—
169C2×Q16—21no—
170C2×Q16—21no—
171C2×SD16—21no—
172C2×M16—41no—
173C4⋊Q8C2×C4×C12711yescharacteristic
174C4⋊Q8C2×C4×C12711yescharacteristic
175C4⋊Q8D4×C12711yescharacteristic
176#126—41no—
177#125—41no—
178#125C2×C4×C12711yescharacteristic
179#124D4×C12711yescharacteristic
180#124C23×C12711yescharacteristic
181#123—41no—
182C22⋊Q8—21no—
183C22⋊Q8—41no—
184C4×Q8—21no—
185#117—41no—
186#117C2×C4×C12711yescharacteristic
187C4⋊C8—21no—
188#103—21no—
189#103—21no—
190#103—21no—
191#102—21no—
192#101—22no—
193#101—41no—
194#99—22no—
195#99—41no—
196C22⋊C8—21no—
197#97C2×C4×C12711yescharacteristic
198C4×C8C2×C4×C12711yescharacteristic
199#41—81no—
200C2×Q8—21no—
201C2×Q8—21no—
202C2×Q8—81no—
203C2×Q8C22⋊C4×C12711yescharacteristic
204C2×Q8C22⋊C4×C12711yescharacteristic
205C2×Q8C2×D4×C12711yescharacteristic
206C2×D4—21no—
207C2×D4C2×D4×C12711yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4C22⋊C4×C12711yescharacteristic
211Q16—81no—
212Q16—81no—
213Q16—81no—
214SD16—81no—
215M16—42no—
216M16—81no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—81no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—81no—
229C22⋊C4—21no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C42—41no—
235C42—81no—
236C42C22⋊C4×C12711yescharacteristic
237C42C22×C4×C12711yescharacteristic
238C23—21no—
239C23#99×C12711yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—41no—
245Q8—81no—
246D4—41no—
247D4—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—82no—
261C2×C4#99×C12711yescharacteristic
262C2×C4C2×C22⋊C4×C12711yescharacteristic
263C8—41no—
264C8—41no—
265C8—82no—
266C22—21no—
267C22—41no—
268C22—41no—
269C22—81no—
270C22C2×#99×C12711yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—81no—
279C4—81no—
280C4—162no—
281C2—21no—
282C2—41no—
283C2—81no—
284C2C127×#212711yescharacteristic
subgroupG/H
center, socleC2×C127#2127
commutatorC42C22×C4×C127
Frattini, cosocle#124C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C22×C4×C127 ◁ #536×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1414C2semidirect
5. C127×#1407C2semidirect
6. #541×C127C4semidirect
9. #494×C127C4semidirect
10. #491×C127C4semidirect
16. #433×C127C4semidirect
138. #13608C127direct (N × H)
146. #1414C2×C127semidirect
147. #1407C2×C127semidirect
148. C127#13608direct (N × H)
149. #541C4×C127semidirect
152. #494C4×C127semidirect
153. #491C4×C127semidirect
159. #433C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32232
C127×#21332
C127×#21292
C127×#14142
C127×#14072
#13608127