Finite Group Databasebeta

← C127×#11835 #44575508

Subgroups — C127×#11835 #44575508

Order 32512.

340 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2634C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic
3C127×#1467C211yesmaximal, characteristic
4C127×#1353C212yesmaximal
5C127×#1346C212yesmaximal
6C2×#125×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#432×C127—21no—
9#423×C127—21no—
10C2×#101×C127—21no—
11#400×C127—21no—
12#400×C127C411yescharacteristic
13#400×C127C2211yescharacteristic
14#398×C127C411yescharacteristic
15#398×C127C2211yescharacteristic
16#395×C127—21no—
17#387×C127—21no—
18#387×C127—21no—
19#383×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×Q8×C127D411yescharacteristic
24C2×M16×C127—22no—
25#125×C127—41no—
26#125×C127—41no—
27C4×Q8×C127—41no—
28C4×Q8×C127—41no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127D411yescharacteristic
37C2×C4⋊C4×C127C2311yescharacteristic
38C2×C42×C127C2×C411yescharacteristic
39C2×C42×C127D411yescharacteristic
40C2×C42×C127D411yescharacteristic
41C4⋊C8×C127—41no—
42C4⋊C8×C127—41no—
43C4⋊C8×C127—41no—
44#101×C127—42no—
45C22⋊C8×C127—22no—
46#97×C127—41no—
47#95×C127—21no—
48#95×C127—21no—
49#95×C127—21no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C2×Q8×C127—21no—
58C2×Q8×C127—21no—
59C2×Q8×C127—41no—
60C2×Q8×C127—41no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127C22⋊C411yescharacteristic
66C22×C4×C127C22⋊C411yescharacteristic
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22×C411yescharacteristic
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72M16×C127—42no—
73M16×C127—42no—
74C2×C8×C127—42no—
75C2×C8×C127—42no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—42no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C42×C127—21no—
88C42×C127—21no—
89C42×C127—21no—
90C42×C127—21no—
91C42×C127—21no—
92C42×C127—21no—
93C23×C127C2×C22⋊C411yescharacteristic
94Q8×C127—42no—
95Q8×C127—42no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—42no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127#9911yescharacteristic
123C2×C4×C127#9911yescharacteristic
124C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C127#13711yescharacteristic
126C8×C127—82no—
127C8×C127—82no—
128C22×C127—21no—
129C22×C127—21no—
130C22×C127C2×#9911yescharacteristic
131C22×C127#41711yescharacteristic
132C22×C127#42111yescharacteristic
133C4×C127—21no—
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—41no—
138C4×C127—41no—
139C4×C127—41no—
140C4×C127—41no—
141C4×C127—41no—
142C4×C127—81no—
143C4×C127—81no—
144C4×C127—81no—
145C4×C127—81no—
146#11835C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—21no—
148C2×C127—21no—
149C2×C127#151311yescharacteristic
150C2×C127#212311yescharacteristic
151C2×C127#213311yescharacteristic
152#2634C2×C12711yescharacteristic
153#1801C2×C12711yescharacteristic
154#1467C2×C12711yescharacteristic
155#1353C2×C12712yes—
156#1346C2×C12712yes—
157C127#1183511yescharacteristic, direct product factor, Sylow
158C2×#125C4×C12711yescharacteristic
159C2×C4×Q8C22×C12711yescharacteristic
160#432—21no—
161#423—21no—
162C2×#101—21no—
163#400—21no—
164#400C4×C12711yescharacteristic
165#400C22×C12711yescharacteristic
166#398C4×C12711yescharacteristic
167#398C22×C12711yescharacteristic
168#395—21no—
169#387—21no—
170#387—21no—
171#383C4×C12711yescharacteristic
172#343C22×C12712yes—
173#324—21no—
174#324C22×C12712yes—
175C22×Q8D4×C12711yescharacteristic
176C2×M16—22no—
177#125—41no—
178#125—41no—
179C4×Q8—41no—
180C4×Q8—41no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×C4×C12711yescharacteristic
186C2×C4⋊C4C2×C4×C12711yescharacteristic
187C2×C4⋊C4C2×C4×C12711yescharacteristic
188C2×C4⋊C4D4×C12711yescharacteristic
189C2×C4⋊C4C23×C12711yescharacteristic
190C2×C42C2×C4×C12711yescharacteristic
191C2×C42D4×C12711yescharacteristic
192C2×C42D4×C12711yescharacteristic
193C4⋊C8—41no—
194C4⋊C8—41no—
195C4⋊C8—41no—
196#101—42no—
197C22⋊C8—22no—
198#97—41no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95C2×C4×C12711yescharacteristic
208#95C2×C4×C12711yescharacteristic
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—41no—
212C2×Q8—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4C22⋊C4×C12711yescharacteristic
218C22×C4C22⋊C4×C12711yescharacteristic
219C22×C4C22⋊C4×C12711yescharacteristic
220C22×C4C22⋊C4×C12711yescharacteristic
221C22×C4C22×C4×C12711yescharacteristic
222C22×C4C2×D4×C12711yescharacteristic
223C22×C4C2×D4×C12711yescharacteristic
224M16—42no—
225M16—42no—
226C2×C8—42no—
227C2×C8—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C23C2×C22⋊C4×C12711yescharacteristic
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4#99×C12711yescharacteristic
275C2×C4#99×C12711yescharacteristic
276C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
277C2×C4#137×C12711yescharacteristic
278C8—82no—
279C8—82no—
280C22—21no—
281C22—21no—
282C22C2×#99×C12711yescharacteristic
283C22#417×C12711yescharacteristic
284C22#421×C12711yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4—81no—
298C2—21no—
299C2—21no—
300C2C127×#151311yescharacteristic
301C2C127×#212311yescharacteristic
302C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
146. #11835C127direct (N × H)
157. C127#11835direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26342
C127×#18012
C127×#14672
C127×#13532
C127×#13462
#11835127