Finite Group Databasebeta

← C127×#10032 #44573705

Subgroups — C127×#10032 #44573705

Order 32512.

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

normal subgroups only

This group has 636 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×#3150C211yesmaximal, characteristic, complemented
2C127×#3100C212yesmaximal, complemented
3C127×#1955C211yesmaximal, characteristic, complemented
4C127×#1480C212yesmaximal, complemented
5C127×#1275C211yesmaximal, characteristic, complemented
6C2×#135×C127—22no—
7#532×C127C2212yes—
8C2×C4×D4×C127C2211yescharacteristic
9#497×C127—22no—
10#496×C127—22no—
11#480×C127—22no—
12#474×C127—22no—
13#459×C127—22no—
14#447×C127—22no—
15C4×D8×C127—24no—
16#431×C127C2212yes—
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×C22⋊C8×C127—22no—
19C2×#97×C127C2211yescharacteristic
20D4⋊C8×C127—24no—
21C2×#41×C127—22no—
22C22×D4×C127D411yescharacteristic
23C23×C4×C127—21no—
24#135×C127—44no—
25#135×C127—44no—
26C2×Q16×C127—22no—
27C2×SD16×C127—24no—
28C2×D8×C127—22no—
29C2×D8×C127—24no—
30C22×C8×C127—21no—
31C22×C8×C127D412yes—
32C4⋊Q8×C127D412yes—
33#127×C127D412yes—
34#124×C127—22no—
35#121×C127—22no—
36#121×C127—22no—
37C4×D4×C127—22no—
38C4×D4×C127—22no—
39C4×D4×C127—22no—
40C4×D4×C127—22no—
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C22⋊C4×C127—21no—
43C2×C42×C127C2311yescharacteristic
44#107×C127—24no—
45C4⋊C8×C127—22no—
46C4⋊C8×C127—22no—
47#102×C127—24no—
48#102×C127—24no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—44no—
51#97×C127—22no—
52C4×C8×C127D414yes—
53C24×C127—21no—
54#41×C127—44no—
55#41×C127—44no—
56C2×Q8×C127—22no—
57C2×D4×C127—22no—
58C2×D4×C127—22no—
59C2×D4×C127—22no—
60C2×D4×C127—22no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C22×C4×C127—21no—
64C22×C4×C127—41no—
65C22×C4×C127—41no—
66C22×C4×C127—42no—
67C22×C4×C127—42no—
68C22×C4×C127—42no—
69C22×C4×C127C2×D411yescharacteristic
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127#4111yescharacteristic
72Q16×C127—44no—
73SD16×C127—48no—
74D8×C127—44no—
75D8×C127—48no—
76C2×C8×C127—22no—
77C2×C8×C127—22no—
78C2×C8×C127—24no—
79C2×C8×C127—41no—
80C2×C8×C127—42no—
81C2×C8×C127D814yescomplemented
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—22no—
85C22⋊C4×C127—42no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—42no—
88C42×C127C2×D412yes—
89C42×C127C2×D412yes—
90C23×C127—22no—
91C23×C127—41no—
92C23×C127—42no—
93C23×C127—41no—
94C23×C127—42no—
95C23×C127—42no—
96C23×C127#12111yescharacteristic
97Q8×C127—44no—
98D4×C127—24no—
99D4×C127—42no—
100D4×C127—44no—
101D4×C127—44no—
102D4×C127—44no—
103D4×C127—84no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—41no—
107C2×C4×C127—42no—
108C2×C4×C127—42no—
109C2×C4×C127—82no—
110C2×C4×C127—81no—
111C2×C4×C127—82no—
112C2×C4×C127—81no—
113C2×C4×C127—82no—
114C2×C4×C127#12012yes—
115C2×C4×C127#12011yescharacteristic
116C2×C4×C127#12112yes—
117C2×C4×C127#12711yescharacteristic
118C2×C4×C127C2×D812yes—
119C2×C4×C127AGL(1,ℤ/8)12yes—
120C8×C127—24no—
121C8×C127—44no—
122C8×C127—81no—
123C22×C127—21no—
124C22×C127—21no—
125C22×C127—44no—
126C22×C127—42no—
127C22×C127—82no—
128C22×C127—81no—
129C22×C127—81no—
130C22×C127—82no—
131C22×C127—82no—
132C22×C127—82no—
133C22×C127#39211yescharacteristic
134C22×C127#45912yes—
135C4×C127—22no—
136C4×C127—22no—
137C4×C127—81no—
138C4×C127—82no—
139C4×C127#44712yes—
140C4×C127#49311yescharacteristic
141C4×C127#49611yescharacteristic
142#10032C12711yesmaximal, characteristic, direct product factor, Sylow
143C2×C127—22no—
144C2×C127—82no—
145C2×C127—162no—
146C2×C127#201011yescharacteristic
147C2×C127#201111yescharacteristic
148C2×C127#201711yescharacteristic
149#3150C2×C12711yescharacteristic, complemented
150#3100C2×C12712yescomplemented
151#1955C2×C12711yescharacteristic, complemented
152#1480C2×C12712yescomplemented
153#1275C2×C12711yescharacteristic, complemented
154C127#1003211yescharacteristic, direct product factor, Sylow
155C2×#135—22no—
156#532C22×C12712yes—
157C2×C4×D4C22×C12711yescharacteristic
158#497—22no—
159#496—22no—
160#480—22no—
161#474—22no—
162#459—22no—
163#447—22no—
164C4×D8—24no—
165#431C22×C12712yes—
166C2×C4⋊C8C22×C12711yescharacteristic
167C2×C22⋊C8—22no—
168C2×#97C22×C12711yescharacteristic
169D4⋊C8—24no—
170C2×#41—22no—
171C22×D4D4×C12711yescharacteristic
172C23×C4—21no—
173#135—44no—
174#135—44no—
175C2×Q16—22no—
176C2×SD16—24no—
177C2×D8—22no—
178C2×D8—24no—
179C22×C8—21no—
180C22×C8D4×C12712yes—
181C4⋊Q8D4×C12712yes—
182#127D4×C12712yes—
183#124—22no—
184#121—22no—
185#121—22no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4D4×C12711yescharacteristic
191C2×C22⋊C4—21no—
192C2×C42C23×C12711yescharacteristic
193#107—24no—
194C4⋊C8—22no—
195C4⋊C8—22no—
196#102—24no—
197#102—24no—
198C22⋊C8—22no—
199C22⋊C8—44no—
200#97—22no—
201C4×C8D4×C12714yes—
202C24—21no—
203#41—44no—
204#41—44no—
205C2×Q8—22no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—42no—
211C2×D4—42no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4C2×D4×C12711yescharacteristic
219C22×C4C2×D4×C12711yescharacteristic
220C22×C4#41×C12711yescharacteristic
221Q16—44no—
222SD16—48no—
223D8—44no—
224D8—48no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—24no—
228C2×C8—41no—
229C2×C8—42no—
230C2×C8D8×C12714yescomplemented
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C22⋊C4—42no—
237C42C2×D4×C12712yes—
238C42C2×D4×C12712yes—
239C23—22no—
240C23—41no—
241C23—42no—
242C23—41no—
243C23—42no—
244C23—42no—
245C23#121×C12711yescharacteristic
246Q8—44no—
247D4—24no—
248D4—42no—
249D4—44no—
250D4—44no—
251D4—44no—
252D4—84no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4—82no—
263C2×C4#120×C12712yes—
264C2×C4#120×C12711yescharacteristic
265C2×C4#121×C12712yes—
266C2×C4#127×C12711yescharacteristic
267C2×C4C2×D8×C12712yes—
268C2×C4AGL(1,ℤ/8)×C12712yes—
269C8—24no—
270C8—44no—
271C8—81no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22—81no—
278C22—81no—
279C22—82no—
280C22—82no—
281C22—82no—
282C22#392×C12711yescharacteristic
283C22#459×C12712yes—
284C4—22no—
285C4—22no—
286C4—81no—
287C4—82no—
288C4#447×C12712yes—
289C4#493×C12711yescharacteristic
290C4#496×C12711yescharacteristic
291C2—22no—
292C2—82no—
293C2—162no—
294C2C127×#201011yescharacteristic
295C2C127×#201111yescharacteristic
296C2C127×#201711yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#392
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×#3150C2semidirect
2. C127×#3100C2semidirect
3. C127×#1955C2semidirect
4. C127×#1480C2semidirect
5. C127×#1275C2semidirect
81. C2×C8×C127D8semidirect
142. #10032C127direct (N × H)
149. #3150C2×C127semidirect
150. #3100C2×C127semidirect
151. #1955C2×C127semidirect
152. #1480C2×C127semidirect
153. #1275C2×C127semidirect
154. C127#10032direct (N × H)
230. C2×C8D8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31502
C127×#31002
C127×#19552
C127×#14802
C127×#12752
#10032127