Finite Group Databasebeta

← C127×#8472 #44572145

Subgroups — C127×#8472 #44572145

Order 32512.

834 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 150 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×#3508C211yesmaximal, characteristic
2C127×#1965C212yesmaximal, complemented
3C127×#1561C211yesmaximal, characteristic, complemented
4C127×#1526C211yesmaximal, characteristic, complemented
5C127×#1489C212yesmaximal, complemented
6#559×C127—22no—
7#550×C127—22no—
8#546×C127—24no—
9#540×C127—22no—
10#535×C127C412yes—
11#533×C127C2211yescharacteristic
12#532×C127—22no—
13C2×#127×C127C2211yescharacteristic
14#518×C127C412yes—
15C4×#41×C127C2211yescharacteristic
16#423×C127C2212yes—
17C2×#100×C127—24no—
18C4×M16×C127C2212yes—
19#332×C127—22no—
20#330×C127—22no—
21Q8⋊C8×C127—22no—
22D4⋊C8×C127—22no—
23C2×#41×C127—24no—
24C2×#41×C127C2×C411yescharacteristic
25C22×D4×C127C2×C412yes—
26C22×D4×C127D414yes—
27C2×M16×C127—22no—
28C2×M16×C127—22no—
29C4⋊Q8×C127D412yes—
30#127×C127—22no—
31#127×C127—21no—
32#127×C127—21no—
33#127×C127—22no—
34#125×C127D412yes—
35#124×C127—24no—
36#124×C127—22no—
37#123×C127—28no—
38C22⋊Q8×C127—22no—
39#121×C127—24no—
40#121×C127—28no—
41#121×C127—24no—
42#120×C127—24no—
43C4×Q8×C127—22no—
44C4×Q8×C127D412yes—
45C4×D4×C127—24no—
46C4×D4×C127—22no—
47C4×D4×C127—24no—
48C4×D4×C127—24no—
49C4×D4×C127D412yes—
50#117×C127—21no—
51#117×C127C2×C411yescharacteristic
52#117×C127C2×C412yes—
53C2×C22⋊C4×C127—24no—
54C2×C42×C127—21no—
55C2×C42×C127C2311yescharacteristic
56C4⋊C8×C127—22no—
57C4⋊C8×C127—22no—
58#100×C127—48no—
59#97×C127—22no—
60C4×C8×C127—22no—
61C24×C127C22⋊C414yes—
62#41×C127—42no—
63#41×C127—84no—
64#41×C127—84no—
65C2×Q8×C127—22no—
66C2×Q8×C127C22⋊C411yescharacteristic
67C2×D4×C127—21no—
68C2×D4×C127—28no—
69C2×D4×C127—22no—
70C2×D4×C127—22no—
71C2×D4×C127—24no—
72C2×D4×C127—24no—
73C2×D4×C127—44no—
74C2×D4×C127—44no—
75C2×D4×C127—44no—
76C2×D4×C127C22⋊C411yescharacteristic
77C22×C4×C127—28no—
78C22×C4×C127—21no—
79C22×C4×C127—22no—
80C22×C4×C127C22×C411yescharacteristic
81C22×C4×C127C2×D412yes—
82M16×C127—24no—
83M16×C127—42no—
84M16×C127—44no—
85C2×C8×C127—42no—
86C2×C8×C127—42no—
87C4⋊C4×C127—22no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—24no—
90C4⋊C4×C127C22⋊C412yes—
91C4⋊C4×C127C22⋊C414yes—
92C22⋊C4×C127—28no—
93C22⋊C4×C127—28no—
94C22⋊C4×C127—21no—
95C22⋊C4×C127—22no—
96C22⋊C4×C127—22no—
97C42×C127—21no—
98C42×C127—22no—
99C42×C127—22no—
100C42×C127C2×D412yes—
101C42×C127C2×D411yescharacteristic
102C42×C127C2×D411yescharacteristic
103C23×C127—24no—
104C23×C127—21no—
105C23×C127—48no—
106C23×C127—44no—
107C23×C127C2×C22⋊C411yescharacteristic
108Q8×C127—22no—
109Q8×C127—42no—
110Q8×C127—42no—
111D4×C127—22no—
112D4×C127—44no—
113D4×C127—42no—
114D4×C127—44no—
115D4×C127—44no—
116D4×C127—44no—
117D4×C127—84no—
118D4×C127—88no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—21no—
123C2×C4×C127—22no—
124C2×C4×C127—24no—
125C2×C4×C127—42no—
126C2×C4×C127—42no—
127C2×C4×C127—42no—
128C2×C4×C127—88no—
129C2×C4×C127C2×C22⋊C411yescharacteristic
130C2×C4×C127C2×C22⋊C411yescharacteristic
131C2×C4×C127#12012yes—
132C2×C4×C127#12012yes—
133C8×C127—44no—
134C8×C127—82no—
135C22×C127—22no—
136C22×C127—21no—
137C22×C127—42no—
138C22×C127—48no—
139C22×C127—41no—
140C22×C127—44no—
141C22×C127—164no—
142C22×C127#37911yescharacteristic
143C4×C127—22no—
144C4×C127—21no—
145C4×C127—42no—
146C4×C127—44no—
147C4×C127—41no—
148C4×C127#41312yes—
149C4×C127#45312yes—
150C4×C127#45512yes—
151#8472C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—41no—
153C2×C127—81no—
154C2×C127—84no—
155C2×C127#178511yescharacteristic
156C2×C127#179212yes—
157#3508C2×C12711yescharacteristic
158#1965C2×C12712yescomplemented
159#1561C2×C12711yescharacteristic, complemented
160#1526C2×C12711yescharacteristic, complemented
161#1489C2×C12712yescomplemented
162C127#847211yescharacteristic, direct product factor, Sylow
163#559—22no—
164#550—22no—
165#546—24no—
166#540—22no—
167#535C4×C12712yes—
168#533C22×C12711yescharacteristic
169#532—22no—
170C2×#127C22×C12711yescharacteristic
171#518C4×C12712yes—
172C4×#41C22×C12711yescharacteristic
173#423C22×C12712yes—
174C2×#100—24no—
175C4×M16C22×C12712yes—
176#332—22no—
177#330—22no—
178Q8⋊C8—22no—
179D4⋊C8—22no—
180C2×#41—24no—
181C2×#41C2×C4×C12711yescharacteristic
182C22×D4C2×C4×C12712yes—
183C22×D4D4×C12714yes—
184C2×M16—22no—
185C2×M16—22no—
186C4⋊Q8D4×C12712yes—
187#127—22no—
188#127—21no—
189#127—21no—
190#127—22no—
191#125D4×C12712yes—
192#124—24no—
193#124—22no—
194#123—28no—
195C22⋊Q8—22no—
196#121—24no—
197#121—28no—
198#121—24no—
199#120—24no—
200C4×Q8—22no—
201C4×Q8D4×C12712yes—
202C4×D4—24no—
203C4×D4—22no—
204C4×D4—24no—
205C4×D4—24no—
206C4×D4D4×C12712yes—
207#117—21no—
208#117C2×C4×C12711yescharacteristic
209#117C2×C4×C12712yes—
210C2×C22⋊C4—24no—
211C2×C42—21no—
212C2×C42C23×C12711yescharacteristic
213C4⋊C8—22no—
214C4⋊C8—22no—
215#100—48no—
216#97—22no—
217C4×C8—22no—
218C24C22⋊C4×C12714yes—
219#41—42no—
220#41—84no—
221#41—84no—
222C2×Q8—22no—
223C2×Q8C22⋊C4×C12711yescharacteristic
224C2×D4—21no—
225C2×D4—28no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—24no—
229C2×D4—24no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4—44no—
233C2×D4C22⋊C4×C12711yescharacteristic
234C22×C4—28no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4C22×C4×C12711yescharacteristic
238C22×C4C2×D4×C12712yes—
239M16—24no—
240M16—42no—
241M16—44no—
242C2×C8—42no—
243C2×C8—42no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—24no—
247C4⋊C4C22⋊C4×C12712yes—
248C4⋊C4C22⋊C4×C12714yes—
249C22⋊C4—28no—
250C22⋊C4—28no—
251C22⋊C4—21no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C42—21no—
255C42—22no—
256C42—22no—
257C42C2×D4×C12712yes—
258C42C2×D4×C12711yescharacteristic
259C42C2×D4×C12711yescharacteristic
260C23—24no—
261C23—21no—
262C23—44no—
263C23—48no—
264C23C2×C22⋊C4×C12711yescharacteristic
265Q8—22no—
266Q8—42no—
267Q8—42no—
268D4—22no—
269D4—44no—
270D4—42no—
271D4—44no—
272D4—44no—
273D4—44no—
274D4—84no—
275D4—88no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—88no—
286C2×C4C2×C22⋊C4×C12711yescharacteristic
287C2×C4C2×C22⋊C4×C12711yescharacteristic
288C2×C4#120×C12712yes—
289C2×C4#120×C12712yes—
290C8—44no—
291C8—82no—
292C22—21no—
293C22—22no—
294C22—41no—
295C22—44no—
296C22—42no—
297C22—48no—
298C22—164no—
299C22#379×C12711yescharacteristic
300C4—21no—
301C4—22no—
302C4—41no—
303C4—42no—
304C4—44no—
305C4#413×C12712yes—
306C4#453×C12712yes—
307C4#455×C12712yes—
308C2—41no—
309C2—84no—
310C2—81no—
311C2C127×#178511yescharacteristic
312C2C127×#179212yes—
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3508C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1965C2semidirect
3. C127×#1561C2semidirect
4. C127×#1526C2semidirect
5. C127×#1489C2semidirect
151. #8472C127direct (N × H)
158. #1965C2×C127semidirect
159. #1561C2×C127semidirect
160. #1526C2×C127semidirect
161. #1489C2×C127semidirect
162. C127#8472direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35082
C127×#19652
C127×#15612
C127×#15262
C127×#14892
#8472127