Finite Group Databasebeta

← C127×#12114 #44575787

Subgroups — C127×#12114 #44575787

Order 32512.

474 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 70 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×#3192C211yesmaximal, characteristic, complemented
2C127×#2190C212yesmaximal, complemented
3C127×#2010C211yesmaximal, characteristic, complemented
4C127×#1339C212yesmaximal, complemented
5C127×#1320C211yesmaximal, characteristic, complemented
6#575×C127C2211yescharacteristic, complemented
7#525×C127—21no—
8C2×#121×C127—21no—
9#509×C127—22no—
10#481×C127—22no—
11#469×C127—21no—
12#469×C127C2212yes—
13#447×C127—22no—
14#421×C127—21no—
15#407×C127C2211yescharacteristic
16#360×C127—22no—
17#349×C127C2212yescomplemented
18H(3,ℤ/4)×C127C2211yescharacteristic, complemented
19C2×#41×C127—21no—
20C22×D4×C127—21no—
21C22×D4×C127—41no—
22C23×C4×C127D411yescharacteristic
23#137×C127—41no—
24AGL(1,ℤ/8)×C127—41no—
25#135×C127—22no—
26C2×D8×C127—21no—
27C2×D8×C127D412yescomplemented
28C2×M16×C127D411yescharacteristic
29C2×M16×C127C2311yescharacteristic
30#123×C127—41no—
31C22⋊Q8×C127—41no—
32#121×C127—22no—
33#121×C127—22no—
34#121×C127—41no—
35#121×C127—41no—
36#121×C127—41no—
37#120×C127—41no—
38C4×D4×C127—42no—
39#117×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C22⋊C4×C127—41no—
42SD32×C127—42no—
43D16×C127—42no—
44M32×C127—22no—
45#106×C127—21no—
46#106×C127D412yescomplemented
47#104×C127—42no—
48#102×C127—22no—
49#102×C127—22no—
50C22⋊C8×C127—22no—
51C24×C127—41no—
52C24×C127D811yescharacteristic
53#41×C127—41no—
54#41×C127—41no—
55#41×C127—41no—
56#41×C127—41no—
57C2×Q8×C127—21no—
58C2×D4×C127—21no—
59C2×D4×C127—22no—
60C2×D4×C127—41no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C2×D4×C127—41no—
64C2×D4×C127—42no—
65C2×D4×C127—81no—
66C2×D4×C127—81no—
67C2×D4×C127—84no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127—41no—
74C22×C4×C127D811yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76Q16×C127—22no—
77SD16×C127—42no—
78D8×C127—22no—
79D8×C127—42no—
80D8×C127—81no—
81M16×C127—41no—
82M16×C127—41no—
83C2×C8×C127—21no—
84C2×C8×C127C2×D412yes—
85C4⋊C4×C127—22no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—42no—
89C22⋊C4×C127—42no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—42no—
94C42×C127—22no—
95C16×C127—42no—
96C23×C127—21no—
97C23×C127—41no—
98C23×C127—42no—
99C23×C127—41no—
100C23×C127—42no—
101C23×C127—82no—
102C23×C127—82no—
103C23×C127—82no—
104C23×C127C2×D811yescharacteristic
105Q8×C127—41no—
106Q8×C127—41no—
107D4×C127—41no—
108D4×C127—42no—
109D4×C127—41no—
110D4×C127—42no—
111D4×C127—82no—
112D4×C127—84no—
113D4×C127—81no—
114D4×C127—84no—
115D4×C127—84no—
116D4×C127—81no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—42no—
124C2×C4×C127—41no—
125C2×C4×C127—42no—
126C2×C4×C127—81no—
127C2×C4×C127—81no—
128C2×C4×C127—82no—
129C2×C4×C127—81no—
130C2×C4×C127#12011yescharacteristic
131C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
132C8×C127—22no—
133C8×C127—41no—
134C22×C127—22no—
135C22×C127—21no—
136C22×C127—41no—
137C22×C127—41no—
138C22×C127—42no—
139C22×C127—41no—
140C22×C127—82no—
141C22×C127—82no—
142C22×C127—81no—
143C22×C127—82no—
144C22×C127—81no—
145C22×C127—82no—
146C22×C127—164no—
147C22×C127#44711yescharacteristic
148C4×C127—21no—
149C4×C127—41no—
150C4×C127—82no—
151C4×C127—82no—
152C4×C127—81no—
153C4×C127#45311yescharacteristic
154C4×C127B(4,𝔽2)11yescharacteristic
155#12114C12711yesmaximal, characteristic, direct product factor, Sylow
156C2×C127—21no—
157C2×C127—41no—
158C2×C127—42no—
159C2×C127—161no—
160C2×C127—162no—
161C2×C127#159511yescharacteristic
162#3192C2×C12711yescharacteristic, complemented
163#2190C2×C12712yescomplemented
164#2010C2×C12711yescharacteristic, complemented
165#1339C2×C12712yescomplemented
166#1320C2×C12711yescharacteristic, complemented
167C127#1211411yescharacteristic, direct product factor, Sylow
168#575C22×C12711yescharacteristic, complemented
169#525—21no—
170C2×#121—21no—
171#509—22no—
172#481—22no—
173#469—21no—
174#469C22×C12712yes—
175#447—22no—
176#421—21no—
177#407C22×C12711yescharacteristic
178#360—22no—
179#349C22×C12712yescomplemented
180H(3,ℤ/4)C22×C12711yescharacteristic, complemented
181C2×#41—21no—
182C22×D4—21no—
183C22×D4—41no—
184C23×C4D4×C12711yescharacteristic
185#137—41no—
186AGL(1,ℤ/8)—41no—
187#135—22no—
188C2×D8—21no—
189C2×D8D4×C12712yescomplemented
190C2×M16D4×C12711yescharacteristic
191C2×M16C23×C12711yescharacteristic
192#123—41no—
193C22⋊Q8—41no—
194#121—22no—
195#121—22no—
196#121—41no—
197#121—41no—
198#121—41no—
199#120—41no—
200C4×D4—42no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C22⋊C4—41no—
204SD32—42no—
205D16—42no—
206M32—22no—
207#106—21no—
208#106D4×C12712yescomplemented
209#104—42no—
210#102—22no—
211#102—22no—
212C22⋊C8—22no—
213C24—41no—
214C24D8×C12711yescharacteristic
215#41—41no—
216#41—41no—
217#41—41no—
218#41—41no—
219C2×Q8—21no—
220C2×D4—21no—
221C2×D4—22no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—42no—
227C2×D4—81no—
228C2×D4—81no—
229C2×D4—84no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4D8×C12711yescharacteristic
237C22×C4C2×D4×C12711yescharacteristic
238Q16—22no—
239SD16—42no—
240D8—22no—
241D8—42no—
242D8—81no—
243M16—41no—
244M16—41no—
245C2×C8—21no—
246C2×C8C2×D4×C12712yes—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C42—22no—
257C16—42no—
258C23—21no—
259C23—41no—
260C23—42no—
261C23—41no—
262C23—42no—
263C23—82no—
264C23—82no—
265C23—82no—
266C23C2×D8×C12711yescharacteristic
267Q8—41no—
268Q8—41no—
269D4—41no—
270D4—42no—
271D4—41no—
272D4—42no—
273D4—82no—
274D4—84no—
275D4—81no—
276D4—84no—
277D4—84no—
278D4—81no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—82no—
291C2×C4—81no—
292C2×C4#120×C12711yescharacteristic
293C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
294C8—22no—
295C8—41no—
296C22—22no—
297C22—21no—
298C22—41no—
299C22—41no—
300C22—42no—
301C22—41no—
302C22—82no—
303C22—82no—
304C22—81no—
305C22—82no—
306C22—81no—
307C22—82no—
308C22—164no—
309C22#447×C12711yescharacteristic
310C4—21no—
311C4—41no—
312C4—82no—
313C4—82no—
314C4—81no—
315C4#453×C12711yescharacteristic
316C4B(4,𝔽2)×C12711yescharacteristic
317C2—21no—
318C2—41no—
319C2—42no—
320C2—162no—
321C2—161no—
322C2C127×#159511yescharacteristic
subgroupG/H
center, socleC2×C127#1595
commutator, Frattini, cosocleC2×M16C23×C127
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3192C2semidirect
2. C127×#2190C2semidirect
3. C127×#2010C2semidirect
4. C127×#1339C2semidirect
5. C127×#1320C2semidirect
6. #575×C127C22semidirect
17. #349×C127C22semidirect
18. H(3,ℤ/4)×C127C22semidirect
27. C2×D8×C127D4semidirect
46. #106×C127D4semidirect
155. #12114C127direct (N × H)
162. #3192C2×C127semidirect
163. #2190C2×C127semidirect
164. #2010C2×C127semidirect
165. #1339C2×C127semidirect
166. #1320C2×C127semidirect
167. C127#12114direct (N × H)
168. #575C22×C127semidirect
179. #349C22×C127semidirect
180. H(3,ℤ/4)C22×C127semidirect
189. C2×D8D4×C127semidirect
208. #106D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31922
C127×#21902
C127×#20102
C127×#13392
C127×#13202
#12114127