Finite Group Databasebeta

← C127×#13673 #44577346

Subgroups — C127×#13673 #44577346

Order 32512.

468 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 58 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×#3292C211yesmaximal, characteristic, complemented
2C127×#2196C212yesmaximal, complemented
3C127×#1619C211yesmaximal, characteristic, complemented
4C127×#1408C211yesmaximal, characteristic, complemented
5C127×#1402C212yesmaximal, complemented
6#576×C127—22no—
7D42×C127C2211yescharacteristic, complemented
8#493×C127C2211yescharacteristic
9#472×C127—22no—
10#459×C127—21no—
11B(4,𝔽2)×C127—22no—
12#453×C127—21no—
13#453×C127C2212yes—
14#443×C127—21no—
15#353×C127C2212yescomplemented
16AΣL(1,𝔽16)×C127—22no—
17#331×C127C2211yescharacteristic, complemented
18D4⋊C8×C127—21no—
19H(5,𝔽2)×C127—21no—
20H(5,𝔽2)×C127D412yescomplemented
21C22×D4×C127—41no—
22AGL(1,ℤ/8)×C127—22no—
23AGL(1,ℤ/8)×C127—22no—
24AGL(1,ℤ/8)×C127—42no—
25AGL(1,ℤ/8)×C127—42no—
26#135×C127—21no—
27#135×C127—42no—
28C2×D8×C127—22no—
29C2×D8×C127—42no—
30C2×D8×C127—41no—
31#131×C127—22no—
32#127×C127D411yescharacteristic, complemented
33#127×C127C2311yescharacteristic
34#121×C127—41no—
35#120×C127—22no—
36#120×C127—42no—
37C4×D4×C127—21no—
38#108×C127—21no—
39C4⋊C8×C127—21no—
40#104×C127—22no—
41#102×C127—41no—
42#100×C127—21no—
43#100×C127D412yescomplemented
44#99×C127—22no—
45#99×C127—42no—
46C4×C8×C127D411yescharacteristic, complemented
47C24×C127—22no—
48#41×C127—22no—
49#41×C127—42no—
50#41×C127—42no—
51C2×D4×C127—21no—
52C2×D4×C127—21no—
53C2×D4×C127—41no—
54C2×D4×C127—41no—
55C2×D4×C127—42no—
56C2×D4×C127—42no—
57C2×D4×C127—42no—
58C2×D4×C127—42no—
59C2×D4×C127—82no—
60C2×D4×C127—81no—
61C2×D4×C127—82no—
62C2×D4×C127—82no—
63C2×D4×C127C2×D412yes—
64C22×C4×C127—41no—
65Q16×C127—21no—
66SD16×C127—22no—
67SD16×C127—42no—
68SD16×C127—42no—
69D8×C127—21no—
70D8×C127—42no—
71D8×C127—42no—
72D8×C127—42no—
73D8×C127—42no—
74D8×C127—82no—
75M16×C127—22no—
76M16×C127—42no—
77C2×C8×C127—21no—
78C2×C8×C127—42no—
79C2×C8×C127—41no—
80C4⋊C4×C127—21no—
81C22⋊C4×C127—22no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—42no—
84C22⋊C4×C127—82no—
85C42×C127C2×D411yescharacteristic
86C23×C127—22no—
87C23×C127—41no—
88C23×C127—42no—
89C23×C127—41no—
90C23×C127—81no—
91C23×C127—82no—
92C23×C127—84no—
93Q8×C127—22no—
94D4×C127—22no—
95D4×C127—22no—
96D4×C127—42no—
97D4×C127—41no—
98D4×C127—42no—
99D4×C127—42no—
100D4×C127—81no—
101D4×C127—81no—
102D4×C127—81no—
103D4×C127—81no—
104D4×C127—82no—
105D4×C127—82no—
106D4×C127—84no—
107D4×C127—164no—
108C2×C4×C127—21no—
109C2×C4×C127—42no—
110C2×C4×C127—42no—
111C2×C4×C127—41no—
112C2×C4×C127—81no—
113C2×C4×C127—81no—
114C2×C4×C127—81no—
115C2×C4×C127—82no—
116C2×C4×C127#12011yescharacteristic
117C8×C127—21no—
118C8×C127—21no—
119C8×C127—42no—
120C8×C127—81no—
121C22×C127—42no—
122C22×C127—42no—
123C22×C127—42no—
124C22×C127—82no—
125C22×C127—81no—
126C22×C127—84no—
127C22×C127—81no—
128C22×C127—81no—
129C22×C127—161no—
130C22×C127—162no—
131C22×C127—162no—
132C22×C127—321no—
133C22×C127B(4,𝔽2)11yescharacteristic
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—42no—
138C4×C127—81no—
139C4×C127—162no—
140#13673C12711yesmaximal, characteristic, direct product factor, Sylow
141C2×C127—21no—
142C2×C127—82no—
143C2×C127—82no—
144C2×C127—82no—
145C2×C127—161no—
146C2×C127#219611yescharacteristic
147#3292C2×C12711yescharacteristic, complemented
148#2196C2×C12712yescomplemented
149#1619C2×C12711yescharacteristic, complemented
150#1408C2×C12711yescharacteristic, complemented
151#1402C2×C12712yescomplemented
152C127#1367311yescharacteristic, direct product factor, Sylow
153#576—22no—
154D42C22×C12711yescharacteristic, complemented
155#493C22×C12711yescharacteristic
156#472—22no—
157#459—21no—
158B(4,𝔽2)—22no—
159#453—21no—
160#453C22×C12712yes—
161#443—21no—
162#353C22×C12712yescomplemented
163AΣL(1,𝔽16)—22no—
164#331C22×C12711yescharacteristic, complemented
165D4⋊C8—21no—
166H(5,𝔽2)—21no—
167H(5,𝔽2)D4×C12712yescomplemented
168C22×D4—41no—
169AGL(1,ℤ/8)—22no—
170AGL(1,ℤ/8)—22no—
171AGL(1,ℤ/8)—42no—
172AGL(1,ℤ/8)—42no—
173#135—21no—
174#135—42no—
175C2×D8—22no—
176C2×D8—42no—
177C2×D8—41no—
178#131—22no—
179#127D4×C12711yescharacteristic, complemented
180#127C23×C12711yescharacteristic
181#121—41no—
182#120—22no—
183#120—42no—
184C4×D4—21no—
185#108—21no—
186C4⋊C8—21no—
187#104—22no—
188#102—41no—
189#100—21no—
190#100D4×C12712yescomplemented
191#99—22no—
192#99—42no—
193C4×C8D4×C12711yescharacteristic, complemented
194C24—22no—
195#41—22no—
196#41—42no—
197#41—42no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—82no—
207C2×D4—81no—
208C2×D4—82no—
209C2×D4—82no—
210C2×D4C2×D4×C12712yes—
211C22×C4—41no—
212Q16—21no—
213SD16—22no—
214SD16—42no—
215SD16—42no—
216D8—21no—
217D8—42no—
218D8—42no—
219D8—42no—
220D8—42no—
221D8—82no—
222M16—22no—
223M16—42no—
224C2×C8—21no—
225C2×C8—42no—
226C2×C8—41no—
227C4⋊C4—21no—
228C22⋊C4—22no—
229C22⋊C4—41no—
230C22⋊C4—42no—
231C22⋊C4—82no—
232C42C2×D4×C12711yescharacteristic
233C23—22no—
234C23—41no—
235C23—42no—
236C23—41no—
237C23—81no—
238C23—82no—
239C23—84no—
240Q8—22no—
241D4—22no—
242D4—22no—
243D4—42no—
244D4—41no—
245D4—42no—
246D4—42no—
247D4—81no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—82no—
252D4—82no—
253D4—84no—
254D4—164no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—82no—
263C2×C4#120×C12711yescharacteristic
264C8—21no—
265C8—21no—
266C8—42no—
267C8—81no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—82no—
272C22—81no—
273C22—84no—
274C22—81no—
275C22—81no—
276C22—161no—
277C22—162no—
278C22—162no—
279C22—321no—
280C22B(4,𝔽2)×C12711yescharacteristic
281C4—21no—
282C4—21no—
283C4—21no—
284C4—42no—
285C4—81no—
286C4—162no—
287C2—21no—
288C2—82no—
289C2—82no—
290C2—82no—
291C2—161no—
292C2C127×#219611yescharacteristic
subgroupG/H
center, socleC2×C127#2196
commutator, Frattini, cosocle#127C23×C127
LCSG ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ #127×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3292C2semidirect
2. C127×#2196C2semidirect
3. C127×#1619C2semidirect
4. C127×#1408C2semidirect
5. C127×#1402C2semidirect
7. D42×C127C22semidirect
15. #353×C127C22semidirect
17. #331×C127C22semidirect
20. H(5,𝔽2)×C127D4semidirect
32. #127×C127D4semidirect
43. #100×C127D4semidirect
46. C4×C8×C127D4semidirect
140. #13673C127direct (N × H)
147. #3292C2×C127semidirect
148. #2196C2×C127semidirect
149. #1619C2×C127semidirect
150. #1408C2×C127semidirect
151. #1402C2×C127semidirect
152. C127#13673direct (N × H)
154. D42C22×C127semidirect
162. #353C22×C127semidirect
164. #331C22×C127semidirect
167. H(5,𝔽2)D4×C127semidirect
179. #127D4×C127semidirect
190. #100D4×C127semidirect
193. C4×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32922
C127×#21962
C127×#16192
C127×#14082
C127×#14022
#13673127