Finite Group Databasebeta

← C127×#12294 #44575967

Subgroups — C127×#12294 #44575967

Order 32512.

302 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3259C211yesmaximal, characteristic
2C127×#2233C211yesmaximal, characteristic, complemented
3C127×#2232C211yesmaximal, characteristic, complemented
4C127×#2089C211yesmaximal, characteristic, complemented
5C127×#1349C211yesmaximal, characteristic, complemented
6C127×#1349C211yesmaximal, characteristic, complemented
7C127×#1323C211yesmaximal, characteristic, complemented
8#540×C127—21no—
9#478×C127—21no—
10#478×C127—21no—
11#469×C127—21no—
12#466×C127C2211yescharacteristic
13#466×C127C2211yescharacteristic
14#459×C127—21no—
15#459×C127—21no—
16#428×C127—21no—
17C2×#107×C127C2211yescharacteristic
18#424×C127C2211yescharacteristic
19#367×C127—21no—
20#366×C127—21no—
21#357×C127—21no—
22#357×C127—21no—
23C22⋊C16×C127C2211yescharacteristic
24C22⋊C16×C127C2211yescharacteristic
25#343×C127—21no—
26#341×C127C2211yescharacteristic
27C2×D8×C127—21no—
28C2×D8×C127D411yescharacteristic
29C2×D8×C127D411yescharacteristic
30C2×M16×C127—21no—
31C2×M16×C127D411yescharacteristic
32C22×C8×C127C2311yescharacteristic
33#127×C127—21no—
34#125×C127—21no—
35#123×C127—41no—
36#123×C127—41no—
37#121×C127—21no—
38#121×C127—21no—
39#121×C127—41no—
40#121×C127—41no—
41C4×D4×C127—21no—
42C4×D4×C127—21no—
43#117×C127D411yescharacteristic
44C2×C4⋊C4×C127—21no—
45C2×C16×C127—21no—
46C2×C16×C127—21no—
47#107×C127—21no—
48#107×C127—21no—
49#107×C127—41no—
50#107×C127D411yescharacteristic
51#107×C127D411yescharacteristic
52#106×C127—21no—
53#106×C127—41no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56#102×C127—21no—
57#102×C127—21no—
58#102×C127—21no—
59#102×C127—21no—
60C2×D4×C127—21no—
61C2×D4×C127—21no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127C2×D411yescharacteristic
70D8×C127—41no—
71D8×C127—41no—
72D8×C127—81no—
73M16×C127—22no—
74M16×C127—41no—
75M16×C127—41no—
76C2×C8×C127—21no—
77C2×C8×C127—41no—
78C2×C8×C127—41no—
79C2×C8×C127C2×D411yescharacteristic
80C2×C8×C127C2×D411yescharacteristic
81C4⋊C4×C127—21no—
82C4⋊C4×C127—21no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127D811yescharacteristic
88C4⋊C4×C127D811yescharacteristic
89C22⋊C4×C127—21no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C42×C127—21no—
95C16×C127—41no—
96C16×C127—41no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127AGL(1,ℤ/8)11yescharacteristic
100D4×C127—41no—
101D4×C127—41no—
102D4×C127—41no—
103D4×C127—41no—
104D4×C127—161no—
105D4×C127—161no—
106D4×C127—161no—
107D4×C127—161no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—81no—
115C2×C4×C127—161no—
116C2×C4×C127—161no—
117C2×C4×C127—161no—
118C2×C4×C127#12011yescharacteristic
119C2×C4×C127C2×D811yescharacteristic
120C8×C127—21no—
121C8×C127—21no—
122C8×C127—42no—
123C8×C127—41no—
124C22×C127—21no—
125C22×C127—21no—
126C22×C127—21no—
127C22×C127—81no—
128C22×C127—81no—
129C22×C127—81no—
130C22×C127—81no—
131C22×C127—81no—
132C22×C127—81no—
133C22×C127#44711yescharacteristic
134C4×C127—21no—
135C4×C127—41no—
136C4×C127—41no—
137C4×C127—81no—
138C4×C127—81no—
139C4×C127—161no—
140C4×C127#45611yescharacteristic
141C4×C127#45811yescharacteristic
142#12294C12711yesmaximal, characteristic, direct product factor, Sylow
143C2×C127—41no—
144C2×C127—161no—
145C2×C127—161no—
146C2×C127#161011yescharacteristic
147C2×C127#219211yescharacteristic
148C2×C127#219411yescharacteristic
149#3259C2×C12711yescharacteristic
150#2233C2×C12711yescharacteristic, complemented
151#2232C2×C12711yescharacteristic, complemented
152#2089C2×C12711yescharacteristic, complemented
153#1349C2×C12711yescharacteristic, complemented
154#1349C2×C12711yescharacteristic, complemented
155#1323C2×C12711yescharacteristic, complemented
156C127#1229411yescharacteristic, direct product factor, Sylow
157#540—21no—
158#478—21no—
159#478—21no—
160#469—21no—
161#466C22×C12711yescharacteristic
162#466C22×C12711yescharacteristic
163#459—21no—
164#459—21no—
165#428—21no—
166C2×#107C22×C12711yescharacteristic
167#424C22×C12711yescharacteristic
168#367—21no—
169#366—21no—
170#357—21no—
171#357—21no—
172C22⋊C16C22×C12711yescharacteristic
173C22⋊C16C22×C12711yescharacteristic
174#343—21no—
175#341C22×C12711yescharacteristic
176C2×D8—21no—
177C2×D8D4×C12711yescharacteristic
178C2×D8D4×C12711yescharacteristic
179C2×M16—21no—
180C2×M16D4×C12711yescharacteristic
181C22×C8C23×C12711yescharacteristic
182#127—21no—
183#125—21no—
184#123—41no—
185#123—41no—
186#121—21no—
187#121—21no—
188#121—41no—
189#121—41no—
190C4×D4—21no—
191C4×D4—21no—
192#117D4×C12711yescharacteristic
193C2×C4⋊C4—21no—
194C2×C16—21no—
195C2×C16—21no—
196#107—21no—
197#107—21no—
198#107—41no—
199#107D4×C12711yescharacteristic
200#107D4×C12711yescharacteristic
201#106—21no—
202#106—41no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205#102—21no—
206#102—21no—
207#102—21no—
208#102—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4C2×D4×C12711yescharacteristic
219D8—41no—
220D8—41no—
221D8—81no—
222M16—22no—
223M16—41no—
224M16—41no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8C2×D4×C12711yescharacteristic
229C2×C8C2×D4×C12711yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4D8×C12711yescharacteristic
237C4⋊C4D8×C12711yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C42—21no—
244C16—41no—
245C16—41no—
246C23—41no—
247C23—41no—
248C23AGL(1,ℤ/8)×C12711yescharacteristic
249D4—41no—
250D4—41no—
251D4—41no—
252D4—41no—
253D4—161no—
254D4—161no—
255D4—161no—
256D4—161no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—81no—
264C2×C4—161no—
265C2×C4—161no—
266C2×C4—161no—
267C2×C4#120×C12711yescharacteristic
268C2×C4C2×D8×C12711yescharacteristic
269C8—21no—
270C8—21no—
271C8—42no—
272C8—41no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—81no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22—81no—
282C22#447×C12711yescharacteristic
283C4—21no—
284C4—41no—
285C4—41no—
286C4—81no—
287C4—81no—
288C4—161no—
289C4#456×C12711yescharacteristic
290C4#458×C12711yescharacteristic
291C2—41no—
292C2—161no—
293C2—161no—
294C2C127×#161011yescharacteristic
295C2C127×#219211yescharacteristic
296C2C127×#219411yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3259C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ #424×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2233C2semidirect
3. C127×#2232C2semidirect
4. C127×#2089C2semidirect
5. C127×#1349C2semidirect
6. C127×#1349C2semidirect
7. C127×#1323C2semidirect
142. #12294C127direct (N × H)
150. #2233C2×C127semidirect
151. #2232C2×C127semidirect
152. #2089C2×C127semidirect
153. #1349C2×C127semidirect
154. #1349C2×C127semidirect
155. #1323C2×C127semidirect
156. C127#12294direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32592
C127×#22332
C127×#22322
C127×#20892
C127×#13492
C127×#13232
#12294127