Finite Group Databasebeta

← C127×#12297 #44575970

Subgroups — C127×#12297 #44575970

Order 32512.

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

normal subgroups only

This group has 290 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×#3262C211yesmaximal, characteristic
2C127×#2236C211yesmaximal, characteristic, complemented
3C127×#2232C211yesmaximal, characteristic
4C127×#2089C211yesmaximal, characteristic, complemented
5C127×#1350C211yesmaximal, characteristic, complemented
6C127×#1349C211yesmaximal, characteristic
7C127×#1323C211yesmaximal, characteristic, complemented
8#542×C127—21no—
9#477×C127—21no—
10#474×C127—21no—
11#468×C127—21no—
12#467×C127C2211yescharacteristic
13#466×C127C2211yescharacteristic
14#464×C127—21no—
15#463×C127—21no—
16#428×C127—21no—
17C2×#107×C127C2211yescharacteristic
18#424×C127C2211yescharacteristic
19#366×C127—21no—
20#366×C127—21no—
21#358×C127—21no—
22#357×C127—21no—
23C22⋊C16×C127C2211yescharacteristic
24C22⋊C16×C127C2211yescharacteristic
25#343×C127—21no—
26#341×C127C2211yescharacteristic
27C2×Q16×C127D411yescharacteristic
28C2×SD16×C127—21no—
29C2×D8×C127D411yescharacteristic
30C2×M16×C127—21no—
31C2×M16×C127D411yescharacteristic
32C22×C8×C127C2311yescharacteristic
33C4⋊Q8×C127—21no—
34#126×C127—41no—
35#124×C127—21no—
36#124×C127—41no—
37#123×C127—41no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—41no—
40#121×C127—21no—
41C4×Q8×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—21no—
50#107×C127—41no—
51#107×C127D411yescharacteristic
52#107×C127D411yescharacteristic
53#106×C127—41no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56#103×C127—21no—
57#103×C127—21no—
58#102×C127—21no—
59#102×C127—21no—
60C2×Q8×C127—21no—
61C2×Q8×C127—41no—
62C2×D4×C127—21no—
63C2×D4×C127—41no—
64C22×C4×C127—41no—
65C22×C4×C127—41no—
66C22×C4×C127C2×D411yescharacteristic
67Q16×C127—41no—
68SD16×C127—81no—
69D8×C127—41no—
70M16×C127—22no—
71M16×C127—41no—
72M16×C127—41no—
73C2×C8×C127—21no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127C2×D411yescharacteristic
77C2×C8×C127C2×D411yescharacteristic
78C4⋊C4×C127—21no—
79C4⋊C4×C127—21no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127D811yescharacteristic
86C4⋊C4×C127D811yescharacteristic
87C22⋊C4×C127—21no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C42×C127—21no—
94C42×C127—41no—
95C16×C127—41no—
96C16×C127—41no—
97C23×C127—41no—
98C23×C127AGL(1,ℤ/8)11yescharacteristic
99Q8×C127—41no—
100Q8×C127—41no—
101Q8×C127—161no—
102D4×C127—41no—
103D4×C127—41no—
104D4×C127—161no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—81no—
113C2×C4×C127—161no—
114C2×C4×C127—161no—
115C2×C4×C127#12011yescharacteristic
116C2×C4×C127C2×D811yescharacteristic
117C8×C127—21no—
118C8×C127—21no—
119C8×C127—42no—
120C8×C127—41no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—81no—
125C22×C127—81no—
126C22×C127—81no—
127C22×C127#44711yescharacteristic
128C4×C127—21no—
129C4×C127—41no—
130C4×C127—41no—
131C4×C127—81no—
132C4×C127—81no—
133C4×C127—81no—
134C4×C127—161no—
135C4×C127#45611yescharacteristic
136C4×C127#45811yescharacteristic
137#12297C12711yesmaximal, characteristic, direct product factor, Sylow
138C2×C127—41no—
139C2×C127—161no—
140C2×C127#161011yescharacteristic
141C2×C127#219211yescharacteristic
142C2×C127#219511yescharacteristic
143#3262C2×C12711yescharacteristic
144#2236C2×C12711yescharacteristic, complemented
145#2232C2×C12711yescharacteristic
146#2089C2×C12711yescharacteristic, complemented
147#1350C2×C12711yescharacteristic, complemented
148#1349C2×C12711yescharacteristic
149#1323C2×C12711yescharacteristic, complemented
150C127#1229711yescharacteristic, direct product factor, Sylow
151#542—21no—
152#477—21no—
153#474—21no—
154#468—21no—
155#467C22×C12711yescharacteristic
156#466C22×C12711yescharacteristic
157#464—21no—
158#463—21no—
159#428—21no—
160C2×#107C22×C12711yescharacteristic
161#424C22×C12711yescharacteristic
162#366—21no—
163#366—21no—
164#358—21no—
165#357—21no—
166C22⋊C16C22×C12711yescharacteristic
167C22⋊C16C22×C12711yescharacteristic
168#343—21no—
169#341C22×C12711yescharacteristic
170C2×Q16D4×C12711yescharacteristic
171C2×SD16—21no—
172C2×D8D4×C12711yescharacteristic
173C2×M16—21no—
174C2×M16D4×C12711yescharacteristic
175C22×C8C23×C12711yescharacteristic
176C4⋊Q8—21no—
177#126—41no—
178#124—21no—
179#124—41no—
180#123—41no—
181C22⋊Q8—21no—
182C22⋊Q8—41no—
183#121—21no—
184C4×Q8—21no—
185C4×D4—21no—
186#117D4×C12711yescharacteristic
187C2×C4⋊C4—21no—
188C2×C16—21no—
189C2×C16—21no—
190#107—21no—
191#107—21no—
192#107—21no—
193#107—41no—
194#107D4×C12711yescharacteristic
195#107D4×C12711yescharacteristic
196#106—41no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199#103—21no—
200#103—21no—
201#102—21no—
202#102—21no—
203C2×Q8—21no—
204C2×Q8—41no—
205C2×D4—21no—
206C2×D4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4C2×D4×C12711yescharacteristic
210Q16—41no—
211SD16—81no—
212D8—41no—
213M16—22no—
214M16—41no—
215M16—41no—
216C2×C8—21no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8C2×D4×C12711yescharacteristic
220C2×C8C2×D4×C12711yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4D8×C12711yescharacteristic
229C4⋊C4D8×C12711yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C42—21no—
237C42—41no—
238C16—41no—
239C16—41no—
240C23—41no—
241C23AGL(1,ℤ/8)×C12711yescharacteristic
242Q8—41no—
243Q8—41no—
244Q8—161no—
245D4—41no—
246D4—41no—
247D4—161no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—81no—
256C2×C4—161no—
257C2×C4—161no—
258C2×C4#120×C12711yescharacteristic
259C2×C4C2×D8×C12711yescharacteristic
260C8—21no—
261C8—21no—
262C8—42no—
263C8—41no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—81no—
268C22—81no—
269C22—81no—
270C22#447×C12711yescharacteristic
271C4—21no—
272C4—41no—
273C4—41no—
274C4—81no—
275C4—81no—
276C4—81no—
277C4—161no—
278C4#456×C12711yescharacteristic
279C4#458×C12711yescharacteristic
280C2—41no—
281C2—161no—
282C2C127×#161011yescharacteristic
283C2C127×#219211yescharacteristic
284C2C127×#219511yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radical#466×C127C22
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×#2236C2semidirect
4. C127×#2089C2semidirect
5. C127×#1350C2semidirect
7. C127×#1323C2semidirect
137. #12297C127direct (N × H)
144. #2236C2×C127semidirect
146. #2089C2×C127semidirect
147. #1350C2×C127semidirect
149. #1323C2×C127semidirect
150. C127#12297direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32622
C127×#22362
C127×#22322
C127×#20892
C127×#13502
C127×#13492
C127×#13232
#12297127