Finite Group Databasebeta

← C127×#12296 #44575969

Subgroups — C127×#12296 #44575969

Order 32512.

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

normal subgroups only

This group has 278 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×#3261C211yesmaximal, characteristic
2C127×#2236C211yesmaximal, characteristic
3C127×#2235C211yesmaximal, characteristic
4C127×#2089C211yesmaximal, characteristic
5C127×#1350C211yesmaximal, characteristic
6C127×#1350C211yesmaximal, characteristic
7C127×#1323C211yesmaximal, characteristic
8#541×C127—21no—
9#479×C127—21no—
10#479×C127—21no—
11#470×C127—21no—
12#467×C127C2211yescharacteristic
13#467×C127C2211yescharacteristic
14#462×C127—21no—
15#462×C127—21no—
16#428×C127—21no—
17C2×#107×C127C2211yescharacteristic
18#424×C127C2211yescharacteristic
19#367×C127—21no—
20#366×C127—21no—
21#358×C127—21no—
22#358×C127—21no—
23C22⋊C16×C127C2211yescharacteristic
24C22⋊C16×C127C2211yescharacteristic
25#343×C127—21no—
26#341×C127C2211yescharacteristic
27C2×Q16×C127—21no—
28C2×Q16×C127D411yescharacteristic
29C2×Q16×C127D411yescharacteristic
30C2×M16×C127—21no—
31C2×M16×C127D411yescharacteristic
32C22×C8×C127C2311yescharacteristic
33C4⋊Q8×C127—21no—
34#126×C127—41no—
35#126×C127—41no—
36#125×C127—21no—
37#125×C127—41no—
38#125×C127—41no—
39C22⋊Q8×C127—21no—
40C22⋊Q8×C127—21no—
41C4×Q8×C127—21no—
42C4×Q8×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#103×C127—21no—
57#103×C127—21no—
58#103×C127—21no—
59#103×C127—21no—
60C2×Q8×C127—21no—
61C2×Q8×C127—21no—
62C22×C4×C127—41no—
63C22×C4×C127C2×D411yescharacteristic
64Q16×C127—41no—
65Q16×C127—41no—
66Q16×C127—81no—
67M16×C127—22no—
68M16×C127—41no—
69M16×C127—41no—
70C2×C8×C127—21no—
71C2×C8×C127—41no—
72C2×C8×C127—41no—
73C2×C8×C127C2×D411yescharacteristic
74C2×C8×C127C2×D411yescharacteristic
75C4⋊C4×C127—21no—
76C4⋊C4×C127—21no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
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—
92C42×C127—21no—
93C42×C127—41no—
94C42×C127—41no—
95C16×C127—41no—
96C16×C127—41no—
97C23×C127AGL(1,ℤ/8)11yescharacteristic
98Q8×C127—41no—
99Q8×C127—41no—
100Q8×C127—41no—
101Q8×C127—41no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—81no—
111C2×C4×C127—161no—
112C2×C4×C127#12011yescharacteristic
113C2×C4×C127C2×D811yescharacteristic
114C8×C127—21no—
115C8×C127—21no—
116C8×C127—42no—
117C8×C127—41no—
118C22×C127—21no—
119C22×C127—21no—
120C22×C127—21no—
121C22×C127#44711yescharacteristic
122C4×C127—21no—
123C4×C127—41no—
124C4×C127—41no—
125C4×C127—81no—
126C4×C127—81no—
127C4×C127—81no—
128C4×C127—81no—
129C4×C127—161no—
130C4×C127#45611yescharacteristic
131C4×C127#45811yescharacteristic
132#12296C12711yesmaximal, characteristic, direct product factor, Sylow
133C2×C127—41no—
134C2×C127#161011yescharacteristic
135C2×C127#219311yescharacteristic
136C2×C127#219511yescharacteristic
137#3261C2×C12711yescharacteristic
138#2236C2×C12711yescharacteristic
139#2235C2×C12711yescharacteristic
140#2089C2×C12711yescharacteristic
141#1350C2×C12711yescharacteristic
142#1350C2×C12711yescharacteristic
143#1323C2×C12711yescharacteristic
144C127#1229611yescharacteristic, direct product factor, Sylow
145#541—21no—
146#479—21no—
147#479—21no—
148#470—21no—
149#467C22×C12711yescharacteristic
150#467C22×C12711yescharacteristic
151#462—21no—
152#462—21no—
153#428—21no—
154C2×#107C22×C12711yescharacteristic
155#424C22×C12711yescharacteristic
156#367—21no—
157#366—21no—
158#358—21no—
159#358—21no—
160C22⋊C16C22×C12711yescharacteristic
161C22⋊C16C22×C12711yescharacteristic
162#343—21no—
163#341C22×C12711yescharacteristic
164C2×Q16—21no—
165C2×Q16D4×C12711yescharacteristic
166C2×Q16D4×C12711yescharacteristic
167C2×M16—21no—
168C2×M16D4×C12711yescharacteristic
169C22×C8C23×C12711yescharacteristic
170C4⋊Q8—21no—
171#126—41no—
172#126—41no—
173#125—21no—
174#125—41no—
175#125—41no—
176C22⋊Q8—21no—
177C22⋊Q8—21no—
178C4×Q8—21no—
179C4×Q8—21no—
180#117D4×C12711yescharacteristic
181C2×C4⋊C4—21no—
182C2×C16—21no—
183C2×C16—21no—
184#107—21no—
185#107—21no—
186#107—41no—
187#107D4×C12711yescharacteristic
188#107D4×C12711yescharacteristic
189#106—21no—
190#106—41no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193#103—21no—
194#103—21no—
195#103—21no—
196#103—21no—
197C2×Q8—21no—
198C2×Q8—21no—
199C22×C4—41no—
200C22×C4C2×D4×C12711yescharacteristic
201Q16—41no—
202Q16—41no—
203Q16—81no—
204M16—22no—
205M16—41no—
206M16—41no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8C2×D4×C12711yescharacteristic
211C2×C8C2×D4×C12711yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4D8×C12711yescharacteristic
225C4⋊C4D8×C12711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C42—21no—
230C42—41no—
231C42—41no—
232C16—41no—
233C16—41no—
234C23AGL(1,ℤ/8)×C12711yescharacteristic
235Q8—41no—
236Q8—41no—
237Q8—41no—
238Q8—41no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—161no—
249C2×C4#120×C12711yescharacteristic
250C2×C4C2×D8×C12711yescharacteristic
251C8—21no—
252C8—21no—
253C8—42no—
254C8—41no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22#447×C12711yescharacteristic
259C4—21no—
260C4—41no—
261C4—41no—
262C4—81no—
263C4—81no—
264C4—81no—
265C4—81no—
266C4—161no—
267C4#456×C12711yescharacteristic
268C4#458×C12711yescharacteristic
269C2—41no—
270C2C127×#161011yescharacteristic
271C2C127×#219311yescharacteristic
272C2C127×#219511yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127AGL(1,ℤ/8)
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
132. #12296C127direct (N × H)
144. C127#12296direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32612
C127×#22362
C127×#22352
C127×#20892
C127×#13502
C127×#13232
#12296127