Finite Group Databasebeta

← C127×#12333 #44576006

Subgroups — C127×#12333 #44576006

Order 32512.

324 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3396C211yesmaximal, characteristic
2C127×#2248C211yesmaximal, characteristic
3C127×#2209C211yesmaximal, characteristic, complemented
4C127×#1670C211yesmaximal, characteristic, complemented
5C127×#1361C211yesmaximal, characteristic
6C127×Q8⋊C16C211yesmaximal, characteristic, complemented
7C127×#1332C211yesmaximal, characteristic, complemented
8#559×C127—21no—
9C2×Q32×C127—21no—
10C2×SD32×C127—22no—
11#495×C127—21no—
12#494×C127C2211yescharacteristic
13#493×C127C2211yescharacteristic
14#475×C127—21no—
15#463×C127—22no—
16#460×C127—21no—
17C8×Q8×C127C2211yescharacteristic
18C4×Q16×C127C2211yescharacteristic
19C4×D8×C127—21no—
20C4⋊C16×C127C2211yescharacteristic
21#358×C127—21no—
22C4×C16×C127C2211yescharacteristic
23#335×C127C2211yescharacteristic
24#332×C127—21no—
25C2×Q16×C127—21no—
26C2×Q16×C127—21no—
27C2×Q16×C127D411yescharacteristic
28C2×SD16×C127—22no—
29C2×D8×C127—21no—
30C2×D8×C127D412yes—
31C4⋊Q8×C127—21no—
32#127×C127—21no—
33#124×C127—22no—
34#124×C127—41no—
35#123×C127—42no—
36C4×Q8×C127—21no—
37C4×Q8×C127D411yescharacteristic
38C4×D4×C127—22no—
39C4×D4×C127—41no—
40Q32×C127—42no—
41SD32×C127—44no—
42C2×C16×C127—21no—
43C2×C16×C127—21no—
44#107×C127D411yescharacteristic
45#106×C127—41no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127D411yescharacteristic
49#103×C127—21no—
50#103×C127—41no—
51#102×C127—22no—
52C4×C8×C127—21no—
53C4×C8×C127C2311yescharacteristic
54C2×Q8×C127—21no—
55C2×Q8×C127—41no—
56C2×Q8×C127D811yescharacteristic
57C2×D4×C127—22no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60C22×C4×C127—42no—
61Q16×C127—21no—
62Q16×C127—21no—
63Q16×C127—42no—
64Q16×C127—41no—
65Q16×C127—41no—
66SD16×C127—82no—
67D8×C127—42no—
68D8×C127—41no—
69D8×C127—41no—
70C2×C8×C127—21no—
71C2×C8×C127—41no—
72C2×C8×C127C2×D411yescharacteristic
73C2×C8×C127C2×D411yescharacteristic
74C4⋊C4×C127—21no—
75C4⋊C4×C127—21no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127D811yescharacteristic
80C22⋊C4×C127—42no—
81C22⋊C4×C127—42no—
82C22⋊C4×C127—42no—
83C42×C127—21no—
84C42×C127—41no—
85C42×C127C2×D411yescharacteristic
86C16×C127—22no—
87C16×C127—41no—
88C23×C127—42no—
89Q8×C127—21no—
90Q8×C127—21no—
91Q8×C127—41no—
92Q8×C127—41no—
93Q8×C127—81no—
94Q8×C127—81no—
95D4×C127—42no—
96D4×C127—42no—
97D4×C127—81no—
98D4×C127—81no—
99D4×C127—161no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—81no—
105C2×C4×C127—162no—
106C2×C4×C127#12011yescharacteristic
107C2×C4×C127C2×D811yescharacteristic
108C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
109C8×C127—21no—
110C8×C127—41no—
111C8×C127—81no—
112C8×C127#13511yescharacteristic
113C8×C127AGL(1,ℤ/8)11yescharacteristic
114C22×C127—82no—
115C22×C127—82no—
116C22×C127—82no—
117C22×C127#44711yescharacteristic
118C4×C127—21no—
119C4×C127—41no—
120C4×C127—41no—
121C4×C127—81no—
122C4×C127—81no—
123C4×C127—161no—
124C4×C127#44911yescharacteristic
125C4×C127#45311yescharacteristic
126C4×C127#50811yescharacteristic
127C4×C127#51011yescharacteristic
128#12333C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—162no—
130C2×C127#162111yescharacteristic
131C2×C127#218911yescharacteristic
132C2×C127#219411yescharacteristic
133#3396C2×C12711yescharacteristic
134#2248C2×C12711yescharacteristic
135#2209C2×C12711yescharacteristic, complemented
136#1670C2×C12711yescharacteristic, complemented
137#1361C2×C12711yescharacteristic
138Q8⋊C16C2×C12711yescharacteristic, complemented
139#1332C2×C12711yescharacteristic, complemented
140C127#1233311yescharacteristic, direct product factor, Sylow
141#559—21no—
142C2×Q32—21no—
143C2×SD32—22no—
144#495—21no—
145#494C22×C12711yescharacteristic
146#493C22×C12711yescharacteristic
147#475—21no—
148#463—22no—
149#460—21no—
150C8×Q8C22×C12711yescharacteristic
151C4×Q16C22×C12711yescharacteristic
152C4×D8—21no—
153C4⋊C16C22×C12711yescharacteristic
154#358—21no—
155C4×C16C22×C12711yescharacteristic
156#335C22×C12711yescharacteristic
157#332—21no—
158C2×Q16—21no—
159C2×Q16—21no—
160C2×Q16D4×C12711yescharacteristic
161C2×SD16—22no—
162C2×D8—21no—
163C2×D8D4×C12712yes—
164C4⋊Q8—21no—
165#127—21no—
166#124—22no—
167#124—41no—
168#123—42no—
169C4×Q8—21no—
170C4×Q8D4×C12711yescharacteristic
171C4×D4—22no—
172C4×D4—41no—
173Q32—42no—
174SD32—44no—
175C2×C16—21no—
176C2×C16—21no—
177#107D4×C12711yescharacteristic
178#106—41no—
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8D4×C12711yescharacteristic
182#103—21no—
183#103—41no—
184#102—22no—
185C4×C8—21no—
186C4×C8C23×C12711yescharacteristic
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8D8×C12711yescharacteristic
190C2×D4—22no—
191C2×D4—41no—
192C2×D4—41no—
193C22×C4—42no—
194Q16—21no—
195Q16—21no—
196Q16—42no—
197Q16—41no—
198Q16—41no—
199SD16—82no—
200D8—42no—
201D8—41no—
202D8—41no—
203C2×C8—21no—
204C2×C8—41no—
205C2×C8C2×D4×C12711yescharacteristic
206C2×C8C2×D4×C12711yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4D8×C12711yescharacteristic
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C42—21no—
217C42—41no—
218C42C2×D4×C12711yescharacteristic
219C16—22no—
220C16—41no—
221C23—42no—
222Q8—21no—
223Q8—21no—
224Q8—41no—
225Q8—41no—
226Q8—81no—
227Q8—81no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—161no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—81no—
238C2×C4—162no—
239C2×C4#120×C12711yescharacteristic
240C2×C4C2×D8×C12711yescharacteristic
241C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
242C8—21no—
243C8—41no—
244C8—81no—
245C8#135×C12711yescharacteristic
246C8AGL(1,ℤ/8)×C12711yescharacteristic
247C22—82no—
248C22—82no—
249C22—82no—
250C22#447×C12711yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—81no—
255C4—81no—
256C4—161no—
257C4#449×C12711yescharacteristic
258C4#453×C12711yescharacteristic
259C4#508×C12711yescharacteristic
260C4#510×C12711yescharacteristic
261C2—162no—
262C2C127×#162111yescharacteristic
263C2C127×#218911yescharacteristic
264C2C127×#219411yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC4×C8C23×C127
prime radical#493×C127C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#2209C2semidirect
4. C127×#1670C2semidirect
6. C127×Q8⋊C16C2semidirect
7. C127×#1332C2semidirect
128. #12333C127direct (N × H)
135. #2209C2×C127semidirect
136. #1670C2×C127semidirect
138. Q8⋊C16C2×C127semidirect
139. #1332C2×C127semidirect
140. C127#12333direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33962
C127×#22482
C127×#22092
C127×#16702
C127×#13612
C127×Q8⋊C162
C127×#13322
#12333127