Finite Group Databasebeta

← C127×#12335 #44576008

Subgroups — C127×#12335 #44576008

Order 32512.

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

normal subgroups only

This group has 312 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×#3393C211yesmaximal, characteristic
2C127×#2247C211yesmaximal, characteristic, complemented
3C127×#2208C211yesmaximal, characteristic
4C127×#1670C211yesmaximal, characteristic, complemented
5C127×#1362C211yesmaximal, characteristic, complemented
6C127×Q8⋊C16C211yesmaximal, characteristic, complemented
7C127×#1331C211yesmaximal, characteristic
8#556×C127—21no—
9C2×Q32×C127—22no—
10C2×SD32×C127—21no—
11#495×C127—21no—
12#494×C127C2211yescharacteristic
13#494×C127C2211yescharacteristic
14#475×C127—21no—
15#464×C127—22no—
16#461×C127—21no—
17C8×Q8×C127C2211yescharacteristic
18C4×Q16×C127—21no—
19C4×D8×C127C2211yescharacteristic
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×C127—21no—
28C2×Q16×C127D412yes—
29C2×SD16×C127—22no—
30C2×D8×C127D411yescharacteristic
31C4⋊Q8×C127—21no—
32C4⋊Q8×C127—21no—
33#126×C127—42no—
34#124×C127—22no—
35C22⋊Q8×C127—41no—
36C4×Q8×C127—22no—
37C4×Q8×C127D411yescharacteristic
38C4×D4×C127—21no—
39#117×C127—41no—
40Q32×C127—44no—
41SD32×C127—42no—
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—22no—
50#103×C127—41no—
51#102×C127—21no—
52C4×C8×C127—21no—
53C4×C8×C127C2311yescharacteristic
54C2×Q8×C127—22no—
55C2×Q8×C127—41no—
56C2×Q8×C127D811yescharacteristic
57C2×D4×C127—21no—
58C22×C4×C127—41no—
59Q16×C127—42no—
60Q16×C127—42no—
61Q16×C127—41no—
62Q16×C127—41no—
63Q16×C127—41no—
64Q16×C127—41no—
65SD16×C127—82no—
66D8×C127—21no—
67D8×C127—21no—
68C2×C8×C127—21no—
69C2×C8×C127—41no—
70C2×C8×C127C2×D411yescharacteristic
71C2×C8×C127C2×D411yescharacteristic
72C4⋊C4×C127—21no—
73C4⋊C4×C127—21no—
74C4⋊C4×C127—42no—
75C4⋊C4×C127—41no—
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—41no—
83C42×C127—21no—
84C42×C127—42no—
85C42×C127C2×D411yescharacteristic
86C16×C127—22no—
87C16×C127—41no—
88C23×C127—41no—
89Q8×C127—21no—
90Q8×C127—21no—
91Q8×C127—42no—
92Q8×C127—42no—
93Q8×C127—81no—
94Q8×C127—81no—
95D4×C127—41no—
96D4×C127—41no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—41no—
100C2×C4×C127—42no—
101C2×C4×C127—81no—
102C2×C4×C127—81no—
103C2×C4×C127—81no—
104C2×C4×C127#12011yescharacteristic
105C2×C4×C127C2×D811yescharacteristic
106C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
107C8×C127—21no—
108C8×C127—41no—
109C8×C127—81no—
110C8×C127#13511yescharacteristic
111C8×C127AGL(1,ℤ/8)11yescharacteristic
112C22×C127—81no—
113C22×C127—81no—
114C22×C127—81no—
115C22×C127#44711yescharacteristic
116C4×C127—21no—
117C4×C127—41no—
118C4×C127—41no—
119C4×C127—82no—
120C4×C127—81no—
121C4×C127—161no—
122C4×C127#44911yescharacteristic
123C4×C127#45311yescharacteristic
124C4×C127#50811yescharacteristic
125C4×C127#51011yescharacteristic
126#12335C12711yesmaximal, characteristic, direct product factor, Sylow
127C2×C127—161no—
128C2×C127#162111yescharacteristic
129C2×C127#218911yescharacteristic
130C2×C127#219511yescharacteristic
131#3393C2×C12711yescharacteristic
132#2247C2×C12711yescharacteristic, complemented
133#2208C2×C12711yescharacteristic
134#1670C2×C12711yescharacteristic, complemented
135#1362C2×C12711yescharacteristic, complemented
136Q8⋊C16C2×C12711yescharacteristic, complemented
137#1331C2×C12711yescharacteristic
138C127#1233511yescharacteristic, direct product factor, Sylow
139#556—21no—
140C2×Q32—22no—
141C2×SD32—21no—
142#495—21no—
143#494C22×C12711yescharacteristic
144#494C22×C12711yescharacteristic
145#475—21no—
146#464—22no—
147#461—21no—
148C8×Q8C22×C12711yescharacteristic
149C4×Q16—21no—
150C4×D8C22×C12711yescharacteristic
151C4⋊C16C22×C12711yescharacteristic
152#358—21no—
153C4×C16C22×C12711yescharacteristic
154#335C22×C12711yescharacteristic
155#332—21no—
156C2×Q16—21no—
157C2×Q16—21no—
158C2×Q16—21no—
159C2×Q16D4×C12712yes—
160C2×SD16—22no—
161C2×D8D4×C12711yescharacteristic
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164#126—42no—
165#124—22no—
166C22⋊Q8—41no—
167C4×Q8—22no—
168C4×Q8D4×C12711yescharacteristic
169C4×D4—21no—
170#117—41no—
171Q32—44no—
172SD32—42no—
173C2×C16—21no—
174C2×C16—21no—
175#107D4×C12711yescharacteristic
176#106—41no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8D4×C12711yescharacteristic
180#103—22no—
181#103—41no—
182#102—21no—
183C4×C8—21no—
184C4×C8C23×C12711yescharacteristic
185C2×Q8—22no—
186C2×Q8—41no—
187C2×Q8D8×C12711yescharacteristic
188C2×D4—21no—
189C22×C4—41no—
190Q16—42no—
191Q16—42no—
192Q16—41no—
193Q16—41no—
194Q16—41no—
195Q16—41no—
196SD16—82no—
197D8—21no—
198D8—21no—
199C2×C8—21no—
200C2×C8—41no—
201C2×C8C2×D4×C12711yescharacteristic
202C2×C8C2×D4×C12711yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—42no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4D8×C12711yescharacteristic
211C22⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—41no—
214C42—21no—
215C42—42no—
216C42C2×D4×C12711yescharacteristic
217C16—22no—
218C16—41no—
219C23—41no—
220Q8—21no—
221Q8—21no—
222Q8—42no—
223Q8—42no—
224Q8—81no—
225Q8—81no—
226D4—41no—
227D4—41no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4#120×C12711yescharacteristic
236C2×C4C2×D8×C12711yescharacteristic
237C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
238C8—21no—
239C8—41no—
240C8—81no—
241C8#135×C12711yescharacteristic
242C8AGL(1,ℤ/8)×C12711yescharacteristic
243C22—81no—
244C22—81no—
245C22—81no—
246C22#447×C12711yescharacteristic
247C4—21no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4—81no—
252C4—161no—
253C4#449×C12711yescharacteristic
254C4#453×C12711yescharacteristic
255C4#508×C12711yescharacteristic
256C4#510×C12711yescharacteristic
257C2—161no—
258C2C127×#162111yescharacteristic
259C2C127×#218911yescharacteristic
260C2C127×#219511yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC2×D8×C127D4
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
2. C127×#2247C2semidirect
4. C127×#1670C2semidirect
5. C127×#1362C2semidirect
6. C127×Q8⋊C16C2semidirect
126. #12335C127direct (N × H)
132. #2247C2×C127semidirect
134. #1670C2×C127semidirect
135. #1362C2×C127semidirect
136. Q8⋊C16C2×C127semidirect
138. C127#12335direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33932
C127×#22472
C127×#22082
C127×#16702
C127×#13622
C127×Q8⋊C162
C127×#13312
#12335127