Finite Group Databasebeta

← C127×#13465 #44577138

Subgroups — C127×#13465 #44577138

Order 32512.

384 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2809C211yesmaximal, characteristic
2C127×#1857C212yesmaximal
3C127×#1857C211yesmaximal, characteristic
4C127×#1394C211yesmaximal, characteristic
5C127×#1394C212yesmaximal
6#519×C127C2211yescharacteristic
7#428×C127—22no—
8#428×C127—21no—
9C2×#101×C127C2212yes—
10C2×#101×C127C2211yescharacteristic
11#400×C127—21no—
12#398×C127—22no—
13#391×C127C2211yescharacteristic
14#391×C127C2212yes—
15#389×C127—21no—
16#387×C127—22no—
17#339×C127—22no—
18#339×C127—21no—
19C22×Q8×C127C2311yescharacteristic
20C2×M16×C127—22no—
21C2×M16×C127—21no—
22C4×Q8×C127—41no—
23C4×Q8×C127—41no—
24#117×C127—22no—
25#117×C127—21no—
26C2×C4⋊C4×C127—22no—
27C2×C4⋊C4×C127—21no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127D412yes—
31C2×C4⋊C4×C127D411yescharacteristic
32C2×C42×C127D412yes—
33C2×C42×C127D411yescharacteristic
34#107×C127—42no—
35#107×C127—41no—
36#106×C127—42no—
37#106×C127—41no—
38#101×C127—22no—
39#101×C127—21no—
40#101×C127Q814yes—
41#101×C127Q812yes—
42#95×C127—21no—
43#95×C127—22no—
44#95×C127—22no—
45#95×C127—22no—
46#95×C127—22no—
47C2×Q8×C127—41no—
48C2×Q8×C127—41no—
49C2×Q8×C127C2×Q812yes—
50C2×Q8×C127C2×Q811yescharacteristic
51C2×Q8×C127#4111yescharacteristic
52C22×C4×C127—21no—
53C22×C4×C127—21no—
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127C2×D412yes—
57C22×C4×C127C2×D411yescharacteristic
58M16×C127—24no—
59M16×C127—22no—
60M16×C127—41no—
61M16×C127—42no—
62C2×C8×C127—42no—
63C2×C8×C127—41no—
64C4⋊C4×C127—22no—
65C4⋊C4×C127—21no—
66C4⋊C4×C127—21no—
67C4⋊C4×C127—22no—
68C4⋊C4×C127—42no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—44no—
71C4⋊C4×C127—42no—
72C4⋊C4×C127—81no—
73C4⋊C4×C127—81no—
74C22⋊C4×C127—41no—
75C42×C127—41no—
76C42×C127—42no—
77C42×C127—42no—
78C42×C127—41no—
79C23×C127#12011yescharacteristic
80Q8×C127—42no—
81Q8×C127—41no—
82Q8×C127—41no—
83C2×C4×C127—22no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—41no—
89C2×C4×C127—41no—
90C2×C4×C127—42no—
91C2×C4×C127—42no—
92C2×C4×C127—42no—
93C2×C4×C127—42no—
94C2×C4×C127—42no—
95C2×C4×C127—41no—
96C2×C4×C127—41no—
97C2×C4×C127—41no—
98C2×C4×C127—42no—
99C2×C4×C127—42no—
100C2×C4×C127C22⋊Q812yes—
101C2×C4×C127C22⋊Q811yescharacteristic
102C2×C4×C127C4⋊Q812yes—
103C2×C4×C127C4⋊Q811yescharacteristic
104C8×C127—44no—
105C8×C127—42no—
106C22×C127—21no—
107C22×C127—21no—
108C22×C127#39511yescharacteristic
109C22×C127B(4,𝔽2)11yescharacteristic
110C22×C127#45811yescharacteristic
111C4×C127—22no—
112C4×C127—21no—
113C4×C127—22no—
114C4×C127—21no—
115C4×C127—42no—
116C4×C127—82no—
117C4×C127—81no—
118C4×C127—81no—
119C4×C127—81no—
120C4×C127—82no—
121#13465C12711yesmaximal, characteristic, direct product factor, Sylow
122C2×C127—21no—
123C2×C127—21no—
124C2×C127#206211yescharacteristic
125C2×C127#220311yescharacteristic
126C2×C127#220411yescharacteristic
127#2809C2×C12711yescharacteristic
128#1857C2×C12712yes—
129#1857C2×C12711yescharacteristic
130#1394C2×C12711yescharacteristic
131#1394C2×C12712yes—
132C127#1346511yescharacteristic, direct product factor, Sylow
133#519C22×C12711yescharacteristic
134#428—22no—
135#428—21no—
136C2×#101C22×C12712yes—
137C2×#101C22×C12711yescharacteristic
138#400—21no—
139#398—22no—
140#391C22×C12711yescharacteristic
141#391C22×C12712yes—
142#389—21no—
143#387—22no—
144#339—22no—
145#339—21no—
146C22×Q8C23×C12711yescharacteristic
147C2×M16—22no—
148C2×M16—21no—
149C4×Q8—41no—
150C4×Q8—41no—
151#117—22no—
152#117—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D4×C12712yes—
158C2×C4⋊C4D4×C12711yescharacteristic
159C2×C42D4×C12712yes—
160C2×C42D4×C12711yescharacteristic
161#107—42no—
162#107—41no—
163#106—42no—
164#106—41no—
165#101—22no—
166#101—21no—
167#101Q8×C12714yes—
168#101Q8×C12712yes—
169#95—21no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—22no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C2×Q8×C12712yes—
177C2×Q8C2×Q8×C12711yescharacteristic
178C2×Q8#41×C12711yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4C2×D4×C12712yes—
184C22×C4C2×D4×C12711yescharacteristic
185M16—24no—
186M16—22no—
187M16—41no—
188M16—42no—
189C2×C8—42no—
190C2×C8—41no—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—22no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—44no—
198C4⋊C4—42no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C22⋊C4—41no—
202C42—41no—
203C42—42no—
204C42—42no—
205C42—41no—
206C23#120×C12711yescharacteristic
207Q8—42no—
208Q8—41no—
209Q8—41no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4C22⋊Q8×C12712yes—
228C2×C4C22⋊Q8×C12711yescharacteristic
229C2×C4C4⋊Q8×C12712yes—
230C2×C4C4⋊Q8×C12711yescharacteristic
231C8—44no—
232C8—42no—
233C22—21no—
234C22—21no—
235C22#395×C12711yescharacteristic
236C22B(4,𝔽2)×C12711yescharacteristic
237C22#458×C12711yescharacteristic
238C4—22no—
239C4—21no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—81no—
246C4—82no—
247C4—81no—
248C2—21no—
249C2—21no—
250C2C127×#206211yescharacteristic
251C2C127×#220311yescharacteristic
252C2C127×#220411yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C127
prime radicalC23×C127#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
121. #13465C127direct (N × H)
132. C127#13465direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28092
C127×#18572
C127×#13942
#13465127