Finite Group Databasebeta

← C127×#11486 #44575159

Subgroups — C127×#11486 #44575159

Order 32512.

364 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2932C211yesmaximal, characteristic
2C127×#2115C212yesmaximal, complemented
3C127×#1327C212yesmaximal, complemented
4C127×#1321C212yesmaximal, complemented
5C2×#131×C127C411yescharacteristic
6C2×#131×C127C2211yescharacteristic
7#532×C127C411yescharacteristic
8C2×M32×C127—22no—
9#435×C127—22no—
10#435×C127—22no—
11#423×C127C2211yescharacteristic
12#408×C127C411yescharacteristic
13#408×C127C2211yescharacteristic
14C2×#97×C127C411yescharacteristic
15#349×C127—22no—
16#349×C127C2214yes—
17C2×#41×C127C2×C411yescharacteristic
18C2×#41×C127C2×C411yescharacteristic
19#131×C127—42no—
20#131×C127—42no—
21C2×M16×C127—21no—
22C2×M16×C127C2×C411yescharacteristic
23C2×M16×C127D412yes—
24C2×M16×C127C2311yescharacteristic
25C22×C8×C127—21no—
26C22×C8×C127C2×C411yescharacteristic
27C22×C8×C127C2×C411yescharacteristic
28C22×C8×C127D412yes—
29C4⋊Q8×C127C811yescharacteristic
30#127×C127C811yescharacteristic
31#124×C127C811yescharacteristic
32#124×C127C811yescharacteristic
33#121×C127—22no—
34C4×D4×C127—22no—
35C2×C42×C127C2×C411yescharacteristic
36M32×C127—24no—
37M32×C127—42no—
38C2×C16×C127—42no—
39C4⋊C8×C127—22no—
40C22⋊C8×C127—22no—
41C22⋊C8×C127—22no—
42#97×C127—21no—
43#97×C127—21no—
44#41×C127—41no—
45#41×C127—41no—
46#41×C127—41no—
47#41×C127—41no—
48C2×Q8×C127C2×C811yescharacteristic
49C2×Q8×C127C2×C811yescharacteristic
50C2×D4×C127—21no—
51C2×D4×C127—22no—
52C2×D4×C127C2×C811yescharacteristic
53C2×D4×C127C2×C811yescharacteristic
54C2×D4×C127M1612yes—
55C22×C4×C127—21no—
56C22×C4×C127—21no—
57C22×C4×C127C22⋊C412yes—
58C22×C4×C127C22×C411yescharacteristic
59M16×C127—42no—
60M16×C127—41no—
61M16×C127—42no—
62M16×C127—41no—
63C2×C8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127—22no—
66C2×C8×C127—21no—
67C2×C8×C127—21no—
68C2×C8×C127—42no—
69C2×C8×C127—41no—
70C2×C8×C127C22⋊C411yescharacteristic
71C2×C8×C127C22⋊C411yescharacteristic
72C2×C8×C127C2×D412yes—
73C4⋊C4×C127—22no—
74C22⋊C4×C127—22no—
75C22⋊C4×C127—22no—
76C42×C127—21no—
77C42×C127C2×C811yescharacteristic
78C42×C127C2×C811yescharacteristic
79C16×C127—44no—
80C23×C127—21no—
81C23×C127C22⋊C812yes—
82C23×C127C2×M1611yescharacteristic
83Q8×C127—41no—
84Q8×C127—41no—
85D4×C127—41no—
86D4×C127—42no—
87D4×C127—41no—
88D4×C127—42no—
89D4×C127—82no—
90C2×C4×C127—21no—
91C2×C4×C127—22no—
92C2×C4×C127—21no—
93C2×C4×C127—22no—
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—41no—
98C2×C4×C127—41no—
99C2×C4×C127—81no—
100C2×C4×C127C22⋊C812yes—
101C2×C4×C127C2×C22⋊C411yescharacteristic
102C2×C4×C127C22×C811yescharacteristic
103C8×C127—22no—
104C8×C127—21no—
105C8×C127—41no—
106C8×C127—41no—
107C8×C127#9912yes—
108C22×C127—21no—
109C22×C127—22no—
110C22×C127—41no—
111C22×C127—42no—
112C22×C127—42no—
113C22×C127—41no—
114C22×C127C2×C22⋊C811yescharacteristic
115C4×C127—22no—
116C4×C127—21no—
117C4×C127—41no—
118C4×C127—41no—
119C4×C127—41no—
120C4×C127C2×#9911yescharacteristic
121C4×C127#41311yescharacteristic
122#11486C12711yesmaximal, characteristic, direct product factor, Sylow
123C2×C127—21no—
124C2×C127—41no—
125C2×C127—42no—
126C2×C127—81no—
127C2×C127#145911yescharacteristic
128#2932C2×C12711yescharacteristic
129#2115C2×C12712yescomplemented
130#1327C2×C12712yescomplemented
131#1321C2×C12712yescomplemented
132C127#1148611yescharacteristic, direct product factor, Sylow
133C2×#131C4×C12711yescharacteristic
134C2×#131C22×C12711yescharacteristic
135#532C4×C12711yescharacteristic
136C2×M32—22no—
137#435—22no—
138#435—22no—
139#423C22×C12711yescharacteristic
140#408C4×C12711yescharacteristic
141#408C22×C12711yescharacteristic
142C2×#97C4×C12711yescharacteristic
143#349—22no—
144#349C22×C12714yes—
145C2×#41C2×C4×C12711yescharacteristic
146C2×#41C2×C4×C12711yescharacteristic
147#131—42no—
148#131—42no—
149C2×M16—21no—
150C2×M16C2×C4×C12711yescharacteristic
151C2×M16D4×C12712yes—
152C2×M16C23×C12711yescharacteristic
153C22×C8—21no—
154C22×C8C2×C4×C12711yescharacteristic
155C22×C8C2×C4×C12711yescharacteristic
156C22×C8D4×C12712yes—
157C4⋊Q8C8×C12711yescharacteristic
158#127C8×C12711yescharacteristic
159#124C8×C12711yescharacteristic
160#124C8×C12711yescharacteristic
161#121—22no—
162C4×D4—22no—
163C2×C42C2×C4×C12711yescharacteristic
164M32—24no—
165M32—42no—
166C2×C16—42no—
167C4⋊C8—22no—
168C22⋊C8—22no—
169C22⋊C8—22no—
170#97—21no—
171#97—21no—
172#41—41no—
173#41—41no—
174#41—41no—
175#41—41no—
176C2×Q8C2×C8×C12711yescharacteristic
177C2×Q8C2×C8×C12711yescharacteristic
178C2×D4—21no—
179C2×D4—22no—
180C2×D4C2×C8×C12711yescharacteristic
181C2×D4C2×C8×C12711yescharacteristic
182C2×D4M16×C12712yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4C22⋊C4×C12712yes—
186C22×C4C22×C4×C12711yescharacteristic
187M16—42no—
188M16—41no—
189M16—42no—
190M16—41no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—42no—
197C2×C8—41no—
198C2×C8C22⋊C4×C12711yescharacteristic
199C2×C8C22⋊C4×C12711yescharacteristic
200C2×C8C2×D4×C12712yes—
201C4⋊C4—22no—
202C22⋊C4—22no—
203C22⋊C4—22no—
204C42—21no—
205C42C2×C8×C12711yescharacteristic
206C42C2×C8×C12711yescharacteristic
207C16—44no—
208C23—21no—
209C23C22⋊C8×C12712yes—
210C23C2×M16×C12711yescharacteristic
211Q8—41no—
212Q8—41no—
213D4—41no—
214D4—42no—
215D4—41no—
216D4—42no—
217D4—82no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4C22⋊C8×C12712yes—
229C2×C4C2×C22⋊C4×C12711yescharacteristic
230C2×C4C22×C8×C12711yescharacteristic
231C8—22no—
232C8—21no—
233C8—41no—
234C8—41no—
235C8#99×C12712yes—
236C22—21no—
237C22—22no—
238C22—41no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22C2×C22⋊C8×C12711yescharacteristic
243C4—22no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4C2×#99×C12711yescharacteristic
249C4#413×C12711yescharacteristic
250C2—21no—
251C2—41no—
252C2—42no—
253C2—81no—
254C2C127×#145911yescharacteristic
subgroupG/H
centerC4×C127C2×#99
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127#1459
prime radical#532×C127C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C2×C8×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2115C2semidirect
3. C127×#1327C2semidirect
4. C127×#1321C2semidirect
122. #11486C127direct (N × H)
129. #2115C2×C127semidirect
130. #1327C2×C127semidirect
131. #1321C2×C127semidirect
132. C127#11486direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29322
C127×#21152
C127×#13272
C127×#13212
#11486127