Finite Group Databasebeta

← C127×#11484 #44575157

Subgroups — C127×#11484 #44575157

Order 32512.

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

normal subgroups only

This group has 368 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×#2930C211yesmaximal, characteristic
2C127×#2115C212yesmaximal, complemented
3C127×#1328C212yesmaximal, complemented
4C127×#1320C212yesmaximal, complemented
5C2×#131×C127C2211yescharacteristic
6C22×M16×C127C411yescharacteristic
7#525×C127C411yescharacteristic
8C2×M32×C127—22no—
9#436×C127—22no—
10#435×C127—22no—
11#424×C127C2211yescharacteristic
12#408×C127C411yescharacteristic
13#407×C127C2211yescharacteristic
14#405×C127C411yescharacteristic
15#349×C127—22no—
16#349×C127C2214yes—
17C2×#41×C127C2×C411yescharacteristic
18C23×C4×C127C2×C411yescharacteristic
19#131×C127—42no—
20C2×M16×C127—21no—
21C2×M16×C127—21no—
22C2×M16×C127—42no—
23C2×M16×C127C2×C411yescharacteristic
24C2×M16×C127D412yes—
25C2×M16×C127C2311yescharacteristic
26C22×C8×C127C2×C411yescharacteristic
27C22×C8×C127C2×C411yescharacteristic
28C22×C8×C127D412yes—
29#123×C127C812yes—
30C22⋊Q8×C127—21no—
31#121×C127—21no—
32#120×C127C812yes—
33C4×D4×C127—22no—
34#117×C127C2×C411yescharacteristic
35M32×C127—24no—
36M32×C127—42no—
37C2×C16×C127—42no—
38C4⋊C8×C127—22no—
39C22⋊C8×C127—22no—
40C22⋊C8×C127—22no—
41#97×C127—21no—
42C4×C8×C127—21no—
43C24×C127C2×C811yescharacteristic
44#41×C127—41no—
45#41×C127—41no—
46C2×Q8×C127M1611yescharacteristic
47C2×D4×C127—22no—
48C2×D4×C127C2×C812yes—
49C2×D4×C127M1611yescharacteristic
50C22×C4×C127—21no—
51C22×C4×C127—21no—
52C22×C4×C127—41no—
53C22×C4×C127—41no—
54C22×C4×C127C22⋊C412yes—
55C22×C4×C127C2×C811yescharacteristic
56C22×C4×C127C22×C411yescharacteristic
57M16×C127—42no—
58M16×C127—41no—
59M16×C127—42no—
60M16×C127—42no—
61M16×C127—41no—
62C2×C8×C127—22no—
63C2×C8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127—21no—
66C2×C8×C127—21no—
67C2×C8×C127—41no—
68C2×C8×C127C22⋊C411yescharacteristic
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C2×D412yes—
71C4⋊C4×C127—22no—
72C4⋊C4×C127—21no—
73C22⋊C4×C127—22no—
74C22⋊C4×C127—22no—
75C22⋊C4×C127C2×C812yes—
76C42×C127—21no—
77C16×C127—44no—
78C23×C127—21no—
79C23×C127—41no—
80C23×C127—81no—
81C23×C127C22⋊C812yes—
82C23×C127C22×C811yescharacteristic
83Q8×C127—41no—
84D4×C127—42no—
85D4×C127—41no—
86D4×C127—82no—
87C2×C4×C127—21no—
88C2×C4×C127—22no—
89C2×C4×C127—21no—
90C2×C4×C127—22no—
91C2×C4×C127—22no—
92C2×C4×C127—21no—
93C2×C4×C127—42no—
94C2×C4×C127—41no—
95C2×C4×C127—41no—
96C2×C4×C127—41no—
97C2×C4×C127C22⋊C812yes—
98C2×C4×C127C2×C22⋊C411yescharacteristic
99C2×C4×C127C2×M1611yescharacteristic
100C8×C127—22no—
101C8×C127—21no—
102C8×C127—41no—
103C8×C127—41no—
104C8×C127#9912yes—
105C22×C127—21no—
106C22×C127—22no—
107C22×C127—42no—
108C22×C127—41no—
109C22×C127—41no—
110C22×C127—41no—
111C22×C127—41no—
112C22×C127—82no—
113C22×C127C2×C22⋊C811yescharacteristic
114C4×C127—21no—
115C4×C127—22no—
116C4×C127—42no—
117C4×C127—41no—
118C4×C127C2×#9911yescharacteristic
119C4×C127#41311yescharacteristic
120#11484C12711yesmaximal, characteristic, direct product factor, Sylow
121C2×C127—21no—
122C2×C127—42no—
123C2×C127—41no—
124C2×C127—81no—
125C2×C127#145911yescharacteristic
126#2930C2×C12711yescharacteristic
127#2115C2×C12712yescomplemented
128#1328C2×C12712yescomplemented
129#1320C2×C12712yescomplemented
130C127#1148411yescharacteristic, direct product factor, Sylow
131C2×#131C22×C12711yescharacteristic
132C22×M16C4×C12711yescharacteristic
133#525C4×C12711yescharacteristic
134C2×M32—22no—
135#436—22no—
136#435—22no—
137#424C22×C12711yescharacteristic
138#408C4×C12711yescharacteristic
139#407C22×C12711yescharacteristic
140#405C4×C12711yescharacteristic
141#349—22no—
142#349C22×C12714yes—
143C2×#41C2×C4×C12711yescharacteristic
144C23×C4C2×C4×C12711yescharacteristic
145#131—42no—
146C2×M16—21no—
147C2×M16—21no—
148C2×M16—42no—
149C2×M16C2×C4×C12711yescharacteristic
150C2×M16D4×C12712yes—
151C2×M16C23×C12711yescharacteristic
152C22×C8C2×C4×C12711yescharacteristic
153C22×C8C2×C4×C12711yescharacteristic
154C22×C8D4×C12712yes—
155#123C8×C12712yes—
156C22⋊Q8—21no—
157#121—21no—
158#120C8×C12712yes—
159C4×D4—22no—
160#117C2×C4×C12711yescharacteristic
161M32—24no—
162M32—42no—
163C2×C16—42no—
164C4⋊C8—22no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167#97—21no—
168C4×C8—21no—
169C24C2×C8×C12711yescharacteristic
170#41—41no—
171#41—41no—
172C2×Q8M16×C12711yescharacteristic
173C2×D4—22no—
174C2×D4C2×C8×C12712yes—
175C2×D4M16×C12711yescharacteristic
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4C22⋊C4×C12712yes—
181C22×C4C2×C8×C12711yescharacteristic
182C22×C4C22×C4×C12711yescharacteristic
183M16—42no—
184M16—41no—
185M16—42no—
186M16—42no—
187M16—41no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8C22⋊C4×C12711yescharacteristic
195C2×C8C22⋊C4×C12711yescharacteristic
196C2×C8C2×D4×C12712yes—
197C4⋊C4—22no—
198C4⋊C4—21no—
199C22⋊C4—22no—
200C22⋊C4—22no—
201C22⋊C4C2×C8×C12712yes—
202C42—21no—
203C16—44no—
204C23—21no—
205C23—41no—
206C23—81no—
207C23C22⋊C8×C12712yes—
208C23C22×C8×C12711yescharacteristic
209Q8—41no—
210D4—42no—
211D4—41no—
212D4—82no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4C22⋊C8×C12712yes—
224C2×C4C2×C22⋊C4×C12711yescharacteristic
225C2×C4C2×M16×C12711yescharacteristic
226C8—22no—
227C8—21no—
228C8—41no—
229C8—41no—
230C8#99×C12712yes—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—82no—
239C22C2×C22⋊C8×C12711yescharacteristic
240C4—21no—
241C4—22no—
242C4—42no—
243C4—41no—
244C4C2×#99×C12711yescharacteristic
245C4#413×C12711yescharacteristic
246C2—21no—
247C2—41no—
248C2—42no—
249C2—81no—
250C2C127×#145911yescharacteristic
subgroupG/H
centerC4×C127C2×#99
commutatorC23C22×C8×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127#1459
prime radical#525×C127C4
LCSG ▷ C23 ▷ 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×#1328C2semidirect
4. C127×#1320C2semidirect
120. #11484C127direct (N × H)
127. #2115C2×C127semidirect
128. #1328C2×C127semidirect
129. #1320C2×C127semidirect
130. C127#11484direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29302
C127×#21152
C127×#13282
C127×#13202
#11484127