Finite Group Databasebeta

← C127×#11537 #44575210

Subgroups — C127×#11537 #44575210

Order 32512.

348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2929C211yesmaximal, characteristic
2C127×#2166C212yesmaximal, complemented
3C127×#1321C212yesmaximal, complemented
4C127×#1320C212yesmaximal, complemented
5C2×#131×C127C411yescharacteristic
6C23×C8×C127C411yescharacteristic
7#525×C127C411yescharacteristic
8#435×C127—22no—
9C8×D4×C127—22no—
10#424×C127C411yescharacteristic
11#408×C127C2211yescharacteristic
12#407×C127C2211yescharacteristic
13#405×C127C2211yescharacteristic
14#364×C127—22no—
15#349×C127C2214yes—
16#347×C127—22no—
17C2×#41×C127C2×C411yescharacteristic
18C23×C4×C127C2×C411yescharacteristic
19#131×C127—42no—
20C2×M16×C127—21no—
21C2×M16×C127C2×C411yescharacteristic
22C2×M16×C127C2311yescharacteristic
23C22×C8×C127—21no—
24C22×C8×C127—21no—
25C22×C8×C127—21no—
26C22×C8×C127—42no—
27C22×C8×C127C2×C411yescharacteristic
28C22×C8×C127C2×C411yescharacteristic
29#123×C127—21no—
30C22⋊Q8×C127—21no—
31#121×C127—21no—
32#120×C127—21no—
33C4×D4×C127—22no—
34#117×C127C2×C411yescharacteristic
35M32×C127—24no—
36C4⋊C8×C127—22no—
37C22⋊C8×C127—22no—
38C22⋊C8×C127—22no—
39#97×C127D412yes—
40C4×C8×C127D412yes—
41C24×C127M1611yescharacteristic
42#41×C127—41no—
43#41×C127—41no—
44C2×Q8×C127M1611yescharacteristic
45C2×D4×C127—22no—
46C2×D4×C127—21no—
47C2×D4×C127M1611yescharacteristic
48C22×C4×C127—21no—
49C22×C4×C127—21no—
50C22×C4×C127—21no—
51C22×C4×C127—41no—
52C22×C4×C127—41no—
53C22×C4×C127M1611yescharacteristic
54C22×C4×C127C22×C411yescharacteristic
55M16×C127—41no—
56M16×C127—42no—
57M16×C127—41no—
58C2×C8×C127—22no—
59C2×C8×C127—21no—
60C2×C8×C127—21no—
61C2×C8×C127—42no—
62C2×C8×C127—42no—
63C2×C8×C127—42no—
64C2×C8×C127—41no—
65C2×C8×C127C22⋊C411yescharacteristic
66C2×C8×C127C22⋊C411yescharacteristic
67C2×C8×C127C2×D412yes—
68C4⋊C4×C127—22no—
69C4⋊C4×C127—21no—
70C22⋊C4×C127—22no—
71C22⋊C4×C127—22no—
72C22⋊C4×C127—21no—
73C42×C127C22⋊C412yes—
74C16×C127—44no—
75C23×C127—21no—
76C23×C127—21no—
77C23×C127—41no—
78C23×C127—42no—
79C23×C127C2×M1611yescharacteristic
80Q8×C127—41no—
81D4×C127—41no—
82D4×C127—44no—
83D4×C127—42no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—22no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—42no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—41no—
94C2×C4×C127—41no—
95C2×C4×C127C2×C22⋊C411yescharacteristic
96C2×C4×C127C2×M1611yescharacteristic
97C8×C127—22no—
98C8×C127—21no—
99C8×C127—41no—
100C8×C127—41no—
101C8×C127#10012yes—
102C22×C127—22no—
103C22×C127—21no—
104C22×C127—41no—
105C22×C127—41no—
106C22×C127—42no—
107C22×C127—42no—
108C22×C127—42no—
109C22×C127—41no—
110C22×C127—41no—
111C22×C127#40711yescharacteristic
112C4×C127—21no—
113C4×C127—42no—
114C4×C127—41no—
115C4×C127—41no—
116C4×C127#41011yescharacteristic
117C4×C127C2×#10011yescharacteristic
118#11537C12711yesmaximal, characteristic, direct product factor, Sylow
119C2×C127—21no—
120C2×C127—42no—
121C2×C127—41no—
122C2×C127—81no—
123C2×C127#146611yescharacteristic
124#2929C2×C12711yescharacteristic
125#2166C2×C12712yescomplemented
126#1321C2×C12712yescomplemented
127#1320C2×C12712yescomplemented
128C127#1153711yescharacteristic, direct product factor, Sylow
129C2×#131C4×C12711yescharacteristic
130C23×C8C4×C12711yescharacteristic
131#525C4×C12711yescharacteristic
132#435—22no—
133C8×D4—22no—
134#424C4×C12711yescharacteristic
135#408C22×C12711yescharacteristic
136#407C22×C12711yescharacteristic
137#405C22×C12711yescharacteristic
138#364—22no—
139#349C22×C12714yes—
140#347—22no—
141C2×#41C2×C4×C12711yescharacteristic
142C23×C4C2×C4×C12711yescharacteristic
143#131—42no—
144C2×M16—21no—
145C2×M16C2×C4×C12711yescharacteristic
146C2×M16C23×C12711yescharacteristic
147C22×C8—21no—
148C22×C8—21no—
149C22×C8—21no—
150C22×C8—42no—
151C22×C8C2×C4×C12711yescharacteristic
152C22×C8C2×C4×C12711yescharacteristic
153#123—21no—
154C22⋊Q8—21no—
155#121—21no—
156#120—21no—
157C4×D4—22no—
158#117C2×C4×C12711yescharacteristic
159M32—24no—
160C4⋊C8—22no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163#97D4×C12712yes—
164C4×C8D4×C12712yes—
165C24M16×C12711yescharacteristic
166#41—41no—
167#41—41no—
168C2×Q8M16×C12711yescharacteristic
169C2×D4—22no—
170C2×D4—21no—
171C2×D4M16×C12711yescharacteristic
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4M16×C12711yescharacteristic
178C22×C4C22×C4×C12711yescharacteristic
179M16—41no—
180M16—42no—
181M16—41no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—41no—
189C2×C8C22⋊C4×C12711yescharacteristic
190C2×C8C22⋊C4×C12711yescharacteristic
191C2×C8C2×D4×C12712yes—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—21no—
197C42C22⋊C4×C12712yes—
198C16—44no—
199C23—21no—
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×M16×C12711yescharacteristic
204Q8—41no—
205D4—41no—
206D4—42no—
207D4—44no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4C2×C22⋊C4×C12711yescharacteristic
220C2×C4C2×M16×C12711yescharacteristic
221C8—22no—
222C8—21no—
223C8—41no—
224C8—41no—
225C8#100×C12712yes—
226C22—22no—
227C22—21no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22#407×C12711yescharacteristic
236C4—21no—
237C4—42no—
238C4—41no—
239C4—41no—
240C4#410×C12711yescharacteristic
241C4C2×#100×C12711yescharacteristic
242C2—21no—
243C2—42no—
244C2—41no—
245C2—81no—
246C2C127×#146611yescharacteristic
subgroupG/H
centerC4×C127#410
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127#1466
prime radical#525×C127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C2×C8×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2166C2semidirect
3. C127×#1321C2semidirect
4. C127×#1320C2semidirect
118. #11537C127direct (N × H)
125. #2166C2×C127semidirect
126. #1321C2×C127semidirect
127. #1320C2×C127semidirect
128. C127#11537direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29292
C127×#21662
C127×#13212
C127×#13202
#11537127