Finite Group Databasebeta

← C127×#11751 #44575424

Subgroups — C127×#11751 #44575424

Order 32512.

364 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3169C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C4×#108×C127C211yesmaximal, characteristic, complemented
4C127×#1349C214yesmaximal, complemented
5#532×C127—21no—
6#500×C127C411yescharacteristic
7#493×C127C411yescharacteristic
8#486×C127—21no—
9#466×C127—21no—
10#466×C127C2212yes—
11C4×D8×C127—21no—
12C4×D8×C127C412yes—
13C2×#108×C127—21no—
14C4×M16×C127—21no—
15C2×C4×C8×C127C2211yescharacteristic
16C4⋊C16×C127—21no—
17C22⋊C16×C127C2212yes—
18#346×C127—21no—
19#341×C127C2212yes—
20C2×#41×C127—41no—
21C2×D8×C127—21no—
22C2×D8×C127C2×C412yes—
23C2×M16×C127—22no—
24C22×C8×C127D411yescharacteristic
25C22×C8×C127C2311yescharacteristic
26C4⋊Q8×C127—21no—
27#127×C127—21no—
28#124×C127—41no—
29#121×C127—22no—
30#121×C127—41no—
31C4×D4×C127—22no—
32C4×D4×C127—41no—
33C2×C42×C127D411yescharacteristic
34C2×C16×C127—22no—
35#108×C127—24no—
36#107×C127—21no—
37#107×C127C2×C412yes—
38#102×C127—22no—
39#102×C127—22no—
40#97×C127—41no—
41C4×C8×C127—41no—
42C4×C8×C127C2×C411yescharacteristic
43C4×C8×C127C2×C411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127D411yescharacteristic
46#41×C127—84no—
47C2×Q8×C127—41no—
48C2×D4×C127—22no—
49C2×D4×C127—42no—
50C2×D4×C127—41no—
51C2×D4×C127—41no—
52C22×C4×C127—42no—
53C22×C4×C127SD1611yescharacteristic
54C22×C4×C127SD1611yescharacteristic
55C22×C4×C127C2×D411yescharacteristic
56D8×C127—42no—
57D8×C127—42no—
58M16×C127—24no—
59M16×C127—42no—
60C2×C8×C127—22no—
61C2×C8×C127—41no—
62C2×C8×C127—42no—
63C2×C8×C127C22⋊C411yescharacteristic
64C2×C8×C127C22⋊C411yescharacteristic
65C2×C8×C127C22×C411yescharacteristic
66C2×C8×C127C2×D411yescharacteristic
67C4⋊C4×C127—22no—
68C4⋊C4×C127—41no—
69C22⋊C4×C127—42no—
70C22⋊C4×C127—42no—
71C42×C127C22⋊C411yescharacteristic
72C42×C127C22⋊C411yescharacteristic
73C42×C127D811yescharacteristic
74C42×C127D811yescharacteristic
75C16×C127—42no—
76C23×C127—42no—
77C23×C127C2×SD1611yescharacteristic
78Q8×C127—82no—
79D4×C127—42no—
80D4×C127—42no—
81D4×C127—82no—
82D4×C127—84no—
83D4×C127—82no—
84C2×C4×C127—22no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—41no—
88C2×C4×C127—42no—
89C2×C4×C127—84no—
90C2×C4×C127#10211yescharacteristic
91C2×C4×C127#10211yescharacteristic
92C2×C4×C127#10211yescharacteristic
93C2×C4×C127#10211yescharacteristic
94C2×C4×C127C2×C22⋊C411yescharacteristic
95C2×C4×C127C2×D811yescharacteristic
96C8×C127—21no—
97C8×C127—21no—
98C8×C127—21no—
99C8×C127—44no—
100C8×C127#10412yes—
101C22×C127—21no—
102C22×C127—21no—
103C22×C127—21no—
104C22×C127—82no—
105C22×C127—82no—
106C22×C127—82no—
107C22×C127C2×#10211yescharacteristic
108C4×C127—21no—
109C4×C127—21no—
110C4×C127—21no—
111C4×C127—21no—
112C4×C127—82no—
113C4×C127#36112yes—
114C4×C127#41011yescharacteristic
115C4×C127C2×#10411yescharacteristic
116#11751C12711yesmaximal, characteristic, direct product factor, Sylow
117C2×C127—41no—
118C2×C127—162no—
119C2×C127#150211yescharacteristic
120C2×C127#214311yescharacteristic
121C2×C127C2×#36111yescharacteristic
122#3169C2×C12711yescharacteristic
123#2163C2×C12711yescharacteristic, complemented
124C4×#108C2×C12711yescharacteristic, complemented
125#1349C2×C12714yescomplemented
126C127#1175111yescharacteristic, direct product factor, Sylow
127#532—21no—
128#500C4×C12711yescharacteristic
129#493C4×C12711yescharacteristic
130#486—21no—
131#466—21no—
132#466C22×C12712yes—
133C4×D8—21no—
134C4×D8C4×C12712yes—
135C2×#108—21no—
136C4×M16—21no—
137C2×C4×C8C22×C12711yescharacteristic
138C4⋊C16—21no—
139C22⋊C16C22×C12712yes—
140#346—21no—
141#341C22×C12712yes—
142C2×#41—41no—
143C2×D8—21no—
144C2×D8C2×C4×C12712yes—
145C2×M16—22no—
146C22×C8D4×C12711yescharacteristic
147C22×C8C23×C12711yescharacteristic
148C4⋊Q8—21no—
149#127—21no—
150#124—41no—
151#121—22no—
152#121—41no—
153C4×D4—22no—
154C4×D4—41no—
155C2×C42D4×C12711yescharacteristic
156C2×C16—22no—
157#108—24no—
158#107—21no—
159#107C2×C4×C12712yes—
160#102—22no—
161#102—22no—
162#97—41no—
163C4×C8—41no—
164C4×C8C2×C4×C12711yescharacteristic
165C4×C8C2×C4×C12711yescharacteristic
166C4×C8D4×C12711yescharacteristic
167C4×C8D4×C12711yescharacteristic
168#41—84no—
169C2×Q8—41no—
170C2×D4—22no—
171C2×D4—42no—
172C2×D4—41no—
173C2×D4—41no—
174C22×C4—42no—
175C22×C4SD16×C12711yescharacteristic
176C22×C4SD16×C12711yescharacteristic
177C22×C4C2×D4×C12711yescharacteristic
178D8—42no—
179D8—42no—
180M16—24no—
181M16—42no—
182C2×C8—22no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8C22⋊C4×C12711yescharacteristic
186C2×C8C22⋊C4×C12711yescharacteristic
187C2×C8C22×C4×C12711yescharacteristic
188C2×C8C2×D4×C12711yescharacteristic
189C4⋊C4—22no—
190C4⋊C4—41no—
191C22⋊C4—42no—
192C22⋊C4—42no—
193C42C22⋊C4×C12711yescharacteristic
194C42C22⋊C4×C12711yescharacteristic
195C42D8×C12711yescharacteristic
196C42D8×C12711yescharacteristic
197C16—42no—
198C23—42no—
199C23C2×SD16×C12711yescharacteristic
200Q8—82no—
201D4—42no—
202D4—42no—
203D4—82no—
204D4—84no—
205D4—82no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—84no—
212C2×C4#102×C12711yescharacteristic
213C2×C4#102×C12711yescharacteristic
214C2×C4#102×C12711yescharacteristic
215C2×C4#102×C12711yescharacteristic
216C2×C4C2×C22⋊C4×C12711yescharacteristic
217C2×C4C2×D8×C12711yescharacteristic
218C8—21no—
219C8—21no—
220C8—21no—
221C8—44no—
222C8#104×C12712yes—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—82no—
227C22—82no—
228C22—82no—
229C22C2×#102×C12711yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—21no—
234C4—82no—
235C4#361×C12712yes—
236C4#410×C12711yescharacteristic
237C4C2×#104×C12711yescharacteristic
238C2—41no—
239C2—162no—
240C2C127×#150211yescharacteristic
241C2C127×#214311yescharacteristic
242C2C2×#361×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3169C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2163C2semidirect
3. C4×#108×C127C2semidirect
4. C127×#1349C2semidirect
116. #11751C127direct (N × H)
123. #2163C2×C127semidirect
124. C4×#108C2×C127semidirect
125. #1349C2×C127semidirect
126. C127#11751direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31692
C127×#21632
C4×#108×C1272
C127×#13492
#11751127