Finite Group Databasebeta

← C127×#11678 #44575351

Subgroups — C127×#11678 #44575351

Order 32512.

362 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 122 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
2C2×#346×C127C211yesmaximal, characteristic, complemented
3C127×#1568C211yesmaximal, characteristic, complemented
4C127×#1333C214yesmaximal, complemented
5#532×C127—21no—
6C22×C16×C127—21no—
7#500×C127C411yescharacteristic
8#493×C127C411yescharacteristic
9#486×C127—21no—
10#466×C127—21no—
11#466×C127C412yes—
12C4×D8×C127—21no—
13C4×D8×C127C2212yes—
14#432×C127—21no—
15C2×C4×C8×C127C2211yescharacteristic
16#346×C127—21no—
17#346×C127C2212yes—
18#335×C127—21no—
19#334×C127C2212yes—
20C2×#41×C127—41no—
21C2×D8×C127—21no—
22C2×D8×C127C2×C412yes—
23C22×C8×C127C2×C411yescharacteristic
24C22×C8×C127D411yescharacteristic
25C4⋊Q8×C127—21no—
26#127×C127—21no—
27#124×C127—41no—
28#121×C127—22no—
29#121×C127—41no—
30C4×D4×C127—22no—
31C4×D4×C127—41no—
32C2×C42×C127D411yescharacteristic
33C2×C16×C127—24no—
34C2×C16×C127—22no—
35#107×C127—21no—
36#107×C127C2×C412yes—
37C4⋊C8×C127—22no—
38#102×C127—22no—
39#102×C127—22no—
40C22⋊C8×C127—41no—
41#97×C127—41no—
42C4×C8×C127C2×C411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127C2311yescharacteristic
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×C127C22⋊C411yescharacteristic
54C22×C4×C127D811yescharacteristic
55C22×C4×C127SD1611yescharacteristic
56D8×C127—24no—
57D8×C127—42no—
58C2×C8×C127—22no—
59C2×C8×C127—22no—
60C2×C8×C127—42no—
61C2×C8×C127C22⋊C411yescharacteristic
62C2×C8×C127C22⋊C411yescharacteristic
63C2×C8×C127C22×C411yescharacteristic
64C2×C8×C127C2×D411yescharacteristic
65C4⋊C4×C127—22no—
66C4⋊C4×C127—41no—
67C22⋊C4×C127—42no—
68C22⋊C4×C127—42no—
69C42×C127C22⋊C411yescharacteristic
70C42×C127D811yescharacteristic
71C42×C127SD1611yescharacteristic
72C42×C127C2×D411yescharacteristic
73C16×C127—24no—
74C23×C127—42no—
75C23×C127#10211yescharacteristic
76Q8×C127—82no—
77D4×C127—42no—
78D4×C127—42no—
79D4×C127—82no—
80D4×C127—82no—
81D4×C127—84no—
82C2×C4×C127—22no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—41no—
86C2×C4×C127—42no—
87C2×C4×C127—84no—
88C2×C4×C127#10211yescharacteristic
89C2×C4×C127#10211yescharacteristic
90C2×C4×C127#10211yescharacteristic
91C2×C4×C127C2×C22⋊C411yescharacteristic
92C2×C4×C127C2×D811yescharacteristic
93C2×C4×C127C2×SD1611yescharacteristic
94C8×C127—21no—
95C8×C127—21no—
96C8×C127—82no—
97C8×C127#10412yes—
98C8×C127#13112yes—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127—82no—
102C22×C127—82no—
103C22×C127—82no—
104C22×C127#36112yes—
105C22×C127C2×#10211yescharacteristic
106C4×C127—21no—
107C4×C127—21no—
108C4×C127—21no—
109C4×C127—21no—
110C4×C127—21no—
111C4×C127—82no—
112C4×C127#40811yescharacteristic
113C4×C127C2×#10411yescharacteristic
114#11678C12711yesmaximal, characteristic, direct product factor, Sylow
115C2×C127—22no—
116C2×C127—162no—
117C2×C127#149211yescharacteristic
118C2×C127#214511yescharacteristic
119C2×C127C2×#36111yescharacteristic
120#3169C2×C12711yescharacteristic
121C2×#346C2×C12711yescharacteristic, complemented
122#1568C2×C12711yescharacteristic, complemented
123#1333C2×C12714yescomplemented
124C127#1167811yescharacteristic, direct product factor, Sylow
125#532—21no—
126C22×C16—21no—
127#500C4×C12711yescharacteristic
128#493C4×C12711yescharacteristic
129#486—21no—
130#466—21no—
131#466C4×C12712yes—
132C4×D8—21no—
133C4×D8C22×C12712yes—
134#432—21no—
135C2×C4×C8C22×C12711yescharacteristic
136#346—21no—
137#346C22×C12712yes—
138#335—21no—
139#334C22×C12712yes—
140C2×#41—41no—
141C2×D8—21no—
142C2×D8C2×C4×C12712yes—
143C22×C8C2×C4×C12711yescharacteristic
144C22×C8D4×C12711yescharacteristic
145C4⋊Q8—21no—
146#127—21no—
147#124—41no—
148#121—22no—
149#121—41no—
150C4×D4—22no—
151C4×D4—41no—
152C2×C42D4×C12711yescharacteristic
153C2×C16—24no—
154C2×C16—22no—
155#107—21no—
156#107C2×C4×C12712yes—
157C4⋊C8—22no—
158#102—22no—
159#102—22no—
160C22⋊C8—41no—
161#97—41no—
162C4×C8C2×C4×C12711yescharacteristic
163C4×C8D4×C12711yescharacteristic
164C4×C8D4×C12711yescharacteristic
165C4×C8C23×C12711yescharacteristic
166#41—84no—
167C2×Q8—41no—
168C2×D4—22no—
169C2×D4—42no—
170C2×D4—41no—
171C2×D4—41no—
172C22×C4—42no—
173C22×C4C22⋊C4×C12711yescharacteristic
174C22×C4D8×C12711yescharacteristic
175C22×C4SD16×C12711yescharacteristic
176D8—24no—
177D8—42no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—42no—
181C2×C8C22⋊C4×C12711yescharacteristic
182C2×C8C22⋊C4×C12711yescharacteristic
183C2×C8C22×C4×C12711yescharacteristic
184C2×C8C2×D4×C12711yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—41no—
187C22⋊C4—42no—
188C22⋊C4—42no—
189C42C22⋊C4×C12711yescharacteristic
190C42D8×C12711yescharacteristic
191C42SD16×C12711yescharacteristic
192C42C2×D4×C12711yescharacteristic
193C16—24no—
194C23—42no—
195C23#102×C12711yescharacteristic
196Q8—82no—
197D4—42no—
198D4—42no—
199D4—82no—
200D4—82no—
201D4—84no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—84no—
208C2×C4#102×C12711yescharacteristic
209C2×C4#102×C12711yescharacteristic
210C2×C4#102×C12711yescharacteristic
211C2×C4C2×C22⋊C4×C12711yescharacteristic
212C2×C4C2×D8×C12711yescharacteristic
213C2×C4C2×SD16×C12711yescharacteristic
214C8—21no—
215C8—21no—
216C8—82no—
217C8#104×C12712yes—
218C8#131×C12712yes—
219C22—21no—
220C22—21no—
221C22—82no—
222C22—82no—
223C22—82no—
224C22#361×C12712yes—
225C22C2×#102×C12711yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—82no—
232C4#408×C12711yescharacteristic
233C4C2×#104×C12711yescharacteristic
234C2—22no—
235C2—162no—
236C2C127×#149211yescharacteristic
237C2C127×#214511yescharacteristic
238C2C2×#361×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC127×#3169C2
LCSG ▷ C2×C8 ▷ 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. C2×#346×C127C2semidirect
3. C127×#1568C2semidirect
4. C127×#1333C2semidirect
114. #11678C127direct (N × H)
121. C2×#346C2×C127semidirect
122. #1568C2×C127semidirect
123. #1333C2×C127semidirect
124. C127#11678direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31692
C2×#346×C1272
C127×#15682
C127×#13332
#11678127