Finite Group Databasebeta

← C127×#2055 #30635007

Subgroups — C127×#2055 #30635007

Order 16256.

324 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C22×SD16×C127C211yesmaximal, characteristic
2C2×C4⋊C8×C127C211yesmaximal, characteristic, complemented
3C2×#103×C127C211yesmaximal, characteristic, complemented
4C2×#102×C127C211yesmaximal, characteristic
5#391×C127C211yesmaximal, characteristic, complemented
6#390×C127C211yesmaximal, characteristic
7#340×C127C211yesmaximal, characteristic, complemented
8C22×Q8×C127C2211yescharacteristic
9C22×D4×C127C2211yescharacteristic
10C2×SD16×C127—22no—
11C2×SD16×C127—22no—
12C2×SD16×C127—22no—
13C22×C8×C127C2211yescharacteristic
14C22×C8×C127C2211yescharacteristic
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C22⋊C4×C127—21no—
18C2×C22⋊C4×C127—21no—
19C2×C42×C127C2211yescharacteristic
20C4⋊C8×C127—22no—
21#103×C127—22no—
22#102×C127—22no—
23#95×C127—21no—
24#95×C127—21no—
25C24×C127—21no—
26C2×Q8×C127—21no—
27C2×Q8×C127—21no—
28C2×Q8×C127—21no—
29C2×Q8×C127—21no—
30C2×Q8×C127—21no—
31C2×Q8×C127D412yes—
32C2×D4×C127—21no—
33C2×D4×C127—21no—
34C2×D4×C127—21no—
35C2×D4×C127—21no—
36C2×D4×C127—21no—
37C2×D4×C127D412yes—
38C22×C4×C127—21no—
39C22×C4×C127—21no—
40C22×C4×C127—21no—
41C22×C4×C127D411yescharacteristic
42C22×C4×C127D411yescharacteristic
43C22×C4×C127C2311yescharacteristic
44SD16×C127—28no—
45C2×C8×C127—21no—
46C2×C8×C127—21no—
47C2×C8×C127—21no—
48C2×C8×C127—21no—
49C2×C8×C127—21no—
50C2×C8×C127D412yes—
51C4⋊C4×C127—21no—
52C4⋊C4×C127—21no—
53C4⋊C4×C127—21no—
54C4⋊C4×C127—21no—
55C22⋊C4×C127—42no—
56C22⋊C4×C127—42no—
57C42×C127—21no—
58C42×C127—21no—
59C23×C127—22no—
60C23×C127—41no—
61C23×C127—41no—
62C23×C127—41no—
63C23×C127—41no—
64C23×C127—41no—
65C23×C127—41no—
66C23×C127C2×D411yescharacteristic
67Q8×C127—22no—
68Q8×C127—22no—
69Q8×C127—41no—
70Q8×C127—41no—
71D4×C127—22no—
72D4×C127—22no—
73D4×C127—41no—
74D4×C127—41no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—22no—
79C2×C4×C127—21no—
80C2×C4×C127—21no—
81C2×C4×C127—41no—
82C2×C4×C127—41no—
83C2×C4×C127—41no—
84C2×C4×C127—41no—
85C2×C4×C127—41no—
86C2×C4×C127—41no—
87C2×C4×C127—41no—
88C2×C4×C127—41no—
89C2×C4×C127SD1612yescomplemented
90C2×C4×C127C2×D411yescharacteristic
91C2×C4×C127C2×D411yescharacteristic
92C2×C4×C127C2×D411yescharacteristic
93C2×C4×C127#4111yescharacteristic
94C2×C4×C127#4111yescharacteristic
95C2×C4×C127#4111yescharacteristic
96C8×C127—22no—
97C8×C127—41no—
98C22×C127—42no—
99C22×C127—42no—
100C22×C127—42no—
101C22×C127—81no—
102C22×C127—81no—
103C22×C127—81no—
104C22×C127—81no—
105C22×C127#12111yescharacteristic
106C22×C127#12111yescharacteristic
107C22×C127#12111yescharacteristic
108C22×C127C2×SD1611yescharacteristic
109C22×C127#13511yescharacteristic
110C22×C127AGL(1,ℤ/8)11yescharacteristic
111C22×C127#13711yescharacteristic
112C4×C127—22no—
113C4×C127—42no—
114C4×C127—41no—
115C4×C127—81no—
116C4×C127—81no—
117C4×C127#12011yescharacteristic
118C4×C127#12311yescharacteristic
119C4×C127#12311yescharacteristic
120C4×C127#12411yescharacteristic
121C2×C127—82no—
122C2×C127#39411yescharacteristic
123C2×C127#46011yescharacteristic
124C2×C127#46111yescharacteristic
125C2×C127#46311yescharacteristic
126C2×C127#46411yescharacteristic
127C2×C127#46511yescharacteristic
128C2×C127#46811yescharacteristic
129#2055C12711yesmaximal, characteristic, direct product factor, Sylow
130C127#205511yescharacteristic, direct product factor, Sylow
131C22×SD16C2×C12711yescharacteristic
132C2×C4⋊C8C2×C12711yescharacteristic, complemented
133C2×#103C2×C12711yescharacteristic, complemented
134C2×#102C2×C12711yescharacteristic
135#391C2×C12711yescharacteristic, complemented
136#390C2×C12711yescharacteristic
137#340C2×C12711yescharacteristic, complemented
138C22×Q8C22×C12711yescharacteristic
139C22×D4C22×C12711yescharacteristic
140C2×SD16—22no—
141C2×SD16—22no—
142C2×SD16—22no—
143C22×C8C22×C12711yescharacteristic
144C22×C8C22×C12711yescharacteristic
145C2×C4⋊C4C22×C12711yescharacteristic
146C2×C4⋊C4C22×C12711yescharacteristic
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C42C22×C12711yescharacteristic
150C4⋊C8—22no—
151#103—22no—
152#102—22no—
153#95—21no—
154#95—21no—
155C24—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8D4×C12712yes—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4D4×C12712yes—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4D4×C12711yescharacteristic
172C22×C4D4×C12711yescharacteristic
173C22×C4C23×C12711yescharacteristic
174SD16—28no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8D4×C12712yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C22⋊C4—42no—
186C22⋊C4—42no—
187C42—21no—
188C42—21no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23C2×D4×C12711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4SD16×C12712yescomplemented
220C2×C4C2×D4×C12711yescharacteristic
221C2×C4C2×D4×C12711yescharacteristic
222C2×C4C2×D4×C12711yescharacteristic
223C2×C4#41×C12711yescharacteristic
224C2×C4#41×C12711yescharacteristic
225C2×C4#41×C12711yescharacteristic
226C8—22no—
227C8—41no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#121×C12711yescharacteristic
236C22#121×C12711yescharacteristic
237C22#121×C12711yescharacteristic
238C22C2×SD16×C12711yescharacteristic
239C22#135×C12711yescharacteristic
240C22AGL(1,ℤ/8)×C12711yescharacteristic
241C22#137×C12711yescharacteristic
242C4—22no—
243C4—42no—
244C4—41no—
245C4—81no—
246C4—81no—
247C4#120×C12711yescharacteristic
248C4#123×C12711yescharacteristic
249C4#123×C12711yescharacteristic
250C4#124×C12711yescharacteristic
251C2—82no—
252C2#394×C12711yescharacteristic
253C2#460×C12711yescharacteristic
254C2#461×C12711yescharacteristic
255C2#463×C12711yescharacteristic
256C2#464×C12711yescharacteristic
257C2#465×C12711yescharacteristic
258C2#468×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC22×D4×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×C127C2semidirect
3. C2×#103×C127C2semidirect
5. #391×C127C2semidirect
7. #340×C127C2semidirect
89. C2×C4×C127SD16semidirect
129. #2055C127direct (N × H)
130. C127#2055direct (N × H)
132. C2×C4⋊C8C2×C127semidirect
133. C2×#103C2×C127semidirect
135. #391C2×C127semidirect
137. #340C2×C127semidirect
219. C2×C4SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×C1272
C2×C4⋊C8×C1272
C2×#103×C1272
C2×#102×C1272
#391×C1272
#390×C1272
#340×C1272
#2055127