Finite Group Databasebeta

← C127×#12291 #44575964

Subgroups — C127×#12291 #44575964

Order 32512.

354 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3245C211yesmaximal, characteristic
2C127×#2233C212yesmaximal, complemented
3C127×#2087C211yesmaximal, characteristic, complemented
4C127×#1347C212yesmaximal, complemented
5C127×#1322C211yesmaximal, characteristic, complemented
6#532×C127—21no—
7#474×C127—22no—
8#466×C127—21no—
9#466×C127C2212yes—
10#459×C127—22no—
11C2×#107×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13#389×C127—21no—
14#367×C127—22no—
15#357×C127—22no—
16C22⋊C16×C127C2212yes—
17#340×C127—21no—
18#340×C127C2211yescharacteristic
19C2×#41×C127—41no—
20C2×D8×C127—21no—
21C2×D8×C127D412yes—
22C22×C8×C127D411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24C4⋊Q8×C127—21no—
25#127×C127—21no—
26#124×C127—41no—
27#121×C127—22no—
28#121×C127—41no—
29C4×D4×C127—22no—
30C4×D4×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—41no—
34C2×C42×C127D411yescharacteristic
35C2×C16×C127—22no—
36#107×C127—21no—
37#107×C127—22no—
38#107×C127D412yes—
39C4⋊C8×C127—22no—
40#102×C127—22no—
41#102×C127—22no—
42#95×C127—41no—
43#41×C127—82no—
44#41×C127—82no—
45C2×Q8×C127—41no—
46C2×D4×C127—22no—
47C2×D4×C127—41no—
48C2×D4×C127—41no—
49C2×D4×C127—42no—
50C22×C4×C127—42no—
51C22×C4×C127—41no—
52C22×C4×C127—41no—
53C22×C4×C127D811yescharacteristic
54C22×C4×C127D811yescharacteristic
55C22×C4×C127C2×D411yescharacteristic
56D8×C127—42no—
57D8×C127—81no—
58C2×C8×C127—21no—
59C2×C8×C127—41no—
60C2×C8×C127—41no—
61C2×C8×C127C2×D412yes—
62C4⋊C4×C127—22no—
63C4⋊C4×C127—22no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—41no—
68C4⋊C4×C127—82no—
69C22⋊C4×C127—42no—
70C22⋊C4×C127—42no—
71C42×C127—21no—
72C42×C127—21no—
73C16×C127—42no—
74C23×C127—42no—
75C23×C127C2×D811yescharacteristic
76Q8×C127—82no—
77D4×C127—42no—
78D4×C127—42no—
79D4×C127—82no—
80D4×C127—82no—
81D4×C127—82no—
82D4×C127—82no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—41no—
89C2×C4×C127—42no—
90C2×C4×C127—42no—
91C2×C4×C127—84no—
92C2×C4×C127—81no—
93C2×C4×C127—81no—
94C2×C4×C127—81no—
95C2×C4×C127—81no—
96C2×C4×C127—81no—
97C2×C4×C127SD3212yes—
98C2×C4×C127#12011yescharacteristic
99C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
100C8×C127—22no—
101C8×C127—41no—
102C22×C127—21no—
103C22×C127—21no—
104C22×C127—82no—
105C22×C127—82no—
106C22×C127—82no—
107C22×C127#44711yescharacteristic
108C22×C127C2×SD3211yescharacteristic
109C22×C127#50911yescharacteristic
110C4×C127—21no—
111C4×C127—22no—
112C4×C127—41no—
113C4×C127—82no—
114C4×C127—82no—
115C4×C127—161no—
116C4×C127#45611yescharacteristic
117C4×C127#45811yescharacteristic
118#12291C12711yesmaximal, characteristic, direct product factor, Sylow
119C2×C127—21no—
120C2×C127—21no—
121C2×C127—162no—
122C2×C127#161011yescharacteristic
123C2×C127#218711yescharacteristic
124C2×C127#219011yescharacteristic
125#3245C2×C12711yescharacteristic
126#2233C2×C12712yescomplemented
127#2087C2×C12711yescharacteristic, complemented
128#1347C2×C12712yescomplemented
129#1322C2×C12711yescharacteristic, complemented
130C127#1229111yescharacteristic, direct product factor, Sylow
131#532—21no—
132#474—22no—
133#466—21no—
134#466C22×C12712yes—
135#459—22no—
136C2×#107C22×C12711yescharacteristic
137C2×C4⋊C8C22×C12711yescharacteristic
138#389—21no—
139#367—22no—
140#357—22no—
141C22⋊C16C22×C12712yes—
142#340—21no—
143#340C22×C12711yescharacteristic
144C2×#41—41no—
145C2×D8—21no—
146C2×D8D4×C12712yes—
147C22×C8D4×C12711yescharacteristic
148C22×C8C23×C12711yescharacteristic
149C4⋊Q8—21no—
150#127—21no—
151#124—41no—
152#121—22no—
153#121—41no—
154C4×D4—22no—
155C4×D4—41no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—41no—
159C2×C42D4×C12711yescharacteristic
160C2×C16—22no—
161#107—21no—
162#107—22no—
163#107D4×C12712yes—
164C4⋊C8—22no—
165#102—22no—
166#102—22no—
167#95—41no—
168#41—82no—
169#41—82no—
170C2×Q8—41no—
171C2×D4—22no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—42no—
175C22×C4—42no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4D8×C12711yescharacteristic
179C22×C4D8×C12711yescharacteristic
180C22×C4C2×D4×C12711yescharacteristic
181D8—42no—
182D8—81no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8C2×D4×C12712yes—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—82no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C42—21no—
197C42—21no—
198C16—42no—
199C23—42no—
200C23C2×D8×C12711yescharacteristic
201Q8—82no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—82no—
207D4—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—84no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4SD32×C12712yes—
223C2×C4#120×C12711yescharacteristic
224C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—82no—
230C22—82no—
231C22—82no—
232C22#447×C12711yescharacteristic
233C22C2×SD32×C12711yescharacteristic
234C22#509×C12711yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—82no—
239C4—82no—
240C4—161no—
241C4#456×C12711yescharacteristic
242C4#458×C12711yescharacteristic
243C2—21no—
244C2—21no—
245C2—162no—
246C2C127×#161011yescharacteristic
247C2C127×#218711yescharacteristic
248C2C127×#219011yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3245C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4⋊C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2233C2semidirect
3. C127×#2087C2semidirect
4. C127×#1347C2semidirect
5. C127×#1322C2semidirect
118. #12291C127direct (N × H)
126. #2233C2×C127semidirect
127. #2087C2×C127semidirect
128. #1347C2×C127semidirect
129. #1322C2×C127semidirect
130. C127#12291direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32452
C127×#22332
C127×#20872
C127×#13472
C127×#13222
#12291127