Finite Group Databasebeta

← C127×#13472 #44577145

Subgroups — C127×#13472 #44577145

Order 32512.

316 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2161C211yesmaximal, characteristic, complemented
2C127×#2153C211yesmaximal, characteristic, complemented
3C2×#361×C127C211yesmaximal, characteristic
4C2×#361×C127C211yesmaximal, characteristic
5C127×#1978C211yesmaximal, characteristic
6C127×#1953C211yesmaximal, characteristic, complemented
7C127×#1385C211yesmaximal, characteristic, complemented
8C22×D8×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11#430×C127—21no—
12C2×#108×C127C2211yescharacteristic
13C2×#108×C127C2211yescharacteristic
14C2×#108×C127C2211yescharacteristic
15#418×C127—21no—
16C2×#100×C127—21no—
17#405×C127C2211yescharacteristic
18#368×C127—22no—
19#364×C127—22no—
20#361×C127—22no—
21#361×C127—22no—
22#344×C127—21no—
23C22×D4×C127—21no—
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28C2×D8×C127—21no—
29C2×D8×C127Q812yes—
30C2×M16×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C2×M16×C127D411yescharacteristic
34C22×C8×C127C2311yescharacteristic
35#117×C127D411yescharacteristic
36M32×C127—21no—
37M32×C127—21no—
38M32×C127—21no—
39M32×C127D412yes—
40C2×C16×C127—21no—
41C2×C16×C127—21no—
42#108×C127—21no—
43#108×C127—21no—
44#108×C127—21no—
45#108×C127—21no—
46#108×C127—21no—
47#108×C127—42no—
48#108×C127D412yes—
49#102×C127—42no—
50#100×C127—42no—
51#97×C127—21no—
52C4×C8×C127—21no—
53C24×C127—41no—
54C2×D4×C127—22no—
55C2×D4×C127—41no—
56C2×D4×C127—41no—
57C2×D4×C127—41no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60C22×C4×C127C2×D411yescharacteristic
61D8×C127—22no—
62D8×C127—22no—
63D8×C127—41no—
64D8×C127—41no—
65M16×C127—21no—
66M16×C127—22no—
67M16×C127—41no—
68M16×C127—41no—
69M16×C127—41no—
70M16×C127—41no—
71M16×C127—41no—
72M16×C127D812yes—
73C2×C8×C127—21no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—41no—
77C2×C8×C127C2×D411yescharacteristic
78C2×C8×C127C2×D411yescharacteristic
79C2×C8×C127C2×Q811yescharacteristic
80C2×C8×C127#4111yescharacteristic
81C2×C8×C127#4111yescharacteristic
82C2×C8×C127#4111yescharacteristic
83C4⋊C4×C127—21no—
84C22⋊C4×C127—21no—
85C42×C127—21no—
86C16×C127—22no—
87C16×C127—41no—
88C23×C127—42no—
89C23×C127—81no—
90C23×C127—81no—
91C23×C127—162no—
92C23×C127#13711yescharacteristic
93D4×C127—42no—
94D4×C127—42no—
95D4×C127—81no—
96D4×C127—81no—
97C2×C4×C127—41no—
98C2×C4×C127#12111yescharacteristic
99C2×C4×C127#12111yescharacteristic
100C2×C4×C127C22⋊Q811yescharacteristic
101C2×C4×C127C2×D811yescharacteristic
102C2×C4×C127#13511yescharacteristic
103C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
104C8×C127—22no—
105C8×C127—42no—
106C8×C127—81no—
107C8×C127—81no—
108C8×C127#12111yescharacteristic
109C8×C127C22⋊Q811yescharacteristic
110C8×C127C22⋊Q811yescharacteristic
111C8×C127#12611yescharacteristic
112C22×C127—41no—
113C22×C127—82no—
114C22×C127—162no—
115C22×C127—162no—
116C22×C127—162no—
117C22×C127#46411yescharacteristic
118C22×C127#46811yescharacteristic
119C22×C127#47411yescharacteristic
120C4×C127—81no—
121C4×C127#39611yescharacteristic
122C4×C127#45911yescharacteristic
123C4×C127#46611yescharacteristic
124C4×C127#47811yescharacteristic
125#13472C12711yesmaximal, characteristic, direct product factor, Sylow
126C2×C127—21no—
127C2×C127—21no—
128C2×C127—21no—
129C2×C127—162no—
130C2×C127#206711yescharacteristic
131#2161C2×C12711yescharacteristic, complemented
132#2153C2×C12711yescharacteristic, complemented
133C2×#361C2×C12711yescharacteristic
134C2×#361C2×C12711yescharacteristic
135#1978C2×C12711yescharacteristic
136#1953C2×C12711yescharacteristic, complemented
137#1385C2×C12711yescharacteristic, complemented
138C127#1347211yescharacteristic, direct product factor, Sylow
139C22×D8C22×C12711yescharacteristic
140C2×M32C22×C12711yescharacteristic
141C2×M32C22×C12711yescharacteristic
142#430—21no—
143C2×#108C22×C12711yescharacteristic
144C2×#108C22×C12711yescharacteristic
145C2×#108C22×C12711yescharacteristic
146#418—21no—
147C2×#100—21no—
148#405C22×C12711yescharacteristic
149#368—22no—
150#364—22no—
151#361—22no—
152#361—22no—
153#344—21no—
154C22×D4—21no—
155C2×D8—21no—
156C2×D8—21no—
157C2×D8—21no—
158C2×D8—21no—
159C2×D8—21no—
160C2×D8Q8×C12712yes—
161C2×M16—21no—
162C2×M16—21no—
163C2×M16—21no—
164C2×M16D4×C12711yescharacteristic
165C22×C8C23×C12711yescharacteristic
166#117D4×C12711yescharacteristic
167M32—21no—
168M32—21no—
169M32—21no—
170M32D4×C12712yes—
171C2×C16—21no—
172C2×C16—21no—
173#108—21no—
174#108—21no—
175#108—21no—
176#108—21no—
177#108—21no—
178#108—42no—
179#108D4×C12712yes—
180#102—42no—
181#100—42no—
182#97—21no—
183C4×C8—21no—
184C24—41no—
185C2×D4—22no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—41no—
191C22×C4C2×D4×C12711yescharacteristic
192D8—22no—
193D8—22no—
194D8—41no—
195D8—41no—
196M16—21no—
197M16—22no—
198M16—41no—
199M16—41no—
200M16—41no—
201M16—41no—
202M16—41no—
203M16D8×C12712yes—
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8C2×D4×C12711yescharacteristic
209C2×C8C2×D4×C12711yescharacteristic
210C2×C8C2×Q8×C12711yescharacteristic
211C2×C8#41×C12711yescharacteristic
212C2×C8#41×C12711yescharacteristic
213C2×C8#41×C12711yescharacteristic
214C4⋊C4—21no—
215C22⋊C4—21no—
216C42—21no—
217C16—22no—
218C16—41no—
219C23—42no—
220C23—81no—
221C23—81no—
222C23—162no—
223C23#137×C12711yescharacteristic
224D4—42no—
225D4—42no—
226D4—81no—
227D4—81no—
228C2×C4—41no—
229C2×C4#121×C12711yescharacteristic
230C2×C4#121×C12711yescharacteristic
231C2×C4C22⋊Q8×C12711yescharacteristic
232C2×C4C2×D8×C12711yescharacteristic
233C2×C4#135×C12711yescharacteristic
234C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
235C8—22no—
236C8—42no—
237C8—81no—
238C8—81no—
239C8#121×C12711yescharacteristic
240C8C22⋊Q8×C12711yescharacteristic
241C8C22⋊Q8×C12711yescharacteristic
242C8#126×C12711yescharacteristic
243C22—41no—
244C22—82no—
245C22—162no—
246C22—162no—
247C22—162no—
248C22#464×C12711yescharacteristic
249C22#468×C12711yescharacteristic
250C22#474×C12711yescharacteristic
251C4—81no—
252C4#396×C12711yescharacteristic
253C4#459×C12711yescharacteristic
254C4#466×C12711yescharacteristic
255C4#478×C12711yescharacteristic
256C2—21no—
257C2—21no—
258C2—21no—
259C2—162no—
260C2C127×#206711yescharacteristic
subgroupG/H
center, socleC2×C127#2067
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2161C2semidirect
2. C127×#2153C2semidirect
6. C127×#1953C2semidirect
7. C127×#1385C2semidirect
125. #13472C127direct (N × H)
131. #2161C2×C127semidirect
132. #2153C2×C127semidirect
136. #1953C2×C127semidirect
137. #1385C2×C127semidirect
138. C127#13472direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21612
C127×#21532
C2×#361×C1272
C127×#19782
C127×#19532
C127×#13852
#13472127