Finite Group Databasebeta

← C127×#13672 #44577345

Subgroups — C127×#13672 #44577345

Order 32512.

274 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3417C211yesmaximal, characteristic
2C127×#2264C211yesmaximal, characteristic, complemented
3C2×Q64×C127C211yesmaximal, characteristic, complemented
4C127×#2222C211yesmaximal, characteristic, complemented
5C127×#1420C211yesmaximal, characteristic, complemented
6C127×#1417C211yesmaximal, characteristic, complemented
7C127×#1401C211yesmaximal, characteristic, complemented
8#578×C127—21no—
9#510×C127—22no—
10#510×C127—21no—
11#508×C127—21no—
12#508×C127C2211yescharacteristic
13C2×Q32×C127—21no—
14C2×Q32×C127C2211yescharacteristic
15C2×Q32×C127C2211yescharacteristic
16#504×C127C2211yescharacteristic
17#473×C127—21no—
18Q64×C127—22no—
19Q64×C127—21no—
20SD64×C127—21no—
21M64×C127C2211yescharacteristic
22C2×C32×C127C2211yescharacteristic
23#368×C127C2211yescharacteristic
24#362×C127—21no—
252−1+4×C127—41no—
26#137×C127—42no—
27#137×C127—41no—
28#137×C127—41no—
29#135×C127—22no—
30#135×C127—21no—
31C2×Q16×C127—22no—
32C2×Q16×C127—21no—
33C2×Q16×C127—21no—
34#131×C127D411yescharacteristic
35Q32×C127—22no—
36Q32×C127—21no—
37Q32×C127—21no—
38Q32×C127—21no—
39Q32×C127D411yescharacteristic
40Q32×C127D412yes—
41SD32×C127—22no—
42SD32×C127—21no—
43D16×C127D411yescharacteristic
44M32×C127—21no—
45M32×C127D411yescharacteristic
46C2×C16×C127—21no—
47C2×C16×C127C2311yescharacteristic
48#108×C127—21no—
49#101×C127—41no—
50C32×C127—21no—
51C32×C127—21no—
52#41×C127—42no—
53#41×C127—41no—
54#41×C127—82no—
55#41×C127—81no—
56#41×C127D811yescharacteristic
57C2×Q8×C127—42no—
58C2×Q8×C127—41no—
59C2×Q8×C127—41no—
60C2×Q8×C127—81no—
61Q16×C127—22no—
62Q16×C127—21no—
63Q16×C127—42no—
64Q16×C127—41no—
65Q16×C127—41no—
66Q16×C127—41no—
67Q16×C127—81no—
68SD16×C127—42no—
69SD16×C127—41no—
70SD16×C127—81no—
71D8×C127—21no—
72M16×C127—21no—
73M16×C127—41no—
74M16×C127D811yescharacteristic
75C2×C8×C127—21no—
76C2×C8×C127C2×D411yescharacteristic
77C16×C127—21no—
78C16×C127C2×D411yescharacteristic
79C16×C127C2×D411yescharacteristic
80Q8×C127—42no—
81Q8×C127—41no—
82Q8×C127—82no—
83Q8×C127—81no—
84Q8×C127—81no—
85Q8×C127—81no—
86Q8×C127D1611yescharacteristic
87D4×C127—21no—
88D4×C127—41no—
89D4×C127—82no—
90D4×C127—81no—
91D4×C127D1611yescharacteristic
92C2×C4×C127—21no—
93C2×C4×C127—82no—
94C2×C4×C127—82no—
95C2×C4×C127—81no—
96C2×C4×C127—81no—
97C2×C4×C127—81no—
98C2×C4×C127C2×D811yescharacteristic
99C8×C127—21no—
100C8×C127—81no—
101C8×C127#12011yescharacteristic
102C8×C127AGL(1,ℤ/8)11yescharacteristic
103C22×C127—21no—
104C22×C127—81no—
105C22×C127#50911yescharacteristic
106C4×C127—21no—
107C4×C127—82no—
108C4×C127—81no—
109C4×C127—161no—
110C4×C127#44711yescharacteristic
111C4×C127C2×D1611yescharacteristic
112#13672C12711yesmaximal, characteristic, direct product factor, Sylow
113C2×C127—21no—
114C2×C127—41no—
115C2×C127—161no—
116C2×C127#218411yescharacteristic
117#3417C2×C12711yescharacteristic
118#2264C2×C12711yescharacteristic, complemented
119C2×Q64C2×C12711yescharacteristic, complemented
120#2222C2×C12711yescharacteristic, complemented
121#1420C2×C12711yescharacteristic, complemented
122#1417C2×C12711yescharacteristic, complemented
123#1401C2×C12711yescharacteristic, complemented
124C127#1367211yescharacteristic, direct product factor, Sylow
125#578—21no—
126#510—22no—
127#510—21no—
128#508—21no—
129#508C22×C12711yescharacteristic
130C2×Q32—21no—
131C2×Q32C22×C12711yescharacteristic
132C2×Q32C22×C12711yescharacteristic
133#504C22×C12711yescharacteristic
134#473—21no—
135Q64—22no—
136Q64—21no—
137SD64—21no—
138M64C22×C12711yescharacteristic
139C2×C32C22×C12711yescharacteristic
140#368C22×C12711yescharacteristic
141#362—21no—
1422−1+4—41no—
143#137—42no—
144#137—41no—
145#137—41no—
146#135—22no—
147#135—21no—
148C2×Q16—22no—
149C2×Q16—21no—
150C2×Q16—21no—
151#131D4×C12711yescharacteristic
152Q32—22no—
153Q32—21no—
154Q32—21no—
155Q32—21no—
156Q32D4×C12711yescharacteristic
157Q32D4×C12712yes—
158SD32—22no—
159SD32—21no—
160D16D4×C12711yescharacteristic
161M32—21no—
162M32D4×C12711yescharacteristic
163C2×C16—21no—
164C2×C16C23×C12711yescharacteristic
165#108—21no—
166#101—41no—
167C32—21no—
168C32—21no—
169#41—42no—
170#41—41no—
171#41—82no—
172#41—81no—
173#41D8×C12711yescharacteristic
174C2×Q8—42no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—81no—
178Q16—22no—
179Q16—21no—
180Q16—42no—
181Q16—41no—
182Q16—41no—
183Q16—41no—
184Q16—81no—
185SD16—42no—
186SD16—41no—
187SD16—81no—
188D8—21no—
189M16—21no—
190M16—41no—
191M16D8×C12711yescharacteristic
192C2×C8—21no—
193C2×C8C2×D4×C12711yescharacteristic
194C16—21no—
195C16C2×D4×C12711yescharacteristic
196C16C2×D4×C12711yescharacteristic
197Q8—42no—
198Q8—41no—
199Q8—82no—
200Q8—81no—
201Q8—81no—
202Q8—81no—
203Q8D16×C12711yescharacteristic
204D4—21no—
205D4—41no—
206D4—82no—
207D4—81no—
208D4D16×C12711yescharacteristic
209C2×C4—21no—
210C2×C4—82no—
211C2×C4—82no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4—81no—
215C2×C4C2×D8×C12711yescharacteristic
216C8—21no—
217C8—81no—
218C8#120×C12711yescharacteristic
219C8AGL(1,ℤ/8)×C12711yescharacteristic
220C22—21no—
221C22—81no—
222C22#509×C12711yescharacteristic
223C4—21no—
224C4—82no—
225C4—81no—
226C4—161no—
227C4#447×C12711yescharacteristic
228C4C2×D16×C12711yescharacteristic
229C2—21no—
230C2—41no—
231C2—161no—
232C2C127×#218411yescharacteristic
subgroupG/H
center, socleC2×C127#2184
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC127×#3417C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ #131×C127 ◁ #504×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2264C2semidirect
3. C2×Q64×C127C2semidirect
4. C127×#2222C2semidirect
5. C127×#1420C2semidirect
6. C127×#1417C2semidirect
7. C127×#1401C2semidirect
112. #13672C127direct (N × H)
118. #2264C2×C127semidirect
119. C2×Q64C2×C127semidirect
120. #2222C2×C127semidirect
121. #1420C2×C127semidirect
122. #1417C2×C127semidirect
123. #1401C2×C127semidirect
124. C127#13672direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34172
C127×#22642
C2×Q64×C1272
C127×#22222
C127×#14202
C127×#14172
C127×#14012
#13672127