Finite Group Databasebeta

← C127×#13670 #44577343

Subgroups — C127×#13670 #44577343

Order 32512.

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

normal subgroups only

This group has 278 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, complemented
2C127×#2263C211yesmaximal, characteristic, complemented
3C2×SD64×C127C211yesmaximal, characteristic, complemented
4C127×#2221C211yesmaximal, 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×D16×C127C2211yescharacteristic
16#504×C127C2211yescharacteristic
17#472×C127—21no—
18SD64×C127—22no—
19SD64×C127—21no—
20D32×C127—21no—
21M64×C127C2211yescharacteristic
22C2×C32×C127C2211yescharacteristic
23#368×C127C2211yescharacteristic
24#361×C127—21no—
252−1+4×C127—41no—
26#137×C127—42no—
27#137×C127—41no—
28AGL(1,ℤ/8)×C127—41no—
29#135×C127—22no—
30#135×C127—21no—
31C2×Q16×C127—22no—
32C2×Q16×C127—21no—
33C2×D8×C127—21no—
34#131×C127D411yescharacteristic
35Q32×C127—22no—
36Q32×C127—21no—
37Q32×C127D411yescharacteristic
38Q32×C127D412yes—
39SD32×C127—22no—
40SD32×C127—21no—
41D16×C127—21no—
42D16×C127—21no—
43D16×C127D411yescharacteristic
44M32×C127—21no—
45M32×C127D411yescharacteristic
46C2×C16×C127—21no—
47C2×C16×C127C2311yescharacteristic
48#108×C127—21no—
49#100×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—81no—
60C2×D4×C127—41no—
61Q16×C127—22no—
62Q16×C127—21no—
63Q16×C127—42no—
64Q16×C127—41no—
65SD16×C127—42no—
66SD16×C127—41no—
67SD16×C127—81no—
68D8×C127—21no—
69D8×C127—41no—
70D8×C127—41no—
71D8×C127—81no—
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
80C23×C127—81no—
81Q8×C127—42no—
82Q8×C127—41no—
83Q8×C127—82no—
84Q8×C127—81no—
85Q8×C127D1611yescharacteristic
86D4×C127—21no—
87D4×C127—41no—
88D4×C127—82no—
89D4×C127—81no—
90D4×C127—81no—
91D4×C127—81no—
92D4×C127D1611yescharacteristic
93C2×C4×C127—21no—
94C2×C4×C127—82no—
95C2×C4×C127—82no—
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—161no—
106C22×C127—321no—
107C22×C127#50911yescharacteristic
108C4×C127—21no—
109C4×C127—82no—
110C4×C127—81no—
111C4×C127#44711yescharacteristic
112C4×C127C2×D1611yescharacteristic
113#13670C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—21no—
115C2×C127—41no—
116C2×C127—161no—
117C2×C127—321no—
118C2×C127#218411yescharacteristic
119#3417C2×C12711yescharacteristic, complemented
120#2263C2×C12711yescharacteristic, complemented
121C2×SD64C2×C12711yescharacteristic, complemented
122#2221C2×C12711yescharacteristic, complemented
123#1420C2×C12711yescharacteristic, complemented
124#1417C2×C12711yescharacteristic, complemented
125#1401C2×C12711yescharacteristic, complemented
126C127#1367011yescharacteristic, direct product factor, Sylow
127#578—21no—
128#510—22no—
129#510—21no—
130#508—21no—
131#508C22×C12711yescharacteristic
132C2×Q32—21no—
133C2×Q32C22×C12711yescharacteristic
134C2×D16C22×C12711yescharacteristic
135#504C22×C12711yescharacteristic
136#472—21no—
137SD64—22no—
138SD64—21no—
139D32—21no—
140M64C22×C12711yescharacteristic
141C2×C32C22×C12711yescharacteristic
142#368C22×C12711yescharacteristic
143#361—21no—
1442−1+4—41no—
145#137—42no—
146#137—41no—
147AGL(1,ℤ/8)—41no—
148#135—22no—
149#135—21no—
150C2×Q16—22no—
151C2×Q16—21no—
152C2×D8—21no—
153#131D4×C12711yescharacteristic
154Q32—22no—
155Q32—21no—
156Q32D4×C12711yescharacteristic
157Q32D4×C12712yes—
158SD32—22no—
159SD32—21no—
160D16—21no—
161D16—21no—
162D16D4×C12711yescharacteristic
163M32—21no—
164M32D4×C12711yescharacteristic
165C2×C16—21no—
166C2×C16C23×C12711yescharacteristic
167#108—21no—
168#100—41no—
169C32—21no—
170C32—21no—
171#41—42no—
172#41—41no—
173#41—82no—
174#41—81no—
175#41D8×C12711yescharacteristic
176C2×Q8—42no—
177C2×Q8—41no—
178C2×Q8—81no—
179C2×D4—41no—
180Q16—22no—
181Q16—21no—
182Q16—42no—
183Q16—41no—
184SD16—42no—
185SD16—41no—
186SD16—81no—
187D8—21no—
188D8—41no—
189D8—41no—
190D8—81no—
191M16—21no—
192M16—41no—
193M16D8×C12711yescharacteristic
194C2×C8—21no—
195C2×C8C2×D4×C12711yescharacteristic
196C16—21no—
197C16C2×D4×C12711yescharacteristic
198C16C2×D4×C12711yescharacteristic
199C23—81no—
200Q8—42no—
201Q8—41no—
202Q8—82no—
203Q8—81no—
204Q8D16×C12711yescharacteristic
205D4—21no—
206D4—41no—
207D4—82no—
208D4—81no—
209D4—81no—
210D4—81no—
211D4D16×C12711yescharacteristic
212C2×C4—21no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4C2×D8×C12711yescharacteristic
218C8—21no—
219C8—81no—
220C8#120×C12711yescharacteristic
221C8AGL(1,ℤ/8)×C12711yescharacteristic
222C22—21no—
223C22—81no—
224C22—161no—
225C22—321no—
226C22#509×C12711yescharacteristic
227C4—21no—
228C4—82no—
229C4—81no—
230C4#447×C12711yescharacteristic
231C4C2×D16×C12711yescharacteristic
232C2—21no—
233C2—41no—
234C2—161no—
235C2—321no—
236C2C127×#218411yescharacteristic
subgroupG/H
center, socleC2×C127#2184
commutator, Frattini, cosocleC2×C16C23×C127
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
1. C127×#3417C2semidirect
2. C127×#2263C2semidirect
3. C2×SD64×C127C2semidirect
4. C127×#2221C2semidirect
5. C127×#1420C2semidirect
6. C127×#1417C2semidirect
7. C127×#1401C2semidirect
113. #13670C127direct (N × H)
119. #3417C2×C127semidirect
120. #2263C2×C127semidirect
121. C2×SD64C2×C127semidirect
122. #2221C2×C127semidirect
123. #1420C2×C127semidirect
124. #1417C2×C127semidirect
125. #1401C2×C127semidirect
126. C127#13670direct (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×#22632
C2×SD64×C1272
C127×#22212
C127×#14202
C127×#14172
C127×#14012
#13670127