Finite Group Databasebeta

← C127×#10632 #44574305

Subgroups — C127×#10632 #44574305

Order 32512.

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

normal subgroups only

This group has 310 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×#1960C211yesmaximal, characteristic
2C127×#1849C211yesmaximal, characteristic
3C127×#1546C212yesmaximal
4C127×#1286C212yesmaximal
5C127×#1281C211yesmaximal, characteristic
6C2×C4⋊Q8×C127C2211yescharacteristic
7#431×C127C2212yes—
8C2×#108×C127—21no—
9C2×#108×C127—21no—
10#423×C127C2212yes—
11C2×#103×C127—21no—
12C2×#103×C127—21no—
13C2×#97×C127C2211yescharacteristic
14#382×C127C2211yescharacteristic
15#332×C127—24no—
16C22×Q8×C127—21no—
17C2×M16×C127—22no—
18C22×C8×C127D411yescharacteristic
19C22×C8×C127D411yescharacteristic
20C4⋊Q8×C127—22no—
21C4⋊Q8×C127—21no—
22C4⋊Q8×C127D412yes—
23C2×C4⋊C4×C127—22no—
24C2×C4⋊C4×C127—21no—
25C2×C42×C127C2311yescharacteristic
26#108×C127—42no—
27#108×C127—42no—
28C4⋊C8×C127—22no—
29C4⋊C8×C127—22no—
30C4⋊C8×C127—22no—
31#103×C127—42no—
32#103×C127—42no—
33C22⋊C8×C127—22no—
34#97×C127—22no—
35C4×C8×C127—22no—
36#95×C127—22no—
37C2×Q8×C127—22no—
38C2×Q8×C127—41no—
39C2×Q8×C127—41no—
40C2×Q8×C127—41no—
41C2×Q8×C127—41no—
42C2×Q8×C127—41no—
43C22×C4×C127—41no—
44C22×C4×C127—41no—
45C22×C4×C127C2×D411yescharacteristic
46C22×C4×C127#4112yes—
47M16×C127—42no—
48M16×C127—42no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C2×C8×C127—42no—
54C2×C8×C127—42no—
55C2×C8×C127D812yes—
56C2×C8×C127SD1612yes—
57C4⋊C4×C127—24no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C42×C127C2×D411yescharacteristic
62C42×C127#4111yescharacteristic
63C42×C127#4112yes—
64C23×C127#12411yescharacteristic
65Q8×C127—42no—
66Q8×C127—42no—
67Q8×C127—81no—
68Q8×C127—81no—
69C2×C4×C127—42no—
70C2×C4×C127—42no—
71C2×C4×C127—81no—
72C2×C4×C127—81no—
73C2×C4×C127—82no—
74C2×C4×C127—81no—
75C2×C4×C127#12111yescharacteristic
76C2×C4×C127#12312yes—
77C2×C4×C127#12311yescharacteristic
78C2×C4×C127#12612yes—
79C2×C4×C127C2×D811yescharacteristic
80C2×C4×C127C2×SD1611yescharacteristic
81C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C127#13711yescharacteristic
83C8×C127—22no—
84C8×C127—22no—
85C8×C127—82no—
86C8×C127—82no—
87C22×C127—22no—
88C22×C127#39711yescharacteristic
89C22×C127#48611yescharacteristic
90C22×C127#48911yescharacteristic
91C4×C127—22no—
92C4×C127—22no—
93C4×C127—82no—
94C4×C127—161no—
95C4×C127#45911yescharacteristic
96C4×C127#46111yescharacteristic
97C4×C127#48011yescharacteristic
98C4×C127#48111yescharacteristic
99#10632C12711yesmaximal, characteristic, direct product factor, Sylow
100C2×C127—21no—
101C2×C127—21no—
102C2×C127#207111yescharacteristic
103C2×C127#208212yes—
104#1960C2×C12711yescharacteristic
105#1849C2×C12711yescharacteristic
106#1546C2×C12712yes—
107#1286C2×C12712yes—
108#1281C2×C12711yescharacteristic
109C127#1063211yescharacteristic, direct product factor, Sylow
110C2×C4⋊Q8C22×C12711yescharacteristic
111#431C22×C12712yes—
112C2×#108—21no—
113C2×#108—21no—
114#423C22×C12712yes—
115C2×#103—21no—
116C2×#103—21no—
117C2×#97C22×C12711yescharacteristic
118#382C22×C12711yescharacteristic
119#332—24no—
120C22×Q8—21no—
121C2×M16—22no—
122C22×C8D4×C12711yescharacteristic
123C22×C8D4×C12711yescharacteristic
124C4⋊Q8—22no—
125C4⋊Q8—21no—
126C4⋊Q8D4×C12712yes—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—21no—
129C2×C42C23×C12711yescharacteristic
130#108—42no—
131#108—42no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135#103—42no—
136#103—42no—
137C22⋊C8—22no—
138#97—22no—
139C4×C8—22no—
140#95—22no—
141C2×Q8—22no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4C2×D4×C12711yescharacteristic
150C22×C4#41×C12712yes—
151M16—42no—
152M16—42no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—42no—
158C2×C8—42no—
159C2×C8D8×C12712yes—
160C2×C8SD16×C12712yes—
161C4⋊C4—24no—
162C4⋊C4—42no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C42C2×D4×C12711yescharacteristic
166C42#41×C12711yescharacteristic
167C42#41×C12712yes—
168C23#124×C12711yescharacteristic
169Q8—42no—
170Q8—42no—
171Q8—81no—
172Q8—81no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—81no—
176C2×C4—81no—
177C2×C4—82no—
178C2×C4—81no—
179C2×C4#121×C12711yescharacteristic
180C2×C4#123×C12712yes—
181C2×C4#123×C12711yescharacteristic
182C2×C4#126×C12712yes—
183C2×C4C2×D8×C12711yescharacteristic
184C2×C4C2×SD16×C12711yescharacteristic
185C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
186C2×C4#137×C12711yescharacteristic
187C8—22no—
188C8—22no—
189C8—82no—
190C8—82no—
191C22—22no—
192C22#397×C12711yescharacteristic
193C22#486×C12711yescharacteristic
194C22#489×C12711yescharacteristic
195C4—22no—
196C4—22no—
197C4—82no—
198C4—161no—
199C4#459×C12711yescharacteristic
200C4#461×C12711yescharacteristic
201C4#480×C12711yescharacteristic
202C4#481×C12711yescharacteristic
203C2—21no—
204C2—21no—
205C2C127×#207111yescharacteristic
206C2C127×#208212yes—
subgroupG/H
center, socleC22×C127#397
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
99. #10632C127direct (N × H)
109. C127#10632direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19602
C127×#18492
C127×#15462
C127×#12862
C127×#12812
#10632127