Finite Group Databasebeta

← C127×#12479 #44576152

Subgroups — C127×#12479 #44576152

Order 32512.

216 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 78 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×#2240C211yesmaximal, characteristic
2C127×#2183C211yesmaximal, characteristic, complemented
3C127×#1674C211yesmaximal, characteristic, complemented
4C127×#1668C211yesmaximal, characteristic
5C127×#1372C211yesmaximal, characteristic, complemented
6C127×#1364C211yesmaximal, characteristic, complemented
7C127×#1361C211yesmaximal, characteristic
8#500×C127C2211yescharacteristic
9#493×C127C2211yescharacteristic
10#462×C127—21no—
11#460×C127—21no—
12C8×Q8×C127C2211yescharacteristic
13C4⋊C16×C127—21no—
14C4⋊C16×C127C2211yescharacteristic
15#357×C127—21no—
16#357×C127—21no—
17#346×C127—21no—
18C4×C16×C127C2211yescharacteristic
19#335×C127C2211yescharacteristic
20#335×C127C2211yescharacteristic
21#332×C127—21no—
22#331×C127—21no—
23C2×Q16×C127—41no—
24C2×SD16×C127—41no—
25C2×D8×C127—21no—
26C2×D8×C127—21no—
27C4⋊Q8×C127—21no—
28#127×C127—21no—
29C4×Q8×C127D411yescharacteristic
30C2×C16×C127—21no—
31C2×C16×C127D411yescharacteristic
32C2×C16×C127D411yescharacteristic
33#107×C127—21no—
34#107×C127—21no—
35C4⋊C8×C127—21no—
36C4⋊C8×C127—21no—
37C4⋊C8×C127—21no—
38C4⋊C8×C127D411yescharacteristic
39#103×C127—41no—
40#102×C127—41no—
41C4×C8×C127—21no—
42C4×C8×C127C2311yescharacteristic
43C2×Q8×C127—41no—
44C2×Q8×C127D811yescharacteristic
45C2×D4×C127—41no—
46C2×D4×C127—41no—
47C2×D4×C127—41no—
48Q16×C127—82no—
49SD16×C127—82no—
50D8×C127—41no—
51D8×C127—41no—
52D8×C127—81no—
53C2×C8×C127—21no—
54C2×C8×C127—41no—
55C2×C8×C127—41no—
56C2×C8×C127C2×D411yescharacteristic
57C2×C8×C127#4111yescharacteristic
58C4⋊C4×C127—21no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C4⋊C4×C127D811yescharacteristic
62C42×C127—21no—
63C42×C127C2×D411yescharacteristic
64C16×C127—21no—
65C16×C127—21no—
66C16×C127—41no—
67C23×C127—81no—
68Q8×C127—21no—
69Q8×C127—21no—
70Q8×C127—81no—
71Q8×C127—81no—
72D4×C127—81no—
73D4×C127—81no—
74D4×C127—81no—
75D4×C127—81no—
76D4×C127—161no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—81no—
80C2×C4×C127#12111yescharacteristic
81C2×C4×C127C2×D811yescharacteristic
82C2×C4×C127#13511yescharacteristic
83C8×C127—21no—
84C8×C127—41no—
85C8×C127—81no—
86C8×C127—81no—
87C8×C127#13511yescharacteristic
88C8×C127#13711yescharacteristic
89C22×C127—161no—
90C22×C127—161no—
91C22×C127—161no—
92C22×C127#46611yescharacteristic
93C4×C127—21no—
94C4×C127—41no—
95C4×C127—41no—
96C4×C127—161no—
97C4×C127#46411yescharacteristic
98C4×C127#47111yescharacteristic
99C4×C127#50911yescharacteristic
100C4×C127#50911yescharacteristic
101#12479C12711yesmaximal, characteristic, direct product factor, Sylow
102C2×C127—321no—
103C2×C127#168211yescharacteristic
104C2×C127#221811yescharacteristic
105C2×C127#222311yescharacteristic
106#2240C2×C12711yescharacteristic
107#2183C2×C12711yescharacteristic, complemented
108#1674C2×C12711yescharacteristic, complemented
109#1668C2×C12711yescharacteristic
110#1372C2×C12711yescharacteristic, complemented
111#1364C2×C12711yescharacteristic, complemented
112#1361C2×C12711yescharacteristic
113C127#1247911yescharacteristic, direct product factor, Sylow
114#500C22×C12711yescharacteristic
115#493C22×C12711yescharacteristic
116#462—21no—
117#460—21no—
118C8×Q8C22×C12711yescharacteristic
119C4⋊C16—21no—
120C4⋊C16C22×C12711yescharacteristic
121#357—21no—
122#357—21no—
123#346—21no—
124C4×C16C22×C12711yescharacteristic
125#335C22×C12711yescharacteristic
126#335C22×C12711yescharacteristic
127#332—21no—
128#331—21no—
129C2×Q16—41no—
130C2×SD16—41no—
131C2×D8—21no—
132C2×D8—21no—
133C4⋊Q8—21no—
134#127—21no—
135C4×Q8D4×C12711yescharacteristic
136C2×C16—21no—
137C2×C16D4×C12711yescharacteristic
138C2×C16D4×C12711yescharacteristic
139#107—21no—
140#107—21no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8D4×C12711yescharacteristic
145#103—41no—
146#102—41no—
147C4×C8—21no—
148C4×C8C23×C12711yescharacteristic
149C2×Q8—41no—
150C2×Q8D8×C12711yescharacteristic
151C2×D4—41no—
152C2×D4—41no—
153C2×D4—41no—
154Q16—82no—
155SD16—82no—
156D8—41no—
157D8—41no—
158D8—81no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8C2×D4×C12711yescharacteristic
163C2×C8#41×C12711yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4D8×C12711yescharacteristic
168C42—21no—
169C42C2×D4×C12711yescharacteristic
170C16—21no—
171C16—21no—
172C16—41no—
173C23—81no—
174Q8—21no—
175Q8—21no—
176Q8—81no—
177Q8—81no—
178D4—81no—
179D4—81no—
180D4—81no—
181D4—81no—
182D4—161no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—81no—
186C2×C4#121×C12711yescharacteristic
187C2×C4C2×D8×C12711yescharacteristic
188C2×C4#135×C12711yescharacteristic
189C8—21no—
190C8—41no—
191C8—81no—
192C8—81no—
193C8#135×C12711yescharacteristic
194C8#137×C12711yescharacteristic
195C22—161no—
196C22—161no—
197C22—161no—
198C22#466×C12711yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—161no—
203C4#464×C12711yescharacteristic
204C4#471×C12711yescharacteristic
205C4#509×C12711yescharacteristic
206C4#509×C12711yescharacteristic
207C2—321no—
208C2C127×#168211yescharacteristic
209C2C127×#221811yescharacteristic
210C2C127×#222311yescharacteristic
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC4×C8C23×C127
prime radical#493×C127C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2183C2semidirect
3. C127×#1674C2semidirect
5. C127×#1372C2semidirect
6. C127×#1364C2semidirect
101. #12479C127direct (N × H)
107. #2183C2×C127semidirect
108. #1674C2×C127semidirect
110. #1372C2×C127semidirect
111. #1364C2×C127semidirect
113. C127#12479direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22402
C127×#21832
C127×#16742
C127×#16682
C127×#13722
C127×#13642
C127×#13612
#12479127