Finite Group Databasebeta

← C127×#13699 #44577372

Subgroups — C127×#13699 #44577372

Order 32512.

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

normal subgroups only

This group has 200 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
1C2×SD64×C127C211yesmaximal, characteristic, complemented
2C2×M64×C127C211yesmaximal, characteristic, complemented
3C127×#2216C211yesmaximal, characteristic, complemented
4C127×#2215C211yesmaximal, characteristic
5C127×#1423C211yesmaximal, characteristic, complemented
6C127×#1416C211yesmaximal, characteristic, complemented
7C127×#1415C211yesmaximal, characteristic, complemented
8C2×Q32×C127C2211yescharacteristic
9C2×D16×C127C2211yescharacteristic
10C22×C16×C127C2211yescharacteristic
11#467×C127—21no—
12#466×C127—21no—
13SD64×C127—22no—
14M64×C127—22no—
15C2×C32×C127C2211yescharacteristic
16C2×C32×C127C2211yescharacteristic
17#366×C127C2211yescharacteristic
18#366×C127C2211yescharacteristic
19#358×C127—21no—
20#357×C127—21no—
21C2×Q16×C127—21no—
22C2×D8×C127—21no—
23C22×C8×C127D411yescharacteristic
24C22⋊Q8×C127—41no—
25#121×C127—41no—
26Q32×C127—21no—
27Q32×C127—21no—
28D16×C127—21no—
29D16×C127—21no—
30C2×C16×C127—21no—
31C2×C16×C127—21no—
32C2×C16×C127D411yescharacteristic
33C2×C16×C127C2311yescharacteristic
34#107×C127—21no—
35#107×C127—21no—
36#103×C127—41no—
37#102×C127—41no—
38C32×C127—21no—
39C32×C127D412yescomplemented
40C2×Q8×C127—41no—
41C2×D4×C127—41no—
42C2×D4×C127—81no—
43C22×C4×C127D811yescharacteristic
44Q16×C127—41no—
45Q16×C127—41no—
46D8×C127—41no—
47D8×C127—41no—
48C2×C8×C127—21no—
49C2×C8×C127—21no—
50C2×C8×C127D811yescharacteristic
51C2×C8×C127C2×D411yescharacteristic
52C4⋊C4×C127—41no—
53C4⋊C4×C127—41no—
54C4⋊C4×C127—81no—
55C22⋊C4×C127—81no—
56C22⋊C4×C127—81no—
57C16×C127—21no—
58C16×C127C2×D411yescharacteristic
59C16×C127#4111yescharacteristic
60C23×C127—81no—
61C23×C127D1611yescharacteristic
62Q8×C127—81no—
63Q8×C127—81no—
64D4×C127—81no—
65D4×C127—81no—
66D4×C127—162no—
67C2×C4×C127—21no—
68C2×C4×C127—21no—
69C2×C4×C127—81no—
70C2×C4×C127—81no—
71C2×C4×C127—81no—
72C2×C4×C127D1611yescharacteristic
73C2×C4×C127C2×D811yescharacteristic
74C8×C127—21no—
75C8×C127#12111yescharacteristic
76C8×C127#13511yescharacteristic
77C22×C127—21no—
78C22×C127—21no—
79C22×C127—21no—
80C22×C127—161no—
81C22×C127—161no—
82C22×C127—161no—
83C22×C127C2×D1611yescharacteristic
84C4×C127—21no—
85C4×C127—161no—
86C4×C127—161no—
87C4×C127—161no—
88C4×C127#46611yescharacteristic
89C4×C127#50811yescharacteristic
90#13699C12711yesmaximal, characteristic, direct product factor, Sylow
91C2×C127—41no—
92C2×C127—321no—
93C2×C127#221511yescharacteristic
94C2×C127#226311yescharacteristic
95C2×C127#226411yescharacteristic
96C2×SD64C2×C12711yescharacteristic, complemented
97C2×M64C2×C12711yescharacteristic, complemented
98#2216C2×C12711yescharacteristic, complemented
99#2215C2×C12711yescharacteristic
100#1423C2×C12711yescharacteristic, complemented
101#1416C2×C12711yescharacteristic, complemented
102#1415C2×C12711yescharacteristic, complemented
103C127#1369911yescharacteristic, direct product factor, Sylow
104C2×Q32C22×C12711yescharacteristic
105C2×D16C22×C12711yescharacteristic
106C22×C16C22×C12711yescharacteristic
107#467—21no—
108#466—21no—
109SD64—22no—
110M64—22no—
111C2×C32C22×C12711yescharacteristic
112C2×C32C22×C12711yescharacteristic
113#366C22×C12711yescharacteristic
114#366C22×C12711yescharacteristic
115#358—21no—
116#357—21no—
117C2×Q16—21no—
118C2×D8—21no—
119C22×C8D4×C12711yescharacteristic
120C22⋊Q8—41no—
121#121—41no—
122Q32—21no—
123Q32—21no—
124D16—21no—
125D16—21no—
126C2×C16—21no—
127C2×C16—21no—
128C2×C16D4×C12711yescharacteristic
129C2×C16C23×C12711yescharacteristic
130#107—21no—
131#107—21no—
132#103—41no—
133#102—41no—
134C32—21no—
135C32D4×C12712yescomplemented
136C2×Q8—41no—
137C2×D4—41no—
138C2×D4—81no—
139C22×C4D8×C12711yescharacteristic
140Q16—41no—
141Q16—41no—
142D8—41no—
143D8—41no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8D8×C12711yescharacteristic
147C2×C8C2×D4×C12711yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—81no—
151C22⋊C4—81no—
152C22⋊C4—81no—
153C16—21no—
154C16C2×D4×C12711yescharacteristic
155C16#41×C12711yescharacteristic
156C23—81no—
157C23D16×C12711yescharacteristic
158Q8—81no—
159Q8—81no—
160D4—81no—
161D4—81no—
162D4—162no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4D16×C12711yescharacteristic
169C2×C4C2×D8×C12711yescharacteristic
170C8—21no—
171C8#121×C12711yescharacteristic
172C8#135×C12711yescharacteristic
173C22—21no—
174C22—21no—
175C22—21no—
176C22—161no—
177C22—161no—
178C22—161no—
179C22C2×D16×C12711yescharacteristic
180C4—21no—
181C4—161no—
182C4—161no—
183C4—161no—
184C4#466×C12711yescharacteristic
185C4#508×C12711yescharacteristic
186C2—41no—
187C2—321no—
188C2C127×#221511yescharacteristic
189C2C127×#226311yescharacteristic
190C2C127×#226411yescharacteristic
subgroupG/H
center, socleC22×C127C2×D16
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC127×#2215C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×C8×C127 ◁ C22×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×SD64×C127C2semidirect
2. C2×M64×C127C2semidirect
3. C127×#2216C2semidirect
5. C127×#1423C2semidirect
6. C127×#1416C2semidirect
7. C127×#1415C2semidirect
39. C32×C127D4semidirect
90. #13699C127direct (N × H)
96. C2×SD64C2×C127semidirect
97. C2×M64C2×C127semidirect
98. #2216C2×C127semidirect
100. #1423C2×C127semidirect
101. #1416C2×C127semidirect
102. #1415C2×C127semidirect
103. C127#13699direct (N × H)
135. C32D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×SD64×C1272
C2×M64×C1272
C127×#22162
C127×#22152
C127×#14232
C127×#14162
C127×#14152
#13699127