Finite Group Databasebeta

← C127×#12533 #44576206

Subgroups — C127×#12533 #44576206

Order 32512.

238 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2254C211yesmaximal, characteristic
2C127×#2252C211yesmaximal, characteristic
3C127×#2241C211yesmaximal, characteristic
4C127×#2241C211yesmaximal, characteristic
5C127×#1710C211yesmaximal, characteristic
6C127×#1707C211yesmaximal, characteristic
7C127×#1312C211yesmaximal, characteristic
8#500×C127C2211yescharacteristic
9#500×C127C2211yescharacteristic
10#500×C127C2211yescharacteristic
11#498×C127—21no—
12#494×C127C2211yescharacteristic
13#487×C127—21no—
14#487×C127—21no—
15#487×C127—21no—
16#367×C127—22no—
17#366×C127—22no—
18#358×C127—22no—
19#358×C127—22no—
20C4×C16×C127C2211yescharacteristic
21C4×C16×C127C2211yescharacteristic
22C82×C127C2211yescharacteristic
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C4⋊Q8×C127—21no—
26C4⋊Q8×C127—21no—
27C4⋊Q8×C127—21no—
28C4⋊Q8×C127—21no—
29C2×C16×C127D412yes—
30C2×C16×C127D412yes—
31#107×C127—21no—
32#107×C127—21no—
33#107×C127—21no—
34#107×C127—21no—
35#107×C127—21no—
36#107×C127—21no—
37#106×C127—42no—
38#103×C127—42no—
39#103×C127—42no—
40#103×C127—42no—
41C4×C8×C127D411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C4×C8×C127C2311yescharacteristic
44C2×Q8×C127—41no—
45C2×Q8×C127—41no—
46C2×Q8×C127—41no—
47C2×Q8×C127—41no—
48Q16×C127—42no—
49Q16×C127—42no—
50C2×C8×C127D812yes—
51C2×C8×C127D812yes—
52C2×C8×C127C2×D411yescharacteristic
53C2×C8×C127C2×D411yescharacteristic
54C4⋊C4×C127—41no—
55C4⋊C4×C127—41no—
56C4⋊C4×C127—41no—
57C4⋊C4×C127—41no—
58C4⋊C4×C127—41no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C4⋊C4×C127—41no—
62C42×C127C2×D411yescharacteristic
63C16×C127—22no—
64C16×C127—22no—
65Q8×C127—81no—
66Q8×C127—81no—
67Q8×C127—82no—
68Q8×C127—82no—
69Q8×C127—82no—
70C2×C4×C127—81no—
71C2×C4×C127—81no—
72C2×C4×C127—81no—
73C2×C4×C127—81no—
74C2×C4×C127#12711yescharacteristic
75C2×C4×C127C2×D811yescharacteristic
76C2×C4×C127C2×D811yescharacteristic
77C8×C127—22no—
78C8×C127—22no—
79C8×C127#13712yes—
80C8×C127#13712yes—
81C22×C127#49311yescharacteristic
82C4×C127—161no—
83C4×C127—161no—
84C4×C127—161no—
85C4×C127—161no—
86C4×C127#49711yescharacteristic
87C4×C127#49711yescharacteristic
88C4×C127#50812yes—
89C4×C127#51012yes—
90#12533C12711yesmaximal, characteristic, direct product factor, Sylow
91C2×C127#172211yescharacteristic
92C2×C127#224911yescharacteristic
93C2×C127#225111yescharacteristic
94#2254C2×C12711yescharacteristic
95#2252C2×C12711yescharacteristic
96#2241C2×C12711yescharacteristic
97#2241C2×C12711yescharacteristic
98#1710C2×C12711yescharacteristic
99#1707C2×C12711yescharacteristic
100#1312C2×C12711yescharacteristic
101C127#1253311yescharacteristic, direct product factor, Sylow
102#500C22×C12711yescharacteristic
103#500C22×C12711yescharacteristic
104#500C22×C12711yescharacteristic
105#498—21no—
106#494C22×C12711yescharacteristic
107#487—21no—
108#487—21no—
109#487—21no—
110#367—22no—
111#366—22no—
112#358—22no—
113#358—22no—
114C4×C16C22×C12711yescharacteristic
115C4×C16C22×C12711yescharacteristic
116C82C22×C12711yescharacteristic
117C2×Q16—21no—
118C2×Q16—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C2×C16D4×C12712yes—
124C2×C16D4×C12712yes—
125#107—21no—
126#107—21no—
127#107—21no—
128#107—21no—
129#107—21no—
130#107—21no—
131#106—42no—
132#103—42no—
133#103—42no—
134#103—42no—
135C4×C8D4×C12711yescharacteristic
136C4×C8D4×C12711yescharacteristic
137C4×C8C23×C12711yescharacteristic
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142Q16—42no—
143Q16—42no—
144C2×C8D8×C12712yes—
145C2×C8D8×C12712yes—
146C2×C8C2×D4×C12711yescharacteristic
147C2×C8C2×D4×C12711yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C42C2×D4×C12711yescharacteristic
157C16—22no—
158C16—22no—
159Q8—81no—
160Q8—81no—
161Q8—82no—
162Q8—82no—
163Q8—82no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4#127×C12711yescharacteristic
169C2×C4C2×D8×C12711yescharacteristic
170C2×C4C2×D8×C12711yescharacteristic
171C8—22no—
172C8—22no—
173C8#137×C12712yes—
174C8#137×C12712yes—
175C22#493×C12711yescharacteristic
176C4—161no—
177C4—161no—
178C4—161no—
179C4—161no—
180C4#497×C12711yescharacteristic
181C4#497×C12711yescharacteristic
182C4#508×C12712yes—
183C4#510×C12712yes—
184C2C127×#172211yescharacteristic
185C2C127×#224911yescharacteristic
186C2C127×#225111yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#493
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
90. #12533C127direct (N × H)
101. C127#12533direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22542
C127×#22522
C127×#22412
C127×#17102
C127×#17072
C127×#13122
#12533127