Finite Group Databasebeta

← C127×#10528 #44574201

Subgroups — C127×#10528 #44574201

Order 32512.

342 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3255C211yesmaximal, characteristic
2C127×#1849C211yesmaximal, characteristic
3C127×#1559C212yesmaximal
4C127×#1531C212yesmaximal
5C127×#1307C211yesmaximal, characteristic
6#533×C127C2212yes—
7#475×C127—22no—
8#470×C127—22no—
9#462×C127—22no—
10#432×C127C2212yes—
11C2×#108×C127—22no—
12#423×C127C2211yescharacteristic
13#423×C127C2211yescharacteristic
14C2×#97×C127C2211yescharacteristic
15#333×C127—22no—
16#332×C127—22no—
17#330×C127—24no—
18C2×Q16×C127—22no—
19C2×M16×C127—21no—
20C2×M16×C127D412yes—
21C22×C8×C127—21no—
22C4⋊Q8×C127D412yes—
23C4⋊Q8×C127D412yes—
24#125×C127—22no—
25C22⋊Q8×C127—22no—
26C22⋊Q8×C127—22no—
27C4×Q8×C127—22no—
28C4×Q8×C127—22no—
29#117×C127—22no—
30C2×C42×C127C2311yescharacteristic
31#108×C127—44no—
32#106×C127—22no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35C4⋊C8×C127—22no—
36#103×C127—24no—
37C22⋊C8×C127—22no—
38#97×C127—22no—
39#97×C127—21no—
40#97×C127D412yes—
41C2×Q8×C127—22no—
42C2×Q8×C127—22no—
43C22×C4×C127C2×D411yescharacteristic
44C22×C4×C127#4112yes—
45Q16×C127—82no—
46M16×C127—42no—
47M16×C127—42no—
48C2×C8×C127—22no—
49C2×C8×C127—22no—
50C2×C8×C127—22no—
51C2×C8×C127—22no—
52C2×C8×C127—41no—
53C2×C8×C127—42no—
54C4⋊C4×C127—22no—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—42no—
60C22⋊C4×C127—42no—
61C42×C127—42no—
62C42×C127C2×D412yes—
63C42×C127C2×D411yescharacteristic
64C42×C127#4111yescharacteristic
65C23×C127#12411yescharacteristic
66Q8×C127—42no—
67Q8×C127—42no—
68Q8×C127—82no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—42no—
72C2×C4×C127—42no—
73C2×C4×C127—42no—
74C2×C4×C127#12011yescharacteristic
75C2×C4×C127#12112yes—
76C2×C4×C127#12111yescharacteristic
77C2×C4×C127#12312yes—
78C8×C127—24no—
79C8×C127—42no—
80C8×C127—82no—
81C8×C127—81no—
82C22×C127—22no—
83C22×C127—21no—
84C22×C127#39411yescharacteristic
85C4×C127—22no—
86C4×C127—22no—
87C4×C127—21no—
88C4×C127—82no—
89C4×C127—82no—
90C4×C127#45311yescharacteristic
91C4×C127#45611yescharacteristic
92#10528C12711yesmaximal, characteristic, direct product factor, Sylow
93C2×C127—41no—
94C2×C127#203911yescharacteristic
95C2×C127#204912yes—
96#3255C2×C12711yescharacteristic
97#1849C2×C12711yescharacteristic
98#1559C2×C12712yes—
99#1531C2×C12712yes—
100#1307C2×C12711yescharacteristic
101C127#1052811yescharacteristic, direct product factor, Sylow
102#533C22×C12712yes—
103#475—22no—
104#470—22no—
105#462—22no—
106#432C22×C12712yes—
107C2×#108—22no—
108#423C22×C12711yescharacteristic
109#423C22×C12711yescharacteristic
110C2×#97C22×C12711yescharacteristic
111#333—22no—
112#332—22no—
113#330—24no—
114C2×Q16—22no—
115C2×M16—21no—
116C2×M16D4×C12712yes—
117C22×C8—21no—
118C4⋊Q8D4×C12712yes—
119C4⋊Q8D4×C12712yes—
120#125—22no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C4×Q8—22no—
124C4×Q8—22no—
125#117—22no—
126C2×C42C23×C12711yescharacteristic
127#108—44no—
128#106—22no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132#103—24no—
133C22⋊C8—22no—
134#97—22no—
135#97—21no—
136#97D4×C12712yes—
137C2×Q8—22no—
138C2×Q8—22no—
139C22×C4C2×D4×C12711yescharacteristic
140C22×C4#41×C12712yes—
141Q16—82no—
142M16—42no—
143M16—42no—
144C2×C8—22no—
145C2×C8—22no—
146C2×C8—22no—
147C2×C8—22no—
148C2×C8—41no—
149C2×C8—42no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C22⋊C4—42no—
157C42—42no—
158C42C2×D4×C12712yes—
159C42C2×D4×C12711yescharacteristic
160C42#41×C12711yescharacteristic
161C23#124×C12711yescharacteristic
162Q8—42no—
163Q8—42no—
164Q8—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4#120×C12711yescharacteristic
171C2×C4#121×C12712yes—
172C2×C4#121×C12711yescharacteristic
173C2×C4#123×C12712yes—
174C8—24no—
175C8—42no—
176C8—82no—
177C8—81no—
178C22—21no—
179C22—22no—
180C22#394×C12711yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—82no—
185C4—82no—
186C4#453×C12711yescharacteristic
187C4#456×C12711yescharacteristic
188C2—41no—
189C2C127×#203911yescharacteristic
190C2C127×#204912yes—
subgroupG/H
center, socleC22×C127#394
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
92. #10528C127direct (N × H)
101. C127#10528direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32552
C127×#18492
C127×#15592
C127×#15312
C127×#13072
#10528127