Finite Group Databasebeta

← C127×#10534 #44574207

Subgroups — C127×#10534 #44574207

Order 32512.

358 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1848C211yesmaximal, characteristic
3C127×#1561C212yesmaximal
4C127×#1493C212yesmaximal
5C127×#1309C211yesmaximal, characteristic
6#533×C127C2212yes—
7#475×C127—22no—
8#470×C127—22no—
9#462×C127—22no—
10C2×#108×C127—22no—
11#423×C127C2211yescharacteristic
12#423×C127C2212yes—
13#423×C127C2211yescharacteristic
14C2×C4×C8×C127C2211yescharacteristic
15#332×C127—22no—
16#332×C127—22no—
17Q8⋊C8×C127—24no—
18C2×Q16×C127—22no—
19C2×M16×C127—21no—
20C2×M16×C127—22no—
21C2×M16×C127D412yes—
22C22×C8×C127—21no—
23C4⋊Q8×C127D412yes—
24C4⋊Q8×C127D412yes—
25#125×C127—22no—
26C22⋊Q8×C127—22no—
27C22⋊Q8×C127—22no—
28C4×Q8×C127—22no—
29C4×Q8×C127—22no—
30#117×C127—22no—
31C2×C42×C127C2311yescharacteristic
32#108×C127—44no—
33#106×C127—22no—
34C4⋊C8×C127—22no—
35C4⋊C8×C127—22no—
36C4⋊C8×C127—22no—
37C4⋊C8×C127—22no—
38#103×C127—24no—
39C4×C8×C127—21no—
40C4×C8×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—
48M16×C127—82no—
49C2×C8×C127—22no—
50C2×C8×C127—22no—
51C2×C8×C127—22no—
52C2×C8×C127—22no—
53C2×C8×C127—41no—
54C2×C8×C127—42no—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—22no—
59C4⋊C4×C127—42no—
60C4⋊C4×C127—42no—
61C22⋊C4×C127—42no—
62C42×C127—42no—
63C42×C127C2×D412yes—
64C42×C127C2×D411yescharacteristic
65C42×C127#4111yescharacteristic
66C23×C127#12411yescharacteristic
67Q8×C127—42no—
68Q8×C127—42no—
69Q8×C127—42no—
70Q8×C127—42no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—22no—
74C2×C4×C127—22no—
75C2×C4×C127—42no—
76C2×C4×C127—42no—
77C2×C4×C127#12011yescharacteristic
78C2×C4×C127#12111yescharacteristic
79C2×C4×C127#12112yes—
80C2×C4×C127#12312yes—
81C8×C127—24no—
82C8×C127—42no—
83C8×C127—81no—
84C8×C127—82no—
85C22×C127—22no—
86C22×C127—21no—
87C22×C127#39411yescharacteristic
88C4×C127—22no—
89C4×C127—21no—
90C4×C127—82no—
91C4×C127—82no—
92C4×C127#45311yescharacteristic
93C4×C127#45611yescharacteristic
94C4×C127#47112yes—
95C4×C127#47312yes—
96#10534C12711yesmaximal, characteristic, direct product factor, Sylow
97C2×C127—41no—
98C2×C127#203911yescharacteristic
99C2×C127#205212yes—
100#3255C2×C12711yescharacteristic
101#1848C2×C12711yescharacteristic
102#1561C2×C12712yes—
103#1493C2×C12712yes—
104#1309C2×C12711yescharacteristic
105C127#1053411yescharacteristic, direct product factor, Sylow
106#533C22×C12712yes—
107#475—22no—
108#470—22no—
109#462—22no—
110C2×#108—22no—
111#423C22×C12711yescharacteristic
112#423C22×C12712yes—
113#423C22×C12711yescharacteristic
114C2×C4×C8C22×C12711yescharacteristic
115#332—22no—
116#332—22no—
117Q8⋊C8—24no—
118C2×Q16—22no—
119C2×M16—21no—
120C2×M16—22no—
121C2×M16D4×C12712yes—
122C22×C8—21no—
123C4⋊Q8D4×C12712yes—
124C4⋊Q8D4×C12712yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42C23×C12711yescharacteristic
132#108—44no—
133#106—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—22no—
138#103—24no—
139C4×C8—21no—
140C4×C8D4×C12712yes—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4C2×D4×C12711yescharacteristic
144C22×C4#41×C12712yes—
145Q16—82no—
146M16—42no—
147M16—42no—
148M16—82no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—22no—
153C2×C8—41no—
154C2×C8—42no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42C2×D4×C12712yes—
164C42C2×D4×C12711yescharacteristic
165C42#41×C12711yescharacteristic
166C23#124×C12711yescharacteristic
167Q8—42no—
168Q8—42no—
169Q8—42no—
170Q8—42no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4#120×C12711yescharacteristic
178C2×C4#121×C12711yescharacteristic
179C2×C4#121×C12712yes—
180C2×C4#123×C12712yes—
181C8—24no—
182C8—42no—
183C8—81no—
184C8—82no—
185C22—21no—
186C22—22no—
187C22#394×C12711yescharacteristic
188C4—21no—
189C4—22no—
190C4—82no—
191C4—82no—
192C4#453×C12711yescharacteristic
193C4#456×C12711yescharacteristic
194C4#471×C12712yes—
195C4#473×C12712yes—
196C2—41no—
197C2C127×#203911yescharacteristic
198C2C127×#205212yes—
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
96. #10534C127direct (N × H)
105. C127#10534direct (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×#18482
C127×#15612
C127×#14932
C127×#13092
#10534127