Finite Group Databasebeta

← C127×#10530 #44574203

Subgroups — C127×#10530 #44574203

Order 32512.

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

normal subgroups only

This group has 402 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×#3253C211yesmaximal, characteristic
2C127×#1848C211yesmaximal, characteristic, complemented
3C127×#1560C212yesmaximal, complemented
4C127×#1492C212yesmaximal, complemented
5C127×#1309C211yesmaximal, characteristic, complemented
6#532×C127C2212yes—
7#476×C127—22no—
8#469×C127—22no—
9#459×C127—22no—
10C2×#108×C127—22no—
11#423×C127C2211yescharacteristic
12#423×C127C2212yes—
13#423×C127C2211yescharacteristic
14C2×C4×C8×C127C2211yescharacteristic
15#333×C127—22no—
16#331×C127—22no—
17D4⋊C8×C127—24no—
18C2×#41×C127—22no—
19C2×D8×C127—22no—
20C2×M16×C127—21no—
21C2×M16×C127—22no—
22C2×M16×C127D412yes—
23C22×C8×C127—21no—
24C4⋊Q8×C127D412yes—
25#127×C127D412yes—
26#124×C127—22no—
27#121×C127—22no—
28#121×C127—22no—
29C4×D4×C127—22no—
30C4×D4×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#102×C127—24no—
39C4×C8×C127—21no—
40C4×C8×C127D412yes—
41#41×C127—82no—
42#41×C127—82no—
43C2×Q8×C127—22no—
44C2×D4×C127—22no—
45C2×D4×C127—22no—
46C2×D4×C127—22no—
47C2×D4×C127—42no—
48C22×C4×C127—42no—
49C22×C4×C127C2×D411yescharacteristic
50C22×C4×C127#4112yes—
51D8×C127—82no—
52M16×C127—42no—
53M16×C127—42no—
54M16×C127—82no—
55C2×C8×C127—22no—
56C2×C8×C127—22no—
57C2×C8×C127—22no—
58C2×C8×C127—22no—
59C2×C8×C127—41no—
60C2×C8×C127—42no—
61C4⋊C4×C127—22no—
62C4⋊C4×C127—22no—
63C22⋊C4×C127—42no—
64C22⋊C4×C127—42no—
65C42×C127C2×D412yes—
66C42×C127C2×D411yescharacteristic
67C42×C127#4111yescharacteristic
68C23×C127—42no—
69C23×C127#12411yescharacteristic
70Q8×C127—82no—
71D4×C127—42no—
72D4×C127—42no—
73D4×C127—42no—
74D4×C127—42no—
75D4×C127—82no—
76D4×C127—84no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—42no—
82C2×C4×C127—82no—
83C2×C4×C127—82no—
84C2×C4×C127#12011yescharacteristic
85C2×C4×C127#12111yescharacteristic
86C2×C4×C127#12112yes—
87C2×C4×C127#12312yes—
88C8×C127—24no—
89C8×C127—42no—
90C8×C127—81no—
91C8×C127—82no—
92C22×C127—22no—
93C22×C127—21no—
94C22×C127—82no—
95C22×C127—82no—
96C22×C127—82no—
97C22×C127#39411yescharacteristic
98C4×C127—22no—
99C4×C127—21no—
100C4×C127—82no—
101C4×C127#45311yescharacteristic
102C4×C127#45611yescharacteristic
103C4×C127#47112yes—
104C4×C127#47212yes—
105#10530C12711yesmaximal, characteristic, direct product factor, Sylow
106C2×C127—41no—
107C2×C127—162no—
108C2×C127#203911yescharacteristic
109C2×C127#205112yes—
110#3253C2×C12711yescharacteristic
111#1848C2×C12711yescharacteristic, complemented
112#1560C2×C12712yescomplemented
113#1492C2×C12712yescomplemented
114#1309C2×C12711yescharacteristic, complemented
115C127#1053011yescharacteristic, direct product factor, Sylow
116#532C22×C12712yes—
117#476—22no—
118#469—22no—
119#459—22no—
120C2×#108—22no—
121#423C22×C12711yescharacteristic
122#423C22×C12712yes—
123#423C22×C12711yescharacteristic
124C2×C4×C8C22×C12711yescharacteristic
125#333—22no—
126#331—22no—
127D4⋊C8—24no—
128C2×#41—22no—
129C2×D8—22no—
130C2×M16—21no—
131C2×M16—22no—
132C2×M16D4×C12712yes—
133C22×C8—21no—
134C4⋊Q8D4×C12712yes—
135#127D4×C12712yes—
136#124—22no—
137#121—22no—
138#121—22no—
139C4×D4—22no—
140C4×D4—22no—
141C2×C42C23×C12711yescharacteristic
142#108—44no—
143#106—22no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—22no—
147C4⋊C8—22no—
148#102—24no—
149C4×C8—21no—
150C4×C8D4×C12712yes—
151#41—82no—
152#41—82no—
153C2×Q8—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—42no—
158C22×C4—42no—
159C22×C4C2×D4×C12711yescharacteristic
160C22×C4#41×C12712yes—
161D8—82no—
162M16—42no—
163M16—42no—
164M16—82no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—42no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C22⋊C4—42no—
174C22⋊C4—42no—
175C42C2×D4×C12712yes—
176C42C2×D4×C12711yescharacteristic
177C42#41×C12711yescharacteristic
178C23—42no—
179C23#124×C12711yescharacteristic
180Q8—82no—
181D4—42no—
182D4—42no—
183D4—42no—
184D4—42no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4#120×C12711yescharacteristic
195C2×C4#121×C12711yescharacteristic
196C2×C4#121×C12712yes—
197C2×C4#123×C12712yes—
198C8—24no—
199C8—42no—
200C8—81no—
201C8—82no—
202C22—21no—
203C22—22no—
204C22—82no—
205C22—82no—
206C22—82no—
207C22#394×C12711yescharacteristic
208C4—21no—
209C4—22no—
210C4—82no—
211C4#453×C12711yescharacteristic
212C4#456×C12711yescharacteristic
213C4#471×C12712yes—
214C4#472×C12712yes—
215C2—41no—
216C2—162no—
217C2C127×#203911yescharacteristic
218C2C127×#205112yes—
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3253C2
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
2. C127×#1848C2semidirect
3. C127×#1560C2semidirect
4. C127×#1492C2semidirect
5. C127×#1309C2semidirect
105. #10530C127direct (N × H)
111. #1848C2×C127semidirect
112. #1560C2×C127semidirect
113. #1492C2×C127semidirect
114. #1309C2×C127semidirect
115. C127#10530direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32532
C127×#18482
C127×#15602
C127×#14922
C127×#13092
#10530127