Finite Group Databasebeta

← C127×#9488 #44573161

Subgroups — C127×#9488 #44573161

Order 32512.

454 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2983C211yesmaximal, characteristic
2C127×#2581C211yesmaximal, characteristic
3C127×#1801C211yesmaximal, characteristic
4C127×#1487C212yesmaximal
5C127×#1286C212yesmaximal
6C2×C4×Q8×C127C2211yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#446×C127—24no—
9#432×C127—22no—
10#431×C127C2212yes—
11#423×C127C2212yes—
12C2×#101×C127—21no—
13#400×C127C412yes—
14#395×C127C412yes—
15#391×C127—21no—
16#389×C127—21no—
17#387×C127—22no—
18#382×C127C2211yescharacteristic
19#343×C127—21no—
20Q8⋊C8×C127—24no—
21C22×Q8×C127C2×C411yescharacteristic
22C22×Q8×C127D411yescharacteristic
23C2×M16×C127—22no—
24C4×Q8×C127—22no—
25C4×Q8×C127—22no—
26C4×Q8×C127—22no—
27C4×Q8×C127—22no—
28C2×C4⋊C4×C127—22no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127C2×C411yescharacteristic
32C2×C4⋊C4×C127C2×C412yes—
33C2×C4⋊C4×C127D411yescharacteristic
34C2×C42×C127—21no—
35C2×C42×C127D412yes—
36C2×C42×C127C2311yescharacteristic
37C4⋊C8×C127—24no—
38C4⋊C8×C127—22no—
39C4⋊C8×C127—22no—
40C4⋊C8×C127—22no—
41#101×C127—42no—
42C22⋊C8×C127—22no—
43#97×C127—24no—
44C4×C8×C127D414yes—
45#95×C127—22no—
46#95×C127—22no—
47#95×C127—22no—
48#95×C127—21no—
49#95×C127C2×C412yes—
50C2×Q8×C127—22no—
51C2×Q8×C127—21no—
52C2×Q8×C127—21no—
53C2×Q8×C127—22no—
54C2×Q8×C127—22no—
55C2×Q8×C127—42no—
56C22×C4×C127—21no—
57C22×C4×C127—22no—
58C22×C4×C127—21no—
59C22×C4×C127C22⋊C412yes—
60C22×C4×C127C22⋊C412yes—
61C22×C4×C127C22×C411yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63C22×C4×C127C2×D411yescharacteristic
64M16×C127—42no—
65M16×C127—42no—
66C2×C8×C127—24no—
67C2×C8×C127—42no—
68C4⋊C4×C127—24no—
69C4⋊C4×C127—22no—
70C4⋊C4×C127—22no—
71C4⋊C4×C127—44no—
72C4⋊C4×C127—41no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C42×C127—22no—
77C42×C127—22no—
78C42×C127—42no—
79C42×C127C2×D412yes—
80C42×C127#4112yes—
81C23×C127C2×C22⋊C411yescharacteristic
82Q8×C127—24no—
83Q8×C127—42no—
84Q8×C127—42no—
85Q8×C127—42no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—22no—
89C2×C4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—41no—
94C2×C4×C127—41no—
95C2×C4×C127—42no—
96C2×C4×C127—42no—
97C2×C4×C127—42no—
98C2×C4×C127—42no—
99C2×C4×C127—41no—
100C2×C4×C127—42no—
101C2×C4×C127C4×D412yes—
102C2×C4×C127#12011yescharacteristic
103C2×C4×C127#12112yes—
104C2×C4×C127#12311yescharacteristic
105C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C127#13712yes—
107C2×C4×C127#13711yescharacteristic
108C8×C127—44no—
109C8×C127—82no—
110C22×C127—21no—
111C22×C127—21no—
112C22×C127#38611yescharacteristic
113C22×C127#41711yescharacteristic
114C22×C127#41911yescharacteristic
115C4×C127—22no—
116C4×C127—21no—
117C4×C127—21no—
118C4×C127—42no—
119C4×C127—42no—
120C4×C127—42no—
121C4×C127—82no—
122C4×C127—81no—
123C4×C127#46812yes—
124C4×C127#47012yes—
125#9488C12711yesmaximal, characteristic, direct product factor, Sylow
126C2×C127—21no—
127C2×C127—21no—
128C2×C127#189111yescharacteristic
129C2×C127#189411yescharacteristic
130C2×C127#191211yescharacteristic
131#2983C2×C12711yescharacteristic
132#2581C2×C12711yescharacteristic
133#1801C2×C12711yescharacteristic
134#1487C2×C12712yes—
135#1286C2×C12712yes—
136C127#948811yescharacteristic, direct product factor, Sylow
137C2×C4×Q8C22×C12711yescharacteristic
138C2×C4×Q8C22×C12711yescharacteristic
139#446—24no—
140#432—22no—
141#431C22×C12712yes—
142#423C22×C12712yes—
143C2×#101—21no—
144#400C4×C12712yes—
145#395C4×C12712yes—
146#391—21no—
147#389—21no—
148#387—22no—
149#382C22×C12711yescharacteristic
150#343—21no—
151Q8⋊C8—24no—
152C22×Q8C2×C4×C12711yescharacteristic
153C22×Q8D4×C12711yescharacteristic
154C2×M16—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×C4×C12711yescharacteristic
163C2×C4⋊C4C2×C4×C12712yes—
164C2×C4⋊C4D4×C12711yescharacteristic
165C2×C42—21no—
166C2×C42D4×C12712yes—
167C2×C42C23×C12711yescharacteristic
168C4⋊C8—24no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172#101—42no—
173C22⋊C8—22no—
174#97—24no—
175C4×C8D4×C12714yes—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—21no—
180#95C2×C4×C12712yes—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—42no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4C22⋊C4×C12712yes—
191C22×C4C22⋊C4×C12712yes—
192C22×C4C22×C4×C12711yescharacteristic
193C22×C4C2×D4×C12711yescharacteristic
194C22×C4C2×D4×C12711yescharacteristic
195M16—42no—
196M16—42no—
197C2×C8—24no—
198C2×C8—42no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—44no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C42—22no—
208C42—22no—
209C42—42no—
210C42C2×D4×C12712yes—
211C42#41×C12712yes—
212C23C2×C22⋊C4×C12711yescharacteristic
213Q8—24no—
214Q8—42no—
215Q8—42no—
216Q8—42no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4C4×D4×C12712yes—
233C2×C4#120×C12711yescharacteristic
234C2×C4#121×C12712yes—
235C2×C4#123×C12711yescharacteristic
236C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
237C2×C4#137×C12712yes—
238C2×C4#137×C12711yescharacteristic
239C8—44no—
240C8—82no—
241C22—21no—
242C22—21no—
243C22#386×C12711yescharacteristic
244C22#417×C12711yescharacteristic
245C22#419×C12711yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—42no—
252C4—82no—
253C4—81no—
254C4#468×C12712yes—
255C4#470×C12712yes—
256C2—21no—
257C2—21no—
258C2C127×#189111yescharacteristic
259C2C127×#189411yescharacteristic
260C2C127×#191211yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
125. #9488C127direct (N × H)
136. C127#9488direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29832
C127×#25812
C127×#18012
C127×#14872
C127×#12862
#9488127