Finite Group Databasebeta

← C127×#9490 #44573163

Subgroups — C127×#9490 #44573163

Order 32512.

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

normal subgroups only

This group has 522 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, complemented
2C127×#2536C211yesmaximal, characteristic
3C127×#1801C211yesmaximal, characteristic, complemented
4C127×#1486C212yesmaximal
5C127×#1286C212yesmaximal, complemented
6C2×C22⋊Q8×C127—21no—
7C2×C4×Q8×C127C2211yescharacteristic
8C2×C4×D4×C127C2211yescharacteristic
9#446×C127—24no—
10#432×C127—22no—
11#431×C127C2212yes—
12#423×C127C2212yes—
13C2×#101×C127—21no—
14#398×C127C412yes—
15#394×C127C412yes—
16#388×C127—22no—
17#382×C127C2211yescharacteristic
18#380×C127—21no—
19#343×C127—21no—
20D4⋊C8×C127—24no—
21C22×Q8×C127D411yescharacteristic
22C22×D4×C127C2×C411yescharacteristic
23C23×C4×C127—21no—
24C2×M16×C127—22no—
25C22⋊Q8×C127—44no—
26C4×Q8×C127—22no—
27C4×Q8×C127—22no—
28C4×D4×C127—22no—
29C4×D4×C127—22no—
30C2×C4⋊C4×C127—22no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127C2×C411yescharacteristic
33C2×C4⋊C4×C127C2×C412yes—
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—21no—
38C2×C42×C127D412yes—
39C2×C42×C127C2311yescharacteristic
40C4⋊C8×C127—24no—
41C4⋊C8×C127—22no—
42C4⋊C8×C127—22no—
43C4⋊C8×C127—22no—
44#101×C127—42no—
45C22⋊C8×C127—22no—
46#97×C127—24no—
47C4×C8×C127D414yes—
48#95×C127—22no—
49#95×C127—21no—
50#95×C127C2×C412yes—
51C24×C127—21no—
52C2×Q8×C127—22no—
53C2×Q8×C127—21no—
54C2×Q8×C127—22no—
55C2×Q8×C127—21no—
56C2×D4×C127—22no—
57C2×D4×C127—42no—
58C22×C4×C127—22no—
59C22×C4×C127—21no—
60C22×C4×C127—42no—
61C22×C4×C127—42no—
62C22×C4×C127—41no—
63C22×C4×C127—41no—
64C22×C4×C127C22⋊C412yes—
65C22×C4×C127C22⋊C412yes—
66C22×C4×C127C22×C411yescharacteristic
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69M16×C127—42no—
70M16×C127—42no—
71C2×C8×C127—24no—
72C2×C8×C127—42no—
73C4⋊C4×C127—24no—
74C4⋊C4×C127—22no—
75C4⋊C4×C127—22no—
76C4⋊C4×C127—44no—
77C4⋊C4×C127—42no—
78C22⋊C4×C127—44no—
79C22⋊C4×C127—44no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C42×C127—22no—
83C42×C127—22no—
84C42×C127C2×D412yes—
85C42×C127#4112yes—
86C23×C127—22no—
87C23×C127—41no—
88C23×C127—41no—
89C23×C127—41no—
90C23×C127—41no—
91C23×C127—41no—
92C23×C127—41no—
93C23×C127C2×C22⋊C411yescharacteristic
94Q8×C127—42no—
95Q8×C127—42no—
96D4×C127—24no—
97D4×C127—42no—
98C2×C4×C127—22no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—22no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127—42no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—42no—
110C2×C4×C127—41no—
111C2×C4×C127—82no—
112C2×C4×C127—82no—
113C2×C4×C127C4×D412yes—
114C2×C4×C127#12011yescharacteristic
115C2×C4×C127#12112yes—
116C2×C4×C127#12311yescharacteristic
117C2×C4×C127AGL(1,ℤ/8)12yes—
118C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C127#13711yescharacteristic
120C8×C127—44no—
121C8×C127—82no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—42no—
125C22×C127—42no—
126C22×C127—42no—
127C22×C127—81no—
128C22×C127—81no—
129C22×C127—81no—
130C22×C127—81no—
131C22×C127#38611yescharacteristic
132C22×C127#41711yescharacteristic
133C22×C127#41811yescharacteristic
134C4×C127—22no—
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—42no—
138C4×C127—42no—
139C4×C127—82no—
140C4×C127—81no—
141C4×C127#46812yes—
142C4×C127#46912yes—
143#9490C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127—21no—
145C2×C127—21no—
146C2×C127—82no—
147C2×C127#189111yescharacteristic
148C2×C127#189511yescharacteristic
149C2×C127#191211yescharacteristic
150#2983C2×C12711yescharacteristic, complemented
151#2536C2×C12711yescharacteristic
152#1801C2×C12711yescharacteristic, complemented
153#1486C2×C12712yes—
154#1286C2×C12712yescomplemented
155C127#949011yescharacteristic, direct product factor, Sylow
156C2×C22⋊Q8—21no—
157C2×C4×Q8C22×C12711yescharacteristic
158C2×C4×D4C22×C12711yescharacteristic
159#446—24no—
160#432—22no—
161#431C22×C12712yes—
162#423C22×C12712yes—
163C2×#101—21no—
164#398C4×C12712yes—
165#394C4×C12712yes—
166#388—22no—
167#382C22×C12711yescharacteristic
168#380—21no—
169#343—21no—
170D4⋊C8—24no—
171C22×Q8D4×C12711yescharacteristic
172C22×D4C2×C4×C12711yescharacteristic
173C23×C4—21no—
174C2×M16—22no—
175C22⋊Q8—44no—
176C4×Q8—22no—
177C4×Q8—22no—
178C4×D4—22no—
179C4×D4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C2×C4×C12711yescharacteristic
183C2×C4⋊C4C2×C4×C12712yes—
184C2×C4⋊C4D4×C12711yescharacteristic
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—21no—
188C2×C42D4×C12712yes—
189C2×C42C23×C12711yescharacteristic
190C4⋊C8—24no—
191C4⋊C8—22no—
192C4⋊C8—22no—
193C4⋊C8—22no—
194#101—42no—
195C22⋊C8—22no—
196#97—24no—
197C4×C8D4×C12714yes—
198#95—22no—
199#95—21no—
200#95C2×C4×C12712yes—
201C24—21no—
202C2×Q8—22no—
203C2×Q8—21no—
204C2×Q8—22no—
205C2×Q8—21no—
206C2×D4—22no—
207C2×D4—42no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4C22⋊C4×C12712yes—
215C22×C4C22⋊C4×C12712yes—
216C22×C4C22×C4×C12711yescharacteristic
217C22×C4C2×D4×C12711yescharacteristic
218C22×C4C2×D4×C12711yescharacteristic
219M16—42no—
220M16—42no—
221C2×C8—24no—
222C2×C8—42no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—44no—
227C4⋊C4—42no—
228C22⋊C4—44no—
229C22⋊C4—44no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C42—22no—
233C42—22no—
234C42C2×D4×C12712yes—
235C42#41×C12712yes—
236C23—22no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23C2×C22⋊C4×C12711yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—24no—
247D4—42no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4C4×D4×C12712yes—
264C2×C4#120×C12711yescharacteristic
265C2×C4#121×C12712yes—
266C2×C4#123×C12711yescharacteristic
267C2×C4AGL(1,ℤ/8)×C12712yes—
268C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
269C2×C4#137×C12711yescharacteristic
270C8—44no—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22#386×C12711yescharacteristic
282C22#417×C12711yescharacteristic
283C22#418×C12711yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—82no—
290C4—81no—
291C4#468×C12712yes—
292C4#469×C12712yes—
293C2—21no—
294C2—21no—
295C2—82no—
296C2C127×#189111yescharacteristic
297C2C127×#189511yescharacteristic
298C2C127×#191211yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127C2×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
1. C127×#2983C2semidirect
3. C127×#1801C2semidirect
5. C127×#1286C2semidirect
143. #9490C127direct (N × H)
150. #2983C2×C127semidirect
152. #1801C2×C127semidirect
154. #1286C2×C127semidirect
155. C127#9490direct (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×#25362
C127×#18012
C127×#14862
C127×#12862
#9490127