Finite Group Databasebeta

← C127×#8532 #44572205

Subgroups — C127×#8532 #44572205

Order 32512.

800 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 150 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×#3548C211yesmaximal, characteristic
2C127×#1994C211yesmaximal, characteristic, complemented
3C127×#1962C212yesmaximal, complemented
4C127×#1561C211yesmaximal, characteristic, complemented
5C127×#1560C212yesmaximal, complemented
6#562×C127C414yescomplemented
7#554×C127—22no—
8#550×C127—22no—
9#547×C127—22no—
10#540×C127—22no—
11#537×C127—24no—
12#533×C127C2211yescharacteristic
13#532×C127C2212yes—
14#423×C127C2211yescharacteristic
15#423×C127C2212yes—
16C2×#104×C127—24no—
17C43×C127C2211yescharacteristic
18#339×C127—22no—
19#333×C127—22no—
20#332×C127—22no—
21#331×C127—22no—
22C2×#41×C127—24no—
23C2×#41×C127D414yes—
24C2×M16×C127—21no—
25C2×M16×C127—22no—
26C4⋊Q8×C127D412yes—
27C4⋊Q8×C127D412yes—
28#127×C127—22no—
29#127×C127D412yes—
30#125×C127—22no—
31#125×C127C2×C412yes—
32#124×C127C2×C414yes—
33#123×C127—28no—
34C22⋊Q8×C127—24no—
35C22⋊Q8×C127—28no—
36C22⋊Q8×C127—22no—
37#121×C127—28no—
38#121×C127—24no—
39#121×C127—28no—
40#121×C127—22no—
41#121×C127—22no—
42C4×Q8×C127—22no—
43C4×D4×C127—24no—
44C4×D4×C127—22no—
45C4×D4×C127—22no—
46#117×C127D412yes—
47C2×C4⋊C4×C127—24no—
48C2×C42×C127—21no—
49C2×C42×C127—22no—
50C2×C42×C127C2311yescharacteristic
51C4⋊C8×C127—22no—
52C4⋊C8×C127—22no—
53C4⋊C8×C127—22no—
54#104×C127—48no—
55#41×C127—44no—
56#41×C127—44no—
57#41×C127—84no—
58#41×C127—84no—
59C2×Q8×C127—22no—
60C2×Q8×C127C22⋊C414yes—
61C2×D4×C127—28no—
62C2×D4×C127—24no—
63C2×D4×C127—22no—
64C2×D4×C127—22no—
65C2×D4×C127C22⋊C414yes—
66C22×C4×C127—28no—
67C22×C4×C127—24no—
68C22×C4×C127—41no—
69C22×C4×C127C2×D411yescharacteristic
70C22×C4×C127C2×D412yes—
71M16×C127—44no—
72M16×C127—42no—
73C2×C8×C127—42no—
74C2×C8×C127—41no—
75C4⋊C4×C127—28no—
76C4⋊C4×C127—24no—
77C4⋊C4×C127—22no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—22no—
80C4⋊C4×C127C22⋊C414yes—
81C22⋊C4×C127—28no—
82C22⋊C4×C127—22no—
83C22⋊C4×C127—24no—
84C22⋊C4×C127—24no—
85C42×C127—22no—
86C42×C127—24no—
87C42×C127—22no—
88C42×C127—41no—
89C42×C127—42no—
90C42×C127C22×C411yescharacteristic
91C42×C127C2×D411yescharacteristic
92C42×C127C2×D412yes—
93C23×C127—24no—
94C23×C127#12011yescharacteristic
95Q8×C127—44no—
96Q8×C127—42no—
97Q8×C127—42no—
98D4×C127—44no—
99D4×C127—42no—
100D4×C127—42no—
101D4×C127—42no—
102D4×C127—42no—
103D4×C127—84no—
104D4×C127—88no—
105C2×C4×C127—22no—
106C2×C4×C127—21no—
107C2×C4×C127—22no—
108C2×C4×C127—21no—
109C2×C4×C127—24no—
110C2×C4×C127—24no—
111C2×C4×C127—44no—
112C2×C4×C127—42no—
113C2×C4×C127—44no—
114C2×C4×C127—44no—
115C2×C4×C127—88no—
116C2×C4×C127C2×C22⋊C411yescharacteristic
117C2×C4×C127C2×C22⋊C412yes—
118C2×C4×C127#12012yes—
119C2×C4×C127#12011yescharacteristic
120C8×C127—82no—
121C8×C127—81no—
122C22×C127—22no—
123C22×C127—21no—
124C22×C127—44no—
125C22×C127—44no—
126C22×C127—44no—
127C22×C127#37911yescharacteristic
128C4×C127—22no—
129C4×C127—21no—
130C4×C127—44no—
131C4×C127—44no—
132C4×C127—44no—
133C4×C127#45312yes—
134C4×C127#45411yescharacteristic
135C4×C127#45512yes—
136C4×C127#45611yescharacteristic
137#8532C12711yesmaximal, characteristic, direct product factor, Sylow
138C2×C127—41no—
139C2×C127—84no—
140C2×C127#179212yes—
141C2×C127#179311yescharacteristic
142#3548C2×C12711yescharacteristic
143#1994C2×C12711yescharacteristic, complemented
144#1962C2×C12712yescomplemented
145#1561C2×C12711yescharacteristic, complemented
146#1560C2×C12712yescomplemented
147C127#853211yescharacteristic, direct product factor, Sylow
148#562C4×C12714yescomplemented
149#554—22no—
150#550—22no—
151#547—22no—
152#540—22no—
153#537—24no—
154#533C22×C12711yescharacteristic
155#532C22×C12712yes—
156#423C22×C12711yescharacteristic
157#423C22×C12712yes—
158C2×#104—24no—
159C43C22×C12711yescharacteristic
160#339—22no—
161#333—22no—
162#332—22no—
163#331—22no—
164C2×#41—24no—
165C2×#41D4×C12714yes—
166C2×M16—21no—
167C2×M16—22no—
168C4⋊Q8D4×C12712yes—
169C4⋊Q8D4×C12712yes—
170#127—22no—
171#127D4×C12712yes—
172#125—22no—
173#125C2×C4×C12712yes—
174#124C2×C4×C12714yes—
175#123—28no—
176C22⋊Q8—24no—
177C22⋊Q8—28no—
178C22⋊Q8—22no—
179#121—28no—
180#121—24no—
181#121—28no—
182#121—22no—
183#121—22no—
184C4×Q8—22no—
185C4×D4—24no—
186C4×D4—22no—
187C4×D4—22no—
188#117D4×C12712yes—
189C2×C4⋊C4—24no—
190C2×C42—21no—
191C2×C42—22no—
192C2×C42C23×C12711yescharacteristic
193C4⋊C8—22no—
194C4⋊C8—22no—
195C4⋊C8—22no—
196#104—48no—
197#41—44no—
198#41—44no—
199#41—84no—
200#41—84no—
201C2×Q8—22no—
202C2×Q8C22⋊C4×C12714yes—
203C2×D4—28no—
204C2×D4—24no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4C22⋊C4×C12714yes—
208C22×C4—28no—
209C22×C4—24no—
210C22×C4—41no—
211C22×C4C2×D4×C12711yescharacteristic
212C22×C4C2×D4×C12712yes—
213M16—44no—
214M16—42no—
215C2×C8—42no—
216C2×C8—41no—
217C4⋊C4—28no—
218C4⋊C4—24no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4C22⋊C4×C12714yes—
223C22⋊C4—28no—
224C22⋊C4—22no—
225C22⋊C4—24no—
226C22⋊C4—24no—
227C42—22no—
228C42—24no—
229C42—22no—
230C42—41no—
231C42—42no—
232C42C22×C4×C12711yescharacteristic
233C42C2×D4×C12711yescharacteristic
234C42C2×D4×C12712yes—
235C23—24no—
236C23#120×C12711yescharacteristic
237Q8—44no—
238Q8—42no—
239Q8—42no—
240D4—44no—
241D4—42no—
242D4—42no—
243D4—42no—
244D4—42no—
245D4—84no—
246D4—88no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—88no—
258C2×C4C2×C22⋊C4×C12711yescharacteristic
259C2×C4C2×C22⋊C4×C12712yes—
260C2×C4#120×C12712yes—
261C2×C4#120×C12711yescharacteristic
262C8—82no—
263C8—81no—
264C22—22no—
265C22—21no—
266C22—44no—
267C22—44no—
268C22—44no—
269C22#379×C12711yescharacteristic
270C4—22no—
271C4—21no—
272C4—44no—
273C4—44no—
274C4—44no—
275C4#453×C12712yes—
276C4#454×C12711yescharacteristic
277C4#455×C12712yes—
278C4#456×C12711yescharacteristic
279C2—41no—
280C2—84no—
281C2C127×#179212yes—
282C2C127×#179311yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3548C2
LCSG ▷ 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×#1994C2semidirect
3. C127×#1962C2semidirect
4. C127×#1561C2semidirect
5. C127×#1560C2semidirect
6. #562×C127C4semidirect
137. #8532C127direct (N × H)
143. #1994C2×C127semidirect
144. #1962C2×C127semidirect
145. #1561C2×C127semidirect
146. #1560C2×C127semidirect
147. C127#8532direct (N × H)
148. #562C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35482
C127×#19942
C127×#19622
C127×#15612
C127×#15602
#8532127