Finite Group Databasebeta

← C127×#13603 #44577276

Subgroups — C127×#13603 #44577276

Order 32512.

334 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3140C211yesmaximal, characteristic
2C2×#355×C127C211yesmaximal, characteristic
3C2×#354×C127C211yesmaximal, characteristic
4C127×#1414C214yesmaximal, complemented
5#533×C127C411yescharacteristic, complemented
6C2×#124×C127C2211yescharacteristic
7#489×C127—21no—
8#489×C127—21no—
9#488×C127C412yescomplemented
10#488×C127C2212yes—
11#419×C127—21no—
12#418×C127—21no—
13C2×#101×C127—21no—
14C2×#99×C127—21no—
15C4×M16×C127C411yescharacteristic, complemented
16#355×C127—21no—
17#355×C127C2212yes—
18#354×C127—21no—
19#354×C127C2212yes—
20C22×Q8×C127D411yescharacteristic
21C22×D4×C127D411yescharacteristic
22C2×M16×C127—21no—
23C2×M16×C127—41no—
24C4⋊Q8×C127—21no—
25#125×C127C2×C412yescomplemented
26#124×C127—41no—
27#124×C127C2×C411yescharacteristic
28#124×C127D411yescharacteristic
29#124×C127D411yescharacteristic
30#124×C127C2311yescharacteristic
31C22⋊Q8×C127—41no—
32C4×Q8×C127—41no—
33#117×C127—21no—
34C2×C22⋊C4×C127—41no—
35C2×C22⋊C4×C127—41no—
36C2×C42×C127C2×C411yescharacteristic
37#103×C127—22no—
38#103×C127—22no—
39#102×C127—22no—
40#102×C127—22no—
41#101×C127—22no—
42#101×C127—41no—
43#99×C127—22no—
44#99×C127—41no—
45#97×C127—21no—
46C4×C8×C127C2×C412yescomplemented
47C24×C127—21no—
48C2×Q8×C127—21no—
49C2×Q8×C127—41no—
50C2×Q8×C127—41no—
51C2×Q8×C127—41no—
52C2×Q8×C127C22⋊C411yescharacteristic
53C2×Q8×C127C2×D411yescharacteristic
54C2×D4×C127—21no—
55C2×D4×C127—41no—
56C2×D4×C127—41no—
57C2×D4×C127C22⋊C411yescharacteristic
58C2×D4×C127C2×D411yescharacteristic
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—81no—
62C22×C4×C127C22⋊C411yescharacteristic
63M16×C127—41no—
64M16×C127—41no—
65M16×C127—42no—
66M16×C127—81no—
67C2×C8×C127—22no—
68C2×C8×C127—81no—
69C4⋊C4×C127—22no—
70C4⋊C4×C127—42no—
71C4⋊C4×C127—41no—
72C22⋊C4×C127—41no—
73C22⋊C4×C127—41no—
74C22⋊C4×C127—41no—
75C22⋊C4×C127—41no—
76C22⋊C4×C127—41no—
77C22⋊C4×C127—42no—
78C22⋊C4×C127—81no—
79C42×C127—21no—
80C42×C127—41no—
81C42×C127C22⋊C411yescharacteristic
82C42×C127C22×C411yescharacteristic
83C23×C127—21no—
84C23×C127—21no—
85C23×C127—41no—
86C23×C127—41no—
87C23×C127—82no—
88C23×C127#9911yescharacteristic
89Q8×C127—41no—
90Q8×C127—41no—
91Q8×C127—81no—
92Q8×C127—82no—
93D4×C127—41no—
94D4×C127—41no—
95D4×C127—81no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—42no—
105C2×C4×C127—81no—
106C2×C4×C127—82no—
107C2×C4×C127—162no—
108C2×C4×C127#9911yescharacteristic
109C2×C4×C127C2×C22⋊C411yescharacteristic
110C8×C127—42no—
111C8×C127—82no—
112C22×C127—41no—
113C22×C127—41no—
114C22×C127—41no—
115C22×C127—81no—
116C22×C127—81no—
117C22×C127—82no—
118C22×C127—161no—
119C22×C127#35411yescharacteristic
120C22×C127#35411yescharacteristic
121C22×C127C2×#9911yescharacteristic
122C4×C127—21no—
123C4×C127—21no—
124C4×C127—41no—
125C4×C127—41no—
126C4×C127—41no—
127C4×C127—41no—
128C4×C127—82no—
129C4×C127—162no—
130#13603C12711yesmaximal, characteristic, direct product factor, Sylow
131C2×C127—21no—
132C2×C127—21no—
133C2×C127—21no—
134C2×C127—81no—
135C2×C127—81no—
136C2×C127C2×#35411yescharacteristic
137#3140C2×C12711yescharacteristic
138C2×#355C2×C12711yescharacteristic
139C2×#354C2×C12711yescharacteristic
140#1414C2×C12714yescomplemented
141C127#1360311yescharacteristic, direct product factor, Sylow
142#533C4×C12711yescharacteristic, complemented
143C2×#124C22×C12711yescharacteristic
144#489—21no—
145#489—21no—
146#488C4×C12712yescomplemented
147#488C22×C12712yes—
148#419—21no—
149#418—21no—
150C2×#101—21no—
151C2×#99—21no—
152C4×M16C4×C12711yescharacteristic, complemented
153#355—21no—
154#355C22×C12712yes—
155#354—21no—
156#354C22×C12712yes—
157C22×Q8D4×C12711yescharacteristic
158C22×D4D4×C12711yescharacteristic
159C2×M16—21no—
160C2×M16—41no—
161C4⋊Q8—21no—
162#125C2×C4×C12712yescomplemented
163#124—41no—
164#124C2×C4×C12711yescharacteristic
165#124D4×C12711yescharacteristic
166#124D4×C12711yescharacteristic
167#124C23×C12711yescharacteristic
168C22⋊Q8—41no—
169C4×Q8—41no—
170#117—21no—
171C2×C22⋊C4—41no—
172C2×C22⋊C4—41no—
173C2×C42C2×C4×C12711yescharacteristic
174#103—22no—
175#103—22no—
176#102—22no—
177#102—22no—
178#101—22no—
179#101—41no—
180#99—22no—
181#99—41no—
182#97—21no—
183C4×C8C2×C4×C12712yescomplemented
184C24—21no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8C22⋊C4×C12711yescharacteristic
190C2×Q8C2×D4×C12711yescharacteristic
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C22⋊C4×C12711yescharacteristic
195C2×D4C2×D4×C12711yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—81no—
199C22×C4C22⋊C4×C12711yescharacteristic
200M16—41no—
201M16—41no—
202M16—42no—
203M16—81no—
204C2×C8—22no—
205C2×C8—81no—
206C4⋊C4—22no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—41no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—81no—
216C42—21no—
217C42—41no—
218C42C22⋊C4×C12711yescharacteristic
219C42C22×C4×C12711yescharacteristic
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23—82no—
225C23#99×C12711yescharacteristic
226Q8—41no—
227Q8—41no—
228Q8—81no—
229Q8—82no—
230D4—41no—
231D4—41no—
232D4—81no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—162no—
245C2×C4#99×C12711yescharacteristic
246C2×C4C2×C22⋊C4×C12711yescharacteristic
247C8—42no—
248C8—82no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—81no—
254C22—82no—
255C22—161no—
256C22#354×C12711yescharacteristic
257C22#354×C12711yescharacteristic
258C22C2×#99×C12711yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—41no—
265C4—82no—
266C4—162no—
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—81no—
272C2C2×#354×C12711yescharacteristic
subgroupG/H
center, socleC2×C127C2×#354
commutatorC42C22×C4×C127
Frattini, cosocle#124C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ C2×#124×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1414C2semidirect
5. #533×C127C4semidirect
9. #488×C127C4semidirect
15. C4×M16×C127C4semidirect
25. #125×C127C2×C4semidirect
46. C4×C8×C127C2×C4semidirect
130. #13603C127direct (N × H)
140. #1414C2×C127semidirect
141. C127#13603direct (N × H)
142. #533C4×C127semidirect
146. #488C4×C127semidirect
152. C4×M16C4×C127semidirect
162. #125C2×C4×C127semidirect
183. C4×C8C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31402
C2×#355×C1272
C2×#354×C1272
C127×#14142
#13603127