Finite Group Databasebeta

← C4×#355×C127 #44576302

Subgroups — C4×#355×C127 #44576302

Order 32512.

532 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 166 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
1C4×#124×C127C211yesmaximal, characteristic
2C2×#355×C127C212yesmaximal
3C4×#101×C127C212yesmaximal, complemented
4C127×#1394C212yesmaximal, complemented
5C2×#124×C127C2211yescharacteristic
6C2×C4×Q8×C127C2211yescharacteristic
7C2×C4×D4×C127C411yescharacteristic
8C2×#101×C127C2214yes—
9C4×M16×C127—22no—
10#391×C127C2211yescharacteristic
11#390×C127C411yescharacteristic
12#388×C127—22no—
13#382×C127C411yescharacteristic
14C4×C22⋊C4×C127—22no—
15C43×C127C411yescharacteristic
16#355×C127C418yesdirect product factor
17#343×C127—22no—
18C22×Q8×C127C2311yescharacteristic
19C22×D4×C127C2×C411yescharacteristic
20C23×C4×C127—21no—
21C2×M16×C127—24no—
22#124×C127—22no—
23#124×C127C2×C414yes—
24C4×Q8×C127—41no—
25C4×Q8×C127—41no—
26C4×D4×C127—41no—
27C4×D4×C127—41no—
28C2×C4⋊C4×C127C2×C411yescharacteristic
29C2×C4⋊C4×C127C2×C411yescharacteristic
30C2×C4⋊C4×C127D412yes—
31C2×C22⋊C4×C127—22no—
32C2×C22⋊C4×C127—21no—
33C2×C22⋊C4×C127—22no—
34C2×C42×C127—21no—
35C2×C42×C127—21no—
36C2×C42×C127C2×C411yescharacteristic
37C2×C42×C127C2×C411yescharacteristic
38C2×C42×C127C2×C411yescharacteristic
39C2×C42×C127D412yes—
40#101×C127—24no—
41#101×C127C2×C418yescomplemented
42#97×C127—42no—
43C4×C8×C127—42no—
44#95×C127—22no—
45#95×C127—22no—
46C24×C127—21no—
47C2×Q8×C127—41no—
48C2×Q8×C127—41no—
49C2×Q8×C127C22×C412yes—
50C2×Q8×C127#4112yes—
51C2×D4×C127—21no—
52C2×D4×C127—41no—
53C2×D4×C127—41no—
54C2×D4×C127C4212yes—
55C22×C4×C127—21no—
56C22×C4×C127—21no—
57C22×C4×C127—21no—
58C22×C4×C127—44no—
59C22×C4×C127—41no—
60C22×C4×C127—41no—
61C22×C4×C127C22⋊C412yes—
62C22×C4×C127C22⋊C411yescharacteristic
63C22×C4×C127C22⋊C411yescharacteristic
64C22×C4×C127C22×C411yescharacteristic
65C22×C4×C127C2×D412yes—
66M16×C127—28no—
67M16×C127—44no—
68C2×C8×C127—44no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—42no—
71C4⋊C4×C127—41no—
72C22⋊C4×C127—28no—
73C22⋊C4×C127—44no—
74C22⋊C4×C127—42no—
75C42×C127—22no—
76C42×C127—21no—
77C42×C127—22no—
78C42×C127—21no—
79C42×C127—21no—
80C42×C127—41no—
81C42×C127—42no—
82C42×C127—42no—
83C42×C127C4212yes—
84C23×C127—22no—
85C23×C127—42no—
86C23×C127—42no—
87C23×C127—41no—
88C23×C127—41no—
89C23×C127C2×C22⋊C411yescharacteristic
90Q8×C127—42no—
91Q8×C127—42no—
92D4×C127—42no—
93D4×C127—42no—
94C2×C4×C127—21no—
95C2×C4×C127—22no—
96C2×C4×C127—21no—
97C2×C4×C127—22no—
98C2×C4×C127—22no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—21no—
102C2×C4×C127—22no—
103C2×C4×C127—41no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—42no—
109C2×C4×C127—42no—
110C2×C4×C127—41no—
111C2×C4×C127—82no—
112C2×C4×C127—82no—
113C2×C4×C127#9911yescharacteristic
114C2×C4×C127#9911yescharacteristic
115C2×C4×C127C2×C4211yescharacteristic
116C2×C4×C127#11711yescharacteristic
117C2×C4×C127C4×D414yes—
118C8×C127—48no—
119C22×C127—21no—
120C22×C127—21no—
121C22×C127—44no—
122C22×C127—42no—
123C22×C127—82no—
124C22×C127—81no—
125C22×C127—81no—
126C22×C127C4×C22⋊C411yescharacteristic
127C22×C127C2×#9911yescharacteristic
128C22×C127#41011yescharacteristic
129C4×C127—21no—
130C4×C127—24no—
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—42no—
134C4×C127—42no—
135C4×C127—41no—
136C4×C127—42no—
137C4×C127—81no—
138C4×C127#35512yesdirect product factor
139C4×#355C12711yesmaximal, characteristic, direct product factor, Sylow
140C2×C127—21no—
141C2×C127—21no—
142C2×C127—82no—
143C2×C127C4×#9911yescharacteristic
144C2×C127C2×#35511yescharacteristic
145C2×C127#213211yescharacteristic
146C4×#124C2×C12711yescharacteristic
147C2×#355C2×C12712yes—
148C4×#101C2×C12712yescomplemented
149#1394C2×C12712yescomplemented
150C127C4×#35511yescharacteristic, direct product factor, Sylow
151C2×#124C22×C12711yescharacteristic
152C2×C4×Q8C22×C12711yescharacteristic
153C2×C4×D4C4×C12711yescharacteristic
154C2×#101C22×C12714yes—
155C4×M16—22no—
156#391C22×C12711yescharacteristic
157#390C4×C12711yescharacteristic
158#388—22no—
159#382C4×C12711yescharacteristic
160C4×C22⋊C4—22no—
161C43C4×C12711yescharacteristic
162#355C4×C12718yesdirect product factor
163#343—22no—
164C22×Q8C23×C12711yescharacteristic
165C22×D4C2×C4×C12711yescharacteristic
166C23×C4—21no—
167C2×M16—24no—
168#124—22no—
169#124C2×C4×C12714yes—
170C4×Q8—41no—
171C4×Q8—41no—
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4C2×C4×C12711yescharacteristic
175C2×C4⋊C4C2×C4×C12711yescharacteristic
176C2×C4⋊C4D4×C12712yes—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—22no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42C2×C4×C12711yescharacteristic
183C2×C42C2×C4×C12711yescharacteristic
184C2×C42C2×C4×C12711yescharacteristic
185C2×C42D4×C12712yes—
186#101—24no—
187#101C2×C4×C12718yescomplemented
188#97—42no—
189C4×C8—42no—
190#95—22no—
191#95—22no—
192C24—21no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8C22×C4×C12712yes—
196C2×Q8#41×C12712yes—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4C42×C12712yes—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—44no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4C22⋊C4×C12711yescharacteristic
208C22×C4C22⋊C4×C12712yes—
209C22×C4C22⋊C4×C12711yescharacteristic
210C22×C4C22×C4×C12711yescharacteristic
211C22×C4C2×D4×C12712yes—
212M16—28no—
213M16—44no—
214C2×C8—44no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C22⋊C4—28no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C42—22no—
222C42—22no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—41no—
227C42—42no—
228C42—42no—
229C42C42×C12712yes—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊C4×C12711yescharacteristic
236Q8—42no—
237Q8—42no—
238D4—42no—
239D4—42no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4#99×C12711yescharacteristic
260C2×C4#99×C12711yescharacteristic
261C2×C4C2×C42×C12711yescharacteristic
262C2×C4#117×C12711yescharacteristic
263C2×C4C4×D4×C12714yes—
264C8—48no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22—42no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22C4×C22⋊C4×C12711yescharacteristic
273C22C2×#99×C12711yescharacteristic
274C22#410×C12711yescharacteristic
275C4—21no—
276C4—24no—
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—41no—
282C4—42no—
283C4—81no—
284C4#355×C12712yesdirect product factor
285C2—21no—
286C2—21no—
287C2—82no—
288C2C4×#99×C12711yescharacteristic
289C2C2×#355×C12711yescharacteristic
290C2C127×#213211yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC22×Q8C23×C127
socleC22×C127C2×#99
prime radicalC22×D4×C127C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×#101×C127C2semidirect
4. C127×#1394C2semidirect
16. #355×C127C4direct (N × H)
41. #101×C127C2×C4semidirect
138. C4×C127#355direct (N × H)
139. C4×#355C127direct (N × H)
148. C4×#101C2×C127semidirect
149. #1394C2×C127semidirect
150. C127C4×#355direct (N × H)
162. #355C4×C127direct (N × H)
187. #101C2×C4×C127semidirect
284. C4#355×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#124×C1272
C2×#355×C1272
C4×#101×C1272
C127×#13942
C4×#355127