Finite Group Databasebeta

← C2×C127×#1407 #44577249

Subgroups — C2×C127×#1407 #44577249

Order 32512.

416 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#497×C127C211yesmaximal, characteristic
2C2×#355×C127C211yesmaximal, characteristic
3C2×#354×C127C211yesmaximal, characteristic
4C127×#1407C214yesmaximal, direct product factor
5C22×Q16×C127—21no—
6C22×SD16×C127—21no—
7C2×C4⋊Q8×C127C411yescharacteristic, complemented
8C2×#124×C127C2211yescharacteristic
9#497×C127—21no—
10#497×C127—21no—
11#497×C127C412yescomplemented
12#497×C127C2212yes—
13C2×#101×C127—21no—
14C2×#99×C127—21no—
15C2×#97×C127C411yescharacteristic, complemented
16#355×C127—21no—
17#355×C127C2212yes—
18#354×C127—21no—
19#354×C127C2212yes—
20C22×Q8×C127—21no—
21C22×Q8×C127D411yescharacteristic
22C22×D4×C127D411yescharacteristic
23C2×Q16×C127—22no—
24C2×Q16×C127—22no—
25C2×Q16×C127—42no—
26C2×Q16×C127—42no—
27C2×SD16×C127—22no—
28C2×SD16×C127—22no—
29C2×SD16×C127—42no—
30C2×SD16×C127—42no—
31C2×M16×C127—41no—
32C22×C8×C127—21no—
33C4⋊Q8×C127—21no—
34C4⋊Q8×C127—41no—
35C4⋊Q8×C127C2×C412yescomplemented
36#124×C127—41no—
37#124×C127C2×C411yescharacteristic
38#124×C127D411yescharacteristic
39#124×C127D411yescharacteristic
40#124×C127C2311yescharacteristic
41C2×C4⋊C4×C127—41no—
42C2×C22⋊C4×C127—41no—
43C2×C22⋊C4×C127—41no—
44C2×C42×C127C2×C411yescharacteristic
45#101×C127—22no—
46#101×C127—41no—
47#99×C127—22no—
48#99×C127—41no—
49#97×C127—21no—
50#97×C127C2×C412yescomplemented
51C24×C127—21no—
52C2×Q8×C127—21no—
53C2×Q8×C127—22no—
54C2×Q8×C127—41no—
55C2×Q8×C127—41no—
56C2×Q8×C127—41no—
57C2×Q8×C127—41no—
58C2×Q8×C127—41no—
59C2×Q8×C127—41no—
60C2×Q8×C127—41no—
61C2×Q8×C127C22⋊C411yescharacteristic
62C2×Q8×C127C2×D411yescharacteristic
63C2×D4×C127—21no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C2×D4×C127C22⋊C411yescharacteristic
67C2×D4×C127C2×D411yescharacteristic
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—41no—
71C22×C4×C127—81no—
72C22×C4×C127C22⋊C411yescharacteristic
73Q16×C127—44no—
74Q16×C127—44no—
75SD16×C127—44no—
76SD16×C127—44no—
77M16×C127—42no—
78M16×C127—81no—
79C2×C8×C127—22no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—81no—
83C4⋊C4×C127—42no—
84C4⋊C4×C127—42no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—42no—
90C22⋊C4×C127—81no—
91C42×C127—21no—
92C42×C127C22⋊C411yescharacteristic
93C42×C127C22×C411yescharacteristic
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—41no—
97C23×C127—41no—
98C23×C127—82no—
99C23×C127#9911yescharacteristic
100Q8×C127—41no—
101Q8×C127—41no—
102Q8×C127—42no—
103Q8×C127—42no—
104Q8×C127—81no—
105Q8×C127—81no—
106Q8×C127—81no—
107D4×C127—41no—
108D4×C127—41no—
109D4×C127—81no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—42no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—42no—
120C2×C4×C127—81no—
121C2×C4×C127—81no—
122C2×C4×C127—82no—
123C2×C4×C127—162no—
124C2×C4×C127#9911yescharacteristic
125C2×C4×C127C2×C22⋊C411yescharacteristic
126C8×C127—24no—
127C8×C127—82no—
128C22×C127—22no—
129C22×C127—41no—
130C22×C127—41no—
131C22×C127—81no—
132C22×C127—81no—
133C22×C127—82no—
134C22×C127—161no—
135C22×C127#35311yescharacteristic
136C22×C127#35311yescharacteristic
137C22×C127C2×#9911yescharacteristic
138C4×C127—21no—
139C4×C127—21no—
140C4×C127—41no—
141C4×C127—41no—
142C4×C127—41no—
143C4×C127—41no—
144C4×C127—82no—
145C4×C127—162no—
146C2×#1407C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—21no—
148C2×C127—21no—
149C2×C127—81no—
150C2×C127—81no—
151C2×C127#140712yesdirect product factor
152C2×C127C2×#35311yescharacteristic
153C2×#497C2×C12711yescharacteristic
154C2×#355C2×C12711yescharacteristic
155C2×#354C2×C12711yescharacteristic
156#1407C2×C12714yesdirect product factor
157C127C2×#140711yescharacteristic, direct product factor, Sylow
158C22×Q16—21no—
159C22×SD16—21no—
160C2×C4⋊Q8C4×C12711yescharacteristic, complemented
161C2×#124C22×C12711yescharacteristic
162#497—21no—
163#497—21no—
164#497C4×C12712yescomplemented
165#497C22×C12712yes—
166C2×#101—21no—
167C2×#99—21no—
168C2×#97C4×C12711yescharacteristic, complemented
169#355—21no—
170#355C22×C12712yes—
171#354—21no—
172#354C22×C12712yes—
173C22×Q8—21no—
174C22×Q8D4×C12711yescharacteristic
175C22×D4D4×C12711yescharacteristic
176C2×Q16—22no—
177C2×Q16—22no—
178C2×Q16—42no—
179C2×Q16—42no—
180C2×SD16—22no—
181C2×SD16—22no—
182C2×SD16—42no—
183C2×SD16—42no—
184C2×M16—41no—
185C22×C8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—41no—
188C4⋊Q8C2×C4×C12712yescomplemented
189#124—41no—
190#124C2×C4×C12711yescharacteristic
191#124D4×C12711yescharacteristic
192#124D4×C12711yescharacteristic
193#124C23×C12711yescharacteristic
194C2×C4⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C22⋊C4—41no—
197C2×C42C2×C4×C12711yescharacteristic
198#101—22no—
199#101—41no—
200#99—22no—
201#99—41no—
202#97—21no—
203#97C2×C4×C12712yescomplemented
204C24—21no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8C22⋊C4×C12711yescharacteristic
215C2×Q8C2×D4×C12711yescharacteristic
216C2×D4—21no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4C22⋊C4×C12711yescharacteristic
220C2×D4C2×D4×C12711yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—81no—
225C22×C4C22⋊C4×C12711yescharacteristic
226Q16—44no—
227Q16—44no—
228SD16—44no—
229SD16—44no—
230M16—42no—
231M16—81no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—81no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—81no—
244C42—21no—
245C42C22⋊C4×C12711yescharacteristic
246C42C22×C4×C12711yescharacteristic
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—82no—
252C23#99×C12711yescharacteristic
253Q8—41no—
254Q8—41no—
255Q8—42no—
256Q8—42no—
257Q8—81no—
258Q8—81no—
259Q8—81no—
260D4—41no—
261D4—41no—
262D4—81no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—162no—
277C2×C4#99×C12711yescharacteristic
278C2×C4C2×C22⋊C4×C12711yescharacteristic
279C8—24no—
280C8—82no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22—81no—
286C22—82no—
287C22—161no—
288C22#353×C12711yescharacteristic
289C22#353×C12711yescharacteristic
290C22C2×#99×C12711yescharacteristic
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—82no—
298C4—162no—
299C2—21no—
300C2—21no—
301C2—81no—
302C2—81no—
303C2C127×#140712yesdirect product factor
304C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#353
commutatorC42C22×C4×C127
Frattini, cosocle#124C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×#1407C2direct (N × H)
7. C2×C4⋊Q8×C127C4semidirect
11. #497×C127C4semidirect
15. C2×#97×C127C4semidirect
35. C4⋊Q8×C127C2×C4semidirect
50. #97×C127C2×C4semidirect
146. C2×#1407C127direct (N × H)
151. C2×C127#1407direct (N × H)
156. #1407C2×C127direct (N × H)
157. C127C2×#1407direct (N × H)
160. C2×C4⋊Q8C4×C127semidirect
164. #497C4×C127semidirect
168. C2×#97C4×C127semidirect
188. C4⋊Q8C2×C4×C127semidirect
203. #97C2×C4×C127semidirect
303. C2C127×#1407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#497×C1272
C2×#355×C1272
C2×#354×C1272
C127×#14072
C2×#1407127