Finite Group Databasebeta

← C127×#11849 #44575522

Subgroups — C127×#11849 #44575522

Order 32512.

376 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2599C211yesmaximal, characteristic
2C127×#1822C211yesmaximal, characteristic
3C127×#1458C211yesmaximal, characteristic
4C127×#1354C212yesmaximal, complemented
5C127×#1346C212yesmaximal, complemented
6C2×C4×Q8×C127C411yescharacteristic
7C2×#117×C127C2211yescharacteristic
8#431×C127—21no—
9#407×C127—21no—
10#398×C127C2211yescharacteristic
11#397×C127C411yescharacteristic
12#395×C127C2211yescharacteristic
13#393×C127C411yescharacteristic
14#388×C127—21no—
15#387×C127—21no—
16#387×C127—21no—
17#385×C127—21no—
18#383×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×Q8×C127C2×C411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C2×M16×C127—22no—
26C4×Q8×C127—41no—
27C4×Q8×C127—41no—
28#117×C127—41no—
29#117×C127—41no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C4⋊C4×C127C2311yescharacteristic
36C2×C22⋊C4×C127—21no—
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127C2×C411yescharacteristic
39C2×C22⋊C4×C127D411yescharacteristic
40C2×C42×C127—21no—
41C2×C42×C127C2×C411yescharacteristic
42C2×C42×C127D411yescharacteristic
43C4⋊C8×C127—41no—
44C22⋊C8×C127—22no—
45C22⋊C8×C127—41no—
46C22⋊C8×C127—41no—
47C4×C8×C127—41no—
48#95×C127—21no—
49#95×C127—21no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127C2×C411yescharacteristic
55#95×C127C2×C411yescharacteristic
56C24×C127C22⋊C411yescharacteristic
57C2×Q8×C127—42no—
58C2×Q8×C127—41no—
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—21no—
62C22×C4×C127—22no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—41no—
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22×C411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73M16×C127—42no—
74M16×C127—42no—
75C2×C8×C127—42no—
76C2×C8×C127—42no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—42no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—42no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—42no—
88C42×C127—21no—
89C42×C127—21no—
90C42×C127—21no—
91C42×C127—21no—
92C42×C127—42no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—41no—
97C23×C127—41no—
98C23×C127C2×C22⋊C411yescharacteristic
99Q8×C127—42no—
100Q8×C127—42no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—22no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127#9911yescharacteristic
128C2×C4×C127#9911yescharacteristic
129C2×C4×C127#13512yes—
130C8×C127—82no—
131C8×C127—82no—
132C22×C127—21no—
133C22×C127—21no—
134C22×C127—42no—
135C22×C127—41no—
136C22×C127—41no—
137C22×C127—41no—
138C22×C127—81no—
139C22×C127C2×#9911yescharacteristic
140C22×C127#41611yescharacteristic
141C22×C127#42111yescharacteristic
142C4×C127—22no—
143C4×C127—21no—
144C4×C127—21no—
145C4×C127—41no—
146C4×C127—42no—
147C4×C127—41no—
148C4×C127—41no—
149C4×C127—41no—
150C4×C127—81no—
151C4×C127—81no—
152C4×C127—81no—
153#11849C12711yesmaximal, characteristic, direct product factor, Sylow
154C2×C127—21no—
155C2×C127—21no—
156C2×C127—81no—
157C2×C127#151611yescharacteristic
158C2×C127#212011yescharacteristic
159C2×C127#213511yescharacteristic
160#2599C2×C12711yescharacteristic
161#1822C2×C12711yescharacteristic
162#1458C2×C12711yescharacteristic
163#1354C2×C12712yescomplemented
164#1346C2×C12712yescomplemented
165C127#1184911yescharacteristic, direct product factor, Sylow
166C2×C4×Q8C4×C12711yescharacteristic
167C2×#117C22×C12711yescharacteristic
168#431—21no—
169#407—21no—
170#398C22×C12711yescharacteristic
171#397C4×C12711yescharacteristic
172#395C22×C12711yescharacteristic
173#393C4×C12711yescharacteristic
174#388—21no—
175#387—21no—
176#387—21no—
177#385—21no—
178#383C4×C12711yescharacteristic
179#343—21no—
180#343C22×C12712yes—
181#324C22×C12712yes—
182#323—21no—
183C22×Q8C2×C4×C12711yescharacteristic
184C23×C4D4×C12711yescharacteristic
185C2×M16—22no—
186C4×Q8—41no—
187C4×Q8—41no—
188#117—41no—
189#117—41no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×C4×C12711yescharacteristic
194C2×C4⋊C4D4×C12711yescharacteristic
195C2×C4⋊C4C23×C12711yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4C2×C4×C12711yescharacteristic
199C2×C22⋊C4D4×C12711yescharacteristic
200C2×C42—21no—
201C2×C42C2×C4×C12711yescharacteristic
202C2×C42D4×C12711yescharacteristic
203C4⋊C8—41no—
204C22⋊C8—22no—
205C22⋊C8—41no—
206C22⋊C8—41no—
207C4×C8—41no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95C2×C4×C12711yescharacteristic
215#95C2×C4×C12711yescharacteristic
216C24C22⋊C4×C12711yescharacteristic
217C2×Q8—42no—
218C2×Q8—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4C22⋊C4×C12711yescharacteristic
228C22×C4C22⋊C4×C12711yescharacteristic
229C22×C4C22⋊C4×C12711yescharacteristic
230C22×C4C22×C4×C12711yescharacteristic
231C22×C4C2×D4×C12711yescharacteristic
232C22×C4C2×D4×C12711yescharacteristic
233M16—42no—
234M16—42no—
235C2×C8—42no—
236C2×C8—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—42no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊C4×C12711yescharacteristic
259Q8—42no—
260Q8—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4#99×C12711yescharacteristic
288C2×C4#99×C12711yescharacteristic
289C2×C4#135×C12712yes—
290C8—82no—
291C8—82no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C2×#99×C12711yescharacteristic
300C22#416×C12711yescharacteristic
301C22#421×C12711yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—42no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—81no—
311C4—81no—
312C4—81no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2C127×#151611yescharacteristic
317C2C127×#212011yescharacteristic
318C2C127×#213511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1354C2semidirect
5. C127×#1346C2semidirect
153. #11849C127direct (N × H)
163. #1354C2×C127semidirect
164. #1346C2×C127semidirect
165. C127#11849direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25992
C127×#18222
C127×#14582
C127×#13542
C127×#13462
#11849127