Finite Group Databasebeta

← C127×#11551 #44575224

Subgroups — C127×#11551 #44575224

Order 32512.

398 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2503C211yesmaximal, characteristic
2C127×#1463C211yesmaximal, characteristic
3C2×#324×C127C211yesmaximal, characteristic
4C127×#1324C212yesmaximal, complemented
5C127×#1319C212yesmaximal, complemented
6C2×C22⋊Q8×C127C411yescharacteristic
7C22×C4⋊C4×C127C2211yescharacteristic
8#407×C127—21no—
9C2×C22⋊C8×C127—21no—
10#400×C127—21no—
11#400×C127—21no—
12#391×C127C411yescharacteristic
13#391×C127C2211yescharacteristic
14#382×C127C411yescharacteristic
15#382×C127C2211yescharacteristic
16#381×C127—21no—
17#381×C127—21no—
18C4×C22⋊C4×C127C411yescharacteristic
19#324×C127—21no—
20#324×C127—21no—
21#324×C127C2212yes—
22#324×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—41no—
28C22×C8×C127—41no—
29C22⋊Q8×C127—41no—
30C22⋊Q8×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—41no—
33C2×C4⋊C4×C127—41no—
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127D411yescharacteristic
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C4⋊C4×C127C2311yescharacteristic
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C42×C127C2×C411yescharacteristic
42C2×C42×C127C2×C411yescharacteristic
43C22⋊C8×C127—22no—
44C22⋊C8×C127—22no—
45C22⋊C8×C127—41no—
46C22⋊C8×C127—41no—
47#95×C127—21no—
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×C127—21no—
55#95×C127—21no—
56C24×C127C22⋊C411yescharacteristic
57C2×Q8×C127—22no—
58C2×Q8×C127—41no—
59C2×Q8×C127—41no—
60C22×C4×C127—21no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—22no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—41no—
72C22×C4×C127—42no—
73C22×C4×C127—42no—
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C22×C411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80M16×C127—82no—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C2×C8×C127—82no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—42no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C42×C127—22no—
94C42×C127—41no—
95C23×C127—22no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—41no—
99C23×C127#9911yescharacteristic
100C23×C127#9911yescharacteristic
101C23×C127C2×C22⋊C411yescharacteristic
102Q8×C127—82no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—42no—
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—42no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—81no—
132C2×C4×C127—81no—
133C2×C4×C127#13112yes—
134C8×C127—82no—
135C8×C127—82no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—42no—
144C22×C127—42no—
145C22×C127#35412yes—
146C22×C127#40811yescharacteristic
147C22×C127C2×#9911yescharacteristic
148C22×C127#41311yescharacteristic
149C4×C127—22no—
150C4×C127—41no—
151C4×C127—41no—
152C4×C127—41no—
153C4×C127—41no—
154C4×C127—41no—
155C4×C127—81no—
156C4×C127—81no—
157C4×C127—81no—
158C4×C127—81no—
159#11551C12711yesmaximal, characteristic, direct product factor, Sylow
160C2×C127—21no—
161C2×C127—21no—
162C2×C127—22no—
163C2×C127—41no—
164C2×C127#146811yescharacteristic
165C2×C127C2×#35411yescharacteristic
166C2×C127#213311yescharacteristic
167#2503C2×C12711yescharacteristic
168#1463C2×C12711yescharacteristic
169C2×#324C2×C12711yescharacteristic
170#1324C2×C12712yescomplemented
171#1319C2×C12712yescomplemented
172C127#1155111yescharacteristic, direct product factor, Sylow
173C2×C22⋊Q8C4×C12711yescharacteristic
174C22×C4⋊C4C22×C12711yescharacteristic
175#407—21no—
176C2×C22⋊C8—21no—
177#400—21no—
178#400—21no—
179#391C4×C12711yescharacteristic
180#391C22×C12711yescharacteristic
181#382C4×C12711yescharacteristic
182#382C22×C12711yescharacteristic
183#381—21no—
184#381—21no—
185C4×C22⋊C4C4×C12711yescharacteristic
186#324—21no—
187#324—21no—
188#324C22×C12712yes—
189#324C22×C12712yes—
190C22×Q8C2×C4×C12711yescharacteristic
191C23×C4C2×C4×C12711yescharacteristic
192C23×C4D4×C12711yescharacteristic
193C23×C4D4×C12711yescharacteristic
194C2×M16—41no—
195C22×C8—41no—
196C22⋊Q8—41no—
197C22⋊Q8—41no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4C2×C4×C12711yescharacteristic
202C2×C4⋊C4C2×C4×C12711yescharacteristic
203C2×C4⋊C4D4×C12711yescharacteristic
204C2×C4⋊C4D4×C12711yescharacteristic
205C2×C4⋊C4C23×C12711yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42C2×C4×C12711yescharacteristic
209C2×C42C2×C4×C12711yescharacteristic
210C22⋊C8—22no—
211C22⋊C8—22no—
212C22⋊C8—41no—
213C22⋊C8—41no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223C24C22⋊C4×C12711yescharacteristic
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—41no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C22⋊C4×C12711yescharacteristic
242C22×C4C22⋊C4×C12711yescharacteristic
243C22×C4C22⋊C4×C12711yescharacteristic
244C22×C4C22×C4×C12711yescharacteristic
245C22×C4C2×D4×C12711yescharacteristic
246C22×C4C2×D4×C12711yescharacteristic
247M16—82no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—82no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—22no—
261C42—41no—
262C23—22no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23#99×C12711yescharacteristic
267C23#99×C12711yescharacteristic
268C23C2×C22⋊C4×C12711yescharacteristic
269Q8—82no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4#131×C12712yes—
301C8—82no—
302C8—82no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22#354×C12712yes—
313C22#408×C12711yescharacteristic
314C22C2×#99×C12711yescharacteristic
315C22#413×C12711yescharacteristic
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—81no—
323C4—81no—
324C4—81no—
325C4—81no—
326C2—21no—
327C2—21no—
328C2—22no—
329C2—41no—
330C2C127×#146811yescharacteristic
331C2C2×#354×C12711yescharacteristic
332C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1324C2semidirect
5. C127×#1319C2semidirect
159. #11551C127direct (N × H)
170. #1324C2×C127semidirect
171. #1319C2×C127semidirect
172. C127#11551direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25032
C127×#14632
C2×#324×C1272
C127×#13242
C127×#13192
#11551127