Finite Group Databasebeta

← C127×#11850 #44575523

Subgroups — C127×#11850 #44575523

Order 32512.

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

normal subgroups only

This group has 396 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×#2484C211yesmaximal, characteristic
2C127×#1821C211yesmaximal, characteristic
3C2×#324×C127C211yesmaximal, characteristic
4C127×#1353C212yesmaximal, complemented
5C127×#1346C212yesmaximal, complemented
6C2×#117×C127C411yescharacteristic
7C22×C4⋊C4×C127C2211yescharacteristic
8#407×C127—21no—
9C2×C22⋊C8×C127—21no—
10#400×C127C411yescharacteristic
11#400×C127C2211yescharacteristic
12#398×C127C411yescharacteristic
13#398×C127C2211yescharacteristic
14#387×C127—21no—
15#387×C127—21no—
16#385×C127—21no—
17#381×C127—21no—
18#381×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C23×C4×C127C2×C411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C2×M16×C127—22no—
27C22×C8×C127—41no—
28#117×C127—41no—
29#117×C127—41no—
30C2×C4⋊C4×C127—21no—
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×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C4⋊C4×C127C2311yescharacteristic
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C42×C127—21no—
43C22⋊C8×C127—22no—
44C22⋊C8×C127—41no—
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×C127C2×C411yescharacteristic
55#95×C127C2×C411yescharacteristic
56C24×C127C22⋊C411yescharacteristic
57C22×C4×C127—21no—
58C22×C4×C127—21no—
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—22no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—41no—
69C22×C4×C127—42no—
70C22×C4×C127—42no—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22×C411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77M16×C127—42no—
78M16×C127—42no—
79C2×C8×C127—42no—
80C2×C8×C127—42no—
81C2×C8×C127—82no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127—42no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C42×C127—42no—
94C23×C127—22no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—41no—
98C23×C127#9911yescharacteristic
99C23×C127#9911yescharacteristic
100C23×C127C2×C22⋊C411yescharacteristic
101C2×C4×C127—21no—
102C2×C4×C127—21no—
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—42no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
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—42no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—81no—
131C2×C4×C127#13512yes—
132C8×C127—82no—
133C8×C127—82no—
134C22×C127—21no—
135C22×C127—21no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127—42no—
142C22×C127—42no—
143C22×C127#35212yes—
144C22×C127C2×#9911yescharacteristic
145C22×C127#41611yescharacteristic
146C22×C127#42111yescharacteristic
147C4×C127—22no—
148C4×C127—41no—
149C4×C127—41no—
150C4×C127—41no—
151C4×C127—41no—
152C4×C127—41no—
153C4×C127—81no—
154C4×C127—81no—
155C4×C127—81no—
156C4×C127—81no—
157#11850C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—21no—
159C2×C127—21no—
160C2×C127—22no—
161C2×C127—41no—
162C2×C127#151611yescharacteristic
163C2×C127C2×#35211yescharacteristic
164C2×C127#213311yescharacteristic
165#2484C2×C12711yescharacteristic
166#1821C2×C12711yescharacteristic
167C2×#324C2×C12711yescharacteristic
168#1353C2×C12712yescomplemented
169#1346C2×C12712yescomplemented
170C127#1185011yescharacteristic, direct product factor, Sylow
171C2×#117C4×C12711yescharacteristic
172C22×C4⋊C4C22×C12711yescharacteristic
173#407—21no—
174C2×C22⋊C8—21no—
175#400C4×C12711yescharacteristic
176#400C22×C12711yescharacteristic
177#398C4×C12711yescharacteristic
178#398C22×C12711yescharacteristic
179#387—21no—
180#387—21no—
181#385—21no—
182#381—21no—
183#381C4×C12711yescharacteristic
184#343—21no—
185#343C22×C12712yes—
186#324—21no—
187#324C22×C12712yes—
188C23×C4C2×C4×C12711yescharacteristic
189C23×C4D4×C12711yescharacteristic
190C23×C4D4×C12711yescharacteristic
191C2×M16—22no—
192C22×C8—41no—
193#117—41no—
194#117—41no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4C2×C4×C12711yescharacteristic
200C2×C4⋊C4C2×C4×C12711yescharacteristic
201C2×C4⋊C4C2×C4×C12711yescharacteristic
202C2×C4⋊C4D4×C12711yescharacteristic
203C2×C4⋊C4D4×C12711yescharacteristic
204C2×C4⋊C4C23×C12711yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42—21no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211C22⋊C8—41no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95C2×C4×C12711yescharacteristic
220#95C2×C4×C12711yescharacteristic
221C24C22⋊C4×C12711yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4C22⋊C4×C12711yescharacteristic
238C22×C4C22⋊C4×C12711yescharacteristic
239C22×C4C22×C4×C12711yescharacteristic
240C22×C4C2×D4×C12711yescharacteristic
241C22×C4C2×D4×C12711yescharacteristic
242M16—42no—
243M16—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—82no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42—42no—
259C23—22no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23#99×C12711yescharacteristic
264C23#99×C12711yescharacteristic
265C23C2×C22⋊C4×C12711yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4#135×C12712yes—
297C8—82no—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22#352×C12712yes—
309C22C2×#99×C12711yescharacteristic
310C22#416×C12711yescharacteristic
311C22#421×C12711yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2C127×#151611yescharacteristic
327C2C2×#352×C12711yescharacteristic
328C2C127×#213311yescharacteristic
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 ◁ C24×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1353C2semidirect
5. C127×#1346C2semidirect
157. #11850C127direct (N × H)
168. #1353C2×C127semidirect
169. #1346C2×C127semidirect
170. C127#11850direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#24842
C127×#18212
C2×#324×C1272
C127×#13532
C127×#13462
#11850127