Finite Group Databasebeta

← C127×#11847 #44575520

Subgroups — C127×#11847 #44575520

Order 32512.

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

normal subgroups only

This group has 432 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×#2598C211yesmaximal, characteristic
2C127×#1822C211yesmaximal, characteristic, complemented
3C127×#1458C211yesmaximal, characteristic, complemented
4C127×#1353C212yesmaximal, complemented
5C127×#1345C212yesmaximal, complemented
6C2×C4×D4×C127C411yescharacteristic
7C2×#117×C127C2211yescharacteristic
8#431×C127—21no—
9#407×C127—21no—
10#400×C127C2211yescharacteristic
11#399×C127C411yescharacteristic
12#394×C127C2211yescharacteristic
13#392×C127C411yescharacteristic
14#388×C127—21no—
15#386×C127—21no—
16#386×C127—21no—
17#385×C127—21no—
18#383×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×D4×C127—21no—
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127—21no—
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—22no—
28C4×D4×C127—41no—
29C4×D4×C127—41no—
30#117×C127—41no—
31#117×C127—41no—
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×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127D411yescharacteristic
43C2×C42×C127C2×C411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C4⋊C8×C127—41no—
46C22⋊C8×C127—22no—
47C22⋊C8×C127—41no—
48C22⋊C8×C127—41no—
49C4×C8×C127—41no—
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×C127—21no—
57C24×C127C22⋊C411yescharacteristic
58C2×D4×C127—41no—
59C2×D4×C127—42no—
60C2×D4×C127—42no—
61C2×D4×C127—42no—
62C2×D4×C127—81no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—22no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—41no—
70C22×C4×C127—42no—
71C22×C4×C127—81no—
72C22×C4×C127—81no—
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22×C411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79M16×C127—42no—
80M16×C127—42no—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—81no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—42no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—42no—
93C22⋊C4×C127—81no—
94C22⋊C4×C127—81no—
95C42×C127—21no—
96C42×C127—21no—
97C42×C127—21no—
98C42×C127—21no—
99C23×C127—22no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127C2×C22⋊C411yescharacteristic
112D4×C127—42no—
113D4×C127—42no—
114D4×C127—84no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—42no—
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—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—84no—
139C2×C4×C127#9911yescharacteristic
140C2×C4×C127#9911yescharacteristic
141C2×C4×C127#13512yes—
142C8×C127—82no—
143C8×C127—82no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—42no—
147C22×C127—42no—
148C22×C127—42no—
149C22×C127—42no—
150C22×C127—41no—
151C22×C127—41no—
152C22×C127—41no—
153C22×C127—81no—
154C22×C127—81no—
155C22×C127—81no—
156C22×C127—81no—
157C22×C127—81no—
158C22×C127C2×#9911yescharacteristic
159C22×C127#41611yescharacteristic
160C22×C127#42111yescharacteristic
161C4×C127—22no—
162C4×C127—21no—
163C4×C127—21no—
164C4×C127—41no—
165C4×C127—41no—
166C4×C127—41no—
167C4×C127—41no—
168C4×C127—81no—
169C4×C127—81no—
170C4×C127—81no—
171#11847C12711yesmaximal, characteristic, direct product factor, Sylow
172C2×C127—21no—
173C2×C127—21no—
174C2×C127—81no—
175C2×C127—82no—
176C2×C127#151611yescharacteristic
177C2×C127#212011yescharacteristic
178C2×C127#213411yescharacteristic
179#2598C2×C12711yescharacteristic
180#1822C2×C12711yescharacteristic, complemented
181#1458C2×C12711yescharacteristic, complemented
182#1353C2×C12712yescomplemented
183#1345C2×C12712yescomplemented
184C127#1184711yescharacteristic, direct product factor, Sylow
185C2×C4×D4C4×C12711yescharacteristic
186C2×#117C22×C12711yescharacteristic
187#431—21no—
188#407—21no—
189#400C22×C12711yescharacteristic
190#399C4×C12711yescharacteristic
191#394C22×C12711yescharacteristic
192#392C4×C12711yescharacteristic
193#388—21no—
194#386—21no—
195#386—21no—
196#385—21no—
197#383C4×C12711yescharacteristic
198#343—21no—
199#343C22×C12712yes—
200#324C22×C12712yes—
201#323—21no—
202C22×D4—21no—
203C22×D4C2×C4×C12711yescharacteristic
204C23×C4—21no—
205C23×C4D4×C12711yescharacteristic
206C2×M16—22no—
207C4×D4—41no—
208C4×D4—41no—
209#117—41no—
210#117—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×C4×C12711yescharacteristic
213C2×C4⋊C4D4×C12711yescharacteristic
214C2×C4⋊C4C23×C12711yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4C2×C4×C12711yescharacteristic
221C2×C22⋊C4D4×C12711yescharacteristic
222C2×C42C2×C4×C12711yescharacteristic
223C2×C42D4×C12711yescharacteristic
224C4⋊C8—41no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227C22⋊C8—41no—
228C4×C8—41no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95C2×C4×C12711yescharacteristic
234#95C2×C4×C12711yescharacteristic
235C24—21no—
236C24C22⋊C4×C12711yescharacteristic
237C2×D4—41no—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—81no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4C22⋊C4×C12711yescharacteristic
253C22×C4C22⋊C4×C12711yescharacteristic
254C22×C4C22⋊C4×C12711yescharacteristic
255C22×C4C22×C4×C12711yescharacteristic
256C22×C4C2×D4×C12711yescharacteristic
257C22×C4C2×D4×C12711yescharacteristic
258M16—42no—
259M16—42no—
260C2×C8—42no—
261C2×C8—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—81no—
273C22⋊C4—81no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C23—22no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23C2×C22⋊C4×C12711yescharacteristic
291D4—42no—
292D4—42no—
293D4—84no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—84no—
318C2×C4#99×C12711yescharacteristic
319C2×C4#99×C12711yescharacteristic
320C2×C4#135×C12712yes—
321C8—82no—
322C8—82no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22C2×#99×C12711yescharacteristic
338C22#416×C12711yescharacteristic
339C22#421×C12711yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—82no—
354C2C127×#151611yescharacteristic
355C2C127×#212011yescharacteristic
356C2C127×#213411yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radical#392×C127C4
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
2. C127×#1822C2semidirect
3. C127×#1458C2semidirect
4. C127×#1353C2semidirect
5. C127×#1345C2semidirect
171. #11847C127direct (N × H)
180. #1822C2×C127semidirect
181. #1458C2×C127semidirect
182. #1353C2×C127semidirect
183. #1345C2×C127semidirect
184. C127#11847direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25982
C127×#18222
C127×#14582
C127×#13532
C127×#13452
#11847127