Finite Group Databasebeta

← C127×#11879 #44575552

Subgroups — C127×#11879 #44575552

Order 32512.

440 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2536C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic, complemented
3C127×#1461C211yesmaximal, characteristic, complemented
4C127×#1346C212yesmaximal, complemented
5C127×#1345C212yesmaximal
6C2×C22⋊Q8×C127—21no—
7C2×C4×Q8×C127C2211yescharacteristic
8C2×C4×D4×C127C411yescharacteristic
9#431×C127—21no—
10#423×C127—21no—
11C2×#101×C127—21no—
12#398×C127C411yescharacteristic
13#398×C127C2211yescharacteristic
14#394×C127C411yescharacteristic
15#394×C127C2211yescharacteristic
16#388×C127—21no—
17#388×C127—21no—
18#382×C127C411yescharacteristic
19#380×C127—21no—
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×Q8×C127D411yescharacteristic
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127—21no—
26C2×M16×C127—22no—
27C22⋊Q8×C127—42no—
28C22⋊Q8×C127—42no—
29C4×Q8×C127—41no—
30C4×Q8×C127—41no—
31C4×D4×C127—41no—
32C4×D4×C127—41no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127C2×C411yescharacteristic
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C4⋊C4×C127C2311yescharacteristic
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C42×C127C2×C411yescharacteristic
46C2×C42×C127D411yescharacteristic
47C2×C42×C127D411yescharacteristic
48C4⋊C8×C127—41no—
49C4⋊C8×C127—41no—
50C4⋊C8×C127—41no—
51#101×C127—42no—
52C22⋊C8×C127—22no—
53C4×C8×C127—41no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127C2×C411yescharacteristic
58#95×C127C2×C411yescharacteristic
59C24×C127—21no—
60C2×Q8×C127—41no—
61C2×Q8×C127—41no—
62C2×Q8×C127D812yes—
63C2×Q8×C127SD1612yes—
64C2×D4×C127—41no—
65C2×D4×C127—42no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—42no—
70C22×C4×C127—42no—
71C22×C4×C127—42no—
72C22×C4×C127C22⋊C411yescharacteristic
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—41no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C22⋊C4×C127—42no—
92C22⋊C4×C127—42no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—42no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C42×C127—21no—
99C42×C127—21no—
100C42×C127—21no—
101C42×C127—21no—
102C42×C127—21no—
103C42×C127—21no—
104C23×C127—22no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127C2×C22⋊C411yescharacteristic
112Q8×C127—42no—
113Q8×C127—42no—
114D4×C127—42no—
115D4×C127—42no—
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—21no—
124C2×C4×C127—21no—
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#10212yes—
142C2×C4×C127#10212yes—
143C2×C4×C127C2×D811yescharacteristic
144C2×C4×C127C2×SD1611yescharacteristic
145C8×C127—82no—
146C8×C127—82no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—42no—
150C22×C127—42no—
151C22×C127—42no—
152C22×C127—81no—
153C22×C127—81no—
154C22×C127—81no—
155C22×C127—81no—
156C22×C127C2×#9911yescharacteristic
157C22×C127C2×#10211yescharacteristic
158C22×C127#42111yescharacteristic
159C4×C127—21no—
160C4×C127—21no—
161C4×C127—21no—
162C4×C127—22no—
163C4×C127—22no—
164C4×C127—21no—
165C4×C127—41no—
166C4×C127—41no—
167C4×C127—41no—
168C4×C127—81no—
169C4×C127—81no—
170C4×C127—81no—
171#11879C12711yesmaximal, characteristic, direct product factor, Sylow
172C2×C127—21no—
173C2×C127—21no—
174C2×C127—82no—
175C2×C127#151911yescharacteristic
176C2×C127#212011yescharacteristic
177C2×C127#213311yescharacteristic
178#2536C2×C12711yescharacteristic
179#1801C2×C12711yescharacteristic, complemented
180#1461C2×C12711yescharacteristic, complemented
181#1346C2×C12712yescomplemented
182#1345C2×C12712yes—
183C127#1187911yescharacteristic, direct product factor, Sylow
184C2×C22⋊Q8—21no—
185C2×C4×Q8C22×C12711yescharacteristic
186C2×C4×D4C4×C12711yescharacteristic
187#431—21no—
188#423—21no—
189C2×#101—21no—
190#398C4×C12711yescharacteristic
191#398C22×C12711yescharacteristic
192#394C4×C12711yescharacteristic
193#394C22×C12711yescharacteristic
194#388—21no—
195#388—21no—
196#382C4×C12711yescharacteristic
197#380—21no—
198#343C22×C12712yes—
199#324—21no—
200#324C22×C12712yes—
201C22×Q8D4×C12711yescharacteristic
202C22×D4C2×C4×C12711yescharacteristic
203C23×C4—21no—
204C2×M16—22no—
205C22⋊Q8—42no—
206C22⋊Q8—42no—
207C4×Q8—41no—
208C4×Q8—41no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C12711yescharacteristic
215C2×C4⋊C4C2×C4×C12711yescharacteristic
216C2×C4⋊C4D4×C12711yescharacteristic
217C2×C4⋊C4C23×C12711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C42C2×C4×C12711yescharacteristic
224C2×C42D4×C12711yescharacteristic
225C2×C42D4×C12711yescharacteristic
226C4⋊C8—41no—
227C4⋊C8—41no—
228C4⋊C8—41no—
229#101—42no—
230C22⋊C8—22no—
231C4×C8—41no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95C2×C4×C12711yescharacteristic
236#95C2×C4×C12711yescharacteristic
237C24—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8D8×C12712yes—
241C2×Q8SD16×C12712yes—
242C2×D4—41no—
243C2×D4—42no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4C22⋊C4×C12711yescharacteristic
251C22×C4C22⋊C4×C12711yescharacteristic
252C22×C4C22⋊C4×C12711yescharacteristic
253C22×C4C22⋊C4×C12711yescharacteristic
254C22×C4C22×C4×C12711yescharacteristic
255C22×C4C2×D4×C12711yescharacteristic
256C22×C4C2×D4×C12711yescharacteristic
257M16—42no—
258M16—42no—
259C2×C8—42no—
260C2×C8—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—21no—
282C23—22no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊C4×C12711yescharacteristic
290Q8—42no—
291Q8—42no—
292D4—42no—
293D4—42no—
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—21no—
303C2×C4—41no—
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—84no—
317C2×C4#99×C12711yescharacteristic
318C2×C4#99×C12711yescharacteristic
319C2×C4#102×C12712yes—
320C2×C4#102×C12712yes—
321C2×C4C2×D8×C12711yescharacteristic
322C2×C4C2×SD16×C12711yescharacteristic
323C8—82no—
324C8—82no—
325C22—21no—
326C22—21no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22C2×#99×C12711yescharacteristic
335C22C2×#102×C12711yescharacteristic
336C22#421×C12711yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—22no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—21no—
350C2—21no—
351C2—82no—
352C2C127×#151911yescharacteristic
353C2C127×#212011yescharacteristic
354C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1801C2semidirect
3. C127×#1461C2semidirect
4. C127×#1346C2semidirect
171. #11879C127direct (N × H)
179. #1801C2×C127semidirect
180. #1461C2×C127semidirect
181. #1346C2×C127semidirect
183. C127#11879direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25362
C127×#18012
C127×#14612
C127×#13462
C127×#13452
#11879127