Finite Group Databasebeta

← C127×#11881 #44575554

Subgroups — C127×#11881 #44575554

Order 32512.

460 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2486C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1346C214yesmaximal, complemented
5C2×#123×C127—21no—
6C2×C4×D4×C127C2211yescharacteristic
7C22×C4⋊C4×C127C411yescharacteristic
8#423×C127—21no—
9C2×#100×C127—21no—
10C2×C22⋊C8×C127—21no—
11#398×C127C2212yes—
12#397×C127C412yes—
13#389×C127—21no—
14#381×C127—21no—
15#380×C127—21no—
16#380×C127C411yescharacteristic
17#343×C127C2212yes—
18#324×C127C2212yes—
19#323×C127—21no—
20C22×D4×C127D411yescharacteristic
21C23×C4×C127—21no—
22C23×C4×C127C2×C411yescharacteristic
23C23×C4×C127D411yescharacteristic
24C2×M16×C127—22no—
25C22×C8×C127—41no—
26#123×C127—42no—
27#123×C127—42no—
28C4×D4×C127—41no—
29C4×D4×C127—41no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—41no—
34C2×C4⋊C4×C127—41no—
35C2×C4⋊C4×C127C2×C412yes—
36C2×C4⋊C4×C127C2311yescharacteristic
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127C2×C411yescharacteristic
40C2×C22⋊C4×C127D411yescharacteristic
41C2×C42×C127D411yescharacteristic
42C4⋊C8×C127—41no—
43C4⋊C8×C127—41no—
44#100×C127—42no—
45C22⋊C8×C127—22no—
46C22⋊C8×C127—41no—
47#95×C127—22no—
48#95×C127—22no—
49#95×C127C2×C412yes—
50C24×C127C22⋊C411yescharacteristic
51C24×C127C22⋊C411yescharacteristic
52C2×D4×C127—41no—
53C2×D4×C127—41no—
54C2×D4×C127D812yes—
55C2×D4×C127SD1612yes—
56C22×C4×C127—21no—
57C22×C4×C127—21no—
58C22×C4×C127—21no—
59C22×C4×C127—21no—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127—42no—
63C22×C4×C127—42no—
64C22×C4×C127—42no—
65C22×C4×C127—42no—
66C22×C4×C127—42no—
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22×C411yescharacteristic
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72M16×C127—42no—
73M16×C127—42no—
74C2×C8×C127—42no—
75C2×C8×C127—42no—
76C2×C8×C127—82no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—42no—
79C4⋊C4×C127—42no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—42no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—44no—
88C42×C127—21no—
89C42×C127—21no—
90C23×C127—21no—
91C23×C127—21no—
92C23×C127—21no—
93C23×C127—21no—
94C23×C127—41no—
95C23×C127—41no—
96C23×C127—41no—
97C23×C127—41no—
98C23×C127#10212yes—
99C23×C127#10212yes—
100C23×C127C2×C22⋊C411yescharacteristic
101D4×C127—42no—
102D4×C127—42no—
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—42no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—42no—
121C2×C4×C127—81no—
122C2×C4×C127—84no—
123C2×C4×C127#9911yescharacteristic
124C2×C4×C127#9911yescharacteristic
125C2×C4×C127C2×D811yescharacteristic
126C2×C4×C127C2×SD1611yescharacteristic
127C8×C127—82no—
128C8×C127—82no—
129C22×C127—21no—
130C22×C127—21no—
131C22×C127—22no—
132C22×C127—22no—
133C22×C127—42no—
134C22×C127—42no—
135C22×C127—42no—
136C22×C127—41no—
137C22×C127—41no—
138C22×C127—41no—
139C22×C127—41no—
140C22×C127—81no—
141C22×C127C2×#9911yescharacteristic
142C22×C127C2×#10211yescharacteristic
143C22×C127#42111yescharacteristic
144C4×C127—21no—
145C4×C127—21no—
146C4×C127—21no—
147C4×C127—41no—
148C4×C127—41no—
149C4×C127—41no—
150C4×C127—82no—
151C4×C127—82no—
152C4×C127#35212yes—
153#11881C12711yesmaximal, characteristic, direct product factor, Sylow
154C2×C127—21no—
155C2×C127—21no—
156C2×C127—42no—
157C2×C127—42no—
158C2×C127#151911yescharacteristic
159C2×C127C2×#35211yescharacteristic
160C2×C127#213511yescharacteristic
161#2486C2×C12711yescharacteristic
162#1800C2×C12711yescharacteristic
163#1459C2×C12711yescharacteristic
164#1346C2×C12714yescomplemented
165C127#1188111yescharacteristic, direct product factor, Sylow
166C2×#123—21no—
167C2×C4×D4C22×C12711yescharacteristic
168C22×C4⋊C4C4×C12711yescharacteristic
169#423—21no—
170C2×#100—21no—
171C2×C22⋊C8—21no—
172#398C22×C12712yes—
173#397C4×C12712yes—
174#389—21no—
175#381—21no—
176#380—21no—
177#380C4×C12711yescharacteristic
178#343C22×C12712yes—
179#324C22×C12712yes—
180#323—21no—
181C22×D4D4×C12711yescharacteristic
182C23×C4—21no—
183C23×C4C2×C4×C12711yescharacteristic
184C23×C4D4×C12711yescharacteristic
185C2×M16—22no—
186C22×C8—41no—
187#123—42no—
188#123—42no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4C2×C4×C12712yes—
197C2×C4⋊C4C23×C12711yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4C2×C4×C12711yescharacteristic
201C2×C22⋊C4D4×C12711yescharacteristic
202C2×C42D4×C12711yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—41no—
205#100—42no—
206C22⋊C8—22no—
207C22⋊C8—41no—
208#95—22no—
209#95—22no—
210#95C2×C4×C12712yes—
211C24C22⋊C4×C12711yescharacteristic
212C24C22⋊C4×C12711yescharacteristic
213C2×D4—41no—
214C2×D4—41no—
215C2×D4D8×C12712yes—
216C2×D4SD16×C12712yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
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—
237C2×C8—82no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—44no—
249C42—21no—
250C42—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23#102×C12712yes—
260C23#102×C12712yes—
261C23C2×C22⋊C4×C12711yescharacteristic
262D4—42no—
263D4—42no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—84no—
284C2×C4#99×C12711yescharacteristic
285C2×C4#99×C12711yescharacteristic
286C2×C4C2×D8×C12711yescharacteristic
287C2×C4C2×SD16×C12711yescharacteristic
288C8—82no—
289C8—82no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—22no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—81no—
302C22C2×#99×C12711yescharacteristic
303C22C2×#102×C12711yescharacteristic
304C22#421×C12711yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4#352×C12712yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2C127×#151911yescharacteristic
319C2C2×#352×C12711yescharacteristic
320C2C127×#213511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1346C2semidirect
153. #11881C127direct (N × H)
164. #1346C2×C127semidirect
165. C127#11881direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#24862
C127×#18002
C127×#14592
C127×#13462
#11881127