Finite Group Databasebeta

← C127×#11570 #44575243

Subgroups — C127×#11570 #44575243

Order 32512.

480 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2542C211yesmaximal, characteristic
2C127×#1465C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1325C214yesmaximal, complemented
5C2×C4⋊Q8×C127C411yescharacteristic
6C2×C22⋊Q8×C127—21no—
7C2×C22⋊Q8×C127—21no—
8C2×C4×D4×C127C2211yescharacteristic
9#407×C127—21no—
10C2×C22⋊C8×C127—21no—
11#399×C127—21no—
12#399×C127—21no—
13#390×C127C412yes—
14#384×C127C2212yes—
15C4×C4⋊C4×C127C411yescharacteristic
16#324×C127C2212yes—
17#324×C127C2212yes—
18#323×C127—21no—
19#323×C127—21no—
20C22×Q8×C127—21no—
21C22×D4×C127C2×C411yescharacteristic
22C23×C4×C127D411yescharacteristic
23C23×C4×C127D411yescharacteristic
24C2×M16×C127—41no—
25C22×C8×C127—41no—
26C4⋊Q8×C127—41no—
27C4⋊Q8×C127—41no—
28C22⋊Q8×C127—44no—
29C22⋊Q8×C127—44no—
30C4×D4×C127—41no—
31C4×D4×C127—41no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127C2×C412yes—
37C2×C4⋊C4×C127C2311yescharacteristic
38C2×C22⋊C4×C127—22no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127D411yescharacteristic
41C2×C22⋊C4×C127D411yescharacteristic
42C2×C42×C127C2×C412yes—
43C2×C42×C127C2×C411yescharacteristic
44C22⋊C8×C127—22no—
45C22⋊C8×C127—22no—
46C22⋊C8×C127—41no—
47C22⋊C8×C127—41no—
48#95×C127—21no—
49C24×C127C22⋊C411yescharacteristic
50C24×C127C22⋊C411yescharacteristic
51C2×Q8×C127—42no—
52C2×Q8×C127—42no—
53C2×Q8×C127—41no—
54C2×Q8×C127—41no—
55C2×D4×C127—22no—
56C2×D4×C127—22no—
57C2×D4×C127—41no—
58C22×C4×C127—22no—
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—22no—
64C22×C4×C127—42no—
65C22×C4×C127—42no—
66C22×C4×C127C22⋊C411yescharacteristic
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22×C411yescharacteristic
69C22×C4×C127C2×D411yescharacteristic
70C22×C4×C127C2×D411yescharacteristic
71M16×C127—82no—
72C2×C8×C127—42no—
73C2×C8×C127—42no—
74C2×C8×C127—82no—
75C4⋊C4×C127—24no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—42no—
78C4⋊C4×C127—44no—
79C4⋊C4×C127—44no—
80C4⋊C4×C127—42no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—44no—
84C22⋊C4×C127—44no—
85C42×C127—21no—
86C42×C127—21no—
87C42×C127—24no—
88C23×C127—21no—
89C23×C127—21no—
90C23×C127—21no—
91C23×C127—21no—
92C23×C127—21no—
93C23×C127—41no—
94C23×C127—41no—
95C23×C127—41no—
96C23×C127—41no—
97C23×C127#10112yes—
98C23×C127C2×C22⋊C411yescharacteristic
99Q8×C127—82no—
100Q8×C127—82no—
101D4×C127—44no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—22no—
105C2×C4×C127—24no—
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—42no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—42no—
119C2×C4×C127—81no—
120C2×C4×C127—81no—
121C2×C4×C127#9911yescharacteristic
122C2×C4×C127#9911yescharacteristic
123C2×C4×C127#13112yes—
124C8×C127—82no—
125C8×C127—82no—
126C22×C127—21no—
127C22×C127—21no—
128C22×C127—22no—
129C22×C127—42no—
130C22×C127—42no—
131C22×C127—41no—
132C22×C127—41no—
133C22×C127—41no—
134C22×C127—41no—
135C22×C127—41no—
136C22×C127—81no—
137C22×C127—81no—
138C22×C127#40811yescharacteristic
139C22×C127C2×#9911yescharacteristic
140C22×C127C2×#10111yescharacteristic
141C4×C127—21no—
142C4×C127—22no—
143C4×C127—44no—
144C4×C127—41no—
145C4×C127—41no—
146C4×C127—41no—
147C4×C127—82no—
148C4×C127#35312yes—
149#11570C12711yesmaximal, characteristic, direct product factor, Sylow
150C2×C127—21no—
151C2×C127—21no—
152C2×C127—42no—
153C2×C127—81no—
154C2×C127#147211yescharacteristic
155C2×C127C2×#35311yescharacteristic
156C2×C127#213511yescharacteristic
157#2542C2×C12711yescharacteristic
158#1465C2×C12711yescharacteristic
159#1459C2×C12711yescharacteristic
160#1325C2×C12714yescomplemented
161C127#1157011yescharacteristic, direct product factor, Sylow
162C2×C4⋊Q8C4×C12711yescharacteristic
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C4×D4C22×C12711yescharacteristic
166#407—21no—
167C2×C22⋊C8—21no—
168#399—21no—
169#399—21no—
170#390C4×C12712yes—
171#384C22×C12712yes—
172C4×C4⋊C4C4×C12711yescharacteristic
173#324C22×C12712yes—
174#324C22×C12712yes—
175#323—21no—
176#323—21no—
177C22×Q8—21no—
178C22×D4C2×C4×C12711yescharacteristic
179C23×C4D4×C12711yescharacteristic
180C23×C4D4×C12711yescharacteristic
181C2×M16—41no—
182C22×C8—41no—
183C4⋊Q8—41no—
184C4⋊Q8—41no—
185C22⋊Q8—44no—
186C22⋊Q8—44no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4C2×C4×C12712yes—
194C2×C4⋊C4C23×C12711yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4D4×C12711yescharacteristic
198C2×C22⋊C4D4×C12711yescharacteristic
199C2×C42C2×C4×C12712yes—
200C2×C42C2×C4×C12711yescharacteristic
201C22⋊C8—22no—
202C22⋊C8—22no—
203C22⋊C8—41no—
204C22⋊C8—41no—
205#95—21no—
206C24C22⋊C4×C12711yescharacteristic
207C24C22⋊C4×C12711yescharacteristic
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—41no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4C22⋊C4×C12711yescharacteristic
224C22×C4C22⋊C4×C12711yescharacteristic
225C22×C4C22×C4×C12711yescharacteristic
226C22×C4C2×D4×C12711yescharacteristic
227C22×C4C2×D4×C12711yescharacteristic
228M16—82no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—82no—
232C4⋊C4—24no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—44no—
236C4⋊C4—44no—
237C4⋊C4—42no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—44no—
241C22⋊C4—44no—
242C42—21no—
243C42—21no—
244C42—24no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23#101×C12712yes—
255C23C2×C22⋊C4×C12711yescharacteristic
256Q8—82no—
257Q8—82no—
258D4—44no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4#99×C12711yescharacteristic
279C2×C4#99×C12711yescharacteristic
280C2×C4#131×C12712yes—
281C8—82no—
282C8—82no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22#408×C12711yescharacteristic
296C22C2×#99×C12711yescharacteristic
297C22C2×#101×C12711yescharacteristic
298C4—21no—
299C4—22no—
300C4—44no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—82no—
305C4#353×C12712yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2C127×#147211yescharacteristic
311C2C2×#353×C12711yescharacteristic
312C2C127×#213511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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×#1325C2semidirect
149. #11570C127direct (N × H)
160. #1325C2×C127semidirect
161. C127#11570direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25422
C127×#14652
C127×#14592
C127×#13252
#11570127