Finite Group Databasebeta

← C127×#11564 #44575237

Subgroups — C127×#11564 #44575237

Order 32512.

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

normal subgroups only

This group has 444 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×#2547C211yesmaximal, characteristic
2C127×#1465C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1319C214yesmaximal, complemented
5C2×C4⋊Q8×C127C411yescharacteristic
6C2×#124×C127C412yes—
7C2×C4×D4×C127C2211yescharacteristic
8#407×C127—21no—
9C2×C22⋊C8×C127—21no—
10#397×C127—21no—
11#397×C127—21no—
12#391×C127C2212yes—
13#380×C127—21no—
14#380×C127—21no—
15C4×C4⋊C4×C127C411yescharacteristic
16#324×C127C2212yes—
17#324×C127C2212yes—
18#323×C127—21no—
19#323×C127—21no—
20C22×Q8×C127C2×C412yes—
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—
28#124×C127—44no—
29C4×D4×C127—41no—
30C4×D4×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127C2311yescharacteristic
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127D411yescharacteristic
38C2×C22⋊C4×C127D411yescharacteristic
39C2×C42×C127C2×C411yescharacteristic
40C2×C42×C127C2×C412yes—
41C22⋊C8×C127—22no—
42C22⋊C8×C127—22no—
43C22⋊C8×C127—41no—
44C22⋊C8×C127—41no—
45#95×C127—21no—
46#95×C127—22no—
47#95×C127—22no—
48C24×C127C22⋊C411yescharacteristic
49C24×C127C22⋊C411yescharacteristic
50C2×Q8×C127—24no—
51C2×Q8×C127—42no—
52C2×Q8×C127—42no—
53C2×D4×C127—22no—
54C2×D4×C127—22no—
55C2×D4×C127—41no—
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×C127C22⋊C411yescharacteristic
65C22×C4×C127C22⋊C411yescharacteristic
66C22×C4×C127C22×C411yescharacteristic
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69M16×C127—82no—
70C2×C8×C127—42no—
71C2×C8×C127—42no—
72C2×C8×C127—82no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—42no—
75C4⋊C4×C127—42no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C22⋊C4×C127—41no—
79C22⋊C4×C127—41no—
80C22⋊C4×C127—44no—
81C22⋊C4×C127—44no—
82C42×C127—21no—
83C42×C127—21no—
84C42×C127—42no—
85C23×C127—21no—
86C23×C127—21no—
87C23×C127—21no—
88C23×C127—21no—
89C23×C127—21no—
90C23×C127—41no—
91C23×C127—41no—
92C23×C127—41no—
93C23×C127—41no—
94C23×C127#10012yes—
95C23×C127C2×C22⋊C411yescharacteristic
96Q8×C127—84no—
97D4×C127—44no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—22no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—42no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—81no—
116C2×C4×C127—81no—
117C2×C4×C127#9911yescharacteristic
118C2×C4×C127#9911yescharacteristic
119C2×C4×C127#13112yes—
120C8×C127—82no—
121C8×C127—82no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—22no—
125C22×C127—42no—
126C22×C127—42no—
127C22×C127—41no—
128C22×C127—41no—
129C22×C127—41no—
130C22×C127—41no—
131C22×C127—41no—
132C22×C127—81no—
133C22×C127—81no—
134C22×C127#40811yescharacteristic
135C22×C127C2×#9911yescharacteristic
136C22×C127C2×#10011yescharacteristic
137C4×C127—21no—
138C4×C127—22no—
139C4×C127—41no—
140C4×C127—41no—
141C4×C127—41no—
142C4×C127—82no—
143C4×C127—82no—
144C4×C127#35412yes—
145#11564C12711yesmaximal, characteristic, direct product factor, Sylow
146C2×C127—21no—
147C2×C127—21no—
148C2×C127—42no—
149C2×C127—81no—
150C2×C127#147111yescharacteristic
151C2×C127C2×#35411yescharacteristic
152C2×C127#213511yescharacteristic
153#2547C2×C12711yescharacteristic
154#1465C2×C12711yescharacteristic
155#1459C2×C12711yescharacteristic
156#1319C2×C12714yescomplemented
157C127#1156411yescharacteristic, direct product factor, Sylow
158C2×C4⋊Q8C4×C12711yescharacteristic
159C2×#124C4×C12712yes—
160C2×C4×D4C22×C12711yescharacteristic
161#407—21no—
162C2×C22⋊C8—21no—
163#397—21no—
164#397—21no—
165#391C22×C12712yes—
166#380—21no—
167#380—21no—
168C4×C4⋊C4C4×C12711yescharacteristic
169#324C22×C12712yes—
170#324C22×C12712yes—
171#323—21no—
172#323—21no—
173C22×Q8C2×C4×C12712yes—
174C22×D4C2×C4×C12711yescharacteristic
175C23×C4D4×C12711yescharacteristic
176C23×C4D4×C12711yescharacteristic
177C2×M16—41no—
178C22×C8—41no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181#124—44no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C23×C12711yescharacteristic
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4D4×C12711yescharacteristic
191C2×C22⋊C4D4×C12711yescharacteristic
192C2×C42C2×C4×C12711yescharacteristic
193C2×C42C2×C4×C12712yes—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198#95—21no—
199#95—22no—
200#95—22no—
201C24C22⋊C4×C12711yescharacteristic
202C24C22⋊C4×C12711yescharacteristic
203C2×Q8—24no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4C22⋊C4×C12711yescharacteristic
218C22×C4C22⋊C4×C12711yescharacteristic
219C22×C4C22×C4×C12711yescharacteristic
220C22×C4C2×D4×C12711yescharacteristic
221C22×C4C2×D4×C12711yescharacteristic
222M16—82no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—82no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—44no—
234C22⋊C4—44no—
235C42—21no—
236C42—21no—
237C42—42no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23#100×C12712yes—
248C23C2×C22⋊C4×C12711yescharacteristic
249Q8—84no—
250D4—44no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4#99×C12711yescharacteristic
271C2×C4#99×C12711yescharacteristic
272C2×C4#131×C12712yes—
273C8—82no—
274C8—82no—
275C22—21no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#408×C12711yescharacteristic
288C22C2×#99×C12711yescharacteristic
289C22C2×#100×C12711yescharacteristic
290C4—21no—
291C4—22no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—82no—
296C4—82no—
297C4#354×C12712yes—
298C2—21no—
299C2—21no—
300C2—42no—
301C2—81no—
302C2C127×#147111yescharacteristic
303C2C2×#354×C12711yescharacteristic
304C2C127×#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×#1319C2semidirect
145. #11564C127direct (N × H)
156. #1319C2×C127semidirect
157. C127#11564direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25472
C127×#14652
C127×#14592
C127×#13192
#11564127