Finite Group Databasebeta

← C127×#9491 #44573164

Subgroups — C127×#9491 #44573164

Order 32512.

544 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2873C211yesmaximal, characteristic
2C127×#2599C211yesmaximal, characteristic
3C127×#1491C212yesmaximal, complemented
4C127×#1464C211yesmaximal, characteristic
5C127×#1288C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×C4×Q8×C127C2211yescharacteristic
8C2×#117×C127C2211yescharacteristic
9#432×C127C2212yes—
10#405×C127—24no—
11C4×M16×C127—21no—
12C4×M16×C127C2212yes—
13#398×C127C411yescharacteristic
14#397×C127C411yescharacteristic
15#395×C127C411yescharacteristic
16#393×C127C411yescharacteristic
17#388×C127—21no—
18#387×C127—21no—
19#387×C127—21no—
20#385×C127—21no—
21#383×C127C2211yescharacteristic
22Q8⋊C8×C127—24no—
23#324×C127—21no—
24#323×C127—21no—
25C22×Q8×C127C2×C411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—24no—
28C2×M16×C127—24no—
29C2×M16×C127—22no—
30C2×M16×C127—22no—
31C22×C8×C127—22no—
32C4×Q8×C127—22no—
33C4×Q8×C127—22no—
34#117×C127—22no—
35#117×C127—22no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127C2×C411yescharacteristic
45C2×C22⋊C4×C127D411yescharacteristic
46C2×C42×C127—21no—
47C2×C42×C127D411yescharacteristic
48C2×C42×C127C2311yescharacteristic
49C4⋊C8×C127—22no—
50C22⋊C8×C127—22no—
51#97×C127—22no—
52#97×C127—22no—
53#97×C127—22no—
54C4×C8×C127—22no—
55C4×C8×C127D414yes—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—21no—
61#95×C127—21no—
62#95×C127C2×C411yescharacteristic
63#95×C127C2×C411yescharacteristic
64C24×C127C22⋊C411yescharacteristic
65C2×Q8×C127—22no—
66C2×Q8×C127—42no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C22⋊C411yescharacteristic
78C22×C4×C127C22×C411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81M16×C127—28no—
82M16×C127—24no—
83M16×C127—24no—
84C2×C8×C127—28no—
85C2×C8×C127—24no—
86C2×C8×C127—42no—
87C4⋊C4×C127—22no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—22no—
90C4⋊C4×C127—42no—
91C4⋊C4×C127—42no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C22⋊C4×C127—22no—
95C22⋊C4×C127—22no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—42no—
98C42×C127—21no—
99C42×C127—21no—
100C42×C127—42no—
101C42×C127C2×D412yes—
102C42×C127#4112yes—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127#10412yes—
108C23×C127C2×C22⋊C411yescharacteristic
109Q8×C127—24no—
110Q8×C127—42no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—24no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—22no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
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#10412yes—
137C2×C4×C127C4×D412yes—
138C2×C4×C127#12011yescharacteristic
139C2×C4×C127#12112yes—
140C2×C4×C127#12311yescharacteristic
141C8×C127—28no—
142C8×C127—82no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—22no—
146C22×C127—42no—
147C22×C127—41no—
148C22×C127—41no—
149C22×C127—81no—
150C22×C127#38611yescharacteristic
151C22×C127C2×#10411yescharacteristic
152C22×C127C2×#10411yescharacteristic
153C4×C127—22no—
154C4×C127—21no—
155C4×C127—22no—
156C4×C127—21no—
157C4×C127—22no—
158C4×C127—41no—
159C4×C127—42no—
160C4×C127—41no—
161C4×C127—81no—
162C4×C127—81no—
163C4×C127—81no—
164#9491C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—21no—
166C2×C127—21no—
167C2×C127—42no—
168C2×C127#189111yescharacteristic
169C2×C127#189611yescharacteristic
170C2×C127#190911yescharacteristic
171#2873C2×C12711yescharacteristic
172#2599C2×C12711yescharacteristic
173#1491C2×C12712yescomplemented
174#1464C2×C12711yescharacteristic
175#1288C2×C12712yescomplemented
176C127#949111yescharacteristic, direct product factor, Sylow
177C22×M16—21no—
178C2×C4×Q8C22×C12711yescharacteristic
179C2×#117C22×C12711yescharacteristic
180#432C22×C12712yes—
181#405—24no—
182C4×M16—21no—
183C4×M16C22×C12712yes—
184#398C4×C12711yescharacteristic
185#397C4×C12711yescharacteristic
186#395C4×C12711yescharacteristic
187#393C4×C12711yescharacteristic
188#388—21no—
189#387—21no—
190#387—21no—
191#385—21no—
192#383C22×C12711yescharacteristic
193Q8⋊C8—24no—
194#324—21no—
195#323—21no—
196C22×Q8C2×C4×C12711yescharacteristic
197C23×C4D4×C12711yescharacteristic
198C2×M16—22no—
199C2×M16—24no—
200C2×M16—24no—
201C2×M16—22no—
202C22×C8—22no—
203C4×Q8—22no—
204C4×Q8—22no—
205#117—22no—
206#117—22no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×C4×C12711yescharacteristic
211C2×C4⋊C4C2×C4×C12711yescharacteristic
212C2×C4⋊C4D4×C12711yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4C2×C4×C12711yescharacteristic
216C2×C22⋊C4D4×C12711yescharacteristic
217C2×C42—21no—
218C2×C42D4×C12711yescharacteristic
219C2×C42C23×C12711yescharacteristic
220C4⋊C8—22no—
221C22⋊C8—22no—
222#97—22no—
223#97—22no—
224#97—22no—
225C4×C8—22no—
226C4×C8D4×C12714yes—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95C2×C4×C12711yescharacteristic
234#95C2×C4×C12711yescharacteristic
235C24C22⋊C4×C12711yescharacteristic
236C2×Q8—22no—
237C2×Q8—42no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4C22⋊C4×C12711yescharacteristic
248C22×C4C22⋊C4×C12711yescharacteristic
249C22×C4C22×C4×C12711yescharacteristic
250C22×C4C2×D4×C12711yescharacteristic
251C22×C4C2×D4×C12711yescharacteristic
252M16—28no—
253M16—24no—
254M16—24no—
255C2×C8—28no—
256C2×C8—24no—
257C2×C8—42no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C42—21no—
270C42—21no—
271C42—42no—
272C42C2×D4×C12712yes—
273C42#41×C12712yes—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#104×C12712yes—
279C23C2×C22⋊C4×C12711yescharacteristic
280Q8—24no—
281Q8—42no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#104×C12712yes—
308C2×C4C4×D4×C12712yes—
309C2×C4#120×C12711yescharacteristic
310C2×C4#121×C12712yes—
311C2×C4#123×C12711yescharacteristic
312C8—28no—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#386×C12711yescharacteristic
322C22C2×#104×C12711yescharacteristic
323C22C2×#104×C12711yescharacteristic
324C4—22no—
325C4—21no—
326C4—22no—
327C4—21no—
328C4—22no—
329C4—42no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C127×#189111yescharacteristic
339C2C127×#189611yescharacteristic
340C2C127×#190911yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1491C2semidirect
5. C127×#1288C2semidirect
164. #9491C127direct (N × H)
173. #1491C2×C127semidirect
175. #1288C2×C127semidirect
176. C127#9491direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28732
C127×#25992
C127×#14912
C127×#14642
C127×#12882
#9491127