Finite Group Databasebeta

← C127×#9528 #44573201

Subgroups — C127×#9528 #44573201

Order 32512.

396 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3113C211yesmaximal, characteristic
2C127×#2985C211yesmaximal, characteristic
3C127×#1559C211yesmaximal, characteristic
4C127×#1487C211yesmaximal, characteristic
5C127×#1467C211yesmaximal, characteristic
6C127×#1307C211yesmaximal, characteristic
7C127×#1287C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×C4×Q8×C127C2211yescharacteristic
10#483×C127C412yes—
11#475×C127—21no—
12#462×C127—21no—
13#451×C127C412yes—
14#446×C127—22no—
15#446×C127—21no—
16C8×Q8×C127—21no—
17#441×C127—22no—
18#433×C127—22no—
19#432×C127C2211yescharacteristic
20#432×C127C2211yescharacteristic
21#432×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23#423×C127C2211yescharacteristic
24#333×C127—21no—
25#332×C127—21no—
26Q8⋊C8×C127—21no—
27Q8⋊C8×C127—21no—
28#324×C127—22no—
29C22×Q8×C127C2×C411yescharacteristic
30C2×Q16×C127—22no—
31C2×M16×C127—21no—
32C4⋊Q8×C127D411yescharacteristic
33C4⋊Q8×C127D411yescharacteristic
34#125×C127—21no—
35C22⋊Q8×C127—21no—
36C22⋊Q8×C127C2×C412yes—
37C4×Q8×C127—21no—
38C4×Q8×C127—21no—
39C4×Q8×C127—21no—
40C4×Q8×C127—21no—
41C4×Q8×C127—21no—
42C4×Q8×C127D412yes—
43#117×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127C2×C411yescharacteristic
46C2×C42×C127—21no—
47C2×C42×C127C2311yescharacteristic
48#106×C127—22no—
49C4⋊C8×C127—22no—
50C4⋊C8×C127—22no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57#103×C127—22no—
58#103×C127—22no—
59C22⋊C8×C127—21no—
60C22⋊C8×C127—21no—
61C22⋊C8×C127C2×C412yes—
62C22⋊C8×C127D412yes—
63#97×C127—22no—
64#97×C127—21no—
65#97×C127—21no—
66#97×C127—21no—
67C4×C8×C127—22no—
68C4×C8×C127D411yescharacteristic
69C4×C8×C127D411yescharacteristic
70C2×Q8×C127—21no—
71C2×Q8×C127—21no—
72C2×Q8×C127—21no—
73C2×Q8×C127—42no—
74C2×Q8×C127C22⋊C412yes—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127C22×C411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127#4111yescharacteristic
80Q16×C127—44no—
81M16×C127—81no—
82C2×C8×C127—22no—
83C2×C8×C127—21no—
84C2×C8×C127—22no—
85C2×C8×C127—21no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127C22⋊C412yes—
98C22⋊C4×C127—22no—
99C42×C127—22no—
100C42×C127—41no—
101C42×C127—41no—
102C42×C127C2×D411yescharacteristic
103C42×C127C2×D411yescharacteristic
104C42×C127C2×D411yescharacteristic
105C42×C127#4111yescharacteristic
106C23×C127C4×D411yescharacteristic
107Q8×C127—22no—
108Q8×C127—22no—
109Q8×C127—42no—
110Q8×C127—41no—
111Q8×C127—41no—
112Q8×C127—41no—
113Q8×C127—41no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—22no—
117C2×C4×C127—22no—
118C2×C4×C127—22no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—81no—
125C2×C4×C127C2×C22⋊C411yescharacteristic
126C2×C4×C127C4×D411yescharacteristic
127C2×C4×C127#12011yescharacteristic
128C2×C4×C127#12111yescharacteristic
129C2×C4×C127#12111yescharacteristic
130C2×C4×C127#12311yescharacteristic
131C8×C127—41no—
132C8×C127—42no—
133C8×C127—41no—
134C8×C127—42no—
135C8×C127—81no—
136C8×C127—81no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127#38611yescharacteristic
141C4×C127—21no—
142C4×C127—21no—
143C4×C127—21no—
144C4×C127—21no—
145C4×C127—21no—
146C4×C127—42no—
147C4×C127—42no—
148C4×C127—42no—
149C4×C127—81no—
150C4×C127#47111yescharacteristic
151C4×C127#47311yescharacteristic
152#9528C12711yesmaximal, characteristic, direct product factor, Sylow
153C2×C127—41no—
154C2×C127#189111yescharacteristic
155C2×C127#190511yescharacteristic
156C2×C127#190811yescharacteristic
157#3113C2×C12711yescharacteristic
158#2985C2×C12711yescharacteristic
159#1559C2×C12711yescharacteristic
160#1487C2×C12711yescharacteristic
161#1467C2×C12711yescharacteristic
162#1307C2×C12711yescharacteristic
163#1287C2×C12711yescharacteristic
164C127#952811yescharacteristic, direct product factor, Sylow
165#533C22×C12711yescharacteristic
166C2×C4×Q8C22×C12711yescharacteristic
167#483C4×C12712yes—
168#475—21no—
169#462—21no—
170#451C4×C12712yes—
171#446—22no—
172#446—21no—
173C8×Q8—21no—
174#441—22no—
175#433—22no—
176#432C22×C12711yescharacteristic
177#432C22×C12711yescharacteristic
178#432C22×C12711yescharacteristic
179#431C22×C12711yescharacteristic
180#423C22×C12711yescharacteristic
181#333—21no—
182#332—21no—
183Q8⋊C8—21no—
184Q8⋊C8—21no—
185#324—22no—
186C22×Q8C2×C4×C12711yescharacteristic
187C2×Q16—22no—
188C2×M16—21no—
189C4⋊Q8D4×C12711yescharacteristic
190C4⋊Q8D4×C12711yescharacteristic
191#125—21no—
192C22⋊Q8—21no—
193C22⋊Q8C2×C4×C12712yes—
194C4×Q8—21no—
195C4×Q8—21no—
196C4×Q8—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8D4×C12712yes—
200#117—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×C4×C12711yescharacteristic
203C2×C42—21no—
204C2×C42C23×C12711yescharacteristic
205#106—22no—
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214#103—22no—
215#103—22no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218C22⋊C8C2×C4×C12712yes—
219C22⋊C8D4×C12712yes—
220#97—22no—
221#97—21no—
222#97—21no—
223#97—21no—
224C4×C8—22no—
225C4×C8D4×C12711yescharacteristic
226C4×C8D4×C12711yescharacteristic
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—42no—
231C2×Q8C22⋊C4×C12712yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4C22×C4×C12711yescharacteristic
235C22×C4C2×D4×C12711yescharacteristic
236C22×C4#41×C12711yescharacteristic
237Q16—44no—
238M16—81no—
239C2×C8—22no—
240C2×C8—21no—
241C2×C8—22no—
242C2×C8—21no—
243C2×C8—41no—
244C2×C8—41no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—22no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4C22⋊C4×C12712yes—
255C22⋊C4—22no—
256C42—22no—
257C42—41no—
258C42—41no—
259C42C2×D4×C12711yescharacteristic
260C42C2×D4×C12711yescharacteristic
261C42C2×D4×C12711yescharacteristic
262C42#41×C12711yescharacteristic
263C23C4×D4×C12711yescharacteristic
264Q8—22no—
265Q8—22no—
266Q8—42no—
267Q8—41no—
268Q8—41no—
269Q8—41no—
270Q8—41no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4C2×C22⋊C4×C12711yescharacteristic
283C2×C4C4×D4×C12711yescharacteristic
284C2×C4#120×C12711yescharacteristic
285C2×C4#121×C12711yescharacteristic
286C2×C4#121×C12711yescharacteristic
287C2×C4#123×C12711yescharacteristic
288C8—42no—
289C8—41no—
290C8—42no—
291C8—41no—
292C8—81no—
293C8—81no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22#386×C12711yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—42no—
305C4—42no—
306C4—81no—
307C4#471×C12711yescharacteristic
308C4#473×C12711yescharacteristic
309C2—41no—
310C2C127×#189111yescharacteristic
311C2C127×#190511yescharacteristic
312C2C127×#190811yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127C4×D4
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
152. #9528C127direct (N × H)
164. C127#9528direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31132
C127×#29852
C127×#15592
C127×#14872
C127×#14672
C127×#13072
C127×#12872
#9528127