Finite Group Databasebeta

← C127×#9527 #44573200

Subgroups — C127×#9527 #44573200

Order 32512.

436 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3112C211yesmaximal, characteristic
2C127×#2981C211yesmaximal, characteristic
3C127×#1557C211yesmaximal, characteristic
4C127×#1487C211yesmaximal, characteristic, complemented
5C127×#1467C211yesmaximal, characteristic, complemented
6C127×#1307C211yesmaximal, characteristic, complemented
7C127×#1287C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×C4×Q8×C127C2211yescharacteristic
10#480×C127C412yes—
11#477×C127—21no—
12#460×C127—21no—
13#448×C127C412yes—
14#440×C127—22no—
15#436×C127—21no—
16#435×C127—22no—
17C8×D4×C127—21no—
18#432×C127C2211yescharacteristic
19#432×C127C2211yescharacteristic
20#432×C127C2211yescharacteristic
21#431×C127C2211yescharacteristic
22#423×C127C2211yescharacteristic
23#408×C127—22no—
24#332×C127—21no—
25#331×C127—21no—
26Q8⋊C8×C127—21no—
27Q8⋊C8×C127—21no—
28#324×C127—22no—
29C2×#41×C127—21no—
30C22×Q8×C127C2×C411yescharacteristic
31C2×SD16×C127—22no—
32C2×M16×C127—22no—
33C2×M16×C127—21no—
34C22×C8×C127—22no—
35C4⋊Q8×C127D411yescharacteristic
36#127×C127D411yescharacteristic
37#124×C127—21no—
38#121×C127—21no—
39#121×C127C2×C412yes—
40C4×Q8×C127—21no—
41C4×Q8×C127—21no—
42C4×Q8×C127—21no—
43C4×Q8×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127D412yes—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127C2×C411yescharacteristic
48C2×C42×C127—21no—
49C2×C42×C127C2311yescharacteristic
50#107×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#102×C127—22no—
59C22⋊C8×C127—22no—
60C22⋊C8×C127—22no—
61C22⋊C8×C127—21no—
62C22⋊C8×C127—21no—
63C22⋊C8×C127C2×C412yes—
64C22⋊C8×C127D412yes—
65#97×C127—21no—
66#97×C127—21no—
67#97×C127—21no—
68C4×C8×C127D411yescharacteristic
69C4×C8×C127D411yescharacteristic
70#41×C127—82no—
71C2×Q8×C127—21no—
72C2×Q8×C127—21no—
73C2×Q8×C127—21no—
74C2×Q8×C127—42no—
75C2×D4×C127—22no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127C22⋊C412yes—
79C22×C4×C127—21no—
80C22×C4×C127—22no—
81C22×C4×C127—21no—
82C22×C4×C127C22×C411yescharacteristic
83C22×C4×C127C2×D411yescharacteristic
84C22×C4×C127#4111yescharacteristic
85SD16×C127—44no—
86M16×C127—82no—
87M16×C127—81no—
88C2×C8×C127—22no—
89C2×C8×C127—21no—
90C2×C8×C127—21no—
91C2×C8×C127—22no—
92C2×C8×C127—41no—
93C2×C8×C127—41no—
94C2×C8×C127—82no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127C22⋊C412yes—
101C22⋊C4×C127—22no—
102C22⋊C4×C127—22no—
103C42×C127—41no—
104C42×C127—41no—
105C42×C127C2×D411yescharacteristic
106C42×C127C2×D411yescharacteristic
107C42×C127C2×D411yescharacteristic
108C42×C127#4111yescharacteristic
109C23×C127—22no—
110C23×C127C4×D411yescharacteristic
111Q8×C127—22no—
112Q8×C127—22no—
113Q8×C127—41no—
114Q8×C127—41no—
115Q8×C127—81no—
116D4×C127—42no—
117D4×C127—41no—
118D4×C127—41no—
119D4×C127—81no—
120D4×C127—82no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—22no—
124C2×C4×C127—22no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—81no—
133C2×C4×C127C2×C22⋊C411yescharacteristic
134C2×C4×C127C4×D411yescharacteristic
135C2×C4×C127#12011yescharacteristic
136C2×C4×C127#12111yescharacteristic
137C2×C4×C127#12111yescharacteristic
138C2×C4×C127#12311yescharacteristic
139C8×C127—41no—
140C8×C127—42no—
141C8×C127—41no—
142C8×C127—42no—
143C8×C127—81no—
144C8×C127—81no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—42no—
149C22×C127—42no—
150C22×C127—42no—
151C22×C127#38611yescharacteristic
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—42no—
158C4×C127—42no—
159C4×C127—81no—
160C4×C127#47111yescharacteristic
161C4×C127#47311yescharacteristic
162#9527C12711yesmaximal, characteristic, direct product factor, Sylow
163C2×C127—41no—
164C2×C127—82no—
165C2×C127#189111yescharacteristic
166C2×C127#190411yescharacteristic
167C2×C127#190811yescharacteristic
168#3112C2×C12711yescharacteristic
169#2981C2×C12711yescharacteristic
170#1557C2×C12711yescharacteristic
171#1487C2×C12711yescharacteristic, complemented
172#1467C2×C12711yescharacteristic, complemented
173#1307C2×C12711yescharacteristic, complemented
174#1287C2×C12711yescharacteristic, complemented
175C127#952711yescharacteristic, direct product factor, Sylow
176#532C22×C12711yescharacteristic
177C2×C4×Q8C22×C12711yescharacteristic
178#480C4×C12712yes—
179#477—21no—
180#460—21no—
181#448C4×C12712yes—
182#440—22no—
183#436—21no—
184#435—22no—
185C8×D4—21no—
186#432C22×C12711yescharacteristic
187#432C22×C12711yescharacteristic
188#432C22×C12711yescharacteristic
189#431C22×C12711yescharacteristic
190#423C22×C12711yescharacteristic
191#408—22no—
192#332—21no—
193#331—21no—
194Q8⋊C8—21no—
195Q8⋊C8—21no—
196#324—22no—
197C2×#41—21no—
198C22×Q8C2×C4×C12711yescharacteristic
199C2×SD16—22no—
200C2×M16—22no—
201C2×M16—21no—
202C22×C8—22no—
203C4⋊Q8D4×C12711yescharacteristic
204#127D4×C12711yescharacteristic
205#124—21no—
206#121—21no—
207#121C2×C4×C12712yes—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×D4—21no—
213C4×D4D4×C12712yes—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C12711yescharacteristic
216C2×C42—21no—
217C2×C42C23×C12711yescharacteristic
218#107—22no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225#103—22no—
226#102—22no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8C2×C4×C12712yes—
232C22⋊C8D4×C12712yes—
233#97—21no—
234#97—21no—
235#97—21no—
236C4×C8D4×C12711yescharacteristic
237C4×C8D4×C12711yescharacteristic
238#41—82no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—42no—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4C22⋊C4×C12712yes—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4C22×C4×C12711yescharacteristic
251C22×C4C2×D4×C12711yescharacteristic
252C22×C4#41×C12711yescharacteristic
253SD16—44no—
254M16—82no—
255M16—81no—
256C2×C8—22no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—82no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4C22⋊C4×C12712yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C42—41no—
272C42—41no—
273C42C2×D4×C12711yescharacteristic
274C42C2×D4×C12711yescharacteristic
275C42C2×D4×C12711yescharacteristic
276C42#41×C12711yescharacteristic
277C23—22no—
278C23C4×D4×C12711yescharacteristic
279Q8—22no—
280Q8—22no—
281Q8—41no—
282Q8—41no—
283Q8—81no—
284D4—42no—
285D4—41no—
286D4—41no—
287D4—81no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4C2×C22⋊C4×C12711yescharacteristic
302C2×C4C4×D4×C12711yescharacteristic
303C2×C4#120×C12711yescharacteristic
304C2×C4#121×C12711yescharacteristic
305C2×C4#121×C12711yescharacteristic
306C2×C4#123×C12711yescharacteristic
307C8—41no—
308C8—42no—
309C8—41no—
310C8—42no—
311C8—81no—
312C8—81no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22#386×C12711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—81no—
328C4#471×C12711yescharacteristic
329C4#473×C12711yescharacteristic
330C2—41no—
331C2—82no—
332C2C127×#189111yescharacteristic
333C2C127×#190411yescharacteristic
334C2C127×#190811yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
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
4. C127×#1487C2semidirect
5. C127×#1467C2semidirect
6. C127×#1307C2semidirect
7. C127×#1287C2semidirect
162. #9527C127direct (N × H)
171. #1487C2×C127semidirect
172. #1467C2×C127semidirect
173. #1307C2×C127semidirect
174. #1287C2×C127semidirect
175. C127#9527direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31122
C127×#29812
C127×#15572
C127×#14872
C127×#14672
C127×#13072
C127×#12872
#9527127