Finite Group Databasebeta

← C127×#10505 #44574178

Subgroups — C127×#10505 #44574178

Order 32512.

402 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3209C211yesmaximal, characteristic
2C127×#1997C211yesmaximal, characteristic
3C127×#1986C211yesmaximal, characteristic
4C127×#1981C211yesmaximal, characteristic
5C127×#1565C211yesmaximal, characteristic
6C127×#1550C211yesmaximal, characteristic
7C127×#1303C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×C4⋊Q8×C127C2211yescharacteristic
10#494×C127—21no—
11#487×C127—21no—
12#462×C127—21no—
13#462×C127—21no—
14#451×C127—22no—
15#431×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#103×C127—22no—
19C4×M16×C127C2211yescharacteristic
20C4×C4⋊C4×C127C2211yescharacteristic
21#343×C127—21no—
22#343×C127—21no—
23#339×C127—21no—
24#339×C127—21no—
25#335×C127—21no—
26#334×C127—21no—
27#333×C127—21no—
28#332×C127—21no—
29C22×Q8×C127D412yes—
30C2×Q16×C127—22no—
31C2×Q16×C127—22no—
32C2×M16×C127—21no—
33C2×M16×C127D411yescharacteristic
34C2×M16×C127D411yescharacteristic
35C22×C8×C127—21no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127—21no—
39C4⋊Q8×C127—21no—
40C4⋊Q8×C127D411yescharacteristic
41C4⋊Q8×C127D411yescharacteristic
42#125×C127—21no—
43C22⋊Q8×C127—21no—
44C22⋊Q8×C127—21no—
45C4×Q8×C127—21no—
46C4×Q8×C127—21no—
47#117×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C42×C127—21no—
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127D411yescharacteristic
58C4⋊C8×C127D411yescharacteristic
59#103×C127—22no—
60#103×C127—22no—
61#103×C127—44no—
62C22⋊C8×C127—21no—
63#97×C127—21no—
64C4×C8×C127—21no—
65C4×C8×C127—21no—
66#95×C127—21no—
67C2×Q8×C127—22no—
68C2×Q8×C127—21no—
69C2×Q8×C127—22no—
70C2×Q8×C127—21no—
71C2×Q8×C127—42no—
72C2×Q8×C127—42no—
73C22×C4×C127—22no—
74C22×C4×C127—41no—
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C22×C4×C127#4111yescharacteristic
78Q16×C127—82no—
79Q16×C127—82no—
80M16×C127—21no—
81M16×C127—21no—
82M16×C127—21no—
83M16×C127—41no—
84M16×C127—41no—
85M16×C127Q1612yescomplemented
86C2×C8×C127—21no—
87C2×C8×C127—21no—
88C2×C8×C127—21no—
89C2×C8×C127—21no—
90C2×C8×C127—42no—
91C2×C8×C127—41no—
92C2×C8×C127—41no—
93C4⋊C4×C127—22no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127—41no—
105C22⋊C4×C127—41no—
106C42×C127—41no—
107C42×C127—41no—
108C42×C127—41no—
109C42×C127C2×D411yescharacteristic
110C42×C127C2×D411yescharacteristic
111C42×C127#4111yescharacteristic
112C42×C127#4111yescharacteristic
113C23×C127#12111yescharacteristic
114Q8×C127—44no—
115Q8×C127—41no—
116Q8×C127—42no—
117Q8×C127—41no—
118Q8×C127—42no—
119Q8×C127—81no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—41no—
123C2×C4×C127—42no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—42no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127—82no—
130C2×C4×C127#12011yescharacteristic
131C2×C4×C127#12111yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127#12311yescharacteristic
134C2×C4×C127#12311yescharacteristic
135C2×C4×C127#12411yescharacteristic
136C2×C4×C127C2×Q1611yescharacteristic
137C2×C4×C127#13511yescharacteristic
138C2×C4×C127#13711yescharacteristic
139C2×C4×C127#13711yescharacteristic
140C8×C127—22no—
141C8×C127—41no—
142C8×C127—41no—
143C8×C127—41no—
144C8×C127—81no—
145C8×C127—81no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127#39411yescharacteristic
149C22×C127#46211yescharacteristic
150C22×C127#46411yescharacteristic
151C4×C127—21no—
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—82no—
155C4×C127—81no—
156C4×C127—82no—
157C4×C127—81no—
158C4×C127#45311yescharacteristic
159C4×C127#45511yescharacteristic
160C4×C127#46211yescharacteristic
161C4×C127#46411yescharacteristic
162C4×C127#46711yescharacteristic
163C4×C127#47011yescharacteristic
164#10505C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—21no—
166C2×C127—21no—
167C2×C127#203711yescharacteristic
168C2×C127#204911yescharacteristic
169C2×C127#205611yescharacteristic
170#3209C2×C12711yescharacteristic
171#1997C2×C12711yescharacteristic
172#1986C2×C12711yescharacteristic
173#1981C2×C12711yescharacteristic
174#1565C2×C12711yescharacteristic
175#1550C2×C12711yescharacteristic
176#1303C2×C12711yescharacteristic
177C127#1050511yescharacteristic, direct product factor, Sylow
178#533C22×C12711yescharacteristic
179C2×C4⋊Q8C22×C12711yescharacteristic
180#494—21no—
181#487—21no—
182#462—21no—
183#462—21no—
184#451—22no—
185#431C22×C12711yescharacteristic
186#423C22×C12711yescharacteristic
187C2×C4⋊C8C22×C12711yescharacteristic
188C2×#103—22no—
189C4×M16C22×C12711yescharacteristic
190C4×C4⋊C4C22×C12711yescharacteristic
191#343—21no—
192#343—21no—
193#339—21no—
194#339—21no—
195#335—21no—
196#334—21no—
197#333—21no—
198#332—21no—
199C22×Q8D4×C12712yes—
200C2×Q16—22no—
201C2×Q16—22no—
202C2×M16—21no—
203C2×M16D4×C12711yescharacteristic
204C2×M16D4×C12711yescharacteristic
205C22×C8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8D4×C12711yescharacteristic
211C4⋊Q8D4×C12711yescharacteristic
212#125—21no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217#117—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C42—21no—
222C2×C42C23×C12711yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C12711yescharacteristic
228C4⋊C8D4×C12711yescharacteristic
229#103—22no—
230#103—22no—
231#103—44no—
232C22⋊C8—21no—
233#97—21no—
234C4×C8—21no—
235C4×C8—21no—
236#95—21no—
237C2×Q8—22no—
238C2×Q8—21no—
239C2×Q8—22no—
240C2×Q8—21no—
241C2×Q8—42no—
242C2×Q8—42no—
243C22×C4—22no—
244C22×C4—41no—
245C22×C4C2×D4×C12711yescharacteristic
246C22×C4C2×D4×C12711yescharacteristic
247C22×C4#41×C12711yescharacteristic
248Q16—82no—
249Q16—82no—
250M16—21no—
251M16—21no—
252M16—21no—
253M16—41no—
254M16—41no—
255M16Q16×C12712yescomplemented
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—42no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C22⋊C4—41no—
276C42—41no—
277C42—41no—
278C42—41no—
279C42C2×D4×C12711yescharacteristic
280C42C2×D4×C12711yescharacteristic
281C42#41×C12711yescharacteristic
282C42#41×C12711yescharacteristic
283C23#121×C12711yescharacteristic
284Q8—44no—
285Q8—41no—
286Q8—42no—
287Q8—41no—
288Q8—42no—
289Q8—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4#120×C12711yescharacteristic
301C2×C4#121×C12711yescharacteristic
302C2×C4#121×C12711yescharacteristic
303C2×C4#123×C12711yescharacteristic
304C2×C4#123×C12711yescharacteristic
305C2×C4#124×C12711yescharacteristic
306C2×C4C2×Q16×C12711yescharacteristic
307C2×C4#135×C12711yescharacteristic
308C2×C4#137×C12711yescharacteristic
309C2×C4#137×C12711yescharacteristic
310C8—22no—
311C8—41no—
312C8—41no—
313C8—41no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22#394×C12711yescharacteristic
319C22#462×C12711yescharacteristic
320C22#464×C12711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—82no—
325C4—82no—
326C4—81no—
327C4—81no—
328C4#453×C12711yescharacteristic
329C4#455×C12711yescharacteristic
330C4#462×C12711yescharacteristic
331C4#464×C12711yescharacteristic
332C4#467×C12711yescharacteristic
333C4#470×C12711yescharacteristic
334C2—21no—
335C2—21no—
336C2C127×#203711yescharacteristic
337C2C127×#204911yescharacteristic
338C2C127×#205611yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
85. M16×C127Q16semidirect
164. #10505C127direct (N × H)
177. C127#10505direct (N × H)
255. M16Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32092
C127×#19972
C127×#19862
C127×#19812
C127×#15652
C127×#15502
C127×#13032
#10505127