Finite Group Databasebeta

← C127×#8374 #44572047

Subgroups — C127×#8374 #44572047

Order 32512.

712 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C127C211yesmaximal, characteristic
2C4×#101×C127C211yesmaximal, characteristic
3C127×#1528C212yesmaximal
4C127×#1491C212yesmaximal
5C127×#1467C211yesmaximal, characteristic
6#557×C127—24no—
7#557×C127—24no—
8C2×C4⋊Q8×C127—21no—
9C2×C4⋊Q8×C127C411yescharacteristic
10C2×#125×C127—21no—
11C2×#125×C127—21no—
12C2×#125×C127C411yescharacteristic
13C2×#125×C127C2211yescharacteristic
14C2×C4×Q8×C127—21no—
15C2×C4×Q8×C127C411yescharacteristic
16C2×C4×Q8×C127C411yescharacteristic
17C2×C4×Q8×C127C2211yescharacteristic
18C2×C4×Q8×C127C2211yescharacteristic
19#432×C127C2212yes—
20C2×#101×C127—21no—
21C4×M16×C127C2212yes—
22#343×C127—21no—
23#330×C127—24no—
24Q8⋊C8×C127—24no—
25#324×C127—21no—
26#324×C127—21no—
27C22×Q8×C127—21no—
28C22×Q8×C127C2×C411yescharacteristic
29C22×Q8×C127D411yescharacteristic
30C2×M16×C127—22no—
31C4⋊Q8×C127—28no—
32C4⋊Q8×C127—22no—
33C4⋊Q8×C127—22no—
34#125×C127—28no—
35#125×C127—28no—
36#125×C127—22no—
37#125×C127—22no—
38#125×C127—22no—
39#125×C127D414yes—
40C4×Q8×C127—28no—
41C4×Q8×C127—22no—
42C4×Q8×C127—22no—
43C4×Q8×C127—22no—
44C4×Q8×C127—22no—
45C4×Q8×C127—22no—
46C4×Q8×C127—22no—
47C4×Q8×C127—22no—
48C4×Q8×C127D414yes—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127—21no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127C2×C411yescharacteristic
58C2×C4⋊C4×C127C2×C411yescharacteristic
59C2×C4⋊C4×C127C2×C411yescharacteristic
60C2×C4⋊C4×C127D411yescharacteristic
61C2×C4⋊C4×C127D411yescharacteristic
62C2×C4⋊C4×C127D411yescharacteristic
63C2×C42×C127—21no—
64C2×C42×C127—21no—
65C2×C42×C127—21no—
66C2×C42×C127C2×C411yescharacteristic
67C2×C42×C127C2×C411yescharacteristic
68C2×C42×C127C2311yescharacteristic
69C4⋊C8×C127—22no—
70#101×C127—24no—
71C22⋊C8×C127—22no—
72#97×C127—22no—
73#97×C127—22no—
74C4×C8×C127—22no—
75C2×Q8×C127—24no—
76C2×Q8×C127—24no—
77C2×Q8×C127—22no—
78C2×Q8×C127—21no—
79C2×Q8×C127—22no—
80C2×Q8×C127—41no—
81C2×Q8×C127—42no—
82C2×Q8×C127—42no—
83C2×Q8×C127C22⋊C412yes—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127C22⋊C411yescharacteristic
89C22×C4×C127C22⋊C411yescharacteristic
90C22×C4×C127C22⋊C411yescharacteristic
91C22×C4×C127C22⋊C411yescharacteristic
92C22×C4×C127C22×C411yescharacteristic
93C22×C4×C127C2×D411yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95M16×C127—24no—
96M16×C127—42no—
97C2×C8×C127—42no—
98C2×C8×C127—42no—
99C4⋊C4×C127—24no—
100C4⋊C4×C127—24no—
101C4⋊C4×C127—24no—
102C4⋊C4×C127—24no—
103C4⋊C4×C127—24no—
104C4⋊C4×C127—21no—
105C4⋊C4×C127—21no—
106C4⋊C4×C127—21no—
107C4⋊C4×C127—24no—
108C4⋊C4×C127—24no—
109C4⋊C4×C127—24no—
110C4⋊C4×C127—22no—
111C4⋊C4×C127—22no—
112C4⋊C4×C127—22no—
113C4⋊C4×C127C22⋊C412yes—
114C4⋊C4×C127C22⋊C412yes—
115C4⋊C4×C127C22⋊C412yes—
116C42×C127—24no—
117C42×C127—24no—
118C42×C127—21no—
119C42×C127—21no—
120C42×C127—21no—
121C42×C127—21no—
122C42×C127—24no—
123C42×C127C2×D412yes—
124C42×C127C2×D412yes—
125C23×C127C2×C22⋊C411yescharacteristic
126Q8×C127—24no—
127Q8×C127—22no—
128Q8×C127—44no—
129Q8×C127—48no—
130Q8×C127#10114yescomplemented
131C2×C4×C127—24no—
132C2×C4×C127—22no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—22no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—22no—
141C2×C4×C127—21no—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—41no—
147C2×C4×C127—42no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127#10412yes—
155C2×C4×C127C2×C22⋊C411yescharacteristic
156C2×C4×C127C2×C22⋊C411yescharacteristic
157C2×C4×C127#12012yes—
158C2×C4×C127#12012yes—
159C8×C127—44no—
160C8×C127—82no—
161C22×C127—21no—
162C22×C127—21no—
163C22×C127#37911yescharacteristic
164C22×C127C2×#10411yescharacteristic
165C22×C127#42111yescharacteristic
166C4×C127—22no—
167C4×C127—24no—
168C4×C127—21no—
169C4×C127—22no—
170C4×C127—22no—
171C4×C127—41no—
172C4×C127—41no—
173C4×C127—42no—
174C4×C127—41no—
175C4×C127—42no—
176C4×C127—42no—
177C4×C127C2×#10112yes—
178#8374C12711yesmaximal, characteristic, direct product factor, Sylow
179C2×C127—21no—
180C2×C127—21no—
181C2×C127#178411yescharacteristic
182C2×C127#178911yescharacteristic
183C2×C127#179611yescharacteristic
184C2×#557C2×C12711yescharacteristic
185C4×#101C2×C12711yescharacteristic
186#1528C2×C12712yes—
187#1491C2×C12712yes—
188#1467C2×C12711yescharacteristic
189C127#837411yescharacteristic, direct product factor, Sylow
190#557—24no—
191#557—24no—
192C2×C4⋊Q8—21no—
193C2×C4⋊Q8C4×C12711yescharacteristic
194C2×#125—21no—
195C2×#125—21no—
196C2×#125C4×C12711yescharacteristic
197C2×#125C22×C12711yescharacteristic
198C2×C4×Q8—21no—
199C2×C4×Q8C4×C12711yescharacteristic
200C2×C4×Q8C4×C12711yescharacteristic
201C2×C4×Q8C22×C12711yescharacteristic
202C2×C4×Q8C22×C12711yescharacteristic
203#432C22×C12712yes—
204C2×#101—21no—
205C4×M16C22×C12712yes—
206#343—21no—
207#330—24no—
208Q8⋊C8—24no—
209#324—21no—
210#324—21no—
211C22×Q8—21no—
212C22×Q8C2×C4×C12711yescharacteristic
213C22×Q8D4×C12711yescharacteristic
214C2×M16—22no—
215C4⋊Q8—28no—
216C4⋊Q8—22no—
217C4⋊Q8—22no—
218#125—28no—
219#125—28no—
220#125—22no—
221#125—22no—
222#125—22no—
223#125D4×C12714yes—
224C4×Q8—28no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×Q8—22no—
232C4×Q8D4×C12714yes—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×C4×C12711yescharacteristic
242C2×C4⋊C4C2×C4×C12711yescharacteristic
243C2×C4⋊C4C2×C4×C12711yescharacteristic
244C2×C4⋊C4D4×C12711yescharacteristic
245C2×C4⋊C4D4×C12711yescharacteristic
246C2×C4⋊C4D4×C12711yescharacteristic
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42C2×C4×C12711yescharacteristic
251C2×C42C2×C4×C12711yescharacteristic
252C2×C42C23×C12711yescharacteristic
253C4⋊C8—22no—
254#101—24no—
255C22⋊C8—22no—
256#97—22no—
257#97—22no—
258C4×C8—22no—
259C2×Q8—24no—
260C2×Q8—24no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8C22⋊C4×C12712yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4C22⋊C4×C12711yescharacteristic
273C22×C4C22⋊C4×C12711yescharacteristic
274C22×C4C22⋊C4×C12711yescharacteristic
275C22×C4C22⋊C4×C12711yescharacteristic
276C22×C4C22×C4×C12711yescharacteristic
277C22×C4C2×D4×C12711yescharacteristic
278C22×C4C2×D4×C12711yescharacteristic
279M16—24no—
280M16—42no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4C22⋊C4×C12712yes—
298C4⋊C4C22⋊C4×C12712yes—
299C4⋊C4C22⋊C4×C12712yes—
300C42—24no—
301C42—24no—
302C42—21no—
303C42—21no—
304C42—21no—
305C42—21no—
306C42—24no—
307C42C2×D4×C12712yes—
308C42C2×D4×C12712yes—
309C23C2×C22⋊C4×C12711yescharacteristic
310Q8—24no—
311Q8—22no—
312Q8—44no—
313Q8—48no—
314Q8#101×C12714yescomplemented
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4#104×C12712yes—
339C2×C4C2×C22⋊C4×C12711yescharacteristic
340C2×C4C2×C22⋊C4×C12711yescharacteristic
341C2×C4#120×C12712yes—
342C2×C4#120×C12712yes—
343C8—44no—
344C8—82no—
345C22—21no—
346C22—21no—
347C22#379×C12711yescharacteristic
348C22C2×#104×C12711yescharacteristic
349C22#421×C12711yescharacteristic
350C4—24no—
351C4—21no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—42no—
357C4—42no—
358C4—42no—
359C4—41no—
360C4—41no—
361C4C2×#101×C12712yes—
362C2—21no—
363C2—21no—
364C2C127×#178411yescharacteristic
365C2C127×#178911yescharacteristic
366C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127C2×C22⋊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
130. Q8×C127#101semidirect
178. #8374C127direct (N × H)
189. C127#8374direct (N × H)
314. Q8#101×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1272
C4×#101×C1272
C127×#15282
C127×#14912
C127×#14672
#8374127