Finite Group Databasebeta

← C127×#8387 #44572060

Subgroups — C127×#8387 #44572060

Order 32512.

998 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C127C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic, complemented
3C127×#1546C212yesmaximal, complemented
4C127×#1486C212yesmaximal, complemented
5C127×#1460C211yesmaximal, characteristic, complemented
6C22×#41×C127—21no—
7#547×C127—24no—
8#547×C127—24no—
9C2×C4⋊Q8×C127C2211yescharacteristic
10C2×#123×C127—22no—
11C2×C22⋊Q8×C127—21no—
12C2×#121×C127C412yes—
13C2×C4×D4×C127C2211yescharacteristic
14C2×C4×D4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C412yes—
16#431×C127C2212yes—
17#423×C127C2212yes—
18C2×#100×C127—21no—
19#343×C127—21no—
20#332×C127—24no—
21D4⋊C8×C127—24no—
22#323×C127—22no—
23C2×#41×C127—28no—
24C2×#41×C127—44no—
25C2×#41×C127—42no—
26C2×#41×C127—42no—
27C22×Q8×C127—21no—
28C22×D4×C127—22no—
29C22×D4×C127C2×C411yescharacteristic
30C22×D4×C127D411yescharacteristic
31C23×C4×C127—22no—
32C23×C4×C127—21no—
33C23×C4×C127C2×C412yes—
34C2×M16×C127—22no—
35C4⋊Q8×C127—22no—
36C4⋊Q8×C127D414yes—
37#123×C127—216no—
38C22⋊Q8×C127—28no—
39#121×C127—24no—
40#121×C127—24no—
41C4×D4×C127—22no—
42C4×D4×C127—22no—
43C4×D4×C127—22no—
44C4×D4×C127D414yes—
45C2×C4⋊C4×C127—22no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127C2×C411yescharacteristic
50C2×C4⋊C4×C127C2×C412yes—
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127—22no—
53C2×C22⋊C4×C127—21no—
54C2×C22⋊C4×C127D412yes—
55C2×C42×C127C2311yescharacteristic
56C4⋊C8×C127—22no—
57C4⋊C8×C127—22no—
58C4⋊C8×C127—22no—
59#100×C127—42no—
60C22⋊C8×C127—22no—
61C4×C8×C127—22no—
62C24×C127—21no—
63C24×C127C22⋊C412yes—
64#41×C127—416no—
65#41×C127—416no—
66C2×Q8×C127—24no—
67C2×Q8×C127—41no—
68C2×Q8×C127—41no—
69C2×Q8×C127—42no—
70C2×D4×C127—28no—
71C2×D4×C127—21no—
72C2×D4×C127—22no—
73C2×D4×C127—22no—
74C2×D4×C127—42no—
75C2×D4×C127—44no—
76C2×D4×C127—44no—
77C2×D4×C127C22⋊C412yes—
78C2×D4×C127D812yes—
79C2×D4×C127SD1612yes—
80C22×C4×C127—28no—
81C22×C4×C127—21no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—24no—
86C22×C4×C127—44no—
87C22×C4×C127—44no—
88C22×C4×C127—44no—
89C22×C4×C127—41no—
90C22×C4×C127—41no—
91C22×C4×C127—42no—
92C22×C4×C127C22⋊C412yes—
93C22×C4×C127C22×C411yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95C22×C4×C127C2×D411yescharacteristic
96M16×C127—42no—
97M16×C127—42no—
98C2×C8×C127—42no—
99C2×C8×C127—42no—
100C4⋊C4×C127—28no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—22no—
103C4⋊C4×C127—24no—
104C4⋊C4×C127—22no—
105C4⋊C4×C127C22⋊C412yes—
106C4⋊C4×C127C22⋊C414yes—
107C22⋊C4×C127—28no—
108C22⋊C4×C127—24no—
109C22⋊C4×C127—24no—
110C42×C127C2×D412yes—
111C42×C127C2×D412yes—
112C23×C127—22no—
113C23×C127—22no—
114C23×C127—22no—
115C23×C127—42no—
116C23×C127—42no—
117C23×C127—42no—
118C23×C127—42no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127#10214yes—
122C23×C127C2×C22⋊C411yescharacteristic
123Q8×C127—44no—
124Q8×C127—44no—
125D4×C127—24no—
126D4×C127—24no—
127D4×C127—24no—
128D4×C127—42no—
129D4×C127—416no—
130C2×C4×C127—22no—
131C2×C4×C127—22no—
132C2×C4×C127—22no—
133C2×C4×C127—24no—
134C2×C4×C127—41no—
135C2×C4×C127—44no—
136C2×C4×C127—416no—
137C2×C4×C127—41no—
138C2×C4×C127—42no—
139C2×C4×C127—41no—
140C2×C4×C127—42no—
141C2×C4×C127—44no—
142C2×C4×C127—44no—
143C2×C4×C127—44no—
144C2×C4×C127—42no—
145C2×C4×C127C2×C22⋊C411yescharacteristic
146C2×C4×C127C2×C22⋊C411yescharacteristic
147C2×C4×C127#12012yes—
148C2×C4×C127#12012yes—
149C2×C4×C127C2×D811yescharacteristic
150C2×C4×C127C2×SD1611yescharacteristic
151C2×C4×C127AGL(1,ℤ/8)12yes—
152C8×C127—82no—
153C8×C127—82no—
154C22×C127—21no—
155C22×C127—21no—
156C22×C127—24no—
157C22×C127—44no—
158C22×C127—44no—
159C22×C127—42no—
160C22×C127—42no—
161C22×C127—42no—
162C22×C127—42no—
163C22×C127—42no—
164C22×C127—82no—
165C22×C127—82no—
166C22×C127#37911yescharacteristic
167C22×C127C2×#10211yescharacteristic
168C22×C127#41811yescharacteristic
169C4×C127—22no—
170C4×C127—21no—
171C4×C127—42no—
172C4×C127—42no—
173C4×C127—44no—
174C4×C127#41312yes—
175C4×C127#44712yes—
176C4×C127#45012yes—
177#8387C12711yesmaximal, characteristic, direct product factor, Sylow
178C2×C127—21no—
179C2×C127—21no—
180C2×C127—44no—
181C2×C127—82no—
182C2×C127#178511yescharacteristic
183C2×C127#178611yescharacteristic
184C2×C127#179611yescharacteristic
185C2×#547C2×C12711yescharacteristic
186#1800C2×C12711yescharacteristic, complemented
187#1546C2×C12712yescomplemented
188#1486C2×C12712yescomplemented
189#1460C2×C12711yescharacteristic, complemented
190C127#838711yescharacteristic, direct product factor, Sylow
191C22×#41—21no—
192#547—24no—
193#547—24no—
194C2×C4⋊Q8C22×C12711yescharacteristic
195C2×#123—22no—
196C2×C22⋊Q8—21no—
197C2×#121C4×C12712yes—
198C2×C4×D4C22×C12711yescharacteristic
199C2×C4×D4C22×C12711yescharacteristic
200C22×C4⋊C4C4×C12712yes—
201#431C22×C12712yes—
202#423C22×C12712yes—
203C2×#100—21no—
204#343—21no—
205#332—24no—
206D4⋊C8—24no—
207#323—22no—
208C2×#41—28no—
209C2×#41—44no—
210C2×#41—42no—
211C2×#41—42no—
212C22×Q8—21no—
213C22×D4—22no—
214C22×D4C2×C4×C12711yescharacteristic
215C22×D4D4×C12711yescharacteristic
216C23×C4—22no—
217C23×C4—21no—
218C23×C4C2×C4×C12712yes—
219C2×M16—22no—
220C4⋊Q8—22no—
221C4⋊Q8D4×C12714yes—
222#123—216no—
223C22⋊Q8—28no—
224#121—24no—
225#121—24no—
226C4×D4—22no—
227C4×D4—22no—
228C4×D4—22no—
229C4×D4D4×C12714yes—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4C2×C4×C12711yescharacteristic
235C2×C4⋊C4C2×C4×C12712yes—
236C2×C4⋊C4D4×C12711yescharacteristic
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4D4×C12712yes—
240C2×C42C23×C12711yescharacteristic
241C4⋊C8—22no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244#100—42no—
245C22⋊C8—22no—
246C4×C8—22no—
247C24—21no—
248C24C22⋊C4×C12712yes—
249#41—416no—
250#41—416no—
251C2×Q8—24no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—42no—
255C2×D4—28no—
256C2×D4—21no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—42no—
260C2×D4—44no—
261C2×D4—44no—
262C2×D4C22⋊C4×C12712yes—
263C2×D4D8×C12712yes—
264C2×D4SD16×C12712yes—
265C22×C4—28no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—24no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4—44no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4C22⋊C4×C12712yes—
278C22×C4C22×C4×C12711yescharacteristic
279C22×C4C2×D4×C12711yescharacteristic
280C22×C4C2×D4×C12711yescharacteristic
281M16—42no—
282M16—42no—
283C2×C8—42no—
284C2×C8—42no—
285C4⋊C4—28no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4C22⋊C4×C12712yes—
291C4⋊C4C22⋊C4×C12714yes—
292C22⋊C4—28no—
293C22⋊C4—24no—
294C22⋊C4—24no—
295C42C2×D4×C12712yes—
296C42C2×D4×C12712yes—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—41no—
305C23—41no—
306C23#102×C12714yes—
307C23C2×C22⋊C4×C12711yescharacteristic
308Q8—44no—
309Q8—44no—
310D4—24no—
311D4—24no—
312D4—24no—
313D4—42no—
314D4—416no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—416no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4C2×C22⋊C4×C12711yescharacteristic
331C2×C4C2×C22⋊C4×C12711yescharacteristic
332C2×C4#120×C12712yes—
333C2×C4#120×C12712yes—
334C2×C4C2×D8×C12711yescharacteristic
335C2×C4C2×SD16×C12711yescharacteristic
336C2×C4AGL(1,ℤ/8)×C12712yes—
337C8—82no—
338C8—82no—
339C22—21no—
340C22—21no—
341C22—24no—
342C22—44no—
343C22—44no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—82no—
350C22—82no—
351C22#379×C12711yescharacteristic
352C22C2×#102×C12711yescharacteristic
353C22#418×C12711yescharacteristic
354C4—21no—
355C4—22no—
356C4—42no—
357C4—42no—
358C4—44no—
359C4#413×C12712yes—
360C4#447×C12712yes—
361C4#450×C12712yes—
362C2—21no—
363C2—21no—
364C2—44no—
365C2—82no—
366C2C127×#178511yescharacteristic
367C2C127×#178611yescharacteristic
368C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#547×C127C2
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
2. C127×#1800C2semidirect
3. C127×#1546C2semidirect
4. C127×#1486C2semidirect
5. C127×#1460C2semidirect
177. #8387C127direct (N × H)
186. #1800C2×C127semidirect
187. #1546C2×C127semidirect
188. #1486C2×C127semidirect
189. #1460C2×C127semidirect
190. C127#8387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#547×C1272
C127×#18002
C127×#15462
C127×#14862
C127×#14602
#8387127