Finite Group Databasebeta

← C127×#8393 #44572066

Subgroups — C127×#8393 #44572066

Order 32512.

998 conjugacy classes of subgroups.

The subgroup lattice has 360 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×#1548C212yesmaximal, complemented
4C127×#1486C212yesmaximal, complemented
5C127×#1460C211yesmaximal, characteristic, complemented
6C22×#41×C127C412yes—
7#547×C127—24no—
8#547×C127—24no—
9C2×C4⋊Q8×C127C2211yescharacteristic
10C2×#123×C127—22no—
11C2×C22⋊Q8×C127C412yes—
12C2×#121×C127—21no—
13C2×C4×D4×C127C2211yescharacteristic
14C2×C4×D4×C127C2211yescharacteristic
15C22×C4⋊C4×C127—21no—
16#431×C127C2212yes—
17#423×C127C2212yes—
18C2×#100×C127—21no—
19#343×C127—21no—
20#333×C127—24no—
21D4⋊C8×C127—24no—
22#323×C127—22no—
23C2×#41×C127—24no—
24C2×#41×C127—24no—
25C2×#41×C127—48no—
26C22×Q8×C127C2×C412yes—
27C22×D4×C127—22no—
28C22×D4×C127C2×C411yescharacteristic
29C22×D4×C127D411yescharacteristic
30C23×C4×C127—22no—
31C23×C4×C127—21no—
32C23×C4×C127C2×C412yes—
33C2×M16×C127—22no—
34C4⋊Q8×C127—22no—
35C4⋊Q8×C127D414yes—
36#123×C127—216no—
37C22⋊Q8×C127—24no—
38C22⋊Q8×C127—24no—
39#121×C127—28no—
40C4×D4×C127—22no—
41C4×D4×C127—22no—
42C4×D4×C127—22no—
43C4×D4×C127D414yes—
44C2×C4⋊C4×C127—28no—
45C2×C4⋊C4×C127—22no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127C2×C411yescharacteristic
49C2×C4⋊C4×C127D411yescharacteristic
50C2×C22⋊C4×C127—22no—
51C2×C22⋊C4×C127—21no—
52C2×C22⋊C4×C127D412yes—
53C2×C42×C127C2311yescharacteristic
54C4⋊C8×C127—22no—
55C4⋊C8×C127—22no—
56C4⋊C8×C127—22no—
57#100×C127—42no—
58C22⋊C8×C127—22no—
59C4×C8×C127—22no—
60C24×C127—21no—
61C24×C127C22⋊C412yes—
62#41×C127—416no—
63#41×C127—48no—
64#41×C127—48no—
65C2×Q8×C127—22no—
66C2×Q8×C127—44no—
67C2×Q8×C127C22⋊C414yes—
68C2×D4×C127—24no—
69C2×D4×C127—28no—
70C2×D4×C127—21no—
71C2×D4×C127—22no—
72C2×D4×C127—22no—
73C2×D4×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—48no—
76C2×D4×C127C22⋊C412yes—
77C22×C4×C127—28no—
78C22×C4×C127—21no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—24no—
83C22×C4×C127—44no—
84C22×C4×C127—48no—
85C22×C4×C127—42no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127C22⋊C412yes—
89C22×C4×C127C22×C411yescharacteristic
90C22×C4×C127C2×D411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92M16×C127—42no—
93M16×C127—42no—
94C2×C8×C127—42no—
95C2×C8×C127—42no—
96C4⋊C4×C127—28no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—22no—
99C4⋊C4×C127—24no—
100C4⋊C4×C127—24no—
101C4⋊C4×C127C22⋊C412yes—
102C22⋊C4×C127—28no—
103C22⋊C4×C127—24no—
104C22⋊C4×C127—24no—
105C42×C127C2×D412yes—
106C42×C127C2×D412yes—
107C23×C127—24no—
108C23×C127—22no—
109C23×C127—22no—
110C23×C127—22no—
111C23×C127—22no—
112C23×C127—42no—
113C23×C127—42no—
114C23×C127—42no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127C2×C22⋊C411yescharacteristic
118Q8×C127—44no—
119Q8×C127—44no—
120D4×C127—24no—
121D4×C127—22no—
122D4×C127—416no—
123D4×C127—42no—
124D4×C127—42no—
125D4×C127#10014yescomplemented
126C2×C4×C127—22no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—24no—
130C2×C4×C127—41no—
131C2×C4×C127—44no—
132C2×C4×C127—44no—
133C2×C4×C127—416no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—44no—
137C2×C4×C127—44no—
138C2×C4×C127—44no—
139C2×C4×C127—42no—
140C2×C4×C127C2×C22⋊C411yescharacteristic
141C2×C4×C127C2×C22⋊C411yescharacteristic
142C2×C4×C127#12012yes—
143C2×C4×C127#12012yes—
144C2×C4×C127#13512yes—
145C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C127#13711yescharacteristic
147C8×C127—82no—
148C8×C127—82no—
149C22×C127—21no—
150C22×C127—21no—
151C22×C127—24no—
152C22×C127—44no—
153C22×C127—44no—
154C22×C127—42no—
155C22×C127—42no—
156C22×C127—42no—
157C22×C127—42no—
158C22×C127—42no—
159C22×C127—82no—
160C22×C127—82no—
161C22×C127#37911yescharacteristic
162C22×C127#41611yescharacteristic
163C22×C127#41711yescharacteristic
164C4×C127—22no—
165C4×C127—21no—
166C4×C127—42no—
167C4×C127—44no—
168C4×C127—42no—
169C4×C127C2×#10012yes—
170C4×C127#44912yes—
171C4×C127#45212yes—
172#8393C12711yesmaximal, characteristic, direct product factor, Sylow
173C2×C127—21no—
174C2×C127—21no—
175C2×C127—44no—
176C2×C127—82no—
177C2×C127#178311yescharacteristic
178C2×C127#178811yescharacteristic
179C2×C127#179611yescharacteristic
180C2×#547C2×C12711yescharacteristic
181#1800C2×C12711yescharacteristic, complemented
182#1548C2×C12712yescomplemented
183#1486C2×C12712yescomplemented
184#1460C2×C12711yescharacteristic, complemented
185C127#839311yescharacteristic, direct product factor, Sylow
186C22×#41C4×C12712yes—
187#547—24no—
188#547—24no—
189C2×C4⋊Q8C22×C12711yescharacteristic
190C2×#123—22no—
191C2×C22⋊Q8C4×C12712yes—
192C2×#121—21no—
193C2×C4×D4C22×C12711yescharacteristic
194C2×C4×D4C22×C12711yescharacteristic
195C22×C4⋊C4—21no—
196#431C22×C12712yes—
197#423C22×C12712yes—
198C2×#100—21no—
199#343—21no—
200#333—24no—
201D4⋊C8—24no—
202#323—22no—
203C2×#41—24no—
204C2×#41—24no—
205C2×#41—48no—
206C22×Q8C2×C4×C12712yes—
207C22×D4—22no—
208C22×D4C2×C4×C12711yescharacteristic
209C22×D4D4×C12711yescharacteristic
210C23×C4—22no—
211C23×C4—21no—
212C23×C4C2×C4×C12712yes—
213C2×M16—22no—
214C4⋊Q8—22no—
215C4⋊Q8D4×C12714yes—
216#123—216no—
217C22⋊Q8—24no—
218C22⋊Q8—24no—
219#121—28no—
220C4×D4—22no—
221C4×D4—22no—
222C4×D4—22no—
223C4×D4D4×C12714yes—
224C2×C4⋊C4—28no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C12711yescharacteristic
229C2×C4⋊C4D4×C12711yescharacteristic
230C2×C22⋊C4—22no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4D4×C12712yes—
233C2×C42C23×C12711yescharacteristic
234C4⋊C8—22no—
235C4⋊C8—22no—
236C4⋊C8—22no—
237#100—42no—
238C22⋊C8—22no—
239C4×C8—22no—
240C24—21no—
241C24C22⋊C4×C12712yes—
242#41—416no—
243#41—48no—
244#41—48no—
245C2×Q8—22no—
246C2×Q8—44no—
247C2×Q8C22⋊C4×C12714yes—
248C2×D4—24no—
249C2×D4—28no—
250C2×D4—21no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—48no—
256C2×D4C22⋊C4×C12712yes—
257C22×C4—28no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—44no—
264C22×C4—48no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C22⋊C4×C12712yes—
269C22×C4C22×C4×C12711yescharacteristic
270C22×C4C2×D4×C12711yescharacteristic
271C22×C4C2×D4×C12711yescharacteristic
272M16—42no—
273M16—42no—
274C2×C8—42no—
275C2×C8—42no—
276C4⋊C4—28no—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4C22⋊C4×C12712yes—
282C22⋊C4—28no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C42C2×D4×C12712yes—
286C42C2×D4×C12712yes—
287C23—24no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊C4×C12711yescharacteristic
298Q8—44no—
299Q8—44no—
300D4—24no—
301D4—22no—
302D4—416no—
303D4—42no—
304D4—42no—
305D4#100×C12714yescomplemented
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—41no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—416no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—42no—
320C2×C4C2×C22⋊C4×C12711yescharacteristic
321C2×C4C2×C22⋊C4×C12711yescharacteristic
322C2×C4#120×C12712yes—
323C2×C4#120×C12712yes—
324C2×C4#135×C12712yes—
325C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
326C2×C4#137×C12711yescharacteristic
327C8—82no—
328C8—82no—
329C22—21no—
330C22—21no—
331C22—24no—
332C22—44no—
333C22—44no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22#379×C12711yescharacteristic
342C22#416×C12711yescharacteristic
343C22#417×C12711yescharacteristic
344C4—21no—
345C4—22no—
346C4—42no—
347C4—44no—
348C4—42no—
349C4C2×#100×C12712yes—
350C4#449×C12712yes—
351C4#452×C12712yes—
352C2—21no—
353C2—21no—
354C2—44no—
355C2—82no—
356C2C127×#178311yescharacteristic
357C2C127×#178811yescharacteristic
358C2C127×#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×#1548C2semidirect
4. C127×#1486C2semidirect
5. C127×#1460C2semidirect
125. D4×C127#100semidirect
172. #8393C127direct (N × H)
181. #1800C2×C127semidirect
182. #1548C2×C127semidirect
183. #1486C2×C127semidirect
184. #1460C2×C127semidirect
185. C127#8393direct (N × H)
305. D4#100×C127semidirect

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×#15482
C127×#14862
C127×#14602
#8393127