Finite Group Databasebeta

← C127×#8391 #44572064

Subgroups — C127×#8391 #44572064

Order 32512.

966 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C127C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic
3C127×#1548C212yesmaximal, complemented
4C127×#1487C212yesmaximal, complemented
5C127×#1460C211yesmaximal, characteristic
6C23×Q8×C127C412yes—
7D4×Q8×C127—24no—
8D4×Q8×C127—24no—
9C2×C4⋊Q8×C127—21no—
10C2×C4⋊Q8×C127C2211yescharacteristic
11C2×C22⋊Q8×C127—22no—
12C2×C22⋊Q8×C127C412yes—
13C2×C4×Q8×C127C2211yescharacteristic
14C2×C4×D4×C127—21no—
15C2×C4×D4×C127C2211yescharacteristic
16#431×C127C2212yes—
17#423×C127C2212yes—
18C2×#100×C127—21no—
19#343×C127—21no—
20#333×C127—24no—
21Q8⋊C8×C127—24no—
22#323×C127—22no—
23C22×Q8×C127—24no—
24C22×Q8×C127—24no—
25C22×Q8×C127—22no—
26C22×Q8×C127—48no—
27C22×Q8×C127C2×C411yescharacteristic
28C22×Q8×C127C2×C412yes—
29C22×D4×C127D411yescharacteristic
30C23×C4×C127—22no—
31C23×C4×C127C2×C412yes—
32C2×M16×C127—22no—
33C4⋊Q8×C127—28no—
34C4⋊Q8×C127—22no—
35C4⋊Q8×C127D414yes—
36C22⋊Q8×C127—216no—
37C22⋊Q8×C127—24no—
38C22⋊Q8×C127—24no—
39C4×Q8×C127—22no—
40C4×Q8×C127D414yes—
41C4×D4×C127—28no—
42C4×D4×C127—22no—
43C4×D4×C127—22no—
44C2×C4⋊C4×C127—22no—
45C2×C4⋊C4×C127—21no—
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×C127D412yes—
52C2×C42×C127—21no—
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×C127C22⋊C412yes—
61C2×Q8×C127—24no—
62C2×Q8×C127—28no—
63C2×Q8×C127—21no—
64C2×Q8×C127—22no—
65C2×Q8×C127—44no—
66C2×Q8×C127—48no—
67C2×Q8×C127—416no—
68C2×Q8×C127—48no—
69C2×Q8×C127—48no—
70C2×Q8×C127C22⋊C412yes—
71C2×Q8×C127C22⋊C414yes—
72C2×D4×C127—22no—
73C2×D4×C127—22no—
74C2×D4×C127SD1612yes—
75C2×D4×C127Q1612yes—
76C22×C4×C127—21no—
77C22×C4×C127—28no—
78C22×C4×C127—21no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—48no—
83C22×C4×C127—44no—
84C22×C4×C127C22⋊C412yes—
85C22×C4×C127C22×C411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
87C22×C4×C127C2×D411yescharacteristic
88M16×C127—42no—
89M16×C127—42no—
90C2×C8×C127—42no—
91C2×C8×C127—42no—
92C4⋊C4×C127—28no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—24no—
95C4⋊C4×C127—24no—
96C4⋊C4×C127—24no—
97C4⋊C4×C127—22no—
98C4⋊C4×C127C22⋊C412yes—
99C22⋊C4×C127—28no—
100C22⋊C4×C127—24no—
101C42×C127—24no—
102C42×C127C2×D412yes—
103C42×C127C2×D412yes—
104C23×C127—22no—
105C23×C127—22no—
106C23×C127—42no—
107C23×C127—42no—
108C23×C127#10314yes—
109C23×C127C2×C22⋊C411yescharacteristic
110Q8×C127—24no—
111Q8×C127—22no—
112Q8×C127—44no—
113Q8×C127—416no—
114Q8×C127—44no—
115Q8×C127#10014yescomplemented
116D4×C127—24no—
117D4×C127—24no—
118C2×C4×C127—24no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—24no—
123C2×C4×C127—22no—
124C2×C4×C127—41no—
125C2×C4×C127—416no—
126C2×C4×C127—44no—
127C2×C4×C127—42no—
128C2×C4×C127—44no—
129C2×C4×C127—44no—
130C2×C4×C127—42no—
131C2×C4×C127C2×C22⋊C411yescharacteristic
132C2×C4×C127C2×C22⋊C411yescharacteristic
133C2×C4×C127#12012yes—
134C2×C4×C127#12012yes—
135C2×C4×C127C2×SD1611yescharacteristic
136C2×C4×C127C2×Q1611yescharacteristic
137C2×C4×C127#13712yes—
138C8×C127—82no—
139C8×C127—82no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—24no—
143C22×C127—44no—
144C22×C127—44no—
145C22×C127—42no—
146C22×C127—42no—
147C22×C127#37911yescharacteristic
148C22×C127C2×#10311yescharacteristic
149C22×C127#41911yescharacteristic
150C4×C127—22no—
151C4×C127—24no—
152C4×C127—21no—
153C4×C127—42no—
154C4×C127—44no—
155C4×C127—42no—
156C4×C127C2×#10012yes—
157C4×C127#44812yes—
158C4×C127#45112yes—
159#8391C12711yesmaximal, characteristic, direct product factor, Sylow
160C2×C127—21no—
161C2×C127—21no—
162C2×C127—44no—
163C2×C127#178311yescharacteristic
164C2×C127#178711yescharacteristic
165C2×C127#179611yescharacteristic
166C2×D4×Q8C2×C12711yescharacteristic
167#1800C2×C12711yescharacteristic
168#1548C2×C12712yescomplemented
169#1487C2×C12712yescomplemented
170#1460C2×C12711yescharacteristic
171C127#839111yescharacteristic, direct product factor, Sylow
172C23×Q8C4×C12712yes—
173D4×Q8—24no—
174D4×Q8—24no—
175C2×C4⋊Q8—21no—
176C2×C4⋊Q8C22×C12711yescharacteristic
177C2×C22⋊Q8—22no—
178C2×C22⋊Q8C4×C12712yes—
179C2×C4×Q8C22×C12711yescharacteristic
180C2×C4×D4—21no—
181C2×C4×D4C22×C12711yescharacteristic
182#431C22×C12712yes—
183#423C22×C12712yes—
184C2×#100—21no—
185#343—21no—
186#333—24no—
187Q8⋊C8—24no—
188#323—22no—
189C22×Q8—24no—
190C22×Q8—24no—
191C22×Q8—22no—
192C22×Q8—48no—
193C22×Q8C2×C4×C12711yescharacteristic
194C22×Q8C2×C4×C12712yes—
195C22×D4D4×C12711yescharacteristic
196C23×C4—22no—
197C23×C4C2×C4×C12712yes—
198C2×M16—22no—
199C4⋊Q8—28no—
200C4⋊Q8—22no—
201C4⋊Q8D4×C12714yes—
202C22⋊Q8—216no—
203C22⋊Q8—24no—
204C22⋊Q8—24no—
205C4×Q8—22no—
206C4×Q8D4×C12714yes—
207C4×D4—28no—
208C4×D4—22no—
209C4×D4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C12711yescharacteristic
215C2×C4⋊C4D4×C12711yescharacteristic
216C2×C22⋊C4—22no—
217C2×C22⋊C4D4×C12712yes—
218C2×C42—21no—
219C2×C42C23×C12711yescharacteristic
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8—22no—
223#100—42no—
224C22⋊C8—22no—
225C4×C8—22no—
226C24C22⋊C4×C12712yes—
227C2×Q8—24no—
228C2×Q8—28no—
229C2×Q8—21no—
230C2×Q8—22no—
231C2×Q8—44no—
232C2×Q8—48no—
233C2×Q8—416no—
234C2×Q8—48no—
235C2×Q8—48no—
236C2×Q8C22⋊C4×C12712yes—
237C2×Q8C22⋊C4×C12714yes—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4SD16×C12712yes—
241C2×D4Q16×C12712yes—
242C22×C4—21no—
243C22×C4—28no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—48no—
249C22×C4—44no—
250C22×C4C22⋊C4×C12712yes—
251C22×C4C22×C4×C12711yescharacteristic
252C22×C4C2×D4×C12711yescharacteristic
253C22×C4C2×D4×C12711yescharacteristic
254M16—42no—
255M16—42no—
256C2×C8—42no—
257C2×C8—42no—
258C4⋊C4—28no—
259C4⋊C4—21no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4C22⋊C4×C12712yes—
265C22⋊C4—28no—
266C22⋊C4—24no—
267C42—24no—
268C42C2×D4×C12712yes—
269C42C2×D4×C12712yes—
270C23—22no—
271C23—22no—
272C23—42no—
273C23—42no—
274C23#103×C12714yes—
275C23C2×C22⋊C4×C12711yescharacteristic
276Q8—24no—
277Q8—22no—
278Q8—44no—
279Q8—416no—
280Q8—44no—
281Q8#100×C12714yescomplemented
282D4—24no—
283D4—24no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—416no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4C2×C22⋊C4×C12711yescharacteristic
298C2×C4C2×C22⋊C4×C12711yescharacteristic
299C2×C4#120×C12712yes—
300C2×C4#120×C12712yes—
301C2×C4C2×SD16×C12711yescharacteristic
302C2×C4C2×Q16×C12711yescharacteristic
303C2×C4#137×C12712yes—
304C8—82no—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—24no—
309C22—44no—
310C22—44no—
311C22—42no—
312C22—42no—
313C22#379×C12711yescharacteristic
314C22C2×#103×C12711yescharacteristic
315C22#419×C12711yescharacteristic
316C4—24no—
317C4—21no—
318C4—22no—
319C4—44no—
320C4—42no—
321C4—42no—
322C4C2×#100×C12712yes—
323C4#448×C12712yes—
324C4#451×C12712yes—
325C2—21no—
326C2—21no—
327C2—44no—
328C2C127×#178311yescharacteristic
329C2C127×#178711yescharacteristic
330C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
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
3. C127×#1548C2semidirect
4. C127×#1487C2semidirect
115. Q8×C127#100semidirect
159. #8391C127direct (N × H)
168. #1548C2×C127semidirect
169. #1487C2×C127semidirect
171. C127#8391direct (N × H)
281. Q8#100×C127semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1272
C127×#18002
C127×#15482
C127×#14872
C127×#14602
#8391127