Finite Group Databasebeta

← C127×#8355 #44572028

Subgroups — C127×#8355 #44572028

Order 32512.

774 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3501C211yesmaximal, characteristic
2C127×#1954C211yesmaximal, characteristic
3C127×#1800C211yesmaximal, characteristic
4C127×#1550C212yesmaximal, complemented
5C127×#1493C212yesmaximal, complemented
6#554×C127—22no—
7#554×C127—24no—
8D4×Q8×C127—22no—
9#544×C127—21no—
10#543×C127C414yes—
11#533×C127C2212yes—
12C2×C22⋊Q8×C127—22no—
13#518×C127—21no—
14C2×C4×D4×C127C2211yescharacteristic
15#423×C127C2212yes—
16C2×C4⋊C8×C127C2211yescharacteristic
17C2×#100×C127—21no—
18C2×C22⋊C8×C127—22no—
19C2×C4×C8×C127C2211yescharacteristic
20#343×C127—21no—
21#333×C127—22no—
22#332×C127—22no—
23Q8⋊C8×C127—24no—
24C22×Q8×C127—22no—
25C22×D4×C127D411yescharacteristic
26C23×C4×C127D412yes—
27C2×M16×C127—22no—
28C22×C8×C127—21no—
29C22×C8×C127—21no—
30C4⋊Q8×C127—24no—
31C4⋊Q8×C127D412yes—
32C4⋊Q8×C127D412yes—
33#125×C127—24no—
34#125×C127—22no—
35C22⋊Q8×C127—24no—
36C22⋊Q8×C127—24no—
37C22⋊Q8×C127—28no—
38C22⋊Q8×C127—24no—
39C22⋊Q8×C127—22no—
40C22⋊Q8×C127—28no—
41C22⋊Q8×C127C2×C414yes—
42C4×Q8×C127—22no—
43C4×Q8×C127D414yes—
44C4×D4×C127—24no—
45C4×D4×C127—24no—
46C4×D4×C127—22no—
47C4×D4×C127—22no—
48#117×C127—22no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127C2×C412yes—
54C2×C42×C127C2311yescharacteristic
55C4⋊C8×C127—22no—
56C4⋊C8×C127—22no—
57C4⋊C8×C127—22no—
58#100×C127—42no—
59C22⋊C8×C127—44no—
60C4×C8×C127—22no—
61C24×C127C22⋊C412yes—
62C2×Q8×C127—24no—
63C2×Q8×C127—22no—
64C2×Q8×C127—82no—
65C2×Q8×C127—82no—
66C2×Q8×C127C22⋊C414yes—
67C2×D4×C127—22no—
68C2×D4×C127—22no—
69C2×D4×C127SD1612yes—
70C2×D4×C127Q1612yes—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—42no—
76C22×C4×C127—42no—
77C22×C4×C127C22⋊C412yes—
78C22×C4×C127C22×C411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81M16×C127—42no—
82M16×C127—42no—
83C2×C8×C127—22no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127—42no—
87C2×C8×C127—41no—
88C2×C8×C127—42no—
89C4⋊C4×C127—24no—
90C4⋊C4×C127—28no—
91C4⋊C4×C127—24no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—24no—
94C4⋊C4×C127—22no—
95C4⋊C4×C127—22no—
96C4⋊C4×C127—22no—
97C4⋊C4×C127C22⋊C414yes—
98C22⋊C4×C127—28no—
99C22⋊C4×C127—24no—
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—44no—
111Q8×C127—42no—
112Q8×C127—42no—
113Q8×C127—84no—
114D4×C127—24no—
115D4×C127—24no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—24no—
119C2×C4×C127—24no—
120C2×C4×C127—22no—
121C2×C4×C127—41no—
122C2×C4×C127—42no—
123C2×C4×C127—42no—
124C2×C4×C127—42no—
125C2×C4×C127—82no—
126C2×C4×C127—84no—
127C2×C4×C127—84no—
128C2×C4×C127C2×C22⋊C412yes—
129C2×C4×C127#12011yescharacteristic
130C2×C4×C127#12012yes—
131C2×C4×C127#12011yescharacteristic
132C2×C4×C127C2×SD1611yescharacteristic
133C2×C4×C127C2×Q1611yescharacteristic
134C2×C4×C127#13712yes—
135C8×C127—42no—
136C8×C127—82no—
137C8×C127—81no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—24no—
141C22×C127—44no—
142C22×C127—42no—
143C22×C127—42no—
144C22×C127—82no—
145C22×C127#37911yescharacteristic
146C22×C127C2×#10311yescharacteristic
147C22×C127#41911yescharacteristic
148C4×C127—21no—
149C4×C127—22no—
150C4×C127—42no—
151C4×C127—44no—
152C4×C127—44no—
153C4×C127#44812yes—
154C4×C127#45112yes—
155C4×C127#45311yescharacteristic
156C4×C127#45511yescharacteristic
157#8355C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—21no—
159C2×C127—21no—
160C2×C127—44no—
161C2×C127#178711yescharacteristic
162C2×C127#179111yescharacteristic
163C2×C127#179211yescharacteristic
164#3501C2×C12711yescharacteristic
165#1954C2×C12711yescharacteristic
166#1800C2×C12711yescharacteristic
167#1550C2×C12712yescomplemented
168#1493C2×C12712yescomplemented
169C127#835511yescharacteristic, direct product factor, Sylow
170#554—22no—
171#554—24no—
172D4×Q8—22no—
173#544—21no—
174#543C4×C12714yes—
175#533C22×C12712yes—
176C2×C22⋊Q8—22no—
177#518—21no—
178C2×C4×D4C22×C12711yescharacteristic
179#423C22×C12712yes—
180C2×C4⋊C8C22×C12711yescharacteristic
181C2×#100—21no—
182C2×C22⋊C8—22no—
183C2×C4×C8C22×C12711yescharacteristic
184#343—21no—
185#333—22no—
186#332—22no—
187Q8⋊C8—24no—
188C22×Q8—22no—
189C22×D4D4×C12711yescharacteristic
190C23×C4D4×C12712yes—
191C2×M16—22no—
192C22×C8—21no—
193C22×C8—21no—
194C4⋊Q8—24no—
195C4⋊Q8D4×C12712yes—
196C4⋊Q8D4×C12712yes—
197#125—24no—
198#125—22no—
199C22⋊Q8—24no—
200C22⋊Q8—24no—
201C22⋊Q8—28no—
202C22⋊Q8—24no—
203C22⋊Q8—22no—
204C22⋊Q8—28no—
205C22⋊Q8C2×C4×C12714yes—
206C4×Q8—22no—
207C4×Q8D4×C12714yes—
208C4×D4—24no—
209C4×D4—24no—
210C4×D4—22no—
211C4×D4—22no—
212#117—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4D4×C12711yescharacteristic
216C2×C22⋊C4—24no—
217C2×C22⋊C4C2×C4×C12712yes—
218C2×C42C23×C12711yescharacteristic
219C4⋊C8—22no—
220C4⋊C8—22no—
221C4⋊C8—22no—
222#100—42no—
223C22⋊C8—44no—
224C4×C8—22no—
225C24C22⋊C4×C12712yes—
226C2×Q8—24no—
227C2×Q8—22no—
228C2×Q8—82no—
229C2×Q8—82no—
230C2×Q8C22⋊C4×C12714yes—
231C2×D4—22no—
232C2×D4—22no—
233C2×D4SD16×C12712yes—
234C2×D4Q16×C12712yes—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C22⋊C4×C12712yes—
242C22×C4C22×C4×C12711yescharacteristic
243C22×C4C2×D4×C12711yescharacteristic
244C22×C4C2×D4×C12711yescharacteristic
245M16—42no—
246M16—42no—
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—42no—
251C2×C8—41no—
252C2×C8—42no—
253C4⋊C4—24no—
254C4⋊C4—28no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—24no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4C22⋊C4×C12714yes—
262C22⋊C4—28no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C42—24no—
266C42C2×D4×C12712yes—
267C42C2×D4×C12712yes—
268C23—22no—
269C23—22no—
270C23—42no—
271C23—42no—
272C23#103×C12714yes—
273C23C2×C22⋊C4×C12711yescharacteristic
274Q8—44no—
275Q8—42no—
276Q8—42no—
277Q8—84no—
278D4—24no—
279D4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4—84no—
291C2×C4—84no—
292C2×C4C2×C22⋊C4×C12712yes—
293C2×C4#120×C12711yescharacteristic
294C2×C4#120×C12712yes—
295C2×C4#120×C12711yescharacteristic
296C2×C4C2×SD16×C12711yescharacteristic
297C2×C4C2×Q16×C12711yescharacteristic
298C2×C4#137×C12712yes—
299C8—42no—
300C8—82no—
301C8—81no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—44no—
306C22—42no—
307C22—42no—
308C22—82no—
309C22#379×C12711yescharacteristic
310C22C2×#103×C12711yescharacteristic
311C22#419×C12711yescharacteristic
312C4—22no—
313C4—21no—
314C4—44no—
315C4—42no—
316C4—44no—
317C4#448×C12712yes—
318C4#451×C12712yes—
319C4#453×C12711yescharacteristic
320C4#455×C12711yescharacteristic
321C2—21no—
322C2—21no—
323C2—44no—
324C2C127×#178711yescharacteristic
325C2C127×#179111yescharacteristic
326C2C127×#179211yescharacteristic
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
4. C127×#1550C2semidirect
5. C127×#1493C2semidirect
157. #8355C127direct (N × H)
167. #1550C2×C127semidirect
168. #1493C2×C127semidirect
169. C127#8355direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35012
C127×#19542
C127×#18002
C127×#15502
C127×#14932
#8355127