Finite Group Databasebeta

← C127×#13067 #44576740

Subgroups — C127×#13067 #44576740

Order 32512.

536 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M32×C127C211yesmaximal, characteristic, complemented
2C2×#466×C127C211yesmaximal, characteristic
3C2×#361×C127C212yesmaximal, complemented
4C127×#1810C211yesmaximal, characteristic, complemented
5C127×#1387C212yesmaximal, complemented
6C22×D8×C127C2211yescharacteristic
7C23×C8×C127C2211yescharacteristic
8C2×#121×C127—21no—
9C2×M32×C127—21no—
10C2×M32×C127—24no—
11C2×M32×C127C2212yes—
12C22×C16×C127—21no—
13#466×C127—21no—
14#466×C127—21no—
15#466×C127C412yes—
16#466×C127C412yes—
17C2×#108×C127C2212yes—
18C2×#107×C127C2211yescharacteristic
19C2×#102×C127—21no—
20#407×C127—21no—
21#361×C127—24no—
22#341×C127—21no—
23C22×D4×C127—21no—
24C22×D4×C127—41no—
25C23×C4×C127D411yescharacteristic
26C2×D8×C127—22no—
27C2×D8×C127—21no—
28C2×D8×C127—22no—
29C2×D8×C127C2×C412yes—
30C2×M16×C127—22no—
31C22×C8×C127—22no—
32C22×C8×C127—22no—
33C22×C8×C127C2×C411yescharacteristic
34C22×C8×C127C2×C411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127D411yescharacteristic
37C22×C8×C127D411yescharacteristic
38C22×C8×C127C2311yescharacteristic
39#121×C127—22no—
40#121×C127—22no—
41#121×C127—41no—
42#121×C127—41no—
43C2×C4⋊C4×C127—21no—
44C2×C22⋊C4×C127—41no—
45M32×C127—24no—
46M32×C127—22no—
47M32×C127D414yescomplemented
48C2×C16×C127—24no—
49C2×C16×C127—22no—
50#108×C127—22no—
51#108×C127—22no—
52#107×C127—21no—
53#107×C127C2×C412yes—
54#102×C127—22no—
55#102×C127—22no—
56C22⋊C8×C127—41no—
57C22⋊C8×C127—41no—
58C24×C127—41no—
59C24×C127SD1611yescharacteristic
60C2×D4×C127—22no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C2×D4×C127—42no—
64C2×D4×C127—41no—
65C2×D4×C127—42no—
66C2×D4×C127—84no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—41no—
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127D811yescharacteristic
73C22×C4×C127D811yescharacteristic
74C22×C4×C127SD1611yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76D8×C127—24no—
77D8×C127—41no—
78D8×C127—41no—
79M16×C127—42no—
80M16×C127—42no—
81C2×C8×C127—22no—
82C2×C8×C127—22no—
83C2×C8×C127—22no—
84C2×C8×C127—21no—
85C2×C8×C127—21no—
86C2×C8×C127—21no—
87C2×C8×C127—21no—
88C2×C8×C127—42no—
89C2×C8×C127C22⋊C411yescharacteristic
90C2×C8×C127C22⋊C411yescharacteristic
91C2×C8×C127C22×C411yescharacteristic
92C2×C8×C127C2×D412yes—
93C2×C8×C127C2×D411yescharacteristic
94C2×C8×C127#4112yes—
95C4⋊C4×C127—22no—
96C4⋊C4×C127—41no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—42no—
99C16×C127—24no—
100C23×C127—22no—
101C23×C127—22no—
102C23×C127—41no—
103C23×C127—42no—
104C23×C127—82no—
105C23×C127—82no—
106C23×C127—82no—
107C23×C127#10211yescharacteristic
108C23×C127#10211yescharacteristic
109C23×C127C2×SD1611yescharacteristic
110D4×C127—42no—
111D4×C127—42no—
112D4×C127—84no—
113D4×C127—84no—
114D4×C127—82no—
115C2×C4×C127—22no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—42no—
123C2×C4×C127—82no—
124C2×C4×C127#10211yescharacteristic
125C2×C4×C127#10211yescharacteristic
126C2×C4×C127C2×C22⋊C411yescharacteristic
127C2×C4×C127#12112yes—
128C2×C4×C127C2×D811yescharacteristic
129C2×C4×C127#13512yes—
130C8×C127—21no—
131C8×C127—21no—
132C8×C127—82no—
133C8×C127C4×D412yes—
134C8×C127#12011yescharacteristic
135C8×C127#12311yescharacteristic
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—44no—
144C22×C127—82no—
145C22×C127—82no—
146C22×C127—82no—
147C22×C127—164no—
148C22×C127#36112yescomplemented
149C22×C127C2×#10211yescharacteristic
150C22×C127#46512yes—
151C4×C127—21no—
152C4×C127—21no—
153C4×C127—82no—
154C4×C127#38611yescharacteristic
155C4×C127#41611yescharacteristic
156C4×C127#46612yes—
157#13067C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—22no—
159C2×C127—22no—
160C2×C127—41no—
161C2×C127—162no—
162C2×C127#189311yescharacteristic
163C2×C127C2×#36111yescharacteristic
164C2×C127#214811yescharacteristic
165C22×M32C2×C12711yescharacteristic, complemented
166C2×#466C2×C12711yescharacteristic
167C2×#361C2×C12712yescomplemented
168#1810C2×C12711yescharacteristic, complemented
169#1387C2×C12712yescomplemented
170C127#1306711yescharacteristic, direct product factor, Sylow
171C22×D8C22×C12711yescharacteristic
172C23×C8C22×C12711yescharacteristic
173C2×#121—21no—
174C2×M32—21no—
175C2×M32—24no—
176C2×M32C22×C12712yes—
177C22×C16—21no—
178#466—21no—
179#466—21no—
180#466C4×C12712yes—
181#466C4×C12712yes—
182C2×#108C22×C12712yes—
183C2×#107C22×C12711yescharacteristic
184C2×#102—21no—
185#407—21no—
186#361—24no—
187#341—21no—
188C22×D4—21no—
189C22×D4—41no—
190C23×C4D4×C12711yescharacteristic
191C2×D8—22no—
192C2×D8—21no—
193C2×D8—22no—
194C2×D8C2×C4×C12712yes—
195C2×M16—22no—
196C22×C8—22no—
197C22×C8—22no—
198C22×C8C2×C4×C12711yescharacteristic
199C22×C8C2×C4×C12711yescharacteristic
200C22×C8D4×C12711yescharacteristic
201C22×C8D4×C12711yescharacteristic
202C22×C8D4×C12711yescharacteristic
203C22×C8C23×C12711yescharacteristic
204#121—22no—
205#121—22no—
206#121—41no—
207#121—41no—
208C2×C4⋊C4—21no—
209C2×C22⋊C4—41no—
210M32—24no—
211M32—22no—
212M32D4×C12714yescomplemented
213C2×C16—24no—
214C2×C16—22no—
215#108—22no—
216#108—22no—
217#107—21no—
218#107C2×C4×C12712yes—
219#102—22no—
220#102—22no—
221C22⋊C8—41no—
222C22⋊C8—41no—
223C24—41no—
224C24SD16×C12711yescharacteristic
225C2×D4—22no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—41no—
230C2×D4—42no—
231C2×D4—84no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4C22⋊C4×C12711yescharacteristic
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4D8×C12711yescharacteristic
238C22×C4D8×C12711yescharacteristic
239C22×C4SD16×C12711yescharacteristic
240C22×C4C2×D4×C12711yescharacteristic
241D8—24no—
242D8—41no—
243D8—41no—
244M16—42no—
245M16—42no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—42no—
254C2×C8C22⋊C4×C12711yescharacteristic
255C2×C8C22⋊C4×C12711yescharacteristic
256C2×C8C22×C4×C12711yescharacteristic
257C2×C8C2×D4×C12712yes—
258C2×C8C2×D4×C12711yescharacteristic
259C2×C8#41×C12712yes—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C16—24no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—42no—
269C23—82no—
270C23—82no—
271C23—82no—
272C23#102×C12711yescharacteristic
273C23#102×C12711yescharacteristic
274C23C2×SD16×C12711yescharacteristic
275D4—42no—
276D4—42no—
277D4—84no—
278D4—84no—
279D4—82no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—42no—
288C2×C4—82no—
289C2×C4#102×C12711yescharacteristic
290C2×C4#102×C12711yescharacteristic
291C2×C4C2×C22⋊C4×C12711yescharacteristic
292C2×C4#121×C12712yes—
293C2×C4C2×D8×C12711yescharacteristic
294C2×C4#135×C12712yes—
295C8—21no—
296C8—21no—
297C8—82no—
298C8C4×D4×C12712yes—
299C8#120×C12711yescharacteristic
300C8#123×C12711yescharacteristic
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—164no—
313C22#361×C12712yescomplemented
314C22C2×#102×C12711yescharacteristic
315C22#465×C12712yes—
316C4—21no—
317C4—21no—
318C4—82no—
319C4#386×C12711yescharacteristic
320C4#416×C12711yescharacteristic
321C4#466×C12712yes—
322C2—22no—
323C2—22no—
324C2—41no—
325C2—162no—
326C2C127×#189311yescharacteristic
327C2C2×#361×C12711yescharacteristic
328C2C127×#214811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#466×C127C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×M32×C127C2semidirect
3. C2×#361×C127C2semidirect
4. C127×#1810C2semidirect
5. C127×#1387C2semidirect
47. M32×C127D4semidirect
148. C22×C127#361semidirect
157. #13067C127direct (N × H)
165. C22×M32C2×C127semidirect
167. C2×#361C2×C127semidirect
168. #1810C2×C127semidirect
169. #1387C2×C127semidirect
170. C127#13067direct (N × H)
212. M32D4×C127semidirect
313. C22#361×C127semidirect

Maximal subgroups

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

subgroupindex
C22×M32×C1272
C2×#466×C1272
C2×#361×C1272
C127×#18102
C127×#13872
#13067127