Finite Group Databasebeta

← C127×#13494 #44577167

Subgroups — C127×#13494 #44577167

Order 32512.

342 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#367×C127C211yesmaximal, characteristic, complemented
2C2×C22⋊C16×C127C211yesmaximal, characteristic
3C127×#1808C211yesmaximal, characteristic
4C127×#1808C211yesmaximal, characteristic
5C127×#1380C211yesmaximal, characteristic, complemented
6C127×#1380C211yesmaximal, characteristic, complemented
7C127×#1380C211yesmaximal, characteristic, complemented
8C23×C8×C127C2211yescharacteristic
9C22×C16×C127C2211yescharacteristic
10C22×C16×C127C2211yescharacteristic
11C2×#107×C127C2211yescharacteristic
12C2×#107×C127C2211yescharacteristic
13C2×#107×C127C2211yescharacteristic
14C2×#107×C127C2211yescharacteristic
15#380×C127—21no—
16#380×C127—21no—
17#367×C127—22no—
18C22⋊C16×C127—22no—
19#340×C127—21no—
20#340×C127—21no—
21C23×C4×C127D411yescharacteristic
22C22×C8×C127—21no—
23C22×C8×C127—21no—
24C22×C8×C127—21no—
25C22×C8×C127—21no—
26C22×C8×C127—21no—
27C22×C8×C127—21no—
28C22×C8×C127D411yescharacteristic
29C22×C8×C127C2311yescharacteristic
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C22⋊C4×C127—41no—
35C2×C22⋊C4×C127—41no—
36C2×C16×C127—21no—
37C2×C16×C127—21no—
38C2×C16×C127—21no—
39C2×C16×C127—21no—
40C2×C16×C127—21no—
41C2×C16×C127D412yes—
42#107×C127—21no—
43#107×C127—21no—
44#107×C127—21no—
45#107×C127—21no—
46#107×C127—21no—
47#107×C127—21no—
48#107×C127—21no—
49#107×C127—21no—
50#95×C127—41no—
51#95×C127—41no—
52C24×C127D811yescharacteristic
53C22×C4×C127—21no—
54C22×C4×C127—21no—
55C22×C4×C127—21no—
56C22×C4×C127—21no—
57C22×C4×C127—21no—
58C22×C4×C127—21no—
59C22×C4×C127—41no—
60C22×C4×C127—41no—
61C22×C4×C127—41no—
62C22×C4×C127—41no—
63C22×C4×C127D811yescharacteristic
64C22×C4×C127C2×D411yescharacteristic
65C2×C8×C127—21no—
66C2×C8×C127—21no—
67C2×C8×C127—21no—
68C2×C8×C127—41no—
69C2×C8×C127—41no—
70C2×C8×C127—41no—
71C2×C8×C127—41no—
72C2×C8×C127C2×D411yescharacteristic
73C2×C8×C127#4111yescharacteristic
74C2×C8×C127#4111yescharacteristic
75C2×C8×C127#4111yescharacteristic
76C2×C8×C127#4111yescharacteristic
77C2×C8×C127#4111yescharacteristic
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C22⋊C4×C127—82no—
87C22⋊C4×C127—82no—
88C16×C127—22no—
89C16×C127—41no—
90C23×C127—21no—
91C23×C127—21no—
92C23×C127—21no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127SD3212yes—
97C23×C127C2×D811yescharacteristic
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—41no—
105C2×C4×C127—81no—
106C2×C4×C127—81no—
107C2×C4×C127—81no—
108C2×C4×C127—81no—
109C2×C4×C127—81no—
110C2×C4×C127—81no—
111C2×C4×C127—81no—
112C2×C4×C127—81no—
113C2×C4×C127—81no—
114C2×C4×C127—81no—
115C2×C4×C127—81no—
116C2×C4×C127—81no—
117C2×C4×C127#12111yescharacteristic
118C2×C4×C127#12311yescharacteristic
119C2×C4×C127#12311yescharacteristic
120C2×C4×C127#13511yescharacteristic
121C2×C4×C127#13711yescharacteristic
122C2×C4×C127#13711yescharacteristic
123C8×C127—41no—
124C8×C127#12311yescharacteristic
125C8×C127#12411yescharacteristic
126C8×C127#12611yescharacteristic
127C8×C127#12611yescharacteristic
128C22×C127—22no—
129C22×C127—22no—
130C22×C127—22no—
131C22×C127—41no—
132C22×C127—41no—
133C22×C127—41no—
134C22×C127—41no—
135C22×C127#46611yescharacteristic
136C22×C127#48011yescharacteristic
137C22×C127#48011yescharacteristic
138C22×C127C2×SD3211yescharacteristic
139C22×C127#50811yescharacteristic
140C22×C127#50911yescharacteristic
141C22×C127#51011yescharacteristic
142C4×C127—41no—
143C4×C127—161no—
144C4×C127—161no—
145C4×C127—161no—
146C4×C127—161no—
147C4×C127#39711yescharacteristic
148C4×C127#47011yescharacteristic
149C4×C127#48511yescharacteristic
150C4×C127#48511yescharacteristic
151#13494C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—42no—
153C2×C127#207511yescharacteristic
154C2×C127#221711yescharacteristic
155C2×C127#222011yescharacteristic
156C2×C127#223311yescharacteristic
157C2×C127#223411yescharacteristic
158C2×C127#223511yescharacteristic
159C2×C127#223711yescharacteristic
160C2×#367C2×C12711yescharacteristic, complemented
161C2×C22⋊C16C2×C12711yescharacteristic
162#1808C2×C12711yescharacteristic
163#1808C2×C12711yescharacteristic
164#1380C2×C12711yescharacteristic, complemented
165#1380C2×C12711yescharacteristic, complemented
166#1380C2×C12711yescharacteristic, complemented
167C127#1349411yescharacteristic, direct product factor, Sylow
168C23×C8C22×C12711yescharacteristic
169C22×C16C22×C12711yescharacteristic
170C22×C16C22×C12711yescharacteristic
171C2×#107C22×C12711yescharacteristic
172C2×#107C22×C12711yescharacteristic
173C2×#107C22×C12711yescharacteristic
174C2×#107C22×C12711yescharacteristic
175#380—21no—
176#380—21no—
177#367—22no—
178C22⋊C16—22no—
179#340—21no—
180#340—21no—
181C23×C4D4×C12711yescharacteristic
182C22×C8—21no—
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8D4×C12711yescharacteristic
189C22×C8C23×C12711yescharacteristic
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—21no—
201C2×C16D4×C12712yes—
202#107—21no—
203#107—21no—
204#107—21no—
205#107—21no—
206#107—21no—
207#107—21no—
208#107—21no—
209#107—21no—
210#95—41no—
211#95—41no—
212C24D8×C12711yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4D8×C12711yescharacteristic
224C22×C4C2×D4×C12711yescharacteristic
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8C2×D4×C12711yescharacteristic
233C2×C8#41×C12711yescharacteristic
234C2×C8#41×C12711yescharacteristic
235C2×C8#41×C12711yescharacteristic
236C2×C8#41×C12711yescharacteristic
237C2×C8#41×C12711yescharacteristic
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C22⋊C4—82no—
247C22⋊C4—82no—
248C16—22no—
249C16—41no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23SD32×C12712yes—
257C23C2×D8×C12711yescharacteristic
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4#121×C12711yescharacteristic
278C2×C4#123×C12711yescharacteristic
279C2×C4#123×C12711yescharacteristic
280C2×C4#135×C12711yescharacteristic
281C2×C4#137×C12711yescharacteristic
282C2×C4#137×C12711yescharacteristic
283C8—41no—
284C8#123×C12711yescharacteristic
285C8#124×C12711yescharacteristic
286C8#126×C12711yescharacteristic
287C8#126×C12711yescharacteristic
288C22—22no—
289C22—22no—
290C22—22no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22#466×C12711yescharacteristic
296C22#480×C12711yescharacteristic
297C22#480×C12711yescharacteristic
298C22C2×SD32×C12711yescharacteristic
299C22#508×C12711yescharacteristic
300C22#509×C12711yescharacteristic
301C22#510×C12711yescharacteristic
302C4—41no—
303C4—161no—
304C4—161no—
305C4—161no—
306C4—161no—
307C4#397×C12711yescharacteristic
308C4#470×C12711yescharacteristic
309C4#485×C12711yescharacteristic
310C4#485×C12711yescharacteristic
311C2—42no—
312C2C127×#207511yescharacteristic
313C2C127×#221711yescharacteristic
314C2C127×#222011yescharacteristic
315C2C127×#223311yescharacteristic
316C2C127×#223411yescharacteristic
317C2C127×#223511yescharacteristic
318C2C127×#223711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC24×C127D8
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#367×C127C2semidirect
5. C127×#1380C2semidirect
6. C127×#1380C2semidirect
7. C127×#1380C2semidirect
151. #13494C127direct (N × H)
160. C2×#367C2×C127semidirect
164. #1380C2×C127semidirect
165. #1380C2×C127semidirect
166. #1380C2×C127semidirect
167. C127#13494direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#367×C1272
C2×C22⋊C16×C1272
C127×#18082
C127×#13802
#13494127