Finite Group Databasebeta

← C127×#17073 #44580746

Subgroups — C127×#17073 #44580746

Order 32512.

1258 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C214yesmaximal
2C127×#1444C214yesmaximal
3C127×#1441C214yesmaximal
4C127×C4⋊#95C211yesmaximal, characteristic
5C127×C4⋊#95C212yesmaximal
6C22×C4⋊C4×C127C2214yes—
7C22×C4⋊C4×C127C2214yes—
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2212yes—
11C22×C42×C127C2211yescharacteristic
12#398×C127—216no—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2214yes—
18C23×C4×C127C2314yes—
19C23×C4×C127C2314yes—
20C23×C4×C127C2314yes—
21C23×C4×C127C2312yes—
22C23×C4×C127C2311yescharacteristic
23C2×C4⋊C4×C127—28no—
24C2×C4⋊C4×C127—28no—
25C2×C4⋊C4×C127—28no—
26C2×C4⋊C4×C127—24no—
27C2×C4⋊C4×C127—42no—
28C2×C4⋊C4×C127—42no—
29C2×C4⋊C4×C127—42no—
30C2×C4⋊C4×C127—42no—
31C2×C4⋊C4×C127—44no—
32C2×C4⋊C4×C127—42no—
33C2×C4⋊C4×C127—42no—
34C2×C4⋊C4×C127—44no—
35C2×C4⋊C4×C127—44no—
36C2×C4⋊C4×C127D418yes—
37C2×C4⋊C4×C127Q818yes—
38C2×C42×C127—42no—
39C2×C42×C127Q814yes—
40#95×C127—28no—
41#95×C127—28no—
42#95×C127—28no—
43#95×C127—28no—
44#95×C127—44no—
45C24×C127C2411yescharacteristic
46C22×C4×C127—22no—
47C22×C4×C127—22no—
48C22×C4×C127—22no—
49C22×C4×C127—22no—
50C22×C4×C127—21no—
51C22×C4×C127—22no—
52C22×C4×C127—21no—
53C22×C4×C127—24no—
54C22×C4×C127—24no—
55C22×C4×C127—24no—
56C22×C4×C127—24no—
57C22×C4×C127—24no—
58C22×C4×C127—24no—
59C22×C4×C127—24no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—24no—
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—24no—
68C22×C4×C127—24no—
69C22×C4×C127—24no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127C2×D418yes—
73C22×C4×C127C2×D414yes—
74C22×C4×C127C2×Q818yes—
75C22×C4×C127C2×Q812yes—
76C22×C4×C127C2×Q814yes—
77C22×C4×C127C2×Q814yes—
78C22×C4×C127#4114yes—
79C4⋊C4×C127—48no—
80C4⋊C4×C127—48no—
81C4⋊C4×C127—416no—
82C4⋊C4×C127—48no—
83C4⋊C4×C127—416no—
84C42×C127—44no—
85C23×C127C22×D412yes—
86C23×C127C22×Q811yescharacteristic
87C23×C127C22×Q812yes—
88C23×C127C2×#4112yes—
89C23×C127H(5,𝔽2)12yes—
90C23×C127H(5,𝔽2)12yes—
91C23×C127H(5,𝔽2)11yescharacteristic
92C23×C1272−1+412yes—
93C23×C1272−1+411yescharacteristic
94C2×C4×C127—24no—
95C2×C4×C127—24no—
96C2×C4×C127—24no—
97C2×C4×C127—24no—
98C2×C4×C127—22no—
99C2×C4×C127—24no—
100C2×C4×C127—24no—
101C2×C4×C127—22no—
102C2×C4×C127—24no—
103C2×C4×C127—24no—
104C2×C4×C127—28no—
105C2×C4×C127—28no—
106C2×C4×C127—28no—
107C2×C4×C127—28no—
108C2×C4×C127—28no—
109C2×C4×C127—28no—
110C2×C4×C127—44no—
111C2×C4×C127—44no—
112C2×C4×C127—44no—
113C2×C4×C127—44no—
114C2×C4×C127—44no—
115C2×C4×C127—44no—
116C2×C4×C127—44no—
117C2×C4×C127—44no—
118C2×C4×C127—44no—
119C2×C4×C127—44no—
120C2×C4×C127—44no—
121C2×C4×C127—44no—
122C2×C4×C127—44no—
123C2×C4×C127—44no—
124C2×C4×C127—44no—
125C2×C4×C127#12514yes—
126C2×C4×C127C4⋊Q818yes—
127C22×C127C2×#12511yescharacteristic
128C22×C127C2×C4⋊Q812yes—
129C22×C127#53412yes—
130C22×C127#53712yes—
131C22×C127#53812yes—
132C22×C127#53912yes—
133C22×C127#54311yescharacteristic
134C22×C127#54312yes—
135C22×C127#54411yescharacteristic
136C22×C127#54412yes—
137C22×C127#54412yes—
138C22×C127D4211yescharacteristic
139C22×C127#54712yes—
140C22×C127D4×Q812yes—
141C22×C127#55012yes—
142C22×C127#55412yes—
143C22×C127#55712yes—
144C22×C127Q8211yescharacteristic
145C22×C127#56212yes—
146C22×C127#56211yescharacteristic
147C22×C127#56411yescharacteristic
148C4×C127—24no—
149C4×C127—28no—
150C4×C127—48no—
151C4×C127—48no—
152C4×C127—84no—
153#17073C12711yesmaximal, characteristic, direct product factor, Sylow
154C2×C127#255111yescharacteristic
155C2×C127#255212yes—
156C2×C127#264611yescharacteristic
157C2×C127#265912yes—
158C2×C127#268212yes—
159C2×C127#272612yes—
160C2×C127#273212yes—
161C2×C127#280612yes—
162C2×C127#284511yescharacteristic
163C2×#398C2×C12714yes—
164#1444C2×C12714yes—
165#1441C2×C12714yes—
166C4⋊#95C2×C12711yescharacteristic
167C4⋊#95C2×C12712yes—
168C127#1707311yescharacteristic, direct product factor, Sylow
169C22×C4⋊C4C22×C12714yes—
170C22×C4⋊C4C22×C12714yes—
171C22×C4⋊C4C22×C12712yes—
172C22×C4⋊C4C22×C12712yes—
173C22×C4⋊C4C22×C12712yes—
174C22×C42C22×C12711yescharacteristic
175#398—216no—
176C2×#95C22×C12714yes—
177C2×#95C22×C12714yes—
178C2×#95C22×C12714yes—
179C2×#95C22×C12714yes—
180C2×#95C22×C12714yes—
181C23×C4C23×C12714yes—
182C23×C4C23×C12714yes—
183C23×C4C23×C12714yes—
184C23×C4C23×C12712yes—
185C23×C4C23×C12711yescharacteristic
186C2×C4⋊C4—28no—
187C2×C4⋊C4—28no—
188C2×C4⋊C4—28no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4D4×C12718yes—
200C2×C4⋊C4Q8×C12718yes—
201C2×C42—42no—
202C2×C42Q8×C12714yes—
203#95—28no—
204#95—28no—
205#95—28no—
206#95—28no—
207#95—44no—
208C24C24×C12711yescharacteristic
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4C2×D4×C12718yes—
236C22×C4C2×D4×C12714yes—
237C22×C4C2×Q8×C12718yes—
238C22×C4C2×Q8×C12712yes—
239C22×C4C2×Q8×C12714yes—
240C22×C4C2×Q8×C12714yes—
241C22×C4#41×C12714yes—
242C4⋊C4—48no—
243C4⋊C4—48no—
244C4⋊C4—416no—
245C4⋊C4—48no—
246C4⋊C4—416no—
247C42—44no—
248C23C22×D4×C12712yes—
249C23C22×Q8×C12711yescharacteristic
250C23C22×Q8×C12712yes—
251C23C2×#41×C12712yes—
252C23H(5,𝔽2)×C12712yes—
253C23H(5,𝔽2)×C12712yes—
254C23H(5,𝔽2)×C12711yescharacteristic
255C232−1+4×C12712yes—
256C232−1+4×C12711yescharacteristic
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—28no—
268C2×C4—28no—
269C2×C4—28no—
270C2×C4—28no—
271C2×C4—28no—
272C2×C4—28no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4#125×C12714yes—
289C2×C4C4⋊Q8×C12718yes—
290C22C2×#125×C12711yescharacteristic
291C22C2×C4⋊Q8×C12712yes—
292C22#534×C12712yes—
293C22#537×C12712yes—
294C22#538×C12712yes—
295C22#539×C12712yes—
296C22#543×C12711yescharacteristic
297C22#543×C12712yes—
298C22#544×C12711yescharacteristic
299C22#544×C12712yes—
300C22#544×C12712yes—
301C22D42×C12711yescharacteristic
302C22#547×C12712yes—
303C22D4×Q8×C12712yes—
304C22#550×C12712yes—
305C22#554×C12712yes—
306C22#557×C12712yes—
307C22Q82×C12711yescharacteristic
308C22#562×C12712yes—
309C22#562×C12711yescharacteristic
310C22#564×C12711yescharacteristic
311C4—24no—
312C4—28no—
313C4—48no—
314C4—48no—
315C4—84no—
316C2C127×#255111yescharacteristic
317C2C127×#255212yes—
318C2C127×#264611yescharacteristic
319C2C127×#265912yes—
320C2C127×#268212yes—
321C2C127×#272612yes—
322C2C127×#273212yes—
323C2C127×#280612yes—
324C2C127×#284511yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
153. #17073C127direct (N × H)
168. C127#17073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C127×#14442
C127×#14412
C127×C4⋊#952
#17073127