Finite Group Databasebeta

← C127×#10455 #44574128

Subgroups — C127×#10455 #44574128

Order 32512.

376 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#477×C127C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic
3C127×#1571C211yesmaximal, characteristic
4C127×#1549C211yesmaximal, characteristic
5C127×#1548C211yesmaximal, characteristic
6C127×#1479C211yesmaximal, characteristic
7C127×#1301C211yesmaximal, characteristic
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×C4×Q8×C127C2211yescharacteristic
10#477×C127—22no—
11#477×C127—22no—
12#431×C127C2211yescharacteristic
13#431×C127C2211yescharacteristic
14C2×#107×C127—21no—
15#423×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#103×C127—21no—
19C2×#101×C127—21no—
20#343×C127—21no—
21#335×C127—22no—
22#333×C127—22no—
23#332×C127—22no—
24Q8⋊C8×C127—22no—
25C22×Q8×C127—21no—
26C22×Q8×C127D411yescharacteristic
27C2×M16×C127—21no—
28C2×M16×C127—21no—
29C22×C8×C127—21no—
30C4⋊Q8×C127—21no—
31C4⋊Q8×C127—21no—
32C4⋊Q8×C127—21no—
33C4⋊Q8×C127D412yes—
34C4×Q8×C127—21no—
35C4×Q8×C127—21no—
36C4×Q8×C127—21no—
37C4×Q8×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C42×C127—21no—
43C2×C42×C127C2311yescharacteristic
44#107×C127—24no—
45C4⋊C8×C127—21no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127D412yes—
52C4⋊C8×C127D412yes—
53#103×C127—24no—
54#101×C127—42no—
55C22⋊C8×C127—21no—
56C22⋊C8×C127—21no—
57C4×C8×C127—21no—
58C4×C8×C127—21no—
59C2×Q8×C127—21no—
60C2×Q8×C127—21no—
61C2×Q8×C127—21no—
62C2×Q8×C127—22no—
63C2×Q8×C127—21no—
64C2×Q8×C127—21no—
65C2×Q8×C127—41no—
66C2×Q8×C127—82no—
67C2×Q8×C127Q1612yes—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—41no—
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127#4111yescharacteristic
73C22×C4×C127#4111yescharacteristic
74M16×C127—41no—
75M16×C127—41no—
76M16×C127—41no—
77M16×C127—41no—
78C2×C8×C127—22no—
79C2×C8×C127—22no—
80C2×C8×C127—41no—
81C2×C8×C127—41no—
82C2×C8×C127—41no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C4⋊C4×C127—22no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C42×C127—41no—
94C42×C127—41no—
95C42×C127C2×D411yescharacteristic
96C42×C127C2×D411yescharacteristic
97C42×C127C2×D411yescharacteristic
98C42×C127#4111yescharacteristic
99C23×C127#12311yescharacteristic
100Q8×C127—22no—
101Q8×C127—22no—
102Q8×C127—41no—
103Q8×C127—41no—
104Q8×C127—82no—
105Q8×C127—82no—
106C2×C4×C127—22no—
107C2×C4×C127—22no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—42no—
113C2×C4×C127—82no—
114C2×C4×C127—81no—
115C2×C4×C127#12011yescharacteristic
116C2×C4×C127#12111yescharacteristic
117C2×C4×C127#12111yescharacteristic
118C2×C4×C127#12111yescharacteristic
119C2×C4×C127#12311yescharacteristic
120C2×C4×C127#12411yescharacteristic
121C2×C4×C127C2×Q1611yescharacteristic
122C2×C4×C127#13511yescharacteristic
123C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C127#13711yescharacteristic
125C8×C127—42no—
126C8×C127—42no—
127C8×C127—81no—
128C8×C127—81no—
129C8×C127—81no—
130C22×C127—21no—
131C22×C127—21no—
132C22×C127#39411yescharacteristic
133C22×C127#48411yescharacteristic
134C22×C127#48511yescharacteristic
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—21no—
138C4×C127—42no—
139C4×C127—81no—
140C4×C127—82no—
141C4×C127#44911yescharacteristic
142C4×C127#45111yescharacteristic
143C4×C127#46711yescharacteristic
144C4×C127#46811yescharacteristic
145C4×C127#47312yes—
146#10455C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—21no—
148C2×C127—21no—
149C2×C127#203611yescharacteristic
150C2×C127#204711yescharacteristic
151C2×C127#204811yescharacteristic
152C2×#477C2×C12711yescharacteristic
153#1801C2×C12711yescharacteristic
154#1571C2×C12711yescharacteristic
155#1549C2×C12711yescharacteristic
156#1548C2×C12711yescharacteristic
157#1479C2×C12711yescharacteristic
158#1301C2×C12711yescharacteristic
159C127#1045511yescharacteristic, direct product factor, Sylow
160C2×C4⋊Q8C22×C12711yescharacteristic
161C2×C4×Q8C22×C12711yescharacteristic
162#477—22no—
163#477—22no—
164#431C22×C12711yescharacteristic
165#431C22×C12711yescharacteristic
166C2×#107—21no—
167#423C22×C12711yescharacteristic
168#423C22×C12711yescharacteristic
169C2×C4⋊C8C22×C12711yescharacteristic
170C2×#103—21no—
171C2×#101—21no—
172#343—21no—
173#335—22no—
174#333—22no—
175#332—22no—
176Q8⋊C8—22no—
177C22×Q8—21no—
178C22×Q8D4×C12711yescharacteristic
179C2×M16—21no—
180C2×M16—21no—
181C22×C8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8D4×C12712yes—
186C4×Q8—21no—
187C4×Q8—21no—
188C4×Q8—21no—
189C4×Q8—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4D4×C12711yescharacteristic
194C2×C42—21no—
195C2×C42C23×C12711yescharacteristic
196#107—24no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8D4×C12712yes—
204C4⋊C8D4×C12712yes—
205#103—24no—
206#101—42no—
207C22⋊C8—21no—
208C22⋊C8—21no—
209C4×C8—21no—
210C4×C8—21no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—22no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—41no—
218C2×Q8—82no—
219C2×Q8Q16×C12712yes—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4C2×D4×C12711yescharacteristic
224C22×C4#41×C12711yescharacteristic
225C22×C4#41×C12711yescharacteristic
226M16—41no—
227M16—41no—
228M16—41no—
229M16—41no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C4⋊C4—22no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C42—41no—
246C42—41no—
247C42C2×D4×C12711yescharacteristic
248C42C2×D4×C12711yescharacteristic
249C42C2×D4×C12711yescharacteristic
250C42#41×C12711yescharacteristic
251C23#123×C12711yescharacteristic
252Q8—22no—
253Q8—22no—
254Q8—41no—
255Q8—41no—
256Q8—82no—
257Q8—82no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4#120×C12711yescharacteristic
268C2×C4#121×C12711yescharacteristic
269C2×C4#121×C12711yescharacteristic
270C2×C4#121×C12711yescharacteristic
271C2×C4#123×C12711yescharacteristic
272C2×C4#124×C12711yescharacteristic
273C2×C4C2×Q16×C12711yescharacteristic
274C2×C4#135×C12711yescharacteristic
275C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
276C2×C4#137×C12711yescharacteristic
277C8—42no—
278C8—42no—
279C8—81no—
280C8—81no—
281C8—81no—
282C22—21no—
283C22—21no—
284C22#394×C12711yescharacteristic
285C22#484×C12711yescharacteristic
286C22#485×C12711yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—82no—
292C4—81no—
293C4#449×C12711yescharacteristic
294C4#451×C12711yescharacteristic
295C4#467×C12711yescharacteristic
296C4#468×C12711yescharacteristic
297C4#473×C12712yes—
298C2—21no—
299C2—21no—
300C2C127×#203611yescharacteristic
301C2C127×#204711yescharacteristic
302C2C127×#204811yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
146. #10455C127direct (N × H)
159. C127#10455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#477×C1272
C127×#18012
C127×#15712
C127×#15492
C127×#15482
C127×#14792
C127×#13012
#10455127