Finite Group Databasebeta

← C127×#10449 #44574122

Subgroups — C127×#10449 #44574122

Order 32512.

408 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C127C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic
3C127×#1571C211yesmaximal, characteristic, complemented
4C127×#1549C211yesmaximal, characteristic, complemented
5C127×#1548C211yesmaximal, characteristic, complemented
6C127×#1478C211yesmaximal, characteristic
7C127×#1301C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#474×C127—22no—
11#474×C127—22no—
12#431×C127C2211yescharacteristic
13#431×C127C2211yescharacteristic
14C2×#107×C127—21no—
15#423×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#102×C127—21no—
19C2×#100×C127—21no—
20#343×C127—21no—
21#335×C127—22no—
22#333×C127—22no—
23#332×C127—22no—
24D4⋊C8×C127—22no—
25C22×Q8×C127—21no—
26C22×D4×C127D411yescharacteristic
27C23×C4×C127—21no—
28C2×M16×C127—21no—
29C2×M16×C127—21no—
30C22×C8×C127—21no—
31C4⋊Q8×C127—21no—
32C4⋊Q8×C127—21no—
33C4⋊Q8×C127—21no—
34C4⋊Q8×C127D412yes—
35C4×D4×C127—21no—
36C4×D4×C127—21no—
37C4×D4×C127—21no—
38C4×D4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C22⋊C4×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#102×C127—24no—
54#100×C127—42no—
55C22⋊C8×C127—21no—
56C22⋊C8×C127—21no—
57C4×C8×C127—21no—
58C4×C8×C127—21no—
59C24×C127—21no—
60C2×Q8×C127—22no—
61C2×Q8×C127—41no—
62C2×Q8×C127—82no—
63C2×D4×C127—21no—
64C2×D4×C127—21no—
65C2×D4×C127—21no—
66C2×D4×C127—21no—
67C2×D4×C127—21no—
68C2×D4×C127Q1612yes—
69C22×C4×C127—21no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127—82no—
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127#4111yescharacteristic
76C22×C4×C127#4111yescharacteristic
77M16×C127—41no—
78M16×C127—41no—
79M16×C127—41no—
80M16×C127—41no—
81C2×C8×C127—22no—
82C2×C8×C127—22no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—22no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C42×C127C2×D411yescharacteristic
97C42×C127C2×D411yescharacteristic
98C42×C127C2×D411yescharacteristic
99C42×C127#4111yescharacteristic
100C23×C127—22no—
101C23×C127—41no—
102C23×C127—41no—
103C23×C127—81no—
104C23×C127—81no—
105C23×C127#12311yescharacteristic
106Q8×C127—82no—
107Q8×C127—82no—
108D4×C127—22no—
109D4×C127—22no—
110D4×C127—41no—
111D4×C127—41no—
112C2×C4×C127—22no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—42no—
116C2×C4×C127—82no—
117C2×C4×C127—82no—
118C2×C4×C127—82no—
119C2×C4×C127—81no—
120C2×C4×C127#12011yescharacteristic
121C2×C4×C127#12111yescharacteristic
122C2×C4×C127#12111yescharacteristic
123C2×C4×C127#12111yescharacteristic
124C2×C4×C127#12311yescharacteristic
125C2×C4×C127#12411yescharacteristic
126C2×C4×C127C2×Q1611yescharacteristic
127C2×C4×C127#13511yescharacteristic
128C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C127#13711yescharacteristic
130C8×C127—42no—
131C8×C127—42no—
132C8×C127—81no—
133C8×C127—81no—
134C8×C127—81no—
135C22×C127—21no—
136C22×C127—21no—
137C22×C127—42no—
138C22×C127—82no—
139C22×C127—82no—
140C22×C127—81no—
141C22×C127—81no—
142C22×C127#39411yescharacteristic
143C22×C127#48411yescharacteristic
144C22×C127#48511yescharacteristic
145C4×C127—21no—
146C4×C127—21no—
147C4×C127—21no—
148C4×C127—81no—
149C4×C127—82no—
150C4×C127#44911yescharacteristic
151C4×C127#45111yescharacteristic
152C4×C127#46711yescharacteristic
153C4×C127#46811yescharacteristic
154C4×C127#47212yes—
155#10449C12711yesmaximal, characteristic, direct product factor, Sylow
156C2×C127—21no—
157C2×C127—21no—
158C2×C127—82no—
159C2×C127#203611yescharacteristic
160C2×C127#204511yescharacteristic
161C2×C127#204911yescharacteristic
162C2×#474C2×C12711yescharacteristic
163#1800C2×C12711yescharacteristic
164#1571C2×C12711yescharacteristic, complemented
165#1549C2×C12711yescharacteristic, complemented
166#1548C2×C12711yescharacteristic, complemented
167#1478C2×C12711yescharacteristic
168#1301C2×C12711yescharacteristic, complemented
169C127#1044911yescharacteristic, direct product factor, Sylow
170C2×C4⋊Q8C22×C12711yescharacteristic
171C2×C4×D4C22×C12711yescharacteristic
172#474—22no—
173#474—22no—
174#431C22×C12711yescharacteristic
175#431C22×C12711yescharacteristic
176C2×#107—21no—
177#423C22×C12711yescharacteristic
178#423C22×C12711yescharacteristic
179C2×C4⋊C8C22×C12711yescharacteristic
180C2×#102—21no—
181C2×#100—21no—
182#343—21no—
183#335—22no—
184#333—22no—
185#332—22no—
186D4⋊C8—22no—
187C22×Q8—21no—
188C22×D4D4×C12711yescharacteristic
189C23×C4—21no—
190C2×M16—21no—
191C2×M16—21no—
192C22×C8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8D4×C12712yes—
197C4×D4—21no—
198C4×D4—21no—
199C4×D4—21no—
200C4×D4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4D4×C12711yescharacteristic
204C2×C22⋊C4—21no—
205C2×C42C23×C12711yescharacteristic
206#107—24no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8D4×C12712yes—
214C4⋊C8D4×C12712yes—
215#102—24no—
216#100—42no—
217C22⋊C8—21no—
218C22⋊C8—21no—
219C4×C8—21no—
220C4×C8—21no—
221C24—21no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—82no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4Q16×C12712yes—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—82no—
236C22×C4C2×D4×C12711yescharacteristic
237C22×C4#41×C12711yescharacteristic
238C22×C4#41×C12711yescharacteristic
239M16—41no—
240M16—41no—
241M16—41no—
242M16—41no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C4⋊C4—22no—
251C4⋊C4—21no—
252C4⋊C4—22no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42C2×D4×C12711yescharacteristic
259C42C2×D4×C12711yescharacteristic
260C42C2×D4×C12711yescharacteristic
261C42#41×C12711yescharacteristic
262C23—22no—
263C23—41no—
264C23—41no—
265C23—81no—
266C23—81no—
267C23#123×C12711yescharacteristic
268Q8—82no—
269Q8—82no—
270D4—22no—
271D4—22no—
272D4—41no—
273D4—41no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—81no—
282C2×C4#120×C12711yescharacteristic
283C2×C4#121×C12711yescharacteristic
284C2×C4#121×C12711yescharacteristic
285C2×C4#121×C12711yescharacteristic
286C2×C4#123×C12711yescharacteristic
287C2×C4#124×C12711yescharacteristic
288C2×C4C2×Q16×C12711yescharacteristic
289C2×C4#135×C12711yescharacteristic
290C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
291C2×C4#137×C12711yescharacteristic
292C8—42no—
293C8—42no—
294C8—81no—
295C8—81no—
296C8—81no—
297C22—21no—
298C22—21no—
299C22—42no—
300C22—82no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22#394×C12711yescharacteristic
305C22#484×C12711yescharacteristic
306C22#485×C12711yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—81no—
311C4—82no—
312C4#449×C12711yescharacteristic
313C4#451×C12711yescharacteristic
314C4#467×C12711yescharacteristic
315C4#468×C12711yescharacteristic
316C4#472×C12712yes—
317C2—21no—
318C2—21no—
319C2—82no—
320C2C127×#203611yescharacteristic
321C2C127×#204511yescharacteristic
322C2C127×#204911yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
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
3. C127×#1571C2semidirect
4. C127×#1549C2semidirect
5. C127×#1548C2semidirect
7. C127×#1301C2semidirect
155. #10449C127direct (N × H)
164. #1571C2×C127semidirect
165. #1549C2×C127semidirect
166. #1548C2×C127semidirect
168. #1301C2×C127semidirect
169. C127#10449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#474×C1272
C127×#18002
C127×#15712
C127×#15492
C127×#15482
C127×#14782
C127×#13012
#10449127