Finite Group Databasebeta

← C127×#10440 #44574113

Subgroups — C127×#10440 #44574113

Order 32512.

492 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C127C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic, complemented
3C127×#1571C211yesmaximal, characteristic, complemented
4C127×#1545C211yesmaximal, characteristic, complemented
5C127×#1545C211yesmaximal, characteristic, complemented
6C127×#1478C211yesmaximal, characteristic, complemented
7C127×#1301C211yesmaximal, characteristic, complemented
8C22×D8×C127—21no—
9C2×#127×C127C2211yescharacteristic
10C2×C4×D4×C127C2211yescharacteristic
11#459×C127—22no—
12#459×C127—22no—
13#431×C127C2211yescharacteristic
14#431×C127C2211yescharacteristic
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#331×C127—22no—
23#331×C127—22no—
24D4⋊C8×C127—22no—
25C22×D4×C127—21no—
26C22×D4×C127—21no—
27C22×D4×C127—21no—
28C22×D4×C127D411yescharacteristic
29C23×C4×C127—21no—
30C2×D8×C127—24no—
31C2×D8×C127—42no—
32C2×D8×C127—42no—
33C2×M16×C127—21no—
34C2×M16×C127—21no—
35C22×C8×C127—21no—
36#127×C127—21no—
37#127×C127—21no—
38#127×C127—21no—
39#127×C127D412yes—
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42C4×D4×C127—21no—
43C4×D4×C127—21no—
44C2×C4⋊C4×C127D411yescharacteristic
45C2×C22⋊C4×C127—21no—
46C2×C42×C127C2311yescharacteristic
47C4⋊C8×C127—21no—
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127D412yes—
54C4⋊C8×C127D412yes—
55#102×C127—24no—
56#100×C127—42no—
57C22⋊C8×C127—21no—
58C22⋊C8×C127—21no—
59C4×C8×C127—21no—
60C4×C8×C127—21no—
61C24×C127—21no—
62C24×C127—41no—
63C2×D4×C127—21no—
64C2×D4×C127—22no—
65C2×D4×C127—21no—
66C2×D4×C127—22no—
67C2×D4×C127—22no—
68C2×D4×C127—21no—
69C2×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127—82no—
79C2×D4×C127—82no—
80C2×D4×C127D812yes—
81C22×C4×C127—21no—
82C22×C4×C127—41no—
83C22×C4×C127—41no—
84C22×C4×C127—82no—
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127#4111yescharacteristic
87C22×C4×C127#4111yescharacteristic
88D8×C127—48no—
89M16×C127—41no—
90M16×C127—41no—
91M16×C127—41no—
92M16×C127—41no—
93C2×C8×C127—22no—
94C2×C8×C127—22no—
95C2×C8×C127—41no—
96C2×C8×C127—41no—
97C2×C8×C127—41no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C4⋊C4×C127—21no—
101C4⋊C4×C127—21no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—41no—
104C42×C127C2×D411yescharacteristic
105C42×C127C2×D411yescharacteristic
106C42×C127C2×D411yescharacteristic
107C42×C127#4111yescharacteristic
108C23×C127—22no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—42no—
112C23×C127—81no—
113C23×C127—81no—
114C23×C127—82no—
115C23×C127—82no—
116C23×C127—81no—
117C23×C127—81no—
118C23×C127#12311yescharacteristic
119D4×C127—22no—
120D4×C127—22no—
121D4×C127—42no—
122D4×C127—41no—
123D4×C127—42no—
124D4×C127—41no—
125D4×C127—82no—
126D4×C127—82no—
127D4×C127—82no—
128D4×C127—81no—
129D4×C127—81no—
130D4×C127—82no—
131C2×C4×C127—22no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—82no—
135C2×C4×C127—82no—
136C2×C4×C127—81no—
137C2×C4×C127#12011yescharacteristic
138C2×C4×C127#12111yescharacteristic
139C2×C4×C127#12111yescharacteristic
140C2×C4×C127#12111yescharacteristic
141C2×C4×C127#12311yescharacteristic
142C2×C4×C127#12411yescharacteristic
143C2×C4×C127C2×D811yescharacteristic
144C2×C4×C127#13511yescharacteristic
145C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C127#13711yescharacteristic
147C8×C127—42no—
148C8×C127—42no—
149C8×C127—81no—
150C8×C127—81no—
151C8×C127—81no—
152C22×C127—21no—
153C22×C127—21no—
154C22×C127—42no—
155C22×C127—82no—
156C22×C127—82no—
157C22×C127—81no—
158C22×C127—81no—
159C22×C127—82no—
160C22×C127—82no—
161C22×C127—82no—
162C22×C127—162no—
163C22×C127—162no—
164C22×C127#39411yescharacteristic
165C22×C127#48011yescharacteristic
166C22×C127#48211yescharacteristic
167C4×C127—21no—
168C4×C127—21no—
169C4×C127—21no—
170C4×C127—81no—
171C4×C127#44711yescharacteristic
172C4×C127#45211yescharacteristic
173C4×C127#46611yescharacteristic
174C4×C127#46811yescharacteristic
175C4×C127#47212yes—
176#10440C12711yesmaximal, characteristic, direct product factor, Sylow
177C2×C127—21no—
178C2×C127—21no—
179C2×C127—82no—
180C2×C127—162no—
181C2×C127#203311yescharacteristic
182C2×C127#204511yescharacteristic
183C2×C127#204811yescharacteristic
184C2×#459C2×C12711yescharacteristic
185#1800C2×C12711yescharacteristic, complemented
186#1571C2×C12711yescharacteristic, complemented
187#1545C2×C12711yescharacteristic, complemented
188#1545C2×C12711yescharacteristic, complemented
189#1478C2×C12711yescharacteristic, complemented
190#1301C2×C12711yescharacteristic, complemented
191C127#1044011yescharacteristic, direct product factor, Sylow
192C22×D8—21no—
193C2×#127C22×C12711yescharacteristic
194C2×C4×D4C22×C12711yescharacteristic
195#459—22no—
196#459—22no—
197#431C22×C12711yescharacteristic
198#431C22×C12711yescharacteristic
199#423C22×C12711yescharacteristic
200#423C22×C12711yescharacteristic
201C2×C4⋊C8C22×C12711yescharacteristic
202C2×#102—21no—
203C2×#100—21no—
204#343—21no—
205#335—22no—
206#331—22no—
207#331—22no—
208D4⋊C8—22no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4D4×C12711yescharacteristic
213C23×C4—21no—
214C2×D8—24no—
215C2×D8—42no—
216C2×D8—42no—
217C2×M16—21no—
218C2×M16—21no—
219C22×C8—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#127D4×C12712yes—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C2×C4⋊C4D4×C12711yescharacteristic
229C2×C22⋊C4—21no—
230C2×C42C23×C12711yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8D4×C12712yes—
238C4⋊C8D4×C12712yes—
239#102—24no—
240#100—42no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C4×C8—21no—
244C4×C8—21no—
245C24—21no—
246C24—41no—
247C2×D4—21no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—82no—
263C2×D4—82no—
264C2×D4D8×C12712yes—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—82no—
269C22×C4C2×D4×C12711yescharacteristic
270C22×C4#41×C12711yescharacteristic
271C22×C4#41×C12711yescharacteristic
272D8—48no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42C2×D4×C12711yescharacteristic
289C42C2×D4×C12711yescharacteristic
290C42C2×D4×C12711yescharacteristic
291C42#41×C12711yescharacteristic
292C23—22no—
293C23—41no—
294C23—41no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23—82no—
299C23—82no—
300C23—81no—
301C23—81no—
302C23#123×C12711yescharacteristic
303D4—22no—
304D4—22no—
305D4—42no—
306D4—41no—
307D4—42no—
308D4—41no—
309D4—82no—
310D4—82no—
311D4—82no—
312D4—81no—
313D4—81no—
314D4—82no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—81no—
321C2×C4#120×C12711yescharacteristic
322C2×C4#121×C12711yescharacteristic
323C2×C4#121×C12711yescharacteristic
324C2×C4#121×C12711yescharacteristic
325C2×C4#123×C12711yescharacteristic
326C2×C4#124×C12711yescharacteristic
327C2×C4C2×D8×C12711yescharacteristic
328C2×C4#135×C12711yescharacteristic
329C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
330C2×C4#137×C12711yescharacteristic
331C8—42no—
332C8—42no—
333C8—81no—
334C8—81no—
335C8—81no—
336C22—21no—
337C22—21no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22—81no—
342C22—81no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—162no—
347C22—162no—
348C22#394×C12711yescharacteristic
349C22#480×C12711yescharacteristic
350C22#482×C12711yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—81no—
355C4#447×C12711yescharacteristic
356C4#452×C12711yescharacteristic
357C4#466×C12711yescharacteristic
358C4#468×C12711yescharacteristic
359C4#472×C12712yes—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—162no—
364C2C127×#203311yescharacteristic
365C2C127×#204511yescharacteristic
366C2C127×#204811yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC2×#459×C127C2
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
2. C127×#1800C2semidirect
3. C127×#1571C2semidirect
4. C127×#1545C2semidirect
5. C127×#1545C2semidirect
6. C127×#1478C2semidirect
7. C127×#1301C2semidirect
176. #10440C127direct (N × H)
185. #1800C2×C127semidirect
186. #1571C2×C127semidirect
187. #1545C2×C127semidirect
188. #1545C2×C127semidirect
189. #1478C2×C127semidirect
190. #1301C2×C127semidirect
191. C127#10440direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#459×C1272
C127×#18002
C127×#15712
C127×#15452
C127×#14782
C127×#13012
#10440127