Finite Group Databasebeta

← C127×#10442 #44574115

Subgroups — C127×#10442 #44574115

Order 32512.

460 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C127C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic, complemented
3C127×#1571C211yesmaximal, characteristic, complemented
4C127×#1545C211yesmaximal, characteristic
5C127×#1545C211yesmaximal, characteristic
6C127×#1479C211yesmaximal, characteristic, complemented
7C127×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C127—21no—
9C2×#127×C127C2211yescharacteristic
10C2×C4×Q8×C127C2211yescharacteristic
11#460×C127—22no—
12#460×C127—22no—
13#431×C127C2211yescharacteristic
14#431×C127C2211yescharacteristic
15#423×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#102×C127—21no—
19C2×#101×C127—21no—
20#343×C127—21no—
21#335×C127—22no—
22#331×C127—22no—
23#331×C127—22no—
24Q8⋊C8×C127—22no—
25C22×Q8×C127D411yescharacteristic
26C22×D4×C127—21no—
27C22×D4×C127—21no—
28C22×D4×C127—21no—
29C2×SD16×C127—24no—
30C2×SD16×C127—42no—
31C2×SD16×C127—42no—
32C2×M16×C127—21no—
33C2×M16×C127—21no—
34C22×C8×C127—21no—
35#127×C127—21no—
36#127×C127—21no—
37#127×C127—21no—
38#127×C127D412yes—
39C4×Q8×C127—21no—
40C4×Q8×C127—21no—
41C4×Q8×C127—21no—
42C4×Q8×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127D411yescharacteristic
45C2×C42×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#101×C127—42no—
57C22⋊C8×C127—21no—
58C22⋊C8×C127—21no—
59C4×C8×C127—21no—
60C4×C8×C127—21no—
61C24×C127—41no—
62C2×Q8×C127—21no—
63C2×Q8×C127—21no—
64C2×Q8×C127—21no—
65C2×Q8×C127—21no—
66C2×Q8×C127—21no—
67C2×Q8×C127D812yes—
68C2×D4×C127—22no—
69C2×D4×C127—22no—
70C2×D4×C127—22no—
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—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127C2×D411yescharacteristic
83C22×C4×C127#4111yescharacteristic
84C22×C4×C127#4111yescharacteristic
85SD16×C127—48no—
86M16×C127—41no—
87M16×C127—41no—
88M16×C127—41no—
89M16×C127—41no—
90C2×C8×C127—22no—
91C2×C8×C127—22no—
92C2×C8×C127—41no—
93C2×C8×C127—41no—
94C2×C8×C127—41no—
95C2×C8×C127—41no—
96C2×C8×C127—41no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—41no—
101C42×C127—41no—
102C42×C127—41no—
103C42×C127C2×D411yescharacteristic
104C42×C127C2×D411yescharacteristic
105C42×C127C2×D411yescharacteristic
106C42×C127#4111yescharacteristic
107C23×C127—42no—
108C23×C127—82no—
109C23×C127—82no—
110C23×C127—81no—
111C23×C127—81no—
112C23×C127#12311yescharacteristic
113Q8×C127—22no—
114Q8×C127—22no—
115Q8×C127—41no—
116Q8×C127—41no—
117D4×C127—42no—
118D4×C127—42no—
119D4×C127—82no—
120D4×C127—82no—
121D4×C127—82no—
122D4×C127—81no—
123D4×C127—81no—
124D4×C127—82no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—81no—
132C2×C4×C127#12011yescharacteristic
133C2×C4×C127#12111yescharacteristic
134C2×C4×C127#12111yescharacteristic
135C2×C4×C127#12111yescharacteristic
136C2×C4×C127#12311yescharacteristic
137C2×C4×C127#12411yescharacteristic
138C2×C4×C127C2×D811yescharacteristic
139C2×C4×C127#13511yescharacteristic
140C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C127#13711yescharacteristic
142C8×C127—42no—
143C8×C127—42no—
144C8×C127—81no—
145C8×C127—81no—
146C8×C127—81no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—82no—
150C22×C127—82no—
151C22×C127—82no—
152C22×C127—162no—
153C22×C127—162no—
154C22×C127#39411yescharacteristic
155C22×C127#48011yescharacteristic
156C22×C127#48211yescharacteristic
157C4×C127—21no—
158C4×C127—21no—
159C4×C127—21no—
160C4×C127—42no—
161C4×C127—81no—
162C4×C127#44711yescharacteristic
163C4×C127#45211yescharacteristic
164C4×C127#46611yescharacteristic
165C4×C127#46811yescharacteristic
166C4×C127#47112yes—
167#10442C12711yesmaximal, characteristic, direct product factor, Sylow
168C2×C127—21no—
169C2×C127—21no—
170C2×C127—162no—
171C2×C127#203311yescharacteristic
172C2×C127#204611yescharacteristic
173C2×C127#204811yescharacteristic
174C2×#460C2×C12711yescharacteristic
175#1801C2×C12711yescharacteristic, complemented
176#1571C2×C12711yescharacteristic, complemented
177#1545C2×C12711yescharacteristic
178#1545C2×C12711yescharacteristic
179#1479C2×C12711yescharacteristic, complemented
180#1301C2×C12711yescharacteristic, complemented
181C127#1044211yescharacteristic, direct product factor, Sylow
182C22×SD16—21no—
183C2×#127C22×C12711yescharacteristic
184C2×C4×Q8C22×C12711yescharacteristic
185#460—22no—
186#460—22no—
187#431C22×C12711yescharacteristic
188#431C22×C12711yescharacteristic
189#423C22×C12711yescharacteristic
190#423C22×C12711yescharacteristic
191C2×C4⋊C8C22×C12711yescharacteristic
192C2×#102—21no—
193C2×#101—21no—
194#343—21no—
195#335—22no—
196#331—22no—
197#331—22no—
198Q8⋊C8—22no—
199C22×Q8D4×C12711yescharacteristic
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C2×SD16—24no—
204C2×SD16—42no—
205C2×SD16—42no—
206C2×M16—21no—
207C2×M16—21no—
208C22×C8—21no—
209#127—21no—
210#127—21no—
211#127—21no—
212#127D4×C12712yes—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4×C12711yescharacteristic
219C2×C42—21no—
220C2×C42C23×C12711yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C12712yes—
228C4⋊C8D4×C12712yes—
229#102—24no—
230#101—42no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233C4×C8—21no—
234C4×C8—21no—
235C24—41no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8D8×C12712yes—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—82no—
253C2×D4—82no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4C2×D4×C12711yescharacteristic
257C22×C4#41×C12711yescharacteristic
258C22×C4#41×C12711yescharacteristic
259SD16—48no—
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C42—41no—
276C42—41no—
277C42C2×D4×C12711yescharacteristic
278C42C2×D4×C12711yescharacteristic
279C42C2×D4×C12711yescharacteristic
280C42#41×C12711yescharacteristic
281C23—42no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23—81no—
286C23#123×C12711yescharacteristic
287Q8—22no—
288Q8—22no—
289Q8—41no—
290Q8—41no—
291D4—42no—
292D4—42no—
293D4—82no—
294D4—82no—
295D4—82no—
296D4—81no—
297D4—81no—
298D4—82no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4#120×C12711yescharacteristic
307C2×C4#121×C12711yescharacteristic
308C2×C4#121×C12711yescharacteristic
309C2×C4#121×C12711yescharacteristic
310C2×C4#123×C12711yescharacteristic
311C2×C4#124×C12711yescharacteristic
312C2×C4C2×D8×C12711yescharacteristic
313C2×C4#135×C12711yescharacteristic
314C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
315C2×C4#137×C12711yescharacteristic
316C8—42no—
317C8—42no—
318C8—81no—
319C8—81no—
320C8—81no—
321C22—21no—
322C22—21no—
323C22—82no—
324C22—82no—
325C22—82no—
326C22—162no—
327C22—162no—
328C22#394×C12711yescharacteristic
329C22#480×C12711yescharacteristic
330C22#482×C12711yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4#447×C12711yescharacteristic
337C4#452×C12711yescharacteristic
338C4#466×C12711yescharacteristic
339C4#468×C12711yescharacteristic
340C4#471×C12712yes—
341C2—21no—
342C2—21no—
343C2—162no—
344C2C127×#203311yescharacteristic
345C2C127×#204611yescharacteristic
346C2C127×#204811yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
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×#1801C2semidirect
3. C127×#1571C2semidirect
6. C127×#1479C2semidirect
7. C127×#1301C2semidirect
167. #10442C127direct (N × H)
175. #1801C2×C127semidirect
176. #1571C2×C127semidirect
179. #1479C2×C127semidirect
180. #1301C2×C127semidirect
181. C127#10442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#460×C1272
C127×#18012
C127×#15712
C127×#15452
C127×#14792
C127×#13012
#10442127