Finite Group Databasebeta

← C127×#9592 #44573265

Subgroups — C127×#9592 #44573265

Order 32512.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1980C211yesmaximal, characteristic
2C127×#1950C211yesmaximal, characteristic, complemented
3C127×#1540C211yesmaximal, characteristic
4C127×#1492C211yesmaximal, characteristic
5C127×#1451C211yesmaximal, characteristic, complemented
6C127×#1303C211yesmaximal, characteristic, complemented
7C127×#1279C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10C2×#108×C127—21no—
11#423×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×#104×C127—21no—
14C2×#104×C127—21no—
15C4×M16×C127C2211yescharacteristic
16C2×C4×C8×C127C2211yescharacteristic
17C4×C4⋊C4×C127C2211yescharacteristic
18#341×C127—21no—
19#332×C127C411yescharacteristic, complemented
20#332×C127C411yescharacteristic, complemented
21#331×C127C411yescharacteristic, complemented
22#331×C127C411yescharacteristic, complemented
23D4⋊C8×C127—21no—
24D4⋊C8×C127—21no—
25#322×C127—21no—
26#322×C127—21no—
27C2×#41×C127—21no—
28C2×M16×C127—21no—
29C2×M16×C127D411yescharacteristic
30C2×M16×C127D411yescharacteristic
31C22×C8×C127—21no—
32C22×C8×C127—21no—
33C4⋊Q8×C127C2×C411yescharacteristic
34#127×C127C2×C411yescharacteristic
35#124×C127—21no—
36#121×C127—21no—
37#121×C127—21no—
38C4×D4×C127—21no—
39C4×D4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C42×C127—21no—
42C2×C42×C127C2311yescharacteristic
43#108×C127—42no—
44C4⋊C8×C127—21no—
45C4⋊C8×C127—21no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127C2×C411yescharacteristic
48C4⋊C8×C127C2×C411yescharacteristic
49C4⋊C8×C127C2×C411yescharacteristic
50C4⋊C8×C127C2×C411yescharacteristic
51#104×C127—42no—
52#104×C127—42no—
53C22⋊C8×C127—21no—
54#97×C127—21no—
55C4×C8×C127—21no—
56C4×C8×C127—21no—
57C4×C8×C127—21no—
58C4×C8×C127D411yescharacteristic
59C4×C8×C127D411yescharacteristic
60#95×C127—21no—
61#41×C127—41no—
62#41×C127—41no—
63#41×C127—41no—
64#41×C127—41no—
65C2×Q8×C127—21no—
66C2×D4×C127—21no—
67C2×D4×C127—21no—
68C2×D4×C127—21no—
69C2×D4×C127—41no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127C2×D411yescharacteristic
73C22×C4×C127#4111yescharacteristic
74C22×C4×C127#4111yescharacteristic
75M16×C127—21no—
76M16×C127—21no—
77M16×C127—21no—
78M16×C127—21no—
79M16×C127—41no—
80M16×C127—41no—
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—21no—
84C2×C8×C127—21no—
85C2×C8×C127—21no—
86C2×C8×C127—21no—
87C2×C8×C127—21no—
88C2×C8×C127—21no—
89C2×C8×C127—42no—
90C2×C8×C127—41no—
91C2×C8×C127—41no—
92C2×C8×C127—41no—
93C4⋊C4×C127—22no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C42×C127—41no—
100C42×C127—41no—
101C42×C127C22×C411yescharacteristic
102C42×C127C2×D411yescharacteristic
103C42×C127#4111yescharacteristic
104C42×C127#4111yescharacteristic
105C23×C127—41no—
106C23×C127#12411yescharacteristic
107Q8×C127—41no—
108Q8×C127—41no—
109D4×C127—41no—
110D4×C127—41no—
111D4×C127—41no—
112D4×C127—41no—
113D4×C127—81no—
114D4×C127—81no—
115D4×C127—81no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—41no—
119C2×C4×C127—42no—
120C2×C4×C127—41no—
121C2×C4×C127—81no—
122C2×C4×C127—81no—
123C2×C4×C127—81no—
124C2×C4×C127—81no—
125C2×C4×C127#11711yescharacteristic
126C2×C4×C127C4×D411yescharacteristic
127C2×C4×C127C4×D411yescharacteristic
128C2×C4×C127#12111yescharacteristic
129C2×C4×C127#12311yescharacteristic
130C2×C4×C127#12611yescharacteristic
131C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C127#13711yescharacteristic
135C8×C127—22no—
136C8×C127—41no—
137C8×C127—41no—
138C8×C127—41no—
139C8×C127—41no—
140C8×C127—41no—
141C8×C127—41no—
142C8×C127—41no—
143C8×C127—81no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—81no—
147C22×C127—81no—
148C22×C127—81no—
149C22×C127#38811yescharacteristic
150C22×C127#48911yescharacteristic
151C22×C127#49011yescharacteristic
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—82no—
156C4×C127—81no—
157C4×C127#44011yescharacteristic
158C4×C127#44211yescharacteristic
159C4×C127#44311yescharacteristic
160C4×C127#44411yescharacteristic
161C4×C127#46811yescharacteristic
162C4×C127#46911yescharacteristic
163#9592C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—21no—
165C2×C127—21no—
166C2×C127—161no—
167C2×C127#192911yescharacteristic
168C2×C127#193211yescharacteristic
169C2×C127#193611yescharacteristic
170#1980C2×C12711yescharacteristic
171#1950C2×C12711yescharacteristic, complemented
172#1540C2×C12711yescharacteristic
173#1492C2×C12711yescharacteristic
174#1451C2×C12711yescharacteristic, complemented
175#1303C2×C12711yescharacteristic, complemented
176#1279C2×C12711yescharacteristic, complemented
177C127#959211yescharacteristic, direct product factor, Sylow
178#532C22×C12711yescharacteristic
179#431C22×C12711yescharacteristic
180C2×#108—21no—
181#423C22×C12711yescharacteristic
182C2×C4⋊C8C22×C12711yescharacteristic
183C2×#104—21no—
184C2×#104—21no—
185C4×M16C22×C12711yescharacteristic
186C2×C4×C8C22×C12711yescharacteristic
187C4×C4⋊C4C22×C12711yescharacteristic
188#341—21no—
189#332C4×C12711yescharacteristic, complemented
190#332C4×C12711yescharacteristic, complemented
191#331C4×C12711yescharacteristic, complemented
192#331C4×C12711yescharacteristic, complemented
193D4⋊C8—21no—
194D4⋊C8—21no—
195#322—21no—
196#322—21no—
197C2×#41—21no—
198C2×M16—21no—
199C2×M16D4×C12711yescharacteristic
200C2×M16D4×C12711yescharacteristic
201C22×C8—21no—
202C22×C8—21no—
203C4⋊Q8C2×C4×C12711yescharacteristic
204#127C2×C4×C12711yescharacteristic
205#124—21no—
206#121—21no—
207#121—21no—
208C4×D4—21no—
209C4×D4—21no—
210C2×C4⋊C4—21no—
211C2×C42—21no—
212C2×C42C23×C12711yescharacteristic
213#108—42no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8C2×C4×C12711yescharacteristic
218C4⋊C8C2×C4×C12711yescharacteristic
219C4⋊C8C2×C4×C12711yescharacteristic
220C4⋊C8C2×C4×C12711yescharacteristic
221#104—42no—
222#104—42no—
223C22⋊C8—21no—
224#97—21no—
225C4×C8—21no—
226C4×C8—21no—
227C4×C8—21no—
228C4×C8D4×C12711yescharacteristic
229C4×C8D4×C12711yescharacteristic
230#95—21no—
231#41—41no—
232#41—41no—
233#41—41no—
234#41—41no—
235C2×Q8—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×D4×C12711yescharacteristic
243C22×C4#41×C12711yescharacteristic
244C22×C4#41×C12711yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—21no—
249M16—41no—
250M16—41no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—41no—
270C42—41no—
271C42C22×C4×C12711yescharacteristic
272C42C2×D4×C12711yescharacteristic
273C42#41×C12711yescharacteristic
274C42#41×C12711yescharacteristic
275C23—41no—
276C23#124×C12711yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—41no—
282D4—41no—
283D4—81no—
284D4—81no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4#117×C12711yescharacteristic
296C2×C4C4×D4×C12711yescharacteristic
297C2×C4C4×D4×C12711yescharacteristic
298C2×C4#121×C12711yescharacteristic
299C2×C4#123×C12711yescharacteristic
300C2×C4#126×C12711yescharacteristic
301C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
302C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
303C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
304C2×C4#137×C12711yescharacteristic
305C8—22no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#388×C12711yescharacteristic
320C22#489×C12711yescharacteristic
321C22#490×C12711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—81no—
327C4#440×C12711yescharacteristic
328C4#442×C12711yescharacteristic
329C4#443×C12711yescharacteristic
330C4#444×C12711yescharacteristic
331C4#468×C12711yescharacteristic
332C4#469×C12711yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2C127×#192911yescharacteristic
337C2C127×#193211yescharacteristic
338C2C127×#193611yescharacteristic
subgroupG/H
centerC2×C4×C127#121
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#388
prime radical#532×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1950C2semidirect
5. C127×#1451C2semidirect
6. C127×#1303C2semidirect
7. C127×#1279C2semidirect
19. #332×C127C4semidirect
20. #332×C127C4semidirect
21. #331×C127C4semidirect
22. #331×C127C4semidirect
163. #9592C127direct (N × H)
171. #1950C2×C127semidirect
174. #1451C2×C127semidirect
175. #1303C2×C127semidirect
176. #1279C2×C127semidirect
177. C127#9592direct (N × H)
189. #332C4×C127semidirect
190. #332C4×C127semidirect
191. #331C4×C127semidirect
192. #331C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#19802
C127×#19502
C127×#15402
C127×#14922
C127×#14512
C127×#13032
C127×#12792
#9592127