Finite Group Databasebeta

← C127×#9785 #44573458

Subgroups — C127×#9785 #44573458

Order 32512.

594 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C127C211yesmaximal, characteristic
2C127×#1964C212yesmaximal, complemented
3C127×#1807C211yesmaximal, characteristic, complemented
4C127×#1752C211yesmaximal, characteristic, complemented
5C127×#1519C212yesmaximal, complemented
6C22×D8×C127C411yescharacteristic, complemented
7C23×C8×C127C2211yescharacteristic
8C2×#121×C127C2212yes—
9#466×C127—21no—
10#466×C127—21no—
11#466×C127—21no—
12#466×C127—21no—
13C2×#107×C127C411yescharacteristic, complemented
14C2×#106×C127—21no—
15C2×#102×C127C412yescomplemented
16C2×#99×C127—24no—
17C2×C22⋊C8×C127C2211yescharacteristic
18C2×#97×C127—21no—
19#380×C127C2212yes—
20C4×C22⋊C4×C127C2211yescharacteristic
21#340×C127—21no—
22#336×C127—21no—
23#327×C127—24no—
24C22×D4×C127—22no—
25C22×D4×C127C2×C412yes—
26C23×C4×C127C2311yescharacteristic
27C2×D8×C127—21no—
28C2×D8×C127—21no—
29C2×D8×C127—42no—
30C22×C8×C127—21no—
31C22×C8×C127—42no—
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127C2×C411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127D411yescharacteristic
37C22×C8×C127D411yescharacteristic
38#121×C127—22no—
39#121×C127—22no—
40#121×C127—22no—
41#121×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127C2×C412yes—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—22no—
46C2×C22⋊C4×C127D412yes—
47C2×C42×C127—21no—
48#107×C127—21no—
49#107×C127—21no—
50#106×C127—42no—
51#102×C127—22no—
52#102×C127—22no—
53#99×C127—48no—
54C22⋊C8×C127—21no—
55C22⋊C8×C127D412yes—
56#97×C127—42no—
57#95×C127—21no—
58#95×C127—22no—
59C24×C127—22no—
60C24×C127C2×D411yescharacteristic
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127—42no—
64C2×D4×C127—42no—
65C2×D4×C127—42no—
66C2×D4×C127—42no—
67C2×D4×C127—44no—
68C2×D4×C127—44no—
69C22×C4×C127—22no—
70C22×C4×C127—22no—
71C22×C4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127—42no—
74C22×C4×C127C22×C411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127#4111yescharacteristic
79C22×C4×C127#4111yescharacteristic
80D8×C127—42no—
81D8×C127—42no—
82C2×C8×C127—22no—
83C2×C8×C127—22no—
84C2×C8×C127—22no—
85C2×C8×C127—22no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—41no—
89C2×C8×C127—41no—
90C2×C8×C127—41no—
91C2×C8×C127C22⋊C411yescharacteristic
92C2×C8×C127C22⋊C411yescharacteristic
93C2×C8×C127C22⋊C411yescharacteristic
94C2×C8×C127C22⋊C411yescharacteristic
95C4⋊C4×C127—22no—
96C4⋊C4×C127—22no—
97C4⋊C4×C127—42no—
98C4⋊C4×C127—42no—
99C22⋊C4×C127—24no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—42no—
102C22⋊C4×C127—44no—
103C42×C127—41no—
104C42×C127—41no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127—42no—
108C23×C127—44no—
109C23×C127—82no—
110C23×C127—82no—
111C23×C127C4×D411yescharacteristic
112C23×C127#12111yescharacteristic
113C23×C127#12711yescharacteristic
114C23×C127AGL(1,ℤ/8)14yes—
115D4×C127—42no—
116D4×C127—42no—
117D4×C127—82no—
118D4×C127—84no—
119D4×C127—82no—
120D4×C127—82no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—42no—
131C2×C4×C127—42no—
132C2×C4×C127—42no—
133C2×C4×C127—44no—
134C2×C4×C127—42no—
135C2×C4×C127—82no—
136C2×C4×C127—82no—
137C2×C4×C127—82no—
138C2×C4×C127C2×C22⋊C411yescharacteristic
139C2×C4×C127C4×D411yescharacteristic
140C2×C4×C127#12111yescharacteristic
141C2×C4×C127#12411yescharacteristic
142C8×C127—21no—
143C8×C127—21no—
144C8×C127—21no—
145C8×C127—42no—
146C8×C127#9912yescomplemented
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—21no—
151C22×C127—21no—
152C22×C127—21no—
153C22×C127—44no—
154C22×C127—82no—
155C22×C127—82no—
156C22×C127—82no—
157C22×C127—164no—
158C22×C127#39011yescharacteristic
159C22×C127#44212yes—
160C22×C127#46912yes—
161C22×C127#49612yes—
162C4×C127—21no—
163C4×C127—21no—
164C4×C127—21no—
165C4×C127—82no—
166C4×C127—82no—
167C4×C127—162no—
168C4×C127C2×#9911yescharacteristic
169C4×C127#41011yescharacteristic
170#9785C12711yesmaximal, characteristic, direct product factor, Sylow
171C2×C127—22no—
172C2×C127—22no—
173C2×C127—22no—
174C2×C127—162no—
175C2×C127#196411yescharacteristic
176C2×C127#197211yescharacteristic
177C2×C127#197611yescharacteristic
178C2×#466C2×C12711yescharacteristic
179#1964C2×C12712yescomplemented
180#1807C2×C12711yescharacteristic, complemented
181#1752C2×C12711yescharacteristic, complemented
182#1519C2×C12712yescomplemented
183C127#978511yescharacteristic, direct product factor, Sylow
184C22×D8C4×C12711yescharacteristic, complemented
185C23×C8C22×C12711yescharacteristic
186C2×#121C22×C12712yes—
187#466—21no—
188#466—21no—
189#466—21no—
190#466—21no—
191C2×#107C4×C12711yescharacteristic, complemented
192C2×#106—21no—
193C2×#102C4×C12712yescomplemented
194C2×#99—24no—
195C2×C22⋊C8C22×C12711yescharacteristic
196C2×#97—21no—
197#380C22×C12712yes—
198C4×C22⋊C4C22×C12711yescharacteristic
199#340—21no—
200#336—21no—
201#327—24no—
202C22×D4—22no—
203C22×D4C2×C4×C12712yes—
204C23×C4C23×C12711yescharacteristic
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—42no—
208C22×C8—21no—
209C22×C8—42no—
210C22×C8C2×C4×C12711yescharacteristic
211C22×C8C2×C4×C12711yescharacteristic
212C22×C8D4×C12711yescharacteristic
213C22×C8D4×C12711yescharacteristic
214C22×C8D4×C12711yescharacteristic
215C22×C8D4×C12711yescharacteristic
216#121—22no—
217#121—22no—
218#121—22no—
219#121—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4C2×C4×C12712yes—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4D4×C12712yes—
225C2×C42—21no—
226#107—21no—
227#107—21no—
228#106—42no—
229#102—22no—
230#102—22no—
231#99—48no—
232C22⋊C8—21no—
233C22⋊C8D4×C12712yes—
234#97—42no—
235#95—21no—
236#95—22no—
237C24—22no—
238C24C2×D4×C12711yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—44no—
246C2×D4—44no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—42no—
252C22×C4C22×C4×C12711yescharacteristic
253C22×C4C2×D4×C12711yescharacteristic
254C22×C4C2×D4×C12711yescharacteristic
255C22×C4C2×D4×C12711yescharacteristic
256C22×C4#41×C12711yescharacteristic
257C22×C4#41×C12711yescharacteristic
258D8—42no—
259D8—42no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22⋊C4×C12711yescharacteristic
270C2×C8C22⋊C4×C12711yescharacteristic
271C2×C8C22⋊C4×C12711yescharacteristic
272C2×C8C22⋊C4×C12711yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C22⋊C4—24no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—44no—
281C42—41no—
282C42—41no—
283C23—41no—
284C23—41no—
285C23—42no—
286C23—44no—
287C23—82no—
288C23—82no—
289C23C4×D4×C12711yescharacteristic
290C23#121×C12711yescharacteristic
291C23#127×C12711yescharacteristic
292C23AGL(1,ℤ/8)×C12714yes—
293D4—42no—
294D4—42no—
295D4—82no—
296D4—82no—
297D4—82no—
298D4—84no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4C2×C22⋊C4×C12711yescharacteristic
317C2×C4C4×D4×C12711yescharacteristic
318C2×C4#121×C12711yescharacteristic
319C2×C4#124×C12711yescharacteristic
320C8—21no—
321C8—21no—
322C8—21no—
323C8—42no—
324C8#99×C12712yescomplemented
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—44no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22—164no—
336C22#390×C12711yescharacteristic
337C22#442×C12712yes—
338C22#469×C12712yes—
339C22#496×C12712yes—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—82no—
344C4—82no—
345C4—162no—
346C4C2×#99×C12711yescharacteristic
347C4#410×C12711yescharacteristic
348C2—22no—
349C2—22no—
350C2—22no—
351C2—162no—
352C2C127×#196411yescharacteristic
353C2C127×#197211yescharacteristic
354C2C127×#197611yescharacteristic
subgroupG/H
center, socleC22×C127#390
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#466×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1964C2semidirect
3. C127×#1807C2semidirect
4. C127×#1752C2semidirect
5. C127×#1519C2semidirect
6. C22×D8×C127C4semidirect
13. C2×#107×C127C4semidirect
15. C2×#102×C127C4semidirect
146. C8×C127#99semidirect
170. #9785C127direct (N × H)
179. #1964C2×C127semidirect
180. #1807C2×C127semidirect
181. #1752C2×C127semidirect
182. #1519C2×C127semidirect
183. C127#9785direct (N × H)
184. C22×D8C4×C127semidirect
191. C2×#107C4×C127semidirect
193. C2×#102C4×C127semidirect
324. C8#99×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1272
C127×#19642
C127×#18072
C127×#17522
C127×#15192
#9785127