Finite Group Databasebeta

← C127×#9783 #44573456

Subgroups — C127×#9783 #44573456

Order 32512.

606 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C127C211yesmaximal, characteristic
2C127×#1964C212yesmaximal, complemented
3C127×#1808C211yesmaximal, characteristic, complemented
4C8×C22⋊C4×C127C211yesmaximal, 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×C127—21no—
14C2×#107×C127C411yescharacteristic, complemented
15C2×#102×C127C412yescomplemented
16C2×#99×C127—24no—
17C2×C22⋊C8×C127C2211yescharacteristic
18C2×C4×C8×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#107×C127—42no—
51#102×C127—22no—
52#102×C127—22no—
53#99×C127—48no—
54C22⋊C8×C127—21no—
55C22⋊C8×C127D412yes—
56C4×C8×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—22no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—42no—
102C22⋊C4×C127—44no—
103C22⋊C4×C127D814yescomplemented
104C42×C127—41no—
105C42×C127—41no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—42no—
109C23×C127—44no—
110C23×C127—82no—
111C23×C127—82no—
112C23×C127C4×D411yescharacteristic
113C23×C127#12111yescharacteristic
114C23×C127#12711yescharacteristic
115C23×C127C2×D812yes—
116C23×C127#13512yes—
117D4×C127—42no—
118D4×C127—42no—
119D4×C127—82no—
120D4×C127—84no—
121D4×C127—82no—
122D4×C127—82no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—24no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—44no—
137C2×C4×C127—82no—
138C2×C4×C127—82no—
139C2×C4×C127—82no—
140C2×C4×C127C2×C22⋊C411yescharacteristic
141C2×C4×C127C4×D411yescharacteristic
142C2×C4×C127#12111yescharacteristic
143C2×C4×C127#12411yescharacteristic
144C8×C127—21no—
145C8×C127—21no—
146C8×C127—21no—
147C8×C127—42no—
148C8×C127#9912yescomplemented
149C22×C127—21no—
150C22×C127—21no—
151C22×C127—21no—
152C22×C127—21no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—42no—
156C22×C127—42no—
157C22×C127—82no—
158C22×C127—82no—
159C22×C127—82no—
160C22×C127—164no—
161C22×C127#39011yescharacteristic
162C22×C127C4×D812yes—
163C22×C127#46612yes—
164C22×C127#49311yescharacteristic
165C22×C127#49511yescharacteristic
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—21no—
169C4×C127—44no—
170C4×C127—82no—
171C4×C127—162no—
172C4×C127C2×#9911yescharacteristic
173C4×C127#41011yescharacteristic
174#9783C12711yesmaximal, characteristic, direct product factor, Sylow
175C2×C127—22no—
176C2×C127—21no—
177C2×C127—22no—
178C2×C127—21no—
179C2×C127—162no—
180C2×C127#196411yescharacteristic
181C2×C127#197011yescharacteristic
182C2×C127#197611yescharacteristic
183C2×#466C2×C12711yescharacteristic
184#1964C2×C12712yescomplemented
185#1808C2×C12711yescharacteristic, complemented
186C8×C22⋊C4C2×C12711yescharacteristic, complemented
187#1519C2×C12712yescomplemented
188C127#978311yescharacteristic, direct product factor, Sylow
189C22×D8C4×C12711yescharacteristic, complemented
190C23×C8C22×C12711yescharacteristic
191C2×#121C22×C12712yes—
192#466—21no—
193#466—21no—
194#466—21no—
195#466—21no—
196C2×#107—21no—
197C2×#107C4×C12711yescharacteristic, complemented
198C2×#102C4×C12712yescomplemented
199C2×#99—24no—
200C2×C22⋊C8C22×C12711yescharacteristic
201C2×C4×C8—21no—
202#380C22×C12712yes—
203C4×C22⋊C4C22×C12711yescharacteristic
204#340—21no—
205#336—21no—
206#327—24no—
207C22×D4—22no—
208C22×D4C2×C4×C12712yes—
209C23×C4C23×C12711yescharacteristic
210C2×D8—21no—
211C2×D8—21no—
212C2×D8—42no—
213C22×C8—21no—
214C22×C8—42no—
215C22×C8C2×C4×C12711yescharacteristic
216C22×C8C2×C4×C12711yescharacteristic
217C22×C8D4×C12711yescharacteristic
218C22×C8D4×C12711yescharacteristic
219C22×C8D4×C12711yescharacteristic
220C22×C8D4×C12711yescharacteristic
221#121—22no—
222#121—22no—
223#121—22no—
224#121—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4C2×C4×C12712yes—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4D4×C12712yes—
230C2×C42—21no—
231#107—21no—
232#107—21no—
233#107—42no—
234#102—22no—
235#102—22no—
236#99—48no—
237C22⋊C8—21no—
238C22⋊C8D4×C12712yes—
239C4×C8—42no—
240#95—21no—
241#95—22no—
242C24—22no—
243C24C2×D4×C12711yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—44no—
251C2×D4—44no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4C22×C4×C12711yescharacteristic
258C22×C4C2×D4×C12711yescharacteristic
259C22×C4C2×D4×C12711yescharacteristic
260C22×C4C2×D4×C12711yescharacteristic
261C22×C4#41×C12711yescharacteristic
262C22×C4#41×C12711yescharacteristic
263D8—42no—
264D8—42no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8C22⋊C4×C12711yescharacteristic
275C2×C8C22⋊C4×C12711yescharacteristic
276C2×C8C22⋊C4×C12711yescharacteristic
277C2×C8C22⋊C4×C12711yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C22⋊C4—22no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—44no—
286C22⋊C4D8×C12714yescomplemented
287C42—41no—
288C42—41no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—44no—
293C23—82no—
294C23—82no—
295C23C4×D4×C12711yescharacteristic
296C23#121×C12711yescharacteristic
297C23#127×C12711yescharacteristic
298C23C2×D8×C12712yes—
299C23#135×C12712yes—
300D4—42no—
301D4—42no—
302D4—82no—
303D4—84no—
304D4—82no—
305D4—82no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—24no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4C2×C22⋊C4×C12711yescharacteristic
324C2×C4C4×D4×C12711yescharacteristic
325C2×C4#121×C12711yescharacteristic
326C2×C4#124×C12711yescharacteristic
327C8—21no—
328C8—21no—
329C8—21no—
330C8—42no—
331C8#99×C12712yescomplemented
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—42no—
339C22—42no—
340C22—82no—
341C22—82no—
342C22—82no—
343C22—164no—
344C22#390×C12711yescharacteristic
345C22C4×D8×C12712yes—
346C22#466×C12712yes—
347C22#493×C12711yescharacteristic
348C22#495×C12711yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—44no—
353C4—82no—
354C4—162no—
355C4C2×#99×C12711yescharacteristic
356C4#410×C12711yescharacteristic
357C2—22no—
358C2—21no—
359C2—22no—
360C2—21no—
361C2—162no—
362C2C127×#196411yescharacteristic
363C2C127×#197011yescharacteristic
364C2C127×#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×#1808C2semidirect
4. C8×C22⋊C4×C127C2semidirect
5. C127×#1519C2semidirect
6. C22×D8×C127C4semidirect
14. C2×#107×C127C4semidirect
15. C2×#102×C127C4semidirect
103. C22⋊C4×C127D8semidirect
148. C8×C127#99semidirect
174. #9783C127direct (N × H)
184. #1964C2×C127semidirect
185. #1808C2×C127semidirect
186. C8×C22⋊C4C2×C127semidirect
187. #1519C2×C127semidirect
188. C127#9783direct (N × H)
189. C22×D8C4×C127semidirect
197. C2×#107C4×C127semidirect
198. C2×#102C4×C127semidirect
286. C22⋊C4D8×C127semidirect
331. 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×#18082
C8×C22⋊C4×C1272
C127×#15192
#9783127