Finite Group Databasebeta

← C127×#11698 #44575371

Subgroups — C127×#11698 #44575371

Order 32512.

514 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2618C211yesmaximal, characteristic
2C2×#343×C127C211yesmaximal, characteristic, complemented
3C2×#324×C127C211yesmaximal, characteristic, complemented
4C127×#1346C212yesmaximal, complemented
5C127×#1345C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×#123×C127—21no—
8C2×#121×C127C411yescharacteristic
9C22×C4⋊C4×C127C2211yescharacteristic
10C2×C22⋊C8×C127—21no—
11#398×C127C411yescharacteristic
12#398×C127C2211yescharacteristic
13#396×C127—21no—
14#396×C127—21no—
15#394×C127C411yescharacteristic
16#394×C127C2211yescharacteristic
17#386×C127—21no—
18#380×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×D4×C127—21no—
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127C2×C411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C2×M16×C127—24no—
29C2×M16×C127—22no—
30C2×M16×C127—41no—
31C2×M16×C127—42no—
32C22×C8×C127—41no—
33C22×C8×C127—41no—
34#123×C127—42no—
35#123×C127—42no—
36#121×C127—41no—
37#121×C127—41no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—41no—
42C2×C4⋊C4×C127—41no—
43C2×C4⋊C4×C127C2×C411yescharacteristic
44C2×C4⋊C4×C127C2×C411yescharacteristic
45C2×C4⋊C4×C127D411yescharacteristic
46C2×C4⋊C4×C127D411yescharacteristic
47C2×C4⋊C4×C127C2311yescharacteristic
48C2×C22⋊C4×C127—21no—
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127—21no—
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C22⋊C8×C127—22no—
55C22⋊C8×C127—41no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127C2×C411yescharacteristic
59#95×C127C2×C411yescharacteristic
60C24×C127—21no—
61C24×C127C22⋊C411yescharacteristic
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—42no—
66C2×D4×C127—42no—
67C2×D4×C127—81no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—22no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—81no—
79C22×C4×C127—81no—
80C22×C4×C127C22⋊C411yescharacteristic
81C22×C4×C127C22⋊C411yescharacteristic
82C22×C4×C127C22⋊C411yescharacteristic
83C22×C4×C127D812yes—
84C22×C4×C127SD1612yes—
85C22×C4×C127C22×C411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
87C22×C4×C127C2×D411yescharacteristic
88M16×C127—24no—
89M16×C127—44no—
90M16×C127—42no—
91C2×C8×C127—44no—
92C2×C8×C127—42no—
93C2×C8×C127—42no—
94C2×C8×C127—82no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—42no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—81no—
104C22⋊C4×C127—42no—
105C22⋊C4×C127—42no—
106C22⋊C4×C127—42no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—81no—
110C22⋊C4×C127—81no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127#9911yescharacteristic
121C23×C127#9911yescharacteristic
122C23×C127#10212yes—
123C23×C127#10412yes—
124C23×C127C2×C22⋊C411yescharacteristic
125D4×C127—82no—
126D4×C127—82no—
127D4×C127—82no—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—22no—
131C2×C4×C127—22no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—42no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—81no—
155C2×C4×C127—81no—
156C2×C4×C127—81no—
157C2×C4×C127#10212yes—
158C2×C4×C127C2×D811yescharacteristic
159C2×C4×C127C2×SD1611yescharacteristic
160C8×C127—44no—
161C8×C127—82no—
162C22×C127—21no—
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—21no—
168C22×C127—42no—
169C22×C127—42no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127—81no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127—81no—
177C22×C127#32712yes—
178C22×C127#32712yes—
179C22×C127C2×#9911yescharacteristic
180C22×C127C2×#10211yescharacteristic
181C22×C127C2×#10411yescharacteristic
182C4×C127—21no—
183C4×C127—22no—
184C4×C127—21no—
185C4×C127—41no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—41no—
189C4×C127—81no—
190C4×C127—81no—
191C4×C127—81no—
192#11698C12711yesmaximal, characteristic, direct product factor, Sylow
193C2×C127—21no—
194C2×C127—21no—
195C2×C127—22no—
196C2×C127—22no—
197C2×C127—161no—
198C2×C127C2×#32711yescharacteristic
199C2×C127#212111yescharacteristic
200C2×C127#213311yescharacteristic
201#2618C2×C12711yescharacteristic
202C2×#343C2×C12711yescharacteristic, complemented
203C2×#324C2×C12711yescharacteristic, complemented
204#1346C2×C12712yescomplemented
205#1345C2×C12712yescomplemented
206C127#1169811yescharacteristic, direct product factor, Sylow
207C22×M16—21no—
208C2×#123—21no—
209C2×#121C4×C12711yescharacteristic
210C22×C4⋊C4C22×C12711yescharacteristic
211C2×C22⋊C8—21no—
212#398C4×C12711yescharacteristic
213#398C22×C12711yescharacteristic
214#396—21no—
215#396—21no—
216#394C4×C12711yescharacteristic
217#394C22×C12711yescharacteristic
218#386—21no—
219#380C4×C12711yescharacteristic
220#343—21no—
221#343C22×C12712yes—
222#324—21no—
223#324C22×C12712yes—
224C22×D4—21no—
225C22×D4C2×C4×C12711yescharacteristic
226C23×C4C2×C4×C12711yescharacteristic
227C23×C4D4×C12711yescharacteristic
228C23×C4D4×C12711yescharacteristic
229C2×M16—24no—
230C2×M16—22no—
231C2×M16—41no—
232C2×M16—42no—
233C22×C8—41no—
234C22×C8—41no—
235#123—42no—
236#123—42no—
237#121—41no—
238#121—41no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—41no—
244C2×C4⋊C4C2×C4×C12711yescharacteristic
245C2×C4⋊C4C2×C4×C12711yescharacteristic
246C2×C4⋊C4D4×C12711yescharacteristic
247C2×C4⋊C4D4×C12711yescharacteristic
248C2×C4⋊C4C23×C12711yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C22⋊C8—22no—
256C22⋊C8—41no—
257#95—21no—
258#95—21no—
259#95C2×C4×C12711yescharacteristic
260#95C2×C4×C12711yescharacteristic
261C24—21no—
262C24C22⋊C4×C12711yescharacteristic
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—81no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4C22⋊C4×C12711yescharacteristic
282C22×C4C22⋊C4×C12711yescharacteristic
283C22×C4C22⋊C4×C12711yescharacteristic
284C22×C4D8×C12712yes—
285C22×C4SD16×C12712yes—
286C22×C4C22×C4×C12711yescharacteristic
287C22×C4C2×D4×C12711yescharacteristic
288C22×C4C2×D4×C12711yescharacteristic
289M16—24no—
290M16—44no—
291M16—42no—
292C2×C8—44no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—82no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#99×C12711yescharacteristic
322C23#99×C12711yescharacteristic
323C23#102×C12712yes—
324C23#104×C12712yes—
325C23C2×C22⋊C4×C12711yescharacteristic
326D4—82no—
327D4—82no—
328D4—82no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4#102×C12712yes—
359C2×C4C2×D8×C12711yescharacteristic
360C2×C4C2×SD16×C12711yescharacteristic
361C8—44no—
362C8—82no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#327×C12712yes—
379C22#327×C12712yes—
380C22C2×#99×C12711yescharacteristic
381C22C2×#102×C12711yescharacteristic
382C22C2×#104×C12711yescharacteristic
383C4—21no—
384C4—22no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—81no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—22no—
397C2—161no—
398C2C2×#327×C12711yescharacteristic
399C2C127×#212111yescharacteristic
400C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC2×#121×C127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#343×C127C2semidirect
3. C2×#324×C127C2semidirect
4. C127×#1346C2semidirect
5. C127×#1345C2semidirect
192. #11698C127direct (N × H)
202. C2×#343C2×C127semidirect
203. C2×#324C2×C127semidirect
204. #1346C2×C127semidirect
205. #1345C2×C127semidirect
206. C127#11698direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26182
C2×#343×C1272
C2×#324×C1272
C127×#13462
C127×#13452
#11698127