Finite Group Databasebeta

← C127×#9829 #44573502

Subgroups — C127×#9829 #44573502

Order 32512.

610 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×#492×C127C211yesmaximal, characteristic
2C127×#1990C211yesmaximal, characteristic, complemented
3C127×#1990C211yesmaximal, characteristic, complemented
4C127×#1957C211yesmaximal, characteristic
5C127×#1957C211yesmaximal, characteristic
6C127×#1834C211yesmaximal, characteristic, complemented
7C2×#322×C127C211yesmaximal, characteristic, complemented
8C22×SD16×C127—22no—
9C2×C4⋊Q8×C127C2211yescharacteristic
10C2×#127×C127C2211yescharacteristic
11#492×C127—22no—
12#492×C127C414yescomplemented
13C2×#102×C127—22no—
14C2×#102×C127—22no—
15C2×C4×C8×C127C2211yescharacteristic
16C2×C4×C8×C127C2211yescharacteristic
17C2×C4×C8×C127C2211yescharacteristic
18#384×C127C2211yescharacteristic
19#384×C127C2211yescharacteristic
20#340×C127—22no—
21#340×C127—22no—
22#340×C127—22no—
23#322×C127—22no—
24C22×Q8×C127—21no—
25C22×D4×C127—21no—
26C22×D4×C127—21no—
27C22×D4×C127—21no—
28C2×SD16×C127—28no—
29C2×SD16×C127—44no—
30C2×SD16×C127—44no—
31C22×C8×C127D412yes—
32C22×C8×C127D412yes—
33C22×C8×C127D412yes—
34C4⋊Q8×C127—21no—
35C4⋊Q8×C127—21no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127C2×C412yes—
38#127×C127—21no—
39#127×C127—21no—
40#127×C127—21no—
41#127×C127C2×C412yes—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C42×C127C2311yescharacteristic
51#102×C127—44no—
52#102×C127—44no—
53C4×C8×C127—21no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C4×C8×C127—21no—
57C4×C8×C127C2×C412yes—
58C4×C8×C127D412yes—
59C24×C127—41no—
60C2×Q8×C127—22no—
61C2×Q8×C127—41no—
62C2×Q8×C127—42no—
63C2×Q8×C127—42no—
64C2×D4×C127—22no—
65C2×D4×C127—22no—
66C2×D4×C127—22no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C2×D4×C127—42no—
71C2×D4×C127—42no—
72C2×D4×C127—42no—
73C2×D4×C127—42no—
74C2×D4×C127—42no—
75C2×D4×C127—42no—
76C22×C4×C127—41no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82SD16×C127—416no—
83C2×C8×C127—22no—
84C2×C8×C127—22no—
85C2×C8×C127—22no—
86C2×C8×C127—22no—
87C2×C8×C127—22no—
88C2×C8×C127—22no—
89C2×C8×C127—22no—
90C2×C8×C127C22⋊C414yes—
91C2×C8×C127SD1614yescomplemented
92C4⋊C4×C127—22no—
93C4⋊C4×C127—22no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—42no—
97C4⋊C4×C127—42no—
98C4⋊C4×C127—42no—
99C4⋊C4×C127—42no—
100C4⋊C4×C127—42no—
101C4⋊C4×C127—42no—
102C42×C127C22×C411yescharacteristic
103C42×C127C2×D411yescharacteristic
104C42×C127#4111yescharacteristic
105C42×C127#4111yescharacteristic
106C23×C127—42no—
107C23×C127—81no—
108C23×C127—81no—
109C23×C127—81no—
110C23×C127—81no—
111C23×C127—81no—
112C23×C127—81no—
113C23×C127#12711yescharacteristic
114Q8×C127—44no—
115Q8×C127—82no—
116D4×C127—44no—
117D4×C127—44no—
118D4×C127—44no—
119D4×C127—82no—
120D4×C127—82no—
121D4×C127—82no—
122C2×C4×C127—42no—
123C2×C4×C127—81no—
124C2×C4×C127—81no—
125C2×C4×C127—81no—
126C2×C4×C127—81no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127—81no—
130C2×C4×C127—81no—
131C2×C4×C127C2×C22⋊C411yescharacteristic
132C2×C4×C127C4×D411yescharacteristic
133C2×C4×C127C4×D411yescharacteristic
134C2×C4×C127#12111yescharacteristic
135C2×C4×C127#12111yescharacteristic
136C2×C4×C127#12411yescharacteristic
137C2×C4×C127C2×SD1612yes—
138C2×C4×C127#13512yes—
139C2×C4×C127AGL(1,ℤ/8)12yes—
140C2×C4×C127AGL(1,ℤ/8)12yes—
141C2×C4×C127AGL(1,ℤ/8)12yes—
142C2×C4×C127#13712yes—
143C8×C127—24no—
144C8×C127—24no—
145C8×C127—42no—
146C22×C127—82no—
147C22×C127—82no—
148C22×C127—82no—
149C22×C127—161no—
150C22×C127—161no—
151C22×C127—161no—
152C22×C127—161no—
153C22×C127#39011yescharacteristic
154C22×C127#49211yescharacteristic
155C22×C127#49511yescharacteristic
156C22×C127#49611yescharacteristic
157C22×C127#49611yescharacteristic
158C22×C127#49611yescharacteristic
159C22×C127#49711yescharacteristic
160C4×C127—82no—
161C4×C127—161no—
162C4×C127—161no—
163C4×C127#41812yes—
164C4×C127C4×SD1612yes—
165C4×C127#44012yes—
166C4×C127#46512yes—
167C4×C127#46812yes—
168C4×C127#49012yes—
169#9829C12711yesmaximal, characteristic, direct product factor, Sylow
170C2×C127—162no—
171C2×C127#171411yescharacteristic
172C2×C127#171511yescharacteristic
173C2×C127#171711yescharacteristic
174C2×C127#171911yescharacteristic
175C2×C127#196111yescharacteristic
176C2×C127#196811yescharacteristic
177C2×C127#197311yescharacteristic
178C2×#492C2×C12711yescharacteristic
179#1990C2×C12711yescharacteristic, complemented
180#1990C2×C12711yescharacteristic, complemented
181#1957C2×C12711yescharacteristic
182#1957C2×C12711yescharacteristic
183#1834C2×C12711yescharacteristic, complemented
184C2×#322C2×C12711yescharacteristic, complemented
185C127#982911yescharacteristic, direct product factor, Sylow
186C22×SD16—22no—
187C2×C4⋊Q8C22×C12711yescharacteristic
188C2×#127C22×C12711yescharacteristic
189#492—22no—
190#492C4×C12714yescomplemented
191C2×#102—22no—
192C2×#102—22no—
193C2×C4×C8C22×C12711yescharacteristic
194C2×C4×C8C22×C12711yescharacteristic
195C2×C4×C8C22×C12711yescharacteristic
196#384C22×C12711yescharacteristic
197#384C22×C12711yescharacteristic
198#340—22no—
199#340—22no—
200#340—22no—
201#322—22no—
202C22×Q8—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C2×SD16—28no—
207C2×SD16—44no—
208C2×SD16—44no—
209C22×C8D4×C12712yes—
210C22×C8D4×C12712yes—
211C22×C8D4×C12712yes—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8C2×C4×C12712yes—
216#127—21no—
217#127—21no—
218#127—21no—
219#127C2×C4×C12712yes—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C42C23×C12711yescharacteristic
229#102—44no—
230#102—44no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8C2×C4×C12712yes—
236C4×C8D4×C12712yes—
237C24—41no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C2×D4×C12711yescharacteristic
258C22×C4C2×D4×C12711yescharacteristic
259C22×C4C2×D4×C12711yescharacteristic
260SD16—416no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8C22⋊C4×C12714yes—
269C2×C8SD16×C12714yescomplemented
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C42C22×C4×C12711yescharacteristic
281C42C2×D4×C12711yescharacteristic
282C42#41×C12711yescharacteristic
283C42#41×C12711yescharacteristic
284C23—42no—
285C23—81no—
286C23—81no—
287C23—81no—
288C23—81no—
289C23—81no—
290C23—81no—
291C23#127×C12711yescharacteristic
292Q8—44no—
293Q8—82no—
294D4—44no—
295D4—44no—
296D4—44no—
297D4—82no—
298D4—82no—
299D4—82no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4C2×C22⋊C4×C12711yescharacteristic
310C2×C4C4×D4×C12711yescharacteristic
311C2×C4C4×D4×C12711yescharacteristic
312C2×C4#121×C12711yescharacteristic
313C2×C4#121×C12711yescharacteristic
314C2×C4#124×C12711yescharacteristic
315C2×C4C2×SD16×C12712yes—
316C2×C4#135×C12712yes—
317C2×C4AGL(1,ℤ/8)×C12712yes—
318C2×C4AGL(1,ℤ/8)×C12712yes—
319C2×C4AGL(1,ℤ/8)×C12712yes—
320C2×C4#137×C12712yes—
321C8—24no—
322C8—24no—
323C8—42no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—161no—
328C22—161no—
329C22—161no—
330C22—161no—
331C22#390×C12711yescharacteristic
332C22#492×C12711yescharacteristic
333C22#495×C12711yescharacteristic
334C22#496×C12711yescharacteristic
335C22#496×C12711yescharacteristic
336C22#496×C12711yescharacteristic
337C22#497×C12711yescharacteristic
338C4—82no—
339C4—161no—
340C4—161no—
341C4#418×C12712yes—
342C4C4×SD16×C12712yes—
343C4#440×C12712yes—
344C4#465×C12712yes—
345C4#468×C12712yes—
346C4#490×C12712yes—
347C2—162no—
348C2C127×#171411yescharacteristic
349C2C127×#171511yescharacteristic
350C2C127×#171711yescharacteristic
351C2C127×#171911yescharacteristic
352C2C127×#196111yescharacteristic
353C2C127×#196811yescharacteristic
354C2C127×#197311yescharacteristic
subgroupG/H
center, socleC23×C127#127
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1990C2semidirect
3. C127×#1990C2semidirect
6. C127×#1834C2semidirect
7. C2×#322×C127C2semidirect
12. #492×C127C4semidirect
91. C2×C8×C127SD16semidirect
169. #9829C127direct (N × H)
179. #1990C2×C127semidirect
180. #1990C2×C127semidirect
183. #1834C2×C127semidirect
184. C2×#322C2×C127semidirect
185. C127#9829direct (N × H)
190. #492C4×C127semidirect
269. C2×C8SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C1272
C127×#19902
C127×#19572
C127×#18342
C2×#322×C1272
#9829127