Finite Group Databasebeta

← C127×#9529 #44573202

Subgroups — C127×#9529 #44573202

Order 32512.

468 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3109C211yesmaximal, characteristic
2C127×#2981C211yesmaximal, characteristic, complemented
3C127×#1557C211yesmaximal, characteristic, complemented
4C127×#1486C211yesmaximal, characteristic, complemented
5C127×#1466C211yesmaximal, characteristic, complemented
6C127×#1307C211yesmaximal, characteristic, complemented
7C127×#1287C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#481×C127C412yes—
11#476×C127—21no—
12#459×C127—21no—
13#447×C127C412yes—
14#442×C127—22no—
15#436×C127—21no—
16#435×C127—22no—
17C8×D4×C127—21no—
18#432×C127C2211yescharacteristic
19#432×C127C2211yescharacteristic
20#432×C127C2211yescharacteristic
21#431×C127C2211yescharacteristic
22#423×C127C2211yescharacteristic
23#408×C127—22no—
24#332×C127—21no—
25#331×C127—21no—
26D4⋊C8×C127—21no—
27D4⋊C8×C127—21no—
28#323×C127—22no—
29C2×#41×C127—21no—
30C22×D4×C127C2×C411yescharacteristic
31C23×C4×C127—21no—
32C2×D8×C127—22no—
33C2×M16×C127—22no—
34C2×M16×C127—21no—
35C22×C8×C127—22no—
36C4⋊Q8×C127D411yescharacteristic
37#127×C127D411yescharacteristic
38#124×C127—21no—
39#121×C127—21no—
40#121×C127C2×C412yes—
41C4×D4×C127—21no—
42C4×D4×C127—21no—
43C4×D4×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46C4×D4×C127D412yes—
47C2×C4⋊C4×C127C2×C411yescharacteristic
48C2×C22⋊C4×C127—21no—
49C2×C42×C127C2311yescharacteristic
50#106×C127—22no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57#102×C127—22no—
58#102×C127—22no—
59C22⋊C8×C127—22no—
60C22⋊C8×C127—22no—
61C22⋊C8×C127—21no—
62C22⋊C8×C127—21no—
63C22⋊C8×C127C2×C412yes—
64C22⋊C8×C127D412yes—
65#97×C127—21no—
66#97×C127—21no—
67#97×C127—21no—
68C4×C8×C127D411yescharacteristic
69C4×C8×C127D411yescharacteristic
70C24×C127—21no—
71#41×C127—82no—
72C2×Q8×C127—21no—
73C2×D4×C127—22no—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—42no—
79C2×D4×C127C22⋊C412yes—
80C22×C4×C127—22no—
81C22×C4×C127—21no—
82C22×C4×C127—41no—
83C22×C4×C127—41no—
84C22×C4×C127—81no—
85C22×C4×C127—81no—
86C22×C4×C127C22×C411yescharacteristic
87C22×C4×C127C2×D411yescharacteristic
88C22×C4×C127#4111yescharacteristic
89D8×C127—44no—
90M16×C127—82no—
91M16×C127—81no—
92C2×C8×C127—22no—
93C2×C8×C127—21no—
94C2×C8×C127—21no—
95C2×C8×C127—22no—
96C2×C8×C127—41no—
97C2×C8×C127—41no—
98C2×C8×C127—82no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—21no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127C22⋊C412yes—
103C22⋊C4×C127—22no—
104C22⋊C4×C127—22no—
105C22⋊C4×C127—41no—
106C22⋊C4×C127—41no—
107C42×C127C2×D411yescharacteristic
108C42×C127C2×D411yescharacteristic
109C42×C127C2×D411yescharacteristic
110C42×C127#4111yescharacteristic
111C23×C127—22no—
112C23×C127—22no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—81no—
116C23×C127—81no—
117C23×C127C4×D411yescharacteristic
118Q8×C127—81no—
119D4×C127—22no—
120D4×C127—22no—
121D4×C127—42no—
122D4×C127—41no—
123D4×C127—41no—
124D4×C127—41no—
125D4×C127—41no—
126D4×C127—81no—
127D4×C127—82no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—22no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—41no—
136C2×C4×C127—82no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127—81no—
140C2×C4×C127C2×C22⋊C411yescharacteristic
141C2×C4×C127C4×D411yescharacteristic
142C2×C4×C127#12011yescharacteristic
143C2×C4×C127#12111yescharacteristic
144C2×C4×C127#12111yescharacteristic
145C2×C4×C127#12311yescharacteristic
146C8×C127—41no—
147C8×C127—42no—
148C8×C127—41no—
149C8×C127—42no—
150C8×C127—81no—
151C8×C127—81no—
152C22×C127—21no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—42no—
156C22×C127—42no—
157C22×C127—42no—
158C22×C127—42no—
159C22×C127—82no—
160C22×C127—82no—
161C22×C127—81no—
162C22×C127—81no—
163C22×C127#38611yescharacteristic
164C4×C127—21no—
165C4×C127—21no—
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—21no—
169C4×C127—42no—
170C4×C127—81no—
171C4×C127#47111yescharacteristic
172C4×C127#47211yescharacteristic
173#9529C12711yesmaximal, characteristic, direct product factor, Sylow
174C2×C127—41no—
175C2×C127—82no—
176C2×C127—82no—
177C2×C127#189111yescharacteristic
178C2×C127#190411yescharacteristic
179C2×C127#190711yescharacteristic
180#3109C2×C12711yescharacteristic
181#2981C2×C12711yescharacteristic, complemented
182#1557C2×C12711yescharacteristic, complemented
183#1486C2×C12711yescharacteristic, complemented
184#1466C2×C12711yescharacteristic, complemented
185#1307C2×C12711yescharacteristic, complemented
186#1287C2×C12711yescharacteristic, complemented
187C127#952911yescharacteristic, direct product factor, Sylow
188#532C22×C12711yescharacteristic
189C2×C4×D4C22×C12711yescharacteristic
190#481C4×C12712yes—
191#476—21no—
192#459—21no—
193#447C4×C12712yes—
194#442—22no—
195#436—21no—
196#435—22no—
197C8×D4—21no—
198#432C22×C12711yescharacteristic
199#432C22×C12711yescharacteristic
200#432C22×C12711yescharacteristic
201#431C22×C12711yescharacteristic
202#423C22×C12711yescharacteristic
203#408—22no—
204#332—21no—
205#331—21no—
206D4⋊C8—21no—
207D4⋊C8—21no—
208#323—22no—
209C2×#41—21no—
210C22×D4C2×C4×C12711yescharacteristic
211C23×C4—21no—
212C2×D8—22no—
213C2×M16—22no—
214C2×M16—21no—
215C22×C8—22no—
216C4⋊Q8D4×C12711yescharacteristic
217#127D4×C12711yescharacteristic
218#124—21no—
219#121—21no—
220#121C2×C4×C12712yes—
221C4×D4—21no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4D4×C12712yes—
227C2×C4⋊C4C2×C4×C12711yescharacteristic
228C2×C22⋊C4—21no—
229C2×C42C23×C12711yescharacteristic
230#106—22no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#102—22no—
238#102—22no—
239C22⋊C8—22no—
240C22⋊C8—22no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8C2×C4×C12712yes—
244C22⋊C8D4×C12712yes—
245#97—21no—
246#97—21no—
247#97—21no—
248C4×C8D4×C12711yescharacteristic
249C4×C8D4×C12711yescharacteristic
250C24—21no—
251#41—82no—
252C2×Q8—21no—
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—42no—
259C2×D4C22⋊C4×C12712yes—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4C22×C4×C12711yescharacteristic
267C22×C4C2×D4×C12711yescharacteristic
268C22×C4#41×C12711yescharacteristic
269D8—44no—
270M16—82no—
271M16—81no—
272C2×C8—22no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—82no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4C22⋊C4×C12712yes—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42C2×D4×C12711yescharacteristic
288C42C2×D4×C12711yescharacteristic
289C42C2×D4×C12711yescharacteristic
290C42#41×C12711yescharacteristic
291C23—22no—
292C23—22no—
293C23—41no—
294C23—41no—
295C23—81no—
296C23—81no—
297C23C4×D4×C12711yescharacteristic
298Q8—81no—
299D4—22no—
300D4—22no—
301D4—42no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—81no—
307D4—82no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—82no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4C2×C22⋊C4×C12711yescharacteristic
321C2×C4C4×D4×C12711yescharacteristic
322C2×C4#120×C12711yescharacteristic
323C2×C4#121×C12711yescharacteristic
324C2×C4#121×C12711yescharacteristic
325C2×C4#123×C12711yescharacteristic
326C8—41no—
327C8—42no—
328C8—41no—
329C8—42no—
330C8—81no—
331C8—81no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22—81no—
342C22—81no—
343C22#386×C12711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4#471×C12711yescharacteristic
352C4#472×C12711yescharacteristic
353C2—41no—
354C2—82no—
355C2—82no—
356C2C127×#189111yescharacteristic
357C2C127×#190411yescharacteristic
358C2C127×#190711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3109C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2981C2semidirect
3. C127×#1557C2semidirect
4. C127×#1486C2semidirect
5. C127×#1466C2semidirect
6. C127×#1307C2semidirect
7. C127×#1287C2semidirect
173. #9529C127direct (N × H)
181. #2981C2×C127semidirect
182. #1557C2×C127semidirect
183. #1486C2×C127semidirect
184. #1466C2×C127semidirect
185. #1307C2×C127semidirect
186. #1287C2×C127semidirect
187. C127#9529direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31092
C127×#29812
C127×#15572
C127×#14862
C127×#14662
C127×#13072
C127×#12872
#9529127