Finite Group Databasebeta

← C127×#9327 #44573000

Subgroups — C127×#9327 #44573000

Order 32512.

492 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3110C211yesmaximal, characteristic
2C127×#2319C211yesmaximal, characteristic
3C127×#1986C211yesmaximal, characteristic, complemented
4C127×#1506C211yesmaximal, characteristic, complemented
5C127×#1490C211yesmaximal, characteristic
6C127×#1300C211yesmaximal, characteristic, complemented
7C127×#1285C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#484×C127—21no—
11#474×C127C412yescomplemented
12#461×C127C412yescomplemented
13#450×C127—21no—
14#440×C127—22no—
15#432×C127C2211yescharacteristic
16#432×C127C2211yescharacteristic
17C4×M16×C127C2211yescharacteristic
18#390×C127—21no—
19#389×C127—21no—
20#388×C127—22no—
21#381×C127—21no—
22#380×C127—21no—
23C4×C4⋊C4×C127C2211yescharacteristic
24#376×C127C2211yescharacteristic
25#339×C127—22no—
26#328×C127—21no—
27#328×C127—21no—
28D4⋊C8×C127—22no—
29C22×D4×C127D411yescharacteristic
30C23×C4×C127—21no—
31C2×SD16×C127—22no—
32C2×M16×C127—21no—
33C4⋊Q8×C127C2×C411yescharacteristic
34C4⋊Q8×C127C2×C411yescharacteristic
35#125×C127—21no—
36C22⋊Q8×C127—21no—
37C22⋊Q8×C127—21no—
38C4×Q8×C127—21no—
39C4×Q8×C127—21no—
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42C4×D4×C127C2×C412yes—
43C4×D4×C127D412yes—
44#117×C127—21no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—22no—
47C2×C4⋊C4×C127D411yescharacteristic
48C2×C22⋊C4×C127—21no—
49C2×C22⋊C4×C127—22no—
50C2×C22⋊C4×C127—22no—
51C2×C42×C127—21no—
52C2×C42×C127D412yes—
53C2×C42×C127C2311yescharacteristic
54#107×C127—22no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127C2×C412yes—
57#103×C127—22no—
58#102×C127—22no—
59C22⋊C8×C127—21no—
60C22⋊C8×C127—21no—
61#97×C127—21no—
62#97×C127—21no—
63#97×C127—21no—
64C4×C8×C127—21no—
65#95×C127—22no—
66#95×C127—21no—
67#95×C127—21no—
68#95×C127D411yescharacteristic
69#95×C127D411yescharacteristic
70C24×C127—21no—
71C2×Q8×C127—21no—
72C2×Q8×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127—42no—
75C2×D4×C127C22⋊C412yes—
76C22×C4×C127—21no—
77C22×C4×C127—22no—
78C22×C4×C127—22no—
79C22×C4×C127—21no—
80C22×C4×C127—22no—
81C22×C4×C127—21no—
82C22×C4×C127—82no—
83C22×C4×C127C2×D411yescharacteristic
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86SD16×C127—44no—
87M16×C127—22no—
88M16×C127—41no—
89C2×C8×C127—22no—
90C2×C8×C127—41no—
91C2×C8×C127—41no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—42no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—82no—
101C4⋊C4×C127C22⋊C412yes—
102C22⋊C4×C127—22no—
103C22⋊C4×C127—22no—
104C22⋊C4×C127—41no—
105C22⋊C4×C127—82no—
106C22⋊C4×C127—82no—
107C42×C127—42no—
108C42×C127—42no—
109C42×C127—41no—
110C42×C127C22×C411yescharacteristic
111C42×C127C2×D411yescharacteristic
112C42×C127#4111yescharacteristic
113C42×C127#4111yescharacteristic
114C23×C127—22no—
115C23×C127—42no—
116C23×C127—42no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127#12011yescharacteristic
120Q8×C127—42no—
121Q8×C127—81no—
122D4×C127—22no—
123D4×C127—22no—
124D4×C127—42no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—41no—
130C2×C4×C127—42no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—42no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—82no—
143C2×C4×C127—82no—
144C2×C4×C127C2×C22⋊C411yescharacteristic
145C2×C4×C127C4×D411yescharacteristic
146C2×C4×C127C4×D411yescharacteristic
147C2×C4×C127#12111yescharacteristic
148C2×C4×C127#12111yescharacteristic
149C2×C4×C127#12311yescharacteristic
150C8×C127—42no—
151C8×C127—42no—
152C8×C127—81no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—42no—
156C22×C127—42no—
157C22×C127—42no—
158C22×C127—82no—
159C22×C127—82no—
160C22×C127#38611yescharacteristic
161C22×C127#45511yescharacteristic
162C22×C127#45611yescharacteristic
163C4×C127—21no—
164C4×C127—21no—
165C4×C127—21no—
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—42no—
169C4×C127—81no—
170C4×C127—82no—
171C4×C127—81no—
172C4×C127—81no—
173C4×C127—81no—
174C4×C127#42112yes—
175#9327C12711yesmaximal, characteristic, direct product factor, Sylow
176C2×C127—21no—
177C2×C127—21no—
178C2×C127—82no—
179C2×C127#188211yescharacteristic
180C2×C127#189711yescharacteristic
181C2×C127#190411yescharacteristic
182#3110C2×C12711yescharacteristic
183#2319C2×C12711yescharacteristic
184#1986C2×C12711yescharacteristic, complemented
185#1506C2×C12711yescharacteristic, complemented
186#1490C2×C12711yescharacteristic
187#1300C2×C12711yescharacteristic, complemented
188#1285C2×C12711yescharacteristic, complemented
189C127#932711yescharacteristic, direct product factor, Sylow
190#533C22×C12711yescharacteristic
191C2×C4×D4C22×C12711yescharacteristic
192#484—21no—
193#474C4×C12712yescomplemented
194#461C4×C12712yescomplemented
195#450—21no—
196#440—22no—
197#432C22×C12711yescharacteristic
198#432C22×C12711yescharacteristic
199C4×M16C22×C12711yescharacteristic
200#390—21no—
201#389—21no—
202#388—22no—
203#381—21no—
204#380—21no—
205C4×C4⋊C4C22×C12711yescharacteristic
206#376C22×C12711yescharacteristic
207#339—22no—
208#328—21no—
209#328—21no—
210D4⋊C8—22no—
211C22×D4D4×C12711yescharacteristic
212C23×C4—21no—
213C2×SD16—22no—
214C2×M16—21no—
215C4⋊Q8C2×C4×C12711yescharacteristic
216C4⋊Q8C2×C4×C12711yescharacteristic
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4C2×C4×C12712yes—
225C4×D4D4×C12712yes—
226#117—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4D4×C12711yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C42—21no—
234C2×C42D4×C12712yes—
235C2×C42C23×C12711yescharacteristic
236#107—22no—
237C4⋊C8—21no—
238C4⋊C8C2×C4×C12712yes—
239#103—22no—
240#102—22no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#97—21no—
244#97—21no—
245#97—21no—
246C4×C8—21no—
247#95—22no—
248#95—21no—
249#95—21no—
250#95D4×C12711yescharacteristic
251#95D4×C12711yescharacteristic
252C24—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—42no—
257C2×D4C22⋊C4×C12712yes—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—82no—
265C22×C4C2×D4×C12711yescharacteristic
266C22×C4C2×D4×C12711yescharacteristic
267C22×C4C2×D4×C12711yescharacteristic
268SD16—44no—
269M16—22no—
270M16—41no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—41no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—82no—
283C4⋊C4C22⋊C4×C12712yes—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—82no—
288C22⋊C4—82no—
289C42—42no—
290C42—42no—
291C42—41no—
292C42C22×C4×C12711yescharacteristic
293C42C2×D4×C12711yescharacteristic
294C42#41×C12711yescharacteristic
295C42#41×C12711yescharacteristic
296C23—22no—
297C23—42no—
298C23—42no—
299C23—41no—
300C23—41no—
301C23#120×C12711yescharacteristic
302Q8—42no—
303Q8—81no—
304D4—22no—
305D4—22no—
306D4—42no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4C2×C22⋊C4×C12711yescharacteristic
327C2×C4C4×D4×C12711yescharacteristic
328C2×C4C4×D4×C12711yescharacteristic
329C2×C4#121×C12711yescharacteristic
330C2×C4#121×C12711yescharacteristic
331C2×C4#123×C12711yescharacteristic
332C8—42no—
333C8—42no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—82no—
341C22—82no—
342C22#386×C12711yescharacteristic
343C22#455×C12711yescharacteristic
344C22#456×C12711yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—81no—
352C4—82no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4#421×C12712yes—
357C2—21no—
358C2—21no—
359C2—82no—
360C2C127×#188211yescharacteristic
361C2C127×#189711yescharacteristic
362C2C127×#190411yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1986C2semidirect
4. C127×#1506C2semidirect
6. C127×#1300C2semidirect
7. C127×#1285C2semidirect
11. #474×C127C4semidirect
12. #461×C127C4semidirect
175. #9327C127direct (N × H)
184. #1986C2×C127semidirect
185. #1506C2×C127semidirect
187. #1300C2×C127semidirect
188. #1285C2×C127semidirect
189. C127#9327direct (N × H)
193. #474C4×C127semidirect
194. #461C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31102
C127×#23192
C127×#19862
C127×#15062
C127×#14902
C127×#13002
C127×#12852
#9327127