Finite Group Databasebeta

← C127×#9339 #44573012

Subgroups — C127×#9339 #44573012

Order 32512.

416 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3239C211yesmaximal, characteristic
2C127×#2995C211yesmaximal, characteristic
3C127×#1966C211yesmaximal, characteristic, complemented
4C127×#1556C211yesmaximal, characteristic, complemented
5C127×#1529C211yesmaximal, characteristic
6C127×#1307C211yesmaximal, characteristic, complemented
7C127×#1291C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C127C2211yescharacteristic
9#529×C127C2211yescharacteristic
10#501×C127—21no—
11#489×C127—21no—
12#484×C127C412yes—
13#481×C127C412yes—
14#475×C127—21no—
15#474×C127—21no—
16#446×C127—21no—
17#436×C127—21no—
18#435×C127—21no—
19#435×C127—21no—
20#433×C127—21no—
21#432×C127C2211yescharacteristic
22#432×C127C2211yescharacteristic
23#432×C127C2211yescharacteristic
24#424×C127—21no—
25#423×C127C2211yescharacteristic
26C2×#101×C127—21no—
27C2×#101×C127—21no—
28C4×M16×C127C2211yescharacteristic
29#332×C127—21no—
30#332×C127—21no—
31#330×C127—21no—
32#329×C127—21no—
33C22×Q8×C127—21no—
34C2×M16×C127—21no—
35C2×M16×C127—21no—
36C2×M16×C127D411yescharacteristic
37C2×M16×C127D411yescharacteristic
38C22×C8×C127—21no—
39C4⋊Q8×C127—21no—
40C4⋊Q8×C127—21no—
41C4⋊Q8×C127—21no—
42C4⋊Q8×C127—21no—
43#126×C127—21no—
44#125×C127D411yescharacteristic
45#124×C127D411yescharacteristic
46#123×C127—21no—
47C22⋊Q8×C127C2×C411yescharacteristic
48#121×C127C2×C411yescharacteristic
49C4×Q8×C127D411yescharacteristic
50C4×D4×C127—21no—
51C4×D4×C127D411yescharacteristic
52#117×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127C2×C412yes—
55C2×C42×C127C2311yescharacteristic
56#107×C127—22no—
57#106×C127—22no—
58C4⋊C8×C127—21no—
59C4⋊C8×C127—21no—
60C4⋊C8×C127—21no—
61C4⋊C8×C127—21no—
62C4⋊C8×C127—21no—
63C4⋊C8×C127—21no—
64C4⋊C8×C127D411yescharacteristic
65C4⋊C8×C127D411yescharacteristic
66#103×C127—22no—
67#102×C127—22no—
68#101×C127—42no—
69#101×C127—42no—
70C22⋊C8×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C22⋊C8×C127C2×C412yes—
75#97×C127—21no—
76#97×C127—21no—
77#97×C127—21no—
78#97×C127—21no—
79#97×C127—21no—
80C4×C8×C127—21no—
81C4×C8×C127—21no—
82C2×Q8×C127—41no—
83C2×Q8×C127—41no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C2×Q8×C127—41no—
87C2×Q8×C127—41no—
88C2×Q8×C127C22⋊C411yescharacteristic
89C2×D4×C127—21no—
90C2×D4×C127C22⋊C411yescharacteristic
91C22×C4×C127—21no—
92C22×C4×C127—22no—
93C22×C4×C127C22×C411yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95C22×C4×C127#4111yescharacteristic
96M16×C127—22no—
97M16×C127—41no—
98M16×C127—41no—
99M16×C127—41no—
100M16×C127—81no—
101C2×C8×C127—22no—
102C2×C8×C127—21no—
103C2×C8×C127—21no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C2×C8×C127—81no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—21no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—22no—
114C4⋊C4×C127—22no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—41no—
117C4⋊C4×C127C22⋊C411yescharacteristic
118C4⋊C4×C127C22⋊C411yescharacteristic
119C22⋊C4×C127—21no—
120C22⋊C4×C127—21no—
121C22⋊C4×C127—21no—
122C22⋊C4×C127—21no—
123C22⋊C4×C127—21no—
124C42×C127—21no—
125C42×C127C2×D411yescharacteristic
126C42×C127C2×D411yescharacteristic
127C42×C127C2×D411yescharacteristic
128C42×C127#4111yescharacteristic
129C23×C127—21no—
130C23×C127C4×D411yescharacteristic
131Q8×C127—41no—
132Q8×C127—81no—
133Q8×C127—81no—
134Q8×C127—81no—
135Q8×C127—81no—
136D4×C127—41no—
137D4×C127—81no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127C2×C22⋊C411yescharacteristic
151C2×C4×C127C4×D411yescharacteristic
152C2×C4×C127#12011yescharacteristic
153C2×C4×C127#12111yescharacteristic
154C2×C4×C127#12111yescharacteristic
155C2×C4×C127#12311yescharacteristic
156C8×C127—42no—
157C8×C127—42no—
158C8×C127—41no—
159C8×C127—41no—
160C8×C127—41no—
161C8×C127—41no—
162C8×C127—81no—
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—21no—
166C22×C127—41no—
167C22×C127—41no—
168C22×C127—41no—
169C22×C127#38611yescharacteristic
170C4×C127—21no—
171C4×C127—21no—
172C4×C127—21no—
173C4×C127—21no—
174C4×C127—21no—
175C4×C127—41no—
176C4×C127—41no—
177C4×C127—41no—
178C4×C127—82no—
179C4×C127#45311yescharacteristic
180C4×C127#45411yescharacteristic
181#9339C12711yesmaximal, characteristic, direct product factor, Sylow
182C2×C127—41no—
183C2×C127—81no—
184C2×C127#188311yescharacteristic
185C2×C127#190211yescharacteristic
186C2×C127#191511yescharacteristic
187#3239C2×C12711yescharacteristic
188#2995C2×C12711yescharacteristic
189#1966C2×C12711yescharacteristic, complemented
190#1556C2×C12711yescharacteristic, complemented
191#1529C2×C12711yescharacteristic
192#1307C2×C12711yescharacteristic, complemented
193#1291C2×C12711yescharacteristic, complemented
194C127#933911yescharacteristic, direct product factor, Sylow
195C2×C4⋊Q8C22×C12711yescharacteristic
196#529C22×C12711yescharacteristic
197#501—21no—
198#489—21no—
199#484C4×C12712yes—
200#481C4×C12712yes—
201#475—21no—
202#474—21no—
203#446—21no—
204#436—21no—
205#435—21no—
206#435—21no—
207#433—21no—
208#432C22×C12711yescharacteristic
209#432C22×C12711yescharacteristic
210#432C22×C12711yescharacteristic
211#424—21no—
212#423C22×C12711yescharacteristic
213C2×#101—21no—
214C2×#101—21no—
215C4×M16C22×C12711yescharacteristic
216#332—21no—
217#332—21no—
218#330—21no—
219#329—21no—
220C22×Q8—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16D4×C12711yescharacteristic
224C2×M16D4×C12711yescharacteristic
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230#126—21no—
231#125D4×C12711yescharacteristic
232#124D4×C12711yescharacteristic
233#123—21no—
234C22⋊Q8C2×C4×C12711yescharacteristic
235#121C2×C4×C12711yescharacteristic
236C4×Q8D4×C12711yescharacteristic
237C4×D4—21no—
238C4×D4D4×C12711yescharacteristic
239#117—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×C4×C12712yes—
242C2×C42C23×C12711yescharacteristic
243#107—22no—
244#106—22no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C12711yescharacteristic
252C4⋊C8D4×C12711yescharacteristic
253#103—22no—
254#102—22no—
255#101—42no—
256#101—42no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8C2×C4×C12712yes—
262#97—21no—
263#97—21no—
264#97—21no—
265#97—21no—
266#97—21no—
267C4×C8—21no—
268C4×C8—21no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8C22⋊C4×C12711yescharacteristic
276C2×D4—21no—
277C2×D4C22⋊C4×C12711yescharacteristic
278C22×C4—21no—
279C22×C4—22no—
280C22×C4C22×C4×C12711yescharacteristic
281C22×C4C2×D4×C12711yescharacteristic
282C22×C4#41×C12711yescharacteristic
283M16—22no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—81no—
288C2×C8—22no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—81no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4C22⋊C4×C12711yescharacteristic
305C4⋊C4C22⋊C4×C12711yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42C2×D4×C12711yescharacteristic
313C42C2×D4×C12711yescharacteristic
314C42C2×D4×C12711yescharacteristic
315C42#41×C12711yescharacteristic
316C23—21no—
317C23C4×D4×C12711yescharacteristic
318Q8—41no—
319Q8—81no—
320Q8—81no—
321Q8—81no—
322Q8—81no—
323D4—41no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4C2×C22⋊C4×C12711yescharacteristic
338C2×C4C4×D4×C12711yescharacteristic
339C2×C4#120×C12711yescharacteristic
340C2×C4#121×C12711yescharacteristic
341C2×C4#121×C12711yescharacteristic
342C2×C4#123×C12711yescharacteristic
343C8—42no—
344C8—42no—
345C8—41no—
346C8—41no—
347C8—41no—
348C8—41no—
349C8—81no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22#386×C12711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—82no—
366C4#453×C12711yescharacteristic
367C4#454×C12711yescharacteristic
368C2—41no—
369C2—81no—
370C2C127×#188311yescharacteristic
371C2C127×#190211yescharacteristic
372C2C127×#191511yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#121×C127C2×C4
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
3. C127×#1966C2semidirect
4. C127×#1556C2semidirect
6. C127×#1307C2semidirect
7. C127×#1291C2semidirect
181. #9339C127direct (N × H)
189. #1966C2×C127semidirect
190. #1556C2×C127semidirect
192. #1307C2×C127semidirect
193. #1291C2×C127semidirect
194. C127#9339direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32392
C127×#29952
C127×#19662
C127×#15562
C127×#15292
C127×#13072
C127×#12912
#9339127