Finite Group Databasebeta

← C127×#10083 #44573756

Subgroups — C127×#10083 #44573756

Order 32512.

526 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#491×C127C211yesmaximal, characteristic, complemented
2C2×#489×C127C211yesmaximal, characteristic
3C127×#2820C211yesmaximal, characteristic
4C127×#1993C211yesmaximal, characteristic, complemented
5C2×#330×C127C211yesmaximal, characteristic, complemented
6C2×#329×C127C211yesmaximal, characteristic
7C127×#1295C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×#125×C127C2211yescharacteristic
10C2×#124×C127C2211yescharacteristic
11#491×C127—22no—
12#491×C127—22no—
13#489×C127—22no—
14#489×C127—22no—
15C2×#103×C127—21no—
16C2×#103×C127—21no—
17C2×#103×C127—21no—
18C2×#102×C127—21no—
19C2×#97×C127C2211yescharacteristic
20C2×#97×C127C2211yescharacteristic
21C2×#97×C127C2211yescharacteristic
22#399×C127—21no—
23#397×C127—21no—
24#396×C127—22no—
25#395×C127—21no—
26#394×C127—21no—
27#382×C127C2211yescharacteristic
28#340×C127—22no—
29#330×C127—22no—
30#329×C127—22no—
31C22×Q8×C127—21no—
32C22×Q8×C127D411yescharacteristic
33C22×D4×C127D411yescharacteristic
34C22×C8×C127—21no—
35C22×C8×C127—21no—
36C22×C8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127—21no—
39C4⋊Q8×C127—21no—
40C4⋊Q8×C127D412yes—
41#125×C127—21no—
42#125×C127—21no—
43#125×C127—21no—
44#125×C127—21no—
45#124×C127—21no—
46#124×C127—21no—
47#124×C127—21no—
48#124×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127D411yescharacteristic
55C2×C4⋊C4×C127D411yescharacteristic
56C2×C4⋊C4×C127D412yes—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—22no—
61C2×C42×C127C2311yescharacteristic
62#103×C127—24no—
63#103×C127—24no—
64#103×C127—24no—
65#102×C127—24no—
66#97×C127—21no—
67#97×C127—21no—
68#97×C127—21no—
69#97×C127—21no—
70#97×C127D412yes—
71#97×C127D412yes—
72#95×C127—22no—
73#95×C127—21no—
74#95×C127—21no—
75C24×C127—21no—
76C2×Q8×C127—21no—
77C2×Q8×C127—22no—
78C2×Q8×C127—21no—
79C2×Q8×C127—42no—
80C2×Q8×C127—44no—
81C2×Q8×C127—41no—
82C2×D4×C127—21no—
83C2×D4×C127—21no—
84C2×D4×C127—42no—
85C22×C4×C127—22no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—41no—
90C22×C4×C127C2×D411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127C2×D411yescharacteristic
93C2×C8×C127—22no—
94C2×C8×C127—22no—
95C2×C8×C127—22no—
96C2×C8×C127—42no—
97C2×C8×C127—41no—
98C2×C8×C127—42no—
99C2×C8×C127—41no—
100C4⋊C4×C127—22no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—22no—
104C4⋊C4×C127—21no—
105C4⋊C4×C127—21no—
106C4⋊C4×C127—42no—
107C4⋊C4×C127—41no—
108C4⋊C4×C127—41no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—82no—
114C22⋊C4×C127—41no—
115C22⋊C4×C127—41no—
116C22⋊C4×C127—41no—
117C22⋊C4×C127—41no—
118C22⋊C4×C127—82no—
119C22⋊C4×C127—82no—
120C42×C127C2×D411yescharacteristic
121C42×C127C2×D411yescharacteristic
122C42×C127C2×D411yescharacteristic
123C42×C127#4111yescharacteristic
124C23×C127—41no—
125C23×C127—42no—
126C23×C127—41no—
127C23×C127—42no—
128C23×C127—41no—
129C23×C127#12011yescharacteristic
130Q8×C127—44no—
131Q8×C127—42no—
132Q8×C127—81no—
133Q8×C127—82no—
134D4×C127—42no—
135D4×C127—81no—
136C2×C4×C127—22no—
137C2×C4×C127—21no—
138C2×C4×C127—22no—
139C2×C4×C127—21no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—42no—
144C2×C4×C127—42no—
145C2×C4×C127—41no—
146C2×C4×C127—42no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—41no—
151C2×C4×C127—82no—
152C2×C4×C127#12011yescharacteristic
153C2×C4×C127#12011yescharacteristic
154C2×C4×C127#12111yescharacteristic
155C2×C4×C127#12111yescharacteristic
156C2×C4×C127#12111yescharacteristic
157C2×C4×C127#12711yescharacteristic
158C8×C127—42no—
159C8×C127—42no—
160C8×C127—42no—
161C22×C127—82no—
162C22×C127—82no—
163C22×C127—81no—
164C22×C127—81no—
165C22×C127—81no—
166C22×C127#39211yescharacteristic
167C22×C127#45412yes—
168C22×C127#45511yescharacteristic
169C22×C127#45512yes—
170C22×C127#45611yescharacteristic
171C4×C127—21no—
172C4×C127—21no—
173C4×C127—21no—
174C4×C127—21no—
175C4×C127—21no—
176C4×C127—21no—
177C4×C127—82no—
178C4×C127—82no—
179C4×C127—81no—
180C4×C127—81no—
181C4×C127—81no—
182#10083C12711yesmaximal, characteristic, direct product factor, Sylow
183C2×C127—161no—
184C2×C127#166212yes—
185C2×C127#166412yes—
186C2×C127#200311yescharacteristic
187C2×C127#200411yescharacteristic
188C2×C127#200711yescharacteristic
189C2×#491C2×C12711yescharacteristic, complemented
190C2×#489C2×C12711yescharacteristic
191#2820C2×C12711yescharacteristic
192#1993C2×C12711yescharacteristic, complemented
193C2×#330C2×C12711yescharacteristic, complemented
194C2×#329C2×C12711yescharacteristic
195#1295C2×C12711yescharacteristic, complemented
196C127#1008311yescharacteristic, direct product factor, Sylow
197C2×C4⋊Q8C22×C12711yescharacteristic
198C2×#125C22×C12711yescharacteristic
199C2×#124C22×C12711yescharacteristic
200#491—22no—
201#491—22no—
202#489—22no—
203#489—22no—
204C2×#103—21no—
205C2×#103—21no—
206C2×#103—21no—
207C2×#102—21no—
208C2×#97C22×C12711yescharacteristic
209C2×#97C22×C12711yescharacteristic
210C2×#97C22×C12711yescharacteristic
211#399—21no—
212#397—21no—
213#396—22no—
214#395—21no—
215#394—21no—
216#382C22×C12711yescharacteristic
217#340—22no—
218#330—22no—
219#329—22no—
220C22×Q8—21no—
221C22×Q8D4×C12711yescharacteristic
222C22×D4D4×C12711yescharacteristic
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C12712yes—
230#125—21no—
231#125—21no—
232#125—21no—
233#125—21no—
234#124—21no—
235#124—21no—
236#124—21no—
237#124—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4D4×C12711yescharacteristic
244C2×C4⋊C4D4×C12711yescharacteristic
245C2×C4⋊C4D4×C12712yes—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42C23×C12711yescharacteristic
251#103—24no—
252#103—24no—
253#103—24no—
254#102—24no—
255#97—21no—
256#97—21no—
257#97—21no—
258#97—21no—
259#97D4×C12712yes—
260#97D4×C12712yes—
261#95—22no—
262#95—21no—
263#95—21no—
264C24—21no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—42no—
269C2×Q8—44no—
270C2×Q8—41no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—42no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4C2×D4×C12711yescharacteristic
280C22×C4C2×D4×C12711yescharacteristic
281C22×C4C2×D4×C12711yescharacteristic
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—42no—
286C2×C8—41no—
287C2×C8—42no—
288C2×C8—41no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—82no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—82no—
308C22⋊C4—82no—
309C42C2×D4×C12711yescharacteristic
310C42C2×D4×C12711yescharacteristic
311C42C2×D4×C12711yescharacteristic
312C42#41×C12711yescharacteristic
313C23—41no—
314C23—42no—
315C23—41no—
316C23—42no—
317C23—41no—
318C23#120×C12711yescharacteristic
319Q8—44no—
320Q8—42no—
321Q8—81no—
322Q8—82no—
323D4—42no—
324D4—81no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4#120×C12711yescharacteristic
342C2×C4#120×C12711yescharacteristic
343C2×C4#121×C12711yescharacteristic
344C2×C4#121×C12711yescharacteristic
345C2×C4#121×C12711yescharacteristic
346C2×C4#127×C12711yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22#392×C12711yescharacteristic
356C22#454×C12712yes—
357C22#455×C12711yescharacteristic
358C22#455×C12712yes—
359C22#456×C12711yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4—81no—
371C2—161no—
372C2C127×#166212yes—
373C2C127×#166412yes—
374C2C127×#200311yescharacteristic
375C2C127×#200411yescharacteristic
376C2C127×#200711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#491×C127C2semidirect
4. C127×#1993C2semidirect
5. C2×#330×C127C2semidirect
7. C127×#1295C2semidirect
182. #10083C127direct (N × H)
189. C2×#491C2×C127semidirect
192. #1993C2×C127semidirect
193. C2×#330C2×C127semidirect
195. #1295C2×C127semidirect
196. C127#10083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#491×C1272
C2×#489×C1272
C127×#28202
C127×#19932
C2×#330×C1272
C2×#329×C1272
C127×#12952
#10083127