Finite Group Databasebeta

← C127×#12145 #44575818

Subgroups — C127×#12145 #44575818

Order 32512.

408 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C127×#2785C211yesmaximal, characteristic, complemented
2C127×#2040C211yesmaximal, characteristic, complemented
3C127×#1604C211yesmaximal, characteristic, complemented
4C127×#1598C211yesmaximal, characteristic
5C127×#1354C211yesmaximal, characteristic, complemented
6C127×#1345C211yesmaximal, characteristic, complemented
7C127×#1324C211yesmaximal, characteristic, complemented
8#537×C127C2211yescharacteristic
9#448×C127—21no—
10#447×C127—21no—
11C2×#104×C127—21no—
12#417×C127—21no—
13#395×C127C2211yescharacteristic
14#394×C127—21no—
15#394×C127C2211yescharacteristic
16#393×C127—21no—
17#388×C127—21no—
18#388×C127—21no—
19#388×C127—21no—
20#382×C127—21no—
21#382×C127C2211yescharacteristic
22#343×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C22×Q8×C127D411yescharacteristic
29C22×D4×C127D411yescharacteristic
30C2×SD16×C127—41no—
31C2×D8×C127—41no—
32C2×M16×C127—21no—
33C22⋊Q8×C127—41no—
34#121×C127—21no—
35#121×C127—21no—
36#121×C127—41no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C4⋊C4×C127C2311yescharacteristic
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C42×C127—21no—
48C2×C42×C127D411yescharacteristic
49#104×C127—42no—
50#103×C127—41no—
51#103×C127—41no—
52#102×C127—41no—
53#102×C127—41no—
54C22⋊C8×C127—21no—
55C22⋊C8×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—21no—
61#95×C127D411yescharacteristic
62#95×C127D411yescharacteristic
63C24×C127—21no—
64#41×C127—41no—
65#41×C127—41no—
66#41×C127—41no—
67#41×C127—41no—
68C2×Q8×C127—21no—
69C2×Q8×C127—41no—
70C2×Q8×C127—81no—
71C2×D4×C127—21no—
72C2×D4×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C2×D4×C127—81no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—41no—
83C22×C4×C127C2×D411yescharacteristic
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86SD16×C127—82no—
87D8×C127—82no—
88M16×C127—41no—
89M16×C127—41no—
90C2×C8×C127—41no—
91C2×C8×C127—41no—
92C2×C8×C127—41no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—81no—
98C4⋊C4×C127—81no—
99C22⋊C4×C127—42no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—41no—
104C22⋊C4×C127—41no—
105C22⋊C4×C127—81no—
106C22⋊C4×C127—81no—
107C22⋊C4×C127—81no—
108C42×C127—21no—
109C42×C127—21no—
110C42×C127—42no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127#12011yescharacteristic
120Q8×C127—41no—
121Q8×C127—41no—
122Q8×C127—42no—
123Q8×C127—81no—
124D4×C127—41no—
125D4×C127—41no—
126D4×C127—42no—
127D4×C127—81no—
128D4×C127—81no—
129D4×C127—81no—
130D4×C127—81no—
131D4×C127—81no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—22no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—81no—
155C2×C4×C127—81no—
156C2×C4×C127#13511yescharacteristic
157C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
158C8×C127—81no—
159C8×C127—81no—
160C8×C127—81no—
161C22×C127—21no—
162C22×C127—21no—
163C22×C127—81no—
164C22×C127—81no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127#44911yescharacteristic
174C22×C127#45411yescharacteristic
175C22×C127B(4,𝔽2)11yescharacteristic
176C4×C127—21no—
177C4×C127—21no—
178C4×C127—42no—
179C4×C127—41no—
180C4×C127—41no—
181C4×C127—81no—
182C4×C127—81no—
183C4×C127—81no—
184C4×C127—81no—
185C4×C127—81no—
186#12145C12711yesmaximal, characteristic, direct product factor, Sylow
187C2×C127—21no—
188C2×C127—21no—
189C2×C127—161no—
190C2×C127—161no—
191C2×C127#159711yescharacteristic
192C2×C127#219911yescharacteristic
193C2×C127#220411yescharacteristic
194#2785C2×C12711yescharacteristic, complemented
195#2040C2×C12711yescharacteristic, complemented
196#1604C2×C12711yescharacteristic, complemented
197#1598C2×C12711yescharacteristic
198#1354C2×C12711yescharacteristic, complemented
199#1345C2×C12711yescharacteristic, complemented
200#1324C2×C12711yescharacteristic, complemented
201C127#1214511yescharacteristic, direct product factor, Sylow
202#537C22×C12711yescharacteristic
203#448—21no—
204#447—21no—
205C2×#104—21no—
206#417—21no—
207#395C22×C12711yescharacteristic
208#394—21no—
209#394C22×C12711yescharacteristic
210#393—21no—
211#388—21no—
212#388—21no—
213#388—21no—
214#382—21no—
215#382C22×C12711yescharacteristic
216#343C22×C12711yescharacteristic
217#327—21no—
218#327—21no—
219#324C22×C12711yescharacteristic
220#324C22×C12711yescharacteristic
221C2×#41—21no—
222C22×Q8D4×C12711yescharacteristic
223C22×D4D4×C12711yescharacteristic
224C2×SD16—41no—
225C2×D8—41no—
226C2×M16—21no—
227C22⋊Q8—41no—
228#121—21no—
229#121—21no—
230#121—41no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4D4×C12711yescharacteristic
234C2×C4⋊C4C23×C12711yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C42—21no—
242C2×C42D4×C12711yescharacteristic
243#104—42no—
244#103—41no—
245#103—41no—
246#102—41no—
247#102—41no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95D4×C12711yescharacteristic
256#95D4×C12711yescharacteristic
257C24—21no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262C2×Q8—21no—
263C2×Q8—41no—
264C2×Q8—81no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—81no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4C2×D4×C12711yescharacteristic
278C22×C4C2×D4×C12711yescharacteristic
279C22×C4C2×D4×C12711yescharacteristic
280SD16—82no—
281D8—82no—
282M16—41no—
283M16—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—81no—
292C4⋊C4—81no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C42—21no—
303C42—21no—
304C42—42no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#120×C12711yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—42no—
317Q8—81no—
318D4—41no—
319D4—41no—
320D4—42no—
321D4—81no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4#135×C12711yescharacteristic
351C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
352C8—81no—
353C8—81no—
354C8—81no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22#449×C12711yescharacteristic
368C22#454×C12711yescharacteristic
369C22B(4,𝔽2)×C12711yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C2—21no—
381C2—21no—
382C2—161no—
383C2—161no—
384C2C127×#159711yescharacteristic
385C2C127×#219911yescharacteristic
386C2C127×#220411yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#1598C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2785C2semidirect
2. C127×#2040C2semidirect
3. C127×#1604C2semidirect
5. C127×#1354C2semidirect
6. C127×#1345C2semidirect
7. C127×#1324C2semidirect
186. #12145C127direct (N × H)
194. #2785C2×C127semidirect
195. #2040C2×C127semidirect
196. #1604C2×C127semidirect
198. #1354C2×C127semidirect
199. #1345C2×C127semidirect
200. #1324C2×C127semidirect
201. C127#12145direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#27852
C127×#20402
C127×#16042
C127×#15982
C127×#13542
C127×#13452
C127×#13242
#12145127