Finite Group Databasebeta

← C127×#12141 #44575814

Subgroups — C127×#12141 #44575814

Order 32512.

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

normal subgroups only

This group has 412 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×#2782C211yesmaximal, characteristic, complemented
2C127×#2040C211yesmaximal, characteristic, complemented
3C127×#1616C211yesmaximal, characteristic, complemented
4C127×#1598C211yesmaximal, characteristic
5C127×#1353C211yesmaximal, characteristic, complemented
6C127×#1345C211yesmaximal, characteristic, complemented
7C127×#1324C211yesmaximal, characteristic, complemented
8#537×C127C2211yescharacteristic
9#481×C127—21no—
10#447×C127—21no—
11C2×#104×C127—21no—
12#417×C127—21no—
13#400×C127—21no—
14#400×C127C2211yescharacteristic
15#397×C127—21no—
16#394×C127C2211yescharacteristic
17#388×C127—21no—
18#386×C127—21no—
19#385×C127—21no—
20#385×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×D4×C127D411yescharacteristic
29C23×C4×C127—21no—
30C2×D8×C127—41no—
31C2×M16×C127—21no—
32C22⋊Q8×C127—41no—
33#121×C127—21no—
34#121×C127—21no—
35#121×C127—41no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127D411yescharacteristic
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×C42×C127D411yescharacteristic
47#106×C127—41no—
48#104×C127—42no—
49#103×C127—41no—
50#102×C127—41no—
51#102×C127—41no—
52#102×C127—41no—
53C22⋊C8×C127—21no—
54C22⋊C8×C127—21no—
55#95×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×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—41no—
73C2×D4×C127—42no—
74C2×D4×C127—41no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—41no—
81C22×C4×C127—81no—
82C22×C4×C127—81no—
83C22×C4×C127—81no—
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
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—41no—
98C4⋊C4×C127—81no—
99C4⋊C4×C127—81no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—42no—
103C22⋊C4×C127—42no—
104C22⋊C4×C127—41no—
105C22⋊C4×C127—41no—
106C22⋊C4×C127—81no—
107C22⋊C4×C127—81no—
108C42×C127—21no—
109C42×C127—21no—
110C23×C127—22no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127#12011yescharacteristic
119Q8×C127—41no—
120Q8×C127—41no—
121D4×C127—41no—
122D4×C127—41no—
123D4×C127—42no—
124D4×C127—81no—
125D4×C127—81no—
126D4×C127—81no—
127D4×C127—81no—
128D4×C127—81no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
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—81no—
152C2×C4×C127—81no—
153C2×C4×C127—84no—
154C2×C4×C127#13511yescharacteristic
155C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
156C8×C127—81no—
157C8×C127—81no—
158C8×C127—81no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—42no—
162C22×C127—42no—
163C22×C127—42no—
164C22×C127—81no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127#44911yescharacteristic
172C22×C127#45411yescharacteristic
173C22×C127B(4,𝔽2)11yescharacteristic
174C4×C127—21no—
175C4×C127—21no—
176C4×C127—41no—
177C4×C127—41no—
178C4×C127—81no—
179C4×C127—81no—
180C4×C127—81no—
181C4×C127—81no—
182C4×C127—81no—
183C4×C127—81no—
184#12141C12711yesmaximal, characteristic, direct product factor, Sylow
185C2×C127—21no—
186C2×C127—21no—
187C2×C127—82no—
188C2×C127—161no—
189C2×C127#159711yescharacteristic
190C2×C127#219711yescharacteristic
191C2×C127#220211yescharacteristic
192#2782C2×C12711yescharacteristic, complemented
193#2040C2×C12711yescharacteristic, complemented
194#1616C2×C12711yescharacteristic, complemented
195#1598C2×C12711yescharacteristic
196#1353C2×C12711yescharacteristic, complemented
197#1345C2×C12711yescharacteristic, complemented
198#1324C2×C12711yescharacteristic, complemented
199C127#1214111yescharacteristic, direct product factor, Sylow
200#537C22×C12711yescharacteristic
201#481—21no—
202#447—21no—
203C2×#104—21no—
204#417—21no—
205#400—21no—
206#400C22×C12711yescharacteristic
207#397—21no—
208#394C22×C12711yescharacteristic
209#388—21no—
210#386—21no—
211#385—21no—
212#385—21no—
213#382C22×C12711yescharacteristic
214#343C22×C12711yescharacteristic
215#327—21no—
216#327—21no—
217#324C22×C12711yescharacteristic
218#324C22×C12711yescharacteristic
219C2×#41—21no—
220C22×D4D4×C12711yescharacteristic
221C23×C4—21no—
222C2×D8—41no—
223C2×M16—21no—
224C22⋊Q8—41no—
225#121—21no—
226#121—21no—
227#121—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C12711yescharacteristic
231C2×C4⋊C4D4×C12711yescharacteristic
232C2×C4⋊C4C23×C12711yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C42D4×C12711yescharacteristic
239#106—41no—
240#104—42no—
241#103—41no—
242#102—41no—
243#102—41no—
244#102—41no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95D4×C12711yescharacteristic
254#95D4×C12711yescharacteristic
255C24—21no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4—41no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4—81no—
276C22×C4C2×D4×C12711yescharacteristic
277C22×C4C2×D4×C12711yescharacteristic
278C22×C4C2×D4×C12711yescharacteristic
279D8—82no—
280M16—41no—
281M16—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C42—21no—
301C42—21no—
302C23—22no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23#120×C12711yescharacteristic
311Q8—41no—
312Q8—41no—
313D4—41no—
314D4—41no—
315D4—42no—
316D4—81no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—81no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
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—81no—
344C2×C4—81no—
345C2×C4—84no—
346C2×C4#135×C12711yescharacteristic
347C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
348C8—81no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22#449×C12711yescharacteristic
364C22#454×C12711yescharacteristic
365C22B(4,𝔽2)×C12711yescharacteristic
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—81no—
376C2—21no—
377C2—21no—
378C2—82no—
379C2—161no—
380C2C127×#159711yescharacteristic
381C2C127×#219711yescharacteristic
382C2C127×#220211yescharacteristic
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×#2782C2semidirect
2. C127×#2040C2semidirect
3. C127×#1616C2semidirect
5. C127×#1353C2semidirect
6. C127×#1345C2semidirect
7. C127×#1324C2semidirect
184. #12141C127direct (N × H)
192. #2782C2×C127semidirect
193. #2040C2×C127semidirect
194. #1616C2×C127semidirect
196. #1353C2×C127semidirect
197. #1345C2×C127semidirect
198. #1324C2×C127semidirect
199. C127#12141direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#27822
C127×#20402
C127×#16162
C127×#15982
C127×#13532
C127×#13452
C127×#13242
#12141127