Finite Group Databasebeta

← C127×#12110 #44575783

Subgroups — C127×#12110 #44575783

Order 32512.

422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3203C211yesmaximal, characteristic, complemented
2C127×#2187C211yesmaximal, characteristic, complemented
3C127×#2184C211yesmaximal, characteristic, complemented
4C127×#2018C211yesmaximal, characteristic, complemented
5C127×#1350C211yesmaximal, characteristic, complemented
6C127×#1349C211yesmaximal, characteristic, complemented
7C127×#1315C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C127—21no—
9C22×D8×C127C2211yescharacteristic
10#537×C127—21no—
11C2×SD32×C127—21no—
12C2×D16×C127—21no—
13#484×C127—21no—
14#480×C127—21no—
15#468×C127—21no—
16#467×C127C2211yescharacteristic
17#466×C127C2211yescharacteristic
18#452×C127—21no—
19#449×C127—21no—
20C2×#100×C127—21no—
21#408×C127C2211yescharacteristic
22#357×C127—21no—
23#357×C127—21no—
24C22⋊C16×C127C2211yescharacteristic
25C22⋊C16×C127C2211yescharacteristic
26#341×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C2×#41×C127D411yescharacteristic
29C22×D4×C127—21no—
30AGL(1,ℤ/8)×C127—42no—
31AGL(1,ℤ/8)×C127—42no—
32C2×Q16×C127D411yescharacteristic
33C2×SD16×C127—21no—
34C2×SD16×C127—41no—
35C2×D8×C127—21no—
36C2×D8×C127—21no—
37C2×D8×C127—42no—
38C2×D8×C127—41no—
39C2×D8×C127D411yescharacteristic
40C2×M16×C127—21no—
41C2×M16×C127D411yescharacteristic
42C22×C8×C127C2311yescharacteristic
43C22⋊Q8×C127—21no—
44C22⋊Q8×C127—21no—
45C22⋊Q8×C127—41no—
46#121×C127—21no—
47#121×C127—21no—
48#121×C127—41no—
49#121×C127—41no—
50#121×C127—41no—
51C2×C4⋊C4×C127—21no—
52SD32×C127—42no—
53D16×C127—42no—
54C2×C16×C127—21no—
55C2×C16×C127—21no—
56#107×C127—21no—
57#107×C127D411yescharacteristic
58#107×C127D411yescharacteristic
59#103×C127—21no—
60#103×C127—21no—
61#102×C127—21no—
62#102×C127—21no—
63#100×C127—42no—
64C22⋊C8×C127—21no—
65C22⋊C8×C127—21no—
66C24×C127—41no—
67#41×C127—41no—
68#41×C127—41no—
69#41×C127—81no—
70#41×C127—81no—
71C2×Q8×C127—21no—
72C2×Q8×C127D811yescharacteristic
73C2×D4×C127—22no—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C2×D4×C127—41no—
81C2×D4×C127—41no—
82C2×D4×C127—41no—
83C2×D4×C127—41no—
84C2×D4×C127D811yescharacteristic
85C22×C4×C127—21no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127C2×D411yescharacteristic
89Q16×C127—41no—
90SD16×C127—44no—
91SD16×C127—81no—
92D8×C127—22no—
93D8×C127—22no—
94D8×C127—41no—
95D8×C127—41no—
96D8×C127—41no—
97D8×C127—44no—
98M16×C127—22no—
99M16×C127—41no—
100M16×C127—41no—
101C2×C8×C127—21no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
104C2×C8×C127C2×D411yescharacteristic
105C2×C8×C127C2×D411yescharacteristic
106C4⋊C4×C127—21no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—41no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—41no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C16×C127—41no—
116C16×C127—41no—
117C23×C127—21no—
118C23×C127—42no—
119C23×C127—41no—
120C23×C127—81no—
121C23×C127—81no—
122C23×C127—161no—
123C23×C127—161no—
124C23×C127AGL(1,ℤ/8)11yescharacteristic
125Q8×C127—41no—
126Q8×C127—41no—
127Q8×C127—41no—
128D4×C127—41no—
129D4×C127—42no—
130D4×C127—41no—
131D4×C127—42no—
132D4×C127—41no—
133D4×C127—81no—
134D4×C127—81no—
135D4×C127—82no—
136D4×C127—81no—
137D4×C127—161no—
138D4×C127—161no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—82no—
148C2×C4×C127—161no—
149C2×C4×C127#12011yescharacteristic
150C2×C4×C127C2×D811yescharacteristic
151C8×C127—21no—
152C8×C127—21no—
153C8×C127—42no—
154C8×C127—41no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—21no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—81no—
162C22×C127—82no—
163C22×C127—81no—
164C22×C127—81no—
165C22×C127—162no—
166C22×C127—162no—
167C22×C127—161no—
168C22×C127—161no—
169C22×C127#44711yescharacteristic
170C4×C127—21no—
171C4×C127—41no—
172C4×C127—81no—
173C4×C127—81no—
174C4×C127—81no—
175C4×C127#45311yescharacteristic
176C4×C127B(4,𝔽2)11yescharacteristic
177#12110C12711yesmaximal, characteristic, direct product factor, Sylow
178C2×C127—41no—
179C2×C127—81no—
180C2×C127—161no—
181C2×C127—162no—
182C2×C127#159511yescharacteristic
183C2×C127#219211yescharacteristic
184C2×C127#219311yescharacteristic
185#3203C2×C12711yescharacteristic, complemented
186#2187C2×C12711yescharacteristic, complemented
187#2184C2×C12711yescharacteristic, complemented
188#2018C2×C12711yescharacteristic, complemented
189#1350C2×C12711yescharacteristic, complemented
190#1349C2×C12711yescharacteristic, complemented
191#1315C2×C12711yescharacteristic, complemented
192C127#1211011yescharacteristic, direct product factor, Sylow
193C2×AGL(1,ℤ/8)—21no—
194C22×D8C22×C12711yescharacteristic
195#537—21no—
196C2×SD32—21no—
197C2×D16—21no—
198#484—21no—
199#480—21no—
200#468—21no—
201#467C22×C12711yescharacteristic
202#466C22×C12711yescharacteristic
203#452—21no—
204#449—21no—
205C2×#100—21no—
206#408C22×C12711yescharacteristic
207#357—21no—
208#357—21no—
209C22⋊C16C22×C12711yescharacteristic
210C22⋊C16C22×C12711yescharacteristic
211#341C22×C12711yescharacteristic
212C2×#41—21no—
213C2×#41D4×C12711yescharacteristic
214C22×D4—21no—
215AGL(1,ℤ/8)—42no—
216AGL(1,ℤ/8)—42no—
217C2×Q16D4×C12711yescharacteristic
218C2×SD16—21no—
219C2×SD16—41no—
220C2×D8—21no—
221C2×D8—21no—
222C2×D8—42no—
223C2×D8—41no—
224C2×D8D4×C12711yescharacteristic
225C2×M16—21no—
226C2×M16D4×C12711yescharacteristic
227C22×C8C23×C12711yescharacteristic
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—41no—
231#121—21no—
232#121—21no—
233#121—41no—
234#121—41no—
235#121—41no—
236C2×C4⋊C4—21no—
237SD32—42no—
238D16—42no—
239C2×C16—21no—
240C2×C16—21no—
241#107—21no—
242#107D4×C12711yescharacteristic
243#107D4×C12711yescharacteristic
244#103—21no—
245#103—21no—
246#102—21no—
247#102—21no—
248#100—42no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C24—41no—
252#41—41no—
253#41—41no—
254#41—81no—
255#41—81no—
256C2×Q8—21no—
257C2×Q8D8×C12711yescharacteristic
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4D8×C12711yescharacteristic
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C2×D4×C12711yescharacteristic
274Q16—41no—
275SD16—44no—
276SD16—81no—
277D8—22no—
278D8—22no—
279D8—41no—
280D8—41no—
281D8—41no—
282D8—44no—
283M16—22no—
284M16—41no—
285M16—41no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8C2×D4×C12711yescharacteristic
290C2×C8C2×D4×C12711yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C16—41no—
301C16—41no—
302C23—21no—
303C23—42no—
304C23—41no—
305C23—81no—
306C23—81no—
307C23—161no—
308C23—161no—
309C23AGL(1,ℤ/8)×C12711yescharacteristic
310Q8—41no—
311Q8—41no—
312Q8—41no—
313D4—41no—
314D4—42no—
315D4—41no—
316D4—42no—
317D4—41no—
318D4—81no—
319D4—81no—
320D4—82no—
321D4—81no—
322D4—161no—
323D4—161no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4—161no—
334C2×C4#120×C12711yescharacteristic
335C2×C4C2×D8×C12711yescharacteristic
336C8—21no—
337C8—21no—
338C8—42no—
339C8—41no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—82no—
348C22—81no—
349C22—81no—
350C22—162no—
351C22—162no—
352C22—161no—
353C22—161no—
354C22#447×C12711yescharacteristic
355C4—21no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4#453×C12711yescharacteristic
361C4B(4,𝔽2)×C12711yescharacteristic
362C2—41no—
363C2—81no—
364C2—161no—
365C2—162no—
366C2C127×#159511yescharacteristic
367C2C127×#219211yescharacteristic
368C2C127×#219311yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ #408×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3203C2semidirect
2. C127×#2187C2semidirect
3. C127×#2184C2semidirect
4. C127×#2018C2semidirect
5. C127×#1350C2semidirect
6. C127×#1349C2semidirect
7. C127×#1315C2semidirect
177. #12110C127direct (N × H)
185. #3203C2×C127semidirect
186. #2187C2×C127semidirect
187. #2184C2×C127semidirect
188. #2018C2×C127semidirect
189. #1350C2×C127semidirect
190. #1349C2×C127semidirect
191. #1315C2×C127semidirect
192. C127#12110direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32032
C127×#21872
C127×#21842
C127×#20182
C127×#13502
C127×#13492
C127×#13152
#12110127