Finite Group Databasebeta

← C127×#12143 #44575816

Subgroups — C127×#12143 #44575816

Order 32512.

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

normal subgroups only

This group has 364 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×#2789C211yesmaximal, characteristic, complemented
2C127×#2040C211yesmaximal, characteristic
3C127×#1610C211yesmaximal, characteristic
4C127×#1604C211yesmaximal, characteristic
5C127×#1354C211yesmaximal, characteristic, complemented
6C127×#1346C211yesmaximal, characteristic, complemented
7C127×#1324C211yesmaximal, characteristic, complemented
8#537×C127C2211yescharacteristic
9#480×C127—21no—
10#448×C127—21no—
11C2×#104×C127—21no—
12#417×C127—21no—
13#401×C127—21no—
14#400×C127—21no—
15#398×C127C2211yescharacteristic
16#395×C127C2211yescharacteristic
17#391×C127—21no—
18#387×C127—21no—
19#387×C127—21no—
20#387×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
29C2×SD16×C127—41no—
30C2×M16×C127—21no—
31C22⋊Q8×C127—41no—
32#121×C127—21no—
33#121×C127—21no—
34#121×C127—41no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C4⋊C4×C127C2311yescharacteristic
41C2×C42×C127—21no—
42C2×C42×C127D411yescharacteristic
43#107×C127—41no—
44#104×C127—42no—
45#103×C127—41no—
46#103×C127—41no—
47#102×C127—41no—
48#102×C127—41no—
49C22⋊C8×C127—21no—
50C22⋊C8×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×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
63#41×C127—41no—
64#41×C127—41no—
65#41×C127—41no—
66#41×C127—41no—
67C2×Q8×C127—21no—
68C2×Q8×C127—42no—
69C2×Q8×C127—41no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—21no—
73C2×D4×C127—41no—
74C22×C4×C127—21no—
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×C127C2×D411yescharacteristic
82C22×C4×C127C2×D411yescharacteristic
83C22×C4×C127C2×D411yescharacteristic
84SD16×C127—82no—
85M16×C127—41no—
86M16×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—41no—
89C2×C8×C127—41no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—42no—
96C4⋊C4×C127—42no—
97C4⋊C4×C127—41no—
98C4⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C42×C127—21no—
102C42×C127—21no—
103C42×C127—81no—
104C23×C127—41no—
105C23×C127#12011yescharacteristic
106Q8×C127—41no—
107Q8×C127—41no—
108Q8×C127—42no—
109Q8×C127—81no—
110D4×C127—41no—
111D4×C127—41no—
112D4×C127—81no—
113D4×C127—81no—
114D4×C127—81no—
115D4×C127—81no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—22no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—42no—
132C2×C4×C127—41no—
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—81no—
141C2×C4×C127—81no—
142C2×C4×C127#13511yescharacteristic
143C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
144C8×C127—81no—
145C8×C127—81no—
146C8×C127—81no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127#44911yescharacteristic
153C22×C127#45411yescharacteristic
154C22×C127B(4,𝔽2)11yescharacteristic
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—42no—
160C4×C127—81no—
161C4×C127—81no—
162C4×C127—81no—
163C4×C127—81no—
164C4×C127—81no—
165C4×C127—81no—
166#12143C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—21no—
168C2×C127—21no—
169C2×C127—161no—
170C2×C127#159711yescharacteristic
171C2×C127#219711yescharacteristic
172C2×C127#220311yescharacteristic
173#2789C2×C12711yescharacteristic, complemented
174#2040C2×C12711yescharacteristic
175#1610C2×C12711yescharacteristic
176#1604C2×C12711yescharacteristic
177#1354C2×C12711yescharacteristic, complemented
178#1346C2×C12711yescharacteristic, complemented
179#1324C2×C12711yescharacteristic, complemented
180C127#1214311yescharacteristic, direct product factor, Sylow
181#537C22×C12711yescharacteristic
182#480—21no—
183#448—21no—
184C2×#104—21no—
185#417—21no—
186#401—21no—
187#400—21no—
188#398C22×C12711yescharacteristic
189#395C22×C12711yescharacteristic
190#391—21no—
191#387—21no—
192#387—21no—
193#387—21no—
194#382C22×C12711yescharacteristic
195#343C22×C12711yescharacteristic
196#327—21no—
197#327—21no—
198#324C22×C12711yescharacteristic
199#324C22×C12711yescharacteristic
200C2×#41—21no—
201C22×Q8D4×C12711yescharacteristic
202C2×SD16—41no—
203C2×M16—21no—
204C22⋊Q8—41no—
205#121—21no—
206#121—21no—
207#121—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4D4×C12711yescharacteristic
212C2×C4⋊C4D4×C12711yescharacteristic
213C2×C4⋊C4C23×C12711yescharacteristic
214C2×C42—21no—
215C2×C42D4×C12711yescharacteristic
216#107—41no—
217#104—42no—
218#103—41no—
219#103—41no—
220#102—41no—
221#102—41no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95D4×C12711yescharacteristic
235#95D4×C12711yescharacteristic
236#41—41no—
237#41—41no—
238#41—41no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—42no—
242C2×Q8—41no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4C2×D4×C12711yescharacteristic
255C22×C4C2×D4×C12711yescharacteristic
256C22×C4C2×D4×C12711yescharacteristic
257SD16—82no—
258M16—41no—
259M16—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—21no—
275C42—21no—
276C42—81no—
277C23—41no—
278C23#120×C12711yescharacteristic
279Q8—41no—
280Q8—41no—
281Q8—42no—
282Q8—81no—
283D4—41no—
284D4—41no—
285D4—81no—
286D4—81no—
287D4—81no—
288D4—81no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#135×C12711yescharacteristic
316C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
317C8—81no—
318C8—81no—
319C8—81no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22#449×C12711yescharacteristic
326C22#454×C12711yescharacteristic
327C22B(4,𝔽2)×C12711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—21no—
340C2—21no—
341C2—161no—
342C2C127×#159711yescharacteristic
343C2C127×#219711yescharacteristic
344C2C127×#220311yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
prime radical#537×C127C22
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×#2789C2semidirect
5. C127×#1354C2semidirect
6. C127×#1346C2semidirect
7. C127×#1324C2semidirect
166. #12143C127direct (N × H)
173. #2789C2×C127semidirect
177. #1354C2×C127semidirect
178. #1346C2×C127semidirect
179. #1324C2×C127semidirect
180. C127#12143direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#27892
C127×#20402
C127×#16102
C127×#16042
C127×#13542
C127×#13462
C127×#13242
#12143127