Finite Group Databasebeta

← C127×#12142 #44575815

Subgroups — C127×#12142 #44575815

Order 32512.

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

normal subgroups only

This group has 354 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×#2794C211yesmaximal, characteristic, complemented
2C127×#2039C211yesmaximal, characteristic
3C127×#1616C211yesmaximal, characteristic
4C127×#1610C211yesmaximal, characteristic
5C127×#1353C211yesmaximal, characteristic, complemented
6C127×#1346C211yesmaximal, characteristic, complemented
7C127×#1325C211yesmaximal, characteristic, complemented
8#537×C127C2211yescharacteristic
9#481×C127—21no—
10#480×C127—21no—
11C2×#104×C127—21no—
12#417×C127—21no—
13#400×C127—21no—
14#400×C127—21no—
15#400×C127C2211yescharacteristic
16#398×C127C2211yescharacteristic
17#387×C127—21no—
18#387×C127—21no—
19#387×C127—21no—
20#387×C127—21no—
21#384×C127C2211yescharacteristic
22#343×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C2×M16×C127—21no—
29C22⋊Q8×C127—41no—
30#121×C127—21no—
31#121×C127—21no—
32#121×C127—41no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C4⋊C4×C127C2311yescharacteristic
41C2×C42×C127—21no—
42C2×C42×C127D411yescharacteristic
43#107×C127—41no—
44#106×C127—41no—
45#104×C127—42no—
46#103×C127—41no—
47#102×C127—41no—
48#102×C127—41no—
49#102×C127—41no—
50C22⋊C8×C127—21no—
51C22⋊C8×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×D4×C127—21no—
69C2×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—41no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—41no—
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82M16×C127—41no—
83M16×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127—41no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—21no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—42no—
95C4⋊C4×C127—42no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C42×C127—21no—
101C42×C127—21no—
102C42×C127—81no—
103C23×C127—41no—
104C23×C127#12011yescharacteristic
105Q8×C127—41no—
106Q8×C127—41no—
107D4×C127—41no—
108D4×C127—41no—
109D4×C127—81no—
110D4×C127—81no—
111D4×C127—81no—
112D4×C127—81no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—22no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
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—42no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127#13511yescharacteristic
140C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
141C8×C127—81no—
142C8×C127—81no—
143C8×C127—81no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—81no—
147C22×C127—81no—
148C22×C127—81no—
149C22×C127#44911yescharacteristic
150C22×C127#45411yescharacteristic
151C22×C127B(4,𝔽2)11yescharacteristic
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—42no—
155C4×C127—41no—
156C4×C127—41no—
157C4×C127—81no—
158C4×C127—81no—
159C4×C127—81no—
160C4×C127—81no—
161C4×C127—81no—
162C4×C127—81no—
163#12142C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—21no—
165C2×C127—21no—
166C2×C127—161no—
167C2×C127#159711yescharacteristic
168C2×C127#219811yescharacteristic
169C2×C127#220311yescharacteristic
170#2794C2×C12711yescharacteristic, complemented
171#2039C2×C12711yescharacteristic
172#1616C2×C12711yescharacteristic
173#1610C2×C12711yescharacteristic
174#1353C2×C12711yescharacteristic, complemented
175#1346C2×C12711yescharacteristic, complemented
176#1325C2×C12711yescharacteristic, complemented
177C127#1214211yescharacteristic, direct product factor, Sylow
178#537C22×C12711yescharacteristic
179#481—21no—
180#480—21no—
181C2×#104—21no—
182#417—21no—
183#400—21no—
184#400—21no—
185#400C22×C12711yescharacteristic
186#398C22×C12711yescharacteristic
187#387—21no—
188#387—21no—
189#387—21no—
190#387—21no—
191#384C22×C12711yescharacteristic
192#343C22×C12711yescharacteristic
193#327—21no—
194#327—21no—
195#324C22×C12711yescharacteristic
196#324C22×C12711yescharacteristic
197C2×#41—21no—
198C2×M16—21no—
199C22⋊Q8—41no—
200#121—21no—
201#121—21no—
202#121—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4D4×C12711yescharacteristic
208C2×C4⋊C4D4×C12711yescharacteristic
209C2×C4⋊C4D4×C12711yescharacteristic
210C2×C4⋊C4C23×C12711yescharacteristic
211C2×C42—21no—
212C2×C42D4×C12711yescharacteristic
213#107—41no—
214#106—41no—
215#104—42no—
216#103—41no—
217#102—41no—
218#102—41no—
219#102—41no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95D4×C12711yescharacteristic
232#95D4×C12711yescharacteristic
233#41—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4C2×D4×C12711yescharacteristic
250C22×C4C2×D4×C12711yescharacteristic
251C22×C4C2×D4×C12711yescharacteristic
252M16—41no—
253M16—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42—21no—
271C42—21no—
272C42—81no—
273C23—41no—
274C23#120×C12711yescharacteristic
275Q8—41no—
276Q8—41no—
277D4—41no—
278D4—41no—
279D4—81no—
280D4—81no—
281D4—81no—
282D4—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4#135×C12711yescharacteristic
310C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
311C8—81no—
312C8—81no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#449×C12711yescharacteristic
320C22#454×C12711yescharacteristic
321C22B(4,𝔽2)×C12711yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2C127×#159711yescharacteristic
337C2C127×#219811yescharacteristic
338C2C127×#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×#2794C2semidirect
5. C127×#1353C2semidirect
6. C127×#1346C2semidirect
7. C127×#1325C2semidirect
163. #12142C127direct (N × H)
170. #2794C2×C127semidirect
174. #1353C2×C127semidirect
175. #1346C2×C127semidirect
176. #1325C2×C127semidirect
177. C127#12142direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#27942
C127×#20392
C127×#16162
C127×#16102
C127×#13532
C127×#13462
C127×#13252
#12142127