Finite Group Databasebeta

← C127×#12277 #44575950

Subgroups — C127×#12277 #44575950

Order 32512.

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

normal subgroups only

This group has 318 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×#2833C211yesmaximal, characteristic
2C127×#2028C211yesmaximal, characteristic
3C127×#1617C211yesmaximal, characteristic
4C127×#1611C211yesmaximal, characteristic
5C127×#1353C211yesmaximal, characteristic
6C127×#1346C211yesmaximal, characteristic
7C127×#1319C211yesmaximal, characteristic
8#544×C127C2211yescharacteristic
9#484×C127—21no—
10#483×C127—21no—
11#419×C127—21no—
12#401×C127—21no—
13#400×C127—21no—
14#400×C127—21no—
15#400×C127C2211yescharacteristic
16#398×C127—21no—
17#398×C127C2211yescharacteristic
18#395×C127—21no—
19#391×C127C2211yescharacteristic
20#387×C127—21no—
21#343×C127C2211yescharacteristic
22#339×C127—21no—
23#328×C127—21no—
24#328×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C22×Q8×C127D411yescharacteristic
28C2×M16×C127—21no—
29C4⋊Q8×C127—41no—
30#125×C127—41no—
31C22⋊Q8×C127—21no—
32C22⋊Q8×C127—21no—
33#117×C127—21no—
34C2×C4⋊C4×C127—21no—
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×C127D411yescharacteristic
42#107×C127—41no—
43#106×C127—41no—
44#103×C127—41no—
45#103×C127—41no—
46#103×C127—41no—
47#103×C127—41no—
48C22⋊C8×C127—21no—
49C22⋊C8×C127—21no—
50#95×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×C127D411yescharacteristic
61#95×C127D411yescharacteristic
62C2×Q8×C127—21no—
63C2×Q8×C127—21no—
64C2×Q8×C127—21no—
65C2×Q8×C127—21no—
66C2×Q8×C127—41no—
67C2×Q8×C127—41no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77M16×C127—41no—
78M16×C127—41no—
79C2×C8×C127—41no—
80C2×C8×C127—41no—
81C2×C8×C127—41no—
82C4⋊C4×C127—21no—
83C4⋊C4×C127—21no—
84C4⋊C4×C127—21no—
85C4⋊C4×C127—21no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—81no—
94C4⋊C4×C127—81no—
95C4⋊C4×C127—81no—
96C22⋊C4×C127—41no—
97C42×C127—41no—
98C42×C127—41no—
99C23×C127#12011yescharacteristic
100Q8×C127—42no—
101Q8×C127—81no—
102Q8×C127—81no—
103Q8×C127—81no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—42no—
117C2×C4×C127—41no—
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—41no—
129C2×C4×C127#13511yescharacteristic
130C2×C4×C127#13711yescharacteristic
131C8×C127—81no—
132C8×C127—81no—
133C8×C127—81no—
134C22×C127—21no—
135C22×C127—21no—
136C22×C127#45211yescharacteristic
137C22×C127#45511yescharacteristic
138C22×C127B(4,𝔽2)11yescharacteristic
139C4×C127—21no—
140C4×C127—21no—
141C4×C127—41no—
142C4×C127—41no—
143C4×C127—81no—
144C4×C127—81no—
145C4×C127—81no—
146C4×C127—81no—
147C4×C127—81no—
148C4×C127—81no—
149C4×C127—81no—
150C4×C127—81no—
151#12277C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—21no—
153C2×C127—21no—
154C2×C127#160611yescharacteristic
155C2×C127#220111yescharacteristic
156C2×C127#220311yescharacteristic
157#2833C2×C12711yescharacteristic
158#2028C2×C12711yescharacteristic
159#1617C2×C12711yescharacteristic
160#1611C2×C12711yescharacteristic
161#1353C2×C12711yescharacteristic
162#1346C2×C12711yescharacteristic
163#1319C2×C12711yescharacteristic
164C127#1227711yescharacteristic, direct product factor, Sylow
165#544C22×C12711yescharacteristic
166#484—21no—
167#483—21no—
168#419—21no—
169#401—21no—
170#400—21no—
171#400—21no—
172#400C22×C12711yescharacteristic
173#398—21no—
174#398C22×C12711yescharacteristic
175#395—21no—
176#391C22×C12711yescharacteristic
177#387—21no—
178#343C22×C12711yescharacteristic
179#339—21no—
180#328—21no—
181#328—21no—
182#324C22×C12711yescharacteristic
183#324C22×C12711yescharacteristic
184C22×Q8D4×C12711yescharacteristic
185C2×M16—21no—
186C4⋊Q8—41no—
187#125—41no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190#117—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4D4×C12711yescharacteristic
196C2×C4⋊C4D4×C12711yescharacteristic
197C2×C4⋊C4C23×C12711yescharacteristic
198C2×C42D4×C12711yescharacteristic
199#107—41no—
200#106—41no—
201#103—41no—
202#103—41no—
203#103—41no—
204#103—41no—
205C22⋊C8—21no—
206C22⋊C8—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95D4×C12711yescharacteristic
218#95D4×C12711yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—41no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C2×D4×C12711yescharacteristic
232C22×C4C2×D4×C12711yescharacteristic
233C22×C4C2×D4×C12711yescharacteristic
234M16—41no—
235M16—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—81no—
251C4⋊C4—81no—
252C4⋊C4—81no—
253C22⋊C4—41no—
254C42—41no—
255C42—41no—
256C23#120×C12711yescharacteristic
257Q8—42no—
258Q8—81no—
259Q8—81no—
260Q8—81no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4#135×C12711yescharacteristic
287C2×C4#137×C12711yescharacteristic
288C8—81no—
289C8—81no—
290C8—81no—
291C22—21no—
292C22—21no—
293C22#452×C12711yescharacteristic
294C22#455×C12711yescharacteristic
295C22B(4,𝔽2)×C12711yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—81no—
307C4—81no—
308C2—21no—
309C2—21no—
310C2C127×#160611yescharacteristic
311C2C127×#220111yescharacteristic
312C2C127×#220311yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC23×C127#120
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
151. #12277C127direct (N × H)
164. C127#12277direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28332
C127×#20282
C127×#16172
C127×#16112
C127×#13532
C127×#13462
C127×#13192
#12277127