Finite Group Databasebeta

← C127×#12236 #44575909

Subgroups — C127×#12236 #44575909

Order 32512.

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

normal subgroups only

This group has 324 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
2C127×#2060C211yesmaximal, characteristic
3C127×#1617C211yesmaximal, characteristic
4C127×#1611C211yesmaximal, characteristic
5C127×#1353C211yesmaximal, characteristic
6C127×#1346C211yesmaximal, characteristic
7C127×#1325C211yesmaximal, characteristic
8#544×C127C2211yescharacteristic
9#484×C127—21no—
10#483×C127—21no—
11#428×C127—21no—
12#400×C127—21no—
13#400×C127—21no—
14#400×C127C2211yescharacteristic
15#398×C127C2211yescharacteristic
16#387×C127—21no—
17#387×C127—21no—
18#387×C127—21no—
19#387×C127—21no—
20#384×C127C2211yescharacteristic
21#343×C127C2211yescharacteristic
22#339×C127—21no—
23#328×C127—21no—
24#328×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C2×M16×C127—21no—
28C4⋊Q8×C127—41no—
29#125×C127—41no—
30C22⋊Q8×C127—21no—
31C22⋊Q8×C127—21no—
32#117×C127—21no—
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#107×C127—41no—
45#106×C127—41no—
46#106×C127—41no—
47#103×C127—41no—
48#103×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×C127D411yescharacteristic
61#95×C127D411yescharacteristic
62C2×Q8×C127—21no—
63C2×Q8×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73M16×C127—22no—
74M16×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—41no—
77C2×C8×C127—41no—
78C4⋊C4×C127—21no—
79C4⋊C4×C127—21no—
80C4⋊C4×C127—21no—
81C4⋊C4×C127—21no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—41no—
97C42×C127—81no—
98C23×C127#12011yescharacteristic
99Q8×C127—81no—
100Q8×C127—81no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—22no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
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#13511yescharacteristic
127C2×C4×C127#13711yescharacteristic
128C8×C127—42no—
129C8×C127—81no—
130C8×C127—81no—
131C22×C127—21no—
132C22×C127—21no—
133C22×C127#45211yescharacteristic
134C22×C127#45611yescharacteristic
135C22×C127B(4,𝔽2)11yescharacteristic
136C4×C127—21no—
137C4×C127—21no—
138C4×C127—42no—
139C4×C127—41no—
140C4×C127—41no—
141C4×C127—81no—
142C4×C127—81no—
143C4×C127—81no—
144C4×C127—81no—
145C4×C127—81no—
146C4×C127—81no—
147C4×C127—81no—
148#12236C12711yesmaximal, characteristic, direct product factor, Sylow
149C2×C127—21no—
150C2×C127—21no—
151C2×C127#160311yescharacteristic
152C2×C127#219811yescharacteristic
153C2×C127#220311yescharacteristic
154#2794C2×C12711yescharacteristic
155#2060C2×C12711yescharacteristic
156#1617C2×C12711yescharacteristic
157#1611C2×C12711yescharacteristic
158#1353C2×C12711yescharacteristic
159#1346C2×C12711yescharacteristic
160#1325C2×C12711yescharacteristic
161C127#1223611yescharacteristic, direct product factor, Sylow
162#544C22×C12711yescharacteristic
163#484—21no—
164#483—21no—
165#428—21no—
166#400—21no—
167#400—21no—
168#400C22×C12711yescharacteristic
169#398C22×C12711yescharacteristic
170#387—21no—
171#387—21no—
172#387—21no—
173#387—21no—
174#384C22×C12711yescharacteristic
175#343C22×C12711yescharacteristic
176#339—21no—
177#328—21no—
178#328—21no—
179#324C22×C12711yescharacteristic
180#324C22×C12711yescharacteristic
181C2×M16—21no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4D4×C12711yescharacteristic
192C2×C4⋊C4D4×C12711yescharacteristic
193C2×C4⋊C4D4×C12711yescharacteristic
194C2×C4⋊C4C23×C12711yescharacteristic
195C2×C42—21no—
196C2×C42D4×C12711yescharacteristic
197#107—41no—
198#107—41no—
199#106—41no—
200#106—41no—
201#103—41no—
202#103—41no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95D4×C12711yescharacteristic
215#95D4×C12711yescharacteristic
216C2×Q8—21no—
217C2×Q8—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4C2×D4×C12711yescharacteristic
225C22×C4C2×D4×C12711yescharacteristic
226C22×C4C2×D4×C12711yescharacteristic
227M16—22no—
228M16—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C22⋊C4—41no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—81no—
252C23#120×C12711yescharacteristic
253Q8—81no—
254Q8—81no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4#135×C12711yescharacteristic
281C2×C4#137×C12711yescharacteristic
282C8—42no—
283C8—81no—
284C8—81no—
285C22—21no—
286C22—21no—
287C22#452×C12711yescharacteristic
288C22#456×C12711yescharacteristic
289C22B(4,𝔽2)×C12711yescharacteristic
290C4—21no—
291C4—21no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C2—21no—
303C2—21no—
304C2C127×#160311yescharacteristic
305C2C127×#219811yescharacteristic
306C2C127×#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
148. #12236C127direct (N × H)
161. C127#12236direct (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×#20602
C127×#16172
C127×#16112
C127×#13532
C127×#13462
C127×#13252
#12236127