Finite Group Databasebeta

← C127×#10499 #44574172

Subgroups — C127×#10499 #44574172

Order 32512.

326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3236C211yesmaximal, characteristic
2C127×#1998C211yesmaximal, characteristic
3C127×#1569C211yesmaximal, characteristic
4C127×#1559C211yesmaximal, characteristic
5C127×#1528C211yesmaximal, characteristic
6C127×#1526C211yesmaximal, characteristic
7C127×#1291C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×#125×C127C2211yescharacteristic
10#501×C127—21no—
11#491×C127—21no—
12#484×C127—21no—
13#483×C127—21no—
14#479×C127—21no—
15#479×C127—21no—
16#432×C127C2211yescharacteristic
17#432×C127C2211yescharacteristic
18#423×C127C2211yescharacteristic
19C4×M16×C127C2211yescharacteristic
20C4×M16×C127C2211yescharacteristic
21#343×C127—21no—
22#343×C127—21no—
23#335×C127—21no—
24#334×C127—21no—
25#333×C127—21no—
26#332×C127—21no—
27#330×C127—21no—
28#330×C127—21no—
29#330×C127—21no—
30#330×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C2×M16×C127—21no—
34C4⋊Q8×C127D411yescharacteristic
35C4⋊Q8×C127D411yescharacteristic
36#125×C127—21no—
37#125×C127—21no—
38#125×C127—21no—
39#125×C127—21no—
40#125×C127—21no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43C4×Q8×C127—21no—
44C4×Q8×C127—21no—
45#117×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C4⋊C4×C127D411yescharacteristic
50C2×C42×C127C2311yescharacteristic
51#107×C127—21no—
52#107×C127—21no—
53#106×C127—21no—
54#106×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127D411yescharacteristic
59C4⋊C8×C127D411yescharacteristic
60#103×C127—21no—
61#103×C127—21no—
62#103×C127—21no—
63#103×C127—21no—
64C22⋊C8×C127—21no—
65C22⋊C8×C127—21no—
66#97×C127—21no—
67#97×C127—21no—
68#97×C127—21no—
69#97×C127D411yescharacteristic
70#97×C127D411yescharacteristic
71C4×C8×C127—21no—
72C4×C8×C127—21no—
73C2×Q8×C127—21no—
74C2×Q8×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127#4111yescharacteristic
79C22×C4×C127#4111yescharacteristic
80M16×C127—22no—
81M16×C127—42no—
82M16×C127—41no—
83M16×C127—42no—
84C2×C8×C127—21no—
85C2×C8×C127—21no—
86C2×C8×C127—21no—
87C2×C8×C127—21no—
88C2×C8×C127—41no—
89C2×C8×C127—41no—
90C2×C8×C127—41no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127—41no—
105C22⋊C4×C127—41no—
106C42×C127—41no—
107C42×C127C2×D411yescharacteristic
108C42×C127C2×D411yescharacteristic
109C42×C127C2×D411yescharacteristic
110C42×C127#4111yescharacteristic
111C23×C127#12311yescharacteristic
112Q8×C127—41no—
113Q8×C127—41no—
114Q8×C127—81no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
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—81no—
124C2×C4×C127—81no—
125C2×C4×C127#12011yescharacteristic
126C2×C4×C127#12111yescharacteristic
127C2×C4×C127#12111yescharacteristic
128C2×C4×C127#12111yescharacteristic
129C2×C4×C127#12311yescharacteristic
130C2×C4×C127#12411yescharacteristic
131C8×C127—22no—
132C8×C127—41no—
133C8×C127—42no—
134C8×C127—41no—
135C8×C127—41no—
136C8×C127—81no—
137C8×C127—81no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127#39411yescharacteristic
142C4×C127—21no—
143C4×C127—21no—
144C4×C127—21no—
145C4×C127—21no—
146C4×C127—21no—
147C4×C127—81no—
148C4×C127—81no—
149C4×C127—81no—
150C4×C127—81no—
151C4×C127#45411yescharacteristic
152C4×C127#45611yescharacteristic
153#10499C12711yesmaximal, characteristic, direct product factor, Sylow
154C2×C127—41no—
155C2×C127#203811yescharacteristic
156C2×C127#204911yescharacteristic
157C2×C127#205011yescharacteristic
158#3236C2×C12711yescharacteristic
159#1998C2×C12711yescharacteristic
160#1569C2×C12711yescharacteristic
161#1559C2×C12711yescharacteristic
162#1528C2×C12711yescharacteristic
163#1526C2×C12711yescharacteristic
164#1291C2×C12711yescharacteristic
165C127#1049911yescharacteristic, direct product factor, Sylow
166#533C22×C12711yescharacteristic
167C2×#125C22×C12711yescharacteristic
168#501—21no—
169#491—21no—
170#484—21no—
171#483—21no—
172#479—21no—
173#479—21no—
174#432C22×C12711yescharacteristic
175#432C22×C12711yescharacteristic
176#423C22×C12711yescharacteristic
177C4×M16C22×C12711yescharacteristic
178C4×M16C22×C12711yescharacteristic
179#343—21no—
180#343—21no—
181#335—21no—
182#334—21no—
183#333—21no—
184#332—21no—
185#330—21no—
186#330—21no—
187#330—21no—
188#330—21no—
189C2×M16—21no—
190C2×M16—21no—
191C2×M16—21no—
192C4⋊Q8D4×C12711yescharacteristic
193C4⋊Q8D4×C12711yescharacteristic
194#125—21no—
195#125—21no—
196#125—21no—
197#125—21no—
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203#117—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4D4×C12711yescharacteristic
207C2×C4⋊C4D4×C12711yescharacteristic
208C2×C42C23×C12711yescharacteristic
209#107—21no—
210#107—21no—
211#106—21no—
212#106—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8D4×C12711yescharacteristic
217C4⋊C8D4×C12711yescharacteristic
218#103—21no—
219#103—21no—
220#103—21no—
221#103—21no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224#97—21no—
225#97—21no—
226#97—21no—
227#97D4×C12711yescharacteristic
228#97D4×C12711yescharacteristic
229C4×C8—21no—
230C4×C8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C2×D4×C12711yescharacteristic
236C22×C4#41×C12711yescharacteristic
237C22×C4#41×C12711yescharacteristic
238M16—22no—
239M16—42no—
240M16—41no—
241M16—42no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C22⋊C4—41no—
264C42—41no—
265C42C2×D4×C12711yescharacteristic
266C42C2×D4×C12711yescharacteristic
267C42C2×D4×C12711yescharacteristic
268C42#41×C12711yescharacteristic
269C23#123×C12711yescharacteristic
270Q8—41no—
271Q8—41no—
272Q8—81no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4#120×C12711yescharacteristic
284C2×C4#121×C12711yescharacteristic
285C2×C4#121×C12711yescharacteristic
286C2×C4#121×C12711yescharacteristic
287C2×C4#123×C12711yescharacteristic
288C2×C4#124×C12711yescharacteristic
289C8—22no—
290C8—41no—
291C8—42no—
292C8—41no—
293C8—41no—
294C8—81no—
295C8—81no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22#394×C12711yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—81no—
309C4#454×C12711yescharacteristic
310C4#456×C12711yescharacteristic
311C2—41no—
312C2C127×#203811yescharacteristic
313C2C127×#204911yescharacteristic
314C2C127×#205011yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
153. #10499C127direct (N × H)
165. C127#10499direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32362
C127×#19982
C127×#15692
C127×#15592
C127×#15282
C127×#15262
C127×#12912
#10499127