Finite Group Databasebeta

← C127×#13461 #44577134

Subgroups — C127×#13461 #44577134

Order 32512.

540 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2683C211yesmaximal, characteristic
2C127×#1867C212yesmaximal
3C127×#1856C211yesmaximal, characteristic
4C127×#1393C211yesmaximal, characteristic
5C127×#1390C212yesmaximal
6C2×C22⋊Q8×C127—22no—
7#518×C127C2211yescharacteristic
8#428×C127—21no—
9C2×#100×C127C2211yescharacteristic
10C2×#99×C127C2212yes—
11#396×C127—22no—
12#395×C127—21no—
13#390×C127C2211yescharacteristic
14#389×C127—21no—
15#386×C127C2212yes—
16#385×C127—22no—
17#342×C127—22no—
18#339×C127—21no—
19C22×Q8×C127—21no—
20C22×D4×C127C2311yescharacteristic
21C23×C4×C127D412yes—
22C2×M16×C127—21no—
23C22⋊Q8×C127—48no—
24C4×D4×C127—41no—
25C4×D4×C127—41no—
26#117×C127—21no—
27C2×C4⋊C4×C127—21no—
28C2×C4⋊C4×C127—22no—
29C2×C4⋊C4×C127—22no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—42no—
32C2×C4⋊C4×C127D411yescharacteristic
33C2×C22⋊C4×C127—22no—
34C2×C22⋊C4×C127—22no—
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127D412yes—
38C2×C42×C127D411yescharacteristic
39#107×C127—41no—
40#106×C127—41no—
41#100×C127—21no—
42#100×C127Q812yescomplemented
43#99×C127—22no—
44#99×C127Q814yescomplemented
45#95×C127—21no—
46#95×C127—22no—
47#95×C127—42no—
48C24×C127C2×D412yes—
49C2×Q8×C127—44no—
50C2×Q8×C127—81no—
51C2×D4×C127—41no—
52C2×D4×C127—41no—
53C2×D4×C127C2×Q811yescharacteristic
54C2×D4×C127C2×Q812yes—
55C2×D4×C127#4111yescharacteristic
56C22×C4×C127—22no—
57C22×C4×C127—21no—
58C22×C4×C127—22no—
59C22×C4×C127—21no—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127—44no—
63C22×C4×C127—42no—
64C22×C4×C127—42no—
65C22×C4×C127C2×D411yescharacteristic
66M16×C127—22no—
67M16×C127—41no—
68C2×C8×C127—41no—
69C4⋊C4×C127—24no—
70C4⋊C4×C127—21no—
71C4⋊C4×C127—21no—
72C4⋊C4×C127—41no—
73C4⋊C4×C127—44no—
74C4⋊C4×C127—44no—
75C4⋊C4×C127—81no—
76C4⋊C4×C127—84no—
77C22⋊C4×C127—24no—
78C22⋊C4×C127—44no—
79C22⋊C4×C127—44no—
80C22⋊C4×C127—42no—
81C22⋊C4×C127—42no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—42no—
84C42×C127—41no—
85C42×C127—41no—
86C23×C127—22no—
87C23×C127—22no—
88C23×C127—42no—
89C23×C127—42no—
90C23×C127#12011yescharacteristic
91C23×C127C22⋊Q812yes—
92C23×C127C4⋊Q812yes—
93Q8×C127—84no—
94D4×C127—41no—
95D4×C127—42no—
96D4×C127—41no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—22no—
100C2×C4×C127—24no—
101C2×C4×C127—42no—
102C2×C4×C127—41no—
103C2×C4×C127—42no—
104C2×C4×C127—41no—
105C2×C4×C127—44no—
106C2×C4×C127—44no—
107C2×C4×C127—42no—
108C2×C4×C127—42no—
109C2×C4×C127—42no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—42no—
114C2×C4×C127—82no—
115C2×C4×C127—82no—
116C2×C4×C127—82no—
117C2×C4×C127—82no—
118C2×C4×C127—82no—
119C2×C4×C127C22⋊Q811yescharacteristic
120C2×C4×C127C4⋊Q811yescharacteristic
121C8×C127—42no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—22no—
125C22×C127—22no—
126C22×C127—42no—
127C22×C127—42no—
128C22×C127—42no—
129C22×C127—42no—
130C22×C127—82no—
131C22×C127#39511yescharacteristic
132C22×C127B(4,𝔽2)11yescharacteristic
133C22×C127#45811yescharacteristic
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—42no—
137C4×C127—44no—
138C4×C127—82no—
139C4×C127—84no—
140C4×C127—81no—
141C4×C127—81no—
142C4×C127—81no—
143#13461C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127—21no—
145C2×C127—21no—
146C2×C127—42no—
147C2×C127—42no—
148C2×C127#206211yescharacteristic
149C2×C127#219611yescharacteristic
150C2×C127#220111yescharacteristic
151#2683C2×C12711yescharacteristic
152#1867C2×C12712yes—
153#1856C2×C12711yescharacteristic
154#1393C2×C12711yescharacteristic
155#1390C2×C12712yes—
156C127#1346111yescharacteristic, direct product factor, Sylow
157C2×C22⋊Q8—22no—
158#518C22×C12711yescharacteristic
159#428—21no—
160C2×#100C22×C12711yescharacteristic
161C2×#99C22×C12712yes—
162#396—22no—
163#395—21no—
164#390C22×C12711yescharacteristic
165#389—21no—
166#386C22×C12712yes—
167#385—22no—
168#342—22no—
169#339—21no—
170C22×Q8—21no—
171C22×D4C23×C12711yescharacteristic
172C23×C4D4×C12712yes—
173C2×M16—21no—
174C22⋊Q8—48no—
175C4×D4—41no—
176C4×D4—41no—
177#117—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4D4×C12711yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4D4×C12712yes—
189C2×C42D4×C12711yescharacteristic
190#107—41no—
191#106—41no—
192#100—21no—
193#100Q8×C12712yescomplemented
194#99—22no—
195#99Q8×C12714yescomplemented
196#95—21no—
197#95—22no—
198#95—42no—
199C24C2×D4×C12712yes—
200C2×Q8—44no—
201C2×Q8—81no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4C2×Q8×C12711yescharacteristic
205C2×D4C2×Q8×C12712yes—
206C2×D4#41×C12711yescharacteristic
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—44no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4C2×D4×C12711yescharacteristic
217M16—22no—
218M16—41no—
219C2×C8—41no—
220C4⋊C4—24no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—44no—
225C4⋊C4—44no—
226C4⋊C4—81no—
227C4⋊C4—84no—
228C22⋊C4—24no—
229C22⋊C4—44no—
230C22⋊C4—44no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—41no—
234C22⋊C4—42no—
235C42—41no—
236C42—41no—
237C23—22no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23#120×C12711yescharacteristic
242C23C22⋊Q8×C12712yes—
243C23C4⋊Q8×C12712yes—
244Q8—84no—
245D4—41no—
246D4—42no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4C22⋊Q8×C12711yescharacteristic
271C2×C4C4⋊Q8×C12711yescharacteristic
272C8—42no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22#395×C12711yescharacteristic
283C22B(4,𝔽2)×C12711yescharacteristic
284C22#458×C12711yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—44no—
289C4—82no—
290C4—84no—
291C4—81no—
292C4—81no—
293C4—81no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2C127×#206211yescharacteristic
299C2C127×#219611yescharacteristic
300C2C127×#220111yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C127
prime radicalC22×D4×C127C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
42. #100×C127Q8semidirect
44. #99×C127Q8semidirect
143. #13461C127direct (N × H)
156. C127#13461direct (N × H)
193. #100Q8×C127semidirect
195. #99Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26832
C127×#18672
C127×#18562
C127×#13932
C127×#13902
#13461127