Finite Group Databasebeta

← C127×#10325 #44573998

Subgroups — C127×#10325 #44573998

Order 32512.

602 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3189C211yesmaximal, characteristic
2C127×#2855C212yesmaximal
3C127×#1817C211yesmaximal, characteristic
4C127×#1520C212yesmaximal
5C127×#1289C211yesmaximal, characteristic
6C2×C22⋊Q8×C127C2212yes—
7C22×C42×C127C2211yescharacteristic
8#484×C127—22no—
9#467×C127—22no—
10#451×C127—22no—
11C2×C22⋊C8×C127C2211yescharacteristic
12C2×C22⋊C8×C127C2211yescharacteristic
13#391×C127—22no—
14#389×C127—22no—
15#387×C127—24no—
16#385×C127—22no—
17#381×C127—22no—
18#380×C127C2212yes—
19#336×C127—22no—
20#328×C127—24no—
21C22×Q8×C127D412yes—
22C23×C4×C127D411yescharacteristic
23C23×C4×C127D411yescharacteristic
24C23×C4×C127C2311yescharacteristic
25C2×Q16×C127—22no—
26C22×C8×C127—21no—
27C22×C8×C127D412yes—
28C22⋊Q8×C127—22no—
29C22⋊Q8×C127—22no—
30C22⋊Q8×C127—22no—
31C22⋊Q8×C127—22no—
32C2×C4⋊C4×C127—24no—
33C2×C4⋊C4×C127—22no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127D412yes—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—22no—
38C2×C42×C127—21no—
39C2×C42×C127—22no—
40C2×C42×C127—22no—
41C2×C42×C127—21no—
42#107×C127—22no—
43#103×C127—24no—
44C22⋊C8×C127—22no—
45C22⋊C8×C127—22no—
46#95×C127—24no—
47#95×C127—24no—
48#95×C127—24no—
49#95×C127D414yes—
50C24×C127C2×D411yescharacteristic
51C2×Q8×C127—22no—
52C2×Q8×C127—22no—
53C2×Q8×C127—44no—
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127—21no—
57C22×C4×C127—21no—
58C22×C4×C127—21no—
59C22×C4×C127—22no—
60C22×C4×C127—22no—
61C22×C4×C127—24no—
62C22×C4×C127—22no—
63C22×C4×C127—42no—
64C22×C4×C127—42no—
65C22×C4×C127Q1612yescomplemented
66C22×C4×C127C2×D412yes—
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127C2×D412yes—
69C22×C4×C127#4111yescharacteristic
70Q16×C127—82no—
71C2×C8×C127—22no—
72C2×C8×C127—42no—
73C2×C8×C127—42no—
74C2×C8×C127—41no—
75C4⋊C4×C127—22no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—44no—
78C4⋊C4×C127—48no—
79C4⋊C4×C127—42no—
80C4⋊C4×C127—42no—
81C22⋊C4×C127—42no—
82C22⋊C4×C127—42no—
83C22⋊C4×C127—42no—
84C22⋊C4×C127—42no—
85C42×C127—41no—
86C42×C127—42no—
87C42×C127—41no—
88C23×C127—41no—
89C23×C127—41no—
90C23×C127#12012yes—
91C23×C127#12111yescharacteristic
92C23×C127C2×Q1611yescharacteristic
93C23×C127#13511yescharacteristic
94C23×C127#13712yes—
95Q8×C127—44no—
96Q8×C127—82no—
97C2×C4×C127—24no—
98C2×C4×C127—22no—
99C2×C4×C127—24no—
100C2×C4×C127—22no—
101C2×C4×C127—24no—
102C2×C4×C127—22no—
103C2×C4×C127—42no—
104C2×C4×C127—41no—
105C2×C4×C127—42no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—42no—
110C2×C4×C127—41no—
111C2×C4×C127—44no—
112C2×C4×C127—44no—
113C2×C4×C127—44no—
114C2×C4×C127—44no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127—44no—
118C2×C4×C127#12011yescharacteristic
119C2×C4×C127#12112yes—
120C2×C4×C127#12711yescharacteristic
121C8×C127—42no—
122C8×C127—81no—
123C22×C127—22no—
124C22×C127—21no—
125C22×C127—22no—
126C22×C127—21no—
127C22×C127—41no—
128C22×C127—41no—
129C22×C127—42no—
130C22×C127#39211yescharacteristic
131C22×C127#45112yes—
132C22×C127#45212yes—
133C22×C127#46711yescharacteristic
134C22×C127#47011yescharacteristic
135C4×C127—21no—
136C4×C127—22no—
137C4×C127—42no—
138C4×C127—42no—
139C4×C127—84no—
140C4×C127—82no—
141C4×C127—82no—
142C4×C127#45812yes—
143#10325C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127—22no—
145C2×C127—22no—
146C2×C127—21no—
147C2×C127—21no—
148C2×C127#200111yescharacteristic
149C2×C127#201011yescharacteristic
150C2×C127#202211yescharacteristic
151#3189C2×C12711yescharacteristic
152#2855C2×C12712yes—
153#1817C2×C12711yescharacteristic
154#1520C2×C12712yes—
155#1289C2×C12711yescharacteristic
156C127#1032511yescharacteristic, direct product factor, Sylow
157C2×C22⋊Q8C22×C12712yes—
158C22×C42C22×C12711yescharacteristic
159#484—22no—
160#467—22no—
161#451—22no—
162C2×C22⋊C8C22×C12711yescharacteristic
163C2×C22⋊C8C22×C12711yescharacteristic
164#391—22no—
165#389—22no—
166#387—24no—
167#385—22no—
168#381—22no—
169#380C22×C12712yes—
170#336—22no—
171#328—24no—
172C22×Q8D4×C12712yes—
173C23×C4D4×C12711yescharacteristic
174C23×C4D4×C12711yescharacteristic
175C23×C4C23×C12711yescharacteristic
176C2×Q16—22no—
177C22×C8—21no—
178C22×C8D4×C12712yes—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4D4×C12712yes—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—21no—
193#107—22no—
194#103—24no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197#95—24no—
198#95—24no—
199#95—24no—
200#95D4×C12714yes—
201C24C2×D4×C12711yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4Q16×C12712yescomplemented
217C22×C4C2×D4×C12712yes—
218C22×C4C2×D4×C12711yescharacteristic
219C22×C4C2×D4×C12712yes—
220C22×C4#41×C12711yescharacteristic
221Q16—82no—
222C2×C8—22no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—41no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—44no—
229C4⋊C4—48no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C42—41no—
237C42—42no—
238C42—41no—
239C23—41no—
240C23—41no—
241C23#120×C12712yes—
242C23#121×C12711yescharacteristic
243C23C2×Q16×C12711yescharacteristic
244C23#135×C12711yescharacteristic
245C23#137×C12712yes—
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4#120×C12711yescharacteristic
270C2×C4#121×C12712yes—
271C2×C4#127×C12711yescharacteristic
272C8—42no—
273C8—81no—
274C22—22no—
275C22—21no—
276C22—22no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22#392×C12711yescharacteristic
282C22#451×C12712yes—
283C22#452×C12712yes—
284C22#467×C12711yescharacteristic
285C22#470×C12711yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—84no—
291C4—82no—
292C4—82no—
293C4#458×C12712yes—
294C2—22no—
295C2—22no—
296C2—21no—
297C2—21no—
298C2C127×#200111yescharacteristic
299C2C127×#201011yescharacteristic
300C2C127×#202211yescharacteristic
subgroupG/H
center, socleC22×C127#392
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
65. C22×C4×C127Q16semidirect
143. #10325C127direct (N × H)
156. C127#10325direct (N × H)
216. C22×C4Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31892
C127×#28552
C127×#18172
C127×#15202
C127×#12892
#10325127