Finite Group Databasebeta

← C127×#9973 #44573646

Subgroups — C127×#9973 #44573646

Order 32512.

632 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×#483×C127C212yesmaximal
2C127×#2659C211yesmaximal, characteristic
3C2×#328×C127C212yesmaximal
4C127×#1445C211yesmaximal, characteristic
5C127×#1280C211yesmaximal, characteristic
6C2×C22⋊Q8×C127C2212yes—
7C22×C4⋊C4×C127C2211yescharacteristic
8#483×C127—24no—
9#483×C127—24no—
10C2×#106×C127—22no—
11C2×#103×C127—22no—
12C2×C22⋊C8×C127C2212yes—
13#398×C127—22no—
14#395×C127—22no—
15#380×C127—22no—
16C2×#95×C127—22no—
17C2×#95×C127C2211yescharacteristic
18C2×#95×C127C2211yescharacteristic
19#328×C127—24no—
20C22×Q8×C127D412yes—
21C23×C4×C127—21no—
22C23×C4×C127—21no—
23C23×C4×C127D412yes—
24C23×C4×C127C2311yescharacteristic
25C22×C8×C127—22no—
26C22⋊Q8×C127—22no—
27C22⋊Q8×C127—22no—
28C22⋊Q8×C127—22no—
29C22⋊Q8×C127—22no—
30C2×C4⋊C4×C127—22no—
31C2×C4⋊C4×C127—22no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127D412yes—
37C2×C4⋊C4×C127D412yes—
38C2×C22⋊C4×C127—22no—
39#106×C127—28no—
40#103×C127—28no—
41C22⋊C8×C127—22no—
42C22⋊C8×C127D414yes—
43#95×C127—24no—
44#95×C127—22no—
45#95×C127—22no—
46#95×C127—44no—
47C24×C127C2×D411yescharacteristic
48C2×Q8×C127—22no—
49C2×Q8×C127—22no—
50C2×Q8×C127—44no—
51C22×C4×C127—22no—
52C22×C4×C127—22no—
53C22×C4×C127—22no—
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127—22no—
57C22×C4×C127—42no—
58C22×C4×C127—42no—
59C22×C4×C127—42no—
60C22×C4×C127—41no—
61C22×C4×C127—42no—
62C22×C4×C127—41no—
63C22×C4×C127—41no—
64C22×C4×C127—41no—
65C22×C4×C127—42no—
66C22×C4×C127—42no—
67C22×C4×C127—42no—
68C22×C4×C127SD1614yes—
69C22×C4×C127C2×D412yes—
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D412yes—
72C22×C4×C127#4111yescharacteristic
73C2×C8×C127—24no—
74C2×C8×C127—44no—
75C4⋊C4×C127—24no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—22no—
78C4⋊C4×C127—42no—
79C4⋊C4×C127—42no—
80C4⋊C4×C127—42no—
81C4⋊C4×C127—82no—
82C4⋊C4×C127—82no—
83C22⋊C4×C127—42no—
84C22⋊C4×C127—42no—
85C23×C127—21no—
86C23×C127—21no—
87C23×C127—22no—
88C23×C127#12011yescharacteristic
89C23×C127#12111yescharacteristic
90C23×C127#12711yescharacteristic
91C23×C127C2×SD1612yes—
92C23×C127#13712yes—
93Q8×C127—44no—
94Q8×C127—82no—
95C2×C4×C127—24no—
96C2×C4×C127—24no—
97C2×C4×C127—41no—
98C2×C4×C127—42no—
99C2×C4×C127—41no—
100C2×C4×C127—42no—
101C2×C4×C127—42no—
102C2×C4×C127—44no—
103C2×C4×C127—44no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127—42no—
107C2×C4×C127—42no—
108C2×C4×C127—42no—
109C2×C4×C127—42no—
110C2×C4×C127—44no—
111C2×C4×C127—44no—
112C2×C4×C127—82no—
113C2×C4×C127—82no—
114C2×C4×C127—81no—
115C2×C4×C127—82no—
116C2×C4×C127—81no—
117C2×C4×C127—81no—
118C2×C4×C127—81no—
119C2×C4×C127#12012yes—
120C2×C4×C127#12112yes—
121C8×C127—44no—
122C22×C127—22no—
123C22×C127—22no—
124C22×C127—22no—
125C22×C127—22no—
126C22×C127—21no—
127C22×C127—21no—
128C22×C127—21no—
129C22×C127—21no—
130C22×C127#39211yescharacteristic
131C22×C127#44812yes—
132C22×C127#45511yescharacteristic
133C22×C127#45611yescharacteristic
134C22×C127#45812yes—
135C22×C127#46112yes—
136C22×C127#49211yescharacteristic
137C22×C127#49711yescharacteristic
138C4×C127—22no—
139C4×C127—22no—
140C4×C127—44no—
141C4×C127—82no—
142C4×C127—82no—
143C4×C127—82no—
144C4×C127—82no—
145#9973C12711yesmaximal, characteristic, direct product factor, Sylow
146C2×C127—21no—
147C2×C127—22no—
148C2×C127—21no—
149C2×C127#160812yes—
150C2×C127#161112yes—
151C2×C127#200711yescharacteristic
152C2×C127#201311yescharacteristic
153C2×C127#202211yescharacteristic
154C2×#483C2×C12712yes—
155#2659C2×C12711yescharacteristic
156C2×#328C2×C12712yes—
157#1445C2×C12711yescharacteristic
158#1280C2×C12711yescharacteristic
159C127#997311yescharacteristic, direct product factor, Sylow
160C2×C22⋊Q8C22×C12712yes—
161C22×C4⋊C4C22×C12711yescharacteristic
162#483—24no—
163#483—24no—
164C2×#106—22no—
165C2×#103—22no—
166C2×C22⋊C8C22×C12712yes—
167#398—22no—
168#395—22no—
169#380—22no—
170C2×#95—22no—
171C2×#95C22×C12711yescharacteristic
172C2×#95C22×C12711yescharacteristic
173#328—24no—
174C22×Q8D4×C12712yes—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4D4×C12712yes—
178C23×C4C23×C12711yescharacteristic
179C22×C8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4D4×C12712yes—
191C2×C4⋊C4D4×C12712yes—
192C2×C22⋊C4—22no—
193#106—28no—
194#103—28no—
195C22⋊C8—22no—
196C22⋊C8D4×C12714yes—
197#95—24no—
198#95—22no—
199#95—22no—
200#95—44no—
201C24C2×D4×C12711yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4SD16×C12714yes—
223C22×C4C2×D4×C12712yes—
224C22×C4C2×D4×C12711yescharacteristic
225C22×C4C2×D4×C12712yes—
226C22×C4#41×C12711yescharacteristic
227C2×C8—24no—
228C2×C8—44no—
229C4⋊C4—24no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#120×C12711yescharacteristic
243C23#121×C12711yescharacteristic
244C23#127×C12711yescharacteristic
245C23C2×SD16×C12712yes—
246C23#137×C12712yes—
247Q8—44no—
248Q8—82no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4#120×C12712yes—
274C2×C4#121×C12712yes—
275C8—44no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22#392×C12711yescharacteristic
285C22#448×C12712yes—
286C22#455×C12711yescharacteristic
287C22#456×C12711yescharacteristic
288C22#458×C12712yes—
289C22#461×C12712yes—
290C22#492×C12711yescharacteristic
291C22#497×C12711yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—82no—
298C4—82no—
299C2—21no—
300C2—21no—
301C2—22no—
302C2C127×#160812yes—
303C2C127×#161112yes—
304C2C127×#200711yescharacteristic
305C2C127×#201311yescharacteristic
306C2C127×#202211yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
145. #9973C127direct (N × H)
159. C127#9973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#483×C1272
C127×#26592
C2×#328×C1272
C127×#14452
C127×#12802
#9973127