Finite Group Databasebeta

← C127×#10346 #44574019

Subgroups — C127×#10346 #44574019

Order 32512.

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

normal subgroups only

This group has 500 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×#2646C211yesmaximal, characteristic
2C127×#1823C212yesmaximal
3C127×#1445C211yesmaximal, characteristic
4C127×#1294C212yesmaximal
5C127×#1280C211yesmaximal, characteristic
6C22×C4⋊C4×C127C2211yescharacteristic
7C2×C22⋊C8×C127C2212yes—
8#400×C127—22no—
9#398×C127—22no—
10#385×C127—22no—
11#380×C127C2212yes—
12C2×#95×C127—22no—
13C2×#95×C127C2211yescharacteristic
14C2×#95×C127C2211yescharacteristic
15#340×C127—22no—
16#340×C127—22no—
17C23×C4×C127—21no—
18C23×C4×C127—21no—
19C23×C4×C127D412yes—
20C23×C4×C127C2311yescharacteristic
21C22×C8×C127—22no—
22C2×C4⋊C4×C127—22no—
23C2×C4⋊C4×C127—22no—
24C2×C4⋊C4×C127—21no—
25C2×C4⋊C4×C127—22no—
26C2×C4⋊C4×C127—22no—
27C2×C4⋊C4×C127D412yes—
28C2×C4⋊C4×C127D412yes—
29C2×C4⋊C4×C127Q812yes—
30C2×C22⋊C4×C127—22no—
31C22⋊C8×C127—22no—
32C22⋊C8×C127—22no—
33#95×C127—22no—
34#95×C127—22no—
35#95×C127—22no—
36#95×C127—22no—
37#95×C127—22no—
38#95×C127—44no—
39C24×C127C2×D411yescharacteristic
40C22×C4×C127—22no—
41C22×C4×C127—22no—
42C22×C4×C127—22no—
43C22×C4×C127—22no—
44C22×C4×C127—22no—
45C22×C4×C127—22no—
46C22×C4×C127—22no—
47C22×C4×C127—42no—
48C22×C4×C127—42no—
49C22×C4×C127—42no—
50C22×C4×C127—41no—
51C22×C4×C127—42no—
52C22×C4×C127—41no—
53C22×C4×C127—41no—
54C22×C4×C127—41no—
55C22×C4×C127—42no—
56C22×C4×C127—42no—
57C22×C4×C127—42no—
58C22×C4×C127C2×D412yes—
59C22×C4×C127C2×Q811yescharacteristic
60C22×C4×C127#4112yes—
61C22×C4×C127#4111yescharacteristic
62C2×C8×C127—42no—
63C2×C8×C127—42no—
64C2×C8×C127—42no—
65C4⋊C4×C127—24no—
66C4⋊C4×C127—42no—
67C4⋊C4×C127—42no—
68C4⋊C4×C127—42no—
69C4⋊C4×C127—82no—
70C4⋊C4×C127—82no—
71C22⋊C4×C127—42no—
72C22⋊C4×C127—42no—
73C23×C127—21no—
74C23×C127—21no—
75C23×C127—22no—
76C23×C127#12011yescharacteristic
77C23×C127C22⋊Q811yescharacteristic
78C23×C127#12411yescharacteristic
79C23×C127#13512yes—
80C23×C127AGL(1,ℤ/8)12yes—
81C2×C4×C127—22no—
82C2×C4×C127—22no—
83C2×C4×C127—41no—
84C2×C4×C127—41no—
85C2×C4×C127—42no—
86C2×C4×C127—44no—
87C2×C4×C127—42no—
88C2×C4×C127—44no—
89C2×C4×C127—42no—
90C2×C4×C127—42no—
91C2×C4×C127—42no—
92C2×C4×C127—42no—
93C2×C4×C127—42no—
94C2×C4×C127—42no—
95C2×C4×C127—42no—
96C2×C4×C127—42no—
97C2×C4×C127—42no—
98C2×C4×C127—42no—
99C2×C4×C127—44no—
100C2×C4×C127—82no—
101C2×C4×C127—81no—
102C2×C4×C127—82no—
103C2×C4×C127—81no—
104C2×C4×C127—81no—
105C2×C4×C127—81no—
106C2×C4×C127—82no—
107C2×C4×C127C22⋊Q812yes—
108C2×C4×C127#12412yes—
109C8×C127—82no—
110C22×C127—22no—
111C22×C127—22no—
112C22×C127—22no—
113C22×C127—22no—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127—21no—
117C22×C127—21no—
118C22×C127#39311yescharacteristic
119C22×C127#44912yes—
120C22×C127#45511yescharacteristic
121C22×C127#45611yescharacteristic
122C22×C127#45812yes—
123C22×C127#47812yes—
124C22×C127#48811yescharacteristic
125C22×C127#49011yescharacteristic
126C4×C127—22no—
127C4×C127—22no—
128C4×C127—82no—
129C4×C127—82no—
130C4×C127—82no—
131C4×C127—82no—
132C4×C127—82no—
133#10346C12711yesmaximal, characteristic, direct product factor, Sylow
134C2×C127—21no—
135C2×C127—22no—
136C2×C127—21no—
137C2×C127#160912yes—
138C2×C127#161212yes—
139C2×C127#202511yescharacteristic
140C2×C127#202811yescharacteristic
141C2×C127#203011yescharacteristic
142#2646C2×C12711yescharacteristic
143#1823C2×C12712yes—
144#1445C2×C12711yescharacteristic
145#1294C2×C12712yes—
146#1280C2×C12711yescharacteristic
147C127#1034611yescharacteristic, direct product factor, Sylow
148C22×C4⋊C4C22×C12711yescharacteristic
149C2×C22⋊C8C22×C12712yes—
150#400—22no—
151#398—22no—
152#385—22no—
153#380C22×C12712yes—
154C2×#95—22no—
155C2×#95C22×C12711yescharacteristic
156C2×#95C22×C12711yescharacteristic
157#340—22no—
158#340—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4D4×C12712yes—
162C23×C4C23×C12711yescharacteristic
163C22×C8—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4D4×C12712yes—
170C2×C4⋊C4D4×C12712yes—
171C2×C4⋊C4Q8×C12712yes—
172C2×C22⋊C4—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—44no—
181C24C2×D4×C12711yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—41no—
193C22×C4—42no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4C2×D4×C12712yes—
201C22×C4C2×Q8×C12711yescharacteristic
202C22×C4#41×C12712yes—
203C22×C4#41×C12711yescharacteristic
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C4⋊C4—24no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#120×C12711yescharacteristic
219C23C22⋊Q8×C12711yescharacteristic
220C23#124×C12711yescharacteristic
221C23#135×C12712yes—
222C23AGL(1,ℤ/8)×C12712yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4C22⋊Q8×C12712yes—
250C2×C4#124×C12712yes—
251C8—82no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#393×C12711yescharacteristic
261C22#449×C12712yes—
262C22#455×C12711yescharacteristic
263C22#456×C12711yescharacteristic
264C22#458×C12712yes—
265C22#478×C12712yes—
266C22#488×C12711yescharacteristic
267C22#490×C12711yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—82no—
274C4—82no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2C127×#160912yes—
279C2C127×#161212yes—
280C2C127×#202511yescharacteristic
281C2C127×#202811yescharacteristic
282C2C127×#203011yescharacteristic
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
133. #10346C127direct (N × H)
147. C127#10346direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26462
C127×#18232
C127×#14452
C127×#12942
C127×#12802
#10346127