Finite Group Databasebeta

← C127×#11908 #44575581

Subgroups — C127×#11908 #44575581

Order 32512.

388 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2567C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic
3C127×#1461C211yesmaximal, characteristic
4C127×#1354C214yesmaximal
5C2×C4⋊Q8×C127C411yescharacteristic
6C2×C4×Q8×C127C2211yescharacteristic
7#431×C127—21no—
8#423×C127—21no—
9C2×#101×C127—21no—
10#395×C127C412yes—
11#395×C127C2212yes—
12#391×C127—21no—
13#389×C127—21no—
14#389×C127—21no—
15#384×C127—21no—
16C4×C4⋊C4×C127C411yescharacteristic
17#343×C127C2212yes—
18#324×C127—21no—
19#324×C127C2212yes—
20C22×Q8×C127C2×C412yes—
21C22×Q8×C127D411yescharacteristic
22C2×M16×C127—22no—
23C4⋊Q8×C127—41no—
24C4⋊Q8×C127—41no—
25C4×Q8×C127—41no—
26C4×Q8×C127—41no—
27C2×C4⋊C4×C127—21no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127—22no—
31C2×C4⋊C4×C127—22no—
32C2×C4⋊C4×C127C2×C411yescharacteristic
33C2×C4⋊C4×C127D411yescharacteristic
34C2×C4⋊C4×C127C2311yescharacteristic
35C2×C42×C127—21no—
36C2×C42×C127C2×C411yescharacteristic
37C2×C42×C127D411yescharacteristic
38C2×C42×C127D411yescharacteristic
39C4⋊C8×C127—41no—
40C4⋊C8×C127—41no—
41C4⋊C8×C127—41no—
42#101×C127—42no—
43C22⋊C8×C127—22no—
44C4×C8×C127—41no—
45#95×C127—22no—
46#95×C127—22no—
47#95×C127C2×C412yes—
48C2×Q8×C127—41no—
49C2×Q8×C127—41no—
50C2×Q8×C127—42no—
51C2×Q8×C127—82no—
52C2×Q8×C127SD1612yes—
53C2×Q8×C127Q1612yes—
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127C22⋊C411yescharacteristic
57C22×C4×C127C22⋊C411yescharacteristic
58C22×C4×C127C22⋊C411yescharacteristic
59C22×C4×C127C22⋊C411yescharacteristic
60C22×C4×C127C22×C411yescharacteristic
61C22×C4×C127C2×D411yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63M16×C127—42no—
64M16×C127—42no—
65C2×C8×C127—42no—
66C2×C8×C127—42no—
67C4⋊C4×C127—24no—
68C4⋊C4×C127—41no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—41no—
71C4⋊C4×C127—42no—
72C4⋊C4×C127—41no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—82no—
75C4⋊C4×C127—82no—
76C42×C127—21no—
77C42×C127—21no—
78C42×C127—21no—
79C42×C127—21no—
80C42×C127—21no—
81C42×C127—21no—
82C42×C127—42no—
83C23×C127C2×C22⋊C411yescharacteristic
84Q8×C127—42no—
85Q8×C127—42no—
86Q8×C127—84no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—22no—
94C2×C4×C127—24no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—42no—
99C2×C4×C127—42no—
100C2×C4×C127—41no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—42no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127#9911yescharacteristic
107C2×C4×C127#9911yescharacteristic
108C2×C4×C127#10312yes—
109C2×C4×C127#10312yes—
110C2×C4×C127C2×SD1611yescharacteristic
111C2×C4×C127C2×Q1611yescharacteristic
112C8×C127—82no—
113C8×C127—82no—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127C2×#9911yescharacteristic
117C22×C127C2×#10311yescharacteristic
118C22×C127#42111yescharacteristic
119C4×C127—21no—
120C4×C127—21no—
121C4×C127—22no—
122C4×C127—22no—
123C4×C127—21no—
124C4×C127—44no—
125C4×C127—41no—
126C4×C127—41no—
127C4×C127—41no—
128C4×C127—82no—
129C4×C127#35612yes—
130#11908C12711yesmaximal, characteristic, direct product factor, Sylow
131C2×C127—21no—
132C2×C127—21no—
133C2×C127#152011yescharacteristic
134C2×C127#212211yescharacteristic
135C2×C127C2×#35611yescharacteristic
136#2567C2×C12711yescharacteristic
137#1801C2×C12711yescharacteristic
138#1461C2×C12711yescharacteristic
139#1354C2×C12714yes—
140C127#1190811yescharacteristic, direct product factor, Sylow
141C2×C4⋊Q8C4×C12711yescharacteristic
142C2×C4×Q8C22×C12711yescharacteristic
143#431—21no—
144#423—21no—
145C2×#101—21no—
146#395C4×C12712yes—
147#395C22×C12712yes—
148#391—21no—
149#389—21no—
150#389—21no—
151#384—21no—
152C4×C4⋊C4C4×C12711yescharacteristic
153#343C22×C12712yes—
154#324—21no—
155#324C22×C12712yes—
156C22×Q8C2×C4×C12712yes—
157C22×Q8D4×C12711yescharacteristic
158C2×M16—22no—
159C4⋊Q8—41no—
160C4⋊Q8—41no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4C2×C4×C12711yescharacteristic
169C2×C4⋊C4D4×C12711yescharacteristic
170C2×C4⋊C4C23×C12711yescharacteristic
171C2×C42—21no—
172C2×C42C2×C4×C12711yescharacteristic
173C2×C42D4×C12711yescharacteristic
174C2×C42D4×C12711yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178#101—42no—
179C22⋊C8—22no—
180C4×C8—41no—
181#95—22no—
182#95—22no—
183#95C2×C4×C12712yes—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—82no—
188C2×Q8SD16×C12712yes—
189C2×Q8Q16×C12712yes—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4C22⋊C4×C12711yescharacteristic
193C22×C4C22⋊C4×C12711yescharacteristic
194C22×C4C22⋊C4×C12711yescharacteristic
195C22×C4C22⋊C4×C12711yescharacteristic
196C22×C4C22×C4×C12711yescharacteristic
197C22×C4C2×D4×C12711yescharacteristic
198C22×C4C2×D4×C12711yescharacteristic
199M16—42no—
200M16—42no—
201C2×C8—42no—
202C2×C8—42no—
203C4⋊C4—24no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—42no—
219C23C2×C22⋊C4×C12711yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—84no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4#99×C12711yescharacteristic
243C2×C4#99×C12711yescharacteristic
244C2×C4#103×C12712yes—
245C2×C4#103×C12712yes—
246C2×C4C2×SD16×C12711yescharacteristic
247C2×C4C2×Q16×C12711yescharacteristic
248C8—82no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22C2×#99×C12711yescharacteristic
253C22C2×#103×C12711yescharacteristic
254C22#421×C12711yescharacteristic
255C4—21no—
256C4—21no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4#356×C12712yes—
266C2—21no—
267C2—21no—
268C2C127×#152011yescharacteristic
269C2C127×#212211yescharacteristic
270C2C2×#356×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
130. #11908C127direct (N × H)
140. C127#11908direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25672
C127×#18012
C127×#14612
C127×#13542
#11908127