Finite Group Databasebeta

← C127×#11574 #44575247

Subgroups — C127×#11574 #44575247

Order 32512.

374 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 106 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×#1467C211yesmaximal, characteristic
3C127×#1461C211yesmaximal, characteristic
4C127×#1325C214yesmaximal
5C2×C4⋊Q8×C127C411yescharacteristic
6C2×C4×Q8×C127C2211yescharacteristic
7#432×C127—21no—
8#431×C127—21no—
9#395×C127—21no—
10#395×C127—21no—
11#391×C127C412yes—
12#389×C127—21no—
13#389×C127—21no—
14#384×C127C2212yes—
15C4×C4⋊C4×C127C411yescharacteristic
16#324×C127—21no—
17#324×C127—21no—
18#324×C127C2212yes—
19#324×C127C2212yes—
20C22×Q8×C127—21no—
21C22×Q8×C127C2×C411yescharacteristic
22C4⋊Q8×C127—41no—
23C4⋊Q8×C127—41no—
24C4×Q8×C127—41no—
25C4×Q8×C127—41no—
26C2×C4⋊C4×C127—21no—
27C2×C4⋊C4×C127—21no—
28C2×C4⋊C4×C127—22no—
29C2×C4⋊C4×C127—22no—
30C2×C4⋊C4×C127C2×C412yes—
31C2×C4⋊C4×C127D411yescharacteristic
32C2×C4⋊C4×C127D411yescharacteristic
33C2×C4⋊C4×C127C2311yescharacteristic
34C2×C42×C127C2×C412yes—
35C2×C42×C127C2×C411yescharacteristic
36C2×C42×C127D411yescharacteristic
37C2×C42×C127D411yescharacteristic
38C4⋊C8×C127—41no—
39C4⋊C8×C127—41no—
40C22⋊C8×C127—22no—
41C22⋊C8×C127—22no—
42#97×C127—41no—
43C4×C8×C127—41no—
44#95×C127—21no—
45#95×C127—22no—
46#95×C127—22no—
47C2×Q8×C127—22no—
48C2×Q8×C127—22no—
49C2×Q8×C127—41no—
50C2×Q8×C127—42no—
51C2×Q8×C127—82no—
52C22×C4×C127—22no—
53C22×C4×C127—22no—
54C22×C4×C127C22⋊C411yescharacteristic
55C22×C4×C127C22⋊C411yescharacteristic
56C22×C4×C127C22⋊C411yescharacteristic
57C22×C4×C127C22⋊C411yescharacteristic
58C22×C4×C127C22×C411yescharacteristic
59C22×C4×C127C2×D411yescharacteristic
60C22×C4×C127C2×D411yescharacteristic
61C2×C8×C127—42no—
62C2×C8×C127—42no—
63C4⋊C4×C127—24no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—42no—
68C4⋊C4×C127—41no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—82no—
71C4⋊C4×C127—82no—
72C42×C127—21no—
73C42×C127—21no—
74C42×C127—21no—
75C42×C127—21no—
76C42×C127—21no—
77C42×C127—21no—
78C42×C127—24no—
79C23×C127C2×C22⋊C411yescharacteristic
80Q8×C127—44no—
81Q8×C127—84no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—22no—
87C2×C4×C127—24no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—21no—
94C2×C4×C127—42no—
95C2×C4×C127—42no—
96C2×C4×C127—41no—
97C2×C4×C127—41no—
98C2×C4×C127—41no—
99C2×C4×C127—42no—
100C2×C4×C127—42no—
101C2×C4×C127—42no—
102C2×C4×C127#9911yescharacteristic
103C2×C4×C127#9911yescharacteristic
104C2×C4×C127#10112yes—
105C2×C4×C127#13112yes—
106C8×C127—82no—
107C8×C127—82no—
108C22×C127—21no—
109C22×C127—21no—
110C22×C127#40811yescharacteristic
111C22×C127C2×#9911yescharacteristic
112C22×C127C2×#10111yescharacteristic
113C4×C127—21no—
114C4×C127—22no—
115C4×C127—22no—
116C4×C127—44no—
117C4×C127—41no—
118C4×C127—41no—
119C4×C127—41no—
120C4×C127—41no—
121C4×C127—82no—
122C4×C127#35612yes—
123#11574C12711yesmaximal, characteristic, direct product factor, Sylow
124C2×C127—21no—
125C2×C127—21no—
126C2×C127#147211yescharacteristic
127C2×C127#212811yescharacteristic
128C2×C127C2×#35611yescharacteristic
129#2567C2×C12711yescharacteristic
130#1467C2×C12711yescharacteristic
131#1461C2×C12711yescharacteristic
132#1325C2×C12714yes—
133C127#1157411yescharacteristic, direct product factor, Sylow
134C2×C4⋊Q8C4×C12711yescharacteristic
135C2×C4×Q8C22×C12711yescharacteristic
136#432—21no—
137#431—21no—
138#395—21no—
139#395—21no—
140#391C4×C12712yes—
141#389—21no—
142#389—21no—
143#384C22×C12712yes—
144C4×C4⋊C4C4×C12711yescharacteristic
145#324—21no—
146#324—21no—
147#324C22×C12712yes—
148#324C22×C12712yes—
149C22×Q8—21no—
150C22×Q8C2×C4×C12711yescharacteristic
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4C2×C4×C12712yes—
160C2×C4⋊C4D4×C12711yescharacteristic
161C2×C4⋊C4D4×C12711yescharacteristic
162C2×C4⋊C4C23×C12711yescharacteristic
163C2×C42C2×C4×C12712yes—
164C2×C42C2×C4×C12711yescharacteristic
165C2×C42D4×C12711yescharacteristic
166C2×C42D4×C12711yescharacteristic
167C4⋊C8—41no—
168C4⋊C8—41no—
169C22⋊C8—22no—
170C22⋊C8—22no—
171#97—41no—
172C4×C8—41no—
173#95—21no—
174#95—22no—
175#95—22no—
176C2×Q8—22no—
177C2×Q8—22no—
178C2×Q8—41no—
179C2×Q8—42no—
180C2×Q8—82no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4C22⋊C4×C12711yescharacteristic
184C22×C4C22⋊C4×C12711yescharacteristic
185C22×C4C22⋊C4×C12711yescharacteristic
186C22×C4C22⋊C4×C12711yescharacteristic
187C22×C4C22×C4×C12711yescharacteristic
188C22×C4C2×D4×C12711yescharacteristic
189C22×C4C2×D4×C12711yescharacteristic
190C2×C8—42no—
191C2×C8—42no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—24no—
208C23C2×C22⋊C4×C12711yescharacteristic
209Q8—44no—
210Q8—84no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#99×C12711yescharacteristic
232C2×C4#99×C12711yescharacteristic
233C2×C4#101×C12712yes—
234C2×C4#131×C12712yes—
235C8—82no—
236C8—82no—
237C22—21no—
238C22—21no—
239C22#408×C12711yescharacteristic
240C22C2×#99×C12711yescharacteristic
241C22C2×#101×C12711yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—44no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4#356×C12712yes—
252C2—21no—
253C2—21no—
254C2C127×#147211yescharacteristic
255C2C127×#212811yescharacteristic
256C2C2×#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 ▷ C22 ▷ 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
123. #11574C127direct (N × H)
133. C127#11574direct (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×#14672
C127×#14612
C127×#13252
#11574127