Finite Group Databasebeta

← C127×#11813 #44575486

Subgroups — C127×#11813 #44575486

Order 32512.

382 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2628C211yesmaximal, characteristic
2C127×#1820C211yesmaximal, characteristic
3C127×#1464C211yesmaximal, characteristic
4C127×#1352C214yesmaximal
5C2×C4⋊Q8×C127C411yescharacteristic, complemented
6C2×#117×C127C2211yescharacteristic
7#432×C127—21no—
8#400×C127C412yescomplemented
9#399×C127C2212yes—
10#395×C127—21no—
11#393×C127—21no—
12#389×C127—21no—
13#382×C127C411yescharacteristic, complemented
14#381×C127—21no—
15#380×C127—21no—
16#342×C127—21no—
17#342×C127C2212yes—
18#324×C127—21no—
19#323×C127C2212yes—
20C22×Q8×C127—21no—
21C23×C4×C127D411yescharacteristic
22C4⋊Q8×C127—41no—
23C4⋊Q8×C127—41no—
24#117×C127—41no—
25#117×C127—41no—
26C2×C4⋊C4×C127—21no—
27C2×C4⋊C4×C127—21no—
28C2×C4⋊C4×C127—22no—
29C2×C4⋊C4×C127C2×C412yes—
30C2×C4⋊C4×C127C2×C411yescharacteristic
31C2×C4⋊C4×C127D411yescharacteristic
32C2×C22⋊C4×C127—22no—
33C2×C22⋊C4×C127—22no—
34C2×C22⋊C4×C127D411yescharacteristic
35C2×C22⋊C4×C127C2311yescharacteristic
36C2×C42×C127C2×C411yescharacteristic
37C2×C42×C127D411yescharacteristic
38C4⋊C8×C127—41no—
39C22⋊C8×C127—22no—
40#97×C127—41no—
41#95×C127—22no—
42#95×C127—21no—
43#95×C127—22no—
44#95×C127—41no—
45#95×C127—41no—
46#95×C127C2×C412yes—
47C24×C127C2×D411yescharacteristic
48C2×Q8×C127—42no—
49C2×Q8×C127—82no—
50C22×C4×C127—22no—
51C22×C4×C127—21no—
52C22×C4×C127—21no—
53C22×C4×C127—22no—
54C22×C4×C127—22no—
55C22×C4×C127—41no—
56C22×C4×C127—42no—
57C22×C4×C127C22⋊C411yescharacteristic
58C22×C4×C127C22⋊C411yescharacteristic
59C22×C4×C127C22⋊C411yescharacteristic
60C22×C4×C127C22⋊C411yescharacteristic
61C22×C4×C127C22×C411yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63C2×C8×C127—42no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—42no—
67C4⋊C4×C127—42no—
68C4⋊C4×C127—41no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—82no—
71C22⋊C4×C127—41no—
72C22⋊C4×C127—41no—
73C22⋊C4×C127—42no—
74C22⋊C4×C127—42no—
75C22⋊C4×C127—82no—
76C42×C127—21no—
77C42×C127—21no—
78C42×C127—21no—
79C42×C127—21no—
80C23×C127—21no—
81C23×C127—21no—
82C23×C127—41no—
83C23×C127—41no—
84C23×C127C2×C22⋊C411yescharacteristic
85C23×C127#13712yes—
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—21no—
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—42no—
97C2×C4×C127—42no—
98C2×C4×C127—41no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127—41no—
102C2×C4×C127—42no—
103C2×C4×C127—42no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127—42no—
107C2×C4×C127—42no—
108C2×C4×C127—82no—
109C2×C4×C127—82no—
110C2×C4×C127—82no—
111C2×C4×C127#9911yescharacteristic
112C2×C4×C127#9911yescharacteristic
113C8×C127—82no—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127—22no—
117C22×C127—42no—
118C22×C127—41no—
119C22×C127—41no—
120C22×C127—81no—
121C22×C127C2×#9911yescharacteristic
122C22×C127#41911yescharacteristic
123C22×C127#42111yescharacteristic
124C4×C127—21no—
125C4×C127—21no—
126C4×C127—41no—
127C4×C127—41no—
128C4×C127—41no—
129C4×C127—41no—
130C4×C127—41no—
131C4×C127—82no—
132C4×C127—82no—
133C4×C127—162no—
134#11813C12711yesmaximal, characteristic, direct product factor, Sylow
135C2×C127—21no—
136C2×C127—21no—
137C2×C127—42no—
138C2×C127#151111yescharacteristic
139C2×C127#212311yescharacteristic
140C2×C127#212811yescharacteristic
141#2628C2×C12711yescharacteristic
142#1820C2×C12711yescharacteristic
143#1464C2×C12711yescharacteristic
144#1352C2×C12714yes—
145C127#1181311yescharacteristic, direct product factor, Sylow
146C2×C4⋊Q8C4×C12711yescharacteristic, complemented
147C2×#117C22×C12711yescharacteristic
148#432—21no—
149#400C4×C12712yescomplemented
150#399C22×C12712yes—
151#395—21no—
152#393—21no—
153#389—21no—
154#382C4×C12711yescharacteristic, complemented
155#381—21no—
156#380—21no—
157#342—21no—
158#342C22×C12712yes—
159#324—21no—
160#323C22×C12712yes—
161C22×Q8—21no—
162C23×C4D4×C12711yescharacteristic
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165#117—41no—
166#117—41no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4C2×C4×C12712yes—
171C2×C4⋊C4C2×C4×C12711yescharacteristic
172C2×C4⋊C4D4×C12711yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4D4×C12711yescharacteristic
176C2×C22⋊C4C23×C12711yescharacteristic
177C2×C42C2×C4×C12711yescharacteristic
178C2×C42D4×C12711yescharacteristic
179C4⋊C8—41no—
180C22⋊C8—22no—
181#97—41no—
182#95—22no—
183#95—21no—
184#95—22no—
185#95—41no—
186#95—41no—
187#95C2×C4×C12712yes—
188C24C2×D4×C12711yescharacteristic
189C2×Q8—42no—
190C2×Q8—82no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4C22⋊C4×C12711yescharacteristic
199C22×C4C22⋊C4×C12711yescharacteristic
200C22×C4C22⋊C4×C12711yescharacteristic
201C22×C4C22⋊C4×C12711yescharacteristic
202C22×C4C22×C4×C12711yescharacteristic
203C22×C4C2×D4×C12711yescharacteristic
204C2×C8—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—82no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23C2×C22⋊C4×C12711yescharacteristic
226C23#137×C12712yes—
227Q8—84no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4#99×C12711yescharacteristic
253C2×C4#99×C12711yescharacteristic
254C8—82no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×#99×C12711yescharacteristic
263C22#419×C12711yescharacteristic
264C22#421×C12711yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4—82no—
274C4—162no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2C127×#151111yescharacteristic
279C2C127×#212311yescharacteristic
280C2C127×#212811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C127C4semidirect
8. #400×C127C4semidirect
13. #382×C127C4semidirect
134. #11813C127direct (N × H)
145. C127#11813direct (N × H)
146. C2×C4⋊Q8C4×C127semidirect
149. #400C4×C127semidirect
154. #382C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26282
C127×#18202
C127×#14642
C127×#13522
#11813127